heat_eq_by_fourier.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib nbagg\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "64 1024 0.4052847345693511\n"
     ]
    }
   ],
   "source": [
    "#line domain\n",
    "xmin = 0.0\n",
    "xmax = np.pi\n",
    "nx = 64\n",
    "dx = (xmax-xmin)/nx\n",
    "\n",
    "#time interval\n",
    "tmin = 0.0\n",
    "tmax = 1.0\n",
    "nt = 1024\n",
    "dt = (tmax-tmin)/nt\n",
    "\n",
    "c = 1.0 #spreading coefficient\n",
    "\n",
    "rsq = c*dt/(dx**2) #constant\n",
    "print(nx,nt,rsq)\n",
    "M = 21 #maximam fourier number\n",
    "#63 1252 0.3999999999999999"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#initialize\n",
    "F = np.zeros(nx)\n",
    "F_M = [np.zeros(nx) for m in range(M)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5000\n",
      "0.3395\n",
      "-0.0000\n",
      "-0.2425\n",
      "0.2500\n",
      "-0.1132\n",
      "-0.0000\n",
      "0.0220\n",
      "-0.0000\n",
      "-0.0087\n",
      "-0.0000\n",
      "0.0044\n",
      "-0.0000\n",
      "-0.0026\n",
      "-0.0000\n",
      "0.0016\n",
      "-0.0000\n",
      "-0.0011\n",
      "0.0000\n",
      "0.0008\n",
      "-0.0000\n"
     ]
    }
   ],
   "source": [
    "#Fourier coefficients\n",
    "A = [0]*M\n",
    "\n",
    "\n",
    "T = np.linspace(tmin, tmax, nt, endpoint = False)\n",
    "X = np.linspace(0, np.pi, nx, endpoint = False)+dx/2\n",
    "F = np.cos(4*X)\n",
    "for i in range(nx//2):\n",
    "    F[i] = 1\n",
    "#F = np.sin(X)\n",
    "\n",
    "for m in range(M):\n",
    "    A[m] = (np.dot(np.cos(m*X),F))/nx\n",
    "for i in range(len(A)): print(format(A[i], '.4f'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_M[0] = np.cos(0*X)*A[0]\n",
    "#dist2 = [np.sqrt(np.dot(F-F_M[0],F-F_M[0])/nx)]\n",
    "#distinf = [max(abs(F-F_M[0]))]\n",
    "#dist1 = [sum(abs(F-F_M[0]))/nx]\n",
    "for m in range(1,M):\n",
    "    F_M[m]=2*np.cos(m*X)*A[m]\n",
    "#   dist2+=[np.sqrt(np.dot(F-F_M[m],F-F_M[m])/nx)]\n",
    "#   distinf+= [max(abs(F-F_M[m]))]\n",
    "#   dist1+= [sum(abs(F-F_M[m]))/nx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "         3.35988574e-17, -7.71422173e-17, -1.69665581e-16, -2.22121150e-16]),\n",
       " array([ 0.00850187,  0.00608272,  0.00193278, -0.00276712, -0.00667965,\n",
       "        -0.00869154, -0.00823031, -0.00542721, -0.00107984,  0.0035748 ,\n",
       "         0.00721225,  0.00879751,  0.0078795 ,  0.00471943,  0.00021649,\n",
       "        -0.00434806, -0.0076754 , -0.00881876, -0.0074528 , -0.00396621,\n",
       "         0.00064894,  0.00507944,  0.00806462,  0.00875507,  0.00695433,\n",
       "         0.00317478, -0.00150813, -0.00576191, -0.00837618, -0.00860707,\n",
       "        -0.00638888, -0.00235278,  0.00235278,  0.00638888,  0.00860707,\n",
       "         0.00837618,  0.00576191,  0.00150813, -0.00317478, -0.00695433,\n",
       "        -0.00875507, -0.00806462, -0.00507944, -0.00064894,  0.00396621,\n",
       "         0.0074528 ,  0.00881876,  0.0076754 ,  0.00434806, -0.00021649,\n",
       "        -0.00471943, -0.0078795 , -0.00879751, -0.00721225, -0.0035748 ,\n",
       "         0.00107984,  0.00542721,  0.00823031,  0.00869154,  0.00667965,\n",
       "         0.00276712, -0.00193278, -0.00608272, -0.00850187]),\n",
       " array([-1.52722472e-16, -1.01245717e-16, -1.56430024e-17,  7.52323547e-17,\n",
       "         1.40749836e-16,  1.58826068e-16,  1.23368263e-16,  4.63278553e-17,\n",
       "        -4.63278553e-17, -1.23368263e-16, -1.58826068e-16, -1.40749836e-16,\n",
       "        -7.52323547e-17,  1.56430024e-17,  1.01245717e-16,  1.52722472e-16,\n",
       "         1.52722472e-16,  1.01245717e-16,  1.56430024e-17, -7.52323547e-17,\n",
       "        -1.40749836e-16, -1.58826068e-16, -1.23368263e-16, -4.63278553e-17,\n",
       "         4.63278553e-17,  1.23368263e-16,  1.58826068e-16,  1.40749836e-16,\n",
       "         7.52323547e-17, -1.56430024e-17, -1.01245717e-16, -1.52722472e-16,\n",
       "        -1.52722472e-16, -1.01245717e-16, -1.56430024e-17,  7.52323547e-17,\n",
       "         1.40749836e-16,  1.58826068e-16,  1.23368263e-16,  4.63278553e-17,\n",
       "        -4.63278553e-17, -1.23368263e-16, -1.58826068e-16, -1.40749836e-16,\n",
       "        -7.52323547e-17,  1.56430024e-17,  1.01245717e-16,  1.52722472e-16,\n",
       "         1.52722472e-16,  1.01245717e-16,  1.56430024e-17, -7.52323547e-17,\n",
       "        -1.40749836e-16, -1.58826068e-16, -1.23368263e-16, -4.63278553e-17,\n",
       "         4.63278553e-17,  1.23368263e-16,  1.58826068e-16,  1.40749836e-16,\n",
       "         7.52323547e-17, -1.56430024e-17, -1.01245717e-16, -1.52722472e-16]),\n",
       " array([-0.00486542, -0.00295046,  0.00012575,  0.00315247,  0.00493842,\n",
       "         0.00478069,  0.00274135, -0.00037695, -0.00334688, -0.00499953,\n",
       "        -0.00468444, -0.00252563,  0.00062724,  0.00353323,  0.0050486 ,\n",
       "         0.00457691,  0.00230382, -0.00087601, -0.00371107, -0.0050855 ,\n",
       "        -0.00445836, -0.00207647,  0.00112268,  0.00387996,  0.00511015,\n",
       "         0.00432906,  0.00184411, -0.00136665, -0.00403951, -0.00512249,\n",
       "        -0.00418933, -0.00160732,  0.00160732,  0.00418933,  0.00512249,\n",
       "         0.00403951,  0.00136665, -0.00184411, -0.00432906, -0.00511015,\n",
       "        -0.00387996, -0.00112268,  0.00207647,  0.00445836,  0.0050855 ,\n",
       "         0.00371107,  0.00087601, -0.00230382, -0.00457691, -0.0050486 ,\n",
       "        -0.00353323, -0.00062724,  0.00252563,  0.00468444,  0.00499953,\n",
       "         0.00334688,  0.00037695, -0.00274135, -0.00478069, -0.00493842,\n",
       "        -0.00315247, -0.00012575,  0.00295046,  0.00486542]),\n",
       " array([-3.39730267e-16, -1.85499829e-16,  5.29436541e-17,  2.67351825e-16,\n",
       "         3.60387857e-16,  2.89815336e-16,  8.76727118e-17, -1.54271490e-16,\n",
       "        -3.26179661e-16, -3.50009085e-16, -2.14941702e-16,  1.77047201e-17,\n",
       "         2.42313570e-16,  3.56917124e-16,  3.09487767e-16,  1.21557433e-16,\n",
       "        -1.21557433e-16, -3.09487767e-16, -3.56917124e-16, -2.42313570e-16,\n",
       "        -1.77047201e-17,  2.14941702e-16,  3.50009085e-16,  3.26179661e-16,\n",
       "         1.54271490e-16, -8.76727118e-17, -2.89815336e-16, -3.60387857e-16,\n",
       "        -2.67351825e-16, -5.29436541e-17,  1.85499829e-16,  3.39730267e-16,\n",
       "         3.39730267e-16,  1.85499829e-16, -5.29436541e-17, -2.67351825e-16,\n",
       "        -3.60387857e-16, -2.89815336e-16, -8.76727118e-17,  1.54271490e-16,\n",
       "         3.26179661e-16,  3.50009085e-16,  2.14941702e-16, -1.77047201e-17,\n",
       "        -2.42313570e-16, -3.56917124e-16, -3.09487767e-16, -1.21557433e-16,\n",
       "         1.21557433e-16,  3.09487767e-16,  3.56917124e-16,  2.42313570e-16,\n",
       "         1.77047201e-17, -2.14941702e-16, -3.50009085e-16, -3.26179661e-16,\n",
       "        -1.54271490e-16,  8.76727118e-17,  2.89815336e-16,  3.60387857e-16,\n",
       "         2.67351825e-16,  5.29436541e-17, -1.85499829e-16, -3.39730267e-16]),\n",
       " array([ 3.03455446e-03,  1.46235862e-03, -8.67481924e-04, -2.74788204e-03,\n",
       "        -3.20461066e-03, -2.00103770e-03,  2.39268379e-04,  2.35561005e-03,\n",
       "         3.25151546e-03,  2.46281803e-03,  3.98140115e-04, -1.87281329e-03,\n",
       "        -3.17346635e-03, -2.82995363e-03, -1.02024831e-03,  1.31804537e-03,\n",
       "         2.97346271e-03,  3.08833571e-03,  1.60314893e-03, -7.12625699e-04,\n",
       "        -2.65919056e-03, -3.22803478e-03, -2.12444144e-03,  7.98202243e-05,\n",
       "         2.24272721e-03,  3.24368228e-03,  2.56409286e-03,  5.56052697e-04,\n",
       "        -1.74007711e-03, -3.13467689e-03, -2.90520762e-03, -1.17055683e-03,\n",
       "         1.17055683e-03,  2.90520762e-03,  3.13467689e-03,  1.74007711e-03,\n",
       "        -5.56052697e-04, -2.56409286e-03, -3.24368228e-03, -2.24272721e-03,\n",
       "        -7.98202243e-05,  2.12444144e-03,  3.22803478e-03,  2.65919056e-03,\n",
       "         7.12625699e-04, -1.60314893e-03, -3.08833571e-03, -2.97346271e-03,\n",
       "        -1.31804537e-03,  1.02024831e-03,  2.82995363e-03,  3.17346635e-03,\n",
       "         1.87281329e-03, -3.98140115e-04, -2.46281803e-03, -3.25151546e-03,\n",
       "        -2.35561005e-03, -2.39268379e-04,  2.00103770e-03,  3.20461066e-03,\n",
       "         2.74788204e-03,  8.67481924e-04, -1.46235862e-03, -3.03455446e-03]),\n",
       " array([-3.97463527e-16, -1.64634784e-16,  1.64634784e-16,  3.97463527e-16,\n",
       "         3.97463527e-16,  1.64634784e-16, -1.64634784e-16, -3.97463527e-16,\n",
       "        -3.97463527e-16, -1.64634784e-16,  1.64634784e-16,  3.97463527e-16,\n",
       "         3.97463527e-16,  1.64634784e-16, -1.64634784e-16, -3.97463527e-16,\n",
       "        -3.97463527e-16, -1.64634784e-16,  1.64634784e-16,  3.97463527e-16,\n",
       "         3.97463527e-16,  1.64634784e-16, -1.64634784e-16, -3.97463527e-16,\n",
       "        -3.97463527e-16, -1.64634784e-16,  1.64634784e-16,  3.97463527e-16,\n",
       "         3.97463527e-16,  1.64634784e-16, -1.64634784e-16, -3.97463527e-16,\n",
       "        -3.97463527e-16, -1.64634784e-16,  1.64634784e-16,  3.97463527e-16,\n",
       "         3.97463527e-16,  1.64634784e-16, -1.64634784e-16, -3.97463527e-16,\n",
       "        -3.97463527e-16, -1.64634784e-16,  1.64634784e-16,  3.97463527e-16,\n",
       "         3.97463527e-16,  1.64634784e-16, -1.64634784e-16, -3.97463527e-16,\n",
       "        -3.97463527e-16, -1.64634784e-16,  1.64634784e-16,  3.97463527e-16,\n",
       "         3.97463527e-16,  1.64634784e-16, -1.64634784e-16, -3.97463527e-16,\n",
       "        -3.97463527e-16, -1.64634784e-16,  1.64634784e-16,  3.97463527e-16,\n",
       "         3.97463527e-16,  1.64634784e-16, -1.64634784e-16, -3.97463527e-16]),\n",
       " array([-2.01004831e-03, -6.89683575e-04,  1.08372195e-03,  2.14524994e-03,\n",
       "         1.79760166e-03,  2.69141047e-04, -1.43611350e-03, -2.19801081e-03,\n",
       "        -1.51607418e-03,  1.61744420e-04,  1.73331601e-03,  2.16630336e-03,\n",
       "         1.17628483e-03, -5.86414140e-04, -1.96390816e-03, -2.05134608e-03,\n",
       "        -7.91291502e-04,  9.88548294e-04,  2.11902842e-03,  1.85755673e-03,\n",
       "         3.75889290e-04, -1.35269309e-03, -2.19271561e-03, -1.59238251e-03,\n",
       "         5.39581367e-05,  1.66485465e-03,  2.18213796e-03,  1.26601393e-03,\n",
       "        -4.81731982e-04, -1.91303678e-03, -2.08770198e-03, -8.90993138e-04,\n",
       "         8.90993138e-04,  2.08770198e-03,  1.91303678e-03,  4.81731982e-04,\n",
       "        -1.26601393e-03, -2.18213796e-03, -1.66485465e-03, -5.39581367e-05,\n",
       "         1.59238251e-03,  2.19271561e-03,  1.35269309e-03, -3.75889290e-04,\n",
       "        -1.85755673e-03, -2.11902842e-03, -9.88548294e-04,  7.91291502e-04,\n",
       "         2.05134608e-03,  1.96390816e-03,  5.86414140e-04, -1.17628483e-03,\n",
       "        -2.16630336e-03, -1.73331601e-03, -1.61744420e-04,  1.51607418e-03,\n",
       "         2.19801081e-03,  1.43611350e-03, -2.69141047e-04, -1.79760166e-03,\n",
       "        -2.14524994e-03, -1.08372195e-03,  6.89683575e-04,  2.01004831e-03]),\n",
       " array([ 7.52722295e-17,  2.02321643e-17, -4.96019313e-17, -8.31664284e-17,\n",
       "        -5.59185161e-17,  1.22177663e-17,  7.14202539e-17,  7.83992925e-17,\n",
       "         2.80517154e-17, -4.28076528e-17, -8.23654903e-17, -6.16965750e-17,\n",
       "         4.08570464e-18,  6.68804621e-17,  8.07713274e-17,  3.56011132e-17,\n",
       "        -3.56011132e-17, -8.07713274e-17, -6.68804621e-17, -4.08570464e-18,\n",
       "         6.16965750e-17,  8.23654903e-17,  4.28076528e-17, -2.80517154e-17,\n",
       "        -7.83992925e-17, -7.14202539e-17, -1.22177663e-17,  5.59185161e-17,\n",
       "         8.31664284e-17,  4.96019313e-17, -2.02321643e-17, -7.52722295e-17,\n",
       "        -7.52722295e-17, -2.02321643e-17,  4.96019313e-17,  8.31664284e-17,\n",
       "         5.59185161e-17, -1.22177663e-17, -7.14202539e-17, -7.83992925e-17,\n",
       "        -2.80517154e-17,  4.28076528e-17,  8.23654903e-17,  6.16965750e-17,\n",
       "        -4.08570464e-18, -6.68804621e-17, -8.07713274e-17, -3.56011132e-17,\n",
       "         3.56011132e-17,  8.07713274e-17,  6.68804621e-17,  4.08570464e-18,\n",
       "        -6.16965750e-17, -8.23654903e-17, -4.28076528e-17,  2.80517154e-17,\n",
       "         7.83992925e-17,  7.14202539e-17,  1.22177663e-17, -5.59185161e-17,\n",
       "        -8.31664284e-17, -4.96019313e-17,  2.02321643e-17,  7.52722295e-17]),\n",
       " array([ 1.39195490e-03,  2.66418231e-04, -1.07454459e-03, -1.54662916e-03,\n",
       "        -7.68107239e-04,  6.31507260e-04,  1.52048411e-03,  1.17999539e-03,\n",
       "        -1.14639239e-04, -1.31657642e-03, -1.45392808e-03, -4.15631469e-04,\n",
       "         9.58745327e-04,  1.55787932e-03,  8.97309926e-04, -4.88825521e-04,\n",
       "        -1.47969597e-03, -1.27408220e-03, -3.82437907e-05,  1.22851860e-03,\n",
       "         1.50189914e-03,  5.60841949e-04, -8.33712826e-04, -1.55412625e-03,\n",
       "        -1.01787103e-03,  3.41436125e-04,  1.42465755e-03,  1.35589890e-03,\n",
       "         1.90758512e-04, -1.12862947e-03, -1.53540610e-03, -7.00651215e-04,\n",
       "         7.00651215e-04,  1.53540610e-03,  1.12862947e-03, -1.90758512e-04,\n",
       "        -1.35589890e-03, -1.42465755e-03, -3.41436125e-04,  1.01787103e-03,\n",
       "         1.55412625e-03,  8.33712826e-04, -5.60841949e-04, -1.50189914e-03,\n",
       "        -1.22851860e-03,  3.82437907e-05,  1.27408220e-03,  1.47969597e-03,\n",
       "         4.88825521e-04, -8.97309926e-04, -1.55787932e-03, -9.58745327e-04,\n",
       "         4.15631469e-04,  1.45392808e-03,  1.31657642e-03,  1.14639239e-04,\n",
       "        -1.17999539e-03, -1.52048411e-03, -6.31507260e-04,  7.68107239e-04,\n",
       "         1.54662916e-03,  1.07454459e-03, -2.66418231e-04, -1.39195490e-03]),\n",
       " array([-1.10152046e-16, -1.22423497e-17,  9.65490754e-17,  1.19521934e-16,\n",
       "         3.62565824e-17, -7.92357785e-17, -1.24298662e-16, -5.88774950e-17,\n",
       "         5.88774950e-17,  1.24298662e-16,  7.92357785e-17, -3.62565824e-17,\n",
       "        -1.19521934e-16, -9.65490754e-17,  1.22423497e-17,  1.10152046e-16,\n",
       "         1.10152046e-16,  1.22423497e-17, -9.65490754e-17, -1.19521934e-16,\n",
       "        -3.62565824e-17,  7.92357785e-17,  1.24298662e-16,  5.88774950e-17,\n",
       "        -5.88774950e-17, -1.24298662e-16, -7.92357785e-17,  3.62565824e-17,\n",
       "         1.19521934e-16,  9.65490754e-17, -1.22423497e-17, -1.10152046e-16,\n",
       "        -1.10152046e-16, -1.22423497e-17,  9.65490754e-17,  1.19521934e-16,\n",
       "         3.62565824e-17, -7.92357785e-17, -1.24298662e-16, -5.88774950e-17,\n",
       "         5.88774950e-17,  1.24298662e-16,  7.92357785e-17, -3.62565824e-17,\n",
       "        -1.19521934e-16, -9.65490754e-17,  1.22423497e-17,  1.10152046e-16,\n",
       "         1.10152046e-16,  1.22423497e-17, -9.65490754e-17, -1.19521934e-16,\n",
       "        -3.62565824e-17,  7.92357785e-17,  1.24298662e-16,  5.88774950e-17,\n",
       "        -5.88774950e-17, -1.24298662e-16, -7.92357785e-17,  3.62565824e-17,\n",
       "         1.19521934e-16,  9.65490754e-17, -1.22423497e-17, -1.10152046e-16])]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = [[[0 for x in range(nx)] for m in range(M)] for t in range(nt)]  #u[t][m][x]\n",
    "\n",
    "u[0]= F_M\n",
    "F_M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "for m in range(M):\n",
    "    for t in range(nt):\n",
    "        u[t][m] = np.dot(np.exp(-t*dt*m**2),u[0][m])#離散化状態"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "for m in range(1,M):\n",
    "    for t in range(nt):\n",
    "        u[t][m] += u[t][m-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "64\n"
     ]
    }
   ],
   "source": [
    "\n",
    "#solution\n",
    "v = np.zeros((nt,nx))\n",
    "\n",
    "#initial data\n",
    "v[0] = F\n",
    "print(len(F))\n",
    "\n",
    "#simulation\n",
    "for t in range(nt-1):\n",
    "    for x in range(1,nx-1):\n",
    "        v[t+1,x] = (1-2*rsq)*v[t,x]+rsq*(v[t,x-1]+v[t,x+1])\n",
    "    #Neumann condition\n",
    "    v[t+1,0] = v[t+1,1]\n",
    "    v[t+1,nx-1] = v[t+1,nx-2]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "i = M-1\n",
    "dist2 = [np.sqrt(np.dot(u[0][i]-v[0],u[0][i]-v[0])/nx)]\n",
    "#distinf = [max(abs(F-F_M[0]))]\n",
    "#dist1 = [sum(abs(F-F_M[0]))/nx]\n",
    "total_f = [sum(u[0][i])/nx]\n",
    "total_i = [sum(v[0])/nx]\n",
    "for t in range(1,nt):\n",
    "    dist2+=[np.sqrt(np.dot(u[t][i]-v[t],u[t][i]-v[t])/nx)]\n",
    "#   distinf+= [max(abs(F-F_M[m]))]\n",
    "#   dist1+= [sum(abs(F-F_M[m]))/nx]\n",
    "    total_f += [sum(u[t][i])/nx]\n",
    "    total_i += [sum(v[t])/nx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
    {
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\" width=\"639.8333333333334\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure()\n",
    "fig1.set_dpi(100)\n",
    "ax = fig1.add_subplot(1,1,1)\n",
    "def animate(t):\n",
    "    ax.clear()\n",
    "    plt.ylim([-1.2,1.5])\n",
    "    \n",
    "    p, = plt.plot(X,u[10*t][M-1])\n",
    "#    p, = plt.plot(X,v[10*t])\n",
    "    time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes)\n",
    "    time_text2 = ax.text(0.05, 0.85,'', transform=ax.transAxes)\n",
    "    time_text.set_text('t = %.2f/%.2f,' \n",
    "                       % ((10*t+1)/nt,tmax))\n",
    "#    time_text2.set_text('L^infty distance = %.3f, L^1 distance = %.3f, ' \n",
    "#                       % (total_f[t],total_i[t]))\n",
    "    if t==nt//10-1:\n",
    "        plt.savefig('question_W_fourier_COMP.png')\n",
    "    \n",
    "anim = animation.FuncAnimation(fig1,animate,frames=nt//10,interval=60,repeat=False)\n",
    "anim.save(\"question_W_fourier_SPEC.gif\", writer=\"imagemagick\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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V9SopLJWByprdaiqToer61RaXafSY3U6crxe5cfrVVpdp5LKWu0rP6FdpcdVcKham0uq9On+Sq0prNCyXUeUW1CqrM3R2d/P368/rtynaUv36rVFu/VK3i69tHCnXpi/U8/P26GJOds1LqtAz8wt0LNZBXpu3g69nLtLkxfv1vRle/XHlfv0Xv5+fbi+RHM3HVTe9lKtKazQ5pIq7Sk7rkNVdaqqbVRjuFmRSKRd/+5FIhHVNYZVcaJBJZW12lV6TJ/ur9TCgsN6P3+//rBotzLmbtPw9zfolzPW6EevLNP3nl+ku55bpDsn5iltfK4GjMvVt59dqNufWahvZSzQj15ZpmfmFmjRjjKdqG+y8t8MAMFF0TWj6LbwwAMPqF+/fm0enzBhgj73uc+d9bnV1dUqKSmJHfn5+VZDt2RnmRzX4+Dg6MTjmlGZun7MXPUfm62vPJGjr/9uvr6VsUC3P7NQtz41Tzc+lqUrR9qd4epHM/WjV5ZpXFaBFu8oU00DxRdIZg1NzcrI3Ka5mw5aew2KrhlFt4UHHnhA/fv3b/P4+PHjddFFF531uenp6QqFQm0OW6FbvvuIvvbkPH3liRzdlJ6tfmOzdeNjWbpu9FxdO2quvvxoZlwLwlUjPV07aq6uHzNXfR/LUv/0bN38eI5ueSJHX3kiR199cp6+9uQ83frUPN361Hx9/XfzdetT82Pv4ebHc9S/xfu4fkz838eVI6NF57rRc3XjY1nqNzZbN6Vn65Ynck7OPl+3PT1f33x6gb759ALd9vR8feN3p9/LrU/Na/Uz6XvyfVwzKtN6OTpTWes3Nvoz+NqT83Tb0/N1+zML9Z1xCzVgXG6r447xp4/vjIueZfzG76I/m5sfz1Hfk7m6Ok4/iy8/mqkbxmTplidy9I3fzde3n12oOyfm6fuTFusHLyzRD19cqrtfXqbBryzT/311ue79wwr9y+SV+skfVmjIq8v1wxeX6vuTFuvOiXn6zriF+ubTC/TVJ6Ml1fbctz41T997fpH+efIK/XrmWo3+cJOem7dDkxfv1pQlezR92V69sTx65nzmqujZ83dXF+nxOVv0f15Ycsbve/WjmRr+/gYdq2u08t8SAPbsKTuuH764VI7r6ab0bB2sqrXyOhRdM4puCxdy6UK8z+i2VyQSUVO4WfVNYdU2hHW8vknVdY2qrGlQ+cmPk4+cPMqORY/SY9GPm0urox85V5xoUFVNo6rrGnW8vkm1DWHVNYbV0NSscHOk3R/5Xsh7CDdH1NDUrLrGsE7UN6mqtlFVNY06eqJBFScadOR4dO7D1XU6VFUX+/j8sx+dHz3RoMqaBlXXNaqmoUl1jWE1hpvV3Gz3PUhSc3NEjeHT76G6Ljr/kZMf6R+sqtX+iprYUXw0epRU1sYuCThQWavDJ38ulTUNOlbXqNqG6M8iHu8hEon+HGoamlRV06gjx+t1qKpO+ytqtKfseOzyih2Ho5eNbDvY+tKRbQertav0mAqPnFDx0Rodrq5T+fF6VdVGfx5N4eZzD3GB89c2hFV+vF77K2q043D0soPlu49o0Y4yLdh2WFmbD+mTjdFLVmavLda7q4s0c9U+/WltsTI3HVTu9lKt2lOuTcVV2lV6TCWVtaqsaeiU//+PnmhQ1uZDSv94i74/aXGrwjtgXK4+3V957m8CwHeRSETv5+9v9Qv277ytqm8KW3k9iq4ZRbeFUzejfXYpsSFDhnAzGoC4qzjRoNcW7dY1ozJjZ3dfydsVl19qAJyfqtpG/ec762MF99an5mvxjjKrr0nnMKPotnBqebGpU6fGHjt69Kh69OjB8mIAfLO5pEp3TsiL/cX5r6+v1OHqOr/HAvAZa/dV6PZnFsb+Xf3F9NU6crze+uvSOcwCW3Rramo0e/ZszZ49W9/4xjfUt2/f2J/LyqK/WQ0cOFADBw5s9byHHnpIPXv21PTp05WTk6O0tDQ2jADguxP1TRoxe0PsL9CvPJGj+VsP+z0WAEnh5ohemL8zdl/JtaPmavqyvdYv7TuFzmEW2KJbWFh4xpvDQqGQ8vLyJElpaWltzvTW19frt7/9rXr16qWLL75YgwYNUkFBQYdfn9ABsOGTjQfUPz07Vngf+2iz6hrtXPcH4NzqGsP6l8krY/9O3vXcIm09UB3XGegcZoEtun4jdABs2V9RoyGvLo/9xfrgm/lxO3MEoLX0j7fE/l189INNqm2I/y+edA4ziq4lhA6ATU3hZj2bVRD7C3bGsr1+jwSknEU7Tq9pPyF7u29z0DnMKLqWEDoAtkUiET08c13smsDNJR27lwDA+Tt6okHf+N18Oa6nu19aqkbLyyOeDZ3DjKJrCaEDEA/VdY36zrjoXd5p43N1nC2EAesikYgeemutHNfTDWOytKfsuK/z0DnMKLqWEDoA8fLp/srYznX//e56rtcFLHs/f3/skoWZq/b5PQ6d4ywoupYQOgDx9PriPbG/eN/L3+/3OEBgFZXXqO/JHc9+OWNNQvxiSecwo+haQugAxFNzc0S/mL469lHqrtJjfo8EBE5TuDm24smtT82Ly2YQ7UHnMKPoWkLoAMRbxYkG3fZ09OaYf3h+MevrAp3sxQU7Y5+cLNiWOBu20DnMKLqWEDoAfli5p1xXjTy9pieAzrFhf2Vs57NE+3eLzmFG0bWE0AHwy6T5O2JnnbyNB/0eB0h6NQ1NunNCnhzX03cn5KmmIbFWN6FzmFF0LSF0APwSbo7onyevkON66j82W/sravweCUhqoz/cJMf19OVHM7Vhf6Xf47RB5zCj6FpC6AD46XB1nb765Dw5rqffvLve73GApLWr9JiuPHk50O8X7PR7nDOic5hRdC0hdAD8NnPVPjmup6tGer4vaA8kq//33qdyXE+3P7PQ193PzobOYUbRtYTQAfBbfVNY38pYIMf19D/vbfB7HCDp7K+oid2A9taKQr/HMaJzmFF0LSF0ABLBG8sLY9cWFpVzrS7QEaM+iF6b+/XfzU/o5froHGYUXUsIHYBEUNcY1jd+F11bd+SfN/o9DpA0DlfX6dpRc+W4niYv3u33OGdF5zCj6FpC6AAkiilLotsDXzMqUyWVtX6PAySFpz7ZKsf1dMsTOTpRn1jLiX0WncOMomsJoQOQKGobwvrayRUYxny42e9xgIRXcaJBN4zJkuN6emF+Yq600BKdw4yiawmhA5BIXlu0W47r6dpRc3Woqs7vcYCENiF7uxzXU7+x2aqqafR7nHOic5hRdC0hdAASyfH6Jt3yRI4c19Pjc7b4PQ6QsKrrGtU/PVuO6+mZuQV+j9MudA4ziq4lhA5Aonlp4U45rqfrRs9V6THO6gJn8nLurti/J2XH6v0ep13oHGYUXUsIHYBEU13XqJtOnql6OnOb3+MACaemoSm2o2D6x8nzyQedw4yiawmhA5CInpu3Q47r6YYxWSo/nhxnq4B4mbp0b2yFkgNJtEIJncOMomsJoQOQiCprGtRvbPSs7ris5Lj+EIiH+qawbns6uub0/85OrjWn6RxmFF1LCB2ARDUuqyB2R3llTYPf4wAJ4e1VRXJcT1eN9FR45ITf43QIncOMomsJoQOQqCpONOjGx6JrhD4/b4ff4wC+awo3a8C4XDmup/96Z73f43QYncOMomsJoQOQyJ7O3CbH9dQ/PVvVdYm/Tihg0wfri+W4nhzX0/ZDx/wep8PoHGYUXUsIHYBEVnasXteNnivH9fTWyn1+jwP46gcvLJHjenrgzXy/RzkvdA4ziq4lhA5Aovvvd9fLcT3d/fIyv0cBfLPlQFXsbO6K3eV+j3Ne6BxmFF1LCB2ARLd055HYX/A7Dyffx7VAZ3h8zhY5rqfvjFuo5uaI3+OcFzqHGUXXEkIHINGFmyP6VsYCOa6njLlsIIHU09DUHNsg4oX5O/0e57zROcwoupYQOgDJYHx2dKmxb/xuvprCzX6PA8RV9pZDsU819lfU+D3OeaNzmFF0LSF0AJLBnrLjsb/oc7eX+j0OEFcPvJkvx/X0L5NX+j3KBaFzmFF0LSF0AJLFkFeXy3E9DXt7nd+jAHFz5Hi9rn40U47r6U9ri/0e54LQOcwoupYQOgDJ4p3V0R2hrh09V1U1rKmL1DBlyR45rqe+j2WppqHJ73EuCJ3DjKJrCaEDkCyq6xpja+r+kTV1kQIikYi+P2mxHNfTiNkb/B7ngtE5zCi6lhA6AMnkNyfX1L2HNXWRAjaXnF47d/XeCr/HuWB0DjOKriWEDkAyWbKzLPYX/65S1tRFsKV/HF07947xuYpEknPt3JboHGYUXUsIHYBk0nJN3WfmFvg9DmBNQ1OzvvJEjhzX04sLknft3JboHGYUXUsIHYBkMy4ruqbubU/PVzhJd4gCziVr80E5rqcrR3oqqaz1e5xOQecwo+haQugAJJvdLdbUzWNNXQTU/W+skeN6+rcpyb12bkt0DjOKriWEDkAyGvzKMjmup/98Z73fowCdruxYvb58cu3cD9cH5+9nOocZRdcSQgcgGb29qsWaurWsqYtgObV2br+x2aptCPs9Tqehc5hRdC0hdACSUVXt6TV1Z65iTV0ERyQS0T88H1071/3TRr/H6VR0DjOKriWEDkCy+q93omvq/ugV1tRFcGwqPr12bn5h8q+d2xKdw4yiawmhA5CsFu9ouabucb/HATrF2I82y3E9fXdCXiDWzm2JzmFG0bWE0AFIVuHmiL75dHRN3WezWFMXya++KaxbTq6d+3LuLr/H6XR0DjOKriWEDkAye5Y1dREgczedXjv3QEDWzm2JzmFG0bWE0AFIZrtKT6+pu3pvsK5nROp56K21clxPP52yyu9RrKBzmFF0LSF0AJLdoOcWyXE9PfnJVr9HAc5bbUNY14+JriQya02R3+NYQecwo+haQugAJLsJ2dvluJ6+/ezCwN28g9SRtfmQHNfTVSM9lR+v93scK+gcZhRdSwgdgGTXcjmmLQeq/B4HOC+PzPpUjuvpJ39Y4fco1tA5zCi6lhA6AMkuEono9mcWynE9PTdvh9/jAB3W0NSsm9Kz5biepi/b6/c41tA5zCi6lhA6AEGQ/vEWOa6n709a7PcoQIe1XBM6iKstnELnMKPoWkLoAATBit3lsaKwr/yE3+MAHfLoB5vkuJ7ufmmp36NYRecwo+haQugABEFTuFlfObnQ/uTFu/0eB2i3cHNEtz41P7CbRLRE5zCj6FpC6AAExfD3N8hxPQ15dbnfowDttqawIvZpxO6yYG9lTecwo+haQugABMX8rYdju0qVHqvzexygXZ78ZKsc19Og5xb5PYp1dA4ziq4lhA5AUNQ1hnXjY1lyXE8zV+3zexzgnCKRiL79bHTFkIk52/0exzo6hxlF1xJCByBIfj0zuoXqv09b7fcowDltLjm9BvTmkuCvAU3nMKPoWkLoAATJR5+WyHE9XTMqU9V1jX6PA5zVxJzorn63P5Mau/rROcwoupYQOgBBUl3XqGtGZcpxPX30Kf9dQ2Ib9NwiOa6nJz/Z6vcocUHnMKPoWkLoAATNv09bLcf19OuZa/0eBTDaVXo8dtnCmsIKv8eJCzqHWaCLbkFBgQYNGqTu3burd+/eGjFihBoaGs75vFAo1Oa4/vrrO/TahA5A0MxctU+O6+nGx7JU1xj2exzgjF7O3SXH9XTrU/MVbg7+ZQsSneNsAlt0jx49qi996Uu64447lJ2drWnTpunSSy/VsGHDzvncUCikRx55RCtXrowdGzZs6NDrEzoAQVN6rE5XjoyeKZu/9bDf4wBndPdLS+W4nh79YJPfo8QNncMssEU3IyNDPXr0UEXF6Y8tJk+erK5du+rAgQNnfW4oFNKkSZMu6PUJHYAgGvLqcjmup+Hvd+yXfyAeSiprY5ctLNpR5vc4cUPnMAts0R0wYIAGDx7c6rHKykp16dJFM2bMOOtzKboAcGaTF++W43r6yhM5ago3+z0O0Mr0ZXvluJ76p2eroSl18knnMAts0b388ss1evToNo/36dNHrs0yQO0AACAASURBVOue9bmhUEiXXXaZunbtqi9+8Yv66U9/qkOHDnXo9QkdgCDaV34idsZsxe5yv8cBWvnJH1bIcT09MutTv0eJKzqHWWCLbrdu3TRhwoQ2j/fr108PPvjgWZ973333afbs2Vq8eLFefPFFXX755bruuutUU1NjfE51dbVKSkpiR35+PqEDEEjfn7RYjusp/eMtfo8CxBw5Xq+rTl5DnrW5Yyenkh1F1yzQRXfixIltHu/bt6+GDh3aoe+1YsUKhUIhTZ061fg16enpZ1ytgdABCJrn5u2Q43r6+4wFKbEYP5LDu6uL5Lierh8zV7UNqbUqCEXXLLBF90IuXTiTPn366Ne//rXxn3NGF0CqaLm96sbiSr/HASRJv5geXed56Fv5fo8SdxRds8AW3QEDBmjIkCGtHquqqmrXzWhn0qdPHz388MPt/npCByCoIpGIbn9moRzX0/jsAr/HAVRd16hrR82V43r6YH2x3+PEHZ3DLLBFNyMjQ5dccokqK0+fbZgyZYq6det2zuXFPmv58uUKhUKaNm1au59D6AAE2RNztspxPQ16bpHfowD6eMMBOa6nqx/NVFVto9/jxB2dwyywRffUhhFpaWnKycnR9OnT1bNnzzYbRgwcOFADBw6M/Xny5Mm6//77NWvWLOXm5mrSpEm67LLLdMMNN6i2trbdr0/oAATZit3lscsX9leYb9QF4uGRWZ/KcT3925SVfo/iCzqHWWCLriRt27ZNd911ly6++GL16tVLw4cPb7MFcFpamtLS0mJ/XrBggW6//Xb91V/9lbp166Y+ffrowQcfVFlZxxaeJnQAgqwx3Kx+Y7PluJ7eWrnP73GQwsLNEX31yXlyXE9Tluzxexxf0DnMAl10/UToAATdQ2+tleN6uv+NNX6PghS2vuho7NOF3WXH/R7HF3QOM4quJYQOQNDNWhNdzumGMVmqb0qt5ZyQOE4tdzdgXG7KLndH5zCj6FpC6AAE3aGqutiZtCU7O3Z5F9BZ7n5pqRzX09iPNvs9im/oHGYUXUsIHYBU8H9eWCLH9fTkJ1v9HgUpqOxYfeyXrdyCUr/H8Q2dw4yiawmhA5AKns0qkON6Gjgxz+9RkIL+tLZYjuvputGptxtaS3QOM4quJYQOQCpYtYdlxuCfYW+vk+N6um/6ar9H8RWdw4yiawmhA5AKGsPN6p9+cpmxFYV+j4MU0hRu1k0ns/fG8kK/x/EVncOMomsJoQOQKn49M7rM2H/MYJkxxE9+YUXs04Si8tT+NIHOYUbRtYTQAUgV7+Xvl+N6un7MXNU1pu51koiv8dnR68PvnJDn9yi+o3OYUXQtIXQAUkVp9ellxhbvYJkxxMcPTq748cQcVvygc5hRdC0hdABSyT/+Plo6Hp+zxe9RkAJYw7k1OocZRdcSQgcglfAxMuKJXflao3OYUXQtIXQAUsmaFjcG7Ss/4fc4CLhf/TF6A+T9b+T7PUpCoHOYUXQtIXQAUglLPSFeGsPN6jc2mrWZq/b5PU5CoHOYUXQtIXQAUs3DJxfv/0WKL94Pu1bsPr1JSUllrd/jJAQ6hxlF1xJCByDVzG6xHSvLjMGWjMxtclxP33t+kd+jJAw6hxlF1xJCByDVlB2rj51py9te6vc4CKjvPb9IjuspI3Ob36MkDDqHGUXXEkIHIBX98MWlclxP6R+zzBg6X0llbeyXqRW7y/0eJ2HQOcwoupYQOgCpaGLOdjmup7TxuX6PggCauWqfHNdTv7HZagw3+z1OwqBzmFF0LSF0AFLR2n2nlxnbe4RlxtC57n8jX47r6aG31vo9SkKhc5hRdC0hdABSUbg5olueyJHjepq+bK/f4yBA6pvCumFMlhzX06w1RX6Pk1DoHGYUXUsIHYBU9Z/vrJfjevr5NJYZQ+dZsrMs9mnB4eo6v8dJKHQOM4quJYQOQKr687rTy4zVNrDMGDrHk59sleN6+sELS/weJeHQOcwoupYQOgCp6sjx08uM5RawzBg6x50T8+S4nsZnF/g9SsKhc5hRdC0hdABS2d0vRZcZG/vRZr9HQQAUldfEfnlaU1jh9zgJh85hRtG1hNABSGXPzdshx/X03Ql5fo+CAPjjyuiyYv3Ts9XEsmJt0DnMKLqWEDoAqSy/8PQyY/sravweB0lu6FssK3Y2dA4ziq4lhA5AKmsMN6vf2Gw5rqe3V7EUFM5fU7hZ/U9maeaqfX6Pk5DoHGYUXUsIHYBU98Cb0bNwv57JWTicv5abkPDpwJnROcwoupYQOgCp7q0VhXJcTzelZyvcHPF7HCSpSfOj13vfwbbSRnQOM4quJYQOQKorPHIidiZufdFRv8dBkhry6nI5rqfRH27ye5SERecwo+haQugApLpIJKLvjFsox/X0+wU7/R4HSaiqtlFffjRTjuspe8shv8dJWHQOM4quJYQOAKRHP9gkx/X049eW+z0KklDW5kNyXE9ffjRT1XWNfo+TsOgcZhRdSwgdAEhzNx2MFZVjFBV00OgPo78oDXmVX5TOhs5hRtG1hNABgFRV06irRkav05239bDf4yDJ3DE+V47radL8HX6PktDoHGYUXUsIHQBE/eiVZXJcT4+xHTA6YF/56ZsZ1+7jZsazoXOYUXQtIXQAEMV2wDgfbPvbfnQOM4quJYQOAKLYDhjn49S2v0Pfyvd7lIRH5zCj6FpC6AAgiu2A0VFN4Wb1T49m5o8r2fb3XOgcZhRdSwgdAJzGdsDoiLX7jsY+BSgq51OAc6FzmFF0LSF0AHAa2wGjI9j2t2PoHGYUXUsIHQCcxnbA6IhT2/6O+oBtf9uDzmFG0bWE0AHAaWwHjPaqrju97W/WZrb9bQ86hxlF1xJCBwCtjfwz2wHj3LK3nN72t6qW3fTag85hRtG1hNABQGtsB4z2YNvfjqNzmFF0LSF0ANAa2wGjPU5t+/v8PLb9bS86hxlF1xJCBwBtsR0wzqaovKbFtr8Vfo+TNOgcZhRdSwgdALTFdsA4m5mrTm77O5ZtfzuCzmFG0bWE0AFAW2vYDhhn8dBba9n29zzQOcwoupYQOgBoi+2AYdJy29+32Pa3Q+gcZhRdSwgdAJzZqe2Af/VHtgPGaS23/d1XfsLvcZIKncOMomsJoQOAM2M7YJzJC/N3ynE9DRjHtr8dRecwo+haQugA4MzYDhhn8n/Z9ve80TnMKLqWEDoAOLOW2wG/MJ/tgPHZbX8P+j1O0qFzmFF0LSF0AGB2ajvge19b4fcoSADzth6W43q6aqTHtr/ngc5hRtG1hNABgJm3Mbod8NWPZup4fZPf48BnYz/aLMf1dM/Ly/weJSnROcwoupYQOgAwO3qiQVee3A54wTa2A051AyfmyXE9Tcje7vcoSYnOYUbRtYTQAcDZ/dNLS+W4nh6fs8XvUeCjg1W1sZsTV+4p93ucpETnMKPoWkLoAODsxmUVyHE9DXpukd+jwEfv5++X43q6YUyW6pvCfo+TlOgcZhRdSwgdAJzd8t1HYmfyDlXV+T0OfPKbd9fLcT3dN32136MkLTqHGUXXEkIHAGdX3xTW9WPmynE9zV5b7Pc48EEkEtGtT82T43qasmSP3+MkLTqHGUXXEkIHAOf279NWy3E9/fe76/0eBT7YdrA6dla/4FC13+MkLTqHWaCLbkFBgQYNGqTu3burd+/eGjFihBoaGs75vIaGBg0fPly9e/dW9+7dNWjQIG3f3rE7QQkdAJzb64v3yHE93frUfEUibAecavj5dw46h1lgi+7Ro0f1pS99SXfccYeys7M1bdo0XXrppRo2bNg5n/vQQw/p0ksv1bRp05Sdna0BAwboiiuuUFVVVbtfn9ABwLlxRi+1/Zwz+p2CzmEW2KKbkZGhHj16qKKiIvbY5MmT1bVrVx04cMD4vOLiYnXt2lWvv/567LGKigp94Qtf0Lhx49r9+oQOAM6NazRTV8trtN/P3+/3OEmNzmEW2KI7YMAADR48uNVjlZWV6tKli2bMmGF83rRp09SlSxdVVla2enzw4MFKS0tr9+sTOgBon1N33f98Gnfdp5IVu8tjZ/MPVtX6PU5So3OYBbboXn755Ro9enSbx/v06SPXdY3PGzFihK644oo2j48aNUq9e/du9+sTOgBoH9ZRTU3js6PrKA+cmOf3KEmPzmEW2KLbrVs3TZgwoc3j/fr104MPPmh83gMPPKB+/fq1eXzChAn63Oc+Z3xedXW1SkpKYkd+fj6hA4B2OFRVFzuzt2I3O2OlirtfXibH9ZT+MTvjXSiKrlmgi+7EiRPbPN63b18NHTrU+LwHHnhA/fv3b/P4+PHjddFFFxmfl56erlAo1OYgdABwbnc9t0iO62l8doHfoyAOqmoaddXI6C8387Ye9nucpEfRNQts0Y33pQuc0QWA85f+8RY5rqe7X1rq9yiIg6zNB+W4nr78aKaO1TX6PU7So+iaBbboDhgwQEOGDGn1WFVVVbtvRvvsUmJDhgzhZjQAsGTBtsNyXE9XjvRUWXPu9c6R3EZ9sEmO62nIq8v9HiUQ6BxmgS26GRkZuuSSS1qtnjBlyhR169atXcuLTZ06NfbY0aNH1aNHD5YXAwBLjtc36epHM+W4nuZuOuj3OLAsbXyuHNfT8/N2+D1KINA5zAJbdE9tGJGWlqacnBxNnz5dPXv2bLNhxMCBAzVw4MBWjz300EPq2bOnpk+frpycHKWlpbFhBABY9uPXlstxPT36wSa/R4FF+ytqYjcfrimsOPcTcE50DrPAFl1J2rZtm+666y5dfPHF6tWrl4YPH95mC+C0tLQ2lyTU19frt7/9rXr16qWLL75YgwYNUkFBx26QIHQA0DEvzN8px/U0YFyu36PAondXF8lxPfUbm63GcLPf4wQCncMs0EXXT4QOADpm7b6jsTN9ReU1fo8DSx5+e50c19P9b6zxe5TAoHOYUXQtIXQA0DFN4Wb1H5stx/X09qoiv8eBBc3NEX3liRw5rqfpy/b6PU5g0DnMKLqWEDoA6LgH3syX43r69cy1fo8CCzaXVMXO2u8qPeb3OIFB5zCj6FpC6ACg495cUSjH9XTz4zkKN0f8Hged7LVFu+W4nm57er4iEX6+nYXOYUbRtYTQAUDH7Sk7Hjvjt2F/5bmfgKTy0ymr5Lie/ue9DX6PEih0DjOKriWEDgA6LhKJ6PZnFspxPb2cu8vvcdCJ6hrDunb0XDmupw/WF/s9TqDQOcwoupYQOgA4P/87e6Mc19O/TF7p9yjoREt3HomdrS89Vuf3OIFC5zCj6FpC6ADg/Hy84YAc19O1o+aqtiHs9zjoJM/MLZDjevqH5xf7PUrg0DnMKLqWEDoAOD/lx+tjZ/7ytpf6PQ46yf/34hI5rqcnP9nq9yiBQ+cwo+haQugA4PydKkVPUYoCofx4va4cGf3lJbeAX146G53DjKJrCaEDgPP3bBYfcwdJy8tRahqa/B4ncOgcZhRdSwgdAJy/5btP37h0uJobl5Ld8Pc3cIOhRXQOM4quJYQOAM5ffVNYN4zJkuN6mr2WpaiSWSQS0TefXiDH9fRKHkvG2UDnMKPoWkLoAODC/GL6ajmup9+8u97vUXABdpUei52d31xS5fc4gUTnMKPoWkLoAODCTFu6V47r6WtPzlMz2wEnrVM/x6/yc7SGzmFG0bWE0AHAheFMYDCcOjP/n+9wZt4WOocZRdcSQgcAFyYSiehbGdFrO1/N2+33ODgPLa+1fi9/v9/jBBadw4yiawmhA4ALN2J29G79f32du/WT0Yrd5bGz8gerav0eJ7DoHGYUXUsIHQBcuDmsv5rUxp1cD3nQc4v8HiXQ6BxmFF1LCB0AXLiKEw2nd9RiO+Ck88MXl8pxPT0+Z4vfowQancOMomsJoQOAzvFPL0XL0hNz2A44mbT6JYVtf62ic5hRdC0hdADQOcZn8/F3Mjp12ck1ozK57MQyOocZRdcSQgcAnYMbmpLTqRsJ2fbXPjqHGUXXEkIHAJ2jvimsGx9jiapk0nJpOLb9tY/OYUbRtYTQAUDn+Y8Za9h0IIm03OxjUzGbfdhG5zCj6FpC6ACg80xfFt1G9itP5LCNbBLg5xVfdA4ziq4lhA4AOs+u0uOcIUwinIGPLzqHGUXXEkIHAJ0nEono709e8/lyLtd8JjK2/Y0/OocZRdcSQgcAnet/Z2+U43r658kr/B4FZ8EqGfFH5zCj6FpC6ACgc32y8fS6rCfqWZc1UZ1a9/gu1j2OGzqHGUXXEkIHAJ3raIudthYWHPZ7HBic2smObX/jh85hRtG1hNABQOe7+2SJSv+YEpWI2PbXH3QOM4quJYQOADrfhOztclxPAyfm+T0KzoBtf/1B5zCj6FpC6ACg863ac/pGp5JKbnRKNNww6A86hxlF1xJCBwCdr6GpWX1Pbgc8a02R3+OgBZaA8w+dw4yiawmhAwA77n8juhnBw2+v83sUtMCmHv6hc5hRdC0hdABgxxvLC+W4nm55IkdhtpdNGDPY9tc3dA4ziq4lhA4A7NhTdvrM4bqio36Pg5N+MX21HNfTMM60xx2dw4yiawmhAwA7IpGIBozLleN6em7eDr/HgaS6xrCuHzNXjutp9tpiv8dJOXQOM4quJYQOAOwZ+9FmOa6nu19a6vcokJS3vTR2lr3sWL3f46QcOocZRdcSQgcA9uRSrBJK+sdb5Liefvgiv3j4gc5hRtG1hNABgD11jWFdNzr6Ufmf+KjcV60uJcnZ7vc4KYnOYUbRtYTQAYBd93HzU0Lg5kD/0TnMKLqWEDoAsOvUMmM3pWerKdzs9zgpa9rS08uKsdybP+gcZhRdSwgdANhVVF4TO5O4prDC73FS1s+mrpLjevrvd9f7PUrKonOYUXQtIXQAYN+dE/PkuJ7GZxf4PUpKqmlo0rWjotdKf7iev+/8Qucwo+haQugAwL4nP9kqx/X0gxeW+D1KSpq/9bAc19OVIz1VnGjwe5yURecwo+haQugAwL4lO8tily8cqqrze5yUM/rDTXJcTz96ZZnfo6Q0OocZRdcSQgcA9tU3hXXDmCw5rqdZa4r8HielRCIR3f7MQjmup98v2On3OCmNzmFG0bWE0AFAfNz/Rr4c19NDb631e5SUsvPwsdjZ9I3FlX6Pk9LoHGYUXUsIHQDEx8xV++S4nvqNzVZDE8uMxcvkxbvluJ5ufWqemllWzFd0DjOKriWEDgDio6SyNnZmccXucr/HSRn/+vpKOa6n/3lvg9+jpDw6hxlF1xJCBwDx873nF8lxPWVkbvN7lJRwrK5R14zKlON6+mTjAb/HSXl0DjOKriWEDgDiJyNzmxzX0/eeX+T3KCkha/MhOa6nq0Z6qqpp9HuclEfnMKPoWkLoACB+Vuwuj12+UHy0xu9xAs/900Y5rqcfv7bc71EgOsfZUHQtIXQAED+N4Wb1G5stx/X0x5X7/B4n0CKRiL759AI5rqeXc3f5PQ5E5zgbiq4lhA4A4utXf1wrx/V0/xtr/B4l0LYdrI6dPd96oNrvcSA6x9lQdC0hdAAQX++t2S/H9XTDmCzVN4X9HiewXsnbJcf1dNvT8xWJsKxYIqBzmFF0LSF0ABBfh6vrYmcal+ws83ucwLr3tRVyXE//O3uj36PgJDqHGUXXEkIHAPH3gxeWyHE9PTFnq9+jBFJVbaO+/Gh0WbGszQf9Hgcn0TnMKLqWEDoAiL/x2QVyXE93Tsjze5RA8jYelON6uvrRTB2rY1mxREHnMKPoWkLoACD+8gsrYpcv7Cs/4fc4gfPb9zfIcT398+QVfo+CFugcZhRdSwgdAMRfU7hZNz+eI8f19MbyQr/HCZTm5ohufWq+HNfTHxbt9nsctEDnMAt00Z06daquvfZaff7zn9fNN9+sTz755JzPmTFjhkKhUJvjmWee6dBrEzoA8Mewt9fJcT3dN32136MEyqbiqtjZ8h2Hj/k9Dlqgc5gFtui+++676tKli8aMGaPc3Fw99NBD6tatm1auXHnW550quvPnz9fKlStjx4EDHdvLm9ABgD/+tLZYjuvp2tFzdaK+ye9xAmPS/B1yXE9/n7GAZcUSDJ3DLLBF97rrrtO//du/tXrs9ttv1w9+8IOzPu9U0a2srLyg1yd0AOCPoycaYisDeBtZGaCzfH/SYjmup7EfbfZ7FHwGncMskEV3z549CoVC+vjjj1s9/vvf/14XXXSR6uvrjc+l6AJA8vvX11fKcT391zvr/R4lEPaVn4hdtrB89xG/x8Fn0DnMAll0MzMzFQqFtGtX6z24582bp1AopIKCAuNzTxXdXr16qWvXrrrmmms0adKkDn9MQ+gAwD9vriiU43rqNzabXdI6weTFu+W4nr7yRI6aws1+j4PPoHOYBbLozpw5U6FQSEeOtP6tMz8/X6FQSMuXLzc+Nzs7W08++aRycnKUnZ2toUOHxq71PZvq6mqVlJTEjlOvRegAIP4OVZ3eJS13e6nf4yS9wa8sk+N6GjF7g9+j4AwoumZJU3SrqqpUUFBwzqOpqSlWdMvLy1t9jzVr1igUCmnFio6t/zd06FD95V/+pU6cMK/JmJ6efsbVGggdAPjjnpej5cz9E1vVXoiWWysvLDjs9zg4A4quWdIUXdOyX589iouLL+jShTM59bzVq81L1XBGFwASy6t50Y/bv/bkPIWbWSXgfL21cp8c11Pfx7JU18hlIImIomuWNEW3I07djDZnzpxWj7/44ou66KKL1NDQ0KHvd6rorlmzpt3PIXQA4K89ZcdjZyJX7Sk/9xNwRj+dskqO62nY2+v8HgUGdA6zQBZdKbq82M9+9rNWj337298+5/JiZ/Lggw+e89KFzyJ0AOC/7z2/SI7r6fE5W/weJSlV1pxequ2TjR1bTx7xQ+cwC2zRPbVhxNixY5WXl6df/epXbTaM2Ldvn7p27ao333wz9tjgwYOVkZGhzMxMZWZm6v7771coFNLYsWM79PqEDgD891zOdjmup9ufWcgmB+dhdovNN46z+UbConOYBbboStEtgK+55hpddNFFuummm9psAVxYWKhQKKQZM2bEHhs1apSuv/56de/eXZ///Od1yy236LXXXuvwaxM6APDflgOnt63dVFzl9zhJ54E38+W4nu5/o/2X7iH+6BxmgS66fiJ0AOC/SCSibz+7UI7raUL2dr/HSSon6pt03ei5clxP7+Xv93scnAWdw4yiawmhA4DE8NQnW+W4nu56bpHfoySVzE0H5bievvxopipOdOwmbsQXncOMomsJoQOAxLCmsCJ2+cKu0uN+j5M0/uud9XJcT//6+spzfzF8Recwo+haQugAIDGEmyO69an5clxPL+fuOvcToPqmsPqPzZbjenpzRaHf4+Ac6BxmFF1LCB0AJI6Rf94kx/V090tL/R4lKeRuL42dBT9UVef3ODgHOocZRdcSQgcAiWPRjrJYcSuprPV7nITn/mmjHNfTPS8v83sUtAOdw4yiawmhA4DE0dDUrP7p0Y/ipy/b6/c4CS3cHNHXnpwnx/X02qLdfo+DdqBzmFF0LSF0AJBY/vvd6M1V/zx5hd+jJLRVe8pjZ7/3Hmn/jqDwD53DjKJrCaEDgMSStTm6XNZVIz2VH6/3e5yE9ficLXJcT9+ftNjvUdBOdA4ziq4lhA4AEktNQ4sNENawAcKZRCIR/X3GAjmup+fn7fB7HLQTncOMomsJoQOAxPPgyS1t/2MGW9qeycbiythlC1sPVPs9DtqJzmFG0bWE0AFA4vnT2mI5rqdrR83V8fomv8dJOOOzC+S4ngaMy1UkEvF7HLQTncOMomsJoQOAxFNZ06CrH82U43qas+GA3+MknIET8+S4np7O3Ob3KOgAOocZRdcSQgcAiemnU1bJcT09PHOd36MklJ2Hj8UuW1i776jf46AD6BxmFF1LCB0AJKa3VxVFL18YPVdVtY1+j5MwnpkbvWzhWxkL1NzMZQvJhM5hRtG1hNABQGKqqm2Mrb4wc9U+v8dJCOHmiG57er4c19P47AK/x0EH0TnMKLqWEDoASFz/9U5084gfvcIWt5KUt700dtnCnrLjfo+DDqJzmFF0LSF0AJC4Fu0oixW7XaUUu2Fvr5Pjehry6nK/R8F5oHOYUXQtIXQAkLhaflT/bFZqf1RfVdOoa09eyvHO6iK/x8F5oHOYUXQtIXQAkNiezYrefHXb0/MVTuGbr95auU+O6+n6MXNVXcfNecmIzmFG0bWE0AFAYttVejx2+cKiHWV+j+Obu19eJsf19N/vrvd7FJwnOocZRdcSQgcAie9Hr0RL3n++k5olr+XauUt3HvF7HJwnOocZRdcSQgcAiW/mqn0pvaZuRuY2Oa6nv89YkNKXbyQ7OocZRdcSQgcAia+q9vSNWKm2pm5TuFlf/130hrwJ2dv9HgcXgM5hRtG1hNABQHL4zxRdUze34PTauYVHTvg9Di4AncOMomsJoQOA5JCqa+o+PDO6du6PX2Pt3GRH5zCj6FpC6AAgOaTimrqVNQ26dlT0ko1Za1g7N9nROcwoupYQOgBIHqm2pu6bKwpja+ceY+3cpEfnMKPoWkLoACB5tFxTd3EKrKn7Ty8tleN6emTWp36Pgk5A5zCj6FpC6AAguZxaU/e/Ar6m7vZDp9fOXb6LtXODgM5hRtG1hNABQHI5tabudQFfU/fpk2vn3v7MQjWnwGUaqYDOYUbRtYTQAUByabmm7turgnmDVmO4Wbc+Fb3x7rkc1s4NCjqHGUXXEkIHAMln2NvRJbcGB3RN3QXbDscuW9hXztq5QUHnMKPoWkLoACD55G0/vYnC7rLgran7qz+uleN6uve1FX6Pgk5E5zCj6FpC6AAg+bRcU/epT7b6PU6nOlxdp2tGZcpxPb2Xv9/vcdCJ6BxmFF1LCB0AJKdJ83fIcT3d+FiWjp5o8HucTvPUJ1vluJ5ufjxHJ+qb/B4HnYjOYUbRtYTQAUByqqxpfb/1QwAAEI1JREFUUN/HsqI3bM3b4fc4naLiRINuGBN9Ty/M3+n3OOhkdA4ziq4lhA4AklfGySW4bkrPDsTOYRNztstxPfUbm62qmuR/P2iNzmFG0bWE0AFA8io9VhdbauzVvN1+j3NBqusa1T89W47r6Zm5BX6PAwvoHGYUXUsIHQAkt8c+2izH9XTrU/NU1xj2e5zz9nLurthGGGXH6v0eBxbQOcwoupYQOgBIbiWVtbr60egqBTOW7fV7nPNS09Ckrz45T47rKf3jLX6PA0voHGYUXUsIHQAkv+Hvb5DjevpWxgI1NDX7PU6HTV26V47r6ZpRmTpQWev3OLCEzmFG0bWE0AFA8ttTdlxXjYxuIDFrTXJtC1zfFI6tCfy/szf6PQ4sonOYUXQtIXQAEAyntgVOG5+rpnDynNV9e1WRHNfTVSM9FR5hu98go3OYUXQtIXQAEAzbDlbHtgX+6NPk+G96U7hZA8blynE9/ebd9X6PA8voHGYUXUsIHQAEx/1vrJHjevqH5xeruTni9zjn9MH64lg5337omN/jwDI6hxlF1xJCBwDBsb7oaKw4ztt62O9xzqq5OaK7nlskx/X04Jv5fo+DOKBzmFF0LSF0ABAs/zZlpRzX090vL1MkkrhndeduOhgr5RuLK/0eB3FA5zCj6FpC6AAgWJbvPhIrkEt3HvF7nDOKRCL6x98vkeN6+tnUVX6Pgzihc5hRdC0hdAAQLJFIRINfWSbH9fTPk1f4Pc4Z5W4vjZXx1Xsr/B4HcULnMKPoWkLoACB4FhYcjhXJZbsS66xuU7hZ//TSUjmup3tfS8wiDjvoHGYUXUsIHQAETyQSiZXJv89YoKraRr9Hivn9gp0JW8JhF53DjKJrCaEDgGDacfiYrh09N6HWqP10f6W+/GimHNfTqA82+T0O4ozOYUbRtYTQAUBwTV+2N2E2kThR36S08dHNIe6cmKfahrCv8yD+6BxmFF1LCB0ABFdzc0Q/m7pKjuupf3q2io/W+DbLyD9vlON6uvrRTJYTS1F0DjOKriWEDgCC7XB1nb7yRE705q8/rFDYhx3TcrYcip1Zfjl3V9xfH4mBzmFG0bWE0AFA8GVtPr05w6t5u+P62qXH6vTVJ+fJcT39+LXlvhRtJAY6hxlF1xJCBwCpYcTsDXJcT9eMytTmkqq4vGYkEtHPp62W43rqNzZb+yv8u3QC/qNzmFF0LSF0AJAaTtQ36Y6TN4MNjNPNYG+uKIydSf7zumLrr4fERucwo+haQugAIHWsKzoaW95rzIebrb7WrtJjuu7k8mYPv71OkQiXLKQ6OocZRdcSQgcAqWXS/B2xs6y5BaVWXqOhqVn/+PslclxP33x6gSprGqy8DpILncOMomsJoQOA1NIUbtaPXlkmx/X01SfnaeWe8k79/sfqGvXwzHWxMr2c3c9wEp3DjKJrCaEDgNSzr/yE+o3NluN6unKkp/HZBWoMN1/w911XdFTfGbcwVnIzMrd1wrQICjqHWWCL7qxZszR48GD9zd/8jUKhkGbMmNHu5xYUFGjQoEHq3r27evfurREjRqihoWMfDxE6AEhNOw4f0/cnLY6V0rtfXqbCIyfO63uFmyN6ccHO2PW/146aq6lL96qZpcTQAp3DLLBF98c//rG+9rWv6Ze//GWHiu7Ro0f1pS99SXfccYeys7M1bdo0XXrppRo2bFiHXp/QAUDqqmsM6/E5W2Jlt+9jWZq9trhDN44dqKzVvX9YEfseAyfmxW35MiQXOodZYItuc3P0o6LKysoOFd2MjAz16NFDFRUVsccmT56srl276sCBA+1+fUIHAMjdXqpbn5oXK6vD3l6nqtrGcz4vc9NB3ZSeHXveyD9vUk1DUxwmRjKic5gFtuie0tGiO2DAAA0ePLjN9+jSpUuHLn8gdAAASSo7Vq9fTF8dK623P7NQkxfv1tSlezVlyZ42x/+b9Wnsa29+PEdZmw/6/RaQ4OgcZhTdz7j88ss1evToNo/36dNHruu2+3UJHQDglEgkohnL9urak+vftuf4yR9W6EBlrd+jIwnQOcwoup/RrVs3TZgwoc3j/fr104MPPmh8XnV1tUpKSmJHfn4+oQMAtFJwqFr/Pm217npuke56bpEGnTy+93z0+IfnF+sff79Ery3arTA3nKGdKLpmSVN0q6qqVFBQcM6jqan1NUznU3QnTpzY5vG+fftq6NChxuelp6crFAq1OQgdAACwiaJrljRFd8aMGWcskp89iotb7/kdr0sXOKMLAAD8QNE1S5qie77O52a0IUOGtHqsqqqKm9EAAEBConOYUXQ/IyMjQ5dccokqKytjj02ZMkXdunVjeTEAAJBw6BxmgS26W7du1ezZs/Xmm28qFApp2LBhmj17tubOnRv7mn379qlr16568803Y4+d2jAiLS1NOTk5mj59unr27MmGEQAAICHROcwCW3RNN4c5jhP7msLCwjOe7d22bZvuuusuXXzxxerVq5eGDx/OFsAAACAh0TnMAlt0/UboAABAPNA5zCi6lhA6AAAQD3QOM4quJYQOAADEA53DjKJrCaEDAADxQOcwo+haQugAAEA80DnMKLqWEDoAABAPdA4ziq4lhA4AAMQDncOMomsJoQMAAPFA5zCj6FpC6AAAQDzQOcwoupYQOgAAEA90DjOKriWEDgAAxAOdw4yiawmhAwAA8UDnMKPoWkLoAABAPNA5zCi6lhA6AAAQD3QOM4quJYQOAADEA53DjKJrCaEDAADxQOcwo+haQugAAEA80DnMKLqWEDoAABAPdA4ziq4lhA4AAMQDncOMomsJoQMAAPFA5zCj6FpC6AAAQDzQOcwoupYQOgAAEA90DjOKriVFRUUKhULKz89XSUkJBwcHBwcHB4eVIz8/X6FQSEVFRX7Xn4RD0bXkVOg4/v/27iUkqv8P4/hRp8xLeUOlsXBn4QVXQRdsQI02USgERQuJHKXaFCmFCYGEVJMILiKrsWXSQNQmNMoIKQML2pRBCxGLoPC20JSs57+Qv790ZnQ8YzbnzPsFB+o784UvDx+np5qZw8XFxcXFxbUWV39//7+uPxGHovuXzMzMqL+/X0NDQ6v+Nzb+lZjsyM9aF/mRHflZ77JSdkNDQ+rv79fMzMy/rj8Rh6JrIZ8/8x4cs8guPOQXHvIzj+zCQ37mkZ09UHQthB8688guPOQXHvIzj+zCQ37mkZ09UHQthB8688guPOQXHvIzj+zCQ37mkZ09UHQtZGJiQpcuXdLExMS/PorlkF14yC885Gce2YWH/MwjO3ug6AIAAMCWKLoAAACwJYouAAAAbImiCwAAAFui6AIAAMCWKLoRYmBgQOXl5UpMTFR2drbq6+tDusPJzMyM6urqlJ2drcTERJWXl+vjx49rcOLIYTa7QLdP3LZt2xqcOLJ8+vRJNTU1KioqUmxsrFwuV0j7mD3z2TF70v3793Xw4EHl5OQoKSlJxcXF8nq9+v3795L7mLs5ZvNj9iSfz6ddu3YpPT1d8fHxysvLU1NTk6anp5fcx+xZE0U3AoyOjmrz5s3au3evurq65PV6lZKSotOnTy+7t7a2VikpKfJ6verq6lJJSYlycnI0Pj6+Bif/98LJzjAMnTlzRn19ffPXu3fv1uDUkeXhw4fasmWLDh8+rLy8vJDLWrTPnmQ+O2ZP2rlzp44cOaLOzk49e/ZMFy5cUGxsrJqampbcx9zNMZsfsyfdvHlTjY2NevDggXp6enTlyhVt2LBBtbW1S+5j9qyJohsBmpublZycrJGRkfm19vZ2xcXF6cuXL0H3DQ8PKy4uTrdu3ZpfGxkZUVJSkq5evfpXzxwpzGYnzb3gt7a2/u0jRrxfv37N//rQoUMhlTVmb46Z7CRmT5K+f//ut+Z2u5WWlhZ0D3P3HzP5ScxeMA0NDUpOTl7wM/0nZs+6KLoRoKSkRBUVFQvWxsbGFBMTo7t37wbd5/V6FRMTo7GxsQXrFRUVIf+Ba3Vms5N4wQ8k1LLG7Pmj6Ibvxo0bMgxDU1NTAR9n7pa2XH4SsxdMS0uL4uPjNTs7G/BxZs+6KLoRIDMzUxcvXvRbdzqdOn/+fNB99fX1ysnJ8VtvaGhQdnb2qp4xUpnNTpp7wc/IyFBcXJzS0tJ07Ngxff369W8d1RJCLWvMnr+VFl1mz9/Ro0eVm5sb9HHmbmnL5Scxe3+anZ3V5OSkent7lZubq7NnzwZ9LrNnXRTdCOBwOOTxePzWCwoK5Ha7g+6rrq5WQUGB37rH49G6detW9YyRymx2klRVVSWfz6cXL16ora1NmZmZysvL0+Tk5N86bsQLtawxe/5WUnSZPX+9vb2KjY1VW1tb0Ocwd8GFkp/E7P0pPj5+/gN5VVVVQd+2IDF7VkbRjQAOh0PXr1/3W8/Pz1dNTU3QfdXV1SosLPRbv3btmtavX7+qZ4xUZrML5NWrVzIMQ3fu3Fmt41nOSoputM/eYispuotF++wNDw/L6XSqrKxs2bLB3PkLNb9Aonn23r59q97e3vnCf/z48aDPZfasi6IbAXjrgnnhvHUhEKfTqZMnT67G0SyJty6YF07RlaJ39sbGxlRYWKiioqJlP73O3PlbSX7BROvs/enRo0cyDENv3rwJ+DizZ10U3QhQUlKiysrKBWvj4+Mhfxht8YtbZWVl1Lw53mx2wTidTp06dWqVTmc9K/0wWjTP3mKrUXSjbfampqa0Z88ebd26VZ8/f172+czdQivNL5honL3FhoeHZRiG7t27F/BxZs+6KLoRoLm5WRs3blzwac7bt2/L4XCE9PVif/6X0+joqJKTk6Pm607MZhfIy5cvZRiGvF7vah/TMlb69WLRPHuLhVN0o3H2fv78qQMHDig9PV3v378PaQ9z9x8z+QUSjbMXSGdnpwzD0OvXrwM+zuxZF0U3Avz/pgcul0vd3d3q6OhQamqq300PSktLVVpaumCttrZWqamp6ujoUHd3t1wuV1R9gbXZ7Nrb23XixAl1dnaqp6dHra2tysjI0Pbt25f8ah47mpyclM/nk8/n044dO5Sfnz//+2/fvkli9oIxkx2zN8ftdsswDLW0tCy4eUFfX9/8HaqYu+DM5Mfszdm/f788Ho8eP36sJ0+e6PLly0pJSdG+ffvmn8Ps2QdFN0J8+PBBZWVlSkhIUFZWlurq6vxuY+tyufz+xWh6elrnzp1TVlaWEhISVF5eroGBgTU8+b9nJrunT59q9+7dSk9Pl8PhkNPplNvtni8n0WRwcDDgbUENw9Dz588lMXvBmMmO2ZuTm5sbNLvBwUFJzN1SzOTH7M1pbGxUYWGhkpKStGnTJhUXF8vj8ejHjx/zz2H27IOiCwAAAFui6AIAAMCWKLoAAACwJYouAAAAbImiCwAAAFui6AIAAMCWKLoAAACwJYouAAAAbImiCwAAAFui6AIAAMCWKLoAAACwJYouAAAAbImiCwAAAFui6AIAAMCWKLoAAACwJYouAAAAbImiCwAAAFui6AIAAMCWKLoAAACwJYouAAAAbImiCwAAAFui6AIAAMCWKLoAAACwJYouAAAAbImiCwAAAFui6AIAAMCWKLoAAACwJYouAAAAbImiCwAAAFui6AIAAMCWKLoAAACwJYouAAAAbImiCwAAAFui6AIAAMCWKLoAAACwpf8By/My/0GIpZMAAAAASUVORK5CYII=\" width=\"639.8333333333334\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = plt.figure()\n",
    "fig1.set_dpi(100)\n",
    "ax = fig1.add_subplot(1,1,1)\n",
    "def animate(t):\n",
    "    ax.clear()\n",
    "    plt.ylim([-1.2,1.5])\n",
    "    \n",
    "    p, = plt.plot(X,F_M[t])\n",
    "#    p, = plt.plot(X,v[t])\n",
    "    time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes)\n",
    "    time_text2 = ax.text(0.05, 0.85,'', transform=ax.transAxes)\n",
    "    time_text.set_text('t = %.2d/%.2d,' \n",
    "                       % (t,M-1))\n",
    "#    time_text2.set_text('L^infty distance = %.3f, L^1 distance = %.3f, ' \n",
    "#                       % (total_f[t],total_i[t]))\n",
    "#    if i==8:\n",
    "#        plt.savefig('W_fourier_exp.png')\n",
    "    \n",
    "anim = animation.FuncAnimation(fig1,animate,frames=M,interval=600,repeat=False)\n",
    "#anim.save(\"question_W_fourier_TRANS.gif\", writer=\"imagemagick\")\n",
    "plt.show()"
   ]
  },
  {
   "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
}