Variational_AutoEncoder.ipynb

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  "metadata": {
    "colab": {
      "name": "Variational_AutoEncoder.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/sayakpaul/TF-2.0-Hacks/blob/master/Variational_AutoEncoder.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pD6XDAg0dfyv",
        "colab_type": "text"
      },
      "source": [
        "The code is taken from https://www.tensorflow.org/beta/guide/keras/custom_layers_and_models#putting_it_all_together_an_end-to-end_example. The intention is to visualize the images that are reconstructed by a VAE. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JOgCeP0ryU6w",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!pip install tensorflow-gpu==2.0.0-beta1"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xevVrKLXyjVK",
        "colab_type": "code",
        "outputId": "fe528efd-0c01-4992-b00d-0377a41a7cea",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        }
      },
      "source": [
        "# Imports\n",
        "import tensorflow as tf\n",
        "from tensorflow.keras.datasets import mnist\n",
        "from tensorflow.keras import layers\n",
        "import numpy as np\n",
        "np.random.seed(7)\n",
        "\n",
        "print(tf.__version__)"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "2.0.0-beta1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XmMBoMqOyv2w",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Data prep\n",
        "(x_train, _), _ = tf.keras.datasets.mnist.load_data()\n",
        "x_train = x_train.reshape(60000, 784).astype('float32') / 255\n",
        "\n",
        "train_dataset = tf.data.Dataset.from_tensor_slices(x_train)\n",
        "train_dataset = train_dataset.shuffle(buffer_size=1024).batch(64)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bFksw51eJPgd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class Sampling(layers.Layer):\n",
        "  \"\"\"Uses (z_mean, z_log_var) to sample z, the vector encoding a digit.\"\"\"\n",
        "\n",
        "  def call(self, inputs):\n",
        "    z_mean, z_log_var = inputs\n",
        "    batch = tf.shape(z_mean)[0]\n",
        "    dim = tf.shape(z_mean)[1]\n",
        "    epsilon = tf.keras.backend.random_normal(shape=(batch, dim))\n",
        "    return z_mean + tf.exp(0.5 * z_log_var) * epsilon\n",
        "\n",
        "\n",
        "class Encoder(layers.Layer):\n",
        "  \"\"\"Maps MNIST digits to a triplet (z_mean, z_log_var, z).\"\"\"\n",
        "\n",
        "  def __init__(self,\n",
        "               latent_dim=32,\n",
        "               intermediate_dim=64):\n",
        "    super(Encoder, self).__init__()\n",
        "    self.dense_proj = layers.Dense(intermediate_dim, activation='relu')\n",
        "    self.dense_mean = layers.Dense(latent_dim)\n",
        "    self.dense_log_var = layers.Dense(latent_dim)\n",
        "    self.sampling = Sampling()\n",
        "\n",
        "  def call(self, inputs):\n",
        "    x = self.dense_proj(inputs)\n",
        "    z_mean = self.dense_mean(x)\n",
        "    z_log_var = self.dense_log_var(x)\n",
        "    z = self.sampling((z_mean, z_log_var))\n",
        "    return z_mean, z_log_var, z\n",
        "\n",
        "\n",
        "class Decoder(layers.Layer):\n",
        "  \"\"\"Converts z, the encoded digit vector, back into a readable digit.\"\"\"\n",
        "\n",
        "  def __init__(self,\n",
        "               original_dim,\n",
        "               intermediate_dim=64):\n",
        "    super(Decoder, self).__init__()\n",
        "    self.dense_proj = layers.Dense(intermediate_dim, activation='relu')\n",
        "    self.dense_output = layers.Dense(original_dim, activation='sigmoid')\n",
        "\n",
        "  def call(self, inputs):\n",
        "    x = self.dense_proj(inputs)\n",
        "    return self.dense_output(x)\n",
        "\n",
        "\n",
        "class VariationalAutoEncoder(tf.keras.Model):\n",
        "  \"\"\"Combines the encoder and decoder into an end-to-end model for training.\"\"\"\n",
        "\n",
        "  def __init__(self,\n",
        "               original_dim,\n",
        "               intermediate_dim=64,\n",
        "               latent_dim=32):\n",
        "    super(VariationalAutoEncoder, self).__init__()\n",
        "    self.original_dim = original_dim\n",
        "    self.encoder = Encoder(latent_dim=latent_dim,\n",
        "                           intermediate_dim=intermediate_dim)\n",
        "    self.decoder = Decoder(original_dim, intermediate_dim=intermediate_dim)\n",
        "\n",
        "  def call(self, inputs):\n",
        "    z_mean, z_log_var, z = self.encoder(inputs)\n",
        "    reconstructed = self.decoder(z)\n",
        "    # Add KL divergence regularization loss.\n",
        "    kl_loss = - 0.5 * tf.reduce_mean(\n",
        "        z_log_var - tf.square(z_mean) - tf.exp(z_log_var) + 1)\n",
        "    self.add_loss(kl_loss)\n",
        "    return reconstructed\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qEPlv2D8MDSR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Instantiate the VAE class\n",
        "num_features = 784\n",
        "nodes = 64\n",
        "latent_vars = 32\n",
        "vae = VariationalAutoEncoder(num_features, nodes, latent_vars)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iJnuaoDqCp4j",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Optimizer and reconstruction loss function\n",
        "optimizer = tf.keras.optimizers.Adam(learning_rate=1e-3)\n",
        "mse_loss_fn = tf.keras.losses.MeanSquaredError()\n",
        "\n",
        "# We want to average out the loss after each epoch\n",
        "loss_metric = tf.keras.metrics.Mean()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3V_sjDnINn-x",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 644
        },
        "outputId": "fe59f1a3-8ad2-4b2d-84dd-77e4a812a508"
      },
      "source": [
        "# Iterate over epochs.\n",
        "for epoch in range(3):\n",
        "  print('Start of epoch %d' % (epoch,))\n",
        "\n",
        "  # Iterate over the batches of the dataset.\n",
        "  for step, x_batch_train in enumerate(train_dataset):\n",
        "    with tf.GradientTape() as tape:\n",
        "      reconstructed = vae(x_batch_train)\n",
        "      # Compute reconstruction loss\n",
        "      loss = mse_loss_fn(x_batch_train, reconstructed)\n",
        "      loss += sum(vae.losses)  # Add KLD regularization loss\n",
        "\n",
        "    grads = tape.gradient(loss, vae.trainable_weights)\n",
        "    optimizer.apply_gradients(zip(grads, vae.trainable_weights))\n",
        "\n",
        "    loss_metric(loss)\n",
        "\n",
        "    if step % 100 == 0:\n",
        "      print('step {}: mean loss = {}'.format(step, loss_metric.result()))"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Start of epoch 0\n",
            "step 0: mean loss = 0.3513181805610657\n",
            "step 100: mean loss = 0.12723110616207123\n",
            "step 200: mean loss = 0.10005825012922287\n",
            "step 300: mean loss = 0.08973503857851028\n",
            "step 400: mean loss = 0.08461252599954605\n",
            "step 500: mean loss = 0.08121258020401001\n",
            "step 600: mean loss = 0.07903553545475006\n",
            "step 700: mean loss = 0.07738673686981201\n",
            "step 800: mean loss = 0.07619763910770416\n",
            "step 900: mean loss = 0.07514350861310959\n",
            "Start of epoch 1\n",
            "step 0: mean loss = 0.0748547613620758\n",
            "step 100: mean loss = 0.07418126612901688\n",
            "step 200: mean loss = 0.07366356253623962\n",
            "step 300: mean loss = 0.07317443937063217\n",
            "step 400: mean loss = 0.07282574474811554\n",
            "step 500: mean loss = 0.07242324203252792\n",
            "step 600: mean loss = 0.0721222311258316\n",
            "step 700: mean loss = 0.07182537019252777\n",
            "step 800: mean loss = 0.0715859979391098\n",
            "step 900: mean loss = 0.07131179422140121\n",
            "Start of epoch 2\n",
            "step 0: mean loss = 0.07124077528715134\n",
            "step 100: mean loss = 0.07106111198663712\n",
            "step 200: mean loss = 0.0709213986992836\n",
            "step 300: mean loss = 0.07076222449541092\n",
            "step 400: mean loss = 0.07065880298614502\n",
            "step 500: mean loss = 0.07050342857837677\n",
            "step 600: mean loss = 0.07039058953523636\n",
            "step 700: mean loss = 0.0702647790312767\n",
            "step 800: mean loss = 0.07016457617282867\n",
            "step 900: mean loss = 0.0700317844748497\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yu3PHSUTXnAH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "outputId": "f7bbf0e1-3506-4af4-bb25-00d5d2d5d486"
      },
      "source": [
        "# Inspection\n",
        "reconstructed.shape, x_batch_train.shape"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(TensorShape([32, 784]), TensorShape([32, 784]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nPPBenqyeiKi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "outputId": "f71fead2-4264-46ed-a710-9853774c2587"
      },
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "sample_recon_image = reconstructed.numpy()[1]\n",
        "sample_recon_image = sample_recon_image.reshape(28, 28)\n",
        "\n",
        "plt.imshow(sample_recon_image, cmap='binary')\n",
        "plt.show()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "voohcffb5FzD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        },
        "outputId": "9ad773c9-c3f6-416c-c014-64bb0f9bf857"
      },
      "source": [
        "##########################\n",
        "### VISUALIZATION\n",
        "##########################\n",
        "\n",
        "n_images = 15\n",
        "image_width = 28\n",
        "\n",
        "fig, axes = plt.subplots(nrows=2, ncols=n_images, \n",
        "                         sharex=True, sharey=True, figsize=(20, 2.5))\n",
        "orig_images = x_batch_train[:n_images].numpy()\n",
        "decoded_images = reconstructed[:n_images].numpy()\n",
        "\n",
        "for i in range(n_images):\n",
        "    for ax, img in zip(axes, [orig_images, decoded_images]):\n",
        "        curr_img = img[i]\n",
        "        ax[i].imshow(curr_img.reshape((image_width, image_width)), cmap='binary')"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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+5mq79y79yeNBibZjusaM3Iau83XJb/PmzTr44JGfy62U5lld/Sbf\nU+k3cjh38di24+ei7bd7bNNc84zS57faaqupzrOgz2+TPBeb4/qS5jcWltY7wv0X2xvPB33nWTNP\nAl3X9dF1XW+o63rDdtttp6qqtGnTJm3atEmbN28e/FVVpaqqVNf10F9+v6oqrVmzRmvWrBkcE9/j\nr/S5NiWgPbB27VqtXbt2cI7YHq6dKbWh65p9ZNV2/o7Pdw5wfQfafGy8dv5+cptKx/a51jjt2/K5\nEVnlc/X5K8k1vzfX57rkkxeYot6W/rLeRsbVp7nkNcfxY30fkZJMufdxdGMcpnm+cWU1q3uaFZPo\nUaavzZpLNqX+0mWHxqHtM139dxZkWbVNJtra0GWzoEs+uQ+Wxsg221WSVR4LS+1rGy/nIsuKHwaS\nivMGxuzcFsb2TZs2td4jbYyyyX95jhDbkeczJdr0K7Yj38Mk8orX7NKXccbofC/jzkXmulbpvF3X\nmW9f7Wvfl7I9n68tHJcsq7nmTrm/dM2Xcn/pGgPy/KjLRhXuYc7vMtqAaclqjM/1lmvpHueSWdex\nXcxav0rjYddvrq45dttcO1yr1e7nY0rj11wyjp/rGgdgXLn2te9zzWPGHevHIX8GOTCudX1vXWPV\nuG3pmmfN125wD1kX+1CaZ3VdK39vXDvPY7r++jLJAtClknYO/++05TVjjDHGGGOMMcYYs4SYZAvY\nqZL2rKpqN9248PMESU/q88FSeDarVjkMmtezpyB/Ph4bySHikL15sV2EWvWBa5buZa5V4Enhmlyv\nbWWx9F6pvVmutD+vrJc+M047I9PyMMTz5Gguqbh9aqht8Zg2ecT3uEb+TOnaGdoQ9SMf2yXXhfBK\n9vlexvnu245t81KU3utq06w9oX2YTxu67EaXHrbp8aQ2YFLazjPX+edrG7KO9Al1zu/FftjHA9wl\n63HA09l23bbQ9D62O4JNyvrF401ucpOhNsVj8/nj2FjyLsfPxPNNSvSMZY9eJN9j6dgsjwjHc0y+\np2jfs0yyrPq0s+v7moS5+vY443efY9veK/WtrKvz7ftLwea3Ubq3NhmVthd06dJi06UPbe0tbSvp\nmrfmuWe+ZmnulPUqz/26rrkQc6o2uvR4HLvRNgaUbHCf+cM4869pU5rPt31nXfrDe7/97W8H72Gv\ns53N40P8PGNkbkuOOp2rXdOaO7TR1l9Kv0m75kGZ/F7XFjvO27UVrm273Cyo63pkXaHUrnyPpb7Q\nJod47qhr8Ty//OUvR15DF3NbSr8d+8xtxtWreS8A1XX926qqjpT0BUlrJR1T1/WZ8z2fMcYYY4wx\nxhhjjJkNk0QAqa7rz0n63JTaYowxxhhjjDHGGGNmwEQLQPOlK3wxh0QRTlUKjyUUimNi6N6vf/1r\nSdIvfvGLoWNyRu14bsL8bnrTm0qStt5666HX47Wha5vUNOgTJt0VPte2RSDKinv4zW9+M/RYCikl\nNA2Z8Jirr8TnfUIjp0lXWCL0qSoH6FAE/UKO/B91hfv9nd/5naHHLLNIn219s95a2Jc23Yr6kuVE\n23/1q19JGpYB8qFvhmo4I8e26VDX9pjFpG27TAwXze3NuhXvP8uG//PW2S4WYwvFXCHKka5tuxyP\nrfq///u/of9LNjvrFfZ9GqG086VrC3HbsaX+n3UmyurnP//50OfzWBivl2XEWIg8x90uBzkselxK\nW8Dj63lbbamaTP58qU30NfSI8/F6bAeyyTK72c1uNvS6NN72hfkmgo701d8+20/atobH15AlcuJ1\n5Cg19p1r5vlVVz8cZ6vwtJhkS29pXshr9E1kw9aAeP/IBBnlrShRR/rY0mnS9V3kY/psLUIe2HCp\nkQX6hH4hs3g+jkVW9EvOW9riupS21EGf7497irYr6xpzq5J9j7KQpJvf/OaS+s2ZF0K/Sn26bZtQ\n17amLhvPfJ7HPGaW5mTY9DyXj+Q52DhbJMelruvib9k2+tj5vO1ZanQpyybPIaTmvvM8Ptsyabz7\nn1Tf6roufifj6FXb1i/skzRqx7LNitdBRrx3m9vcRlLTH+M95/vvkt24Y+HSs4LGGGOMMcYYY4wx\nZqoseATQ5s2bi0lw82s5GVI8llUzVifxoMRIjSuuuEKSdOWVV0qSrr32WknN6lz0kLLqdtvb3lZS\nsxq3ww47SJK23377wbG3uMUtJDWrmzkBZGQaXoY+K7d9EkoiK1Ylr7/++sExeIiREf/zGM/Lai6y\nudWtbiVJuv3tby9JuuUtbzk4lhXfaXg05yLqVaRPQjxAr3LUWJTVVVddJamRDf+XVnm571vf+taS\npB133FGSdLvb3U6SFEuF5ogqKHnOFjP5ZUl+2fuLrkmNnK677jpJTX+84YYbRs6DvmSdQl70y3hs\nTmY434SisyDqQvaYIKvoQcCOIZuf/exnkhrdiv2I+8bbiY4hKzxW0qhOwWLIpc1bHWWVvU38H+07\nckOfkBW6V/J6IpMsK+y+1MgzJzIs3cM06JPUs+vYLBseYx/EftEHkVX2rkuNfmLHt91226HHKCv6\nKfLtkkubDvaFUryZPD/oSorNfSIbZBX7IDK65pprJElXX3310DHR28o9ISvkwXwBPZNG5w0lL2OX\n53g+dEVfZE90KVoAeTFn4jG2D1uF3JhD8HqcZ2GzkRf9j8corxwttBQiNrpsVpt9jzYL+WGz/vd/\n/1dSM0bGe0RPGPOyrYpjYbZZXW2flKqqirrSlXw/vi+NRm0iqzgnwEbxyNiIzOJ1sOvIZJtttpHU\nzFGRTzw23k/pHrvuZdaUIuy4//y/1OgPdp5H5FmKLmXuSZ9EZlGvkNVSS7aeI1lj+3L0BTKINp7X\n6IfY+mznpEY+2CbkhPzib8O2qL2uZNDzpaqqzkTBbQnBoz3OUfn0rXj/eb5Of8x9V2r6GbZ71113\nlSTd4Q53GHo/HlOKpMr3MumOhzVr1nRGTWfbVYoy5LX8eybKF1uf7TsyinJFFswLsl7x20dq5hX5\n+y59/+PKavFHVWOMMcYYY4wxxhgzUxY8AqiqqqJXZ64ShnH1jNW37K2LkRoXXXSRJOnHP/6xJOni\niy+WNBrdITURQKy0sWKJB2GvvfYaHLt+/XpJzUpd9uzNij77rnMuH6lZfURWrGBefvnlg2OQ1aWX\nXipJuuCCC4Y+G70NrNhy/zvttJMkaffdd5ck7bbbboNj161bJ6mRa87v1HUv41JV1VjlF3O+I6nx\nDKNHrHYTTSY1crvsssskSRdeeKGkxvMZV8TxCOC9Y5UXWe25556DY5EbHr6S92Uhctq0eTlL+R/o\nS+gUK97R64kH/eyzz5bUyAvZxvtDdtw7HoR9991XkrTHHnsMjqWPItucC2cxKeW/yNGKPCIfSfrp\nT38qSfrJT34iqemPeBQi9ENsF7pFf0RmUtMP8Ux1eV0mpa7rsfIPlfZS58iDHLkiNX1y48aNkhqZ\ncUzJ64mOEM1C/9t7770HxxKlhyc0RyJMm67z5j3qOS+NNDoWokNEJkqNjl1yySWSGtnxmRgtBNw3\nsir1wV122UVS0wfRxbjXf1pevHiuSJvNL0Wr5PvFZiMzqRkLs37lXGbSaB+84x3vKKnpgzzG54yb\nOR9c173Mlz7RDXkswZZLo/namGfF8RA94zXsO2NBnGfl3Ip4OQ888EBJzdxKamwWY8FSikbIuVak\npm/iKecROUiNPUfHsFnIMNpAroG+0NewWTvvvPPgWOapzB1Kc9FpRbW0zT3myrEY5+9ZRlmHpMZm\nMd9iTkqfjeM8+sT9E61x5zvfWVIjO6mRH/N29Kr0W2RWzDXHin0GuSGrHKUvNXI7//zzJTUyw97F\n+VjOIUUEC2NgnDdgs4jYi3Z9VrT9Doyv5dyvsd/QJ7Nuxd+G9EPkhI3nM6W8QYyDzDvpf8wXpEZe\n6Bv9sJS7cdLxMP7e6Srtnn/vxHvLkcDoVvxtyO8cXmMuymPXThrkQZ9jPi81cwbkWopinCuqsC91\nXQ++g3j/OV9m11iIXtGn0Ks4N0dG2HX6JWNA/B2N/eG+mb/vs88+kprfiFLz2xCZ8dlSHrhxI2Ud\nAWSMMcYYY4wxxhizwlmUKmAl2iJ/8oqu1Kxc4rljRZeVN6mJODjvvPOGjsmVGKTRXC2s4EbPILDK\nmfcwdlVlmAZd+/jzXs64csnqbpYV8pGkH/7wh5JGvel4DmLEACuWrEaWIl+Az7EqiSehFKUxjT2x\nJdoiWEr5L1ip5Z5y9Fh8jszwqiOrkpcETyf6xUpwvHauiFLKn7QQ1azaPHk5KkNqPMI5H1L05CGn\n73znO5IamZYigNATvFLoLNcsVe5DTuNUs5gV2bbEFX+eo1v0MbzBUuPlPPfccyWNRkt16RbeFjxd\nMbKA9uBJ6FM1cL70jcQD9CrKiu8bvUIueKOkxladc845Q8cg3+gVww4R1YN9Ry54VKQmWrGtIt00\nibKKtO3bz9GcUtNHcuQP8pEazzB9L+c+iJEM3Gf2dPJdxu+J15AVY0Opiso05NeV0yZ7+JAZ9xjb\nTnQBMkMuUqNP9EuOQealCCBkxTHMVaKsGPuynSpVzZxGtFRbJF6WYVcFHNqf7TpzKqmRHf0PL2j0\nuAN9ibkD/TBGSgKyZSzIFWUiC131qpTTgfGfOQSyivYdWf3gBz+Q1MzF0LGoC+gJc4ac6yx+T0Sx\n5LwSs5hnSeVoorYqlzmCRWrugX6IXY/9kHkD8qNfYqtirknum8gDdKZUuS9H+efKRbHt04yW6hPJ\nnXObSo0+ITN0JkZ4Ml/4/ve/P3QM9ijqCjqGrIi0Q0axf+Uqh6WIltL9TYOueW+ek8bxEH3DDiGn\n2A/bfu/w2agvzLmYO6BbpUisPA4S3VKKAJq0H7Z9Po+H2VZF3aJP5t+GUVY/+tGPJDW/e3hEL+Oc\nnCgW5qQ5H1y8NtFAOX9gKXp4Uuq6HsgltrdtnoUtj+M3/Q+94hFdkhr7xbwd+5bzd0mj+U6JHs52\nUxq1UaVKkPO1WY4AMsYYY4wxxhhjjFnhLEoOoJKHK6+Ksxqes/9LzWocK5VEYZSiWlixZCWU68SM\n5FyLFUDawCpdXG3n2uz9zJ+RpufJmyufRo5uYYU1etRoO3LAU8ejJH3ve9+T1MiT1UfuP3oQeM4j\n18ZjhUdBalZSc+6KWUdLlc6Vc0nxGD3EeSUcGcVVXrwteNVZ3eY7j9EEueIcx+LVi1XAWC3H417S\nq4WoTtG2Kp7zI0lNm7OXJfZDvFLoHx6T7HmO584VBkq6lftfSY8WImdSPH/WsehBwIOL1wlZnXHG\nGYNjkBXeBWTFin/0JOVoI/oYx8YqAnjckVkpumyaVXa6vgvIUS3Rk0Y/wTNMxEGMxPv2t78tqfGm\n55xesaIQ3wPX4v7x0MWItRyt1+c+J6ErqgUbm/OLxD6I/UJWyAj5SI3O0U/xmJaqy6G7jLc5vwa6\nFM+DnUdmpUi9aYyFpeeQqzCVcrBg33OF0NgHsevIk3tEh6KHPOcPyZX50K/YDmx+yb7DtCte9cmn\nQd+IusW94yGnH0b7fuaZZ0pq9A6dKkVk5miQXCkML2h8jued80UWOvIn59GIuVVylUu8wDGqhShY\n5JjHiVJ0E30J3SXyhbE3tiP3sVKV3WnKrGuexWPOeSc1NgsZIQ/GP2k0Eo/Px/kV5Gp+fD85J0l8\nnt8rzd8nZa6odED/0YeSXuW8ItFm0QexXbmqXLTvvMe1iCpgzhFzSzFeYMdKNnzalQuhK68N/TDn\nNZUa+eQcbjFqkfk8epgjVOKcNEeW0pZcJTO2I+fdKUWXTapj8bdhSc9ylBT9p5RHkd87/I5Gn6RG\nVrnaY6nqMe+hE8gTuxZlRSRVnreVIoCmoVtdtipH3SCruAOI54xz6BO/naXGnjEGlCrSAvaHNvA/\nUUNEKMZ2ISPsXFzD6Mqv24UjgIwxxhhjjDHGGGNWOF4AMsYYY4wxxhhjjFnhLPgWsK7QPml0y0mp\nlCEhVrxWSrhHSCOhdoQUl8o+Et5GCB+hVoRDxy1VhFjl8sBdJVfnS9+EqjlBbwzjJnQNmRHmx1Ym\nqQmFzIkXCbcthZXlrXmlrRxt7S0xzYR7XSHvyIp2xvYiI0IieYwJVZEf90/iM7Y/RL3KyYCzbset\ndXkbYg6llpowv2kkCZXK209yctC8RSDKi3BSHgkZRkZSI1M+zxYbkp/F5OF5q2BOch6Pzcd09ZNZ\nbRVoS8ZO/4shpDmEm+2FhI1KjdzyNiZ0rFSetG0rWOk7nVZZzb50JQnlXkrbVnMJYOR41llnDY4h\n3J37Rq94jElH8xbZHA4dw6LnKg2a72sS4rlL42IO42a8i+3N95BLvUtNv+S+2cZFH4zX5nvA1nSV\nkc1h8ciuFN4+jZB36Jo3tIWqS6NbkOh7Mbk4OodM0CfuLSZnzDqStxJ0bSsh1H1WCVXb5g5561db\n+LvUzAvyeBjnWegZcwXC/NGxUnL3XJo5h7jHNpe2ReV7mZU9y99vHs9LssJWoUdx6wl9k3EMGcXy\nyPnaOTFwKRl71iHaGWU3TVl1nautyEack+Yt42yTI+GsNNoPmZNS8j5uM+WYXG65VCY8J8zOW6cj\ns5IVz7NdL20BY6sf8kNmcf7OXIL7Zqs384doszlPHnd5Pc7vcjqOUgqHfE+TEMeheA1ez32hVCCI\n9qMLzCWwXVIzVuZ5FuNhtPE54W7W61LxG9obt+jAtGxV29wq6xbvoVPx+8Vm8chcPaY8QS/ob2xN\n4t6irPj9mNO3IKNS4SUeu+z8pHOHrnmoNPpdIqNSugse0ac4F+P4/DuasT7KPn9PyCqnDZFGt35x\nvrnuqw+OADLGGGOMMcYYY4xZ4cwZAVRV1TGSHiHpyrqu99/y2jaSjpO0XtJGSYfWdX1t2znS+QYr\neqWojexBgOjxYMU3l/qLK2ys5uIxyEkF48olXpsYuSA1q5Jdq5MlpllGsk8irFzCNcqKlV8es0dB\narwilIneY489JDWrvPF8rKgjq+wNiEm8cmnJrlLA00wi17UympNdokPSaCllVsbjKi/nXr9+vaTG\n24KnOHox8ULgYeazJPyKCQ3xQrB6nFfIZ0GfBOM5+iZ6k/DA4DnAGxw9CMBqOKV/6Z9xdT+XtAY8\npTExLzpbSpC80OTospINow9hu+iHMVKD/kZJdxLGlqJachlS9CbrkdTYvFxGftaRQKVItTa9irab\ne0Nm9NGYBJrve/fddx96RK9icnf0lNeyLsckocikq+TttKiqaiTaJz7PXkfkET3EOdoMWxP7IDJn\nLES/SmXbsVnoGv0L3Ynll3mP8/Qp0z5f2j6PHiGrrHPRHhMVhMywW4xpUvO90/eIvuMeSxGLnC8n\nwY7zhjyX6JMofVL62PcceRpL9aJT6B3yivaZsYz5FXMH9CTOM5gzxATGUmPL43iYS0/PKuog0xWJ\nlyPy4n0wR+C1HMUoNUr8N7cAACAASURBVPfC3IGxEPsT7TvX4PN5HhNtVpZNjmIsfX4SuuSexz7m\n2bFUN/qDHUOv4jHIar/99pPUyIx5RCkRfv6eOAf6JTVyyDIr9cNpRFp3Re4DtrUUhUN/xK7zGHWP\ne6HvoVfYo2gD8ziR5+YxagW55aIRs5o3rF27duR3YHyeiyKUohbzzhHGs5K88twdory4Nt8Jn81l\nvKVmzoXelSLx8nknoet3JuNlTmwd743XkBFz0WjfuRdkxRyiFAGE/mL7coLjOCdt+53Tp7/Mh9L8\nIUcw54TUUa+QEbLB3sdjkAlzB6JhkWEpuTuPeZyL/ZDnyKyrgMS49JmVfVjSQ9NrR0k6qa7rPSWd\ntOV/Y4wxxhhjjDHGGLMEmTMCqK7rr1ZVtT69/ChJh2x5fqykkyX9TZ8LtpWBz/k0WAkrRbW07fOM\n52Wlcq+99pLUeD3zfmFpdBUul1KOK8Ss+LIKl73qkbiPbz70XWlvKxssNSvAOWIgrjDiVdlnn30k\nNd48Vnfj6jneFu4te+/iinjeAzvLiIN47i794r1SHp6cI4JV3vgd410hWgpZoTvR44cXDG8o50Gf\niMyIn8/e/5JnapZRCdljn3OBRA8xuoR+IK/oXUNO3Cv/I4vYD7MXmrbghY9ezxyhMatcGpmuVfes\nY6XcYXhJ6EfRO0T/Q0boGvIgj1CEe6T/ES2FF0Jq+mEuBTzrCKD4nbTJraTTvJZlFfVq7733ltRE\n/qxbt05SM05EG5Aj0vCk4NWKkQfRS1Vq5zSJeVpKpWd5jf+zh0pqvErICJlFvcJGUeIXHcm5kaRR\nLzq6gxePvigN65g06qGKbZ+UGA0b4TVsbS59HCN2eI73m4iU6JlDVne6050kNfdbKrXNvAM5InNs\nXdQr5Jjtesm+T6vsbSmSIff9bLOiRxd50X8YF2NEBZEZ9EPGNj4bc7XgYebazBWQU4zwzJGd0y4z\n3UbJZmW9497i68iN8YyxMN4THmEiNZAVso/zLOYR9E36Vp5LxHbwWilXyzRzj/QZA/PcN9os5IeM\n8j1Kja1CVvyf5yNS45XPvxnQoThvoD9nmc06wqwks6zbeR4vjeaqjJGtgK2iDzJvQM7xM7yGntIG\nZB9llecNsS933dd82bx5c2deKcg2PtpvbFSO2Ij9hXELuXHvOdpHasZTrsF5sIGMi1Jjx3KUUB+b\nMi6bN28uRr22jSElO5rnDl2y4vdz7j8xajGXhkd/sFmxtHmOSu+SxzR20pTsUmmOEImv5zUH7jt+\nt3ksREfQoTgfyDkF0SNkFvshn+NaHFP6zTvufGu+s7Md6romc+LlknZoO7CqqmdVVXVaVVWnlbaG\nmAbLqj+W1XhYXv2xrPpjWfXHsuqPZTUelld/LKv+WFb9sazGw/Lqj2XVH8uqPxNXAavruq6qqnUZ\nuK7royUdLUkbNmyo03sjx+fV3dLKZa7iwipaXDXDI0wkEKtxeFniqnj2cOGZ4Xwx7wErdXk1fBqr\nvF2yajle0uiKcyRXjkFWcTUWryeyypUmomeK83H/yIOV4nhe3suRB9OgS1ZdOShod2kVNe8pZlU1\nejxZCSd6ANCnaHB4LVcM68pp07ZyH9+bj9dlXN1CLrkaWGxPruqCjsWVbuRFf0TueP3iXv7sEcz9\nMMqrLfKu9N1Psx927bfuqiBFv8HLgncBr7DUeKR45Hy5epXUeCQ4D7rF+aKs0PlZeNGzrNpymmSZ\nZA9s9P5ih+k/RGhGWaFPeIbxKKFP0TOF1wZ9xVblR6mxWbOIkirpFecveevRq9z3SlVdiGrhHmMf\nREZEeqIPpZwTyBpdQ66MDV0e4lJ+jflGtWRZxciDeP9cK++hz9EAUqNPVP/CY4lcpMaLxziW+07M\nB0e/pG9jw5FZKcIz55iKsprEO9wlr65IPN4reUG5LyKdkFfUAaIV0Q/mSowJpTw5tAEdZf7BuCg1\n0RuzqPTVdyxsywVTymmIbHIl2Th3REbYMe4fWcVcVLzG/WMnkX38DrKdKEVqzJcsq7YoDch6Xqpc\nmeek9KNo3/Gi77vvvpKa+0dGMWox2ywiy0pjYbYX4T4Hz+ebA2jceUOez5W+N+4JfeBe45jFXJRq\nctxjrkooNTYw92X6cTxvztM47YqYJZtVmmfmSJccLR/ngoxpjPncZ9zFgV2mb3KtnL8rno97zznP\nory6qmDCfOWVZbVmzZqifc/VHXNUYKnfMCflmDh34P7y3KFURZnnOfcR54u2MPexLt2adO6wZs2a\nom1sm4vm3z5SIyt0g/Eyyoo5Ka9lWxjnDnnXEddGznHuwDwrV/yN9zLf39jzjQC6oqqqHbdccEdJ\nV87zPMYYY4wxxhhjjDFmxsx3AehESYdveX64pBOm0xxjjDHGGGOMMcYYM236lIH/mG5M+LxtVVWX\nSPp7Sa+TdHxVVUdIulDSoeNctBTm11YulnCnGNKfw7EIe48hpDlsigSEJFK94IILBscSFslnCBkt\nhb1DTuZYSnw5zbDl0rnylpNSmF9O1JtDGaVm+wWhuci6JCtkTsgaofKErpXC/9tCOOe6v3HpSqzZ\nRkxOSIgej+hZTHxKWCMyJtSUpI0XXXTR4NicBJrHriTQOYy0K4HnLMhhl3l7U+yHhCXnZKpxSwV6\ngrzQn/zZeG5kTPgpoZVRZ0tbPNruZVbk0FSul7cvSE2YbU7iGG0W/TAnEqX8+caNGwfHct+Em6Kj\n2Ky4pSonzF4I/ZHKobt5m1Ap8SJ6gI4QBs+9Sc12G/oY/e6cc86RJJ111lmDY3NCVrYXEMYdZUW7\nSt/htGnbYpDHx7xtIeo8/Qn5MRaWytPmrYRsG4sh7zmBY94CVgrjzomEp7kFhfNv2rSpmIw026mu\nrSeUm0YOtBc9kEaLPCAbxsIoK/QUG5e3RcetCVmPcoLv+HxaOtcnsWb+DuM2U2xVtPnSsH3P4yF9\nljlDtO/YQK6Zt2BGnc3tW4ixL5O3COTvJc4d6H/cP3apa5s3WxGxXWeeeebgWMaAnLCe+VacZ+Xt\n0LPYNgdx60npmjzS7lJ/xEbl7TVxO0209VKji+eff76k4bGQuT3nwb4ztsatheOMgbNKAp3P2/ab\nRxotdNOlV3kLDnPSc889d3AsczTsO7Jhq34u3BLbXtp6Mm1KNrBtiz3tKSVtRl/yViip0U0+x/yA\n8YH5ltToKnN25I7c4hy+rX2lBOObN2+eyM7HLb4lWfEdYZdpQ5QVtiqXuI/3xPwSvUOnSikveI4+\n0p+Zm5YS13f1x0lSXkQ2bdrUef68zTvbJ6npN9HmS8O2BfjdyOfRq1jEBXuYCyFwvjgnRfY5bUlp\nrj3uttU+VcCe2PLWA8a6kjHGGGOMMcYYY4xZFGa3lNtCXdfFFdG8ypc9UrHUH9EsrLSxihhL38Kl\nl14qqfE+4ZGKq7ysmhHpw2pcTPCUj83JcWcV1VIir4zSBlYK4ypvLlsHUVYcz+ou8sWLxwqmNOph\nxiNcKgGcI5LaSixPg9IqeH49vsdKbix7m5N6smJd8oqgR6x6o08x0Vcux8rKeC47KTUrwjnRa/ye\nFsIL2rbaTnuibtGngD4QowTQB+SFt5PHmCQ0l5rO5ZSj3chlZkse9bnuaVLaPMP0Q+yTNNoP0a3o\nyUP/kGv2dsboIWSF566rrGaW1Xwi5eZDn4Tc9L/YD/Gc8IitKdlYZPPDH/5QUmPviW6Rmn5GX8Iz\nTH8sRZTk/jetZL2RNvnn6L/sdYoRnjznGNoZo1Z5Df2hLyKr2Ke5XyIN+B+bVepL2fMZmW8ix3yO\ntWvXFuWez48cSmNhtmGlMr0cg4zw2qFP0V6hN+hTLtEddYbntC97QGdJVz9Hx0pl4HmOjjEOxkhM\nxkrmDoyDzB2i15N7JVltTjAaZYEMkVcpanzW0UD5/Hzf3HO079hsbFYp2TBzWaI5GAPPO+88Sc0Y\nEc9DP8z2PYJs0N35lgTuS1ef5r1cEjpGlnFv6BX9JkYAMWb9+Mc/ltT0x1JkGedBjxgviNqI32Pu\nh6VI61nIrSsylv+xWdHGoBN5Dh1/m/C95/k7kT9ESMVjiShDr+jbcY6eowlK3/u0o6S65rhZt7J9\nkho94z2+y67iJfRH5hKxX+dIWHSV1+PYzDWiDc3XjhGr05JdqR/Sf3hEt2I/RLfiGCkN2xj0hX6H\nrHiMvwE4DzIiEg+dirLKdp3rTKOARIQS8KVIoxxtlmUV25ujgrin2F7uAf3hdzM2LEYUcW3Ok39P\nx3GDORjt6or8Wqgk0MYYY4wxxhhjjDFmmbDgEUBStxcRWNVl1SuuRrM6xuoZK2TxGFYoWY0jMgOv\nZ1yNY9WMfcesrnPe6EHntRypEaNEZpk3IpJz/9CWWNI1e4ZzuVKpiUrAU5DLIcbz8RxvDSuWJe9s\n9lzPUi7xuqV9kLyf9ank8URWRGfEc6NHeISRHY9xr3uOvEB38v7c+Lnc9j7RctMk6xT3gOcgfqe0\nDY9BLhsqNV6WHJmBZ7j0XeGdyueLUYBECS30Xv4S2YPHd1nKC4asStGK9De8LXj0eIz6wrXwpudo\nhihX9JrvLu8lXgiyNwfZlLx42cNBxEHUPbwq2Cz0iv9jP8RG4SFGd/gOoldsnGipSfthW6RijsrI\ntiv2g6xXpWhYbD0RB/RFPFTRxvA9kBeHKKnsHZMaGbdFTeX7moToHe76LvJYWLLH3C/9IHrb0CP0\nCw8nsor3xvyDPoi9yh672A6uxXslOzAtSmNyW64A2lOKLuM+c9ulxotM5A/yQ9fi+bhXHrN9j23i\nu8rtnSvH2CzJuhXnDtiQnEMrgox4ZAxEVlEX6M/MRemHpTlp/i7HzQMxLl2RP/m7RFbRZuXckKXx\nKOdUzGNhjJbKZZyz7OO1macxt+M7jFFtXfc5LuNELeZxWmpkRB+knSX7nqPS0a9SlDXny7+h4rXb\n9KhPZO986VNqPs9N4+6G/Husa57FXAFdQk7RvmHz2ux0lFdbXrXSeDWN6OGuvDY5IqQU1YIc6Td8\nNv42zvmRGA+RVTwfNjDndKMN8XtC19vaG9+bZvRwaZ7VtpMm2g10LduqOHdCJtgoxkL+j7LKvwOw\n76UIzzY59MmhPBeOADLGGGOMMcYYY4xZ4SxKBFBXtQtWyXKG9+hJ4hhWGFmxi6tfeR8e//PZuIeW\nVV72W7Mqzopm9BDmVddSFbBZVA8oeRCyV5aV27jSmr0jrDTG1X3uk8/n6lXRi4osiJbifBBXOfP3\nslARByVZZe8K9xrvDRnl+46ePlZ5WRnP+RHiHupc7YT/kXe8NivJOQIhyhPZL2TkBu0pefLQTfZH\n50gAaTTfQa70Fb11PN95550lNTrKZ2I1tuw9W4hcGnOR+2OUA+0kyz+6Fr1N2Lpc0QlZxe+dHC+c\nL1dbideeq+rIQpL7Y96rLjVtR0ale6IfEs2Sc5zFPFTICr2CHKEotXtZunISTEKfCCNkg62JYyF9\nhD6IPkW9YgzEM8xYiHyj1wldw0PO+UtVMNpyj8R7yVXfJqHL25y9eNjYmM8BmdBncgUraTS3AeME\nMoqRAox96Bf3yHVyLojYzpJedeUxmw99qoDlnElRXnNVSZEaOdH/cpWiOB5iv8nNgizRrZK9zLZv\n1nnLIm1Vv/ieYl/IfZOxLEaq4AkmMoP7pu/GuVTO8YZuIfs4DscIRmn29r30XbTZKvQp6gy60hVp\nz+ew84yJ9Mc4b8DW58jhHM0cr4FOd+XunDQCqC1KI74vjUYARdvN53M+o9hXctVa9IG+x++aeE1e\ny1F9peiXHOkZmXYf7Bpnc05RdCK2izajAxwbdYu+wyPnRY+iviBD7Bnnz9Ei+XNSuRLltKIWq6oq\nRmjlMTjPr0oRS9xjKUoI+85jtGfxetJo1S9sGHodj83jdVdlwUntWeyHpZ1EebzOuXYi+fdu1Kss\nIz7P/CDKlfPkSDXaEOezyJP25uhYqWzr+rD4v5qMMcYYY4wxxhhjzExZ8AiguHJZytvSJ9N7zg2B\nJyGusOEp4L3sVY6wQscqOyuiuWJUbGdXNMa0PDBz7fOEHHFQ2peJrHIuIKmREdVM8CRwj/F++Hz0\nKsTrxBVxVjez93cWXrzNmzcX5d62Ik4744o2r9Fu5Bm9mOgjOpNXe2NVJ+4buSLPUtRKrtxR2mM6\nbcbxqOecXPFz6FapahEyJGKMfdfIOPZH+l+M3ojnix6VXNkpt7vtvial5BXIe9LbKu9JjS5x3yVv\nE3LgWqX9wbmKGLpV6ofZtpbs70JFleXcW6XKJ20RiNHrjc3C68t+a7zpMVKDiA/eA9oQ7z1HHPSp\neDNfqqrq9AhmL2OpvTzP+WzieMnn0C9sF8dGvUJuyCx7PEve1q4ojWnZrzVr1ozks4vXzLanFH1D\nP0IPSrkJeC1HyuYoH6nRT86XPeXxe8pRNDmKN5572rltSjYxj4PIK9pYxiJsDOeJ+QPRO+RTyqsF\njAHkl8pRgLF/Q1f0wazJsqJP5YowkZybLsoT2ZCLjLEQex/tU+6H6AbRHrHKXylCdFbM9T3kfHil\nqHT6QrbHpTEL/UIX161bJ2l4Tka0B+9lG1jKvVGKPM3XnnQeP9f3kW0q9x9lxWulSkr5PLn6YKl6\nKjaLPp1zmpQi2HP13lnOsboiYrl3bEuuxBzJv/NiP8yVl/g8/bJ0njzH5Tuif0ZyXqXILHIAlc6V\n5+2lHQ98Dj1BN2I/RNbR3kjlKBTkyZws/97pyrVY2hU0a3uW51fIiHGoZBuQEXItVeLK/QU7V4oA\nwvbn3xDx2m2yKuEqYMYYY4wxxhhjjDFmCC8AGWOMMcYYY4wxxqxwFmULGHQlscoJtGL4VA5lhxia\nTIgj4VK57HAMzyOML4eRl0q15jDt0law0haL+TBXydO2rWCRXN4ybxWRmnC2HHZbaj/hgnwHeXtK\nDDflef6eZ1VSuc+WJmSEPsSkXoQw5mRbUa6lZKhSoyM5/C+eD3mUQkN5LYcfl5KWTavMa5eceEQ3\nSgntCIfMSRxjKD/b3whdzwnW4lZCzpcTM5aSo/IcmU4rtHYu+iR1LCWW5N7oP7kktdQk0cu2is+U\nEtDyXrY5sQ3oZG77QiYTz9B/0K/YXmSFbpQSn5bKncfXI7vttpuk0dK3JbIdmqVe1XVdDH3OiYzz\nmFhKBp7LvUYbkbdaZH2I42juV8iX/0u6nXW5lBx2UjZt2lR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            "text/plain": [
              "<Figure size 1440x180 with 30 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}