05. Preventing Overfitting/02. Dropout - MXNet.ipynb

{
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  "metadata": {
    "colab": {
      "name": "Dropout - MXNet (From Scratch).ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "L3KIZndDdgt4",
        "colab_type": "code",
        "outputId": "f0f725c0-91e3-4797-dbc5-f70c766bc14c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 151
        }
      },
      "source": [
        "!pip install mxnet-cu100"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: mxnet-cu100 in /usr/local/lib/python3.6/dist-packages (1.4.1)\n",
            "Requirement already satisfied: graphviz<0.9.0,>=0.8.1 in /usr/local/lib/python3.6/dist-packages (from mxnet-cu100) (0.8.4)\n",
            "Requirement already satisfied: requests>=2.20.0 in /usr/local/lib/python3.6/dist-packages (from mxnet-cu100) (2.21.0)\n",
            "Requirement already satisfied: numpy<1.15.0,>=1.8.2 in /usr/local/lib/python3.6/dist-packages (from mxnet-cu100) (1.14.6)\n",
            "Requirement already satisfied: chardet<3.1.0,>=3.0.2 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (3.0.4)\n",
            "Requirement already satisfied: idna<2.9,>=2.5 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (2.8)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (2019.3.9)\n",
            "Requirement already satisfied: urllib3<1.25,>=1.21.1 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (1.24.3)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1YN4PT_Idstj",
        "colab_type": "text"
      },
      "source": [
        "#MXNet (From Scratch)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CLGHa8i6WEaA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import mxnet as mx\n",
        "from mxnet import nd, autograd, gluon\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "mx.random.seed(1)\n",
        "\n",
        "data_ctx = mx.cpu()\n",
        "model_ctx = mx.gpu()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "huuK9vLaWEcO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def transform(data, label):\n",
        "    return data.astype('float32')/255.0, label.astype('float32')\n",
        "\n",
        "train_mnist = gluon.data.vision.MNIST(train = True, transform = transform)\n",
        "test_mnist = gluon.data.vision.MNIST(train = False, transform = transform)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sAXcT8nSWEYo",
        "colab_type": "code",
        "outputId": "0a7ef0fd-652b-40be-96c6-faf4345572b7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "image, label = train_mnist[798]\n",
        "print(image.shape, label.shape)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(28, 28, 1) ()\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SIQSLxiFWEXg",
        "colab_type": "code",
        "outputId": "25e9bdd8-b9d6-4c09-cc30-ab2983a5b0d0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "plt.imshow(image.reshape((28, 28)).asnumpy())\n",
        "plt.title(label)\n",
        "plt.show()\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Jn5G0soE+3sf2aHEhRrZHJZ2v4Zt6fKWkJcXyEkkPNtjLewzLtO3tppVXw8/d0E13HxED\nv0m6UFNX/P9X0t800UObvj4k6dnitr7p3iTdramXgbs1dW3kSklHSFolaaOkH0qaO0S9/YuktZKe\n01TQ5jfU29maekn/nKQ1xe3Cpp+7kr4aed74eC+QFBf8gKQIP5AU4QeSIvxAUoQfSIrwA0kRfiCp\n/wcdBFP3ZvnQXQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oF-WKS-xX73T",
        "colab_type": "text"
      },
      "source": [
        "##Creating data loader for training and testing"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IVmMwE94WEWY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "batch_size = 64\n",
        "training_data = gluon.data.DataLoader(train_mnist, batch_size = batch_size, shuffle = True)\n",
        "testing_data = gluon.data.DataLoader(test_mnist, batch_size = batch_size, shuffle = False)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5HUXvMyHYKoM",
        "colab_type": "text"
      },
      "source": [
        "##Building the model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n6LpOyKS9gKf",
        "colab_type": "text"
      },
      "source": [
        "###Understanding dropout function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yM-HAEo87wrT",
        "colab_type": "code",
        "outputId": "ba7b1e91-8134-4309-a2ee-05da749a6115",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "layer = nd.random.normal(0, 1, (1, 10))\n",
        "a = nd.random.uniform(0, 1, layer.shape)\n",
        "prob = 0.4\n",
        "keep = 1 - prob\n",
        "mask = a < keep\n",
        "print(a)\n",
        "print(mask)\n",
        "print(layer)\n",
        "print(layer * mask)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "[[0.23734096 0.9831371  0.792735   0.04023623 0.34534866 0.18300699\n",
            "  0.9539874  0.5292981  0.6002937  0.9280305 ]]\n",
            "<NDArray 1x10 @cpu(0)>\n",
            "\n",
            "[[1. 0. 0. 1. 1. 1. 0. 1. 0. 0.]]\n",
            "<NDArray 1x10 @cpu(0)>\n",
            "\n",
            "[[ 1.37109    -0.23789984  0.14867957 -0.49851316 -0.84815776  0.07811152\n",
            "  -0.38241303 -0.05334064 -0.31002352 -1.7337203 ]]\n",
            "<NDArray 1x10 @cpu(0)>\n",
            "\n",
            "[[ 1.37109    -0.          0.         -0.49851316 -0.84815776  0.07811152\n",
            "  -0.         -0.05334064 -0.         -0.        ]]\n",
            "<NDArray 1x10 @cpu(0)>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u7Vdh54QWESq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "weight_scale = .01\n",
        "\n",
        "#  Allocate parameters for the first hidden layer\n",
        "W1 = nd.random_normal(shape = (784, 256), scale=weight_scale, ctx=model_ctx)\n",
        "b1 = nd.random_normal(shape = 256, scale=weight_scale, ctx=model_ctx)\n",
        "\n",
        "#  Allocate parameters for the second hidden layer\n",
        "W2 = nd.random_normal(shape = (256, 128), scale=weight_scale, ctx=model_ctx)\n",
        "b2 = nd.random_normal(shape = 128, scale=weight_scale, ctx=model_ctx)\n",
        "\n",
        "#  Allocate parameters for the output layer\n",
        "W3 = nd.random_normal(shape=(128, 10), scale=weight_scale, ctx=model_ctx)\n",
        "b3 = nd.random_normal(shape=10, scale=weight_scale, ctx=model_ctx)\n",
        "\n",
        "params = [W1, b1, W2, b2, W3, b3]\n",
        "\n",
        "for param in params:\n",
        "    param.attach_grad()\n",
        "    \n",
        "def dropout(layer, drop_prob = 0.5):\n",
        "    # drop_prob is what is the probability that a each neuron will get droped\n",
        "    keep_prob = 1 - drop_prob\n",
        "    mask = nd.random.uniform(0, 1, layer.shape).as_in_context(model_ctx) < keep_prob\n",
        "    scale = 1/keep_prob if keep_prob > 0.0 else 0.0\n",
        "    return layer * mask * scale\n",
        "\n",
        "def neuralnetworks(inputs):\n",
        "    layer1 = dropout(nd.relu(nd.dot(inputs, W1) + b1), 0.2)\n",
        "    layer2 = dropout(nd.relu(nd.dot(layer1, W2) + b2), 0.2)\n",
        "    return nd.softmax(nd.dot(layer2, W3) + b3)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HW4Jzb46EyyD",
        "colab_type": "text"
      },
      "source": [
        "##Defining our objective function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "avO1uf5fItMV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def categoricalcrossentropy(predictions, labels):\n",
        "    return -nd.sum(labels * nd.log(predictions))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3qr1NTDkE7Kh",
        "colab_type": "text"
      },
      "source": [
        "##Defining our parameters optimizer"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hvFKa4WuI9c-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sgd(params, lr):\n",
        "    for param in params:\n",
        "        param[:] = param - lr * param.grad"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lbHoiGM3ZrQY",
        "colab_type": "text"
      },
      "source": [
        "##Defining our accuracy function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-3osTW97ZuHR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def accuracy(predictions, labels):\n",
        "    return nd.mean(predictions.argmax(1) == labels.argmax(1))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UlkEn5XxFPkd",
        "colab_type": "text"
      },
      "source": [
        "##Training the  model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kVao6lbWCizF",
        "colab_type": "code",
        "outputId": "ab3ad68c-a1f7-46e4-c91c-c48a14269f1a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 185
        }
      },
      "source": [
        "epochs = 10\n",
        "num_batches = 60000/batch_size\n",
        "learning_rate = .001\n",
        "losses = []\n",
        "accs = []\n",
        "\n",
        "for epoch in range(epochs):\n",
        "    cumulative_loss = 0\n",
        "    cumulative_acc = 0\n",
        "    for features, labels in training_data:\n",
        "        features = features.as_in_context(model_ctx).reshape((-1, 784))\n",
        "        labels = labels.as_in_context(model_ctx).one_hot(10)\n",
        "        with autograd.record():\n",
        "            output = neuralnetworks(features)\n",
        "            loss = categoricalcrossentropy(output, labels)\n",
        "        loss.backward()\n",
        "        sgd(params, learning_rate)\n",
        "        cumulative_loss += loss\n",
        "        cumulative_acc += accuracy(output, labels)\n",
        "    print(f'Epoch: {epoch} Loss: {cumulative_loss.asscalar()/num_batches} Accuracy: {cumulative_acc.asscalar()/num_batches}')\n",
        "    losses.append(cumulative_loss.asscalar()/num_batches)\n",
        "    accs.append(cumulative_acc.asscalar()/num_batches)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch: 0 Loss: 91.01678333333334 Accuracy: 0.5009833333333333\n",
            "Epoch: 1 Loss: 24.889610416666667 Accuracy: 0.8861333333333333\n",
            "Epoch: 2 Loss: 16.524120833333335 Accuracy: 0.9255833333333333\n",
            "Epoch: 3 Loss: 12.392048958333334 Accuracy: 0.9443666666666667\n",
            "Epoch: 4 Loss: 10.018997916666667 Accuracy: 0.9546333333333333\n",
            "Epoch: 5 Loss: 8.511573958333333 Accuracy: 0.9617166666666667\n",
            "Epoch: 6 Loss: 7.417365104166667 Accuracy: 0.9663\n",
            "Epoch: 7 Loss: 6.6508859375 Accuracy: 0.9693333333333334\n",
            "Epoch: 8 Loss: 5.983238020833333 Accuracy: 0.9727833333333333\n",
            "Epoch: 9 Loss: 5.368407291666666 Accuracy: 0.9754\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JJOc7DOepwEE",
        "colab_type": "text"
      },
      "source": [
        "##Lets see test accuracy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dvvQC3oQYu5A",
        "colab_type": "code",
        "outputId": "f6d152f0-e13d-4295-fac3-cb2da1dac13a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "acc = 0.0\n",
        "batches = 0\n",
        "for features, labels in testing_data:\n",
        "    features = features.as_in_context(model_ctx).reshape((-1, 784))\n",
        "    labels = labels.as_in_context(model_ctx).one_hot(10)\n",
        "    predictions = neuralnetworks(features)\n",
        "    acc += accuracy(predictions, labels)\n",
        "    batches += 1\n",
        "print(f'Test Accuracy: {acc.asscalar()/batches}')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Test Accuracy: 0.9686504777070064\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hIBgjWVBYu3t",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plot(losses = losses, accs = accs, model = neuralnetworks, samples = 5):\n",
        "    plt.plot(losses, 'r')\n",
        "    plt.title('Loss during Training')\n",
        "    plt.xlabel('Epoch')\n",
        "    plt.ylabel('Loss')\n",
        "    plt.show()\n",
        "    \n",
        "    plt.plot(accs, 'g')\n",
        "    plt.title('Accuracy during Training')\n",
        "    plt.xlabel('Epoch')\n",
        "    plt.ylabel('Accuracy')\n",
        "    plt.show()\n",
        "    \n",
        "    for i, batch in enumerate(test_mnist):\n",
        "        features = batch[0].as_in_context(model_ctx).reshape((1, 784))\n",
        "        labels = batch[1]\n",
        "        predictions = model(features).argmax(1).asscalar()\n",
        "        plt.imshow(features.reshape((28, 28)).asnumpy())\n",
        "        plt.title(f'Predicted: {predictions}, Target: {labels}')\n",
        "        plt.show()\n",
        "        if i == samples:\n",
        "            break"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mkorWu1EYu2b",
        "colab_type": "code",
        "outputId": "a9ff5371-0221-4a84-9160-85258cecc095",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 3477
        }
      },
      "source": [
        "plot(samples = 10)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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FV2JmdkjqDYL/Qvrq6DpgLfB24D051dQa/ItlZtYm6v3W0KqIeFNEdEXE0RHxZqC83xoC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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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SO4GrgQuyqqkc7d6/mx88+gO++dA3qd9WT830Gq477TrOOPwMX2xmZgddlkcKi4CVEfEi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\noWBmZm0cCmZm1sahYGZmbf4/loYUjRgaPlIAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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5EzdwzL6F9fMv+W5hfYiKf4VOW3xGxdped/v7+q3kLb9Zohx+s0Q5/GaJcvjNEuXwmyXK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\n+M0S5fCbJcrhN0uUw2+WqP8HMSMTgWJpncQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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8Zoly+M0S5fCbJcrhN0uUw2+WKJ/n3wZsnLRTxdrIl6e0sZPX2vzsmoq12FB++TaNLn//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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Ov1miHH6zRPmQXmuqB859dcXa/Yd8tanzvmHt+Iq1S884pvC+ox4sPlx4S+A1v1miHH6z\nRDn8Zoly+M0S5fCbJcrhN0uUw2+WKO/nt7p0zesurH+h+4YWdfJyc5a/qWJt1A+3/P341XjNb5Yo\nh98sUQ6/WaIcfrNEOfxmiXL4zRLl8Jslyvv5G2C4ik/Y3KXKp4quxer3HDDo+5772eIfWn7b6BcH\n/dhQ/bkVnwq7vuVSTfz98qY+/lDnNb9Zohx+s0Q5/GaJcvjNEuXwmyXK4TdLlMNvlqhaTtE9GfgW\nMIHslNyzI+LLkrYHrgemkJ2m+9iI+HPzWu1c51//rsL6sSddUtfj3/HFrxXWi/elF1sfg75rjY8/\n+N6q2XPuqYX1XbinafPeEtSy5t8AfCwidgcOAE6TtDtwJjA3InYB5ua3zWyIqBr+iFgREffk19cA\nDwITgSOAq/JhVwFHNqtJM2u8AX3mlzQF2Ae4C5gQESvy0pNkHwvMbIioOfySxgI3AB+JiNWltYgI\nsu0B5e43S1KvpN71rKurWTNrnJrCL6mLLPjXRsSN+eSVkrrzejewqtx9I2J2RPRERE8XIxvRs5k1\nQNXwSxJwBfBgRFxUUroFmJlfnwnc3Pj2zKxZajmk983ACcB9khbm0z4JnA98V9JJwBPAsc1psfNN\nvf7pwvr8940qrE8bWd9htZ1s/rrKz332k28tvO+fP1T59N4Ar//9Y4X15u1k3DJUDX9E/BpQhfLB\njW3HzFrF3/AzS5TDb5Yoh98sUQ6/WaIcfrNEOfxmiVL2zdzW2Ebbx/5Kb+/gC0dMK6wvPbz4p78f\nOewbhfVmHjZbTbWf7t7r6/9WsTb5c3c2up3k3RVzWR3PVNo1vxmv+c0S5fCbJcrhN0uUw2+WKIff\nLFEOv1miHH6zRPkU3S0w+ub5hfVdq/wMykHHn1ZY7zpxZcXaT/e4vvC+hyw+rrC+ac6rCutRZY/y\nlIVPVaz5ePv28prfLFEOv1miHH6zRDn8Zoly+M0S5fCbJcrhN0uUj+c324L4eH4zq8rhN0uUw2+W\nKIffLFEOv1miHH6zRDn8ZomqGn5JkyXdLukBSfdL+vd8+jmSlktamF9mNL9dM2uUWn7MYwPwsYi4\nR9LWwN2SbstrF0fEl5rXnpk1S9XwR8QKYEV+fY2kB4GJzW7MzJprQJ/5JU0B9gHuyiedLmmRpCsl\njatwn1mSeiX1rmddXc2aWePUHH5JY4EbgI9ExGrgUmBnYG+ydwYXlrtfRMyOiJ6I6OliZANaNrNG\nqCn8krrIgn9tRNwIEBErI2JjRGwCvgkUn43SzDpKLVv7BVwBPBgRF5VM7y4ZdhSwuPHtmVmz1LK1\n/83ACcB9khbm0z4JHC9pbyCAJcApTenQzJqilq39vwbKHR98a+PbMbNW8Tf8zBLl8JslyuE3S5TD\nb5Yoh98sUQ6/WaIcfrNEOfxmiXL4zRLl8JslyuE3S5TDb5Yoh98sUQ6/WaJaeopuSU8BT5RMGg88\n3bIGBqZTe+vUvsC9DVYje9sxInaoZWBLw/+ymUu9EdHTtgYKdGpvndoXuLfBaldvfttvliiH3yxR\n7Q7/7DbPv0in9tapfYF7G6y29NbWz/xm1j7tXvObWZs4/GaJakv4JR0q6WFJj0k6sx09VCJpiaT7\n8tOO97a5lyslrZK0uGTa9pJuk/Ro/rfsORLb1FtHnLa94LTybV12nXa6+5Z/5pc0HHgE+AdgGbAA\nOD4iHmhpIxVIWgL0RETbvxAi6SBgLfCtiNgzn3YB8ExEnJ+/cI6LiP/skN7OAda2+7Tt+dmkuktP\nKw8cCZxIG5ddQV/H0obl1o41/zTgsYh4PCJeAr4DHNGGPjpeRNwBPNNv8hHAVfn1q8j+87Rchd46\nQkSsiIh78utrgL7Tyrd12RX01RbtCP9EYGnJ7WW0cQGUEcDPJd0taVa7myljQkSsyK8/CUxoZzNl\nVD1teyv1O618xyy7wZzuvtG8we/lDoyINwKHAaflb287UmSf2TppX21Np21vlTKnlf+rdi67wZ7u\nvtHaEf7lwOSS25PyaR0hIpbnf1cBN9F5px5f2XeG5Pzvqjb381eddNr2cqeVpwOWXSed7r4d4V8A\n7CJpJ0lbAccBt7Shj5eRNCbfEIOkMcAhdN6px28BZubXZwI3t7GXzXTKadsrnVaeNi+7jjvdfUS0\n/ALMINvi/zvgU+3ooUJfU4F788v97e4NuI7sbeB6sm0jJwGvBOYCjwK/ALbvoN6uBu4DFpEFrbtN\nvR1I9pZ+EbAwv8xo97Ir6Ksty81f7zVLlDf4mSXK4TdLlMNvliiH3yxRDr9Zohx+s0Q5/GaJ+n+X\nawvz0N0dgQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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4zTLl8JtlyuE3y5R/ursVfnlPaXnLGr9tPHu/E0vry3fu3nH+rc/7eVP3X/L9XavW7txr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\nZcrhN8uUw2+Wqf8HUhwCDoDKAlkAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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F+YCh5psnaUDSwHa2NlWsmbVOXeGXNJoi+N+IiOvT5HWSJqX2ScD6oeaNiP6I6IuIvtGM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\nMuXwm2XK4TfLlMNvlimH3yxTDr9Zpv4fvKOx8+BAmnEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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NMuXwm2XK4TfLlMNvlimH3yxT/kqvJb00+SPJ+uP7XJysz1v9ZtXa0Bffbqgnaw1v+c0y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\nDr9Zphx+s0w5/GaZ+n8ipiWeX9R7+gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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6ICCARcA5EbG00sIGa2gcruLvuG+VhT88rLh+0g+a1Ek6fr9BhfXzHz2zsD70pIX1bOdN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\niXL4zRLl8JslyuE3S5TDb5Yoh98sUf8He2NhDNBT030AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}