17_generative_adversarial_networks_implementation.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyMAuQtEtatMLnjgs5oANTkA",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/dlsyscourse/public_notebooks/blob/main/17_generative_adversarial_networks_implementation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mpn1ti5Urdsv"
      },
      "source": [
        "# Lecture 17: Generative adversarial networks implementation\n",
        "\n",
        "In this lecture, we are going to implement a version of generative adversarial training.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qXysoqn-vZuF"
      },
      "source": [
        "## Prepare the codebase\n",
        "\n",
        "To get started, please clone a version of needle repo from the github. You should be able to use the need repo after finishng HW2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JjEIRTyr8ajf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f459c270-8644-4eaa-be48-5bc265b32879"
      },
      "source": [
        "# Code to set up the assignment\n",
        "from google.colab import drive\n",
        "drive.mount('/content/drive')\n",
        "%cd /content/drive/MyDrive/\n",
        "!mkdir -p 10714f22\n",
        "%cd /content/drive/MyDrive/10714f22\n",
        "# comment out the following line if you run it for the second time\n",
        "# as you already have a local copy of code\n",
        "# !git clone https://github.com/myrepo/needle lecture17\n",
        "!ln -s /content/drive/MyDrive/10714f22/lecture17 /content/needle"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n",
            "/content/drive/MyDrive\n",
            "/content/drive/MyDrive/10714f22\n",
            "Cloning into 'lecture17'...\n",
            "remote: Enumerating objects: 917, done.\u001b[K\n",
            "remote: Counting objects: 100% (184/184), done.\u001b[K\n",
            "remote: Compressing objects: 100% (115/115), done.\u001b[K\n",
            "remote: Total 917 (delta 104), reused 122 (delta 68), pack-reused 733\u001b[K\n",
            "Receiving objects: 100% (917/917), 265.21 KiB | 1.99 MiB/s, done.\n",
            "Resolving deltas: 100% (531/531), done.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Xe3vClsD9jlq",
        "outputId": "ede8f7b5-3e3b-45de-e52b-590fe67e6f38"
      },
      "source": [
        "!python3 -m pip install pybind11"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting pybind11\n",
            "  Downloading pybind11-2.10.1-py3-none-any.whl (216 kB)\n",
            "\u001b[K     |████████████████████████████████| 216 kB 5.3 MB/s \n",
            "\u001b[?25hInstalling collected packages: pybind11\n",
            "Successfully installed pybind11-2.10.1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DFxG3p3S1sBq"
      },
      "source": [
        "We can then run the following command to make the path to the package available in colab's environment as well as the PYTHONPATH."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bix8OXLuCOKt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a8ccf8ba-ff33-441e-ddd3-4697dd625b5c"
      },
      "source": [
        "%set_env PYTHONPATH /content/needle/python:/env/python\n",
        "import sys\n",
        "sys.path.append(\"/content/needle/python\")"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "env: PYTHONPATH=/content/needle/python:/env/python\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BBIuE2jc1DaU"
      },
      "source": [
        "## Components of a generative advesarial network\n",
        "\n",
        "There are two main components in a generative adversarial network\n",
        "- A generator $G$ that takes a random vector $z$ and maps it to a generated(fake) data $G(z)$.\n",
        "- A discriminator that attempts to tell the difference between the real dataset and the fake one.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T-1piPnmkMVg"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_mBCkBtSa54H"
      },
      "source": [
        "import needle as ndl\n",
        "import numpy as np\n",
        "from needle import nn\n",
        "from matplotlib import pyplot as plt"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cbT1kk_4k6HE"
      },
      "source": [
        "### Parpare the training dataset\n",
        "\n",
        "For demonstration purpose, we create our \"real\" dataset as a two dimensional gaussian distribution. \n",
        "\n",
        "\\begin{equation} \n",
        "X \\sim \\mathcal{N}(u, \\Sigma), \\Sigma = A^T A \n",
        "\\end{equation}"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qrIYM_PDbhFm"
      },
      "source": [
        "A = np.array([[1, 2], [-0.2, 0.5]])\n",
        "mu = np.array([2, 1])\n",
        "# total number of sample data to generated\n",
        "num_sample = 3200\n",
        "data = np.random.normal(0, 1, (num_sample, 2)) @ A + mu"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "3yDlolmEizvN",
        "outputId": "d1854b12-26ff-4b51-f0ea-b1630b1e992f"
      },
      "source": [
        "plt.scatter(data[:,0], data[:,1], color=\"blue\", label=\"real data\")\n",
        "plt.legend()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fc63ddf0990>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nz4nFUT8m0wO"
      },
      "source": [
        "Our goal is to create a generator that can generate a distribution that matches this distribution."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1InC1BAQnC6l"
      },
      "source": [
        "### Generator network $G$\n",
        "\n",
        "Now we are ready to build our generator network G, to keep things simple, we make generator an one layer linear neural network."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7MPePSoJm_YW"
      },
      "source": [
        "model_G = nn.Sequential(nn.Linear(2, 2))"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ibevU5pCnStH"
      },
      "source": [
        "def sample_G(model_G, num_samples):\n",
        "    Z = ndl.Tensor(np.random.normal(0, 1, (num_samples, 2)))\n",
        "    fake_X = model_G(Z)\n",
        "    return fake_X.numpy()"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2cifleRqj-j2"
      },
      "source": [
        "fake_data_init = sample_G(model_G, 3200)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "n-ZhutLVkGgU",
        "outputId": "0baf6625-7c0b-4a81-df5f-c7d8c4217a37"
      },
      "source": [
        "plt.scatter(data[:,0], data[:,1], color=\"blue\", label=\"real data\")\n",
        "plt.scatter(fake_data_init[:,0], fake_data_init[:,1], color=\"red\", label=\"G(z) at init\")\n",
        "plt.legend()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fb60d4aed50>"
            ]
          },
          "metadata": {},
          "execution_count": 60
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KVNer3vnpDxm"
      },
      "source": [
        "At the initialization phase, we just randomly initialized the weight of $G$, as a result, it certainly does not match the training data. Our goal is to setup a generative adveserial training to get it to close to the training data."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MsI-zBsgp9tC"
      },
      "source": [
        "### Discriminator $D$\n",
        "\n",
        "Now let us build a discriminator network $D$ that classifies the real data from the fake one. Here we use a three layer neural network. Additionally, we make use of the Softmax loss to measure the classification likelihood. Because we are only classifying two classes. Softmax function becomes the sigmoid function for prediction.\n",
        "\n",
        "\\begin{equation}\n",
        "    \\frac{\\exp(x)} {\\exp(x) +\\exp(y)} =\\frac{1}{1 + exp(y-x)} \n",
        "\\end{equation}\n",
        "\n",
        "We simply reuse SoftmaxLoss here since this is readily available in our current set of homework iterations. Most implementation will use a binary classification closs instead (BCELoss)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oettjmbLp9a8"
      },
      "source": [
        "model_D = nn.Sequential(\n",
        "    nn.Linear(2, 20),\n",
        "    nn.ReLU(),\n",
        "    nn.Linear(20, 10),\n",
        "    nn.ReLU(),\n",
        "    nn.Linear(10, 2)\n",
        ")\n",
        "loss_D = nn.SoftmaxLoss()"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AtcTUZertq3D"
      },
      "source": [
        "## Generative advesarial training\n",
        "\n",
        "A Generative adversarial training process iteratively update the generator $G$ and discriminator $D$ to play a \"minimax\" game.\n",
        "\n",
        "\\begin{equation}\n",
        "    \\min_D\\max_G\\{-E_{x\\sim Data} \\log D(x) - E_{z\\sim Noise} \\log(1- D(G(z))\\}\n",
        "\\end{equation}\n",
        "\n",
        "Note that however, in practice, the $G$ update step usually use an alternative objective function.\n",
        "\n",
        "\\begin{equation}\n",
        "    \\min_G \\{-E_{z\\sim{Noise}} \\log(D(G(z))\\}\n",
        "\\end{equation}\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mwzkIy2VsxZe"
      },
      "source": [
        "### Generator update\n",
        "\n",
        "Now we are ready to setup the generator update. In the generator update step, we need to optimize the following goal:\n",
        "\n",
        "\\begin{equation}\n",
        "    \\min_G \\{-E_{z\\sim{Noise}} \\log(D(G(z))\\}\n",
        "\\end{equation}\n",
        "\n",
        "Let us first setup an optimizer for G's parameters.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DFEqvNyJpEcP"
      },
      "source": [
        "opt_G = ndl.optim.Adam(model_G.parameters(), lr=0.01)"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fCJtUQFUu-mo"
      },
      "source": [
        "\n",
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fexOFSSZvjRu"
      },
      "source": [
        "To optimize the above loss function, we just need to generate a fake data $G(z)$, send it through the discriminator $D$ and compute the negative log-likelihood that the fake dataset is categorized as real. In another word, we will feed in $y= 1$ as label here.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NhPHESKKpCoA"
      },
      "source": [
        "def update_G(Z, model_G, model_D, loss_D, opt_G):\n",
        "    fake_X = model_G(Z)\n",
        "    fake_Y = model_D(fake_X)\n",
        "    batch_size = Z.shape[0]\n",
        "    ones = ndl.ones(batch_size, dtype=\"int32\")\n",
        "    loss = loss_D(fake_Y, ones)\n",
        "    loss.backward()\n",
        "    opt_G.step()"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9Qsn3cFwv-f5"
      },
      "source": [
        "### Discriminator update\n",
        "\n",
        "Now, let us also setup the discriminator update step. The discriminator step optimizes the following objective:\n",
        "\n",
        "\\begin{equation}\n",
        "    \\min_D\\{-E_{x\\sim Data} \\log D(x) - E_{z\\sim Noise} \\log(1- D(G(z))\\}\n",
        "\\end{equation}\n",
        "\n",
        "Let us first setup an optimizer to learn $D$'s parameters."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WOf4qlOvv-JV"
      },
      "source": [
        "opt_D = ndl.optim.Adam(model_D.parameters(), lr=0.01)"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WfBh-6Adwnw9"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c3gqNBcnxCF0"
      },
      "source": [
        "The discriminator loss is also a normal classification loss, by labeling the generated data as $y=0$(fake) and real data as $y=1$(real). Importantly, we also do not need to propagate gradient back to the generator in discriminator update, so we will use the detach function to stop the gradient propagation.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H4RwEfQ4nluL"
      },
      "source": [
        "def update_D(X, Z, model_G, model_D, loss_D, opt_D):\n",
        "    fake_X = model_G(Z).detach()\n",
        "    fake_Y = model_D(fake_X)\n",
        "    real_Y = model_D(X)\n",
        "    assert X.shape[0] == Z.shape[0]\n",
        "    batch_size = X.shape[0]\n",
        "    ones = ndl.ones(batch_size, dtype=\"int32\")\n",
        "    zeros = ndl.zeros(batch_size, dtype=\"int32\")\n",
        "    loss = loss_D(real_Y, ones) + loss_D(fake_Y, zeros)\n",
        "    loss.backward()\n",
        "    opt_D.step()"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S-0El6XyyPNe"
      },
      "source": [
        "## Putting it together\n",
        "Now we can put it together, to summarize, the generative adverserial training cycles through the following steps:\n",
        "- The discriminator update step\n",
        "- Generator update step"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EeF1zzALyO83"
      },
      "source": [
        "def train_gan(data, batch_size, num_epochs):\n",
        "    assert data.shape[0] % batch_size == 0\n",
        "    for epoch in range(num_epochs):\n",
        "        begin = (batch_size * epoch) % data.shape[0]\n",
        "        X = data[begin: begin+batch_size, :]\n",
        "        Z = np.random.normal(0, 1, (batch_size, 2))\n",
        "        X = ndl.Tensor(X)\n",
        "        Z = ndl.Tensor(Z)\n",
        "        update_D(X, Z, model_G, model_D, loss_D, opt_D) \n",
        "        update_G(Z, model_G, model_D, loss_D, opt_G)\n",
        "\n",
        "train_gan(data, 32, 2000)"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KCqCAuzazp8B"
      },
      "source": [
        "We can plot the generated data of the trained generator after a number of iterations. As we can see, the generated dataset $G(z)$ after get closer to the real data after training."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "2gWdtbKEs1vW",
        "outputId": "b781a776-4053-463b-ae04-8b52897c0cd6"
      },
      "source": [
        "fake_data_trained = sample_G(model_G, 3200)\n",
        "\n",
        "plt.scatter(data[:,0], data[:,1], color=\"blue\", label=\"real data\")\n",
        "plt.scatter(fake_data_init[:,0], fake_data_init[:,1], color=\"red\", label=\"G(z) at init\")\n",
        "plt.scatter(fake_data_trained[:,0], fake_data_trained[:,1], color=\"pink\", label=\"G(z) trained\")\n",
        "\n",
        "plt.legend()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fc6354e5b90>"
            ]
          },
          "metadata": {},
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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iExV9o6i/bkd8z6RU7mEf9Lp1ZYZPRJUALgTwr6ZtcwCAmR8BcAWAuUTUBeAwgKmcjxJfXQODLAI+p556Kn7zm9/03H/wwQfR2tqKCRNUYVu28shWGAJqQLx8cjQaRXl5ueVzrCSSmRkXXnghli+Pvy5LIxTBl7RElKG3IEDA9f/ciu9MjqBvGdA3pMxNzfBO/M+MZgDVyjVkzMYtGDVUbW9vB95+PoK6USnqATQeBdXrVu1jXECAwriGXJnhM3MbM4eZeb9p2yMxYw9m/jkzn8rMY5n5HGb+sxvnTUkOAj65lkdOJV2sk092wjnnnIO33nqrZ3xtbW3YtGkTTjrpJDQ1NeHvf/87ACRdEATBc7REgI+bbHchAgZWco+xN6gsN7l1zxkDBIOWzze3LPy3f3ZQD6C5cHip121xSytkEfDRkWt55PPPPx8bNmzoCdomopNPdsKQIUPwq1/9CtOmTcOYMWMwceJEbNy4EeXl5Vi0aBG+8Y1vYPz48Rg6dGgmb40guIvZhWL8Ga6UrTuUklmmGMa5JZJsyAF0dAK3Le6dGBqzfe1xAK3nwEu9bkU8LQeIPLIgZEmipILLdHcDO/8Rwohwp1XHQuzZF8TQy8/oub91xXrUDNe4h88Zox1z+5EArvtJNZavip9k5lJ4TcTT8ozIIwtCllj5w10kEABGVlkbewAID4x3ld62eATaOuLNZVtHAG9+ZnIPxzwKh7pCiDLQtCuE7z1Ujadfjzf2hczl96XFYWaQ7pPyAOXl5Zg+fbr28RNOOAEnnHBCHkeUPV5eCQpFQGI6o4uZdFakMh+Jbhhjhv7jWTswamivFMOft4RRf7i3OcrgwWEcPBifDhoKAeEwsHevqt5NK83TZXxn8MvLyxGJRBAOhz1t9IsJZkYkEtFmBAlCVlgpYqaBMRdxyxwwA5Xl3ZhWG4lzxSxfFU5yzQDxmvoRi2Tzzk6gf3+gNanqKP/4zuCPHDkS27dvR9ZVuEJalJeXY+TIkYUehlAsmGf0WdLdDbjhHWXurcodckw3Ft+s0i6tjLxBMKhX1DTjFe183xn8srIyjB49utDDEAQhU9IJyKZw77R1BNAvlL2v3zD2ZirLo/jxrB1YviqMcBg4cAA4erT38YoKZ8Ye8I52vgRtBUHIL04DskYGzHkTgOOqejYzoycoOuueasu0R7cYNbQTFRXAwoXAY4/16uqEw4DDuklPCa6JwRcEIb84ceOYCyRbIsCuXuc4EUBQxnjh/G0YPOBoVin5bR0BtO7XF1+1twPXXAMYeRhz5gCHD1v76w369/em4JrvXDqCIPgcJ1k4AZN/Zcu2pCIrs689U5iB5pZQT4HV4pubVRVujLaOQM9jRkF7czNgKrLXEg4DNgXzBUMMviAIeaOhAXj7+RH4nxnxxhWAsuCGYe/qRvSjrdj0t4M4aUDmRj0Vo6eOibufmHZpF7C1wytB2kTE4AuCkBeMpuDt7WG0tvYa1/ZoCP3Lu4GueMMeIODE/q2WAVWn2D030Y2jS7vMBK8EaRMRgy8IQl4wNwU3G9fqaqBpaXJPByC73PojnYSyPmx5DGbgpgdyY5W9FKRNRIK2giDkBSs3x7TaCP628F3Xz8UMLP59WJvB07o/aKlvU1vbK55pI5cfR//+ymfvxSBtImLwBUHIC4abw9yQZNmCrVkFXnUQAfMub8XH20KWGjiJs/vKSuDQIWD1amDkSGDZMuD4452dKxpVaZvRqBJE86qxB3yolikIgj9paABefiKCRf+2FWV5ciZHo8BDz1bhki8fSCsYm05RFZBb9ct0sVPLFB++IAh5oa4OuPJzTSjLo18hEAAu+fKBpGycVLS3K9eO0/5CXs3KSURcOoIg5I1QIP8eBW3zkhR0d6uZvhMCgcL2qnWKzPAFQXCfRLnj0SOy6jSXDZlKL4RjwzVcO4GAXhGiu7uwvWqdIjN8QRDcxRBHM6ppj3SqZuOv5T8eZ5Y6TpdIJF4+IRhU2vY6Ctmr1imuGXwiaiKi94loHRElfbKkuJ+IthDReiIa79a5BUHwEJu35bRbVTqYpY4zMfpmjh4FBgxQAVodXvfluz3DP5+Zx2kixP8E4ITY32wADhQpBEHwFS0R55HOPGJIHWfL3r0qG0dn9L1aYWuQT5fOZQD+HyvWADiGiI7L4/kFQcg1m5oLPQIt5uCtuRZg64r1jmf/gwer//X1yQFdL1fYGrhp8BnAi0S0lohmWzw+AsCnpvvbY9viIKLZRNRIRI3S1UoQfMSmJs+4cqwwgrfTaiNYfHMzaoZ3IhAAaoZ3Onb5HDigsnHq6lRFraGP7/UKWwPXCq+IaAQz7yCioQBeAjCfmV83Pf57AHcx85ux+6sA/AczayM5UnglCB7HxVaFuaStI4BZ91Rj+aowtq5Yj5rhyeNt2hVylK/vpSIrK/JSeMXMO2L/dxPRMwDOAvC6aZcdAMzFyiNj2wRB8BM+MfIGXV3oMfaAPi/fab6+1wOzdrji0iGiSiIaYNwGcBGADxJ2ew7Ad2LZOucA2M/MO904vyAIeSIx5dIHBALxjch1efnG9lBIaen4NTBrh1s+/GEA3iSi9wD8FcAfmPlPRDSHiObE9lkJ4BMAWwAsBjDPpXMLgpAvnPajLQA673Sigb9t8QhLQTWju1Vnp8qn92tg1g5XXDrM/AmAsRbbHzHdZgDXu3E+QRDyTMyNwx2dWWnU55KubqCzK6BtU2hgzPbtultt29YbgF2wQN0fNUoZe68HZu0QtUxBEOxpiaBrQzP6BLw5szdgBh58Jn1lTCu8Hpi1Q9QyBUHImEMf7ED/Pt429oBKj8xEGTMRv7tt7BAtHSEzGhqAmhoVEaupSU8qMJvnCvmjJQKsWY/KoHWA1ovOAbtMm9pavfql4abySz59psgMX0if3m7U6n5zs3OpwGyeK6RHNoqVRjZONKr12XvRl2+njLllizLmCxaor52hd19d7X/fvFPEhy+kT02N+sUk4sTxmc1zBeeYDHYPgQDwxWpnRn/Nel+lXgLxxVU6PGzuXMPOhy8uHSF9dJUnTipSsnmu4Byr9MloVG13go+MPbOqkk1l7I3m5KVMaRn8Uvcdz5sH9Omj1uJ9+qj7Tkh83wwFqUScVKTo9vFzNYsX0Rls03bjY627MILtv1kPfrVRzexbIsoF5COcZON4UMQz75SOwTd8x83Nakpg+I5LxejPmwc8/HDvt767W91PZfSt3reDB4Gysvj9nKY2FGM1ixfRGezYduNj/fIXIlj0780YWRXLrz/SqVxBgweiK+oP80AER9LHMsMvJR9+qfuO+/SxnuIEg0psRIfufQuHgf79M6tIaWgormoWL5LCh298rDohMbNZ8GJwNpFoFAh+3dJtHYeHzZ1riA8fEN+xbj2bap2re3+MThDRqPqfjsGuq8v8uXaUusvOzLCwMu7GTL9vKC5ga3ysujRGot4/L+FUPsEKu05VpULpGPxC+Y69YoR061mr7eYxBzRfEa/53EvdZWfFsDBwzhjgvAnqvyk7x/j4Igf84+eIRlUlrZ0Ojg7xGipKx+AXwndcaCNkNtz9+lnvMzuhV03imK1WAMb75pWLGaBcREZuv4Efukq7jJOPpKEBOHRI3e5b5v0K2h4ImH9/DWbdU42mXSG1QEyRneOn5iT5oHR8+ED+fceFjBskFjgBvX58ZjWznz0beOih+OfpxhwMqimW8b4BycevqCjcLysQ0K/3S6SyxuojT/xIEveJvtLoObeNjq4u9TGno5GzbFnRf+xJiA/fIFe+Yx2FjBtYzXi7upTBZla3E4293dii0fj3LRcz6lTTU7vH7VxMbq+svLSyMaH7SF5+QqVdRl9pxKQ+63HZRGf9W70Es5qvpNuScObMPAzOR5SWwc83hcw5T3Wx0RktuzGbn2O1CrA7bypSub+sHp8+Xa3Za2qAKVP0QimAe+6dQrvpbLB666fVRvDzG1XapWEsG/5zK/b/YS0euLEp72PMBObk4HFledRRKmZnpyc+Gs9QWi6dfONkjZ0r7NxJ9fX6cQHWj11zDbB0afIU0ur4ZneVUzdaKveX7vHEMa5cqd+PKPvmHR5O77Uami7tErA2pF6DGWAAAYtxOk3F9MBHk1fEpVMoCtna3i5IbeeOSRxzOKwCvg8/nNrYm4PgDQ1AVRVw9dXOZsOpViSpVg7t7crYNzXltjedh9N7rfIPRg3TSyR43dgbsOYa7SQVE/DER+MZxODnkoYG4Kabeg2ekRqRD+wuNqmMlhHrePxx4PBhIJLCV5p4fGNlY/U8nWtFZ4wDAXU8J8baGH8uM7K8JA0Rky/Ga0oSobpfBIGAcuNsXbEe3asb4RObroXIOnPYSSqmgdcyiAuJGPxMcJr7NnNmvNGLRIAZM+L3z2UAUBektjOu5nFYrQQSqa5OPn6q51ldcKyMNKCyimbPVj76VBivK5crq3QuJrn8bBObiR/pxBmVzVh4QxMW39yMmuHKZ++XWbyBEw9zVxdSCqUZSP59PGLw08Vp0G7BAhUxSuTo0d4ZbjoBQDeNh51xNY/Dzmdu0NysrEpVVe+YUq2hrS44hpG2ms4Z7pqwzQ88FIr/ZVtd7Nx4D51eTHId3LVQw6wsj2LuZa1xPV2LkUAAjox9MCj594lkbfCJ6HgieoWINhDRh0R0k8U+XyOi/US0LvZ3e7bnLRhO0xHtjJ7xmN2xzMapqkqtDNwyHobRsjOg7e3pqU2ZVy92a+jEKZfxOolU0FUn9WBcfBJF2wxSTQ3dNMBO0nuzTFtNdW3iDmvfvK4w2g8wAwfbUy9JnPjuidRXyfgpCQo3vh5dAH7AzKcAOAfA9UR0isV+bzDzuNjfnS6cN/dY/eqcBu3sjJ7xmO5Y5hk2szKmR4/G7+NGmuHhw/aPd3fbpzomYqxedCuIcNi6Csgw5ql0fSIRvcDL0aMqTVOXu3/11akNsJurqCyCu06uTTsi1kbPby4cMwfbCXPurUmSTjCj892HQr3zF6Le67+HsmY9QdYGn5l3MvM7sdsHAXwEwFk0JRdk+qNNfN68eda/Oqda8PX16luYSFmZ8kfX1OhnpcFgat85oDceuvfAvP2aa5z5583uCyfTx23brN0ey5YBra3xs2EnMYJEOjv17xtzfIwk8YKiG2/ivm6417II7jpZHPzHIyOSDKOHM6xTcqRTGfvlq8Jx0gl79gWxZ1/QVkahuhpYskR9vaqrk9+HElTY0OJqHj4R1QB4HcBpzHzAtP1rAH4DYDuAzwD8OzN/qDnGbACzAWDUqFFnNjvxIxtkmvdu9TzzNMFMZaXanrjvnDnJlatGlo4RuA2HgX/5F/t89ooK50bQKsFY9x44zaM3M3du/GtyMn1MJ+nZTg4hG4wxVFWlzjBKledvVVfg5DtmtR+gvgMLF9p+H3Vvi7mM4MaqBvzXuD+iatZVwNBhaN3djb4DQhhY6U+r39EJzLx7tCPfvJnEj8fJe1fs5CUPn4j6Qxn175mNfYx3AFQz81gADwB4VnccZl7EzBOYecKQIUPSG0SmflOr5+kMUVsbMHFivPFjVsY0caZXV6d+3MZMt39/4Kmn9EbXmFHb+dYNdOkHuvdg0aL0Z9NPPaX+GzPaVJSV9YqqVVX1ul/MAV0zutVStmzbps6Xytib30PdxKK5OX7FYLUyam9X280zfl2cJBJJ6WNIuThoaMC9B2djyKoG0OIHQbtbUDU0iP4+DtaWh+KbmJhTS7euWG8po2D1E/BS1qwXcWWGT0RlAH4P4AVmvtfB/k0AJjBzq91+aVfaZnp5T3emabS7T8TJbFCHeYy6makxTruKVbdnzXPnAo8+mhxDsKK2VrlUZsxI3j8UUutu85j791cX0HQIhYABA+yNuVF4Zbc6NCqOAXWRdFLF63SFZJ7xZ1CZm3IRYRyzdjJw8wKgXKOE6jOMytlptREsvrk5LtsosUG5Tg+vkMXtXsFuhp+1wSciArAUwF5m/p5mn+EAWpiZiegsAE9DzfhtT562wU9nWW4u9z90KPVs0AmJFxbdeKwwxtjQoAKMTo5vRTrnzDfmz8HudRoEAsmvt6wMuO465xchKwy3CuD8gmw1FjuM15pqEpL4XZwyBVi5Ety8DTuCo04lnDwAACAASURBVPAf3fV4q7qu17i1RIBX/wwMHaae36eP8zF5nKZdIYyeOkYrB2E8nupnUOoN1XJt8M8F8AaA9wEYH8NtAEYBADM/QkQ3AJgLldFzGMC/MfOfUx07bYOfiT4soIwIUXzefEWF2mY1A3U6w3c627bTsTHjpK1gOquKfGP+paa6MIXD9hfhcBjo6Eh/hWBg9/m6heHOsXodOk2jRMzfX6u2hUWCeQbfvbrRMj/AWAGUmjZOuuTUh8/MbzIzMfMYU9rlSmZ+hJkfie3zc2Y+lZnHMvM5Tox9RjgpirHycR89qtwEic/7xS+sqypnz3ZWbalzHIbD1mO0y1oJhYADB/RqkYZP2PweeA1z3zw7Yz93LrBvn/2xIhF1gZ47N7PX2t6eW2MPqDHu369v+O4kS6m9HXj+j8Ca9eCPthadsWdOzr7R5dlv2x2SytksKT21zHT9/Lr1oZN1o13GzMqVyc+1WxGkmvFaZQql495Jdfx8osuQ8iu6lZmTFWCR+ekT6eoCyi6In4zqfPjff7ga510ZLin3TCbk1KWTS3Ji8DMIoqWN+WJgZKLs3dvro00M/hnLdl3wMB0DWFkJlJer81VWOhdsq662HpuQPbrJhJML8orngOHH5WRYXiDKQPD8ZNs0rTaCH8/agVFDO/HZ3hCaaATO/VZ6KZulisgjm8l1b9vEAp5IRFW0Pv64uqCsXKlPHa2vt851T+ei3NamzpmuOmdzs5JANiSR/VyymW/CYfuiNJ1rT1eRbGbosMzH5QOimuLq5avC+Py0MQicPwEj//cYMfYuUXoG300lRauKy1S1AHYl93V1hXdlmC8YgjMiEb1v3RB1s/qu2AnGGexuycWIPUMm10khc0rPpeMWOv+8zh1iLOtTuZS8nFYppI+uurqsDBg4ULneBg9WAXlzmmntZGDW9b0zfD+rotlgpFomQqQWxeKvTx9x6eQC3UxeN1szpiupXEpOlvmCf4hErLuFHT3au5JKFMe78WZgwZ3Kd2/0KChC7JqYMIuxzwXF+U3KFU6aeFspTBL1NvBI5VJKfLxIf+xCMgyomf3lVxT1587M4F070X7PvcCqP1nu48Ws4mJAXDpOcVrQZGS7PPJIvB880/puJwJgQtHAK54DFXFWDgBg105g6qUAgDZUYBYWYTl6fxdWKhyCc8Sl4wZOimQM18zKle5ptO7d62y/QCC9hiWCNymSrBztPLLjMLD4wZ67lWjHjxH/uxgwQIx9rhCD7xQHjSvQL1YcY6e86BTDfeR0BRaNpm4gInifA/sLPQLXaNoVQpRVcVU0CvCuncA99cCqF+L2G4X435YsaHOHGHyn6HLEzPnqhvStLoc9cQZu16jEaU9ZoXionQwaMLDQo3CN0VPHIHj+BJRdMAHBr09A89T5ScYeALYh/rdFlIcOVblsMO9hxOA7xSp7xqoCtr1dPys3z8DtOixl0glK8DdGZk6RuOWi+w+gGwFsRQ2mQRnT21CPNsT/htpQgdsQX/TInOMOVbluMO9hxOA7xSq7Jt2AdzDYO6O46SZ9gVYqbXahuCiyzBzu7ETwgZ8gAEYNmrEYszENDViOOszCIjShGlEQmlCdFLA1cOJBTYtU7T1LpA9icXzD8kVdnSqOikbVf13uWDhsbZi7u3tnFDpHZXOz3iVkpHAWySxQiDHr+uIx9sygu++Mc91YBWbV9kNYiJuSVgKAy1W2iTN6XazL9auM9yiOb1mh0BVRLVyYeS69TiiNqFdlcelSmekXE0WSmQNm4JlfW/rpR2EbpqEBizEbNWhGAIwhiGAIIkkrAdclkJ26SEtAy0Hy8LPFiUyyUyGysjL7Lk7mz8o4rwR2/Y/fFTGZ1ar3d78B338PrL7texBGOLAPAZ1aWoztwWq8trTJ3bRMJzLURdQHUeSRC40Tg6/romWgk2+Wwiz/UztZBWz96NaJRoFnnwbuv0e7yxGEECBGGTtoSemkjWe66PSpgkF1riLrg2hn8IunIaaXcdJcJFUOvW6NK8bev9ROBub/ABh0TKFHkj7MQMsuVURl4cIx6EIQXDkAZW0Ov6e5cKtYtZIsohl9OvhwSuFDFi7MbvYWDsd/Mc0ZB4K/qJ2sXDir31az+mOO7W376CdadgFTLwWvegGMmA6QBX0oivJ2h9Xiuepf6KYkus9xxWIQ0cVE9DERbSGiWy0e70tET8Yef5uIatw4ry9oaFApmJkuU40gsPl45owDwT8Y7Qr9roJpkkcwLlNRS889lPSzk1l7ro1wYoZdCRp7wAWXDhEFATwI4EIA2wH8jYieY+YNpt2uBfAPZv4CEU0FcDeAq7I9t+dJJbgWCNhfCKqrk32LUpTlX2Zd7+/etBo3DgEI6ub4R46kPq6b7UUFW9yYYpwFYAszf8LMnQBWALgsYZ/LACyN3X4aQC2R39awGZDKOOuMPRGwbJn1TESycvyL39Mv9+9TKpc2PvskDh1KHWdqbi45iYNC4YbBHwHgU9P97bFtlvswcxeA/QCKv0llpoUcVt0fDL+94F/83q5w4KDcHTsdiQMrHZwS1cZJF885EYloNhE1ElHjnj17Cj2c7LDzXVZUqGCsFYkVvCKmVhwsflD5v/3Kgf29AecVz6mYhNukkjiw0sGZMQOYObMktXHSxQ2DvwPA8ab7I2PbLPchoj4ABgGwXOcx8yJmnsDME4YMGeLC8AqIrl1hOKwCVAsX2rc7NBC/fXGw6gUlD7zvH/4LuHd2AhWVvQHn4cepALSd0c/Ua6tbGTc0WOvgHD2qxmemRLRx0sUNg/83ACcQ0WgiCgGYCuC5hH2eA3BN7PYVAFazlyu+3MIqHWzZMqC1VT3mNF2sBDQ+SoZVLwCXX1ToUaRHVxfQ3qZaUZkp76cC0Toy/Ykzq99DMAj0768uMFVVytin0/NBfjdJZG3wYz75GwC8AOAjAE8x84dEdCcRXRrb7ZcAwkS0BcC/AUhK3SxajHSwxx9X96dPj/cxOkkXKwGNj6LHnH//h1cKPZr0CAT0/vtUgehshP6iUaCtrbfRe7oNftL53ZRIDMCVSltmXglgZcK22023OwBc6ca5fElieqbhYwSc5QNbVQqGQqoXnFUGhF26Z0WF+kJv2GD9eCLhMPCPf7hf7l5KGPn3RkpmZf/CjiddjGCzld5PqkB0vrqwhULxbp10irisfp/TpwNvvQU89JD7Yy0gngvaFiVWPvh0fIxWrp8lS5RriFm5icyPHXus9XGCQXWcDz9Uz5s71/68oRBw8KAY+2zxc/59Z6cKNlsFnBP60xaUJUsyr6S1+n0yA488UnQZQCKelg90an25EIpyej6d2mYopIJggweLTk82JOrk+KnsxPju7N8HPPCz3rz72snq4jV0mJrZp9DRyRtG4da8ecrQd3eryc3s2c5m6HZqmuEwcPiwr3R4RC2z0OjU+nJVYZjqfHYVwIYefyr1TkFP7WTgP25PDnL6hbZDwDfOL/QonNGnDzBokH5yMneuMvpWMuZA5hLjHq4OFrXMQqNT68uFUJTufGVlquoxELBfWRgTADH2mTP/B/419gDQzyfNdfr3V9INdivRRYuASZOSffQzZ6rvul3/CTt8mgEkPvx8kG+1vsTzhcPKwEcivc0qBPepnQw8+6I/5Y7NeLkiOBhUs3Zm9b1OZbC7u6199J2dqZ9rVxzp08w5cemUAtIkJfckZuL4lY7DqjjMC755K8z2ykknK6PJSTp2jkjFsAD1u0lsO+pjH77M8EsBMfa5pXYy8MM7/G3smYFdO71t7BNxMsuePTu92Xh1taqZOXy493djFIIZj3vY2KdCDL7Qi58ySbyCMbPv4/NwWKyhiaeNfaJ7pb5eHysJBHoDtlYSJ6GQimuZMeJqujRNI1DrU2MPiMEvDXR+yMR9Hn88u8rIUsTPOfYG0ah38untMDcCApThHTDAet/jj1fB2poaVURF1NtwJhgErr0WeOwx67iaLiDr00CtGTH4pUDiDyURY3Y6fbpk5zjFkEoYNrzQI3EHL8/szSQWQenclUY1u6Gg2dbWm6zQ3Q0sjbXnsJI10bmAfBqoNSMGvxSoq9PP8o00TSODR0jNjTerfrTDjysON5iXs3LM3HRTsjSyHXYKs+ZK98SLyJQpzlRsfYgY/FJBJ8V87LHOcpErK1NLMZQCtZOBy6/wbz/aRLwkj5CKSMRdmfBt26z19ZcuVcqcRdj0XNIySwmrasPp053P7InURaKtLbfj9DIrnrMWEfMbzMnSCaWGXTW5hytpUyHSCoIenQyDHWVlmVco+p3Vb/t7du9nQ2+nAus2udK5ygOShy/oqa9P3w89cGByG8ZSwS/+7s5O1VkrGlUNTIw8+//+L9WAxW/GHsjeABvxKieZaIkB2iJRzBSDX+rU1aUfrN27Vy13ly2zbuFYzPihL21XF3D3ncqwf/1s4IKJwPlneT/PPhXV1dmlDR97rEo9dnLhMHSnamqUCmein9+nPXPF4JcCqWYn6c7WjdmPWbMH8Lerww5zt6pZ1wMrn/duRlPHYeB/7vC3YddRWZld2nAkogy1IZuQal/DuD/yiPN+Fh5fCYgPv9ixkkJO1ALR7TNxIrB6dXo6Ik70TYBkfRKvcuPNyVk5HYeBjg7gGE2jmXzT3a3eTy9p1HuZcFitUrP9/iX6+Z381vKA+PBLGSfdtnRqni+/rJbA6aSn6YpTwuH448yZk707KNc58DfeDPzzlckrl/J+qserVy5Y3d1A/e3+d9lki5OKckAZ+zlzsj9f4nc92852eUBm+MVOvrttpTPLMaeJeu17WDtZFVfZuanMolqFZtdOZfBLGadNe4yUy3RUZJ0oZub7t6YhZzN8IrqHiDYS0XoieoaILIXAiaiJiN4nonVEJBY8n+S7TDwd7f+6OvXDe/zx3IwlG2Zdnzom4RVjD6i2g6WOE2Nvrpjdu9fZcSsq1Iog1XfaB5IM2bp0XgJwGjOPAbAJwA9t9j2fmcfprjxCjrBSCsx1mbhhyBM1ShJpaFCzrKuvzt1YMsWrBlS3EvJLumghqayMN9RO3I/hMNCvnwrcAmpyovtOp/qteSCgm5XBZ+YXmbkrdncNgJHZD0lwlWy6beXyC2q4fvKg1Z+Rs8jLBjQxLdRP8giFJPFiaWWgzY+ZdfGdpGPa/dasJBwKkNrpmg+fiJ4H8CQzL7N4bCuAf0D99n7BzItsjjMbwGwAGDVq1JnNmTQYFrIn1xkHmVT4GhjBOQcXiyMowwEMxBCkeWHxagerXTuVcZ91vVqFlHJmTiaZXkYHLENa5K23gF/8ItnHXlGhZvZW37FMZBd03/ccSDhkJa1ARC8DsNKAXcDMv4vtswDABADfYosDEtEIZt5BREOh3EDzmfn1VAOXoG0ByfUX1Gn6phUVFUrc6uGHtbswgLZwNeYfrMeRTmAxZqMSaQhv1U5WzciN/rRGgLaQfvtoVGXjlKJxTySfMguJZBKEzWNAN6ugLTNfwMynWfwZxv67AC4BUGdl7GPH2BH7vxvAMwDOyvC1CPki100g7AJZds2jAbXqWLlSvw8R3pq7DMMON+FXnXVYjjrMwiI0odqZe8eY3R9zbK+RN8ryC0U0Cjz7tBh7g0Lq3GQShHUa0M2xnz/bLJ2LAdwC4FJmtpw+EVElEQ0wbgO4CMAH2ZxXyAO5zjjQ+U/DYeU2spJzNrNtG7BwIbpC8fswCJgzB1evrIvzRi1HHUajCXVYhjakyP/3UhcrZiWV8OzTwP33FHo0/kLX/jBbDh1K3xA7SZ7Ig58/2yydnwMYAOClWMrlIwBARJ8jopWxfYYBeJOI3gPwVwB/YOY/ZXleIdfkOrvHKsC1bBnQ2qoeMx7XaaeMGoUG1GEWq5l7FIQmVGNm2eNomPSQdiFinu1HQehCwvFrJ3urixWR6kg25ZtqbIJzBgzIjcifIdGQjiF2kjyRh8ItKbwS9Fjp5+e7CYRN8LhmQZ02zAA4iwk/gHm4Hg+DAO8Gag2kuCp9qqvVjDydbDCnSQFuB1xd8vOLtIKQGU7z6XM9Bs3MyC7MMGWK/WGnoQFbUdNr7AFvuXKs8GptQC7JRh0TUFf9gwdVDwcnlJUpd2IqlyLgflPzPBRu9XHtSIKQKwwXTwKjRlnP4gcPBn75S/3hpqGhN2undrIy9F5y4+jIVW1AOJyXeoiMyEYd06CzUxVdOWnac/SoWtUaM/cFC/RLRbcraOvrrVezLhZJygxf8C26MAOgfuM6Ftb+EZUrVgCv/DW+GbkXpBJ0LtZoNDfFVaXSz6Ctzbm4WnOzypAB1JfManUQCrlfrZ5NkaRDxOALvqafyQNjJPjYSaQ8cGMTqhbc2Gvkvabhb3XRyWVKZnt7YWb32bhqgkEV4M8kIOv0AmdkyNx0k/XKYMAAXzY199i3XRCcYaXMcDimOGCstA0/fTcC2IoaPFD7HOZd3grympG3o6tLFVsVU0pmRYX68Jz61RPp7lbGtr4+vdTLvXvtM78SsbsYOhVeS4c8pGVKlo7gS+wKgevrgReuacDD3fHVtbziOdDw4/I3SDeIRlWbwmyorQX+8pfklD8z+WpIY3xAhr7MTTdlvsKorlbR+aeecnYMI6smmyrvxGO5iUvV7ZKlIxQddhk6dXXAQ8csSJJSIK9muTDrg5PmQK3h7knHHdK/PzBjhprZ2vmwzQYw28wYHYbhMlwhdXWq7iJT42u0H4xEeus47F6j4XNPJ9gaDudPbTbX1e0Qgy/4lFQZbP33WvxIvKqASQQcPGCvglldrdQbmdOTFTh0CJg5U91ubXXm+84kM4YIOOUU/cUilZF0GlBNxLhYGO4Pu5n+ggVqVZGOK2jhQqXbZLyuYFDdz4X/Pg9pmWLwBV+SshDY6key+EH79J00iEYZ3B0FGwY4WxfBwEHAPfWquCoaVf/vqQf+8oYy0uaZcboGoLNTuU6A3toKtzOSmFUmTFeXum1cWJxmmyxcmOzTTzfW0t5uvzoxLgoAsGRJ6ouM8fjSpb0Xwe5udT8XssZ56F0hBl/wJSkz2Orrk3R2sOoFoL0t63N3dzGo6ygoGAC5Jay2txWYMR147Y/AhV9WFbWvvmw9m6yvT/98kYhqNmMYqlx0YTL7n9Mt2qurAx57LN4IH3usij+k81q7u+0zcQypArM7adkya0O7cGF++9TmIS1TgrZC0dHQALz26wjqp21C1dAgsLsFZGjGr34761RMZlaG3sF+3M0I9Elxvo4OoG0vcPig8x4E8+Yp/3W6v1/jeID7ncaCQTXDzxSdjMY11yh11Obm1MFlIyhsVzBlJVWgkxHxSJ/adMhKD7+QiMEXnGD+rQ4eDEyZEMHiHzShb6j3u82dR8F334norPnoM3xo3sYW3bcPgY7DShbhwH5wWQhknk3u3wc88DPglZdiT7AwIrosDeOFOzGEVsdzOnNO59jZ2BNdlko4rGbjgP1rTrw4upH1ksfGJW4hWTpC0ZKYuhyJAD+buy3O2AMAhcoQmf9jfGfx2WjryN/XPjBwoHLPfP1s4IGfgYKB3qpeIqC8XO0YjepnjOYsDbNe+oIFaibKrAK6TguRjOM53Z9ZBTnDYTVmnZ88W2VKXTZKJNLrijJcRebXbO49O316r468Gz5x3TGmTCl4f9pMEIMv+BorF2vVIOssk6pB3Vi+KoxZ91Rn5XkAlLvGEebMICtxtvJ+arsdhr+9oUGlWJoLc2bMiDc2hvGzK2oyjjdlivNZfmenSvGMRlXQMhfBRbu4gpXP3DD+ut6zQPY+cSu/+sSJyp1W4P60mSAuHcHXWLlYo680WtoxZiBwvlrpdq9uzNiVf7QLOHqkGxWV9vnq3NkJuvvOXkkEXfzArrjK7KaoqrJOO6ysVC8u8coXCiVnJZl9+In+8lSY/da5kM6eN0/fttLOZ54Lt4vu9TU06GMfHnHz2Ll0RC1T8DVWipmt+4MYckzyLL91f6+B3rY7hJrhmaVo9gkCqz8chHPHtKOyXB+4o2BApVUa7G5RGj6J6OoDgsH4Gakux7xNk3l09Cgwd64KeCYarpqa9Iw9ED8D1yiYZsXKlfrH7Gb/bhcsJQaPzSsGI73VCicNGAqMuHQEX5PoYp1WG7GMMXZ0Ajc90Gs0bls8Akc6M0ulJAIunHAIj60cjKZdIX2cMtgn3h3wzJPJs9SOw8D/e9S6EOiYYzIaXw/MyohapUemawxzVV1qxm5Miec2xzJ0S7VMU0/tUjHtCrtyVaHsImLwhbyQq97MZhfrty+I4NFbmlE1qLvHpcMM7NkXxMy7R2P5qt4c7+WrwuiOZu7ODASAS758AKOnjkFzi6Zqs28oPh99xTLglP+lthuPjzsF+MPvrAuBElvp6QqF7HxTOiPqxBgGgznLB0+ioUH/OsLh+HMnRuqtKoOzuUBlumJwQ7s/x4jBF3JOrkUA6+qAprcjaPjPrajoGz+DJgKOdAXjjD2gZJL79c3uvKOGKpfQbYtHJGf+BALA6BHJTxoWBs4ZA5w3Qf0fFu59Ef37J+9vLvJZuDB5JRAKAf/6r/rgq86w65rIG1RUqOBsPrqdGV8QneFeuDB+m9UMHHDvAmUncWBXnZuL/rkuIwZfyDm5KFY0rxhunBpB1wa9/3REuBPTaiPYumI9ulc3YuuK9Uom2aFHR+eyaY+GUFGBnsyfpl0hRKPAoa4Q8MXqXmPulFQzy7o6tRIwZ4wsWQI89BAwZ06y0beb5SZmn4TDvWmX+ZjRm7Ez4Fbj0L1PRmprthcou3TOhQutXTdlZbl3eblAVlk6RHQHgFkA9sQ23cbMSZEXIroYwEIAQQCPMvNdTo4vWTrFgdvFiokxta0r1tsHYPsE0XaI4wKszC7IyZw0Gg0vh91LVsk228QLTeczId0vSD6Koezey0RZ53BYXQg88l7nrNI2ZvAPMfNPbfYJAtgE4EIA2wH8DcA0Zt6Q6vhi8IsDt3+ficdLmWIZDGbmX+0TBLpsnnee5W8qc3TSAvmcbReCdL8g+XyffHgRLXSl7VkAtjDzJ8zcCWAFgMvycF7BI7gtAphoG7bttpG6JUrL2DNDBVNPGg1MOiOzAWZKHsSzPEm6X5B8vU956ECVb9ww+DcQ0XoiWkJEx1o8PgLAp6b722PbLCGi2UTUSESNe/bs0e0m+Ai3f5+JLlTLoKlBmivYtu5QfDC1jybVTrc9W9JVmSwGMvmC5ON9yqdSZp5I6dIhopcBDLd4aAGANQBaATCA/wPgOGaemfD8KwBczMzXxe5PB3A2M9+QanDi0hGssPK9T6tVWTrZ+OW7o0BwRBWw9wBwpFPN9AcPBHZF4i8cRMCJNekHZQV/4UOlTCBLlw4zX8DMp1n8/Y6ZW5i5m5mjABZDuW8S2QHgeNP9kbFtgpASq/x9q+y35avC2BFJo6F1IkTK2LfsVcYeUP9b9gLDw/G582LsS4M8dKDKN1m5dIjIXCf+zwA+sNjtbwBOIKLRRBQCMBXAc9mcVygNdC7UKVOsXb5NNCK5eMepYA4RsPsfyTO3aFTN+K1y54XiJg8dqPJNtj78nxDR+0S0HsD5AL4PAET0OSJaCQDM3AXgBgAvAPgIwFPM/GGW5xVKAJ0LdeVKa5fvud8Kq/x382zcfN+OaFQf3D2SmeaO4HOKMIguapmCZ3HNhdoSATY1Z+537RsL5AqCDyh0WqYgZIRrLtRhYWczfZ0Q1+CBaZ5QELyJGHzBs7jqQjVr2OhUDYmAYYOTt7fsVasEQfA5YvAFz5IzF6rOV9/drQK0iUSjwFZJLBP8jzRAETxNLvpsoG/IOhCr2w5I4FYoCmSGL/iajHT2R2vSN0eP0Pv5nWT6CILHEYMv5JxcNT/JWOokMYjb1yRnbHcxEASfI2mZQk7JpbBhzlRyWyLKZ2/IK4weIcVWgm/ImTxyrhGD739yKV3uU6kTQcgpkocvFIxM24M6oQilTgQhp4jBF3JKLo2yOU/f3MLwg1+ul7x5QbBA0jKFnFJfb+3Dd0N/yogBvP18BP8zo7mnhWH/QKeSUgDE9y4IJmSGL+SUXOtP1dUB939vR1y/WgBSLCUIFsgMX8g5OSmeMiPFUoLgCDH4gj8xp07qkGIpQYhDDL7gP5zIHUuxlCAkIQZf8B9bd9gbeymWEgRLxOAL/sPOjXOeZb2JIAiQLB3Bj4jAmSBkhBh8wX+IwJkgZIS4dAT/YfjmReBMENIiK4NPRE8CODF29xgA+5h5nMV+TQAOAugG0KUT9hEExwwLi4EXhDTJyuAz81XGbSL6GYD9Nrufz8yt2ZxPEARByBxXXDpERAD+BcDX3TieIAiC4D5uBW2/AqCFmTdrHmcALxLRWiKabXcgIppNRI1E1Lhnzx6XhicIgiCknOET0csAhls8tICZfxe7PQ3AcpvDnMvMO4hoKICXiGgjM79utSMzLwKwCFANUFKNTxAEQXBGSoPPzBfYPU5EfQB8C8CZNsfYEfu/m4ieAXAWAEuDLwiCIOQGN3z4FwDYyMzbrR4kokoAAWY+GLt9EYA7nRx47dq1h4joYxfG6DWqABRjAFtel7+Q1+UvnL6uat0Dbhj8qUhw5xDR5wA8ysxTAAwD8IyK66IPgCeY+U8Oj/1xMaZwElGjvC7/IK/LX8jr0pO1wWfm71ps+wzAlNjtTwCMzfY8giAIQnaItIIgCEKJ4HWDv6jQA8gR8rr8hbwufyGvSwMxS+ajIAhCKeD1Gb4gCILgEmLwBUEQSgRfGHwimk9EG4noQyL6SaHH4yZE9AMiYiKqKvRY3ICI7ol9VuuJ6BkiOqbQY8oUIrqYiD4moi1EdGuhx+MGRHQ8Eb1CRBtiv6ebCj0mNyGiIBG9S0S/L/RY3IKIjiGip2O/q4+IaGKmx/K8wSei8wFcBmAsM58K4KcFHpJrENHxUIVo2wo9Fhd5CcBpzDwGwCYAPyzweDKCiIIAHgTwTwBOATCNiE4p7KhcA7Ve3gAAArVJREFUoQvAD5j5FADnALi+SF6XwU0APir0IFxmIYA/MfNJUCnuGb8+zxt8AHMB3MXMRwAlz1Dg8bjJfQBugRKXKwqY+UVm7ordXQNgZCHHkwVnAdjCzJ8wcyeAFVATD1/DzDuZ+Z3Y7YNQxqMoWoUR0UgA3wDwaKHH4hZENAjAVwH8EgCYuZOZ92V6PD8Y/C8C+AoRvU1ErxHRlwo9IDcgossA7GDm9wo9lhwyE8AfCz2IDBkB4FPT/e0oEsNoQEQ1AM4A8HZhR+Ia/xdqAhUt9EBcZDSAPQAei7mqHo1J1GSEJ1oc2ilyQo1xMNTy80sAniKiz7MP8klTvK7boNw5vsOJgioRLYByHzTkc2yCM4ioP4DfAPgeMx8o9HiyhYguAbCbmdcS0dcKPR4X6QNgPID5zPw2ES0EcCuA/8r0YAXHTpGTiOYC+G3MwP+ViKJQIkKeF8vXvS4iOh3qyv1eTGNoJIB3iOgsZt6VxyFmhAMF1e8CuARArR8uzBp2ADjedH9kbJvvIaIyKGPfwMy/LfR4XGISgEuJaAqAcgADiWgZM19d4HFly3YA25nZWIU9DWXwM8IPLp1nAZwPAET0RQAh+FwJj5nfZ+ahzFzDzDVQH+p4Pxj7VBDRxVDL6kuZub3Q48mCvwE4gYhGE1EISiTwuQKPKWti3el+CeAjZr630ONxC2b+ITOPjP2epgJYXQTGHjGb8CkRGb3DawFsyPR4npjhp2AJgCVE9AGATgDX+HjWWAr8HEBfqEY3ALCGmecUdkjpw8xdRHQDgBcABAEsYeYPCzwsN5gEYDqA94loXWzbbcy8soBjEuyZD6AhNvH4BMCMTA8k0gqCIAglgh9cOoIgCIILiMEXBEEoEcTgC4IglAhi8AVBEEoEMfiCIAglghh8QRCEEkEMviAIQonw/wE4YRpwJ2fM2gAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "prU6W4Hd19pj"
      },
      "source": [
        "### Inspect the trained generator\n",
        "\n",
        "We can compare the weight/bias of trained generator $G$ to the parameters we use to genrate the dataset. Importantly, we need to compare the covariance $\\Sigma= A^T A$ here instead of the transformation matrix."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jcnu6eCgtR0Y"
      },
      "source": [
        "gA, gmu = model_G.parameters()"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZwnY5BWTtdP1",
        "outputId": "05f66e53-4261-4626-c540-b71b5a53f511"
      },
      "source": [
        "A.T @A"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.04, 1.9 ],\n",
              "       [1.9 , 4.25]])"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EV8e1ov5tlkM",
        "outputId": "077e6d67-14b7-45c9-a6e7-4602196e34ba"
      },
      "source": [
        "gA = gA.numpy()\n",
        "gA.T @ gA"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.80765074, 1.8812442 ],\n",
              "       [1.8812442 , 5.0232944 ]], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QwYq79Pkt1FV",
        "outputId": "f79d1c73-5be3-44c7-8221-6729621dc503"
      },
      "source": [
        "A"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1. ,  2. ],\n",
              "       [-0.2,  0.5]])"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Htjcsj4vt2L-",
        "outputId": "7933208f-1f2a-4114-8ccd-ec2051f304d6"
      },
      "source": [
        "gA"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.23406495, -0.22800203],\n",
              "       [-0.86767757, -2.2296433 ]], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7K_sWQEI2Wlk"
      },
      "source": [
        "We can also compare the mean"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "00oNrAke2bc4",
        "outputId": "f8cb0329-dd2c-4742-e1f1-31b4f9f5f6ef"
      },
      "source": [
        "gmu, mu"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(needle.Tensor([[2.00028   1.2296444]]), array([2, 1]))"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0HKfa2d_0EtO"
      },
      "source": [
        "## Modularizing GAN \"Loss\"\n",
        "\n",
        "We can modularize GAN step as in a similar way as loss function. The following codeblock shows one way to do so."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L0EolNkR_XeQ"
      },
      "source": [
        "class GANLoss:\n",
        "    def __init__(self, model_D, opt_D):\n",
        "        self.model_D = model_D\n",
        "        self.opt_D = opt_D\n",
        "        self.loss_D = nn.SoftmaxLoss()\n",
        "\n",
        "    def _update_D(self, real_X, fake_X):\n",
        "        real_Y = self.model_D(real_X)\n",
        "        fake_Y = self.model_D(fake_X.detach())\n",
        "        batch_size = real_X.shape[0]\n",
        "        ones = ndl.ones(batch_size, dtype=\"int32\")\n",
        "        zeros = ndl.zeros(batch_size, dtype=\"int32\")\n",
        "        loss = self.loss_D(real_Y, ones) + self.loss_D(fake_Y, zeros)\n",
        "        loss.backward()\n",
        "        self.opt_D.step()\n",
        "\n",
        "    def forward(self, fake_X, real_X):\n",
        "        self._update_D(real_X, fake_X)\n",
        "        fake_Y = self.model_D(fake_X)\n",
        "        batch_size = real_X.shape[0]\n",
        "        ones = ndl.ones(batch_size, dtype=\"int32\")\n",
        "        loss = self.loss_D(fake_Y, ones)\n",
        "        return loss\n"
      ],
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yXQZw5NwAosQ"
      },
      "source": [
        "model_G = nn.Sequential(nn.Linear(2, 2))\n",
        "opt_G = ndl.optim.Adam(model_G.parameters(), lr = 0.01)\n",
        "\n",
        "model_D = nn.Sequential(\n",
        "    nn.Linear(2, 20),\n",
        "    nn.ReLU(),\n",
        "    nn.Linear(20, 10),\n",
        "    nn.ReLU(),\n",
        "    nn.Linear(10, 2)\n",
        ")\n",
        "opt_D = ndl.optim.Adam(model_D.parameters(), lr=0.01)\n",
        "gan_loss = GANLoss(model_D, opt_D)\n",
        "\n",
        "\n",
        "def train_gan(data, batch_size, num_epochs):\n",
        "    assert data.shape[0] % batch_size == 0\n",
        "    for epoch in range(num_epochs):\n",
        "        begin = (batch_size * epoch) % data.shape[0]\n",
        "        X = data[begin: begin+batch_size, :]\n",
        "        Z = np.random.normal(0, 1, (batch_size, 2))\n",
        "        X = ndl.Tensor(X)\n",
        "        Z = ndl.Tensor(Z)\n",
        "        fake_X = model_G(Z)\n",
        "        loss = gan_loss.forward(fake_X, X)\n",
        "        loss.backward()\n",
        "        opt_G.step()\n",
        "\n",
        "train_gan(data, 32, 2000)"
      ],
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "eYNLN08VxzzL",
        "outputId": "27a8ec12-813e-49fd-e3d0-b210afe2188b"
      },
      "source": [
        "fake_data_trained = sample_G(model_G, 3200)\n",
        "\n",
        "plt.scatter(data[:,0], data[:,1], color=\"blue\", label=\"real data\")\n",
        "plt.scatter(fake_data_init[:,0], fake_data_init[:,1], color=\"red\", label=\"G(z) at init\")\n",
        "plt.scatter(fake_data_trained[:,0], fake_data_trained[:,1], color=\"pink\", label=\"G(z) trained\")\n",
        "\n",
        "plt.legend()"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fc6354da210>"
            ]
          },
          "metadata": {},
          "execution_count": 33
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}