MNIST Classification.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MNIST Classification\n",
    "\n",
    "Classification of hand written digits 0--9 using a Multi Layer Perceptron\n",
    "\n",
    "- Input: $28 \\times 28$ grayscale images, scaled to $[0, 1)$   \n",
    "- Output: Class label\n",
    "- Hidden layers $tanh$, RELU or sigmoid activations\n",
    "\n",
    "Demonstration on the classical MNIST dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read the dataset and split it into a test and training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib.pylab import plt\n",
    "from sklearn.datasets import fetch_mldata\n",
    "mnist = fetch_mldata('MNIST original')\n",
    "\n",
    "step = 2\n",
    "train_offset = 0\n",
    "features = mnist['data'][train_offset:-1:step].copy()/255\n",
    "target = mnist['target'][train_offset:-1:step].copy()\n",
    "\n",
    "test_offset = 1\n",
    "features_test = mnist['data'][test_offset:-1:step].copy()/255\n",
    "target_test = mnist['target'][test_offset:-1:step].copy()\n",
    "\n",
    "assert(train_offset != test_offset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a35382390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(target)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A NN plotter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load \"DrawNN.py\"\n",
    "#Code from https://gist.github.com/craffel/2d727968c3aaebd10359\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def draw_neural_net(ax, left, right, bottom, top, layer_sizes, bias=0, draw_edges=False):\n",
    "    '''\n",
    "    Draw a neural network cartoon using matplotilb.\n",
    "    \n",
    "    :usage:\n",
    "        >>> fig = plt.figure(figsize=(12, 12))\n",
    "        >>> draw_neural_net(fig.gca(), .1, .9, .1, .9, [4, 7, 2])\n",
    "    \n",
    "    :parameters:\n",
    "        - ax : matplotlib.axes.AxesSubplot\n",
    "            The axes on which to plot the cartoon (get e.g. by plt.gca())\n",
    "        - left : float\n",
    "            The center of the leftmost node(s) will be placed here\n",
    "        - right : float\n",
    "            The center of the rightmost node(s) will be placed here\n",
    "        - bottom : float\n",
    "            The center of the bottommost node(s) will be placed here\n",
    "        - top : float\n",
    "            The center of the topmost node(s) will be placed here\n",
    "        - layer_sizes : list of int\n",
    "            List of layer sizes, including input and output dimensionality\n",
    "        - bias : Boolean\n",
    "            Draw an extra bias node at each layer\n",
    "        - draw_edges : Boolean\n",
    "            If false, omit edge connections\n",
    "    '''\n",
    "    n_layers = len(layer_sizes)\n",
    "    v_spacing = (top - bottom)/float(max(layer_sizes)+bias)\n",
    "    h_spacing = (right - left)/float(len(layer_sizes) - 1)\n",
    "    # Nodes\n",
    "    for n, layer_size in enumerate(layer_sizes):\n",
    "        layer_top = v_spacing*(layer_size - 1)/2. + (top + bottom)/2.\n",
    "        bias_node = (bias if n<len(layer_sizes)-1 else 0)\n",
    "        for m in range(layer_size+bias_node ):\n",
    "            node_color = 'w' if m<layer_size else 'b'\n",
    "            circle = plt.Circle((n*h_spacing + left, layer_top - m*v_spacing), v_spacing/8.,\n",
    "                                color=node_color, ec='k', zorder=4)\n",
    "            ax.add_artist(circle)\n",
    "    # Edges\n",
    "    if draw_edges:\n",
    "        for n, (layer_size_a, layer_size_b) in enumerate(zip(layer_sizes[:-1], layer_sizes[1:])):\n",
    "            layer_top_a = v_spacing*(layer_size_a - 1)/2. + (top + bottom)/2.\n",
    "            layer_top_b = v_spacing*(layer_size_b - 1)/2. + (top + bottom)/2.\n",
    "            for m in range(layer_size_a+bias):\n",
    "                for o in range(layer_size_b):\n",
    "                    line = plt.Line2D([n*h_spacing + left, (n + 1)*h_spacing + left],\n",
    "                                      [layer_top_a - m*v_spacing, layer_top_b - o*v_spacing], \n",
    "                                      c='k')\n",
    "                    ax.add_artist(line)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate a Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.autograd\n",
    "from torch.autograd import Variable\n",
    "\n",
    "# The sizes of layers from input to output\n",
    "#sizes = [3,3,10,20,3,4]\n",
    "sizes = [28*28, 100, 10]\n",
    "\n",
    "# Generate the network\n",
    "g = torch.tanh\n",
    "sm = torch.nn.Softmax(dim=0)\n",
    "identity = lambda x: x\n",
    "\n",
    "D = len(sizes)\n",
    "Weight = []\n",
    "Bias = []\n",
    "Func = []\n",
    "for i in range(D-1):\n",
    "    # For layer i, Weights are a S_{i+1} \\times S_{i} matrix\n",
    "    W = Variable(torch.randn(sizes[i+1],sizes[i]).double(), requires_grad=True)\n",
    "    # For layer i, Biases are a S_{i+1} \\times 1 matrix (a vector)\n",
    "    b = Variable(torch.randn(sizes[i+1],1).double(), requires_grad=True)\n",
    "    Weight.append(W)\n",
    "    Bias.append(b)\n",
    "    Func.append(g)\n",
    "    \n",
    "#Reset the final layer to sigmoid mapping\n",
    "#Func[-1] = torch.sigmoid\n",
    "Func[-1] = sm\n",
    "\n",
    "# Define the exact functional form\n",
    "# x: A S_0 \\times B matrix where each column is a training example with S_0 features\n",
    "def mlp_fun(x, Weight, Bias, Func):\n",
    "    f = Variable(x, requires_grad=False)\n",
    "    NumOfLayers = len(Weight)\n",
    "    for i in range(NumOfLayers):\n",
    "        #print(f)\n",
    "        f = Func[i](torch.matmul(Weight[i], f) + Bias[i])\n",
    "        #print(Func[i])\n",
    "        #print(f)\n",
    "    return f\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize the network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FRwBr6iS9IToC+AfwjyW9NjpivzDWGWy/UdLjTdM8GN0CrKNt23OSvmX7ZHQLcKVWT9VP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\nS+WeimTxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c85c588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "sizes_plot = sizes.copy()\n",
    "sizes_plot[0] = 28\n",
    "fig = plt.figure(figsize=(8, 8))\n",
    "ax = fig.gca()\n",
    "ax.axis('off')\n",
    "draw_neural_net(ax, .1, .9, .1, .9, sizes_plot, bias=1, draw_edges=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the Output for a few examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a353b86a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ca51400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0cabd630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a34fd2b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3508a6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c599780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2a20f8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAC09JREFUeJzt3WuMVPUZx/Hv4+IFkEqbpdUul5Vo\nSAkJsWysQUNMbRNMDfiiRElUsCW8EAtWEYU3xniJL6ppFdOEVC5aU23ECyYGMV5CMA0RiMYCoSUW\ncBUQaAQ1ol3z9MXMnD27OzM7uzt7zjzD75OQ/e/Zc/b8V3/5z//cnmPujkhEZ+XdAZHBUnglLIVX\nwlJ4JSyFV8JSeCUshVfCUnglLIVXwhqRdwekuZjZkC/ZurvVsp5GXglL4ZWwFF4JS+GVsBReqcrM\nZpvZPjPbb2b35t2fNNP9vFKJmbUA/wJ+CXQC7wHz3X1PlW10tkEawuXAfnf/yN2/BZ4D5ubcp4TC\nK9W0AR+nvu8sLuvBzBab2Q4z25FZz9BFCqmu3Md3n2mBu68B1kB9pg210sgr1XQCE1Lfjwc+zakv\nfSi8Us17wKVmdrGZnQPcCGzKuU8JTRukInfvMrPbgdeBFmCtu+/OuVsJnSqTutKpMpEaKLxSVzNm\nzMDdB/1vxowZNe9L4ZWwFF4JS+GVsBReCUvhlbAUXglL4ZWwFF4JS+GVsBReCUvhlbAUXglL4ZWw\nFF4JS+GVsBReCUvhlbAUXglL4ZWwFF4JS+GVsBReqcjMJpjZ22a218x2m9myvPuUpoo5Uk0XcJe7\n7zKzMcBOM3ujWn3eLGnklYrc/bC77yq2vwD2UqbEaV4UXqmJmbUDlwHb8+1JN4VX+mVm5wMbgTvc\n/VSZnyfFpY8dO5ZZv4YU3kZ+2YbUh5mdTSG4z7r7i+XWcfc17t7h7h3jxo3LrG+DDm/xZRtPAtcC\nU4H5Zja1Xh2T/JmZAU8Be939sbz709tQzjYkL9sAMLPSyzYqHom2trZ6e3v7EHZ5Zjlw4ADHjx+v\nqdznMLkSuBn40MzeLy5b5e6v5dinxFDCW+5lGz/rvZKZLQYWA0ycOJEdOzJ950ZoHR0due7f3bdR\n/r0UDWEoc96aX7aRx3xImt9QwtvQL9uQ5jeU8Db0yzak+Q16ztvoL9uQ5jekexuKR50NceQpZx5d\nYZOwFF4JS+GVsJr2ft7169cn7RMnTiTtd999N2nPmTMHgKuuuipZduTIkaSdXi6NRyOvhKXwSlhN\nMW04ffp00n7ooYd6fAVoaWkpu92rr74KwJQpU5JlU6d23xg3fvz4pD127NgeXyV/GnklrKYYeVeu\nXJm0V69ePeDt9+3bl7T37Om+o/Oll15K2rNmzQJg48aNyTKNwvnSyCthKbwSVthpw4EDB5L2888/\nP+z727p1KwA33HBDsmzDhg1J+8ILLxz2PkhPGnklLIVXwgo7bUh/ZGdZK+Ctt95K2lu2bEnat9xy\nS2Z9kAKNvBKWwithhZo2pM8w3H///VXXde9+kPm7774ru07pDMHs2bOTZevWret3u5KFCxcm7cmT\nJydt3Y2WjX5HXjNba2afmdk/U8t+YGZvmNm/i1+/P7zdFOmrlpF3PbAaeDq17F7gTXd/pFij7F7g\nnvp3r7JKN9uUpEfNc889N2nfdtttSbt0kDV9+vRk2SWXXJK0H3744aT9zTffVN3fvHnzkvbmzZv7\n/N7IiqW9dgCfuPt1efenpN+R1923Av/ttXguUDrc3wBcX+d+SWNZRqE2b0MZ7AHbj9z9MBQKEAM/\nrLRiXuUvpT7MbDzwK+Avefelt2E/YHP3NcAagI6Ojj7loAbi5ZdfHtR26anCo48+WnXdVatWJe3R\no0cn7eXLl1fd7ujRo0n75MmTA+1iI/sjsAIYk3dHehvsyHvUzC4CKH79rH5dkkZhZtcBn7n7zn7W\nC1VcehOwoNheALxSn+5Ig7kSmGNmB4DngJ+b2V97r5RXMcV+pw1m9jfgaqDVzDqB+4BHgL+b2W+B\nQ8C8yr+hfjZtqr0UWvroP/1I0EAsWbIkaR88eBCAJ554ot/t7r77bgC2b2+Y1zcMiruvBFYCmNnV\nwHJ3vynXTqX0G153n1/hR9fUuS8iAxLqCpvkx93fAd7JuRs9NG1402cKzjvvvEH9jhEjuv/zXHDB\nBTVvV3om7pVXug8F5s6dO6g+SGW6MUfCCjXy1nKzTcnMmTOHZd+V9pvu26lThVeVffDBB8kyjbz1\np5FXwlJ4JaxQ04bCO+0K+rur7Prr63uvUGnflfabnk6U1vn888+TZV1dXUk7fSAog6eRV8JSeCWs\npv38WrFiRdJeu3ZtLn1IX0petmxZ0p40aVIe3Wk6GnklLIVXwgo1bXj88ceTdvqk/6FDh/qsm363\nRPqofyBlSdNFq0t3lQ3E0qVLk3ZbW9uAt5fqNPJKWKFG3mnTpiXtdHmlBx98sM+6pSd4oefBUrpM\nVDnbtm1L2umRPl1oulbpm3l0brf+NPJKWAqvhBX2syxd0GPkyJFJ+8svvwR63uX1zDPPlG2Xk94u\nfTm6P+ntRo0a1aePUn+1lHuaYGZvm9leM9ttZsuKy1XySXJVy7ShC7jL3X8CXAEsMbOpdJd8uhR4\ns/i9SGZqeQDzMFCqjvOFme0F2iiUfLq6uNoGCs83ZVavLH3XWGtra9L++uuvgfJ3edVisNuVpgrQ\n/Tot3YA+vAZ0wGZm7cBlwHZqLPmkck8yXGoOr5mdD2wE7nD3U7Vul1dBCml+NZ1tMLOzKQT3WXd/\nsbj4qJld5O6H8y75lJ5C1FIUZDg8/XR3BVhNF7JRy9kGA54C9rr7Y6kfqeST5KqWkfdK4GbgQzN7\nv7hsFTmVfConXQR6zJhCMcMHHnigrvtob28HYOLEicmyRYsWJe1mHW3NbCyF8qbTAAd+4+7/yLdX\nBbWcbdgGVDpbr5JPze9PwGZ3/7WZnQOM6m+DrIS9wibDz8y+B8wCFgK4+7fAt3n2Ka0pwpsu51R6\nS1D67TwnTpxI2vfcU/up6PS6paqTZ9gl38nAMWCdmU0HdgLL3P2r9EpmthhYDD2nVcNNN+ZINSOA\nnwJ/dvfLgK8ocyU1r9OhCq9U0wl0unup0PALFMLcEJpi2lDOggULyi6/8847M+5JXO5+xMw+NrMp\n7r6PwgH6nrz7VdK04ZW6+R3wbPFMw0fArTn3J6HwSlXu/j7QkXc/ytGcV8JSeCUshVfCUnglLIVX\nwlJ4JSyFV8JSeCWsTC9S7Ny587iZfQUcz3K/GWqlvn+bqlBXkWl43X2cme1w94a8YjNUzfy3NSJN\nGyQshVfCyiO8a3LYZ1aa+W9rOJmH192b9n9wM/9tjUjTBgkr0/Ca2Wwz22dm+80sbFVJlX1tDJmF\n18xagCeBa4GpwPxiqdSIVPa1AWQ58l4O7Hf3j4rP/z9HoUxqOO5+2N13FdtfAOmyr6U3tmwA6vv2\nbukhy/C2AR+nvu8sLgttMGVfpT6yDG+5klFeZlkYgy37KvWRZXg7gQmp78cDn2a4/7qqVva1+PNc\ny76eCbIM73vApWZ2cfEx6hsplEkNR2VfG0NmN+a4e5eZ3Q68DrQAa919d1b7r7OGL/t6Jsj6rrLX\ngNey3OdwOJPKvprZ74FFFI5PPgRudffT1bfKhq6wSUVm1gYsBTrcfRqFT8wb8+1VN4VX+jMCGGlm\nIygUlm6Yg2yFVypy90+AP1CYvx8GTrr7lnx71U3hlYqK92bMBS4GfgyMNrObyqyXy7v2FF6p5hfA\nf9z9mLv/D3gRmNl7JRWXlkZ0CLjCzEYVz21fQ+E+joag8EpFxYroLwC7KJwmO4sGelpE9XmlKne/\nD7gv736Uo5FXwlJ4JSyFV8JSeCUshVfCUnglLIVXwlJ4JSyFV8JSeCUshVfCUnglLIVXwlJ4JSyF\nV8JSeCUshVfCUnglLIVXwjL30CVypcGY2THg4BB+xSR3r+n5eYVXwtK0QcJSeCUshVfCUnglLIVX\nwlJ4JSyFV8JSeCUshVfC+j8YeJyqBo6SHwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c7c1630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a351a6470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c557f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c0dfb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c7b7128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3508d588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ca1f048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b0efa20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0cbe74e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0cbe7630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0cb48898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b23e8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\naTm8lpbDa2k5vJaWw2tpObyW1v8Bp0Xxx5JWg2IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ca2d128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDq+l5fBaWg6vpeXwWlr/B6MV+vpTMuPsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b12a8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\noqXwSrT+D6RSxE+P4oBZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b23ecf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a34ed5748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1070983c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0cbcc588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0caa4048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3533ba20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c6804e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c680780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrIRz0uNkGY8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ca2f320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3532bd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1060d59e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c0c3e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ny+G1ZDm8liyH15Ll8FqyHF5LlsNryfo/sX9QqGRkLHQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1d500438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ca511d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1070a5438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a350b2588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b0e7048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c718358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b2504e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c7db748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFF4J6/9SejW2nm2JCQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a35249f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0cb48978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a31930c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3534cdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c711cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a352073c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c0db7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3506b588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b20d048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a34ff9358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ca3d4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ca3d668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c8d2f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1d6ce470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3532bba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1070c0160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3522e940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b03ca58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c162438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a34fcd588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c5ab048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a352e7358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0cbe54e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0cbe5780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a35279a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a353527b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a35511710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a34ea4160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b1acc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npfV/AAhxe2fISIsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a35229048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a35271198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c8e5588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1d39f048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c72ba20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nK2EpvBLW/wFY23JNxoFW7wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c9144e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c9145c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nlsIr0VJ4JVr/B9sHcluP0FGOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a352717f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c659ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ca6ca20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3522e278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ca2d710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c881d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3551e5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3539d588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3530c048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c7eba20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b26e4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b26eeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAACp9JREFUeJzt3V2MVOUdx/HvDxBTkNo2ULS8uBAJ\nlphUyGpNSQhiLyQ1VWMxYjAUSvbCCtjYtOqFXnghFw1pE0wTUnlpJJhKMZqIpcY3IqnKS4gWN1pi\nKa5uFVJFRRtL/PdiZs/O7s7MDruzc+aZ/X1ueObs2Z3/6o+Hc86c838UEZilaEzeBZgNlcNryXJ4\nLVkOryXL4bVkObyWLIfXkuXwWrIcXkvWuLwLsNYyefLkaGtrG/L3Hz9+nFOnTqmWfR1eq6u2tjYO\nHjw45O9vb2+veV8fNliyHF5LlsNryXJ4rSpJ10l6S9IxSffkXU8ph9cqkjQWeBhYCswDlkual29V\nvRxeq+Yq4FhEvBMRXwKPATfkXFPG4bVqpgHvlrzuKm7rQ1KHpIOSDp48ebJhxTm8Vk25DwsGPDcW\nEZsjoj0i2qdMmdKAsgocXqumC5hR8no68H5OtQzg8Fo1B4A5kmZJGg/cCjyVc00ZfzxsFUXEWUl3\nAnuBscCWiDiac1kZh9eqiog9wJ686yjHhw2WLIfXkuXwWrIcXkuWw2vJcngtWQ6vJcvhtWQ5vJYs\nh9eS5fBashxeS5bDa8lyeC1ZDq8ly+G1ZDm8liyH15Ll8FqyHF5LlsNryXJ4LVkOryXL4bWKJM2Q\n9IKkTklHJa3Pu6ZSbjpi1ZwF7o6Iw5ImAYckPRsRb+ZdGHjmtSoiojsiDhfHnwKdlGlxmheH12oi\nqQ2YD7yabyW9HF4blKQLgD8Dd0XEJ2W+nl5z6WZebMPqQ9J5FIK7IyJ2l9snuebSzb7Yhg2fJAGP\nAJ0RsTHvevobztWGbLENAEk9i21UPBMd7rq0o825rMM7QhYCtwNvSDpS3HZfse1p7oYT3nKLbXy/\n/06SOoAOgJkzZw5rXdrR5lzW4R0JEfEy5delaArDOeZt6sU2rPUNJ7xNvdiGtb7hhLepF9uw1jfk\nY95mX2zDWt+w7m1o5sU2rPX5EzZLlsNryXJ4LVkOryXL4bVkObyWLIfXkuXwWrJa9gHMJ554Ihs/\n+eSTVfc9duxYNu7o6MjG11xzTTaeMWMG1lw881qyHF5LVkscNnz22WfZeO3atQBs27ZtSD9r//79\n2XjWrFnZePfuwuNbV1xxxZB+rtWfZ15LlsNryWqJw4YjR45k43KHC5dddlk2vummm7Lx/Pnzgb5X\nI7q6urLxSy+9lI0XLFgAwPPPP59tW7x48dCLtmHzzGvJcngtWS1x2LBhw4YB29atW5eNN27s7Zcx\nduzYAfsuW7YsG3/11VfZeM2aNdl469atAKxcuTLb9vrrr2fjCy+88FzLtmEadOaVtEXSh5L+XrLt\nW5KelfSP4p/fHNkyzQaqZebdBmwC/liy7R7guYjYUOxRdg/w6/qXV5u33357wLa5c+dm43KzbSVj\nxvT+fX7ooYey8TPPPAPAiRMnsm07duzIxnfccUfN75GaYmuvg8B7EXF93vX0GHTmjYh9wH/6bb4B\n2F4cbwdurHNd1lzWU+jN21SGesI2NSK6odCAGPh2pR3zan9p9SFpOvAj4A9519LfiJ+wRcRmYDNA\ne3v7gHZQzeyLL77Ixp9//vmAr3/yyYBWta3ot8CvgEl5F9LfUGfeDyRdDFD888P6lWTNQtL1wIcR\ncWiQ/ZJqLv0U0HPNaCVQ/YZZS9VC4MeSjgOPAUskPdp/p7yaKQ562CBpJ7AYmCypC3gA2AD8SdLP\ngBPAsso/IR+vvPJKNh7qlYCdO3dm41FyiNBHRNwL3AsgaTHwy4hYkWtRJQYNb0Qsr/Cla+tci9k5\naYlP2GzkRcSLwIs5l9FHS4T3/vvvz8arV68G4PHHH8+2LV26NBvffPPN2Xj8+PFA34+Ed+3alY0f\nfPDBqu97/vnnD7FiqwffmGPJaomZd8WK3nOIRx8tnAzv3bs323bbbbdl4yuvvDIbL1y4EIDOzt4P\nj0q/bzDLl1c6HbBG8MxryXJ4LVktcdhQqucp30svvTTb1t3dnY0PHDhQdtyjdJ240jvIek7qSh8p\nmjSp6T4xHVU881qyHF5LVssdNkyYMAGA1157Ldu2adOmbFx64/rMmTMBmDevd8nkW265JRvPnj07\nG3/00UdA38OKiRMn1qlqGwrPvJYsh9eS1XKHDT2mT5+ejcs9XTxUS5YsqdvPsuHxzGvJatmZd6Rc\ncskleZdgRZ55LVkOryXLhw397Nu3LxufPn06x0psMLW0e5oh6QVJnZKOSlpf3O6WT5arWg4bzgJ3\nR8R3gauBn0uaR2/LpznAc8XXZg1TywOY3UBPd5xPJXUC0yi0fFpc3G07heebcutXVi8ff/xxNi59\nPEgSABdddFHDa7LyzumETVIbMB94lRpbPrndk42UmsMr6QLgz8BdEVFzE4O8GlJY66vpaoOk8ygE\nd0dE7C5u/kDSxRHRPRpaPk2dOhWARYsW5VyJ9ajlaoOAR4DOiNhY8iW3fLJc1TLzLgRuB96Q1LPs\nzn0k0PJpKJ5++umy20tXERpNJH2DQnvTy4EAVkfE3/KtqqCWqw0vA6rwZbd8an2/A/4SET+RNB6Y\nkHdBPfwJm1Uk6evAIuCnABHxJfBlnjWVcniBs2fPZuOjR4/mWEnTmQ2cBLZK+h5wCFgfEWdKd5LU\nAXRA76NVjeAbc6yaccAC4PcRMR84Q5lPUvO6HOrwWjVdQFdEvFp8vYtCmJuCDxuAM2d6/xXcv39/\njpU0l4j4t6R3Jc2NiLconKC/mXddPRxeG8xaYEfxSsM7wKqc68k4vFZVRBwB2vOuoxyHl77NQ1at\n6p1YetYbBpgzZ05Da7LB+YTNkuWZFxg3rvc/w5YtW8qOrfl45rVkObyWLIfXkuXwWrIcXktWQ682\nHDp06JSkM8CpRr5vA02mvr+bG6NV0dDwRsQUSQcjoik/sRmuVv7dmpEPGyxZDq8lK4/wbs7hPRul\nlX+3ptPw8EZEy/4PbuXfrRn5sMGS1dDwSrpO0luSjklKtquk2742h4aFV9JY4GFgKTAPWF5slZoi\nt31tAo2cea8CjkXEO8Xn/x+j0CY1ORHRHRGHi+NPgdK2r9uLu20HbsynwtGhkeGdBrxb8rqruC1p\nQ2n7avXRyPCWaxkVDXz/uhtq21erj0aGtwuYUfJ6OvB+A9+/rqq1fS1+veXbvuatkeE9AMyRNKv4\nGPWtFNqkJsdtX5tDw27MiYizku4E9gJjgS0RkWpjsFHV9rVZNfqusj3Anka+50gYTW1fJf0CWEPh\n/OQNYFVE/Dffqgr8CZtVJGkasA5oj4jLKfyLeWu+VfVyeG0w44CvSRpHobF005xkO7xWUUS8B/yG\nwvF7N3A6Iv6ab1W9HF6rqHhvxg3ALOA7wERJK8rsl8taew6vVfND4J8RcTIi/gfsBn7Qfyc3l7Zm\ndAK4WtKE4rXtayncx9EUHF6rqNgRfRdwmMJlsjE00dMibrRnVUXEA8ADeddRjmdeS5bDa8lyeC1Z\nikj6llprMpKGHaiIqHTfSB+eeS1ZDq8ly+G1ZDm8liyH15Ll8FqyHF5LlsNryXJ4LVkOryXL4bVk\nObyWLIfXkuXwWrIcXkuWn2GzejsF/GsY31/zkrW+Gd2S5cMGS5bDa8lyeC1ZDq8ly+G1ZDm8liyH\n15Ll8FqyHF5L1v8BV8cmyZi4+vMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c85cf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b03cac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3505f780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c110668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c0b49e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1070c0278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nlsIrwVJ4JVgKrwRL4ZVgKbwSLIVXgvV/6ZOjulJ5BHUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c145cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a353bb588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b214048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a35309a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ca0d4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ca0d358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1069e4400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0b11eba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhKXwSlgKr4Sl8EpY/wdtI0CWOgPd7QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3534f3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c930b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108401a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2a242780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a35255f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a353c5588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0c7ff048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nh9eS5fBashxeS9b/AWs8e6pIzMRqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a34fd1a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAC4CAYAAACVQbxWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJVoKr0RL4ZVo/R8N9XfYKIn3YwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0cbfe4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#def draw_output(x)\n",
    "\n",
    "#IDX = [100,200, 400, 500, 600, 650, 700, 701, 702, 900, 1000, 1100, 1200, 1300]\n",
    "\n",
    "IDX = range(1,len(features_test),315)\n",
    "\n",
    "for idx in IDX: \n",
    "    #x = features_test[idx]\n",
    "    x = features[idx]\n",
    "    #x = features[idx]\n",
    "    plt.figure(figsize=(3,3))\n",
    "    #x[x>0] = 1\n",
    "    plt.subplot(1,2,1)\n",
    "    plt.imshow(x.reshape(28,28), cmap='gray_r')\n",
    "    f = mlp_fun(torch.DoubleTensor(x.reshape(28*28,1)), Weight, Bias, Func)\n",
    "    plt.subplot(1,2,2)\n",
    "    plt.imshow(f.data, cmap='gray_r')\n",
    "    plt.xticks([])\n",
    "    #print(f)\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 2.378387734958743\n",
      "1000 1.7272492755074893\n",
      "2000 1.602493989505685\n",
      "3000 1.5648466330010187\n",
      "4000 1.5659125038512083\n",
      "5000 1.5429795291626844\n",
      "6000 1.5436121869116093\n",
      "7000 1.5382010590474693\n",
      "8000 1.5345709012729494\n",
      "9000 1.5248479385395444\n",
      "10000 1.5306243912145319\n",
      "11000 1.5235479277524178\n",
      "12000 1.5352315140320578\n",
      "13000 1.5353052963414244\n",
      "14000 1.5189450012088854\n",
      "15000 1.5175162586404967\n",
      "16000 1.5209352909230838\n",
      "17000 1.5111448996278434\n",
      "18000 1.5184969928240497\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-57-4a0af89a1bd8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     20\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m     \u001b[0;31m# Compute the derivative of the error with respect to Weights and Biases\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 22\u001b[0;31m     \u001b[0mE\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbackward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     23\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m     \u001b[0;31m# Take the step and reset weights\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/cemgil/anaconda/envs/py36/lib/python3.6/site-packages/torch/autograd/variable.py\u001b[0m in \u001b[0;36mbackward\u001b[0;34m(self, gradient, retain_graph, create_graph, retain_variables)\u001b[0m\n\u001b[1;32m    165\u001b[0m                 \u001b[0mVariable\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    166\u001b[0m         \"\"\"\n\u001b[0;32m--> 167\u001b[0;31m         \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mautograd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbackward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgradient\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mretain_graph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcreate_graph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mretain_variables\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    168\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    169\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mregister_hook\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhook\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/cemgil/anaconda/envs/py36/lib/python3.6/site-packages/torch/autograd/__init__.py\u001b[0m in \u001b[0;36mbackward\u001b[0;34m(variables, grad_variables, retain_graph, create_graph, retain_variables)\u001b[0m\n\u001b[1;32m     97\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     98\u001b[0m     Variable._execution_engine.run_backward(\n\u001b[0;32m---> 99\u001b[0;31m         variables, grad_variables, retain_graph)\n\u001b[0m\u001b[1;32m    100\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    101\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# Cross Entropy\n",
    "Error = torch.nn.CrossEntropyLoss(size_average=True, reduce=True)\n",
    "\n",
    "# Number of examples in the Training set \n",
    "N = len(target)\n",
    "\n",
    "eta = 1\n",
    "MAX_ITER = 50000\n",
    "BatchSize = min(1000, N)\n",
    "EE = []\n",
    "for epoch in range(MAX_ITER):\n",
    "    idx = np.random.choice(N, size=BatchSize, replace=False)\n",
    "    x = features[idx]\n",
    "    #idx = [epoch%N]\n",
    "    f = mlp_fun(torch.DoubleTensor(x.T), Weight, Bias, Func)\n",
    "    y = Variable(torch.LongTensor(target[idx].reshape([len(idx)])), requires_grad=False)\n",
    "    # Measure the error\n",
    "    E = Error(f.transpose(0,1), y)\n",
    "    EE.append(E.data.numpy())\n",
    "    \n",
    "    # Compute the derivative of the error with respect to Weights and Biases\n",
    "    E.backward() \n",
    "    \n",
    "    # Take the step and reset weights\n",
    "    for i in range(D-1):\n",
    "        Weight[i].data.add_(-eta*Weight[i].grad.data)\n",
    "        Bias[i].data.add_(-eta*Bias[i].grad.data)\n",
    "        Weight[i].grad.zero_()\n",
    "        Bias[i].grad.zero_()\n",
    "    \n",
    "    if epoch % 1000 == 0:\n",
    "        print(epoch, E.data[0])\n",
    "        \n",
    "plt.plot(EE)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variable containing:\n",
      " 1.7225  1.3250  0.7938\n",
      "-0.6385  1.7780 -0.1159\n",
      "[torch.FloatTensor of size 2x3]\n",
      "\n",
      "Variable containing:\n",
      " 0.9138  0.3886  0.7129\n",
      " 0.0862  0.6114  0.2871\n",
      "[torch.FloatTensor of size 2x3]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "sm = torch.nn.Softmax(dim=0)\n",
    "inp = Variable(torch.randn(2, 3))\n",
    "print(inp)\n",
    "print(sm(inp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binary Cross Entropy Loss\n",
    "\n",
    "$y$: target\n",
    "\n",
    "$$\n",
    "y \\log(\\theta) + (1-y) \\log(1-\\theta)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/cemgil/anaconda/envs/py36/lib/python3.6/site-packages/torch/nn/functional.py:1189: UserWarning: Using a target size (torch.Size([1, 1])) that is different to the input size (torch.Size([10, 1])) is deprecated. Please ensure they have the same size.\n",
      "  \"Please ensure they have the same size.\".format(target.size(), input.size()))\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "Target and input must have the same number of elements. target nelement (1) != input nelement (10)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-69-2a45fa05c249>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmlp_fun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDoubleTensor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m28\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m28\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mWeight\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mBias\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mFunc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mVariable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDoubleTensor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtarget\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0midx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m     \u001b[0mE\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mE\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mloss_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mE\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/cemgil/anaconda/envs/py36/lib/python3.6/site-packages/torch/nn/modules/module.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *input, **kwargs)\u001b[0m\n\u001b[1;32m    355\u001b[0m             \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_slow_forward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0minput\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    356\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 357\u001b[0;31m             \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mforward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0minput\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    358\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mhook\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_forward_hooks\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    359\u001b[0m             \u001b[0mhook_result\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhook\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/cemgil/anaconda/envs/py36/lib/python3.6/site-packages/torch/nn/modules/loss.py\u001b[0m in \u001b[0;36mforward\u001b[0;34m(self, input, target)\u001b[0m\n\u001b[1;32m    428\u001b[0m         \u001b[0m_assert_no_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtarget\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    429\u001b[0m         return F.binary_cross_entropy(input, target, weight=self.weight,\n\u001b[0;32m--> 430\u001b[0;31m                                       size_average=self.size_average)\n\u001b[0m\u001b[1;32m    431\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    432\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/cemgil/anaconda/envs/py36/lib/python3.6/site-packages/torch/nn/functional.py\u001b[0m in \u001b[0;36mbinary_cross_entropy\u001b[0;34m(input, target, weight, size_average)\u001b[0m\n\u001b[1;32m   1190\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnelement\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mtarget\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnelement\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1191\u001b[0m         raise ValueError(\"Target and input must have the same number of elements. target nelement ({}) \"\n\u001b[0;32m-> 1192\u001b[0;31m                          \"!= input nelement ({})\".format(target.nelement(), input.nelement()))\n\u001b[0m\u001b[1;32m   1193\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1194\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mweight\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Target and input must have the same number of elements. target nelement (1) != input nelement (10)"
     ]
    }
   ],
   "source": [
    "loss_fn = torch.nn.BCELoss()\n",
    "\n",
    "E = Variable(torch.DoubleTensor([0]))\n",
    "for idx in [100,101,102]:\n",
    "    x = features[idx]\n",
    "    f = mlp_fun(torch.DoubleTensor(x.reshape(28*28,1)), Weight, Bias, Func)\n",
    "    y = Variable(torch.DoubleTensor(target[idx].reshape([1,1])))\n",
    "    E = E + loss_fn(f, y)\n",
    "\n",
    "print(E/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Variable containing:\n",
       " 11.8843\n",
       "[torch.DoubleTensor of size 1]"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Batch Mode\n",
    "\n",
    "loss_fn = torch.nn.BCELoss(size_average=False)\n",
    "\n",
    "idx = range(0,100)\n",
    "x = features[idx]\n",
    "f = mlp_fun(torch.DoubleTensor(x.T), Weight, Bias, Func)\n",
    "y = Variable(torch.DoubleTensor(target[idx].reshape([1, len(idx)])))\n",
    "loss_fn(f, y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross Entropy Loss \n",
    "\n",
    "Target class labels $y$ in $[0, C-1]$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "-0.0144  1.7189 -0.1805\n",
      " 0.1935 -0.9968  0.8177\n",
      "-0.1434 -0.6371  0.4233\n",
      "-1.2651  1.1258 -1.2078\n",
      "[torch.DoubleTensor of size 4x3]\n",
      "\n",
      "\n",
      " 0\n",
      " 0\n",
      " 0\n",
      " 2\n",
      "[torch.LongTensor of size 4]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Number of data points \n",
    "N = 4\n",
    "# Number of data points\n",
    "C = 3\n",
    "\n",
    "CEloss = torch.nn.CrossEntropyLoss(reduce=True, size_average=False)\n",
    "#X = np.array([[1,-1,-1],[2,1,0],[-1,3,-2],[1,2,3]])\n",
    "X = np.random.randn(N, C)\n",
    "\n",
    "x = torch.DoubleTensor(X)\n",
    "print(x)\n",
    "y = torch.LongTensor(N).random_(C)\n",
    "print(y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Variable containing:\n",
       " 6.8918\n",
       "[torch.DoubleTensor of size 1]"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inp = Variable(x, requires_grad=True)\n",
    "target = Variable(y)\n",
    "out = CEloss(inp, target)\n",
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.8918203841043004"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xx = x.numpy()\n",
    "t = y.numpy()\n",
    "E = 0\n",
    "for n,i in enumerate(t):\n",
    "    E += -xx[n,i] + np.log(np.sum(np.exp(xx[n,:])))\n",
    "\n",
    "E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1., -1., -1.],\n",
       "       [ 2.,  1.,  0.],\n",
       "       [-1.,  3., -2.],\n",
       "       [ 1.,  2.,  3.]])"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       " 1 -1 -1\n",
       " 2  1  0\n",
       "-1  3 -2\n",
       " 1  2  3\n",
       "[torch.DoubleTensor of size 4x3]"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "A = torch.LongTensor(*[10,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "   44    75    35\n",
       "   20    73    92\n",
       "   58    89     1\n",
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       "    0    66    27\n",
       "   68     7    63\n",
       "   84     9     3\n",
       "   74    52    45\n",
       "   66    27    57\n",
       "   16     5    55\n",
       "[torch.LongTensor of size 10x3]"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "A.random_(100)"
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  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = mlp_fun(torch.DoubleTensor(x.reshape(28*28,1)), Weight, Bias, Func)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Variable containing:\n",
       " 0.6451\n",
       "[torch.DoubleTensor of size 1]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "loss_fn(f, Variable(torch.DoubleTensor([[0]])))"
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  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Variable containing:\n",
       " 5.5262\n",
       "[torch.DoubleTensor of size 1]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "loss_fn(Variable(torch.DoubleTensor([0])),Variable(torch.DoubleTensor([0.2])))"
   ]
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  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
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      "499 0.4217836558818817\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "# N is batch size; D_in is input dimension;\n",
    "# H is hidden dimension; D_out is output dimension.\n",
    "N, D_in, H, D_out = 64, 100, 10, 2\n",
    "\n",
    "# Create random Tensors to hold inputs and outputs\n",
    "x = Variable(torch.randn(N, D_in), requires_grad=False)\n",
    "y = Variable(torch.randn(N, D_out), requires_grad=False)\n",
    "\n",
    "# Use the nn package to define our model and loss function.\n",
    "model = torch.nn.Sequential(\n",
    "    torch.nn.Linear(D_in, H),\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(H, D_out),\n",
    ")\n",
    "loss_fn = torch.nn.MSELoss(size_average=True, reduce=True)\n",
    "\n",
    "# Use the optim package to define an Optimizer that will update the weights of\n",
    "# the model for us. Here we will use Adam; the optim package contains many other\n",
    "# optimization algoriths. The first argument to the Adam constructor tells the\n",
    "# optimizer which Tensors it should update.\n",
    "learning_rate = 1e-4\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)\n",
    "for t in range(500):\n",
    "    # Forward pass: compute predicted y by passing x to the model.\n",
    "    y_pred = model(x)\n",
    "\n",
    "    # Compute and print loss.\n",
    "    loss = loss_fn(y_pred, y)\n",
    "    print(t, loss.data[0])\n",
    "\n",
    "    # Before the backward pass, use the optimizer object to zero all of the\n",
    "    # gradients for the variables it will update (which are the learnable\n",
    "    # weights of the model). This is because by default, gradients are\n",
    "    # accumulated in buffers( i.e, not overwritten) whenever .backward()\n",
    "    # is called. Checkout docs of torch.autograd.backward for more details.\n",
    "    optimizer.zero_grad()\n",
    "\n",
    "    # Backward pass: compute gradient of the loss with respect to model\n",
    "    # parameters\n",
    "    loss.backward()\n",
    "\n",
    "    # Calling the step function on an Optimizer makes an update to its\n",
    "    # parameters\n",
    "    optimizer.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    " \\ell(x, y) = L = \\{l_1,\\dots,l_N\\}^\\top, \\quad\n",
    "    l_n = - w_n \\left[ y_n \\cdot \\log x_n + (1 - y_n) \\cdot \\log (1 - x_n) \\right],\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Variable containing:\n",
       "1.00000e-02 *\n",
       "  9.0495\n",
       "[torch.DoubleTensor of size 1x1]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlp_fun(torch.DoubleTensor(x.reshape(28*28,1)), Weight, Bias, Func)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Softmax\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "x = np.random.randn(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.12539562 -2.65632588]\n",
      "[ 0.94168006  0.05831994]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a34ff6470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#x = np.array([-1, -1, 1])\n",
    "\n",
    "sm = np.exp(x)\n",
    "sm = sm/np.sum(sm)\n",
    "\n",
    "print(x)\n",
    "print(sm)\n",
    "\n",
    "plt.imshow(sm.reshape(1,len(sm)), cmap='gray_r', vmin=0, vmax=1)\n",
    "plt.show()"
   ]
  }
 ],
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  "kernelspec": {
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   "language": "python",
   "name": "conda-env-py36-py"
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