Figure7.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create plots for Figure 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Import necessary libraries\n",
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "plt.rcParams['text.usetex'] = False\n",
    "\n",
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "from functools import partial\n",
    "import glob, os\n",
    "import pickle\n",
    "import copy\n",
    "from PDEsolvers import HeatEqn_FT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# User inputs\n",
    "data_name = 'Heat_Eqn_exp29'  # Prefix of data files\n",
    "folder_name = 'Heat_exp29c/'  # Folder to be created for saved output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Heat_exp29c/Heat_Eqn_exp29_2019_08_04_05_22_13_599012_model.pkl\n",
      "0.0710781492292881\n",
      "0.06387144327163696\n"
     ]
    }
   ],
   "source": [
    "# Find the model with lowest validation error\n",
    "import math\n",
    "\n",
    "def BestErrorFile(folder_name):\n",
    "\n",
    "    filename_best = ''\n",
    "    best_error = 10**6\n",
    "\n",
    "    current_dir = os.getcwd()\n",
    "    os.chdir(\"./\" + folder_name)\n",
    "    for file in glob.glob(\"*.pkl\"):\n",
    "        with open(file, 'rb') as f:\n",
    "            params = pickle.load(f)\n",
    "            if not math.isnan(params['minRegTest']):\n",
    "                if params['minRegTest'] < best_error:\n",
    "                    filename_best = file\n",
    "                    best_error = params['minRegTest']\n",
    "    os.chdir(current_dir)\n",
    "\n",
    "    return filename_best\n",
    "\n",
    "pkl_file = folder_name + BestErrorFile(folder_name)\n",
    "\n",
    "with open(pkl_file, 'rb') as f:\n",
    "     params = pickle.load(f)\n",
    "\n",
    "params['model_restore_path'] = params['model_path']\n",
    "print(pkl_file)\n",
    "print(params['minTest'])\n",
    "print(params['minTrain'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./Heat_exp29c/Heat_Eqn_exp29_2019_08_04_05_22_13_599012_model.ckpt\n"
     ]
    }
   ],
   "source": [
    "# Get all the needed things from the network\n",
    "\n",
    "tf.reset_default_graph()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    saver = tf.train.import_meta_graph(params['model_path']+'.meta')\n",
    "    saver.restore(sess, params['model_path'])\n",
    "    \n",
    "    L_mat = sess.run(tf.get_default_graph().get_tensor_by_name(\"dynamics/L:0\"))\n",
    "    IFT = sess.run(tf.get_default_graph().get_tensor_by_name(\"decoder_inner/IFT:0\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.8610129e-03 -1.0000083e+00 -1.0012273e+00 -4.0001421e+00\n",
      " -4.0069337e+00 -9.0014553e+00 -9.0015297e+00 -1.6016428e+01\n",
      " -1.6016998e+01 -2.4997129e+01 -2.5010124e+01 -3.5992432e+01\n",
      " -3.5995045e+01 -4.8951012e+01 -4.9028839e+01 -6.3908646e+01\n",
      " -6.4093338e+01 -8.0977509e+01 -8.1173203e+01 -1.0002786e+02\n",
      " -1.0004730e+02]\n"
     ]
    }
   ],
   "source": [
    "# Calculate eigenvalues and eigenvectors\n",
    "lam, V = np.linalg.eig(L_mat)\n",
    "lam = np.log(lam)\n",
    "ind = np.argsort(lam)\n",
    "ind = np.flip(ind,0)\n",
    "lam = np.sort(lam)\n",
    "lam = np.flip(lam,0)\n",
    "network_lam = lam/params['delta_t']\n",
    "print(lam/params['delta_t'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x239.76 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "exact_lam = 0*lam\n",
    "\n",
    "for k in np.arange(10):\n",
    "    exact_lam[2*k+1:2*k+3] = [-(k+1)**2,-(k+1)**2]\n",
    "\n",
    "plt.figure(figsize=(5,3.33))\n",
    "Network, = plt.plot(-np.real(network_lam),np.imag(network_lam),'ob',markersize=10,markerfacecolor=\"None\")\n",
    "Exact, = plt.plot(-np.real(exact_lam),np.imag(exact_lam),'*r',markersize=10)\n",
    "plt.ylim(-30,30)\n",
    "plt.xlim(0,105)\n",
    "plt.rcParams['axes.labelsize'] = 10\n",
    "plt.rcParams['xtick.labelsize'] = 10\n",
    "plt.rcParams['ytick.labelsize'] = 10\n",
    "plt.title('$-\\log(\\lambda)/dt$',fontsize=10)\n",
    "plt.xlabel('Real')\n",
    "plt.ylabel('Imag')\n",
    "plt.legend([Network,Exact],['Network','Exact'],fontsize=10)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 108x72 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot eigenvectors for a particular wavenumber\n",
    "k = 1\n",
    "\n",
    "x_pts = np.linspace(-np.pi,np.pi,129)\n",
    "x_pts = x_pts[0:128]\n",
    "\n",
    "f = V.T.dot(IFT)\n",
    "f = np.real(f)\n",
    "\n",
    "plt.figure(figsize=(1.5,1))\n",
    "plt.plot(x_pts,f[ind[2*k-1],:],'-g',linewidth=1.5)\n",
    "plt.plot(x_pts,f[ind[2*k],:],'--m',linewidth=1.5)\n",
    "plt.xticks([-3,0,3], ['','',''])\n",
    "plt.yticks([-0.1,0,0.1],['','',''])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 108x72 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot eigenvectors for a particular wavenumber\n",
    "k = 3\n",
    "\n",
    "x_pts = np.linspace(-np.pi,np.pi,129)\n",
    "x_pts = x_pts[0:128]\n",
    "\n",
    "f = V.T.dot(IFT)\n",
    "f = np.real(f)\n",
    "\n",
    "plt.figure(figsize=(1.5,1))\n",
    "plt.plot(x_pts,f[ind[2*k-1],:],'-g',linewidth=1.5)\n",
    "plt.plot(x_pts,f[ind[2*k],:],'--m',linewidth=1.5)\n",
    "plt.xticks([-3,0,3], ['','',''])\n",
    "plt.yticks([-0.25,0,0.25],['','',''])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 108x72 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot eigenvectors for a particular wavenumber\n",
    "k = 8\n",
    "\n",
    "x_pts = np.linspace(-np.pi,np.pi,129)\n",
    "x_pts = x_pts[0:128]\n",
    "\n",
    "f = V.T.dot(IFT)\n",
    "f = np.real(f)\n",
    "\n",
    "plt.figure(figsize=(1.5,1))\n",
    "plt.plot(x_pts,f[ind[2*k-1],:],'-g',linewidth=1.5)\n",
    "plt.plot(x_pts,f[ind[2*k],:],'--m',linewidth=1.5)\n",
    "plt.xticks([-3,0,3], ['','',''])\n",
    "plt.yticks([-0.5,0,0.5],['','',''])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tensorflow",
   "language": "python",
   "name": "tensorflow"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}