VAE_cell_cycle.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "VAE_cell_cycle.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/dauparas/tensorflow_examples/blob/master/VAE_cell_cycle.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cF-I3eoGGh1E",
        "colab_type": "text"
      },
      "source": [
        "https://github.com/PMBio/scLVM/blob/master/tutorials/tcell_demo.ipynb"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pXQG7VtQVk6Z",
        "colab_type": "text"
      },
      "source": [
        "Variational Autoencoder Model (VAE) with latent subspaces based on:\n",
        "https://arxiv.org/pdf/1812.06190.pdf"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bL6BBloIUobY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "3dbfbfea-fa38-4181-a93e-d6d4157f1d90"
      },
      "source": [
        "#Step 1: import dependencies\n",
        "from tensorflow.keras import layers\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "import tensorflow as tf\n",
        "from keras import regularizers\n",
        "import time\n",
        "from __future__ import division\n",
        "\n",
        "import tensorflow as tf\n",
        "import tensorflow_probability as tfp\n",
        "tfd = tfp.distributions\n",
        "\n",
        "%matplotlib inline\n",
        "plt.style.use('dark_background')\n",
        "\n",
        "import pandas as pd"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using TensorFlow backend.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vabGonnvuhAq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import os\n",
        "from matplotlib import cm\n",
        "import h5py\n",
        "import scipy as SP\n",
        "import pylab as PL"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t0kV0AD3ubRT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = os.path.join('data_Tcells_normCounts.h5f')\n",
        "f = h5py.File(data,'r')\n",
        "Y = f['LogNcountsMmus'][:]                 # gene expression matrix\n",
        "tech_noise = f['LogVar_techMmus'][:]       # technical noise\n",
        "genes_het_bool=f['genes_heterogen'][:]     # index of heterogeneous genes\n",
        "geneID = f['gene_names'][:]            # gene names\n",
        "cellcyclegenes_filter = SP.unique(f['cellcyclegenes_filter'][:].ravel() -1) # idx of cell cycle genes from GO\n",
        "cellcyclegenes_filterCB = f['ccCBall_gene_indices'][:].ravel() -1        # idx of cell cycle genes from cycle base ..."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9j1BJeiuvJo-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# filter cell cycle genes\n",
        "idx_cell_cycle = SP.union1d(cellcyclegenes_filter,cellcyclegenes_filterCB)\n",
        "# determine non-zero counts\n",
        "idx_nonzero = SP.nonzero((Y.mean(0)**2)>0)[0]\n",
        "idx_cell_cycle_noise_filtered = SP.intersect1d(idx_cell_cycle,idx_nonzero)\n",
        "# subset gene expression matrix\n",
        "Ycc = Y[:,idx_cell_cycle_noise_filtered]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g0NLm-DTvO0L",
        "colab_type": "code",
        "outputId": "4450067c-dbe1-43e4-f13d-1bca72aed15d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 79
        }
      },
      "source": [
        "plt = PL.subplot(1,1,1);\n",
        "PL.imshow(Ycc,cmap=cm.RdBu,vmin=-3,vmax=+3,interpolation='None');\n",
        "#PL.colorbar();\n",
        "plt.set_xticks([]);\n",
        "plt.set_yticks([]);\n",
        "PL.xlabel('genes');\n",
        "PL.ylabel('cells');"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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HlFYrSGm1ghRUytnv2GwJq0cvGgPca10EqZIrmT3QdsIeg3LppTKSK6klo48+\nICGJBUQo9iYrLyURn7AXpN/mSAN7JOUjpROlVdDTPLI+PLmFXfJ1uYw8ypGQ0moF6zc4/i2rJ/JY\nTqrkShKbLSHx+ZWMPvo25YA/c8mHB++RYb53SWm1guy4lU4O3c8i+6IzyZSf/iQcx8dZ0344jiPx\n+ZVszFtvpJHxAY/J+vBk0nvjdcYLjuMjYPQjtmKzJaRKrmRhe/02RzL6UBu969JQ0mPtNTLM9y6L\noBl5JJZUyZUscsl82Fo2f/XpROcLvb+cUky6rAgjCQVVJDZbQgoq5ax/hxl+jKd0XuyOyiBVjWGQ\nW2+ksbaoDFKcOa4pHntJaAKL5NCfE3Sel1YrmJ0/V1LL5g+1v9PfVI+ceZZPLr4oIrmSWjLlpz8N\n9FFBpZxM+elPIhR7s7FEvy4nbaf4Mn8B5YNQ7M1CSAsq5QZRZPohjvN/fcbmk/5zGt74n9i4/5bi\nXrduHSkqKiI3b94kAIirqyt59OjRe8snpOUxw/3RR9kGziB9Ar7LAcJxTeFz9J4KPw2nal6XCu77\n2ht+OIbhQcP2OI6PjxaKvcm55/ktnAX6oWDN26TvdkdlMMfZu8rpO9FoGRoe9D5cB+2OIoP332FC\noq+YaD2aJPCudnzCXrBwQNomnWQUd47jHcA0GWXiqSdkd1QGsRq1mYU7Rb8uJyKP5QbONao8o1+X\nM5oJxd7EceZR8uHBe2TgtpstcNJXXPq0nn36KZtkHeYHEcsRm5jzjTqj6WU1ajMZfjiGtJvlT3ZH\nZbBkGdoeLafvVKP8Foq9DfCif+kHmX7s9N9R+urLQHN5oH3q05rSjdJ1Y0SKQb0Pdt1miRv65c89\nz2chg0cfZbMPA61L25t9+qnB2J0X/sJ4qy+H9EOiL1e91kUQjuPD1d4lr9RZp++YpmGd9KJt6tMg\n+nU5W2Q1nx/vmk/69S28NrDwyebyScfQe+N1g3bOPc9vEdbZ95s/WF37aYeIUOxtEHqoX1Y/fJVe\n557ns5BTWq55HxZeG4jLkvOMfvq0obJGdVVzeeI4PrzQZcl5JjOdFp9lIYC0jf9Ecf8tU0lAQAA6\ndeqEadOmAQAKCgowduzYf1tvks9KfOXpDADMnED/UqDOHwpXMqQwEZkb3FO7XN7b6vf2tWDT2fe+\ny0/NZ9vVomc32fOSpGjI4gKxauU+g/JGAgHmrQ8C0GS31Ydp83iHyuFtfpCX5hi8s+nYk/1+tn98\ni7oJYb8BAMzaOEFoYcO2c0ILGwzddx8pkb/j5bVLCE8ugbw0B50X/NyijUfXH+FKhhRD991v8e7M\nwZPY4nvF4NmbMgXGHfsTAL8FkUzVAAAgAElEQVR183tSgLyQ5Vj0cW8AQOLtxzi8zQ9W7bug48Dh\nsHXpjTJFA4hOB62qnrXj96QAInMTLPz2PL788gB7ruJkSAj7DaoGDVznnQIAmJjxdmonWzMMnDmf\nlaW0jjz1D9h14U0S0sx4fL7+c1z8I4ONQR8aaqV4dikU42Z6wf/wedTkp7J38/o6AuD5pKwoYM/3\n7TnNfnMKVQs6xZ4+AyOBAE9/C8GVDKnBu9CFAxitKFCe23qtQUfPKbiSIYWt1xo2njNn9uPMmf2Y\ntz6ImdhO7TvO6gFA6o0wKMrfGvT1xd5rWLVyH6qyk3i80itgIjLHlQwptpxPhNfnX7D2MtLK0c2z\nPwbvvsfTRSbFBy5tAKCFHBKdDkMXNpkz5ZUSAMDT30IMylE+STPjAQAfLfucyfxVf0PZIzodmsO0\nedtgrGc3t+nYE9PmbcOZM/th67UGfk94nuwOS25RV83VIj+Od8pRHpQpGth7gYkIid9PYDZ3gJcf\nRflb+D0pQAcxP784Oc/fES7WqC3OwqA5C/H86vUW/Y364XELOlk4umDVyn2ozEowkIPmQQ4CExEc\nXNsx+lHaTPJZicuPmsy/lqYmcJy4CwAw5edn7HnvEWIM9OL9HsYCI8jL36Jjr07svaOlqAW+/w7e\nq9U3btz4L6/31VM2qFkI3JNcqcFXznrMNlJQKScSmYI8yZUS+2mHSERqCbHw2kCGH44hEpmCrYRX\nXkoi2RW1RCj2Jn2/+YOFL71rxc1xHHmSKyWuS0NJ11VXSHD8W4OyBZVy8vvLIvIkV2pQR9KYmaW/\nraJb85nBf5FD97OYmUQo5rdXEhm/pXde+AuJzZawlXH7uYHEfNhagwB8umKMz69kWymO44j9tEMk\npbiGbckoninFNeTDg/fI+IDHrI7+1XaKL8OZ1olMKyVCsTcZffQBmfLTnyxrjvaVUlxDgp7mkdCk\nQpJeKmP1hWJvZubotzmSRGWWEatRm8kw37skNKmQZUzSrNKCSjkL0ZLIFEQiU5BhvnfJlJ/+JL03\nXmfbxfRSGcmuqCUbI1KIRKYgHeYHsfoFlXJi6rmKbZklMt5UEppUaDAu/d/DD8eQrTfSyMaIFGI9\nZhtLW+687CLJrqhlffg/ySFjTzwiBZVy4vfgjcFKsvkqKKW4KWOPjoXj+NBNGuInkSmI59477N3R\nR9kku6KWZcXpJ7zotx+aVMh4cPRRNksAWh+eTJzmBLBdX7tZ/mT00QdEIlOQwLg8IpEpiPuGCIOE\no5TiGrbi9nvwxiCJg/KHrnz1zYZ05UrDCV2XhrJ3o48+IBzHh7xR2Z4eFMf4pN9+SnENic2WsDlM\nx06395R/dJ52Xx1OYrMl7B1daT/JlZLYbAmjkU/YC7I7KoNcfFFEXJacJ/uiM4mbz1WW3cpxfPYj\nHceikOfkckoxSS+VMZPDuy66y00qrCY243ey52ZDviIFlXKWvDM+4DHpv+UGSS+VkS4rwpgsUPzo\nvKCp+QWVcrLyUhJJL5UR+2mHGA+pTNN6+nNLnz/6F31OabnjVjrbcf1XVtzW1tb/8nofFNXUo+RN\nAfx/2oOxszdj/dLBiC9RAgAuBG6Ag7kxLIUCVNepITAR4bPFOxF+djtMhPzz/kM6Y+rqVfj1cAAA\noCA2ANZ25nh1bArrw9ald4t+fX7+C+p6BYxNBHieV4VOQ6axdyM338CRa2lwszMzqOM8eh1GH3mM\nhUt2sWdRl76HrEGHWz8FY8+mQ1BWy+DgPpTvY9U+OI9eh882noOjqzPWB8fDSMA7i0yt2kJTr0Tw\nV3yI2PXXVQCAiqj9cG10kAkFRihRaPDL4S8wcukxHH+ch5jTZyFr4FczjhYm+OeKIYhcPojVAYAS\nhQayBh3a9eyHbyIzcTFVwuqsORIDABCYCHAv+DQaIw4hbFwJPS2qQVDjaraLrRAVHB+d037AGFgI\njTHg2ygcWDII7SxN8eb6XqTHPoCDhRDDV/OOpP3+d1h7f+0Zi4zoE/jhYR6Gbb2D44s8EDCnP7Jj\nI3A6hHfO1mt06D1xA0QmxpA16ODUjXduXnpVhkf5NdBp1LA1F2LiqafQ6IAZRx5htrs9S+SIyZMZ\nJFesndQLx3b9iDVeXZB1bRdiEosga9Dh6dEZOJ9UDFmDDjlnl8DBQoSU6D/hNn49dn/Le+mlmfEs\nKgbgk3pEVnbobifCBzP4sENLoQAhyWWQNeiQEhmGwws+YM+Tr1+CRsc7Kret/x7OViZYuPw7AEBV\ndhJzYAJNYXp7g59h0LSNOBZXiKNBsXh5jXc8qjQ69BjSF/YdrFEQG4Al3uPRrYM1NDogPLEIlkIB\nbB0s0Lk/vzI797IcH++NxjeLxeg+9hPceVWGzX78jtHUxgHOViZILucdgSNcrOE+diLDZdq8bRi0\n8y723OT5HvEdPxcG776HjCe8o/Nh8CrkPORXppP6t2erbipXKeUKLAuOx8Q5W6DT8I6/sMQiAEBW\nzDUAgEbHO7u/aYxY+mXTSHy+L5LRr5JTY+6m1fBob8ESUQDgi8GumD+wA/yuvkJZygNsGeGK0K1j\n4OncpFeGrz4PBwt+JfrLnL5YvfsSBk75GoVlcgDAsTg+kmNuyEuUKDQoUWjw+m44zrwog42pMeoq\neeff9ddV0KrqIRQYIfb0GQDAUDd7vH32BAWyOqxb4oEjsdls3ABQoeT5qqjn551QYISUN1KUK1Ww\nsHeGay8HnqdaAgdzY7Zzzq7idwzGIjM4W5lg2i8JaA40yMLOnI8ykXEqjJ0+tEW5fwf/9QSc2joV\nEYp5p1loUiHpMD+IOM48amBTpF9d+mXbeiONLAp5TvKlcmLhtYGtmNNKawzsdPqrJv30XXrmh+WI\nTUQobplaT9vRdxy8a+WeL5Wz8xhouq3IYznxCXvByunbz/yf5DAHI7UPDz8c0wIvukoUir1JRGoJ\n6TA/iORL5cyxqI9nh/lB7PnAbTcNVt5CsTfJl/LnuOjjT/GLyixjqe50VWs/7RBpN8ufiHfcYmP7\n7Gw8SSutIS5LzpOI1BJGt36bI0nbKb4kNltC/J/kEI5rOgQnrbSGJT3o88dx5lEy/HCMgf1+8P47\nZOuNNBKbLWGOan1aBz3NI7HZEvL7yyJGB0qv5isUC68N7H1stsTAdxCRWsJoPMz3LrOZ0tWd+4YI\nZof23HvHwH8iFPNJH/lSOTvXwnzYWmZrp+3q0/73l0VMhjstPtsiaYTjOOZgphfFfVHIcyIU8wkq\nlL9ppTXEbtJ+ZruOz68kGyNSGB2o446Oj7ZlNuQrhnO+lD+sjM4luktJK61hK2PKG/35pL+T1J8D\nXVaEkajMMhKbLSH5UjnpvOwiCXqaR/KlcsZ/7wuJBjIbmlRIBu+/Q4Ke5pFzz/NJvpQ/qCo0qZBY\njdpMdkdlEP8nOSw5ieLh9+ANs9PT/ugY4vMryczgvwjHNSULpZXWsB0g3RlResTnV5KozDKSL5UT\nlyXnDY62oOPTn3OUN+ee55Puq8MN+N1j7TXm/Ke4UTv1lJ/+JDOD/2Lv9H1kww/HkPEBj1scjKZ/\nRWWWEe8LiezwPP0x/1dW3CdOnPiX1/sgK7cYADBi5rfwXrYH0sx4OPXkbb/SklpcyZCi/Yzvcebg\nSew5k4BRPzzGSd+fEXbsJzhaGKPz0HFY8+V+AEBiSS2MBDyaBc/vGfRT8CqL/Xa04Fe9f5zdBnN7\nZ5jbOaHTp03B++IpfFhP/wnjWuBLbWU5NSo4Whij98f86nvF9lCsvJKG9gPGGthdM/5sSnzY+vUP\nLNa3oZa3kWU+5m1bU//xnOF1ZMcRlkTk1tYC0sx4uE/fjhEzv8WQ+Yv5MfTxwtbr6egm7oG1v/Jf\n6qoSKYpr+a/4X0V8Ys/vqWX4fOtvBvZ3it+M+duRGX0VAFBeUAMAkJdmY4n3eMTtGoPaxhT78/P7\no6utCG4fdIG1yAQqBe8/KM/Kgrw0B18F/InNa32RU6NCdS6/QutqK0JNYTa6LjkDNzsLmLVxgnjK\nRtTkp+LZpVCITE0YPttn90fUk7dwsBBiwOQJLWj+zbcBmDhnC2b0bIvuH63HpRe8zNSqtC1szgAv\nS21GrMPEOVsMwjMXrz6Oa5kVkMUFIvHKBajreVr538+GfU9P5Dy8zuzQydcvYfm6eQD41XFHzymY\n7W4PRwtjJh+aeiUu3cjk+WFhjObwvKAaLyJvAQDmzx2MjfvDAPC275waFSYFxiPU7xTrw6yNE0bM\n5HMeJI18dHLvDwsh3/biwL+gKH/L7PYWQmNcuhTH+DS0sx3ajvmGb2dAe9aWVlWPrrYihmdVbjIW\nL93N8NRqdPh4fwy2LhQDAOoa7fx0nADYahsArJy6AAB8wtNh38EGS7ZfwpSFe9B39gEoJYVY53MA\n3T9ajwEevM+KjnGSz0qUyVU4/TAXL69dwpIBTvj+XCI2RqSh8r4ffonNwQczpsLeSoTNa31xJ+gX\nAzwO7AlmobgT52xBYqmc4TRm3l5cXDwQVzKkeHVsCoYtWgKf0BdY58P7V04vH8LKBv+8HRZCY2wI\nfIpFZ5+j9xA3lCRFszFRfswLeor+jk0+tBEzv8WqlfuQHxdpwO+Vc/ph2RBXdj9l4R7YduyMmoIM\n3As+jVs/BQPg0/CpnwUAROZCPDpzFi+vXcKEk39BHz48EAsAeFtTh8WeLvAZ0ZWn4XcxBuGCfwf+\npeJOTEz8l9f7oEe3jnD2mIiyR6cQeekQPD5dgMitoyG0sMGGeQMwp7cDvj+wHHt/3AZZeTEebR0J\nTb2S1S94/hBHTvHKc2TnNngeeRTp0nqs2fElKzNozkKYWtmxe1uvNThzZj/CU0rg2MMDIgsr9Bo5\nDACfvFD26BQCgvagslSOpdvWobpei+p6LcoenULmT7MBAG5tRKjTEKT98R3qNAR9xwyBhcgYDYom\np6itS28kBS+F67DpsPVaA4GJCH0mz8GAb6Pg7DERI7y9QXRaCC1sICniY12tnLrg3NkDkMUF4vrr\nKri1EcHWpTe8Fs2DyMoO48TOqNMQqOTVmOXREYqaekRtHIHIS4ewfPFQjO5sCy/fB/iwkxUm+azE\nogHt8TBoBduah5zjt+7Dv1gKkZUdvtrzNQAgcutoAEBcxBEo6jX4YGs0rERNLP/kbBKqyxX4fN91\nCC1sEBX2Ax4GrUBQ8D7E7B0PB/ehcGsjgsCkyXFS8PtaDP5oELq1NYN9dw9YOLqg79TPEP7bQVzw\nHgSAT5jpYGWKrz7pg7Zmxhgn5id7ws3jCAjag6mrV6FdHy8k3/ZHnYYg9NfvcNr/Auo0BG5tRJjW\nwx51GsL6NLdrjy4jPkbpg5NIv+PfNL5Lh/Di8i58PqA9quu1CP31O8yfPQAJN4/jkw+cUZmVAFMb\nB5b0IZ41H9+O4idLZFYVS3iq0/BJI7SNXv2aksHo+zoNQach0/DlUFccO8J/MNd4dcazMysZ7Z2t\nhLizZihGeHsj6x6/sEm5soO1062dJUzMLMHJOBgbGWH5jvX4dEw3JN06DruuA1Fdr4WVSIDpnwyB\nW+PZLP3bWWLYgvmYvGQWSmvqkXXvBKrreaXef1OTo//Ij1/DbXTTWRmEEBQ8vQHTRrvZwom8+UUW\nF8gS0AQmQvj/tAdGAgFC/b9ER88pODS1F65s8EJ1XjJ+DtyGQTOnwa5zD5ZdPL4PT5tzZ3nlGbZE\njA87WeHqck8E/7IPxXI1VByHX+b2h9+TAvz6hQdCvAfB2MgIwb/sY857z7mL+AzHf3wDUeM8HjJ/\nMYZ2bDKVaOqVyKlRYU5v3ixxfN5AtLe3gOfcRajTEKSW8wuZY3GF8HS2hZmxEWZMcMO5LwbB0cYU\nPcfPAgAEze6DvlM/w+gjj3F/E3+W0JFTu/DVnq+xdt9GuE/8lPEr+gqfNLd2SEe4tRExc+vziEOY\nObE7jIyNYdd1ILqNnAmzNk64f5A3T/WbPhcAcHOlJ/pMngMAuLv+QzaW+BIldswfCADIrlBA3N4S\nVfV83L2tgwWqy5ri4v8O/EvFHRISYnBdvnzZ4P59UFTJoSQpGl9cSMbsZYfAyVWwFAqg5moxvmtb\nAMC8fu3gZm+JNh06AuDTtSlY2HdE/3Y8AxcGP0MHKxMcf5CDAx+5oW13DyjUOiReuQDbdm3Yavn3\nf36Pguo6DHRpgw7d7FBb+hbe47tDWqfF6tHdYG5ihHU+BzBmeGdkFspgZ2YMOzNj/PqyFAq9bC1z\nEyM4WfAHKo3q64QTH7vjo4+HobMXn3AjK8zAd/ey0VvcAR3E4xESvB3pUVeQ8uNkfLt8KF7dewq3\nYYPReeg4xO7hV/e3gtbi0jPeHje+Wxso1DooJQUImDMAn/osxNRe7WBuYoTa4tfYtPMMgr4cBi0h\nuJBQhCt330Cp1iFu1xj4hKfDb2ZfyBp0mLQ1gmXQcerGTMjzv+Ll1b2Y0Is/xGf4ej4rrY+DGVYM\n64xfN42EpVCAQ4/yoVDrcHrBQKRHXUH26UWI/HUnEktk6GIrhMAIEBobwdSK59UBv03YdOM1sqtV\nyK5W4eyCAXCyMEFxwm1wkkIQHcHsRTsQ9Iy3f45YFoDNl5Ph6WwLOzNjbB/VGQDgOW0jTvyeguLi\nWniN6IyLySXQEoIj19Lw8bJPYW7C2+SH7Yhmv6V1Wnz2xWS8ffIHHjYmffx8wB8KtQ4eHaxga2aM\nIVuiYGdmjJNRrxHzvAie0zZC2Kiw1JwMC4bz/f/sPRjCxoOfxnZtg1kHY6FQ8wdP7bqZATszY2RU\nKPA6tRwKtY7JhbmJEZRqHaRZCehoLcTk7vYAgEGfn8T2xtX5itHdWIZfRUENLIUCSOu0EC/gMwRD\nX1XAWGAEM1tHVOUmo4utEB6d7XD6UjI8pm6EsakZKuu0MDYygq2FEMVyNRRqHY4+zEXYskHY+lEP\nbB3fA5+fTUBlnRZ7f9yGyL18ZqJCrcPYrm2RdGgiw3vNVHcUPwxA0EM+OWRkZ56Xp54V401qOQAg\nIHAH6jVaEJ0OK/ZHoL5WgqHrL+Pr8DR0GjINIXH5CJgvxq3d47DjCw9Ehf2AX+/yu9zTje0q1Dok\nlCpRVadBfnUdbM2MEbp7EsxNjLBlhCs0WoKeH23AwPbWuJNWjtriLCjUOtQpVFCodTh4PY3t9rbN\n6AM7s6ZVb07MSSz7JZ7dj1/uj4SnhRjY3R7mJkaY2Ysf06rBHWElEqBOQzDF3Qm2ZsaoU2nx3dKm\nIzHSbl0G0QuKuZ5YjDPHzmPjyK7IjL6K3lO3QqHW4X62FD7h6VCodXgrU2P7cr4NM2MjbBndFalh\n29DzwwG832HEaPxZwMtkf3dHRo/aqjomu3RXPNTZEiej+CSzhJwqmJsYYVp3/oMVud4L+75q8sP8\nXfi39pRhw4aRtLQ0kp+fTwCQAQMGkMDAwH8bx70+PJkdRESPTm0ex03tp/R4SY5rOnqSxli+yw7X\nPGKg+QFPQnHTsZfUVt28jYjUEiIUezObpD5e+nbB5v3rtzHx1BMWVSIUexvEPuvHgjaPbBjme5eY\neq5i7yh9aEC//kVjcGn9/ltukISCKha/+j7c6F9q9w2MyzNIrKG0ou3oxxjTA49ohA/H8Yk5Fl4b\nSEJBFemx9hqLmaWXPh2EYv5Ar4jUEjLM924LnjUft/7hX/q80PcddJgfRNaHJxvUo7Gx9J7a6oVi\nbwP8aLu0HP3bvM93yaj+mPSPENWPIdfHQZ8e+nkDNAbYdWnoOw9yovJE8eM4/shSKqfDD8eQhIIq\n5uuhB2PRvvWPg9XnJaUhlTv9MdGIFX2c6Rj7bY5kfVO6N6eXm89VEhiX1yIem+OaolfoPNbPCRCK\nvZnfi/qjhGJvNle9LySSHmuvtYh0EYr5I3v1x9tclvTHxHGcQZx5c11w7nm+ga/sfX8tvDaQzssu\nGtBBKOajaJaEJrBy/TZHkg923W7B117rIlh8vr4M0j6orvqvxnH7+/tj0qRJqKysBACkpKRg1KhR\n7y3f0aU9bDr2xNLBriA6fjXYx4GP5kg/OR0An6t/IcQXRgIBbL3WIOnqRQyYwdsfqe3aSCAwsB81\nP2RKmhnPtl5qrhbf++9g8bAA2PGxhTI+FjkgaA/b4pUoNJjYrQ1kcYHMXkfBpmNPZFY2ICHsNww/\n+NDg3fAvliL4l30A+DTW2NNnUC+TsPf6sc/6MbuLt6wFAHZoTp1CBZ1GDSOBABEXD6GPgxkuhPjC\nrZcjGyu9XvzQFC0AACdXDUUfBzP06s2vrBd8axhrTvsY4e0NAEj5cTLGrliOLVsC0MfBDOOO/YlR\nPzzG2e8+w4UQXzz/7iN09JyC8MDVMDGzhLm9M8pTHyM+8hhKX95jW78+DmYwtW4LgZER/Nd8CKWk\nAIu3rMWgOQvh2McL94LXGOAwcdkiTOzWBolXLrBnN4/MYz6L+MhjEBgZIT7yGCrv+yEj+gRKFBrM\nWPul/nBgJDBGRvQJnN77CTsDhMpTeeojAMDakERs8v0WyeH74D7xU7Tt7oHaYl6OOojHY8MfmTC1\ncWD1VgQ9RUDQHiZTY1fwByCZ2ztj6Vw+jptGQgHAhRBf2Pf0ZDIF8DHkHWYeZmX7OJix9pw9JqLo\n6iaDvIGOjWew/Lz1I+SFLGcx1G0692Ox7hHLPDBw5nzM3nMLe+7l4HZKKdYejgIA9HRtg/u5lUwe\n/jz/K2t79p5bUDcebgbwsieLC8SFEF8AgEDIm16KMgsNaGvZGLlETQTPzq/HpO72GLrwc8yf1BOf\nLd6JCyG++PmAP+MZ0GQqeXVsCiZ1t8fORjPZ4gsp6DLiY5QoNCy9vcuIj/FD6As49RsFI4EAJQoN\n4iOPoSY/FRnRJyArzGD42JrxkRaBn/RGUUIMbh6Zx971mTwH3cd+gjdlchx/kIPPv/yEvcuIPgGB\nkRE2HNiE2rIiXAjxZTkidMcniwvExG5tWB2RlR0GtrfBy2uX4DZ6JjtIjLZHYdQPjyG9dwi/7viI\n0YH6pcrTn+Gvp000fbZ/PC6v580x4lnzcSyQ9zu8+GEiSq/zMf1jl/hh1a4NaGPW5BOi5wj9Xfjb\npwMWFRUZ3Gu12veWrVdpUVuchaEzNqG2OAvGoqYQPHraXNKhiTh5JwuVWQmQxQXiqz1fo4cbv/Xp\nMpA//9jBnbdRR4X9gLf3T2LI3hiDfszaOIGr5J1a6Xf8cf1pAXpNmA3XYdPx9v5JZgs84HcNtl5r\nYGosQEhcPgQm/PnSxXI1Bu28C8+5iwzaVUoK4G5vCiOBAH/uGM1sZQCQ96oEq1buQ0fPKUi7dZkp\ncX04fHInww8AOnvNQKjfKdh6rWHnixxbNhhv75+E67BpeFPJK4i0MjkUdWoILWxg67UGbst4c9Sg\nnXdZ22NXLMcfqaXIqVEhLpr3M6ga4+g+WrUCHT2nsEOnbq7kt3nuq8ORGpcBTT0/se9vGo7k65fQ\ns605EgpqkFOjQmV2EjpZi9Cuz3BYOrrAqd9IjF12HJ29psNE2LR9NRIYw93eFGInS4is2+Lm5cdI\nvHIBkvQ4LDnJH9Rj4egCa5EAY/u0w6Cdd9kk59Ra3HpdAaLToef4WXC3N8Wq08+wwO8hiuVq5NfU\nw9nKBD/MMAz19Pf7CoQQ+By6w85fAfjT4vLu8RMp8coFeLq2weLgeCz/uDds2ndiIaN11eVYP6ob\nOwwMAOJ2jUF8bhW7z03n/9dfXWUJftjDf8iTSprsjtO628HWiTfrUZu5rdcaXDi5GgAMQt0+We+D\nG7586OqFEF8WjkiTNmZ/vgddFgXDzNYRsrhACIQilOeV4a8iBYrlaljamCLzp9k48JEb5EoVXPq4\not/0uSirqYe8vumgtbf3mxzmH3i5oW23gez+wLHtSJfWo6LRKXnx1DoAwKltk1kZ8az5KHrFO0U3\n/zMJzh4TMcf/Ceo0Ory6+wDtrE3x9v5JtDUTYu+P29Bv+lw8yudpZmzEm5yq6/lzXOb1dYR9T09E\nnvoH1PVqOFuZYOrqVfg5oQQVr1/gu+WDwVWWYOWOdXC2MoGTpQlkcYGYsKvpsKWkW8fRsy2vK9xX\nh8Oh52A4WZqgz/obAIBdC8X4eHx3RJ76B/ZN6okPu/Imq7bdPWBuYgShsRF+CbgM9w/7Y9/5RHy4\nYA70oViuRlIZB4DXFypFNcavOIkLIb6wtDEzOA3Q2coEISm8SenR1pHY8EcmhjpbosuIj2HdwY2V\nK7+1Bw8OfIRVuzbwYyjjYG5iBNdh0/Hy2iV24FuxXM3oFRuyBQs8OmH7Df6D1UE8HvH7WgZN/Cv4\nW4q7sLAQH374IQghMDExwTfffIOMjIz3lq8sl8DUxgELvuUdhvrZdzSmtZzT4OlvIWxF8PMBf7Rr\n/PpnP+UVkiQ9DuWcBgu2XkBVvZY52yhYO7vBrttAlHMaTP2OzyKsk6sgK87B8xI5pvo9QqFcDaee\nPVmG5MpRXXEmmP8KdrQWouD5Q2Q+/NMgLvx88E7k1Kjge2wbbmZXo7q0nL0rSYrG3E2rUZYSC1uX\n3hjY3ga2rk11U+/4syzNuAv8F9aoMZ5aFheILouCUavSoW87C3QZtx7blw7Crh18lmZxFYfC11Ko\nuVoUPgjAiyD+q16SmojCRsavHNUVp/Ydh1sbETux8Kr/zzASCJB49zme/jgVS315p9XALXdQKFcj\n86fZqM5Nxnc/bkatSodalQ6FDwJQqlAhpaAGViIB7Lr0w+S991CSFA1tQz1u+83GxAXTEL5jLLSN\ncae1Kh0S/7kehXI1fniQi7ZdB6I6LxmPrvF23IsbRwLgj8uVq3SoqG1A4vcTMNy16QCnz/q3BwCE\nbxkNW681eLR1JLRaHdZfTcXW3/iTBwct9DOUJ06FjtZCvA76DB9+/A3GrliOWpUOey68hLHAiI1n\n4ZJdyHmegl07glD4LBpcZTHaDxiDmvxUqLUEOo0KtSodk787N5JQ3hjTbt3WHLUqHaauXoWdvryS\no1m/tEyHbnb4YGs0TvfZ3CUAAB3VSURBVC3gIzUiLx1C28YVYkxek5L/814KrEQCTP3Hc4x0tUXX\nAd0A8EfMWji6wGP2XLR17QJF+VvYeq3B7eOLUZbCO5/9YnPQrYM1alU6nHtZjnZ25rBva4Hu3dqi\nR3sr2FuJkFOjglO/kYgr4qOZwjMr8eDybYMdXm6FArN2RULdmO24rzFzsUKpgqkN7+x7ee0S+o3j\n44eTr19CSVI0rm0aga9Ck8BJCrHmy/0YvesuZq85ham92kFaUIEt6/ljZpd483Ooy7j1yKlRoe/X\nt2Bq1RZHTu1CccJt2Hqtwb2Qy1g0oD26Df0Qns7WEFraINiXX8kq1Dp8sDUa7Vxs2DG20dlSqHQE\nCaVKPPP/BM9PfoqYvGrEHuY/Nj9eT0OHNmYI/MdenH5eBJ8tfGRHXshy/JZSBiuRAF0GDcWpBWJU\nFZdggIstk1sAsDY1Zrtv68ZTSkXWbTGtux1SIn9HrUrHjmftvOBnBFxuOiUy6hb/+7HvBIz/bAJC\nVwyGiZklBu28i+nHnrBxebS3wMJziSh4egMCEyHLD+loLUTnBT/DzswYAiMjdG9rhreFNahV6aDT\ntMzs/XfwtxS3j48P1qxZg44dO6K4uBhisRirV69+b3krB3s01Epx8Ud+22hq44AyJS/89Czgj3bd\nRUDQHizf+BMAPuWbbkNE1k3RIk4WJrh7aik8pm5EbYNhyq0kPQ6S9Dg4WZhg9uSeeHnjJvp5OENW\nmIHUMjly4h7AxVqI13fDsekG7xj4KTaHnfv7qKAWkmhfiKeONdiuHQpLgaVQgN+isjCtux0aZIbh\naVvG90D8tUOw7eiGezlSyAqa6vab9DX7TSMDuro3mXve/rYKNiIBbEQCOLgPxYJ+joxxERdj8erY\nFCTcPI7sqnrMCebDCl9c+BYu1ryCWLhkF2LDj6BMqcHru7ywnDmzH0Snw4hpw+AyZh26D+IjJ65s\nHwsXayG6LApGWuRBPM+tQrlSw/rvZGOKod3t8ayoFqUvY1Dw9Abse3pCKSmApVCAiJNB+HjfPShq\neGHn1Doklykw/bv7ODy5B0xEJki4eRyzt19Gws3jzJFUptRg3W9JSCuSITKrCkNXnmU8DvzzLf9b\nYMQcy/lxkbgXfBqPtvKKX62UMXkBgH/eeo0ypQabb2XBc+4ixP6/9q49Kqqqbz+MDMNlZLyCmCgm\npmgakvdbWol54TW01F7NRNNMNE2t1DRvJIppmJlGeTfxliJIioKagspFRFAQBBEBmRkQ5nqAkWF/\nfxz2njOjftm36u3zXedZay+GmXP22Zdz9vnt3+X5/bwDZwoqkRlziPXFtcFbRlN0ExKpAxRtu+AR\np4O8eRN09h+Hzs1lKMtIYMd1Gb0U5dmXMeRzXpUhVziy30oqOav5dnfmt7Spv57A9fX+GBzEj7tH\nY0c4O/ALwKdbLa5fCnc3HLmpQnFuBVwdJFj+Ns8gaKipA1dejLvpOejUQGOcFvstMy5fvK/DON/W\nOBV1Fa4OEozo2BwO9hIcnuKLqO+2Q+4ohamuHr3eXgLVzUt41aOBec5TgYgNMyFTtGBt2L1uC+pM\n1ejcgt8JTHmzI0Iu3EPEb7nMbRWwqFu6B0yA1NkVKQ0vA4CXyHcvGgyuvBh9AhagzlTNwt4pDXJa\n7LfQ1tRBnX0Zbu2aYaafBwBeSOk1bgy4R/WQKxwxYs05q+fo5eHz0b2HB8YNao/5s/kd2ZL5oSjV\nmdDTwwXv7UnHL5lKTJ++Ah9G8i+d9F8jsSb0MCZ3c8OK19vj4u4FrL52TZxACJB9+ig6NHFAfd0j\n5mZI59XVQYL1R3hX3nZv8udW5qczAyL3qJ7Rs7q09ETqmjdZ/Vs+H4Zph2+i9/wonD/+O4L2XUdd\njRFNWrogaam1QNmmQSX204/L4BvIq8BaBXyNF7r6QGmsQyOJHVwdJBgzwAuuDhJ8v/itx1wHnwV/\nqAjfvXs3adKkCfu/SZMmZMeOHU89Put+FXN+v/9QTybuTmEsfEJn826fnyRLf8smA9YlEMfeH7P8\nblTBP3r7ZRZCqjfySnwajj56+2USei6PBb/ojRaWt5ZjNpIvTt5i+esWRWex6+uNPJHTrtQiojfy\njG22JFN6Ix9cQXMLOvWdwzL5RN18QBZFZ5F3dyYzljBqPHR/Zwt5d2cyGbAugYWzchwffkyzV1OD\nZ1GFnpzPLyfO/eexMTmUUUKSix6S2Bwl0Rv5kGq9kWPF1lmfspzRPJWU1e5JQSyT9qaSjRfzWT0c\nx+cppFlU9EY+E3ZRhZ71h9ZD61VqDORWmcaK2Uzqy+cJrNRbkgpX6o1k4u4Ukni3guiNPKsbvQY9\nJ/FuBUuEqzfyAQ/5ah3JLtNahXxznCWBq97I520MOnDNqh/U0Ozz6QkW6EQNZzMOprMglj5rzrBs\n5JV6o1VeRNqWQxklVv0TEl65BYaTPmvOEKXGwO4j23Gu1BvJ3mv3SWklT+tA71tqaIxIvscCZ6S+\nQUSpMRBZz5ks8a/eyJGQ+Fw252N/vkruP9SzBLyd5kaRI5mlJDZHyQiNOI7Pui5sa69VcURvtGRj\nj0i+99h4pt2vZLk5Oc46ea1T3zlWYyF8vmg/OY4fA72RY0RN4YkFbHxoXTQ3ZLMRIVasgpHXS6wY\nP5UaAzmSWWqVuJteJ+ZWGVkUnUX6hpxlhEzC53XAugSiN3Kk/cyjRN+QuFn4TNPPA8POsXPaTYsk\nXRdGk0MZJU81jFPDut7Ity8kPpecyVWRSr2ReEzczvopzChP6+m5Io4lRx4Ydo5lWxLSOQjn788Y\nJ59p4U5PT3+m72i5X8VPBrWoCwdFyP61P72YWf6X/pbNjqNZpenxT5oA+ju1Ojcdvop0nhfFUkPR\nc2niUHoOtTjbDvKTrkGj1Gyt/yvP3GbRV5T1kB4XfDSDHMviLfGUTlZY/46UIpKr0pLkoodk0t5U\nlgaJLgz0WJr6STgutC7hAyZsV69VcWTlmdvMu4NGuU3cnUJkPWeSV5eftjo3ueghmbI/jSWH7TQ3\ninRdGE1cBi5gx3VdGM0S6uaqtKRFQBjJVWnZgxF24Q45k6tiUWAcxzFPoje2XHps/AdtOE/CEwtY\nm2k9boHhzMPIlqMlV6UlbafuZ22iEZ22i03rf//EPGRohGTzUaGk68Joq4S8T/LmoH/p3NnOG416\nFB7bY9mpJ/LJ2FLIUq8JYbLgrgujyZiIK+wFTx/qVxbHWvWJejzRlycdZ6mvdaov93e2WHGVvPxZ\nDGk7dT87nr6ghR4QdP5oe59UaFsoxSn9rt20SJKr0rKFmN6nO1IsQhAVqtrPPEpaBIRZeYHtTy8m\nuSotCYnPZfcX9RhJLnrInmsq6AjnQ0iDKuyTkI6XehfR+4l61bi+8SXJVWmt+IT2pxczIUz4rAmf\nveSihyzStP3MoyxSWbhG0Ofbdp3iOI60HLORjaXtX6lvEBMC/lKvEolEgiZNLNbYpk2bwt7e/qnH\n6428PrYkJZY5tvvM4aO0ljZkDGk74XvMnPMNuIel0F7eCgd7CZq2540ry74+wupq7GDPrMP+3199\n7FqUX6F5h25Q592EsbyYGQU/2ngJSd9NgNfAf7GtCGVaA/hIySelRAOA4KgcDH1vNTNQCPH15+sx\ncMwi5MVvfozt8FxSESa8zxsndWX3Hjv3y29OwrOxFIFLjuH49v14mJfGjFcGVSE8fN+A9vJWNG7u\nCqmzKzq0sE5z1NijA5JLtAhLvI+mg3m1DA1gyDh+EGsXb4C5QfVSms7r/UNHd4Zj01ZQF6ng0MgO\nBRoTCjQm+H+4GZHfbIWDkz02bV2O0htJKL97FyZDFTwbS6HoH4zUNW8yo6bJTGDitPBsLEVikQat\nug/BoYQCfHkwA1HfbWcRj1TtVF9P0LaLFzoNG8vaP/vNjvhsTghGzp7J6gSAhK1TcXX7B4i8Wc6i\nAylO3alAWUYCfkq+j1nHspkqQ9E/mKmQAKBTn064m8Qbu5QxDXNQmoe7SWdwedkQAHxyWgo7iQQv\nDuKDVpq045kKJ7z/Jbq89Q5UXB27dwFgziBeT9190Wl4D+W9GW6ePMzaSucC4BNv0HOdW3qixYu8\n55O5IX2M1NkVeQnH8dsPEZjw/pdoFfA1SlJi0WHaXphq6zBkXiQKNPwcNna0h9zdC9tWh+Or+AJ8\n9VYntrVfEm5hh5TJm8LzVYun192keNSZqhGzfTc/J6VFAPhgFAqJvRRfzl9rFYnqIAhqk9hLMWpV\nAloFfA2Fs5R5cHk2luJB+hl4NpZi347TKNCY8IZ3C7To3Ae92yiwY8cqjNiWgvo6E14I3ICSlFhs\n+3oSJk60+CpnK/V4efh8rFq0DlWFFubAl9zkWH/2DiKWj0GXT06iONvC+AgAg6dPQ1N3OQDgq/gC\nqz59Org9XgjcABVXx3zDAeBKsQYOLgoM3ZgIjy694NlYCo2S95DzmhSBD2etRV2NkfG+AHxw07bN\nlnXIzUWKsux0NHJwRElKLKKOXobU2RVTwxMx46jFI2Rf0j24j7QwZ1LPoRkfjcDIFXzk94TNSZh1\nLJslk/Ye+jZUhQ/wZ/GHq/v7779PcnJyyOrVq8nq1atJTk4OmTx58lOPrzbVkVbjt7K3Jt1CS32t\nGbMm7U0lHhO3k6AD14jLwAXMf1atNZAey06R5adzrLgJ1FoD45HotzaeaPRGK+4TW4mZlkXRWWTI\nt78TTcO2i7LxCYuQwF0j2CpzHL99pn7m2WVaMuNgOslVaUnT4auIWmtg0pJT3znE68PDZMQPSY/V\nR1Ulwu8o/wKVIL84eYvkqrRsWyyUIGgRSpuahm0mlf7dAsOJuoFpzvZa9LPahlmQvvVDz+Wx39pM\n3kk0eiPR6I1EPvgzsiXprlU9Gr2RfddzRRxpPiqUFFXo2e90e5hZqiFhF+6QGQfTiUZvJCWVeqLW\nGkjYhTtk+9VCq7bE3CojTYevemzsOY7nEz+fX07y1Tqi0RufyA9CxyvowDWSWaphYyKUoGkbXQYu\nIBq9kbEZ0j6ptQZyo1RDtl4uZLzUwoS8tmxv4YkFj7XXd+lvpN/aeLbrSbxbwbhVwhMLSPuZR9nY\nCs8VJtQQzntRhZ4M2nCeJY8IPprBeFiE0r5aa7Cqb+PFfKLRG8mVwodsfjmO35VQ1UWLgDCmrtPo\njcRzyh5Wj9Q3iJRU6klJg7px6OaLxMFvOvvf9p66UviQ+Hx6giTkqR8bkze2XGJzTeeCPh9bku5a\nSae0/ifduy9/FkNG/JDEpGP67NNdi1prYPOeq9JaJeSg8ylcE17beIGUVOrJjVIN2zlQxkeqJqS+\n6EL1o3zwZ+SNLZeIg990kqvSEo3eyFgEaZvpfNLkxsL5tl2fYnOUpPM8Xj35l0rc+/btw9ixY6FS\nqaBSqTB27Fjs37//qcfX1tUje8dUFOycghcCN6D/Rxau7DeXnmafKw0mdBv4Mra+7YP2/YYy6fVW\neTV8u7jhfGYZAGCIF+8meLuiGhE/828tUk+w+FQenJwsEpeKq0NwFC/tncitZFL2/IFeCH37ZXgM\n+wIqrg5cg7scTTHkM+cE3v/BYhyoB1BjJnh7Zzoqa8xYsSsNdaZ6yN29MGBqODb/qzOmRCQj59BC\npD4wwEUhQ02D18JH//aFTleDKduvYuhG3j1uTEQqauqs3ScdGtmhqbsccncv7Ivj8y1+8ZoXegR+\nhcjkYoRcuIeRDeHFx24/ZJZxD7mMfaam2lk/paBd/wDU15mQ+sCAN17kx4u6Xp4t1ODQrXL0W30e\ncqmEeUkM+GAqpu1KQ42ZYF7fNug2fRcAYMq/+yLi2gPkV9XCf8o4qPW8f2uNmfD9BDC9RysER+Xg\n5KcDsHLpBFy6r2Hjtuatl3CnyoTGMgmGd2wJhbMUDo3soK01Qy6V4KejNzGluztSHxhwukCDGjNB\nDw85So9/xqQQIapNZvRp7YKgPdcwbFMiEm7zrnveH/6CHdctKZ88mjjhvVfb4M05u9FOIcOXYV/g\n8LUSFuLd0rkR6gF4vjoYmWoOE7t7sH6lPDBALpUgJC4X73VzQ+UFPg2bXv0AlQ1upWPWX4DOVM8k\nrJl+Hrh0nzfm0fDzc0teQyN7CfIP88Y7v1bOOL1kCACgqMKIBR/4ocZMMCT0dxge1eOVz+Og6B+M\n1r6vQWeqR36VCRfTStkcF2lrEBfcB7/M5aXVDSNfQp/WLog5GIp2Cov72n2tCWMiUtn/57PVVmM5\nry/P/ezRwRPBPyZDZ6pH3oFgNHOSQmLvgFLDIzRr3QL1hL835e5e2N2Q1ixgxzVsm/AK7saH41KR\nFjVmgpaD+LiE1zclIblEj8M3SiFzkqJfGzkOZ1viGnSmehi1NTiWU45Zx7KxPWIlAKCVnN+xy+wl\nGPDBVAD8ruemmneNVfQPxq4MFfZlqlDTsCsb2KsNurZxReFp3nf+yAzevXOIF+89Yi+xQ1qpDtrL\nW6GQNUJyiYa1w7O3P6unxkzwUZ+2GNqtFYYsOwvOZMbRY9ehM9XjeOhYdq98n1LKztfWmpFVXo3s\nihrU6ioQPISP4m7pbI+qWjO2rOaZTCtrzHBoZIeFX81CjZmgw2s8VUA9wOaj+AJ/7Pi9vPbhVQ85\n0kOtYzWeBc+qDH/mYnpUZ8UHTD9LfYNIbI7S6m1D9ZrNR4USzyl7SFmVgbgFhrNIuny1jukny6oM\n7E1mq6PkOD51UbtpkSztF5WWbPl7qRGUtk8YtUelJo7jDUFlVQbGZEb1lWVVvBGl2YgQMmlvKpO4\n6THNR4Va6eaEaZZsvxsYdo5JEN6zj5H04iriPfuYVRScsNDIL6HU3GluFGk2IoREXueNLE86N1+t\nI/lqHbuu7d+WYzaSPmvOkJZjNpLmo0JZ3c7957FxLKsyMI5j79nHmG7Stk+9VsWRW2UaxuxGi9Ao\nV1ZlYGPeeMhicj6/nP1uK9kKr89x1tzSNOUZx/Gc6mEX7pCyKgNx6juHbL1cSHquiGP3H81sI/UN\nYtcSjiOViqn0Yysd0b7T74TXFn4Ou3CH9SFfrWPXWhSdRaS+QWy3IizCnSPl0BZey3fpb2To5ovM\nAGl773Mc91iUYei5PHa/UMZIqa8l20rT4atYZKz/94mMxZHOzejtl0m+WsciC6ljAMdxTJKnfQyJ\nzyWeU/YwyV5YqO49X617LKsTtev80XNCz++1Ko4x79lmSqL30t5r91l6QOF4CO+rviFnmR1J6stn\nExIyJ14pfGiVVShfrWM7ScrpTcc4Nkf52Dpk26eI5HtP7B+thzId/qUS95+F0lCL9k0ceb/YhQew\n9jeez2Hq4rks2ATgIw/9XvdDjy/OYMqMUXjhpdZQyCQIWfw2TuxZjivRG1Frrkf0wkGYt3oBDCYz\nWvvyrjerNy1B276jWV0V1WbcqayGb18v/Di+G0Z5N0XCKt6dZ+d4Xn+5+WoJKqrNaNvg31moNeGT\nyOsoPbseW7Z/xeo6t+Q1BOzgfckVMgl0NWbma/pxcACq6+qR+UCHkl8X4PCmH6wyZ3cd+S7uHPwE\nQ31bM6lp8PKzzM/3xam7WL2vb0pC9Md9MHomn6kk85u30CdgAZp7yPH7znlIKzPiRG6lVRactgon\nVi/F5uC+0JcV4MO5m3BgbwhuHLC4SdWYCU7kVuLEbTV0tWYoZBLUmAkUMglK9Y8wcWcadKZ6aIuz\ncWJufxRFfoyrO2ejotoM7eWtqIgPhfImb0cwmMy4F7WUl1DXD8fFbUEYt/s6/L+/iq/iCyBr4Bf5\n/bNB2HutFGsDfLA/S42u83k2veZO9oi8WY7GHh2gkEng/vIgFGpNMJuqcTavnLHdNXOyZuVT5/L+\n3TJ7O/gtOYOeA70B8GyJCpkEMns73FBV40JeOVwd7VHO1eEFv9fRsbkz9szqw7LQhAd2RVjifXR5\n6x0k3deg+eufs2v0nTSFSWQTR/GZzxefvoPO/pZkttUPH/D+1Q0BRQaTGfc0/G7kX98lsf4H+rgx\n6aqZUyO8PncfAKBNM2cc2BsCuUMj6Ez16L0iAV6TIpBWZoSpgXCoxkxwvczikkddPmurHyF2Rk+s\nHcHrmRWePihIsATg3Nc9wp5VlkAxubsXPur1AotEVLTgs7JrL29FYEPErUtLTxxc7g+Fpw+uHj+F\nnoF8lniFTAK5uxfaNHNCa7k9+nVrhYxT36LqYjh2ZfAS8OEbFmn093tVWNDfE6fXj8GEbq2sdMUV\n1WZcO7oCsflVGLbsDPoEDGX9VPQPxv5177Exrq6rZ/w7AO9LbTCZcew2r4++XKzBvfSbiJnHRyZu\nGt2J1UX/ntq5CO/4tMDZu5V4oLfEjwz9cDqGf3WW1e+icESNtgK5Zzfj4vFv4OTaDO0VDog5yCcm\nDgq/hOzI+SyLkMQOWD+Kv14jiR02Xy3B5M/nwMFegqHtXOE37j12LZm9HVZvWoIaM0FDnBImd3PD\nwCVxbEwAYFDoRTYnp+YPwJ/FXy5xm81mZilNL64iSo2BFFbo2FtIqTGQTnOjSK5Ky6RNmn+O4zjm\naUF1VdRVS6kxkAHrEthbyjZ/ZHpxlZUkTiWsZiNCSK5Ky9y/2kzeyd7aSo2BbLyYz/R+tC20vW6B\n4WRMxBX29pX1nEmUGn5XMGjDeaLUGJikMjDsHGkzeSfjiaD1DViXYOV6lqvSks7zosjp20rmQUOl\n2MIKHbOA0/YJ3862UqzUN4jxSdAivBatQ6kxkKbDVzFXMNoO+pf2S6mxSNVKjYHE3CqzsuK/sjiW\nLIrOIv7fJ5JXl58mSo2BdJxznM0xlS44zsLlQTkaaF/aTYu0mlMqjSo1hifaLOj42o6JrcT5ybEb\nzEXuUEYJaTV+K+m1Ko7dV1LfIHKl0MJ/nl5cxead3qdS3yCml+Q4a90oHa+2U/cTpcZAXlkcy9pC\n7xelxkBWnrnNrpGr0jLbDfVSoNKv0HuEtkM4jrbjsz+9mP1Gr0WP25FSZMVB3yIgjPRbG8+OobtI\npcbApHC3wHDGSWM7nrT+wgod6RtyluWbpPVR6ZPjeFc2pcZAxv58lbSdup/do7R/1OZCx5fjeDsT\nrYtKm4UVOsbzTY8XSvZZDzQkvbiKRF4vsRojn09PMC8XOtbC9Yb2R+pr4dN5d2cy6TDrV9JvbTxz\nCVZqDEya5jheC0A9wwordGw8qJdTi4AwptsOu3DH6llrNX4r8Z597In3atYDjdXcCT1inlXitmv4\n8JdCrVajqKjor65WhAgRIv6r0a5dO7i5uf3hcX/Lwi1ChAgRIv4+/C06bhEiRIgQ8fdBXLhFiBAh\n4jmDuHCLECFCxHMGceEWIUKEiOcM4sIt4rnFsmXLcPv2bVy6dAkHDhzAwoUL8eKLL+LUqVNIS0vD\nxYsX0akT73u7a9cubN68GUlJSSgoKMC4cRb/7EWLFiElJQU3btzAypUrAQDOzs44efIkMjIykJWV\nhfHjx/8TXRQh4qn4y/24xSKWv7v07NmTXL9+nchkMiKXy0leXh5ZuHAhiY+PJ97e3gQA6d27N0lI\nSCAAyK5du8jhw4eJnZ0d8fHxIXfu3CEAyLBhw8iPP/5IABA7OzsSExNDBg0aRMaOHUsiIiLY9Vxd\nXf/xPotFLLQ8neJPhIj/xxgwYABOnDiB2tpa1NbWIiYmBo6Ojujfvz+OHLGwuslkFj6PqKgoEEKQ\nk5MDd3eeB8bf3x/+/v64fp2PzpTL5ejYsSMuXbqEjRs3Yt26dTh58iQSExP/sx0UIeJ/gbhwi/iv\ngUQigUajQY8ePZ74e22tJRmsXUMssp2dHUJDQxEREfHY8X5+fhg5ciRCQkKQkJCANWvW/D0NFyHi\nT0LUcYt4LpGUlISAgADIZDK4uLhg9OjR4DgOhYWFeOcdS5LY7t27/6/1xMXFYdq0aXBx4XmTW7du\njZYtW8LDwwMcx+GXX37Bhg0b4Ofn97f2R4SIPwNR4hbxXCItLQ3R0dHIzMyESqVCVlYWtFotJk2a\nhG3btmHZsmWQSqU4ePAgMjMzn1rP2bNn4ePjgytXeFpfg8GAyZMnw9vbGxs2bEB9fT0ePXqEjz/+\n+D/VNREingn/uKJdLGL5vxQXFxcCgDg5OZHU1FTSo0ePf7xNYhHLf6KIEreI5xYRERHo0qULHB0d\nsWfPHmZgFCHivx0iyZQIESJEPGcQjZMiRIgQ8ZxBXLhFiBAh4jmDuHCLECFCxHMGceEWIUKEiOcM\n4sItQoQIEc8ZxIVbhAgRIp4z/A9+vzNaK4ca8gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_6-2yCBD5Ruu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = np.delete(Y, idx_cell_cycle_noise_filtered, axis=1)\n",
        "X = Y #base case\n",
        "U = Y[:,idx_cell_cycle_noise_filtered]\n",
        "\n",
        "mean = np.mean(X, axis=0)\n",
        "variance = np.var(X, axis=0)\n",
        "\n",
        "indx_small_mean = np.argwhere(mean < 0.00001)\n",
        "X = np.delete(X, indx_small_mean, axis=1)\n",
        "\n",
        "mean = np.mean(X, axis=0)\n",
        "variance = np.var(X, axis=0)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c67eDerA50oQ",
        "colab_type": "code",
        "outputId": "9b638107-6d45-41cf-f83c-f3b59fd782c1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "fano = variance/mean\n",
        "\n",
        "print(fano.shape)"
      ],
      "execution_count": 123,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(30233,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cWicK7mu6OqQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "indx_small_fano = np.argwhere(fano < 1.0)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gqCp8-x-6isu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = np.delete(X, indx_small_fano, axis=1)\n",
        "\n",
        "mean = np.mean(X, axis=0)\n",
        "variance = np.var(X, axis=0)\n",
        "\n",
        "fano = variance/mean"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R8sO_eVINycy",
        "colab_type": "code",
        "outputId": "63c5ad42-bf46-4a19-b55d-a5878bdbeca6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "print(fano.shape)"
      ],
      "execution_count": 126,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(8892,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4E1cgAP9UtB_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Reconstruction loss\n",
        "def x_given_z(z, output_size):\n",
        "  with tf.variable_scope('M/x_given_w_z'):\n",
        "    act = tf.nn.leaky_relu\n",
        "    \n",
        "    h = z\n",
        "    h = tf.layers.dense(h, 8, act)\n",
        "    h = tf.layers.dense(h, 16, act)\n",
        "    h = tf.layers.dense(h, 32, act)\n",
        "    h = tf.layers.dense(h, 64, act)\n",
        "    h = tf.layers.dense(h, 128, act)\n",
        "    h = tf.layers.dense(h, 256, act)\n",
        "    loc = tf.layers.dense(h, output_size)\n",
        "    #log_variance = tf.layers.dense(x, latent_size)\n",
        "    #scale = tf.nn.softplus(log_variance)\n",
        "    scale = 0.01*tf.ones(tf.shape(loc))\n",
        "    return tfd.MultivariateNormalDiag(loc, scale)\n",
        "\n",
        "#KL term for z\n",
        "def z_given_x(x, latent_size): #+\n",
        "  with tf.variable_scope('M/z_given_x'):\n",
        "    act = tf.nn.leaky_relu\n",
        "    h = x\n",
        "    \n",
        "    h = tf.layers.dense(h, 256, act)\n",
        "    h = tf.layers.dense(h, 128, act)\n",
        "    h = tf.layers.dense(h, 64, act)\n",
        "    h = tf.layers.dense(h, 32, act)\n",
        "    h = tf.layers.dense(h, 16, act)\n",
        "    h = tf.layers.dense(h, 8, act)\n",
        "    \n",
        "    loc = tf.layers.dense(h,latent_size)\n",
        "    log_variance = tf.layers.dense(h, latent_size)\n",
        "    scale = tf.nn.softplus(log_variance)\n",
        "#     scale = 0.01*tf.ones(tf.shape(loc))\n",
        "    return tfd.MultivariateNormalDiag(loc, scale)\n",
        "\n",
        "def z_given(latent_size):\n",
        "  with tf.variable_scope('M/z_given'):\n",
        "    loc = tf.zeros(latent_size)\n",
        "    scale = 0.01*tf.ones(tf.shape(loc))\n",
        "    return tfd.MultivariateNormalDiag(loc, scale)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6cz7pGYjU6Mo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Connect encoder and decoder and define the loss function\n",
        "tf.reset_default_graph()\n",
        "\n",
        "x_in = tf.placeholder(tf.float32, shape=[None, X.shape[1]], name='x_in')\n",
        "x_out = tf.placeholder(tf.float32, shape=[None, X.shape[1]], name='x_out')\n",
        "\n",
        "z_latent_size = 2\n",
        "\n",
        "beta = 0.000001\n",
        "\n",
        "#KL_z\n",
        "zI = z_given(z_latent_size)\n",
        "zIx = z_given_x(x_in, z_latent_size)\n",
        "zIx_sample = zIx.sample()\n",
        "zIx_mean = zIx.mean()\n",
        "#kl_z = tf.reduce_mean(zIx.log_prob(zIx_sample)- zI.log_prob(zIx_sample))\n",
        "kl_z = tf.reduce_mean(tfd.kl_divergence(zIx, zI)) #analytical\n",
        "\n",
        "#Reconstruction\n",
        "xIz = x_given_z(zIx_sample, X.shape[1])\n",
        "rec_out = xIz.mean()\n",
        "rec_loss = tf.losses.mean_squared_error(x_out, rec_out)\n",
        "\n",
        "loss = rec_loss + beta*kl_z\n",
        "optimizer = tf.train.AdamOptimizer(0.001).minimize(loss)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oVaO0RxsY7Ht",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Helper function\n",
        "def batch_generator(features, x, u, batch_size):\n",
        "  \"\"\"Function to create python generator to shuffle and split features into batches along the first dimension.\"\"\"\n",
        "  idx = np.arange(features.shape[0])\n",
        "  np.random.shuffle(idx)\n",
        "  for start_idx in range(0, features.shape[0], batch_size):\n",
        "    end_idx = min(start_idx + batch_size, features.shape[0])\n",
        "    part = idx[start_idx:end_idx]\n",
        "    yield features[part,:], x[part,:] , u[part, :]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gm1vfi3hYzuK",
        "colab_type": "code",
        "outputId": "b00dd92d-f51d-4899-9037-acc55124918e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "n_epochs = 5000\n",
        "batch_size = X.shape[0]\n",
        "start = time.time()\n",
        "with tf.Session() as sess:\n",
        "  sess.run(tf.global_variables_initializer())\n",
        "  \n",
        "  \n",
        "  for i in range(n_epochs):\n",
        "    gen = batch_generator(X, X, U, batch_size) #create batch generator\n",
        "    rec_loss_ = 0\n",
        "    kl_z_ = 0\n",
        "    \n",
        "    for j in range(np.int(X.shape[0]/batch_size)):\n",
        "      x_in_batch, x_out_batch, u_batch = gen.__next__()\n",
        "      \n",
        "      \n",
        "      _, rec_loss__, kl_z__= sess.run([optimizer, rec_loss, kl_z], feed_dict={x_in: x_in_batch, x_out: x_out_batch})\n",
        "      rec_loss_ += rec_loss__\n",
        "      kl_z_ += kl_z__\n",
        "      \n",
        "    if (i+1)% 50 == 0 or i == 0:\n",
        "      zIx_mean_, rec_out_= sess.run([zIx_mean, rec_out], feed_dict ={x_in:X, x_out:X})\n",
        "      end = time.time()\n",
        "      print('epoch: {0}, rec_loss: {1:.3f}, kl_z: {2:.2f}'.format((i+1), rec_loss_/(1+np.int(X.shape[0]/batch_size)), kl_z_/(1+np.int(X.shape[0]/batch_size))))\n",
        "      start = time.time()"
      ],
      "execution_count": 133,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch: 1, rec_loss: 0.488, kl_z: 5038.03\n",
            "epoch: 50, rec_loss: 0.256, kl_z: 1169.19\n",
            "epoch: 100, rec_loss: 0.254, kl_z: 1150.47\n",
            "epoch: 150, rec_loss: 0.256, kl_z: 1138.06\n",
            "epoch: 200, rec_loss: 0.253, kl_z: 891.83\n",
            "epoch: 250, rec_loss: 0.250, kl_z: 493.30\n",
            "epoch: 300, rec_loss: 0.248, kl_z: 730.26\n",
            "epoch: 350, rec_loss: 0.243, kl_z: 559.81\n",
            "epoch: 400, rec_loss: 0.238, kl_z: 564.55\n",
            "epoch: 450, rec_loss: 0.234, kl_z: 710.93\n",
            "epoch: 500, rec_loss: 0.228, kl_z: 784.23\n",
            "epoch: 550, rec_loss: 0.222, kl_z: 896.33\n",
            "epoch: 600, rec_loss: 0.217, kl_z: 1257.52\n",
            "epoch: 650, rec_loss: 0.208, kl_z: 1527.80\n",
            "epoch: 700, rec_loss: 0.195, kl_z: 1799.51\n",
            "epoch: 750, rec_loss: 0.185, kl_z: 2238.79\n",
            "epoch: 800, rec_loss: 0.169, kl_z: 2253.14\n",
            "epoch: 850, rec_loss: 0.163, kl_z: 2524.81\n",
            "epoch: 900, rec_loss: 0.153, kl_z: 2371.30\n",
            "epoch: 950, rec_loss: 0.138, kl_z: 2567.25\n",
            "epoch: 1000, rec_loss: 0.129, kl_z: 2703.91\n",
            "epoch: 1050, rec_loss: 0.119, kl_z: 2730.01\n",
            "epoch: 1100, rec_loss: 0.110, kl_z: 2854.48\n",
            "epoch: 1150, rec_loss: 0.104, kl_z: 2838.82\n",
            "epoch: 1200, rec_loss: 0.099, kl_z: 2848.78\n",
            "epoch: 1250, rec_loss: 0.092, kl_z: 2902.38\n",
            "epoch: 1300, rec_loss: 0.094, kl_z: 2743.52\n",
            "epoch: 1350, rec_loss: 0.086, kl_z: 2913.92\n",
            "epoch: 1400, rec_loss: 0.079, kl_z: 2738.15\n",
            "epoch: 1450, rec_loss: 0.075, kl_z: 2695.68\n",
            "epoch: 1500, rec_loss: 0.072, kl_z: 2631.96\n",
            "epoch: 1550, rec_loss: 0.066, kl_z: 2619.38\n",
            "epoch: 1600, rec_loss: 0.276, kl_z: 5195.00\n",
            "epoch: 1650, rec_loss: 0.247, kl_z: 2940.30\n",
            "epoch: 1700, rec_loss: 0.241, kl_z: 1825.31\n",
            "epoch: 1750, rec_loss: 0.236, kl_z: 1415.02\n",
            "epoch: 1800, rec_loss: 0.230, kl_z: 1225.71\n",
            "epoch: 1850, rec_loss: 0.226, kl_z: 1231.15\n",
            "epoch: 1900, rec_loss: 0.220, kl_z: 1264.15\n",
            "epoch: 1950, rec_loss: 0.212, kl_z: 1333.83\n",
            "epoch: 2000, rec_loss: 0.205, kl_z: 1449.89\n",
            "epoch: 2050, rec_loss: 0.198, kl_z: 1722.17\n",
            "epoch: 2100, rec_loss: 0.192, kl_z: 1952.83\n",
            "epoch: 2150, rec_loss: 0.186, kl_z: 2188.21\n",
            "epoch: 2200, rec_loss: 0.180, kl_z: 2312.91\n",
            "epoch: 2250, rec_loss: 0.175, kl_z: 2320.98\n",
            "epoch: 2300, rec_loss: 0.167, kl_z: 2494.97\n",
            "epoch: 2350, rec_loss: 0.162, kl_z: 2534.96\n",
            "epoch: 2400, rec_loss: 0.159, kl_z: 2485.46\n",
            "epoch: 2450, rec_loss: 0.152, kl_z: 2470.98\n",
            "epoch: 2500, rec_loss: 0.150, kl_z: 2546.58\n",
            "epoch: 2550, rec_loss: 0.143, kl_z: 2635.48\n",
            "epoch: 2600, rec_loss: 0.137, kl_z: 2575.49\n",
            "epoch: 2650, rec_loss: 0.132, kl_z: 2556.10\n",
            "epoch: 2700, rec_loss: 0.128, kl_z: 2502.45\n",
            "epoch: 2750, rec_loss: 0.126, kl_z: 2708.18\n",
            "epoch: 2800, rec_loss: 0.120, kl_z: 2577.95\n",
            "epoch: 2850, rec_loss: 0.113, kl_z: 2625.05\n",
            "epoch: 2900, rec_loss: 0.113, kl_z: 2510.52\n",
            "epoch: 2950, rec_loss: 0.107, kl_z: 2573.50\n",
            "epoch: 3000, rec_loss: 0.105, kl_z: 2498.15\n",
            "epoch: 3050, rec_loss: 0.103, kl_z: 2485.70\n",
            "epoch: 3100, rec_loss: 0.101, kl_z: 2390.64\n",
            "epoch: 3150, rec_loss: 0.101, kl_z: 2433.73\n",
            "epoch: 3200, rec_loss: 0.097, kl_z: 2279.95\n",
            "epoch: 3250, rec_loss: 0.090, kl_z: 2303.65\n",
            "epoch: 3300, rec_loss: 0.088, kl_z: 2240.98\n",
            "epoch: 3350, rec_loss: 0.087, kl_z: 2256.19\n",
            "epoch: 3400, rec_loss: 0.085, kl_z: 2204.10\n",
            "epoch: 3450, rec_loss: 0.082, kl_z: 2199.10\n",
            "epoch: 3500, rec_loss: 0.082, kl_z: 2147.36\n",
            "epoch: 3550, rec_loss: 0.080, kl_z: 2091.81\n",
            "epoch: 3600, rec_loss: 0.078, kl_z: 2094.17\n",
            "epoch: 3650, rec_loss: 0.075, kl_z: 2095.87\n",
            "epoch: 3700, rec_loss: 0.076, kl_z: 2082.63\n",
            "epoch: 3750, rec_loss: 0.074, kl_z: 2055.43\n",
            "epoch: 3800, rec_loss: 0.070, kl_z: 2018.21\n",
            "epoch: 3850, rec_loss: 0.070, kl_z: 2024.04\n",
            "epoch: 3900, rec_loss: 0.067, kl_z: 1994.23\n",
            "epoch: 3950, rec_loss: 0.071, kl_z: 1973.09\n",
            "epoch: 4000, rec_loss: 0.066, kl_z: 1976.65\n",
            "epoch: 4050, rec_loss: 0.062, kl_z: 1942.60\n",
            "epoch: 4100, rec_loss: 0.061, kl_z: 1930.08\n",
            "epoch: 4150, rec_loss: 0.058, kl_z: 1919.03\n",
            "epoch: 4200, rec_loss: 0.060, kl_z: 1893.53\n",
            "epoch: 4250, rec_loss: 0.056, kl_z: 1897.14\n",
            "epoch: 4300, rec_loss: 0.060, kl_z: 1889.32\n",
            "epoch: 4350, rec_loss: 0.057, kl_z: 1847.00\n",
            "epoch: 4400, rec_loss: 0.056, kl_z: 1810.34\n",
            "epoch: 4450, rec_loss: 0.055, kl_z: 1853.19\n",
            "epoch: 4500, rec_loss: 0.056, kl_z: 1782.88\n",
            "epoch: 4550, rec_loss: 0.051, kl_z: 1817.94\n",
            "epoch: 4600, rec_loss: 0.050, kl_z: 1781.25\n",
            "epoch: 4650, rec_loss: 0.056, kl_z: 1756.28\n",
            "epoch: 4700, rec_loss: 0.052, kl_z: 1764.26\n",
            "epoch: 4750, rec_loss: 0.049, kl_z: 1793.30\n",
            "epoch: 4800, rec_loss: 0.047, kl_z: 1734.55\n",
            "epoch: 4850, rec_loss: 0.045, kl_z: 1763.27\n",
            "epoch: 4900, rec_loss: 0.043, kl_z: 1716.00\n",
            "epoch: 4950, rec_loss: 0.045, kl_z: 1727.20\n",
            "epoch: 5000, rec_loss: 0.042, kl_z: 1735.31\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5d60cwLs8Zlj",
        "colab_type": "code",
        "outputId": "2cd864ff-98cc-440e-ab5c-8f537474b0b6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "from sklearn.decomposition import TruncatedSVD\n",
        "svd = TruncatedSVD(n_components=2, n_iter=7, random_state=42)\n",
        "svd.fit(U.T)  \n",
        "\n",
        "\n",
        "print(svd.explained_variance_ratio_)  \n",
        "\n",
        "print(svd.explained_variance_ratio_.sum())  \n",
        "\n",
        "print(svd.singular_values_)  \n",
        "\n",
        "U_ = svd.components_\n",
        "\n",
        "U_ = U_.T"
      ],
      "execution_count": 134,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.55983905 0.04389005]\n",
            "0.6037290921647739\n",
            "[482.32958745  71.86901165]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "95Z5NCPEUvBk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a7PErTumPWnO",
        "colab_type": "code",
        "outputId": "ffb498b9-5753-4a7f-c41c-20c2f9d71052",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 370
        }
      },
      "source": [
        "fig, axs = plt.subplots(1, 2, figsize=(14,5))\n",
        "axs[0].scatter(zIx_mean_[:,0],zIx_mean_[:,1], c=U_[:,0], cmap='viridis', s=5.0);\n",
        "axs[0].set_xlabel('z1')\n",
        "axs[0].set_ylabel('z2')\n",
        "\n",
        "fig.suptitle('X1')\n",
        "plt.show()"
      ],
      "execution_count": 136,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jhDV/XYPKn/iToi8ZqLpVmyUrsAKVcs+1ckZHyu50qNfVQ1X1wboOTgoAANA9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\nAIAAUaAAAAAAIED/H9E6uvkvRkwXAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1008x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uE_W2YMTS2dZ",
        "colab_type": "code",
        "outputId": "55eef38f-3086-46c5-bbd3-7c4948790a33",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 370
        }
      },
      "source": [
        "fig, axs = plt.subplots(1, 2, figsize=(14,5))\n",
        "axs[0].scatter(wIxy_mean_[:,0],wIxy_mean_[:,1], c=U_[:,1], cmap='viridis', s=5.0);\n",
        "axs[0].set_xlabel('w1')\n",
        "axs[0].set_ylabel('w2')\n",
        "\n",
        "axs[1].scatter(zIx_mean_[:,0],zIx_mean_[:,1], c=U_[:,1], cmap='viridis', s=5.0);\n",
        "axs[1].set_xlabel('z1')\n",
        "axs[1].set_ylabel('z2')\n",
        "\n",
        "fig.suptitle('X1')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7Afz+TJob95uO1+PqD24nM/tscCCY4QbHwdcUJcvdjmWBJ81H/ieGse/1kmM+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\n",
            "text/plain": [
              "<Figure size 1008x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oJjSdjS4z5LN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "error = np.abs(X-rec_out_)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g8oa-7RqjUA9",
        "colab_type": "code",
        "outputId": "ff8d0d6d-e579-4fdb-f74a-0e5169b367f1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "plt.plot(np.reshape(error, -1), '*', markersize=0.1);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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1uz3KxAt7b0KPBLvSPY6aA2iua2ALD58/nd9N7WgrzMeW6h0e2jh/Frn8HXTG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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EkwHGY6SjtdC",
        "colab_type": "code",
        "outputId": "e644b829-0dc8-4b6a-e553-d569bcdea17f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "plt.hist(np.reshape(error, -1), bins=50);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7+4lEIkQiEYqLi1PvVVdXE41G6enpoaCgIFUvLCykp6eHaDTKli1bUvW8vDyOHz9ONBol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\niBgpJERExEghISIiRv8HEDYaRD5MdP0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}