examples/example-1-sindy-vanderpol.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Demo: Van der Pol Oscillator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### created by Yuying Liu, 11/21/18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "module_path = os.path.abspath(os.path.join('..'))\n",
    "if module_path not in sys.path:\n",
    "    sys.path.append(module_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pySINDy.sindy import SINDy\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from pySINDy.utils.generator import van_der_pol_generator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Set parameters to initialize the Van der Pol system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = 1.2\n",
    "xinit = [0.1, 5.0]\n",
    "dt = 0.01\n",
    "len_t = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### generate Van der Pol oscillator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = van_der_pol_generator(mu, xinit, dt, len_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### use SINDy model to fit the data and find coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = SINDy(name='my_sindy_model')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/findiff/findiff.py:242: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  yd[ref_multi_slice] += w * y[off_multi_slice]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<pySINDy.sindy.SINDy at 0x11e706d30>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(data, dt, poly_degree=3, cut_off=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### display coefficients and corresponding term to the coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.        ],\n",
       "       [ 0.        , -0.99921292],\n",
       "       [ 0.99995369,  1.19923454],\n",
       "       [ 0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ],\n",
       "       [ 0.        , -1.19753646],\n",
       "       [ 0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['1',\n",
       " 'u0',\n",
       " 'u1',\n",
       " 'u0^{2}',\n",
       " 'u0u1',\n",
       " 'u1^{2}',\n",
       " 'u0^{3}',\n",
       " 'u0^{2}u1',\n",
       " 'u0u1^{2}',\n",
       " 'u1^{3}']"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.descriptions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 3200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot_coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}