04_Training_in_Keras.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3ee870f1",
   "metadata": {},
   "source": [
    "# 4. Training a Neural Network - Keras"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "226ecfcd",
   "metadata": {},
   "source": [
    "In the last notebook we built upon the first neural network which is capable of creating a highly intricate abstract image from a set of input vectors. Adopting the method of gradient descent the weights and biases of the network were altered such that its output images could approximate a specified target image.\n",
    "\n",
    "In this notebook the neural network and the approximation mechanism will be rebuilt in Keras."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3447b189",
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from time import sleep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2d0afa2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer structure of the network:  [2, 30, 30, 30, 30, 1]\n"
     ]
    }
   ],
   "source": [
    "# define structure of the network\n",
    "\n",
    "# dimensions of input, hidden and output layers\n",
    "N0 = 2\n",
    "N1 = 30\n",
    "N2 = 1\n",
    "\n",
    "# number of hidden layers, minimum number of hidden layers to be used: 1\n",
    "layer_count = 4\n",
    "\n",
    "# size of all the layers in a list, this includes input and output layers\n",
    "layers = [N0]\n",
    "\n",
    "for l in range(layer_count):\n",
    "    layers.append(N1)\n",
    "    \n",
    "layers.append(N2)\n",
    "\n",
    "print(\"Layer structure of the network: \", layers)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "faf25de2",
   "metadata": {},
   "source": [
    "With the structure of the neural network being determined in the cell above it now has to be initialized in Keras. A *sequential* network is made where the layers follow one another sequentially. Then an initializer, which determines the way the weights are initially set, is chosen. Like in the notebooks before the weights shall be uniformly distributed random numbers between -10 and 10. The layers are then added one by one as *dense* layers which correspsond to fully connected layers. For the dense layers the layer size, activation function, use of bias vectors and kernel initializer have to be specified. We use the layer sizes defined above, our trusty sigmoid activation and the random initializer for the *kernel* (kernel is a synonym for the weights matrix)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d60f1995",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2022-09-05 13:14:37.002635: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcudart.so.11.0'; dlerror: libcudart.so.11.0: cannot open shared object file: No such file or directory\n",
      "2022-09-05 13:14:37.002675: I tensorflow/stream_executor/cuda/cudart_stub.cc:29] Ignore above cudart dlerror if you do not have a GPU set up on your machine.\n",
      "2022-09-05 13:14:39.011728: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcuda.so.1'; dlerror: libcuda.so.1: cannot open shared object file: No such file or directory\n",
      "2022-09-05 13:14:39.011767: W tensorflow/stream_executor/cuda/cuda_driver.cc:269] failed call to cuInit: UNKNOWN ERROR (303)\n",
      "2022-09-05 13:14:39.011796: I tensorflow/stream_executor/cuda/cuda_diagnostics.cc:156] kernel driver does not appear to be running on this host (batch1372.desy.de): /proc/driver/nvidia/version does not exist\n",
      "2022-09-05 13:14:39.011993: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 FMA\n",
      "To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.\n"
     ]
    }
   ],
   "source": [
    "# construct the network in keras\n",
    "from tensorflow import keras\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "from keras.initializers import RandomUniform\n",
    "\n",
    "# make a network where all layers are connected sequentially\n",
    "net = Sequential()\n",
    "\n",
    "# set the weights initializer\n",
    "initializer = RandomUniform(minval=-10, maxval=10)\n",
    "\n",
    "# make the first layer with the input shape as an argument\n",
    "net.add(Dense(layers[1], input_shape = (layers[0],), activation = 'sigmoid', \n",
    "              use_bias = True, kernel_initializer = initializer))\n",
    "\n",
    "# make all the other layers\n",
    "for i in range(2, len(layers)):\n",
    "    net.add(Dense(layers[i], activation = 'sigmoid', use_bias = True, kernel_initializer = initializer))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40a9dfb1",
   "metadata": {},
   "source": [
    "Adding the layers to the network only yields a very abstract and conceptual construction. To put it in \"functional form\", so to speak, it has to be compiled first specifiying the method by which the loss is determined and by which the network is beign trained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e10586a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# compile the network\n",
    "\n",
    "net.compile(loss = 'mean_squared_error', \n",
    "            optimizer = keras.optimizers.SGD(learning_rate = 0.5), \n",
    "            metrics = ['accuracy'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edaa4093",
   "metadata": {},
   "source": [
    "The making of the input and target data has been written as functions to further compactify the code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "09cf0d4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# construct input data and the target image\n",
    "\n",
    "# size of the image\n",
    "M = 100\n",
    "\n",
    "def make_input(dim):\n",
    "    \n",
    "    y1, y2 = np.meshgrid(np.linspace(-0.5, 0.5, dim), np.linspace(-0.5, 0.5, dim))\n",
    "\n",
    "    y1_flat = y1.flatten()\n",
    "    y2_flat = y2.flatten()\n",
    "\n",
    "    y_in = np.empty((len(y1_flat), 2))\n",
    "    y_in[:,0] = y1_flat\n",
    "    y_in[:,1] = y2_flat\n",
    "    \n",
    "    return y_in\n",
    "    \n",
    "\n",
    "def make_target(dim):\n",
    "\n",
    "    target = np.zeros((dim, dim))\n",
    "    quad_1 = np.ones((dim//2, dim//2))\n",
    "    target[:dim//2, dim//2:] = quad_1\n",
    "    target[dim//2:, :dim//2] = quad_1\n",
    "    \n",
    "    target = np.reshape(target, (dim**2, 1))\n",
    "    \n",
    "    return target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c6ebe459",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_target = make_target(M)\n",
    "y_in = make_input(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "77646fdb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot target image\n",
    "\n",
    "plt.figure(figsize = (15, 10), facecolor = \"white\")\n",
    "\n",
    "plt.imshow(np.reshape(y_target, (M, M)))\n",
    "plt.colorbar()\n",
    "\n",
    "plt.xticks([], [])\n",
    "plt.yticks([], [])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cbf25d0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# helper storage array for calculated costs\n",
    "\n",
    "batches = 2000\n",
    "\n",
    "costs = np.empty(batches)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74ba9b62",
   "metadata": {},
   "source": [
    "To run the approximation i.e. selection of the right weights the network is trained with the function `train_on_batch` 2000 times. The for loop can be omitted by using the function `fit` instead, though, it was not used such that the images at any point in the training can be viewed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "29733675",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this is where the approximation actually happens\n",
    "\n",
    "for i in range(batches):\n",
    "    \n",
    "    costs[i] = net.train_on_batch(y_in, y_target)[0]\n",
    "    if i == 0:\n",
    "        y_out = net.predict_on_batch(y_in)\n",
    "        \n",
    "        plt.figure(figsize = (15, 10), facecolor = \"white\")\n",
    "\n",
    "        plt.imshow(np.reshape(y_out, (M, M)))\n",
    "        plt.colorbar()\n",
    "\n",
    "        plt.xticks([], [])\n",
    "        plt.yticks([], [])\n",
    "\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cf156e8",
   "metadata": {},
   "source": [
    "Now that the network has been trained it can be used to make a \"prediction\" of some sort by making the final approximation of the target image. This is done with the function `predict_on_batch`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a2b77163",
   "metadata": {},
   "outputs": [],
   "source": [
    "# view the approximation of the target using the fully trained network\n",
    "\n",
    "y_out = net.predict_on_batch(y_in)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "915bfc5e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAo0AAAI1CAYAAACzNMBVAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAA3o0lEQVR4nO3df6yk910v9s/MnHP2l+1db7x2kl0nxOzFN3auRZAdQlGjpFQYlnbFHxAZVGgUiYXIKiogQK2EFSIQrhAghKl6uYrIpai2kEC1e5sYEipHVRrsuwq3EMwlW7CT3SWJf6/319lzdubpH6ZL19/Pd2dm58eZ88zrFVnK+e53nnnmmWfmfM9nnvd8Ok3TNAEAANfQ3eodAABg8Vk0AgAwlEUjAABDWTQCADCURSMAAENZNAIAMJRFIwBAi3z0ox+NW2+9Nd7znvek/940Tfz0T/90HD58OO6555740pe+NNJ2LRoBAFrkIx/5SDz55JPVf//MZz4TJ06ciBMnTsTv/d7vxcc+9rGRtmvRCADQIh/4wAdi//791X9//PHH48d//Mej0+nE+9///njttdfi61//+tDtWjQCACyR06dPx+23337l50OHDsXp06eH3m5lnDtZ6+yInbFn/L0DlkqnW/49evDu14ux3R1/t1J3ZtBJx/d2t0/32ybyfX19UJ77q51+OndnpzwO+ZGJ6FT/Zft6/uRmvPRKfmwWyf0f2hMvz2k/L17+1ti1a9eVn48dOxbHjh2b+f2OtWjcGXviO3vfO9rkZnA9+zNd2mrDlujuLv+4/B/+3Z8XY/es7ZzH7rBNPXlhRzr+fbsvzXlPrt9mky8i/uxi+Rq5feW1dO6dq71ibCXKsYiIXgv/EHvf/Se3ehdG8vIr/XjmT98xl/t633+xK44fP37dtz948GCcPPnPx/XUqVNx8ODBobdr39kFADBnTUQM5vS/SR09ejT+4A/+IJqmib/4i7+IvXv3xtve9rahtxur0ggAwGL7kR/5kXjqqafipZdeikOHDsUv//Ivx+bmZkRE/NRP/VQcOXIkPv3pT8fhw4dj9+7d8fu///sjbXd2i8ZxSuSz+ig7uQ7ER9YwB8nr7K29xb8mia3TT34PfMeOVyqzF/Pa+uyj6Ocur6dzP7SznLujs5bObeNHzu3UpOfxVnj00Uev+e+dTid+93d/d+ztOhMBABjKx9MAABN645rGdn+aqdIIAMBQKo0AAFMwjWTzIlNpBABgqPErjW9OBk0j1TXPpLVENcxe8jrb3cm/jBhqbu0tZko6Ik97Z+npb13ZVYxFSES3URNN9Fu+nnDWAgAwlGsaAQCmQHoaAIClZ9EIAMBQk388XQumzOoi32y7swjHRAjIwPXqlq/TVUEYrmFRgyHjtIXb3c3bALIcmojo+3gaAIBlJwgDADAFgjAAACw9lUYAgAk1Eb7cGwAArqON4JtW0dXk8RiJ5klTc7NqQ6jlIFyXTvLaWQnpabafRU11s5gm/C6XhefVAADAUK5pBACYUBON72kEAACVRgCASTUR/XYXGqfRRnCMIzROaGZR2xBqOQjXRaAAYHtTaQQAmFAT0tMAAKDSCAAwuU70o3IJW0uoNAIAMJRFIwAAQ8334+mxEsYL0IZQy0G4Lo1zH1gyTUQMWv7Wp9IIAMBQgjAAAFMgCAMAwNJTaQQAmFAT7a80Lu6icRFCM1oOAgBExCIvGgEAtpFB0+5Ko2saAQAYSqURAGBCy3BNo0ojAABDqTQCAEyoiU70W16La8eicZ5Jay0HAYAl1I5FIwDAFpOeBgBg6ak0AgBMSHoaAABiGSuNswrNTEo4BgBYYMu3aAQAmLpO9Jt2f4Db7kcHAMBUqDQCAEyoiYhBy2tx7X50AABMhUrjtYwTRMmCLJOqbVNABgAWjq/cAQBg6ak0AgBMqGmkpwEAQKURAGAaBq5pBABg2ak0Tss8k9ZaDgLAQmkiot/yWly7Hx0AAFOh0ggAMDHpaQAAUGkEAJjUMvSetmjcCpOGVrIgjJaDAMAMtXtJDADAVKg0AgBMQb/x5d4AACw5lUYAgAk10fHl3gAAoNK4HUlEsw31m0Ex1uv4u3URbDb9dHy105vznsD2Npjbl3tvzTrAOzYAAEOpNAIATKiJmOM1jfmnA7Om0ggAwFAqjQAAE2qi0/rvabRoBKauk7S1HCQXbotZAGwfFo0AAFMwaPlVf+1+dAAATIVKIwDAhJomoj+372ncGu1+dAAATIVKIwDAxDoxCOlpgIkNomwjKD89f+cG68XYDd2dW7AnwHbj42kAAIZSaQQAmFATgjAAAKDSCAAwDf2W1+IsGoG56DdlG8GWBw0X0mpH+Ai4PhaNAAATaqITg6bdfwm3u44KAMBUqDQCAExB269pbPejAwBgKlQagenrltf1bEZ/C3Zkeb3av5CO39zbPdF2+03W2Sei11GDYLk1ETHwPY0AACw7lUYAgIl1ot/y7xFTaQQAYCiVRgCACbmmEQAAQqURmIUkSbtZSd0yG7u7qxNvI0tKS0lDnWsaAQBYehaNAAAM5eNpAIAJNU1HEAYAAFQagelL2giKwczOmcHFYmxvd9cW7Akst75KIwAAy06lEQBgQk1EDHzlDgAA28mTTz4Zd955Zxw+fDgefvjh4t+/9rWvxYc+9KF473vfG/fcc098+tOfHrpNlUYAgIl1Fuaaxn6/Hw8++GB89rOfjUOHDsV9990XR48ejbvuuuvKnF/5lV+JD3/4w/Gxj30snn322Thy5Eg8//zz19zuYjw6AACm4plnnonDhw/HHXfcEWtra/HAAw/E448/ftWcTqcTr7/+ekREnDlzJt7+9rcP3a5KIzB9nfK6no2m2YIdWQ67O2sT3f7V/oV0/Obe7om2C8ukiYhBM59rGl988cW49957r/x87NixOHbs2JWfT58+HbfffvuVnw8dOhRPP/30Vdv4+Mc/Ht/7vd8bv/M7vxPnz5+Pz33uc0Pv16IRAGAbOXDgQBw/fnyibTz66KPxkY98JH7u534uvvjFL8aP/diPxZe//OXodusfQls0AgBMQX9Brvo7ePBgnDx58srPp06dioMHD14155Of/GQ8+eSTERHxXd/1XbG+vh4vvfRS3HrrrdXtLsajAwBgKu677744ceJEPPfcc7GxsRGPPfZYHD169Ko573jHO+LP//zPIyLib//2b2N9fT0OHDhwze2qNAIATKiJztyuaRxmZWUlHnnkkbj//vuj3+/HRz/60bj77rvjoYceinvvvTeOHj0av/EbvxE/8RM/Eb/1W78VnU4nPvWpT0UnuR79qu3Oaf+BNqq9wfR6xdAlOZiZWe2Ux7vm3GC9GLuhu2OauwMsgCNHjsSRI0euGvvEJz5x5f/fdddd8YUvfGGsbVo0AgBMwaDlV/21+9EBADAVKo0AABNqmoj+glzTOCsqjQAADGXRCADAUD6eBqauk3QUWG9GT/gyOy/2Lxdj71rduQV7Au2zKF+5MysqjQAADKXSCAAwoTe+3Lvdtbh2PzoAAKZCpREAYAr60e5rGsdfNA7pS3hFo2cYLK2V8q1FEGa+XuifT8cPreya854AbaHSCAAwoSakpwEAQKURAGBy0tMAAKDSCAAwDQPp6es0asq6Rvoatq+VMil9dpC1qhvMfl+W1HrlPXS1I8UOXB+VRgCACTVNRF96GgCAZafSCAAwBdLTAAAsvcWtNE4apGExCDQtpSYJwryeBmEuzH5nlsC5wXox9raedoHAdC3uohEAYJtooqONIAAAqDQCAExB27/cW6URAIChVBqZrWkEmoRptp/V8q3l7CALZgjCTMNmU3bWuaGr8wvMUxPhmkYAAFBpBACYAl/uDQDA0lNpBACYVON7GgEAQKWRbWDSBLb09dw1K+Xfo+cHO7ZgT9qnnySlb+pmLRqBeWrC9zQCAIBKIwDANLimEQCApafSCAAwoWXoCGPRSPuNE6QRmpmO5JhvNtrazUqv40MjYPa80wAAMJRKIwDAFLT942mVRgAAhlJpBACYUBPaCAIAgEojXCVLWktUT0UvyvZ3jE9SGhaXNoIAACw9lUYAgEk10tMAAKDSCAAwKW0EoWZRL8ZvZhC20IZwfP3yOKx2+luwIwBMi0UjAMAUtL3SuKDlIgAAFolKIwDAhHSEAQCAUGkEAJiKpuWVRotGrm1RU9I14+zvPJPWS5aq7mxsFmN7upe2YE8AmJZttiIAAGArqDQCAEzBINr98bRKIwAAQ6k0AgBMqGna/+XeFo1cWy0sst0CMpnsMcwiHBORB2RaHI7pXNooxm7sXdyCPQFgWiwaAQCmoO1fudOCchEAALOm0ggAMDFtBAEAQKURAGAa2n5No0Uj1ydLGbc1UV0zq6T1pGqtDDMzSnA362XLwLf2Xk9mrs3k/gGYPotGAIAJNdH+72lsQWkIAIBZU2kEAJhU0+qeDRGh0ggAwAhUGpmecYIhbQ3NjHUMKte+ZH+qjhNuGcestruxWQzd1itbCwrCAG0yiPlc07hVV0624Dc3AACzZtEIAMBQPp4GAJhQE/P7cm8fTwMAsLDGrzSOmief1QX2tMOyhWbGMeprZ5G71yT3t6/rgw2gzTpz+3LvrfqtuGS/jQEAuB7+9AcAmAJf7g0AwNJTaQQAmIJ5pae3ikojAABDza7SuAgf7Etwt8Oskr/bKZWd7GunO/r53Qwqj3XSY1s7hoPy9b+jszrZfQEssKZRaQQAANc0AgBMw7y+p3GrqDQCADCUSiMAwBQsQpxjltq9aJznsyd0s/3Mu7XeqLLQy+oYL9UkhBLRH/m+pnFcmsuXi7FLzWYxttrpTXxfAMxHuxeNAABzIj0NAMDSs2gEAGAoH08DAEyoiY6PpwEAQKVxWrY6Zy+93RpZe8DOyugv1Sy53Kn89dukSesxVJLWzWa5D//Hxf3F2NE9Fya7f4AF0vJv3FFpBABgOJVGAIBJNb5yBwAAVBoBAKai5Rc1jr9onFfgYquDJdvNoh6vZQvojPM8VI5NFnrp7NpZTtwo2/JFRDTJeDXwMmnLwDEe7/906oPF2Le+64/TuXev7brePYJtqz+FFp69rDUoTIlKIwDAFLimEQCApWfRCAAwBU0zn/9G8eSTT8add94Zhw8fjocffjid80d/9Edx1113xd133x0/+qM/OnSbPp4GAGiRfr8fDz74YHz2s5+NQ4cOxX333RdHjx6Nu+6668qcEydOxK/92q/FF77whbj55pvjhRdeGLpdlUYAgAk18cY1jfP4b5hnnnkmDh8+HHfccUesra3FAw88EI8//vhVc/7Nv/k38eCDD8bNN98cERG33nrr0O0ubqWxDanbRU00z5NjMLbOrjI53NlZpqcHlzbyDWQJzHFSmVN4zrp7ysfw+qXyMdzY7U98X8A/yxLYEtXt8+KLL8a999575edjx47FsWPHrvx8+vTpuP3226/8fOjQoXj66aev2sZXvvKViIj47u/+7uj3+/Hxj388vu/7vu+a97u4i0YAgO2iiYg5pacPHDgQx48fn2gbly9fjhMnTsRTTz0Vp06dig984APx13/917Fv377qbfz5AQDQIgcPHoyTJ09e+fnUqVNx8ODBq+YcOnQojh49Gqurq/Gud70rvu3bvi1OnDhxze1aNAIAtMh9990XJ06ciOeeey42Njbisccei6NHj1415wd/8AfjqaeeioiIl156Kb7yla/EHXfccc3t+ngaAGAKFuUy/pWVlXjkkUfi/vvvj36/Hx/96Efj7rvvjoceeijuvffeOHr0aNx///3xZ3/2Z3HXXXdFr9eLX//1X4+3vOUt19xup2lGf4g3dfbHd3b/84kfDFtsUc7qZVcJe62849BINx9888V8/NKlcnDOz3nv3f+iGLv9354qxv71oS/OY3dm6szgYjq+t6sVIkzD++4/Gcf/7/Wt3o2hdtxxMA7+6oNzua/9v/EnE1/TeD1UGgEApqHlNRnXNAIAMJRKIwDAxEb74u3tTKURAIChVBqX0Ty77QjdVHVWVtPxZsdaOfjyq8XQYGMz3/A8j3nlXBrsLB/Dj9/yhWTm9vq79dygvBh/NXpbsCfAQmr5r7zt9Y4NAMCWUGkEAJhUE65pBAAAlUYAgGlwTSMAAMtOpZHZmlVSe7ulsrPj0K0cm1dfL4YGr58r5zWDCXdqCjr53529V88WY2/tXSjGNpu81d5qZzETyV/a2FmMfaAcApaWaxoBAFhyKo0AANOwzT4EG5dKIwAAQ1k0AgAwlI+n2Z5qAZvtFJDp99Phwatly8Amm7sIj7USxmlWyiDL85f3FmP7u2VgJiLipm6ZLulVQjez8jcbF4uxe9eygE7S9hFYTgvwtjxLKo0AAAyl0ggAMKkmIrQRBABg2ak0AgBMwSJcaj5LKo0AAAyl0jhLbf+Tg9El50Jz+fLot59VO8YZefW+24qx1/p7irFuJ2mPGBGDJII4q8aCl5rNdPztvXIfdnclpYFraPmvfZVGAACGUmkEAJgG6WkAAJadSiMAwBR0Wn5No0XjtQiyMEOdldFffs0gORcrn4J0uuU/jBW6GUflNXLh1vJDjM2mjLJcGOStFHf2svaEs4nCdCsfuNzc2z2T+wPYriwaAQAm1YT0NAAAqDQCAEysIz0NAAAWjQAADNXuj6eln5mlbpnmzZLLERHdG29MBisfY/TLRHGzfqkYG2zk7e/SpHStDeGMXiOH/uRrxdjJn9hfjP37bvm4IiK+f/fZqe9TTbcWQ2+pfpMl07e/XkcNhAXQ8mWHVxkAAEO1u9IIADAvKo0AACw7lUYAgGloeaVxvotGwRQWSRIO6d5wQzF2+TsOpzffvKF8+ez5D6dHvvvm7Ll0fHDhQjl30jaAc37tDV47U4z9/P6/H2MLZchos8lbDl5oNoqxnZ38rW0l2W4bAhSThlsGbfhNN6OATxvOj+3mzedz04bzsyVUGgEAJtWEL/cGAACVRgCAKei0/JN0lUYAAIZSaQQAmIaWVxrnu2istTIbI52Wtmmr3L7TS8Z7Seu3ZCwiIlaTw7OSH7JONl57vKOqJV4HSUpwmyXTmwn3t1M7tqurxdDg5jIRHRHx+r/cV4x9833lvO7Bi+ntdx4v72vHZ76Z71eS7Ozu3p1O7b31tvLmN+0pxgY7yvuPiOieLdPX8drrlf0qn4fOzp351GQfLr5zXzq3/zMvlWPJMaglU7O5rw7W07mZs4O8PeGXN94y8jYy71l7uRjb311L5652yveVWsvCLL08iDwNfGFQto98LXlPONvk71UXBuV5s5GkymsGTf6cdTujp5d7lcdWzsvfJ7L7qs3Nxlcr+5qN76x83rgzeQ/akZzPq5VjO875kZlVqjt77dXS9dk3GrwyKL/NICLi7zb3FmNPnrknnfvv/v49V/381XP/Op3H/Pl4GgCAoSwaAQAYyjWNAABTID0NAMDSG6vSuOPdnfjW/3nHVWOHd72Qzr1jRzl++8or6dwDvfLC2b3d/OLhrD1Yt7L2zS4qXtSWUJO2ARvHNFqG1S7Sf7N667dy/PnLeaDgf3/924uxP/77ciwi4sI/lqGXZme+D28/VJ6j77vx1WLsma++M7399/9X/1cx9t//zBfTuZvJ87taORdHPcdrx/ZMciH6P1zOQzd/8uq9xdjnTt6Zzu0mf0J/7zv+fTr3vbu/Woz911/9z4qxF//b29PbNyvl4115LQ8kddaTC+8v5Rfj918oAzrNZj53VGkILiI6O3aUY2v5OR798rmstY5skrmpwRRKHlnwcAzVwFp6X2O8N2fbrdw+3Yfa48pCkZXfRWnQMgnipYHKiGiS8WwsIiKS10PTqzyG5K25kwSlOhv5+dW5VAataq+n5lISOKudt5vJeOVcfmf/7676+eubo4fgtpyOMAAALDuLRgAAhhKEAQCYVBOt/3JvlUYAAIYaq9L4ztXz8T8e/IsJ7q5yEXh1fHnMM6Azeu+HybeyUpnXj/IC6uc3b0nn/sVL7yrGbtiZd/w4/K/KoMNtu/JuKO/e8/Vi7L/Z9w/lxG9Jb566XH1JlReBDypdcc405UXn/WRurxIyWE3G71rNLyR/z21fKMZ++bYy4FPTr/xZ/Upygft/9x9+uNyvr/9jevvm7NlirLOv7CgRETG4oQz5dM4nXXFi8tBLus3ahf/Z+MXKBf3jBOEWtftTct4t6J4unYmfh60+57b6/sexjXb1eqg0AgAwlGsaAQCmwJd7AwCw9FQaAQCmQaURAIBlp9LI1JwZlG3e/vTCW9O5f3PxUDG2u5snW3/mnZ8txj6061w6d0cnaeM1hv4YfyVeasp07LkmacEVEWeTlm4bTf4322DEv+VWO3nidjX5U3dn5UKb3Z0y3V5ry5mltfvJMYiI+NPzZSvC276QbDdpb/bGeLK/tTZxSXuy/gsv5tvdaoMRWwBuR9sp4Qqz0vKXgUojAABDqTQCAEyo00hPAwCASiMAwFQ0eaeutrBobLl+0p4sC3BERFxIQhyrlfaGN3R2FGN7u7uKsQ/fcCbfsdr4yPLAS/Z4L0cePsha8w2ivP1mpcXbejKex2Dykv5aJcgyafm/l7xn1VoO9qIcr83NjteXN8rzICLikf/4wWJs/7nk8Vbuq0nuq7NRObrdZBtCGQBTZ9EIADANLf971TWNAAAMZdEIAMBQPp4GAJgCX7kDAMDSU2lsuV6Sft7dWUvn7o58fFRZcnlQuSo4Syln6dya7PbV/artQ3J/m8nc2n5lKePdlbT5zk75UluJsoXfNNTS4pM6MyjbPH7u7Lenc8+/vLsY258FpSvp6Uyzvp7/w64kwV3brlQ1MEstf4tRaQQAYCiVRgCASWkjCAAAKo0AANPR8kqjRSPXZbMpwxbjhFsmDbJkIZaIvLXfa4O8oP7WJIdya2/PyPu1qHpjfIAwTngpDf70LqVzu7vKVpWXdyaBlZXRw0DNpTKIExHR6ZaPt7dvXzq3/+qrI98fAFezaAQAmIaWVxpd0wgAwFAqjQAAUyA9DQDA0rNoBABgKB9Pc8Us2gDOqt3fDd0kiRsRN3fKNO7bRt6D5ZO1mRwkyfiIiLOD8nm4beVMOvett5Tjl/bcVk4co41gbG6mw52Ncrw5sD+fe+FCOfdSngAH4GoWjQAA0+CaRgAAlp1FIwAAQ/l4GgBgUk37v3LHonEJXWryQME/Xi4DAV+9fFM69+0rZ4uxd63sLMZWO2tj7h1brRujh1O+sp7HjHavlufYxdVk4qASlEpCL83lsjVhRERz9lw5dvDWdG73HQfLXXj+VL7dzbxtIcCysmgEAJiGllcaXdMIAMBQKo0AANOg0ggAwLJTaQQAmFAnpKdpoR2dLMYacWilLDz3Oq+ncz997s5ibGe3TLx+5KYXxtw7tlqtdeRtvfLt4kM3PpvO/bPT/7IY2/VK0mbyxZfzfVhfv9YuXj33TJnk7914Qz53z65y7u1vT+defu6r5WDS0hJgWVg0AgBMQ8v/rnRNIwAAQ6k0AgBMagk6wqg0AgAw1NJVGvtNpW1ZS2WhhlobwZOXy2Ozr/JnxU/tOz3Rfo0je84uRz+du9mU47Xgz2qnN9mOtVStjWB2vO7dUbbwi4j4gUN/U4w984VvKcYunz8/3s4lsnZ/gxdeSud2b9mfDOYnee+WW4qx/osvjrdzwHJRaQQAYNlZNAIATEMzp/9G8OSTT8add94Zhw8fjocffrg674//+I+j0+nE8ePHh27TohEAoEX6/X48+OCD8ZnPfCaeffbZePTRR+PZZ8vv1T179mz89m//dnznd37nSNu1aAQAaJFnnnkmDh8+HHfccUesra3FAw88EI8//ngx75d+6ZfiF3/xF2Pnzp0jbXdhgzDjBFZqHSxGv31+X/2k+0N1bho4Gf0xrCbhg9VOvqa/kIQ9zg7yY/C23loxdkM3PzneXU4dSxawyYIpEXmoYiXyYEovOQ69yt87tdBLJtvff9gsx77Zz7uLHF4tu+Uc6O1I52aPLXtc05C9dmqvkdr5nOkmx3y18py9be21cr8q4ZRZGFQCNp3V5C1vR/6cRfb67SaPd5Cf48DyWZSv3Dl9+nTcfvvtV34+dOhQPP3001fN+dKXvhQnT56MH/iBH4hf//VfH2m7C7toBACg9OKLL8a999575edjx47FsWPHRr79YDCIn/3Zn41PfepTY92vRSMAwDTMqdJ44MCBawZXDh48GCdPnrzy86lTp+LgwYNXfj579mx8+ctfjg9+8IMREfGNb3wjjh49Gk888cRVi9E3c00jAECL3HfffXHixIl47rnnYmNjIx577LE4evTolX/fu3dvvPTSS/H888/H888/H+9///uHLhgjLBoBACY3r6/bGaGaubKyEo888kjcf//98e53vzs+/OEPx9133x0PPfRQPPHEE9f9EH08DQDQMkeOHIkjR45cNfaJT3winfvUU0+NtM25Lhpriehx0s9Z2jNLOdfmZjYr+7WejL82qCWay0N5Wy9PVe7rlnOzNHEtCZxleW+dQke8cVK3WSp6nCRu9px1a7GzZL+mkTzOju+718qxb2sup7d/PTkX/vTC3nTuK0kC+1+sfSOd+9behWJsd9LZr9fJ2/1lxzZvHBnRTw75ar7Z2JMc81rC/4O7TxRj/+u+u8v7n3Nbvv5rZ4qx3r78OYvksXWT82OwLj0NvGFR0tOz4uNpAACG8vE0AMA0qDQCALDsVBoBAKag7dc0zmzROGkrs0nDLRF5wOV8MnZmkKdIVpOgwTtX8kO2u5v14JuwL98YaiGjyzH6Rfq1Y54Z53kY9fablbvPQkJpi7eYTWu+2jZv7u0uxo7uKUMsERHnBq8UY09f2pPO/d/OvacY29kpoyz7ksBMRMSNvYvF2J7ORj63u16MHejlc3d0ynM/G4uIONQrw0ODd9xaTpxGEKYSCEol53j/TNkOMiKie0MSOev6cAZYXiqNAADT0PJKoz+bAQAYSqURAGBSI3Zr2c5UGgEAGMqiEQCAoSb+eHqc1oC1xG2W2q3OTbZ7YZAnhLPWafuTFn6HVnamt5+ncdryjZNyzkyafJ6V2n5lqeo0UR0xs5aDk7qhW55jH9yZN/f7jrVni7G/3iyT2s9v3JLe/uXLZeq3t3I2nXtb51wxlr1GIvKkdO3Y9qJMNHculef4ND7J6fTKc6FT+ZaD5nKZ6s7GIiIG58pj092xI9mBSnp7wtcpsL10/um/Ntv636YAACw8QRgAgGlo+QcMKo0AAAyl0ggAMAXaCP7/NNEUwZdxWgNmYY83xsu569U2ceVlprf0dqVzq2GJGZhFkGVRAyvzNk7Lwez8GOfjgnmGZsZpT/hd3fL8+lerX0tv/8qgPF61R7U/CZHs6uTtL8c5NutNGS7pnimDJVM5w7MgzM4ksBIRnZWydWP/5bLFY0SkQZbBRhJeqh2XyvsdwHal0ggAMA0trzS6phEAgKFUGgEApkGlEQCAZafSCAAwqUZ6+ipNRFyOqxOBWUoyIuJs0trvQpM32Nmf1DtvTRKkEbNJt867FSKTqx7bpjw/+pGfo2m6fkHbEGb7mqWsIyJu6paPofYtB92k6dU0Hu+p5JA365cm3u7IVvMEeHPbW4qxlV35ty9cPnmqHMxalnbn9y0NAFtJpREAYBpaXmnc+hIKAAALT6URAGAK2n5No0ojAABDjVVpPD/oxBfXr27P9fpgbzr3/TtfLMbeVmn3N+mF95MGWUZt61e7PYtjnOcna0WYtSEcVM6PWYVIJpXtw6yiGrXX3v954fCM7jExSJ6fbh666+/dWYxtHqiE7k5/PbmvJAiTjUVEpC0tW16GAFrNx9MAANPQ8r8Lt74sAgDAwlNpBACYAkEYAACW3liVxh2dfhxeff2qsdt6m+nc1c6ekbebXUxf62AxTtBh1ICLcMv89Se88KOXhFDGlT3vaaaisq+ThmZqFiFMM6pLlY5Qz154ezHW2bkjmTm5pp8EUTby96Xe+Y1irHupcrx7ZXyoqYVe0h1reckBuFoTrmkEAADXNAIATINKIwAAy06lEQBgQp2QngYAgPEqjaudbrytl7fcerNJE9HjtParkYqenUnTz/O8/0mT1rXzaNKkdbf2N1ulNV+5zdn8zVdrDXg5yuTwhSZPKV8alG8tzU3lNyp0VvK3oOZynsrOJyfvNRcupFO7z58uBzfz+xpkqWyAa1FpBABg2bmmEQBgCjot/35WlUYAAIZSaQQAmNQSdIQZe9FYC7OU84RbWAyLEJqJpizq95NgSUQemknva4zXU22/xnlNbib7eyZLA0XEjm4ZLtm4tQzCrH5tV35nFy8WQ9VwTPIYmkuX0qn9yjgAw/l4GgCAoXw8DQAwBfP6cu+t+hRcpREAgKFUGgEApqHlQRiVRgAAhhqr0thEmcJscyK62uatpcZ5HrKU8Va3FpyG7DFMmqiOGPMcT5LWmVr6etL736y0ETyfjL82WEvn3rxatvE7/9Zy7v4bykR1RESzo5zbf+W1dG4MtPsDFoNrGgEAWHquaQQAmIbt/4HbNak0AgAwlEojAMCkmvld07hVxl40jhp8mWe4ZZ6BlVFbvEVMvl/dMQIYo7Z3fGPu6K3uhGPmbxavndrzkLUiPFsJwrw2KN8u+pVz9OaV88XYxVvK86vZk7cR7Fwq76u7Vm4zImKwLggDMA8qjQAA09DyOolrGgEAGEqlEQBgQp1o/zWNKo0AAAyl0ggAMA1T6JK3yMZsI9jMJNk5acp4VonmcdLLvc7WFm17Y8ztN/nj6iZ19c3K+b+orR9noZY8nkZ7wVnI9jdLSUdErCdJ6bOD0c+mtcp5sLOzWYxt7Cvnbb51b3r71b87nQyu5juxvl7bvaXWWRn97b0ZVF7oWZK+5b8UgTofTwMAMJSPpwEApkAQBgCApafSCAAwqSZa/+XeYy0aO9GZScu+SYMs2ymwsgiqxyC56H21k4cisoDMMoVjFsE4LRo3K3NfG5TnQq01YC/bxhhZoP5aErS6KQ+3rCXtBZvzeRtBcp21tfwfeuVrurNZBpciIpp++Zpu+pW2jQPtHKHtVBoBAKag0/LaibIbAABDqTQCAExDy69pVGkEAGAolUYAgClo+/c0TrxorCWfJ23XJ+U8f+kxz9qIRf68Z53Iaq32xkn+brVFaBc4VlI6bQ2Y334zaUCZpqQjYjW7wrvJX6cXBjuKse5meRybbn5sB3v3lIPfeCGdG90k4S/JW005d/ckx7b2DRYbG6PfYfJcNpcvj357YOGpNAIATKqJ1vdmV84DAGAolUYAgClo+zWNKo0AAAw1ZhvBsq1crYWfIEs71J7HQXrdxvYPH2yn0Ev+HERcSMbPN/lLPQu9pIGXytz1yvH65uZN5XaTLoC99fyc6WyW4y3/A37qmkuXRp+8lrdzjCRMU3uFNE35L53K+0dzOWlb2PJrwVgSLT+NrewAABjKohEAgKEEYQAAJtQJQRgAABg3CNMpgjAspywAlXUBGkQeqlgEWx16GafLSxZ6OV/p1nN+UD4Pq5XnYS0JvdT+ksy2MEjCDxERz51/SzG28+XyMay9loc1OmfOlffVH+NcqnU4EbaI5uzZYqxz443p3E6vfL9vascw60BT6fjTWVsrt7uZdI/R2YftpGla/x6j0ggAwFCuaQQAmALXNAIAsPRUGgEApkGlEQCAZafSyHXJ2gtmaeTBAvzVtdUp6XFlSen1JCl9qXJsx0lE98Y5NMn9bVS2/PyZ/cXYrpfKJGz3taS3YEQMXi8Tvk2Wzh1XlqpuedrxzQbr68VYb8/ufHKSnk5T0hHRSY5tNWmd6O7cUd5+YyOd21xOktawAFzTCADA0lNpBACYVBOL8fHaDKk0AgAwlEojAMA0tLvQaNHI9GRtBCPyi+azcMo4bfVqFjX0kj22LPASkYdeNpN5N1ZatKX3X7mvsaIlYxzaM+d2FWP7XilbBnbOXUhvP1jP2wuOLAlq1VXaEy5RQGbwetm2MSKie9MNxVjWWjAiD710BvmxzeZmQafOrvI8ioiIixfL2wvHwMxZNAIATIH0NAAAS8+iEQCAoXw8DQAwDS2/FlqlEQCAoVQamZrVTpmq3GzyfO6gllgd0XZKSUfkSenNytzVpB3bLd2dybw8xdpPWw7mydILTZnLrj0zG8ljWKvMzv7Y7p0vW8I1SUu7N/5hsvNjLNWkdbIPLa0iNJuVdn0b5fnR6VWOV9aisZvPzVLVacvBzex7AyK6e28qxvqvnsn3azCF9pMwIkEYAACWnkUjAMCkmjn+N4Inn3wy7rzzzjh8+HA8/PDDxb//5m/+Ztx1111xzz33xPd8z/fEV7/61aHbtGgEAGiRfr8fDz74YHzmM5+JZ599Nh599NF49tlnr5rz3ve+N44fPx5/9Vd/FT/0Qz8Uv/ALvzB0uxaNAAAT6kREp2nm8t8wzzzzTBw+fDjuuOOOWFtbiwceeCAef/zxq+Z86EMfit27d0dExPvf//44derU0O0KwjBTtbDGpSTosKjhlppxWgNmc29Owi0R9WM2ql4S7NjdWcsnJ1mPWmgme3pu7OZBhf03le0BOxvlBppKu8BmsKBXk2dhj5aGYyIimqRdX+effskUstBLpY3gyPdfO7YXywBV78Bb0qn9F18uB4VjaLnTp0/H7bfffuXnQ4cOxdNPP12d/8lPfjK+//u/f+h2LRoBAKZhTl/88OKLL8a999575edjx47FsWPHrmtbf/iHfxjHjx+Pz3/+80PnWjQCAGwjBw4ciOPHj1f//eDBg3Hy5MkrP586dSoOHjxYzPvc5z4Xv/qrvxqf//znY8eOHUPv1zWNAABTsCjXNN53331x4sSJeO6552JjYyMee+yxOHr06FVz/vIv/zJ+8id/Mp544om49dZbR3p8Fo0AAC2ysrISjzzySNx///3x7ne/Oz784Q/H3XffHQ899FA88cQTERHx8z//83Hu3Ln44R/+4fj2b//2YlGZbnfWOw4A0HpjfIfiPBw5ciSOHDly1dgnPvGJK///c5/73Njb3HaLxqxFWltlKdjtpltJRHeTIvekrQVnZZzWgDs6+Utqd7eSXt5i2X4NaonX5LW3u9Iz694DJ4uxf9h8e7nJ/mI+5xGRtxfM3n+yRHVEK1LVzeUySZ+NRUR0Vspzv6m0EcyOzcitBSPyVHaSqI6I6O3fV4z1X35l5P0C/tm2WzQCACyepvV/eGz/UhYAADOn0ggAMAWVK3ZaQ6URAIChxqo0NtEsVRBlq83qWM8zYFO7r6xl4CJ0jquFXjI39yrt1La5HZ3Vyr+ULQNrx+sDe/9jMfbc5dvKiZVzvNMdvaXkXFsOjhqOiWhty8FBpfVjd0/Z/rJTCQk12XgSmsnCMRGVgMzGRjq3s6ts19m78cZ0bv/s2ezO0rmwjHw8DQAwDS3/I8PH0wAADKXSCAAwqSai0/Ir+FQaAQAYSqURAGAaWn5No0XjEqqlsueZql6JMmlZbdc3RnvBcdLPWRvA3d0yOVxPE7fTaqd8biIiNpt+Mjc/3t+y+tJU9+latjxpXXvdtLXl4KA8DyIiYrNM18dapX1m1l4wS0pX2hDWUtWZ5tz5crP7b853K0lgD9bz9oTM0JtfJ9vo5dF2Fo0AANPQ8gWuaxoBABhKpREAYAo62+lSk+ug0ggAwFAqjVyRBWRmFY7JtruahGMiIi4l+zVO4KW23d29ykX6pLKATBaOiYjY07lcjA1uSNoujhMiYaENNsogTLeXv/Y6yXgzajhmXP3yHG2ydoER0X3L/nLuN19I5zaXy3MctlWo7TqoNAIAMJRKIwDApJqIMb4hbltSaQQAYCiVRgCACXWiaX162qKx5QZJYKQbo3fQmKdaJ5Jx9neeXW2WTfY89CrPTRaPWT90YzG24+8m3avxZN1jZtIl5o07K8dqAZ+sU8x2++WTdIqphUWyIEwnOQbVIzBhaKZJQjsREZ1d5Ta6e29K5/ZfeTXZ8DZ7zrZarUMSC8tvWAAAhlJpBACYhpZXm1UaAQAYSqURAGAa5lVp3KLLQVUaAQAYSqWRhScRvRjS56HyR/WFwWox9vo7yrebA0maOSLS+HUt5ZwloluhlizdRtdMNRsb+fhKeS5kieo0JR2RJ6XHmVtJWg/OnS83u39fOrd7cb28/YUL+T6wHOb55d75l43MnN/GAAAMpdIIADAFbf9yb5VGAACGUmkEAJiGllcaLRpbblFbBtIO/UoS5uXBnmLs0v7Rz8U09FJpwdcMRv/AJAvN1II0M2kvWAt11doLbneVX6BZG7/OrtFaC0ZENOO0ERxn7ma5X00SjomI6N68r9zs+qXkvrKmmlyT8OPCsmgEAJhY0/pKo+U8AABDqTQCAEyqCZVGAABQaQQAmIaWZtr+PxaNwNR9Y3NfMdbJ3kxrCeVx0sRjzM2S1rX0dDY+k0T1uLJE8Tb7SKy5nKSULyetBdfKdpQR+bmUJqojIvqTpZebpF1gRERn165irHfTDeXdn3m9suHt9ZxNrNYWk23Fx9MAAAyl0ggAMAXaCAIAsPRUGgEApqHllUaLRq6pXwkZ9Ba0zVNtf5fJPJ+bQeUN8ivrby3G1l5bgDfT5PyotSGsBWRmInvO2nwuJ+dNs7FRjHVWKr+isnaQlcPVZAGMWmgmay9YaTnYvH623Ieb95Zj5y/mt98sHy8sOotGAIBJNVH/RoiWWMxyEQAAC0WlEQBgYk3rr2lUaQQAYCiVRgCAaWh5pdGiseUGMfoJ3I3R06JZSnlWqV2J6PGMc7wmfc66ldZgf3PmbcXYrpcnfB6n8WY8YSszrQVnp7l8eaSxiEp7wVravUnO8UoiOk1V19LT2b5dKFsOdvfemN6+//IryUa313M2scr7T/E68ytgYVg0AgBMQ8sX/q5pBABgKJVGAIBJ+Z5GAABQaWyNcQIvg8pVxdlot/J3xTihmVFNI/AyznHIzOJxLbJJA029yvF6/pX9xdhtr+ahhomNEwJJxytBh6S94Ja3Foxod3vBN8laC0ZU2gv2evncZLj6LtHvj7ZjEWlAprlwoRjr7r8536+VMsyjteA/Kc797fK+3LT+9anSCADAUBaNAAAM5eNpAIBp8JU7AAAsO5XGBTaNcEt/wr96ZnXd/zihl0nDLeOY533VbHUYp/bcZAGZ1SxlEBEXzu4ob38xCcKMc4KN082lNncGVYBaOGYhOsVsc7WOMFlAprNrV76R5LztdPLnpsnOm6xLTETeKSY5v5pz59Obd/fvK8b6L7yY39d2ql6N8TqtBsvmGTibJl+5AwAAKo0AANOxnarC10GlEQCAoVQaAQCmQaURAIBlp9K4ILLUbi0RvdmUra76Y6R+a63faknYUc0qEV07DqOqtUJcVIvaCjF7fqvHtin3obtZnredStJyrn+rVysDSZu4rW4tOI45JsjnbbCxWYz11tbyyavZr7lKy8FkrKm1FsxS1VlrwUorxO7O8hsGOpXH0Fy6lO/DdpK1xay0ynzz+8KCvsISTSteX9eyvX6bAgCwJVQaAQAm1UT+/Z0totIIAMBQKo0AANPQ8msaLRpnaJxAQxZu2Yz8AuzBGCflanKh8TyDIbVjkIVbJm15GBHRSy7+HydIs91CM5nsmM+7NeHum9aT0WQfepOFr5ZSFh4YI4TWCoPyvXFQCYt0syBMrxbgyloDVubWAjIjzmvOXyjGuvv25pv45guj3dd2UwuRvfl9YZwWosyURSMAwDS0vNK4/csqAADMnEUjAABD+XgaAGBiTcTAx9MAACw5lcYpmbQN4GaS2tusJI+zlX6Wkn5jbjmeJYzHNerjrSWiJ20NWJUkHcd5vNl+tSFRPSu1VPZdt36jGDuzcrC8/TTS0+OkibNzoXbhejqebbfSki5JhjaLUIUY5xhsI7V2fc1G2Zqvs3NnvpGV8ldiJy7n2x11xypf9txcLrfbqZwfndXyMTSb+eNdVNnrodZGNG3RuB00EU3Lv8lgmz4zAADMk0ojAMA0LMKnCTOk0ggAwFAqjQAA09CC64OvxaLxGmbVBvDSiBfK1srAWeilN0abuFo4ZZwWfNk2ssc7TsvDcXSr4ZbR24CNGpCpHYPtFJCpncuzai/4n978/xRjj+96ZzHWm1UbwUowbBbt9mrhluzCf2ao8l7TXLxYjHXWVvNtJEGY2naz0EqTvaeMEepo1rP2mxHdvTcWY/2XXh55u9tNEZDxUloYFo0AAJNqmmpavi22T6kEAIAto9IIADANLb+mUaURAIChVBoBAKagafk1jUu3aBwnEZ2lZrOU9Bvjo7cBzJLHq0nqrtYaMEtKTyPJmz22fuUxZI83e6nUktqZWpo5fWS1zaabqLyItRycme/Y9Vwx9kf7ysTqWi3FWks/p1MXtF3fPI3TSnHJZO36mouVlPJNZUq5yRLVFdm7R9PPf2ekH2PWFhz9crxT2a/s8S6sWrK8eE2LTy+KpVs0AgBMX+OaRgAAsGgEAGAoH08DAEyqiYiWX0+9sIvGcQIrk99XfvFxFgxZrwZhJgt8ZOGWWmvALGxRewyZWrgla/lXC/NsJHMnvey+2t4wG6xcFz1pW7xsHyYNx0QsX0Dm7b0LxdiFW8tjcNNqJQgzoVoLv2aQPQ+1oFRyPqbnaH777L7q+7XFv2hq53hLr88aJK0FIyI6u3aWYzvLsTf+IQlgZdMq+5AGZGqtEJNwS/eGPenc/mtnKvcIk1vYRSMAwLbS8m8tWK7yBwAA10WlEQBgQk0swKUmM6bSCADAUCqNAACTaprWX9M410XjPBPRb9xf+eRl6djNyBPRl5InP0sN16xVEomrSZ6u1jIwkz6uGSWiNysPd9KXRfpoxwg+p4nqyNsb1lvSaQM4KzcmKeFzt5fzmp1r6e3Hag04VsvB8jmvfCECbVZ5Hx+cO1+M9Wrp6ST5n7YRrJ2347QRzMZ7tRZ8ybvjYI4neS0BnhyHTvXxvnluuz/y3U5UGgEApsA1jQAALD2VRgCAaWj5NY0qjQAADDVWpfGrp2+M7/ovb57VvgCtUb5P7I3/pRh76abKze+Z8u4A29bq81u9B6P5T+5/X7z00nNzua9bbrllLvfzZp2maWlzUQAApsbH0wAADGXRCADAUBaNAAAMZdEIAMBQFo0AAAxl0QgAwFAWjQAADGXRCADAUBaNAAAM9f8CtSLZbuWkH+8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the approximation\n",
    "\n",
    "plt.figure(figsize = (15, 10), facecolor = \"white\")\n",
    "\n",
    "plt.imshow(np.reshape(y_out, (M, M)))\n",
    "plt.colorbar()\n",
    "\n",
    "plt.xticks([], [])\n",
    "plt.yticks([], [])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a162060c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot of the cost function\n",
    "\n",
    "plt.figure(figsize = (10, 7), facecolor = 'white')\n",
    "\n",
    "# plt.ioff()\n",
    "plt.plot(costs)\n",
    "\n",
    "plt.title(\"Cost function\", fontsize = 15)\n",
    "plt.xlabel(\"Number of iterations\", fontsize = 15)\n",
    "plt.ylabel(\"Cost\", fontsize = 15)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2f339596",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "cms-analysis",
   "language": "python",
   "name": "cms-analysis"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}