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neb_opt_utils.F
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!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2025 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief Module with utility to perform MD Nudged Elastic Band Calculation
!> \note
!> Numerical accuracy for parallel runs:
!> Each replica starts the SCF run from the one optimized
!> in a previous run. It may happen then energies and derivatives
!> of a serial run and a parallel run could be slightly different
!> 'cause of a different starting density matrix.
!> Exact results are obtained using:
!> EXTRAPOLATION USE_GUESS in QS section (Teo 09.2006)
!> \author Teodoro Laino 10.2006
! **************************************************************************************************
MODULE neb_opt_utils
USE cp_log_handling, ONLY: cp_logger_get_default_io_unit,&
cp_to_string
USE input_section_types, ONLY: section_vals_type,&
section_vals_val_get
USE kinds, ONLY: default_string_length,&
dp
USE neb_types, ONLY: neb_type,&
neb_var_type
USE neb_utils, ONLY: neb_calc_energy_forces,&
reorient_images
USE particle_types, ONLY: particle_type
USE replica_types, ONLY: replica_env_type
#include "../base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'neb_opt_utils'
LOGICAL, PARAMETER, PRIVATE :: debug_this_module = .FALSE.
PUBLIC :: accept_diis_step, &
neb_ls
REAL(KIND=dp), DIMENSION(2:10), PRIVATE :: acceptance_factor = &
(/0.97_dp, 0.84_dp, 0.71_dp, 0.67_dp, 0.62_dp, 0.56_dp, 0.49_dp, 0.41_dp, 0.0_dp/)
CONTAINS
! **************************************************************************************************
!> \brief Performs few basic operations for the NEB DIIS optimization
!> \param apply_diis ...
!> \param n_diis ...
!> \param err ...
!> \param crr ...
!> \param set_err ...
!> \param sline ...
!> \param coords ...
!> \param check_diis ...
!> \param iw2 ...
!> \return ...
!> \author Teodoro Laino 10.2006
! **************************************************************************************************
FUNCTION accept_diis_step(apply_diis, n_diis, err, crr, set_err, sline, coords, &
check_diis, iw2) RESULT(accepted)
LOGICAL, INTENT(IN) :: apply_diis
INTEGER, INTENT(IN) :: n_diis
REAL(KIND=dp), DIMENSION(:, :), POINTER :: err, crr
INTEGER, DIMENSION(:), POINTER :: set_err
TYPE(neb_var_type), POINTER :: sline, coords
LOGICAL, INTENT(IN) :: check_diis
INTEGER, INTENT(IN) :: iw2
LOGICAL :: accepted
CHARACTER(LEN=default_string_length) :: line
INTEGER :: i, iend, ind, indi, indj, info, istart, &
iv, iw, j, jv, k, lwork, np, nv
INTEGER, ALLOCATABLE, DIMENSION(:) :: IWORK
LOGICAL :: increase_error
REAL(dp), DIMENSION(:, :), POINTER :: work
REAL(KIND=dp) :: eps_svd
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: S, Work_dgesdd
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: U, VT, wrk, wrk_inv
REAL(KIND=dp), DIMENSION(:), POINTER :: awrk, cwrk, ref, step
iw = cp_logger_get_default_io_unit()
accepted = .FALSE.
! find the index with the minimum element of the set_err array
nv = MINLOC(set_err, 1)
IF (iw2 > 0) WRITE (iw2, '(A,I3)') "Entering into the DIIS module. Error vector number:: ", nv
set_err(nv) = 1
eps_svd = 1.0E-10_dp
ALLOCATE (step(sline%size_wrk(1)*sline%size_wrk(2)))
ALLOCATE (ref(sline%size_wrk(1)*sline%size_wrk(2)))
err(:, nv) = RESHAPE(sline%wrk, (/sline%size_wrk(1)*sline%size_wrk(2)/))
crr(:, nv) = RESHAPE(coords%wrk, (/coords%size_wrk(1)*coords%size_wrk(2)/))
jv = n_diis
IF (ALL(set_err == 1) .AND. apply_diis) THEN
IF (iw2 > 0) WRITE (iw2, '(A)') "Applying DIIS equations"
! Apply DIIS..
DO jv = 2, n_diis
np = jv + 1
IF (iw2 > 0) WRITE (iw2, '(A,I5,A)') "Applying DIIS equations with the last", &
jv, " error vectors"
ALLOCATE (wrk(np, np))
ALLOCATE (work(np, np))
ALLOCATE (wrk_inv(np, np))
ALLOCATE (cwrk(np))
ALLOCATE (awrk(np))
awrk = 0.0_dp
wrk = 1.0_dp
wrk(np, np) = 0.0_dp
awrk(np) = 1.0_dp
DO i = 1, jv
indi = n_diis - i + 1
DO j = i, jv
indj = n_diis - j + 1
wrk(i, j) = DOT_PRODUCT(err(:, indi), err(:, indj))
wrk(j, i) = wrk(i, j)
END DO
END DO
IF (iw2 > 0) THEN
line = "DIIS Matrix"//cp_to_string(np)//"x"//cp_to_string(np)//"."
WRITE (iw2, '(A)') TRIM(line)
WRITE (iw2, '('//cp_to_string(np)//'F12.6)') wrk
END IF
! Inverte the DIIS Matrix
work = TRANSPOSE(wrk)
! Workspace query
ALLOCATE (iwork(8*np))
ALLOCATE (S(np))
ALLOCATE (U(np, np))
ALLOCATE (VT(np, np))
ALLOCATE (work_dgesdd(1))
lwork = -1
CALL DGESDD('S', np, np, work, np, S, U, np, vt, np, work_dgesdd, lwork, iwork, info)
lwork = INT(work_dgesdd(1))
DEALLOCATE (work_dgesdd)
ALLOCATE (work_dgesdd(lwork))
CALL DGESDD('S', np, np, work, np, S, U, np, vt, np, work_dgesdd, lwork, iwork, info)
! Construct the inverse
DO k = 1, np
! Invert SV
IF (S(k) < eps_svd) THEN
S(k) = 0.0_dp
ELSE
S(k) = 1.0_dp/S(k)
END IF
VT(k, :) = VT(k, :)*S(k)
END DO
CALL DGEMM('T', 'T', np, np, np, 1.0_dp, VT, np, U, np, 0.0_dp, wrk_inv, np)
DEALLOCATE (iwork)
DEALLOCATE (S)
DEALLOCATE (U)
DEALLOCATE (VT)
DEALLOCATE (work_dgesdd)
cwrk = MATMUL(wrk_inv, awrk)
! Check the DIIS solution
step = 0.0_dp
ind = 0
DO i = n_diis, n_diis - jv + 1, -1
ind = ind + 1
step = step + (crr(:, i) + err(:, i))*cwrk(ind)
END DO
step = step - crr(:, n_diis)
ref = err(:, n_diis)
increase_error = check_diis_solution(jv, cwrk, step, ref, &
iw2, check_diis)
! possibly enlarge the error space
IF (increase_error) THEN
accepted = .TRUE.
sline%wrk = RESHAPE(step, (/sline%size_wrk(1), sline%size_wrk(2)/))
ELSE
DEALLOCATE (awrk)
DEALLOCATE (cwrk)
DEALLOCATE (wrk)
DEALLOCATE (work)
DEALLOCATE (wrk_inv)
EXIT
END IF
DEALLOCATE (awrk)
DEALLOCATE (cwrk)
DEALLOCATE (wrk)
DEALLOCATE (work)
DEALLOCATE (wrk_inv)
END DO
IF (iw2 > 0) THEN
line = "Exiting DIIS accepting"//cp_to_string(MIN(n_diis, jv))//" errors."
WRITE (iw2, '(A)') TRIM(line)
END IF
END IF
IF (ALL(set_err == 1)) THEN
! always delete the last error vector from the history vectors
! move error vectors and the set_err in order to have free space
! at the end of the err array
istart = MAX(2, n_diis - jv + 2)
iend = n_diis
indi = 0
DO iv = istart, iend
indi = indi + 1
err(:, indi) = err(:, iv)
crr(:, indi) = crr(:, iv)
set_err(indi) = 1
END DO
DO iv = indi + 1, iend
set_err(iv) = -1
END DO
END IF
DEALLOCATE (step)
DEALLOCATE (ref)
END FUNCTION accept_diis_step
! **************************************************************************************************
!> \brief Check conditions for the acceptance of the DIIS step
!> \param nv ...
!> \param cwrk ...
!> \param step ...
!> \param ref ...
!> \param output_unit ...
!> \param check_diis ...
!> \return ...
!> \author Teodoro Laino 10.2006
! **************************************************************************************************
FUNCTION check_diis_solution(nv, cwrk, step, ref, output_unit, check_diis) &
RESULT(accepted)
INTEGER, INTENT(IN) :: nv
REAL(KIND=dp), DIMENSION(:), POINTER :: cwrk, step, ref
INTEGER, INTENT(IN) :: output_unit
LOGICAL, INTENT(IN) :: check_diis
LOGICAL :: accepted
REAL(KIND=dp) :: costh, norm1, norm2
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: tmp
accepted = .TRUE.
ALLOCATE (tmp(SIZE(step)))
IF (accepted) THEN
! (a) The direction of the DIIS step, can be compared to the reference step.
! if the angle is grater than a specified value, the DIIS step is not
! acceptable.
norm1 = SQRT(DOT_PRODUCT(ref, ref))
norm2 = SQRT(DOT_PRODUCT(step, step))
costh = DOT_PRODUCT(ref, step)/(norm1*norm2)
IF (check_diis) THEN
IF (costh < acceptance_factor(MIN(10, nv))) accepted = .FALSE.
ELSE
IF (costh <= 0.0_dp) accepted = .FALSE.
END IF
IF (output_unit > 0 .AND. (.NOT. accepted)) THEN
WRITE (output_unit, '(T2,"DIIS|",A)') &
"The direction of the DIIS step, can be compared to the reference step.", &
"If the angle is grater than a specified value, the DIIS step is not", &
"acceptable. Value exceeded. Reset DIIS!"
WRITE (output_unit, '(T2,"DIIS|",A,F6.3,A,F6.3,A)') &
"Present Cosine <", costh, "> compared with the optimal value <", &
acceptance_factor(MIN(10, nv)), "> ."
END IF
END IF
IF (accepted .AND. check_diis) THEN
! (b) The length of the DIIS step is limited to be no more than 10 times
! the reference step
IF (norm1 > norm2*10.0_dp) accepted = .FALSE.
IF (output_unit > 0 .AND. (.NOT. accepted)) THEN
WRITE (output_unit, '(T2,"DIIS|",A)') &
"The length of the DIIS step is limited to be no more than 10 times", &
"the reference step. Value exceeded. Reset DIIS!"
END IF
END IF
IF (accepted .AND. check_diis) THEN
! (d) If the DIIS matrix is nearly singular, the norm of the DIIS step
! vector becomes small and cwrk/norm1 becomes large, signaling a
! numerical stability problems. If the magnitude of cwrk/norm1
! exceeds 10^8 then the step size is assumed to be unacceptable
IF (ANY(ABS(cwrk(1:nv)/norm1) > 10**8_dp)) accepted = .FALSE.
IF (output_unit > 0 .AND. (.NOT. accepted)) THEN
WRITE (output_unit, '(T2,"DIIS|",A)') &
"If the DIIS matrix is nearly singular, the norm of the DIIS step", &
"vector becomes small and Coeff/E_norm becomes large, signaling a", &
"numerical stability problems. IF the magnitude of Coeff/E_norm", &
"exceeds 10^8 THEN the step size is assumed to be unacceptable.", &
"Value exceeded. Reset DIIS!"
END IF
END IF
DEALLOCATE (tmp)
END FUNCTION check_diis_solution
! **************************************************************************************************
!> \brief Perform a line minimization search in optimizing a NEB with DIIS
!> \param stepsize ...
!> \param sline ...
!> \param rep_env ...
!> \param neb_env ...
!> \param coords ...
!> \param energies ...
!> \param forces ...
!> \param vels ...
!> \param particle_set ...
!> \param iw ...
!> \param output_unit ...
!> \param distances ...
!> \param diis_section ...
!> \param iw2 ...
!> \author Teodoro Laino 10.2006
! **************************************************************************************************
SUBROUTINE neb_ls(stepsize, sline, rep_env, neb_env, coords, energies, forces, &
vels, particle_set, iw, output_unit, distances, diis_section, iw2)
REAL(KIND=dp), INTENT(INOUT) :: stepsize
TYPE(neb_var_type), POINTER :: sline
TYPE(replica_env_type), POINTER :: rep_env
TYPE(neb_type), OPTIONAL, POINTER :: neb_env
TYPE(neb_var_type), POINTER :: coords
REAL(KIND=dp), DIMENSION(:), INTENT(INOUT) :: energies
TYPE(neb_var_type), POINTER :: forces, vels
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
INTEGER, INTENT(IN) :: iw, output_unit
REAL(KIND=dp), DIMENSION(:), INTENT(INOUT) :: distances
TYPE(section_vals_type), POINTER :: diis_section
INTEGER, INTENT(IN) :: iw2
INTEGER :: i, np
REAL(KIND=dp) :: a, b, max_stepsize, xa, xb, xc_cray, ya, &
yb
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: Icoord
! replaced xc by xc_cray to work around yet another bug in pgf90 on CRAY xt3
ALLOCATE (Icoord(coords%size_wrk(1), coords%size_wrk(2)))
CALL section_vals_val_get(diis_section, "NP_LS", i_val=np)
CALL section_vals_val_get(diis_section, "MAX_STEPSIZE", r_val=max_stepsize)
Icoord(:, :) = coords%wrk
xa = 0.0_dp
ya = SUM(sline%wrk*forces%wrk)
xb = xa + MIN(ya*stepsize, max_stepsize)
xc_cray = xb
i = 1
DO WHILE (i <= np - 1)
i = i + 1
coords%wrk = Icoord + xb*sline%wrk
CALL reorient_images(neb_env%rotate_frames, particle_set, coords, vels, &
output_unit, distances, neb_env%number_of_replica)
neb_env%avg_distance = SQRT(SUM(distances*distances)/REAL(SIZE(distances), KIND=dp))
CALL neb_calc_energy_forces(rep_env, neb_env, coords, energies, forces, &
particle_set, iw)
yb = SUM(sline%wrk*forces%wrk)
a = (ya - yb)/(2.0_dp*(xa - xb))
b = ya - 2.0_dp*a*xa
xc_cray = -b/(2.0_dp*a)
IF (xc_cray > max_stepsize) THEN
IF (iw2 > 0) WRITE (iw2, '(T2,2(A,F6.3),A)') &
"LS| Predicted stepsize (", xc_cray, ") greater than allowed stepsize (", &
max_stepsize, "). Reset!"
xc_cray = max_stepsize
EXIT
END IF
! No Extrapolation .. only interpolation
IF ((xc_cray <= MIN(xa, xb) .OR. xc_cray >= MAX(xa, xb)) .AND. (ABS(xa - xb) > 1.0E-5_dp)) THEN
IF (iw2 > 0) WRITE (iw2, '(T2,2(A,I5),A)') &
"LS| Increasing the number of point from ", np, " to ", np + 1, "."
np = np + 1
END IF
!
IF (ABS(yb) < ABS(ya)) THEN
ya = yb
xa = xb
END IF
xb = xc_cray
END DO
stepsize = xc_cray
coords%wrk = Icoord
DEALLOCATE (Icoord)
END SUBROUTINE neb_ls
END MODULE neb_opt_utils