no_filtered.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "no_filtered.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyMwCFZiwtl+bZchZsHbYkUC",
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "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/Usually-zz/2021_IMC/blob/main/no_filtered.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c9h5kk-ib6_8"
      },
      "source": [
        "import torch\n",
        "import torch.optim as optim\n",
        "import torch.distributions as D\n",
        "import torch.nn.functional as F\n",
        "\n",
        "import torch.nn as nn\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import sklearn.datasets as datasets\n",
        "\n",
        "from matplotlib.backends.backend_pdf import PdfPages\n",
        "\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from sklearn.cluster import KMeans\n",
        "from sklearn.mixture import GaussianMixture\n",
        "from sklearn.decomposition import PCA\n",
        "\n",
        "import seaborn as sns\n",
        "\n",
        "%matplotlib inline"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WuSgZm0zuqxm"
      },
      "source": [
        "def compute_p_y_given_z(Y, Theta):\n",
        "  \"\"\" Returns NxC\n",
        "  p(y_n | z_n = c)\n",
        "  \"\"\"\n",
        "  mu = torch.exp(Theta['log_mu'])\n",
        "  sigma = torch.exp(Theta['log_sigma']) + 1e-6\n",
        "\n",
        "  dist_Y = D.Normal(mu, sigma)\n",
        "  return dist_Y.log_prob(Y.reshape(no, 1, nf)).sum(2) # <- sum because IID over G\n",
        "\n",
        "def compute_p_s_given_z(S, Theta):\n",
        "  \"\"\" Returns NxC\n",
        "  p(s_n | z_n = c)\n",
        "  \"\"\"\n",
        "  psi = torch.exp(Theta['log_psi'])\n",
        "  omega = torch.exp(Theta['log_omega'])  + 1e-6\n",
        "\n",
        "  dist_S = D.Normal(psi, omega)\n",
        "  return dist_S.log_prob(S.reshape(-1,1)) \n",
        "\n",
        "def compute_p_y_given_gamma(Y, Theta):\n",
        "  \"\"\" NxCxC\n",
        "  p(y_n | gamma_n = [c,c'])\n",
        "  \"\"\"\n",
        "\n",
        "  mu = torch.exp(Theta['log_mu'])\n",
        "  sigma = torch.exp(Theta['log_sigma'])  + 1e-6\n",
        "\n",
        "  mu2 = mu.reshape(1, nc, nf)\n",
        "  mu2 = (mu2 + mu2.permute(1, 0, 2)) / 2.0 # C x C x G matrix \n",
        "\n",
        "  sigma2 = sigma.reshape(1, nc, nf)\n",
        "  sigma2 = (sigma2 + sigma2.permute(1,0,2)) / 2.0\n",
        "\n",
        "  dist_Y2 = D.Normal(mu2, sigma2)\n",
        "  return  dist_Y2.log_prob(Y.reshape(-1, 1, 1, nf)).sum(3) # <- sum because IID over G\n",
        "\n",
        "def compute_p_s_given_gamma(S, Theta):\n",
        "  \"\"\" NxCxC\n",
        "  p(y_n | gamma_n = [c,c'])\n",
        "  \"\"\"\n",
        "  psi = torch.exp(Theta['log_psi'])\n",
        "  omega = torch.exp(Theta['log_omega'])  + 1e-6\n",
        "\n",
        "  psi2 = psi.reshape(-1,1)\n",
        "  psi2 = psi2 + psi2.T\n",
        "\n",
        "  omega2 = omega.reshape(-1,1)\n",
        "  omega2 = omega2 + omega2.T\n",
        "\n",
        "  dist_S2 = D.Normal(psi2, omega2)\n",
        "  return dist_S2.log_prob(S.reshape(-1, 1, 1))\n",
        "\n",
        "def compute_r_v_2(Y, S, Theta):\n",
        "  \"\"\"Need to compute\n",
        "  p(gamma = [c,c'], d= 1 | Y,S)\n",
        "  p(z = c, d=0 | Y,S)\n",
        "  \"\"\"\n",
        "  log_pi = F.log_softmax(Theta['is_pi'])\n",
        "  log_tau = F.log_softmax(Theta['is_tau'].reshape(-1)).reshape(nc,nc)\n",
        "  log_delta = F.log_softmax(Theta['is_delta'])\n",
        "\n",
        "  p_y_given_z = compute_p_y_given_z(Y, Theta)\n",
        "  p_s_given_z = compute_p_s_given_z(S, Theta)\n",
        "\n",
        "  p_data_given_z_d0 = p_y_given_z + p_s_given_z + log_pi\n",
        "  p_data_given_d0 = torch.logsumexp(p_data_given_z_d0, dim=1) # this is p(data|d=0)\n",
        "\n",
        "  p_y_given_gamma = compute_p_y_given_gamma(Y, Theta)\n",
        "  p_s_given_gamma = compute_p_s_given_gamma(S, Theta)\n",
        "\n",
        "  p_data_given_gamma_d1 = (p_y_given_gamma + p_s_given_gamma + log_tau).reshape(no, -1)\n",
        "\n",
        "  # p_data_given_d1 = torch.logsumexp(p_data_given_gamma_d1, dim=1)\n",
        "\n",
        "  p_data = torch.cat([p_data_given_z_d0 + log_delta[0], p_data_given_gamma_d1 + log_delta[1]], dim=1)\n",
        "  p_data = torch.logsumexp(p_data, dim=1)\n",
        "\n",
        "  r = p_data_given_z_d0.T + log_delta[0] - p_data\n",
        "  v = p_data_given_gamma_d1.T + log_delta[1] - p_data\n",
        "\n",
        "  p_singlet = torch.exp(p_data_given_d0 + log_delta[0] - p_data)\n",
        "\n",
        "  return r.T, v.T.reshape(-1,nc,nc), p_data, p_singlet"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5k-fw2WGuuSa"
      },
      "source": [
        "def Q(Theta, Y, S, r, v, ignored_indices):\n",
        "\n",
        "  log_pi = F.log_softmax(Theta['is_pi'])\n",
        "  log_tau = F.log_softmax(Theta['is_tau'].reshape(-1)).reshape(nc,nc)\n",
        "  log_delta = F.log_softmax(Theta['is_delta'])\n",
        "\n",
        "  p_y_given_z = compute_p_y_given_z(Y, Theta)\n",
        "  p_s_given_z = compute_p_s_given_z(S, Theta)\n",
        "\n",
        "  log_rd0z = p_s_given_z + p_y_given_z + log_pi + log_delta[0]\n",
        "\n",
        "  p_y_given_gamma = compute_p_y_given_gamma(Y, Theta)\n",
        "  p_s_given_gamma = compute_p_s_given_gamma(S, Theta)\n",
        "\n",
        "  log_rd1g = p_y_given_gamma + p_s_given_gamma + log_tau + log_delta[1]\n",
        "\n",
        "\n",
        "  q1 = log_rd0z * r.exp()\n",
        "  q2 = log_rd1g * v.exp()\n",
        "\n",
        "  return q1.sum() + q2.sum()"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YiZmmIu7s465",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eccbe2e6-e9c6-470c-a41c-8c6416fb0799"
      },
      "source": [
        "%pip install scanpy"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: scanpy in /usr/local/lib/python3.7/dist-packages (1.8.1)\n",
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            "Requirement already satisfied: statsmodels>=0.10.0rc2 in /usr/local/lib/python3.7/dist-packages (from scanpy) (0.10.2)\n",
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            "Requirement already satisfied: packaging in /usr/local/lib/python3.7/dist-packages (from scanpy) (21.0)\n",
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            "Requirement already satisfied: setuptools in /usr/local/lib/python3.7/dist-packages (from numba>=0.41.0->scanpy) (57.4.0)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.7/dist-packages (from pandas>=0.21->scanpy) (2018.9)\n",
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          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "maD89jcqtA9j",
        "outputId": "e9696b33-6671-49f5-98a1-96020d6e03b4"
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/gdrive')\n",
        "\n",
        "import os\n",
        "os.chdir('/content/gdrive/MyDrive/Colab Notebooks/')\n",
        "\n",
        "import scanpy as sc\n",
        "adata = sc.read_h5ad(\"basel_zuri_subsample.h5ad\")\n",
        "adata = adata[adata.obs.Area > 50,:]\n",
        "\n",
        "cell_sel = np.random.choice(adata.shape[0], size=1000)\n",
        "adata = adata[cell_sel,:]"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Drive already mounted at /content/gdrive; to attempt to forcibly remount, call drive.mount(\"/content/gdrive\", force_remount=True).\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "13JTsdk0tO59"
      },
      "source": [
        "YY = adata.X\n",
        "SS = adata.obs.Area\n",
        "\n",
        "nc = 15 # number of clusters?\n",
        "nf = YY.shape[1]\n",
        "no = YY.shape[0]\n",
        "\n",
        "YY = np.arcsinh(YY / 5.)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "fQoBYsF1tQPl",
        "outputId": "067978bb-8a11-4588-fa43-b33b7192d0b4"
      },
      "source": [
        "pca = PCA(n_components=2)\n",
        "Z = pca.fit_transform(YY)\n",
        "\n",
        "plt.scatter(Z[:,0], Z[:,1]);"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "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": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "vWih6GuQtSP9",
        "outputId": "913be144-a622-4c13-c608-4d411ed65f34"
      },
      "source": [
        "N_INIT = 10\n",
        "\n",
        "kms = [KMeans(nc).fit(YY) for i in range(N_INIT)]\n",
        "inertias = [k.inertia_ for k in kms]\n",
        "km = kms[np.argmin(np.array(inertias))]\n",
        "init_labels = km.labels_\n",
        "\n",
        "plt.scatter(Z[:,0], Z[:,1], c=init_labels);"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "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": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wIWpIZtkXwhn",
        "outputId": "2f16763d-5920-496f-9c32-2ee57cac9d80"
      },
      "source": [
        "inertias"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[2083.6135274645944,\n",
              " 2075.037451104287,\n",
              " 2087.3370139551503,\n",
              " 2065.3625772487494,\n",
              " 2079.651672511577,\n",
              " 2076.4529816773083,\n",
              " 2068.1433925376004,\n",
              " 2073.9259613886325,\n",
              " 2074.6402572793177,\n",
              " 2068.3360842135908]"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "2QkmWmaCtV8o",
        "outputId": "3d2e7652-e731-44d9-98f9-9e1258267844"
      },
      "source": [
        "mu_init = np.array([YY[init_labels == i,:].mean(0) for i in np.unique(init_labels)])\n",
        "sigma_init = np.array([YY[init_labels == i,:].std(0) for i in np.unique(init_labels)])\n",
        "\n",
        "psi_init = np.array([SS[init_labels == i].mean() for i in np.unique(init_labels)])\n",
        "omega_init = np.array([SS[init_labels == i].std() for i in np.unique(init_labels)])\n",
        "pi_init = np.array([np.mean(init_labels == i) for i in np.unique(init_labels)])\n",
        "tau_init = np.ones((nc,nc))\n",
        "tau_init = tau_init / tau_init.sum()\n",
        "\n",
        "Z_mu_init = pca.transform(mu_init)\n",
        "\n",
        "plt.scatter(Z[:,0], Z[:,1]);\n",
        "plt.scatter(Z_mu_init[:,0], Z_mu_init[:,1]);"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wWS7NQdckOi4P/e8A/BmA/xvT9joSnaLgpMCYA8D5qTK+/NzJhtn5RKFYa7AcpTjFtmjFFNUC4fJ7vh5ZIVBmFGSGtMxYfJ7683uAb30BOHcKmLsEuOFe4MqNtT+LvFDZWkmYUEMrDKJNGmuYHqvOgLeeWAw6Y+yfiWhZHNvqdGQCWoA6nCoKvwJVo37H7jFs3Xtc663LYvG6UvuwqEJMonCPDr8Rm5vzcH6q1ND44vCrZ5SLzP7wQGij+Pwe4KnPAMXpczv3WvXfQM2om2bZhAk1tCqkZLpI6cIlnUPLKkWJ6NNEdJiIDp8+fbpVu205t12ztCnb5fFpVVXhrddcYvV5VHRVoYC5RkmwynKiUBQ2vvjKc69pdVvGJwrRel9+6wszxpxTLOCHT3y2rio0OFjcP7Qylj6fcfYeVSHzuvtzXst7lfqJ2kikm4klhg4A0x7617o1hu5/wXNeBoViJVbBKI4uPt3qxgg6bRgAeMUg9moTk9bBpQNCx/e39kM0B6gwwrsv7kLOy6BUYXUDTs7Lxmb4ZNlSALR66DbI0iBbbcCTfkxJolUx9K4m+BAGi1jixD9NlnmJrexsw2OlqgVZE+LMUZ6cKkkLtYz2M3dJNcwS/C1bAAAoCO5vnIUzOoEzv1RAlDh7q6QCbEJfrigpGs6gx4DN4lJUMkS1KWiSyqtl3ZhMwz1xaLNwVFW3Rot7N9xbH0NHtcnIg6WNih/FNyjpZA0KxTK2PXUcF4oV6f03NaLNXry0XQ9wRUnRiCWGTkRfAfBtACuI6BQR/Xoc2+0UWvmwlRnD8GNHcefusZbEWU25f2glbl+ztOaRcyVD09mCKB7vZQjz+jzofPx5fZ7RPowX967cCNz4JxjHQlQY4VRlITYXP6nWpUd1sIgj/utXoZRxdrIobyTy19/GHbvHwq0fxIzteoBrQh2N2GLoNnRSDN3E04kz/huVpOY8m6C61qqc9/Fpw2XKvD4P992ozhiy6SAEzEgoiLJcosR/415baGZ9gIhlm/dJ/yZaW3ExdDUuhh4B0+ni8LoVVi3OmglD9SVKSqd4m/ipavqvqj4MVqzqODtZxPBjR3H41TNCDZuR0Tx2aYy5lyG8Y3YPJiaLtd82I/4rO2+ACWP5KkxnknHmwNum0iZJArgTcQZdgekLOjQ4YG1Umk2YPPC4GRnNY/ixo3W55MOPVdvv+a+fiQFRvei8+MqGYpnVVeYGdc1VHj9XyPQb86HBAdwpGdRn0iifrxnhDAGfuGYmJCXLTpKd97anjlsbdFXYQtZkO+raTJhiN1eUFB4XchGgS8UThTV0Zf/twrTsvxmViYNfeFo4yM3r8zB674dq+xVVXN6miL8HjzXOcJcuhNOf8xoUMnlIQPbMzOvzcG6yCJH5vX1NtW5BFN5RrUGoUhtlPLRplfCemkgAhA3XtEseIq3oQi6uBV0AkzZtIk9naHCg2ri4DagWDUWeUHDhbsvIsfBFOApkMxb/56JZEAOw69BJ4f5FBUNx1sGOTxTQr1hknSqVpbM20cIuoXq+Ml/6K8+9Ji2+UhVl2S4Srl0+3ypVMEjYhX/XFq+1OIMeQPdwqx7GrRuuiPVYskR4aNOqxuyPLFWn/ah6OipPLRirFBnEXYdOti1jRjZwMgBb9x436uEqOv+cl615v7aoQmeyGoPxiQKGBgdw89UDdddc50WXGdOGJUSZM8PrVmibpwAz2Ua7PvUB6XdMjLVqkBPBj/nO3WOY1ZOpZSu1o/K0m3Ax9ACqh1tXpTc0OIDfe/x5XCzFU1hUZlXpVV0DClUmRDAP3NQgAtHTMftzXq2tXvBzoPrSq3RZJgrF2u91PVz9EID3LZ2LL1tkqXDCBiB5yuLjR/LWYmiya5CdrjkQLcw/cNNK7LjlKmmYzybbySRs9faFRq17GcFjnigUkfOy2CkJ+Tjiw3noAWRT2SwRxicK2Lr3OAa/8LQwz3jLyLHYjDknP1HA40eqHtnL29fj4ObrG14KmabK2uXzG2KwNkaaKHxHeqA6Ywl6kV6GajMZ3eJjEN4MRAcDcPDFM9IwRxTm9XnSEELYArOMxNO+9ZpLtAvzslx1m5CMiSZPscKw7anGGZMI2THfteeo02VpMs5DDyCr0uNel9/jDGYAmApR2aJLfTNN9RoZzUv7UoqoMNRlpdgunOqOK8wMQNUMpNnkvCzuu3FmMMpPFJAlqt2fsIuz5QrDnN4sLhQrDVkul0nyuPm1M2kmobtvwfskezrOThZr4ShV9ksYeeMk6Kcn4Rii4gx6gODDrTOA3PMAmqc7DuiNny7Vi0+DbY+xWK56ZoC51IDpiyGb6meJ8BO5HmEs29/D1eT+xIWoGCl4PVThIx2TU2VhiKRf03haN2ia1lL4nx/TYqYwOfai39jKAzTD8LazC1acuLRFDabpYV6WGuRe4yRqmpeqy4/MeAb3b5J+JkuBE3Vfuu2vv42DL55pPNbl83F8/McN8XdRxaBN1x0dIoMsqyqVXU+VUfeyhHfMEl9rXoDD/39gWl9997++1tCr1MsSdnzMrDNTmLTBqJ2MVNWhot/YHGOzKkk7Jb3SVYpGxDTPuZnGPENoyKyxlcmVefgVxnDfjVdoX2AT0aSR0Tzu2nNU6DEH+42OjObxLwJjDgD/8uIZY8PK/y3brym8dF9WOcpfeF1DbzZ9rNxo84Yn8/o8MFYNW4iMPt8m/3+efSTa05zeHq3x0tVSqGZ8h189g4slv8HMYFZPVrjALYrV2zY9txHkapYaY1pEwZxB16BTvmsFDPXTPpNm0EFUndj5tu/cPSY0IP05D3Nm9Sg7uZuEdLhK4NDggHJBVPR5n8KI2TZu5mSJUGFMueYQLI7SDRrz+jxc8KU2Mlb1qN++UKp52gwznrzK+Mn2dE5gWIPHrXtmZYumIg2bQrGC9y3tx3dOnjPqxiRT3pT9RvVsBmmW4bU5hiTT1VkuJsp4fuU7QtW4GaT/xkrwff/yc+KXxb8oGzy36y5fpCzwGBocwM5NqxoeiAyq2Sq6AhHTDI+zk0WMjOatX0CTNQRT1UVOhTHs3LQKQHUw8z8D3CjayDnkvCwYQ8N1KJZZQ9iEoTqdr4SYVeiMTJRaCtnC/qGXzhp3Ywoqb3JkvzEtPuKL+iKiGt60FEB1rYduswgSXHBsdZk/oRrj41WMsv6j/kKU4Lk9fiSvzWcHgGyWUPGFj7LZ6gsUZ8bKjv0nrEv2TV5YUego52UxqycjDBfMzXnCZ+Dwq2dq4SwTaPr4htetkOq5iDCRLgiGZ0yMTJRaClWRk43Gik2jFZMsLdUMMA7DmxZRsK416DqdZl2a19a9x4VGohnwik5AXcXIPSLZuX3t6OsYu+9D0t9ve+p4w1pAscxq8UnVC21joMcnCti5aZXxoGj6wspeSgBCQ0/U6E0XimVp7FpEcNHMJn2RH58sPKKK6+u2G3aBr9WNxjm6wUI268gSxVZ5mgZRsK4Nuci8GO6l6XRNtm64IlYNkTjgVaEygzJRKGLLyDHh30ZG85HatpkUp3D8cXsZ/NralIrL0tmCYTO+zQnJ+Zoac9FAI2zUkaWGAqsMAePnCrhj9xgulMrwAm9if87DAzdVvdyDm6+XFpWJkDULmZwqaYuCWt1o3BTVon6nG+E46VoPXZUDbSqZ28ywy0B/Dq+fK0jDK0FyXgb3D63UltPvOnQSqy9tFGpS6bbMDlobAab5+4SZjB2eASKCx5h1HuXIaF4oXRwMoYm8rzDFQPzaykIX/uvAs2KKZVYnuZvzMnWaMIwBxcB1iFJxHLwXc3Mezvv6rKrCizxMEgw5PXLoJL529PWG1NNWkZZFy2bTtR66bBFEFkMUeQiqFmFRyU/YGPMsHrjpSgD6cnoGCEu4VV54oViRevZ+hgYHat6kbLHPn7Fz2zVq8SzdzIDrrctmFjqBMZk6oggulPby9vV4Zfv6WnGTyOMdGhyoiWf5K4zfvlDCzk2rcLGkv7GFYhl3BBZqbfDfC6LGtFrVtbl/aCW+uPEqeNn6qzFRKGL4UXn5vmn7vTBt+tKyaNlsutagy6bhMglckSeQhIeJT81tFifPThbrQkq8vF/FI4dOWr2AMs/JPwjeP7QS7/nJOdJtZIiU+9yx/4Q2/z8/UZAer+gZuG3NUmHI5J2ze2qZMCZyw1v3Hm/IbClWGLbuPW6VLx9VyjhsKE12bYsVJhwIRCqeouM2/V4Q2fvqwi31dG3IBRBnr5yfKjV8z8uQ0HgPDQ7gs088L5VUbQVzZvXU6ayEKa0xLYryv4CAuiTaVGPkP944L92Gv8hGtE/TzBrV8YpCMasvnV8LV/T3eXj7QqlO9VG0aBoMy8kWzCcKRW3hTRDbwhn/WoIszQ9QhytU11b0t617j0sFue7cPRZLm740LFo2m6426EFkXkmJMRx+9Ywwe6KZFaImzLQ3a13xk+wFDFavrnn3PLzyVkGaoWEzAIn2aZpZY2sQg7omQQ83qtywqvBGBp9pmFSI+p8F1cChmmGqrm1mWtbXrxcjG8CCg7LsGe20isyk4gy6D9lDxVh9izD+cM7qyTRMq4PQ9Cpas8z+3JwXWrY1CsFrJapePfjiGWUbtajFRcPrVtT1LNX9Nqgds3b5fHHjh+f3AN/6AnDuFHZXFuDBzEbsrVyr3QcD8F8//w3lgua8Pq9h4dE/+KkGqDt3j+GO3WPKXHLTZ6E/52lnWLJrG1RNNG2EwuWPRYOMW9yMh64w6FHV/0QUio2tyABgQ+ZZ3N2zB4vpTYyzhXiwtBF7md4YhMXfBMLoWAwMkwnBF1DVRs1WjkC3T//97O/zcLFYroW9ZBk+XpYahMAOvngGH/zjf8TkVKX2bDz03h/g/cfuA4rV41qSeRPbvYeBIoyunapxs5elmvyurPBGNdvi56UKe5kMkjkvq+2uxbcra37un/XYDMwi+WO3uBkfqV8UtVmEscmlFrEh8yy2ew9jSeZNZGjGGGzIPBvhDMIfyx/1/k2oY8l5WTy0aRVe2b5e2AJP9AKadHc3kSNQMbxuRcP9PDtZBAPVjnen5HinJF78D944X/dsLD7yYM2Yc/poCnf37Gn4rUE2Z42B/pxSIdHfss0kTVSWpaJq0GK7mDg0OIDRez8kzfwZnygAz+/Bs7M+g5dmfQLP9n5G+3zx/UdZ3AyTJdMtpN5Dt1mEiarcd3fPHvTRVN1n3BjsnWqely7i97w9yOGi0bHkvAzmz5klnMGYlkTrKgxN5QgmJqdwfqrRO53XVw0RrN3+jHTxTXW8pjUDP403hZ8vprcaPrNZC1fl0wevjal+TH6iUJOE4Od53eWLhPF5nRqnirmSVoIfn30IU0/+FQao+pwtIfVshtcgRFncTItuebNIvUG3VWfjD0WYRcbFZG4MTLl9zVLjBbT+nIdzhSIW9+ew+IJ4n6JjuVCsCA1OMFSl6gm55t3zhNrmZcawdvszmJwqCQ3xgRdO1/Y9MprH8KONKZT+UIXsvom64fBjt2l2Pc4WYongPo6zBcbbCKIrmw+7BkKYqQr2r+uIOPDC6dCNIWSH/1v4MnqZmdMANKqGhqFZ8rlpIfUGPWyF2WwvU/fgmHSjidsYEFVT6EwN+pxZPTNaLTuXAOca49qiYxFdCxtPaGQ0j++cPCc9LlWc3G+gd+w/IVxk9ut/q+Lu/jBE2G5CD5Y24o96/6ZudjPJevFgaaPBr8UEy+aDhjVs6zpR6qRsYAhmmZh6tqo89nexN4WVWDIHJo5CvDjlc9PQci5I6mPothVmMtlUU2MwyXrrPotiDBiz0/iue6jf0yjCxRjwrcqqus/8pfh+dOJluu+a4h9MZC/lRKFYi5mev1hqqGD0k58o4K49RxuOhwHoVfyOs7dyLb77vt8H5l4CgIC5l+Brl24WhhBURVFA1TMPZvmI1nRaoQmkkrSQwY9Vxhu0SPi5yGmIa+FT5ojZZsmELXBKOqn30G1lMaMYp72Va4EipjNL3sI4WxBrZomOuof6B083/J0IuCEzhvt8n8mmwTaeUNgc4mDBlsxb9YcWJgpFeBlChiCURiDIF2inykxb1NOf8/D+Db8B4Ddqn20E8LygQ9SBF04Lt6HSoBE9X/6GF6bIzoM32Ahmkdjkf6zj+UUAACAASURBVOu6HfFtvva+Ycwf/Xxd2IU7MGuXz1fWIITFpGDNhLSGblJp0EVTKdO+gFELHPZWrm35AihQNQjXXe7zmM6dEn4vOB0OToN1FaciTyhs2OAds+u7EIleVpGhK1aqYlcXSxXrsJjKmJuk8/lRKXZetnmf0JBJax0g79sqOs6brx7A40fyDYaNrzUEn3+Zgfbfz5HRvLEs9AM3rcT7Bz8MLJuHs09twdypNzDOFuB/lTfhrctubIoxB+LTLU9Ly7kgqTPoUVfBo8Q0m40qr5wBePxIHqsvnQ8AWIOFeBcaPUj/dFhUiq9aDJZ5QmHb9AXDWqKXVXYvzhWK2LlpVSyxaH+DCtEzImv51xdQTfQjkkngHXdEgwr36mXNiv3M6slg16GTmJvzMNvLYGKyKK3E5YvC112+SDgA8PtpU2084Jc/vnIj5l1ZDSkuAfDzivfPf0xRDH0cEgBpVW8kFqGxbm0jRB8G8L8BZAE8zBjbrvr+6tWr2eHDhyPvV0TU7t2tLqM3hee4+9MiJ1kvNhc/WRfS4Z7rB8v/1PD9UnY27qffxP95+2eFL9SqbU9LvTPehT7YbOHRwycbslvm9VWzbXRqkVkivPjAR5TfsbmfJsZQxCuBrvVBlt/zdbEUMAGze+ThDP+xXnf5ImnjDC9D8LIUShNI1PFe9AzrmmWYXjvR/vzItiOaUem2ZYPtAqfsGiVd8IuIjjDGVsv+HtlDJ6IsgD8H8EEApwD8GxHtZYx9L+q2w2A6lVI1QwDCaWU3E9Mcd26Q96I+nv8GLcS7fukPsfXKjdgq2L5KjwNAg4eXnyhIm0q/fUFvzAF9w2XAPGY6MprH+YuNwmo6VCmF/BmRNnFm1dADf45kZyMT9AKqg0KZMRSDguiGiOK+sviwP0U0iEmoQde+TrUd0bOli1mbGukws/K0tJwLEkfI5WcB/Adj7CUAIKK/B/BLANpi0E2mUroHgP9vZDSPux49irLEOtmq5kUhTI57MJ7/ypVyT1SXqy3qsSk7c1NHUxa/F71gJv0mw8yq/CmFQUmBty+UlFo9wcFAVVylGhRMniDZIjDQaETDxIdlxUOAnedqG/qSHZPsHT386pmGWUbYBc40qjfGkbY4AMCf8Hxq+rM6iOjTRHSYiA6fPi3ODogDkzRF05S8HftPSI25KpuiGYyzhZLP62PiGYnDqfNEdS9h3Ocqi9/708ju3D2GZZv3Ycf+Exhet0Lahi1MZlIwpVAkKaATXlvz7nl1v5E1MI5y7Qb6c3ho0yq89MB6aR53MO5rm9onk40GquEzmzCE7P2b12feZwCQv6O7Dp1sSDWUPbudvsAZhpbloTPGvsQYW80YW71okTh/NQ5MhPBNPRiVkWu1aK4ux52fp8wGyYwK7/oTNyqNFpGRkKXzAfoc4bAv7iOHTta0QGwHhT4vg1feKkgbF/Nn7+arB0I3WObrBPw6mdZUyDSJli2YETfza6Fs3dvYHByo3qfRez9k5cXK3r/7brzCqh5ElQ3khys4iuj0Bc4wxBFyyQPwl8Itmf6sbeimUqZhGdvc4GaiynH3LxDKYv8y727bU+KXOQprl8/HLauX1vXVLDOmjMHqjHKhWMbWvceFoZf+Ps9Y/4RjqtMtP54KCgoZAgB4/VzBWvfcT9DYmcZ9hwYHhIvVB188g2Wb99U91yqnRdRE2ySurXr/TGPWNqEbp+A4QxwG/d8AvIeILkPVkH8cwCdi2G7TMFloC9P9p9kDgCzH3W8MbQsvbA2hjp96Z29NY9zGszN5gf1Swf6Y6tsXGsMF2QyBMWa0OKvS6ZZh8k3TnrAiZHrlMp0af7MJ3YK+6WEFPdyoKcE6R0uXBy97vwZ8sfQ0LXCGIa60xY8AeAjVtMW/ZYz9ger7zUxbNEXlaYyM5q1K7oGq0bxYKkd6icPSn/NmNFxgl8K1bPM+6XbDDlCqphay4wPCCaLJDHGfl0GxzLRxcD+iikovY6eqGAdehrDjFrHUrirdDgh3DUXwe++fVclSErNEqDAWyZByYTbZ/eKpn6Jc+qSnGsaJLm0xFoNuSxIMuowwGRNZInxx41XWg0Bc8FhnGGS55/05D3Nm9YRK3VTll+sMEvcuWx3ukuWKB/O34zgm03PjEgP+wVGVlw+oQygq5vV56OvtEV57fn9kaaoQfNfWwKry4P0hxTQKatnQ9Dz0tGG7OOZ/gNtl0HnYJNjTU6eBPTKaF0qjehmqlcCH8fhUoQtZ9sJde47iixuvqr24wXOZ7WWEOulxpI7ykJQozBbM31bNaExK91W6KkF4RSqA2n1ULeiHvQpcMkDmhfMMMJOwWFg9FNUain+faUw1jBNn0APYZEzM6/NqL0I7yRJJy9MBWLU668952Lqh/pxEMdm1y+fj0EtnlU0t/PvSFd/49cyBqowB33aZMUyVKvCyVLeAq9I0mdWTEc48+ADg/39uhGTGyv+5bAAhAJOS1L/adyhcvN7fxk+1oP/DcxeMtysKqQDqAWPnplVGA7zNO6TTDuLHyjOcutk7N8EZdNQbHJnWhgjGqg/YnbvHsLg/h/f85Bz84I3zTT7aRsqMYZckm0LW01M2E5kzq14wS9bw4zsnz0mbWgSLdUy9fH8tQPD7XJBrzqyehhd69aXzjWLy/tmUaIFPhn+AuvWaS4SZK5kMSReY+7xqM3E+GNnOKPzfVy1662aIJtlGqgEjuCAre1dM0wVNnw2GajaWX0XSdSoS0/UGPfhQ2bxswayLnJdti1Gf05sVhiMA+fnYVBPKwiTfe/3HyHmZWmPkDAGfuKZ+QdQ2hKXy7s4VinWLv5wwaXI2x+W/hvzcTMJBnEKxIi77h3ksnaNKXVSlrJqqjeqypPzXWmSQvQxhcqokVZv0Y3MPdI2q/XRznL3rDbrsoQoTmy0Uy5icquCV7euN0sfiwMuQ0pioii5M1eZkRjb4ks3qydbUHsOe/2LF4p5toYjK0NuEBYI5/PcPrawbtC5TxNUBudE2fbqCHY9k5xWHVriNxknwu3NzHs5PlWrPhc6LjqOSU6TR1M09R1PfsUiH7KGqMCbseG+yPX8ZuSn9Oa9mOGzqCn/2snnKv/f2kLDC0qaTk6kh5R6TyfnP6c1K92/bZSoMsnMKXnuT/cZZkTinN1sbhEXyBKpu9yZV0iYMDQ7g4ObrpVILsu/OmdXTUKSm6opkcw/6c2bSATadttJI1xt0le6F/wWx2V4YbRGiqpHtz3lW2QqHXjqr/HuhWBGWzdu8/LJSchG82EV3/lOlCm6+eqB2bf2LkwBiMUwqZIPGbWuWWu/X5PqYDtLnp8p419zZIADvmju7bsZj0jJNZYy3jBzD8nu+jmWb92H5PV/HlhF5e7kw2CidqtIUf275/IZ7sHWDmXRAWhtXmNL1IRdZc4bJqRJGRvO16a0qXY1DqOpliBYKdZydLGL4saPWZfhlxrSxWFms0TQFTDQNP3+xJMwiWdyfM3p5ihWGAy+cbrj+3FA9cNNK47ivjrAqjjbb9meviPK4g1rkk77QhB9/uz1/uCBqyzTbLKgwhFE6FfHKWwVlCz/V/Upr4wpTut6g8wciWHJ8drJYF3vrzRKmNMaWAaGMOSeMpgrPN9dphkT1UIKLYdueOt7wHX8+t0m4SebNx9nbMViBmJ8oYPjReMTIRAvqukYSst8C4kXSQrGszF4xva9fee416ecyg267uGgqqRE27dHEAYmr52in0pUGXfSgzpnV0+Bx+g3Lgx+7yqhSrtXces0lWH3pfDx+5FQt20REf59XVxUaNofeNH/dJB1N5c3HNUX+7BPPN5STFysMn33ieTCQdPHMxJiFaSTBEc0Qwiygm3qesgX+MmO1maifZjWNMLmvUbzptDauMKXrSv9lpecy40MAXp5uUbZl5Ji080y7eMig2MPLEsplhqC597KEHR8Ta4bIMG0J5zeIc3MefhToYsT1SmTePJdTiPIiijR5VH1Z+XkMr1sh1RXx53Bftnmf9FkYmB6sTA1KWP0g07UFWRs9oPoczOntwbnCTG/SOFIgReha3aVJm6UZ6ZNOywVmhUOyNEX/Axy2Z2WzUOl3+AWTZPFuvg2bF1RmxPwDXxCuue4PKfHBBJB781Ff7uD9MunLSlB37+HfYTBPbdWdx8hoHr+zZ8xY2E3X1Fq0/c8+8bxxz1JTBycMqlCTSYu7TqFZPUu7XsvFtHDIRFM5SSvlXoYwvG4F7pR4deXptEvuScqwLdMOUx24Y/+JhvWBYpnhjt1jtSYQohZ3UWPpwYHOpC+rSeiDH6VpnYLuPHbsP2FszG0H4Jnn31wyUiVPEFzgtPVAuyUk0uy1IRmpN+imKYQDgalmMI3OpJFCf87DR6/6aRx44XRdY4dmwLerMkA85qn6jqotmf+l49KlMh2T/EQBa7c/I3w5dcJLsu3qfqsjeP11fVlNS+jDoDoP03MMs7i37anjoeR0RQ6OvwqUFxHxgdqmgKcbBLbalT6ZeoNucgH5iyJa0MtPFHDH7jF87slj0opMImDnxlXSh7QZoZrKtI6MLO0SmPEIZDFhL0tCAyFaEFOtHfi739y5ewyHXz1Tlzmh83pNPUJbgtsbZwuxRGDUx9mCukXibU8dj73xx2wvg7XbnxF6pbrrYxJikWnMhz2PYNOInkx1MZlvTxSSaoUH2im0K30y9QZddmFlovwyj15VXg+m9kqaNSqPTxRq+5V5lf7v+FMzVVkuqv6eOhiAXYdOYvWl82vbFumMB1GFvMIuLgXlbB8sbRTG0B8sbcTZqWJtNnbfjVdY1QSYaLIUihVhfvnQ4ACG162QxtBFzUJks6dgRsqsnnB1g34HZ2hwoCGHXUWznvVO02dpV/pk6hdFbRYnbB5cPzyuKdMjb9ZiqsmCbZisBFX2hil8wAxOzWXI2ogBjYumBOA2TVckQHzvZ7Jc6vuyckTNNlREaYDhz+RRLVz6U0JN89dt4M0tZMZSlSETJGoWjIhmLDC2YoBwWS5NwuTChjXm/ME6/OoZ4e/XLp+P773+49in8AAadD7ieuhlg0PQcMTVVUh1nKpj2blJHubiBO+9KuOH4zdKutTE4LNkO3gHz12UEQTo0zzDYvKMmFRJm24rDHE6K0DzMlBagc6gd4WWi1/fgnuBQYEjWSWdjpuvrk5LZb8/+OIZpTHfkHkWz/Z+Bi/N+gSe7f0MNmSebfhORiIEcuCF07X/NtFm0Yk7cUx1Tm5bs9RKSCyIiV6KbArPACPBpaC2iUgTRLVPWcwzS1SrdPVfR9G1U12jQrFcV3UryggCqvFrPjCZMq/PU54rYeb5VSFT7OT7iEtvR/Z8xr3AmGYBr9TH0P2oqt/CZqPs/tfXsPrS+aF+H8yLXkJvYrv3MFBEXRhAltKWn1Z25C8Rj3lyr/TO3WO1RVGgcbFXlpWgSy3j29916CRyXsY4v9lPsLG1DNWCYZgX2n9usu3mvBk/R7bozO938DqKrp0/xi0sbJq8tnYfddkwsush0o+578ZqG8GgrAWHod4pkCGTlli7fD52feoD2t+boHo3415gDDNAdEoMvytCLhzV1E3VvotQzWSRGdZ+TSGKjGd7P4Mlmcasi1OVhbh26k8AVI3L/DmzFManccpuE2MNn9fsS2ebrjS0uQamja1HRvNSyYWo8VpVQU8wnKUrTNMdy8hoHv/42J/jD3v+WljYdOQnPoiDm6/XNkuWLbap9GN0YSBR6ChowJYtyNVaDpr0q7VF9W7KzjnsjMA2hJOkEI0LuUwzMppXenpr3i3WFb99zVK8vH09VONeGGMO6POiAeCBm67EdZcvkk7beYNlPk3durcx71g1ZNvGY0XT1WKZYc6sHqvwy4ThmsLQ4IAwtKPKGDANLQ0NDkivjT+E5g/bVELmyw8NDuAPf+IJaWET//3wuhXwso1XkheSyUJrXGY3zLEFpXhFUr3fOXkOX9x4FV7Zvh4vPvCRyMY8eI9U76aN1LMJtnr7nRSi6YqQC39AZfT3efjOyXMNn69dPl/bnNeWDIDsdLNjVV60n8eP5LUpf4C9cQZmGvCavhwy4xC2M5EJ9w+tFPYNFR2zraiUbKDm1zToqcpkAUzOp6/wQ+Hni+mt2u/5Mfpz4YPCZ8HCHN05mzy7/hzyVihgBo9XNov0X5e4vGHbatVO0ljvCoOuqhbNeVkw1tiUGKguaPLqx+F1K0LplQeZO53/fcfuMWVeNFD1RMI0y7CBLy6aviy2A5uXIYDqpYGD3pBJfNL0hbYxRjLPHaguRMsaSWcC4Tfj/OK5S4BzjYvnr2NB3e9tjZfunFXFZ354tW+caxamx8sgXgdoVt62zTXuJI31rgi5qB7EB25aiXOKkEldk4GPXYV5fTOtsPpzXt2/TTg7WcRde6p63Hsr12Jz8ZM4VVmICiOcqiysCUXxh7kVYmA2L6pN96KB/lw11e5jV0mny6adeEyx6ZqjmrWBVYu1REawwkJmd9xwL+DVG4ECZmH86rsjeZ+yZ4R/HgxZqLJWVM9bXAZMlbnUzC5VYWlFS8S46AoPXTbCDvRX28zJsgA43NsR9VccGc3jd3aPNUjTqvAvqu2tXFsThvIfF39YwuR680IR1VTWj82LqqtM9cPT+obXrVB2oIlzem/qTelmPrr72dfbY7SoW8eV1ZkXvvUF4NwpYO4S5G64F+/nn4dEJpvgN9x+j9Ska1CQOA2Y6n2MuygpDjpJUKwrDLqqDHdkNI/zUyXtNuq8iuf3YPIb92J24YdYXVmATbM/gd0X1tQZgZ4MoWQqoeeDC13t2H8Ck1Mla2PuZQmMVY93YDpljouFBUMFQPgX1WSg8HvcgF3n97DTe9OS66jhg9C/v3LjjGGPCZWCqAh+H+7ac9Qo3TZuWdtO7CrUKYJiXWHQVSPs2u3PGMfFR0bzGMoeROmrv4W+8gUAwJLMm/g8+0ucz5TqcsfDGHOgXujKlnl9Ht6+MFMJyZUMgyGOqJ7Gjv0nrAYalccdd3zS1JuKusidpPhpULPG/7mMocEBqfRycBtxe81J83g7JcfchK4w6IB8hDV9qRmAux49ig/NvbdmzDlBTe12QKiGAYJVqUFjGoenEcY7lf2mGd6ayTnKFgrn9XmYmCwqB6ykeZNhr6FuUOOpkiaYGMUkGs4wrfaSTMcZ9DgfipHRvFWMulxhmK1IPWsnrejP6d+XyiO08bjb5a2p9vvez39DWv1qG35ohRELew212S+GhQUmRrFdhlMmmMdpVyOKZtFRBj3uh8I2dAAA45UFwurOYO54K+HemKycPe7wgM4jtPUW2xWflO1X1t2HgEhVtVxbf+ve43V55XEQ5hrqZBCKZVYrnuGDRX+fB8bQ0H9UZxTbYTiDgntlxmr/5ka9k3LMTYiUtkhEtxDRcSKqEJG0HDUu4q7YCnPTHixtxCTrrfvMnzseN/05TxkLzRLVYuStSq9SVe7FXdXXDmQDoO3AKMukmSgUI6VmxgmvgpU549xp4mmlZyeLmCgU6xa8dWmTQHsMp0wwz/95XPc6KUT10L8L4CYAfxXDsWiJ+6EIszC2t3ItUESDpvbXmF383CTU42UIWzdUBZZUkqr++DjQmvBFMA2Oi4HxfSYx/cyUuOL6qucyadN6VSMYVXqj6m/+tMl2FOeYZP90YsaNikgGnTH2fQAgRaFCnMT9UJhW0AUR5Y7bwNMJ/V1mgBmRKz6dve7yRTXjPDfnoViu1DonBcvBOa0OX2wZOVbXjajTF5WA+AZGncOQpGm9zLBFqVJut+FU9fS9bPO+2n31NynPEhlJCieVlsXQiejTAD4NAEuXLg21jbgfChMp1WZw3eWLtPokwfjrRKGInJfFQwZNHVrFyGhe2Fouad5nGEwGRt2Cp85hSNK0XjaIRXk3/KHCdix+y2R/gZkaieHHjgJsZvApM4bHj+TrWih2Elr5XCL6BwDvEvzpc4yxr05/5x8B/C5jzEgTN4p8btSsAf+qNxGQ68mgUKzE0nnHlCwRXnzgI8rvxN2lJUgc2Rcq3Q8C8PL29ZGPM6mYSqqOjOaFTad5yI17kXEX75iiew7CVJVyzfeBzFuguUuqkgcxF1OZEKaKm5PUqlWdfK7WQ2eM/UK8hxSNKCGF4Ko3YwjVnEGElyWAVTvL6JAp+flfJj4db2iI8KONGBmN9uLHlS2kChnE4X22Km85zH5Mszb488r3EZRjkDXKaAUmz0HQs+7rzSobpgebtuDca8BTn6n+d4uN+o79J0IZcyBZ4TAbukKcixO2zZwMopk2ajs+dhV23FIvQiVrHZclqvWO9ItSDT92tJb5sLg/V3s5lmTeRIaqVanbvYfx7JN/ESlDIq5sIZnRJiBybDRu0a6492O7QM+zSQb6c9LZYKs1tk2fA37sL29fj/6++gyvIHf37GnQfEexUNWvCWCqWx+WKEY5SeEwGyLF0InolwH8KYBFAPYR0RhjbF0sR9YEwraZEyHrWOL/t6zxdJkxYReeYplh21PHaymI7x/5lLAhwh3s77Fp/w0AgM89eazmMRGA23yddmTElS0kihHzY4jqZcadtyzzwsPuJ+wCve4at9IzDPMcqP5GABZnJAV2507V/bMVhUYmWWyimXWYdbmkVMFG8tAZY08yxpYwxmYxxn4qycYcUMuGmmArmXr/0Ercvmap0FOXDS081jo0OCCtPl1MbyE/UcBdjx6tm/4yAI8cOoktIwpZWMSXeyvKOd+5aVUsrcniTFFVeeFh9xM25193jVvpGYZ5DmR/G+jP4eXt65GZu0T8w8DnzeoC5Pf6J6dKVT1+H16G6t5j0czatm6iVbNJEzqqUtSWYNnvwnd4+M8fT0m/n/OymO1lGhawOGEkU+8fWol9z78u3aYKkjREGGcLqotpknj9V557TWlU48wWalaaZJwpqirjEXY/zSi3j5KxFcZDDPMcaH9zw73VmHnRd029XPVzH80oNAp6/Wcni/CyhP6cV1fZKrouUZ7hJMkHpNagi8p+Rca8d7odHL/ZgFzr2/RhC75cYYw5AOCGe1H66m+hxycGNsl68RA+rgwf6UJLSVO7ExHnoKMyHjs3rQq9nzjK7f1ZLrzuwF+gZbL9sOGLMM+B9jcCzXdRlovJQGo7SKn63Y7dZ6ldb0GS5ANSa9BNF0AXvXN2Q3qSrOGFiXcoa1tmSl1U6MqN6AFq2uvjlQV4uPd2XLv+0/i2Ij/YJLTULv0UU0yMjU54iaMyHu0Y3ETXPkpM2dZDNL1uNsdfh4Hmu27ADnM9bAxrnDHvJLWo6xiDbnsDTBdARTd764YrQnttUXuANhz2lRvRN/1yLAGwFdVrcf6ivCnHrddcEnr/SUJlOEyElzg645GEwS3KtN1ES4Vjc92aiW4gDXM9TA1r3AuySZIP6AiDHuYGqMp+/YhGUdnDBswU08gKQqJOs3TetarQwzTLpdXE5Q35tyO7s7sOnRSe/2wvU7tmMtmEZh+/iijTdpMWdByVYFWrnxvVQBrmepga1rhj3kkKYXaEQQ9zA1RlvxzVKBp82IKGVFYQokuVIgD9fZ40rq4bhGQzgKRWtsXlDZlWLAavnuh3F0vm5Sat0vGOMm1XiVD5NUuGBges29U1E9VAGeZ6mBrWZsS8kzDLAzqksCjMDeApg9xLyRJh7fL5yvQkVaGDKpTiT7caXrdCKkXKU7tG7/2QsuhIRZIWYEyIKz0tbCgr6v6blV4XJIr0sUpeOZhGJ3u+oqb02qJL9Qt7PfxFUKKm7kD6JHP9dISHHtZ7uX9opXAa6Zd75V3pAQg9sUcPn8Shl85qPRhuUIcGB3D41TMNolXBh1GmEKDbj+xaZIgavDEZrSyCiGsAMv3+nN56IxB1/60aQKNM201UQ/kgJJu58nWXOJ4Nk23oZt3NDGMkKeYdNx1h0OO8AbIptD/GyikUyzj44hmj7TIAyzbvq2UN7Ny0qu5hfOi9P8D7//F3ga9WU7lu6f0lPDr1cw3bCRqkIMPrVgi10U01QVrdCiyuDACTqr9shvAHv1w/gEfdfyszGMJO24PGT+YSjE8Uag6OKMsljmfDdBsmA2WzwhhJinnHTUcY9DhvgMwziJKZ4odnDbx8+u3aZx8s/RMGj/4lwPPJz72GbfQlXMxUqg0zfExOV34qvRxNuFO1vtDqIoi4BmPRdoL68aJnIur+O8Wb8xu/VdueFqbdzs15AOQz1zieDdNttDvVL47BIinl/n46wqAD8d2AuHTPdVk0fs/+k1OPoCdzoe7vfTSFu3v2NDTKYFB7OTv2nzBSdLQNFTQrBh9mMFa9KLYvUFRnoBO9OVk4XBcmj+PZMN1GpwyUMtrV9FpHxxj0qPAbIKM/5+FiqWLkqfv1zJdt3qf9/mJqbCpd/bxRqyVLJPVyZAVPwm0rFn5a7RnZDMa6FyVsSCLKS5aUDAZTJiQZVLLPOXE8G6bb6MSB0k+Syv39dLRBt5nyqLIkcl621rvTv71lC3LCGLq/cMck332cLcQSgVEfZwuE294lSbc0NeZBT8d/nebmPHjTcgey77eTpL4onCROs4OENcxxeM022+i0gdJPUrPNOtag2055VBfan74Y/K2uTNok3/3B0sZ60X9UNVkeLM2UR/u3feCF01ahIVUsWdTKjivOTUyqBYvaQVJfFCC50+wgYQ1zHF5zp3veprR7DUBGxxp0W09OdgMGfHoeImQLSP6/A/VZAxli8DdC2lu5FihiuvPQWxhnC/BgaWNtQTRYFGTbvHrT+y/BgRdO45zAgxcKFlVYKOXIVpDUFwWQP3N37TlqLajVTKIY1Ti85k72vE1J6hpAxxp0W0+umTcgaPQvE8TV91aubVgA9R9bcCp/89UDOPDC6dq/J6dKwurSeX0eHj+Sl3qNSfZ4RcR9n6IKUXFUC+rtbCMnoxuMajtJ6kykYw26rSfXyhtgkjPN6Z9OJQtO5R8/kq8LBYlKtM41fwAACmxJREFU2AkQGnn/TCXJHq+IOO9TWCGq4OB63eWL8PgRs2YFSYr3O5pLEgfNjjXopp5cOxaxhDnTmWoD0uBi5NYNVxiFj/yGLthoWAT3wJM6NVQR14sSRohKFCcPVv3qSOrsp9l0woJx2ukILRcRQ4ON7c9E2iytajTs14AB0HBsO265Cjs+Jm51ZRoW4ToVqkbDHO6Bm1yntBJGiEo0uNrKViV19tNMktSGrZvpWA8d0HtyrUiBk2U+PHDTSqH6oc2Crcww6DzAoAeexKlhK7CRleXYeNd9XgaFYkWp2dMtJD3dtFvoWA/dhFYsCMahxmerLKfyALvJA9cha/ShagAiu7bBIYDn8rPAd26+ujsHz05bfE8rqTboXLvC9PMwxPEg24ZFZAPAQ5tWSSVDuxGRhPLtmgYgsmt725qldfdnTm9PgwQDA3DghdNxn0ZHkGZJ2k6io0MuOsJqWtgQRxaJ7WJSUlOmkoDoWtr2ywT011aUmgokwyPVPU/NWLzsxMX3NJJqgx5W08LkgeffEWWc2DzIUTq2OwNeT1yVnCbXVjaQ9/d5WLv9mbYNtLpr0KxqV+dkJINUG/Qw3rPJAx/8DgNqRj3YY1RH2heTWpnK1sprKZPzffvCTAFYOwqNdNegmdfIORntJ9Ux9DBtrEwWOWWpbbyEPzi9lbW1A9K9mNTqVLZWXkvRuocort6MdnUqdNdA9vf8REH6jDo6h1R76GGmgSZGwdRwbBk5VleUIvLYZA2jZ3sZLL/n65FL1ttJq2cfra6KDXqkSYir666BqorZP+gC7ZcvcNiTag8dMGsa68dktd7kOyOjeWGFod9jGxnN4+0LJeG2CsVKLYeal6xvGZHruSeRVs8+ojRajoMkZHroroHo70FaPatwxEfqDbotqheCh09kHs51ly+q/feO/SeUvR35d0y6D3FkpexJpdUGrt1Vse0eUAD9NQj+XUZ+oqAMFTqSSapDLqYEFfnWvHseXnmrUBemAdCwCBbEn4Os8kK5QbP1VHWNNJpJmMXNdqSytXNhLimZHrpr4P+7zEEhoPa5C8PEQysSBLreoIsU+Q6+eKahAGXt9me0+uR+Ay2LVRJQM2g2qoxANX++HSlxUVIrgfYbuFYQfFl3blrVEecpGnRFwm9pyrxqB61qjhIp5EJEO4joBSJ6noieJKL+uA6sVagU+fyYeNP+UIJo+k0AbluztHYDZVP0tcvnC7fPvaZWix9FkTewXcPoRDpZmEoUotGFCh32xCERYkLUGPo3AfwMY+xKAP8O4J7oh9RaTBX5dHFfkSBW8EXZuWlVndcvi3fu+tQHGkrW+7wMguH2Vi1epTm1Mg5a9bI2i+CgO5CAxd200ap3KFLIhTH2tO+fhwB8LNrhtB5TRT7V1FRWTGQSz5V9x6QLEtAao9ppTTJaTdoGPFfGHz+teofijKH/GoDdsj8S0acBfBoAli5dGuNuoyFr8hxU5Gt3PLhVD4Ro4ca94GrSNuC1+1lPI616h4hpMieI6B8AvEvwp88xxr46/Z3PAVgN4Cam2yCA1atXs8OHD4c43OYQV9/JZiJqQZfzsrGm5an2AbgXXEYr7o2j84kjy4WIjjDGVkv/bmB/dTv4VQC/AeAGxtikyW+SZtCTiOjmA801qrIUNi5p4JDj2q85WoHOoEcKuRDRhwHcDeC/mxrzVtOJL5ptF6S4SFssuJU4YSpHEogaQ/8zALMAfJOqi4iHGGO/GfmoYqJVuZ8mx2EzqLRLgTFtsWCHmk4INTrsiJS2yBj7L4yxSxhjq6b/lxhjDiQjnSxMjnK7POUklK47WgMvqOt0vSBHPanWcklCCCHMoBKHBopOtldEu7VQHK3DtKDO0VmkuvQ/CSGEMINK1BSnKKEmFwvuDkwL6hydRao99CSEEMJ421E9ZdmsYNtTx52CngNAY+Gc7nNHZ5BqDz0JBRJhve0onrLM+z87WWxrezRHcjAtqHN0Fqk26ED7QwjtGFRMVRydgl73wrNZXJZLuohcWBQGV1jUXESVizIIwMvb1zf/oJpIJ9YaOMxx93eGphYWOZKJaFZw/mIJE4XG3qWdnmOelFoDR3Nw99cOZ9BTSjDUJNMb6fQc83YVYTlag7u/djiD3iUkYYG4GSSh1sDRPNz9tcMZ9C6i3QvEzSAJtQaO5uHurx2pzkPvJsJUhqaBJNQaOJqHu792OA89BXTzwlFaQ0mOKu7+2uHSFlOA0zF3OLoDXdqiC7mkALdw5HA4AGfQU0Ec6owOh6PzcQY9BbiFI4fDAbhF0VTgFo4cDgfgDHpqSGOOucPhsMOFXBwOhyMlOIPucDgcKcEZdIfD4UgJzqA7HA5HSnAG3eFwOFJCW0r/ieg0gFdj3uxCAG/GvM124s4n2bjzSTZpOx+gek5zGGOLZF9oi0FvBkR0WKVx0Gm480k27nySTdrOBzA7JxdycTgcjpTgDLrD4XCkhDQZ9C+1+wBixp1PsnHnk2zSdj6AwTmlJobucDgc3U6aPHSHw+HoapxBdzgcjpSQGoNORDuI6AUiep6IniSi/nYfUxSI6BYiOk5EFSLq2PQrIvowEZ0gov8gos3tPp6oENHfEtEbRPTddh9LHBDRJUR0gIi+N/28/Xa7jykKRDSbiP6ViI5On8+2dh9THBBRlohGiehrqu+lxqAD+CaAn2GMXQng3wHc0+bjicp3AdwE4J/bfSBhIaIsgD8H8IsA3gvgViJ6b3uPKjJ/B+DD7T6IGCkBuIsx9l4AawD8jw6/RxcBXM8YuwrAKgAfJqI1bT6mOPhtAN/XfSk1Bp0x9jRjrDT9z0MAlrTzeKLCGPs+Y+xEu48jIj8L4D8YYy8xxqYA/D2AX2rzMUWCMfbPAM60+zjigjH2OmPsO9P//WNUjUbHCuuzKm9P/9Ob/l9HZ34Q0RIA6wE8rPtuagx6gF8D8I12H4QDAwBe8/37FDrYWKQdIloGYBDAc+09kmhMhyfGALwB4JuMsY4+HwAPAbgbQEX3xY7qWERE/wDgXYI/fY4x9tXp73wO1WnkrlYeWxhMzsfhaAVE9A4AjwO4gzH2o3YfTxQYY2UAq6bX0Z4kop9hjHXkmgcRfRTAG4yxI0T087rvd5RBZ4z9gurvRPSrAD4K4AbWAQn2uvNJAXkAl/j+vWT6M0eCICIPVWO+izH2RLuPJy4YYxNEdADVNY+ONOgA1gLYQEQfATAbwE8Q0SOMsdtFX05NyIWIPozqtGQDY2yy3cfjAAD8G4D3ENFlRNQL4OMA9rb5mBw+iIgA/A2A7zPG/rjdxxMVIlrEM9yIKAfggwBeaO9RhYcxdg9jbAljbBmq788zMmMOpMigA/gzAO8E8E0iGiOiv2z3AUWBiH6ZiE4B+ACAfUS0v93HZMv0IvX/BLAf1cW2PYyx4+09qmgQ0VcAfBvACiI6RUS/3u5jishaAL8C4Prp92Zs2hvsVH4awAEieh5Vh+KbjDFlql+acKX/DofDkRLS5KE7HA5HV+MMusPhcKQEZ9AdDocjJTiD7nA4HCnBGXSHw+FICc6gOxwOR0pwBt3hcDhSwv8Hy4UF9YFBZVcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H_IZRGBft5or"
      },
      "source": [
        "## Very slightly corrupted theta:\n",
        "Theta = {\n",
        "    'log_mu': np.log(mu_init + 1e-6),\n",
        "    'log_sigma': np.log(sigma_init + 1e-6), #np.zeros_like(sigma_init),\n",
        "    'log_psi': np.log(psi_init + 1e-6),\n",
        "    'log_omega': np.log(omega_init + 1e-6),\n",
        "    \"is_delta\": np.log([0.95, 1-0.95]),\n",
        "    'is_pi': np.log(pi_init),\n",
        "    'is_tau': np.log(tau_init)\n",
        "}\n",
        "\n",
        "Theta = {k: torch.tensor(v, requires_grad=True) for (k,v) in Theta.items()}\n",
        "#Theta['is_delta'].requires_grad = False\n",
        "#Theta['is_tau'].requires_grad = False\n",
        "#Theta['log_psi'].requires_grad = False"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "s0s0n52Xig3w",
        "outputId": "5c88890d-e137-441b-f4e2-60213396c39a"
      },
      "source": [
        "Theta['log_psi'].exp()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([102.3026, 144.2121, 114.9750, 112.1188,  76.7778, 123.3714, 140.5938,\n",
              "        100.0154, 119.6667,  88.3750,  74.9773,  99.4074, 113.8028,  98.8659,\n",
              "         88.3391], dtype=torch.float64, grad_fn=<ExpBackward>)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IpaZW5gNb13K"
      },
      "source": [
        "N_ITER = 1000\n",
        "N_ITER_OPT = 100\n",
        "lr = 1e-3\n",
        "tol = 1e-2\n",
        "\n",
        "Y = torch.tensor(YY)\n",
        "S = torch.tensor(SS)"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7eo_fyb1t82R",
        "outputId": "092469a8-4bf1-41a6-9b62-71f9b19118cc"
      },
      "source": [
        "opt = optim.Adam(Theta.values())\n",
        "\n",
        "ls = []\n",
        "qs = []\n",
        "for i in range(N_ITER):\n",
        "\n",
        "  print(i)\n",
        "\n",
        "  # E Step:\n",
        "  with torch.no_grad():\n",
        "    r, v, L, p_singlet_em = compute_r_v_2(Y, S, Theta)\n",
        "\n",
        "  # M step (i.e. maximizing Q):\n",
        "  for j in range(N_ITER_OPT):\n",
        "\n",
        "    opt.zero_grad()\n",
        "    q = -Q(Theta, Y, S, r, v, None)\n",
        "    # print(q)\n",
        "    q.backward()\n",
        "    opt.step()\n",
        "    \n",
        "  if i % (10 - 1) == 0:\n",
        "    print(\"L: {}; {}; {}\".format(L.sum(), F.log_softmax(Theta['is_delta'], 0).exp(), F.log_softmax(Theta['is_pi'], 0).exp()))\n",
        "\n",
        "  # Check for convergence\n",
        "  if i > 0 and abs(ls[-1] - L.sum()) < tol:\n",
        "    break\n",
        "\n",
        "  qs.append(-q.sum())\n",
        "  ls.append(L.sum())"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:59: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:60: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:61: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:3: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n",
            "  This is separate from the ipykernel package so we can avoid doing imports until\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:4: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n",
            "  after removing the cwd from sys.path.\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n",
            "  \"\"\"\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "L: 102353.08251251368; tensor([0.9398, 0.0602], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.0850, 0.0349, 0.0894, 0.1123, 0.0499, 0.0323, 0.0337, 0.0616, 0.0362,\n",
            "        0.0444, 0.0980, 0.0746, 0.0659, 0.0756, 0.1062], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
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            "        0.0327, 0.1599, 0.0481, 0.0403, 0.0426, 0.0662], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
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            "        0.0523, 0.1334, 0.0525, 0.0509, 0.0354, 0.0580], dtype=torch.float64,\n",
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            "        0.0677, 0.1224, 0.0735, 0.0525, 0.0305, 0.0337], dtype=torch.float64,\n",
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            "        0.0772, 0.1320, 0.0999, 0.0616, 0.0224, 0.0205], dtype=torch.float64,\n",
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            "        0.0787, 0.1176, 0.1190, 0.0723, 0.0163, 0.0136], dtype=torch.float64,\n",
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            "        0.0709, 0.1077, 0.1414, 0.0810, 0.0124, 0.0093], dtype=torch.float64,\n",
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            "        0.0615, 0.1151, 0.1610, 0.0886, 0.0093, 0.0064], dtype=torch.float64,\n",
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            "        0.0714, 0.1329, 0.1812, 0.0993, 0.0067, 0.0044], dtype=torch.float64,\n",
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            "        0.0976, 0.1447, 0.1932, 0.1055, 0.0043, 0.0029], dtype=torch.float64,\n",
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            "        0.1052, 0.1492, 0.1989, 0.1084, 0.0029, 0.0019], dtype=torch.float64,\n",
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            "        0.1076, 0.1512, 0.2014, 0.1095, 0.0020, 0.0014], dtype=torch.float64,\n",
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            "        0.1082, 0.1518, 0.2024, 0.1099, 0.0014, 0.0010], dtype=torch.float64,\n",
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            "        0.1084, 0.1520, 0.2029, 0.1101, 0.0010, 0.0007], dtype=torch.float64,\n",
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            "        0.1085, 0.1520, 0.2032, 0.1101, 0.0007, 0.0005], dtype=torch.float64,\n",
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            "        7.0360e-03, 2.0742e-02, 6.1528e-02, 1.0850e-01, 1.5207e-01, 2.0358e-01,\n",
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            "        7.0687e-03, 2.0799e-02, 6.1544e-02, 1.0855e-01, 1.5211e-01, 2.0396e-01,\n",
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            "        7.0719e-03, 2.0806e-02, 6.1551e-02, 1.0855e-01, 1.5212e-01, 2.0401e-01,\n",
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            "        7.0750e-03, 2.0814e-02, 6.1561e-02, 1.0857e-01, 1.5215e-01, 2.0410e-01,\n",
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            "        7.0769e-03, 2.0821e-02, 6.1560e-02, 1.0858e-01, 1.5215e-01, 2.0412e-01,\n",
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            "        7.0779e-03, 2.0822e-02, 6.1567e-02, 1.0859e-01, 1.5217e-01, 2.0415e-01,\n",
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            "L: 118089.63851251084; tensor([0.0817, 0.9183], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([7.7779e-02, 3.5594e-02, 1.3293e-01, 2.1011e-03, 8.6935e-02, 3.4506e-06,\n",
            "        7.0791e-03, 2.0823e-02, 6.1568e-02, 1.0860e-01, 1.5218e-01, 2.0416e-01,\n",
            "        1.1024e-01, 5.1137e-06, 3.5315e-06], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "235\n",
            "236\n",
            "237\n",
            "238\n",
            "239\n",
            "240\n",
            "241\n",
            "242\n",
            "243\n",
            "L: 118089.6687014538; tensor([0.0817, 0.9183], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([7.7792e-02, 3.5597e-02, 1.3294e-01, 2.0335e-03, 8.6933e-02, 2.3797e-06,\n",
            "        7.0798e-03, 2.0827e-02, 6.1571e-02, 1.0860e-01, 1.5218e-01, 2.0420e-01,\n",
            "        1.1024e-01, 3.5291e-06, 2.4383e-06], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "244\n",
            "245\n",
            "246\n",
            "247\n",
            "248\n",
            "249\n",
            "250\n",
            "251\n",
            "252\n",
            "L: 118089.68103924647; tensor([0.0817, 0.9183], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([7.7794e-02, 3.5597e-02, 1.3295e-01, 1.9722e-03, 8.6936e-02, 1.6592e-06,\n",
            "        7.0801e-03, 2.0828e-02, 6.1581e-02, 1.0861e-01, 1.5219e-01, 2.0421e-01,\n",
            "        1.1025e-01, 2.4634e-06, 1.7028e-06], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "253\n",
            "254\n",
            "255\n",
            "256\n",
            "257\n",
            "258\n",
            "259\n",
            "260\n",
            "261\n",
            "L: 118089.69809041874; tensor([0.0817, 0.9183], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([7.7783e-02, 3.5601e-02, 1.3296e-01, 1.9161e-03, 8.6944e-02, 1.1619e-06,\n",
            "        7.0802e-03, 2.0827e-02, 6.1580e-02, 1.0861e-01, 1.5220e-01, 2.0423e-01,\n",
            "        1.1026e-01, 1.7270e-06, 1.1942e-06], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "262\n",
            "263\n",
            "264\n",
            "265\n",
            "266\n",
            "267\n",
            "268\n",
            "269\n",
            "270\n",
            "L: 118089.70697497542; tensor([0.0817, 0.9183], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([7.7808e-02, 3.5602e-02, 1.3297e-01, 1.8664e-03, 8.6948e-02, 8.1361e-07,\n",
            "        7.0810e-03, 2.0832e-02, 6.1580e-02, 1.0862e-01, 1.5220e-01, 2.0423e-01,\n",
            "        1.1025e-01, 1.2099e-06, 8.3680e-07], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "271\n",
            "272\n",
            "273\n",
            "274\n",
            "275\n",
            "276\n",
            "277\n",
            "278\n",
            "279\n",
            "L: 118089.71218465551; tensor([0.0817, 0.9183], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([7.7818e-02, 3.5604e-02, 1.3297e-01, 1.8209e-03, 8.6945e-02, 5.6875e-07,\n",
            "        7.0825e-03, 2.0835e-02, 6.1581e-02, 1.0863e-01, 1.5221e-01, 2.0424e-01,\n",
            "        1.1026e-01, 8.4584e-07, 5.8503e-07], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "280\n",
            "281\n",
            "282\n",
            "283\n",
            "284\n",
            "285\n",
            "286\n",
            "287\n",
            "288\n",
            "L: 118089.71568085693; tensor([0.0817, 0.9183], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([7.7827e-02, 3.5607e-02, 1.3299e-01, 1.7795e-03, 8.6946e-02, 3.9697e-07,\n",
            "        7.0827e-03, 2.0838e-02, 6.1581e-02, 1.0863e-01, 1.5221e-01, 2.0425e-01,\n",
            "        1.1025e-01, 5.9025e-07, 4.0823e-07], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "289\n",
            "290\n",
            "291\n",
            "292\n",
            "293\n",
            "294\n",
            "295\n",
            "296\n",
            "297\n",
            "L: 118089.71782089175; tensor([0.0816, 0.9184], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([7.7826e-02, 3.5607e-02, 1.3300e-01, 1.7414e-03, 8.6952e-02, 2.7623e-07,\n",
            "        7.0831e-03, 2.0837e-02, 6.1584e-02, 1.0863e-01, 1.5222e-01, 2.0426e-01,\n",
            "        1.1026e-01, 4.1048e-07, 2.8387e-07], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "298\n",
            "299\n",
            "300\n",
            "301\n",
            "302\n",
            "303\n",
            "304\n",
            "305\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iwBHdonfvJPu",
        "outputId": "beb6fe12-114f-459e-c24e-77aaa900317d"
      },
      "source": [
        "F.log_softmax(torch.tensor(Theta['is_delta']), 0).exp()"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:1: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
            "  \"\"\"Entry point for launching an IPython kernel.\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0.0816, 0.9184], dtype=torch.float64)"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0LCtshQaDPWX",
        "outputId": "0f40feca-69a4-46f0-9dc8-cc3a4e3f1836"
      },
      "source": [
        "with torch.no_grad():\n",
        "  r, v, L, p_singlet_em = compute_r_v_2(Y,S,Theta)\n",
        "\n",
        "p_singlet_em = p_singlet_em.numpy()"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:59: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:60: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:61: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vOpIWvCPDrMe"
      },
      "source": [
        "#adata.obs"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wCRRwGeADefM",
        "outputId": "dd83869c-1f33-4dd3-99f5-48341a324c10"
      },
      "source": [
        "adata.obs['p_singlet_em'] = p_singlet_em\n",
        "adata.obs['probability_single_cell_em'] = adata.obs.p_singlet_em"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Trying to set attribute `.obs` of view, copying.\n",
            "Observation names are not unique. To make them unique, call `.obs_names_make_unique`.\n",
            "Observation names are not unique. To make them unique, call `.obs_names_make_unique`.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "id": "uIn2wY-Tx3sM",
        "outputId": "f4e4484d-d4d8-4f28-8199-ad4f2d92bf53"
      },
      "source": [
        "sc.pl.scatter(adata, x = 'ECadherin', y = 'Vimentin', color = 'probability_single_cell_em')"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 541.714x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "25Go_Wy4EPDu"
      },
      "source": [
        "p_doublet_em = 1 - p_singlet_em\n",
        "adata.obs['p_doublet_em'] = p_doublet_em\n",
        "adata.obs['probability_doublet_cell_em'] = adata.obs.p_doublet_em"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "id": "6q1sZ7-dEPsI",
        "outputId": "d93a7e69-fd03-4241-dc5f-87ec13c727d5"
      },
      "source": [
        "sc.pl.scatter(adata, x = 'ECadherin', y = 'Vimentin', color = 'probability_doublet_cell_em')"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 541.714x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "3O5vNG0rwf_X",
        "outputId": "1c9d0dc9-ccae-4f2c-f25a-6c12078f6e78"
      },
      "source": [
        "plt.plot(torch.tensor(psi_init), label=\"before\")\n",
        "plt.plot(Theta['log_psi'].exp().detach().numpy(), label=\"after\")\n",
        "plt.legend()\n",
        "plt.xlabel(\"cluster number\")\n",
        "plt.ylabel(\"cell size\")"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'cell size')"
            ]
          },
          "metadata": {},
          "execution_count": 22
        },
        {
          "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": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "Edg3CQn793Ly",
        "outputId": "3349fe56-3874-42f0-fafe-14d9bdb63801"
      },
      "source": [
        "plt.plot(ls)\n",
        "plt.xlabel(\"iter\")\n",
        "plt.ylabel(\"ll\")"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'll')"
            ]
          },
          "metadata": {},
          "execution_count": 23
        },
        {
          "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": "code",
      "metadata": {
        "id": "ZKYXu0PwDA6p"
      },
      "source": [
        "def ll(Y, S, Theta):\n",
        "  \"\"\"compute\n",
        "  p(gamma = [c,c'], d= 1 | Y,S)\n",
        "  p(z = c, d=0 | Y,S)\n",
        "  \"\"\"\n",
        "  log_pi = F.log_softmax(Theta['is_pi'], 0)\n",
        "  log_tau = F.log_softmax(Theta['is_tau'].reshape(-1), 0).reshape(nc,nc)\n",
        "  log_delta = F.log_softmax(Theta['is_delta'], 0)\n",
        "\n",
        "  p_y_given_z = compute_p_y_given_z(Y, Theta)\n",
        "  p_s_given_z = compute_p_s_given_z(S, Theta)\n",
        "\n",
        "  p_data_given_z_d0 = p_y_given_z + p_s_given_z + log_pi\n",
        "  p_data_given_d0 = torch.logsumexp(p_data_given_z_d0, dim=1) # this is p(data|d=0)\n",
        "\n",
        "  p_y_given_gamma = compute_p_y_given_gamma(Y, Theta)\n",
        "  p_s_given_gamma = compute_p_s_given_gamma(S, Theta)\n",
        "\n",
        "  p_data_given_gamma_d1 = (p_y_given_gamma + p_s_given_gamma + log_tau).reshape(Y.shape[0], -1)\n",
        "\n",
        "  # p_data_given_d1 = torch.logsumexp(p_data_given_gamma_d1, dim=1)\n",
        "\n",
        "  p_data = torch.cat([p_data_given_z_d0 + log_delta[0], p_data_given_gamma_d1 + log_delta[1]], dim=1)\n",
        "  #p_data = torch.logsumexp(p_data, dim=1)\n",
        "\n",
        "  #r = p_data_given_z_d0.T + log_delta[0] - p_data\n",
        "  #v = p_data_given_gamma_d1.T + log_delta[1] - p_data\n",
        "\n",
        "  #p_singlet = torch.exp(p_data_given_d0 + log_delta[0] - p_data)\n",
        "\n",
        "  #return r.T, v.T.reshape(-1,nc,nc), -p_data, p_singlet\n",
        "\n",
        "  return torch.logsumexp(p_data, dim=1).sum()"
      ],
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3UC-L0W2DR1x"
      },
      "source": [
        "## Very slightly corrupted theta:\n",
        "Theta1 = {\n",
        "    'log_mu': np.log(mu_init + 1e-6),\n",
        "    'log_sigma': np.log(sigma_init + 1e-6), #np.zeros_like(sigma_init),\n",
        "    'log_psi': np.log(psi_init + 1e-6),\n",
        "    'log_omega': np.log(omega_init + 1e-6),\n",
        "    \"is_delta\": np.log([0.95, 1-0.95]),\n",
        "    'is_pi': np.log(pi_init),\n",
        "    'is_tau': np.log(tau_init)\n",
        "}\n",
        "\n",
        "Theta1 = {k: torch.tensor(v, requires_grad=True) for (k,v) in Theta1.items()}\n",
        "#Theta1['is_delta'].requires_grad = False\n",
        "#Theta1['is_tau'].requires_grad = False\n",
        "#Theta1['log_psi'].requires_grad = False"
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SNg3l2tWAuVQ",
        "outputId": "abff20b4-a7d6-4900-f91a-3e28570d9649"
      },
      "source": [
        "opt = optim.Adam(Theta1.values())\n",
        "\n",
        "loss = []\n",
        "for epoch in range(N_ITER * N_ITER_OPT):\n",
        "\n",
        "  #print(i)\n",
        "\n",
        "  opt.zero_grad()\n",
        "  nlls = -ll(Y, S, Theta1) #nll\n",
        "  nlls.backward()\n",
        "  opt.step()\n",
        "\n",
        "  if epoch % (100 - 1) == 0:\n",
        "    print(\"L: {}; {}; {}\".format(nlls, F.log_softmax(Theta1['is_delta'], 0).exp(), F.log_softmax(Theta1['is_pi'], 0).exp()))\n",
        "      \n",
        "  if epoch > 0 and abs(loss[-1] - nlls) < tol:\n",
        "    break\n",
        "  \n",
        "  loss.append(nlls)"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "L: -102353.08251251368; tensor([0.9499, 0.0501], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.0761, 0.0330, 0.0801, 0.1011, 0.0540, 0.0350, 0.0320, 0.0649, 0.0390,\n",
            "        0.0480, 0.0881, 0.0809, 0.0709, 0.0819, 0.1149], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -104682.48812802607; tensor([0.9387, 0.0613], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.0862, 0.0353, 0.0904, 0.1130, 0.0500, 0.0325, 0.0303, 0.0596, 0.0358,\n",
            "        0.0444, 0.0990, 0.0754, 0.0657, 0.0759, 0.1065], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -106403.21764391685; tensor([0.9228, 0.0772], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.0976, 0.0345, 0.1021, 0.1205, 0.0464, 0.0307, 0.0275, 0.0535, 0.0333,\n",
            "        0.0420, 0.1094, 0.0710, 0.0614, 0.0700, 0.1002], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -107848.107983748; tensor([0.9023, 0.0977], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1091, 0.0358, 0.1132, 0.1234, 0.0433, 0.0293, 0.0254, 0.0482, 0.0321,\n",
            "        0.0392, 0.1184, 0.0663, 0.0581, 0.0644, 0.0939], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -109081.62371838558; tensor([0.8768, 0.1232], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1198, 0.0361, 0.1208, 0.1256, 0.0416, 0.0282, 0.0238, 0.0433, 0.0316,\n",
            "        0.0370, 0.1272, 0.0619, 0.0560, 0.0596, 0.0877], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -110225.2022448808; tensor([0.8450, 0.1550], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1282, 0.0414, 0.1215, 0.1288, 0.0399, 0.0275, 0.0215, 0.0387, 0.0316,\n",
            "        0.0356, 0.1342, 0.0577, 0.0556, 0.0555, 0.0822], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -111188.92714172015; tensor([0.8081, 0.1919], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1344, 0.0470, 0.1185, 0.1343, 0.0386, 0.0269, 0.0201, 0.0345, 0.0318,\n",
            "        0.0347, 0.1394, 0.0541, 0.0561, 0.0520, 0.0777], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -112101.66449831784; tensor([0.7665, 0.2335], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1400, 0.0517, 0.1160, 0.1429, 0.0382, 0.0264, 0.0199, 0.0322, 0.0322,\n",
            "        0.0352, 0.1341, 0.0514, 0.0562, 0.0491, 0.0747], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -112882.90254474666; tensor([0.7218, 0.2782], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1464, 0.0555, 0.1144, 0.1505, 0.0385, 0.0259, 0.0201, 0.0306, 0.0326,\n",
            "        0.0368, 0.1247, 0.0495, 0.0563, 0.0469, 0.0712], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -113543.38610870557; tensor([0.6753, 0.3247], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1541, 0.0610, 0.1147, 0.1453, 0.0396, 0.0258, 0.0204, 0.0293, 0.0334,\n",
            "        0.0390, 0.1167, 0.0485, 0.0574, 0.0456, 0.0690], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -114100.0905764513; tensor([0.6288, 0.3712], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1609, 0.0648, 0.1149, 0.1381, 0.0404, 0.0259, 0.0209, 0.0279, 0.0344,\n",
            "        0.0412, 0.1125, 0.0479, 0.0584, 0.0446, 0.0671], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -114561.7586050409; tensor([0.5840, 0.4160], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1666, 0.0673, 0.1144, 0.1348, 0.0409, 0.0259, 0.0205, 0.0267, 0.0344,\n",
            "        0.0435, 0.1100, 0.0473, 0.0589, 0.0434, 0.0654], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -114948.27407984971; tensor([0.5419, 0.4581], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1714, 0.0688, 0.1137, 0.1316, 0.0416, 0.0258, 0.0204, 0.0258, 0.0341,\n",
            "        0.0455, 0.1082, 0.0471, 0.0604, 0.0420, 0.0636], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -115285.99188425338; tensor([0.5024, 0.4976], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1758, 0.0714, 0.1127, 0.1247, 0.0425, 0.0252, 0.0204, 0.0252, 0.0340,\n",
            "        0.0470, 0.1068, 0.0476, 0.0638, 0.0409, 0.0620], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -115580.52499922372; tensor([0.4659, 0.5341], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1809, 0.0715, 0.1110, 0.1195, 0.0437, 0.0243, 0.0205, 0.0250, 0.0342,\n",
            "        0.0480, 0.1056, 0.0489, 0.0664, 0.0401, 0.0604], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -115832.24268952679; tensor([0.4326, 0.5674], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1873, 0.0666, 0.1092, 0.1182, 0.0452, 0.0238, 0.0206, 0.0250, 0.0349,\n",
            "        0.0491, 0.1049, 0.0506, 0.0662, 0.0396, 0.0587], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -116087.49712561756; tensor([0.4018, 0.5982], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1943, 0.0618, 0.1067, 0.1197, 0.0469, 0.0234, 0.0208, 0.0253, 0.0360,\n",
            "        0.0481, 0.1034, 0.0527, 0.0648, 0.0391, 0.0570], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -116278.54899084683; tensor([0.3740, 0.6260], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.1998, 0.0613, 0.1030, 0.1213, 0.0483, 0.0231, 0.0209, 0.0255, 0.0370,\n",
            "        0.0466, 0.1019, 0.0547, 0.0633, 0.0386, 0.0548], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -116441.90986362485; tensor([0.3495, 0.6505], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2048, 0.0612, 0.0995, 0.1219, 0.0495, 0.0228, 0.0207, 0.0257, 0.0378,\n",
            "        0.0455, 0.1008, 0.0566, 0.0626, 0.0380, 0.0526], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -116599.19355347758; tensor([0.3278, 0.6722], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2095, 0.0624, 0.0964, 0.1211, 0.0504, 0.0225, 0.0202, 0.0260, 0.0383,\n",
            "        0.0445, 0.0993, 0.0582, 0.0635, 0.0375, 0.0504], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -116749.80229840436; tensor([0.3089, 0.6911], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2154, 0.0595, 0.0938, 0.1188, 0.0509, 0.0223, 0.0192, 0.0263, 0.0384,\n",
            "        0.0439, 0.0965, 0.0599, 0.0695, 0.0371, 0.0484], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -116867.27280118101; tensor([0.2919, 0.7081], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2216, 0.0575, 0.0918, 0.1161, 0.0511, 0.0221, 0.0179, 0.0268, 0.0383,\n",
            "        0.0437, 0.0943, 0.0618, 0.0735, 0.0367, 0.0466], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -116970.09100872118; tensor([0.2767, 0.7233], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2280, 0.0557, 0.0903, 0.1133, 0.0510, 0.0220, 0.0166, 0.0273, 0.0381,\n",
            "        0.0440, 0.0929, 0.0638, 0.0756, 0.0365, 0.0450], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117061.4749009016; tensor([0.2628, 0.7372], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2349, 0.0533, 0.0893, 0.1088, 0.0510, 0.0219, 0.0153, 0.0280, 0.0380,\n",
            "        0.0446, 0.0918, 0.0662, 0.0769, 0.0364, 0.0437], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117146.76707848685; tensor([0.2499, 0.7501], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2423, 0.0491, 0.0889, 0.1037, 0.0513, 0.0219, 0.0143, 0.0288, 0.0379,\n",
            "        0.0456, 0.0907, 0.0688, 0.0778, 0.0364, 0.0425], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117223.78004338019; tensor([0.2381, 0.7619], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2502, 0.0414, 0.0891, 0.0987, 0.0520, 0.0219, 0.0134, 0.0297, 0.0378,\n",
            "        0.0469, 0.0905, 0.0718, 0.0785, 0.0366, 0.0415], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117354.91455306648; tensor([0.2268, 0.7732], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2586, 0.0307, 0.0898, 0.0940, 0.0530, 0.0220, 0.0127, 0.0308, 0.0377,\n",
            "        0.0486, 0.0913, 0.0751, 0.0782, 0.0368, 0.0407], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117434.78734691282; tensor([0.2166, 0.7834], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2648, 0.0258, 0.0901, 0.0895, 0.0538, 0.0218, 0.0120, 0.0318, 0.0373,\n",
            "        0.0501, 0.0919, 0.0779, 0.0767, 0.0368, 0.0397], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117501.18230817755; tensor([0.2072, 0.7928], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2695, 0.0225, 0.0902, 0.0852, 0.0544, 0.0215, 0.0113, 0.0326, 0.0371,\n",
            "        0.0517, 0.0924, 0.0803, 0.0761, 0.0366, 0.0386], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117555.51552758134; tensor([0.1989, 0.8011], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2735, 0.0205, 0.0901, 0.0810, 0.0548, 0.0211, 0.0106, 0.0334, 0.0371,\n",
            "        0.0530, 0.0928, 0.0823, 0.0760, 0.0363, 0.0375], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117604.16367221036; tensor([0.1913, 0.8087], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2774, 0.0192, 0.0901, 0.0770, 0.0548, 0.0205, 0.0101, 0.0342, 0.0372,\n",
            "        0.0542, 0.0930, 0.0838, 0.0763, 0.0360, 0.0363], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117652.13351742084; tensor([0.1845, 0.8155], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2812, 0.0184, 0.0901, 0.0731, 0.0543, 0.0198, 0.0095, 0.0350, 0.0375,\n",
            "        0.0553, 0.0931, 0.0851, 0.0768, 0.0356, 0.0352], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117716.79078092703; tensor([0.1779, 0.8221], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2864, 0.0179, 0.0905, 0.0697, 0.0487, 0.0192, 0.0091, 0.0359, 0.0383,\n",
            "        0.0569, 0.0936, 0.0863, 0.0779, 0.0353, 0.0342], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117775.22205648596; tensor([0.1718, 0.8282], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2922, 0.0177, 0.0910, 0.0662, 0.0440, 0.0186, 0.0088, 0.0370, 0.0392,\n",
            "        0.0587, 0.0944, 0.0872, 0.0767, 0.0350, 0.0333], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117834.90100520474; tensor([0.1660, 0.8340], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.2979, 0.0168, 0.0915, 0.0621, 0.0407, 0.0179, 0.0084, 0.0380, 0.0402,\n",
            "        0.0605, 0.0946, 0.0877, 0.0765, 0.0347, 0.0323], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117878.50520629105; tensor([0.1607, 0.8393], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3034, 0.0157, 0.0923, 0.0585, 0.0378, 0.0172, 0.0081, 0.0390, 0.0412,\n",
            "        0.0622, 0.0945, 0.0877, 0.0768, 0.0342, 0.0314], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117919.45983199084; tensor([0.1556, 0.8444], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3090, 0.0146, 0.0930, 0.0553, 0.0350, 0.0164, 0.0078, 0.0400, 0.0422,\n",
            "        0.0640, 0.0945, 0.0862, 0.0777, 0.0337, 0.0305], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117949.12244691528; tensor([0.1508, 0.8492], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3149, 0.0136, 0.0938, 0.0525, 0.0319, 0.0157, 0.0075, 0.0411, 0.0433,\n",
            "        0.0658, 0.0945, 0.0837, 0.0791, 0.0332, 0.0295], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -117978.17082348818; tensor([0.1466, 0.8534], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3200, 0.0127, 0.0946, 0.0497, 0.0290, 0.0150, 0.0073, 0.0420, 0.0442,\n",
            "        0.0677, 0.0944, 0.0819, 0.0801, 0.0327, 0.0287], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118002.9593206401; tensor([0.1427, 0.8573], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3246, 0.0118, 0.0953, 0.0469, 0.0264, 0.0144, 0.0071, 0.0428, 0.0450,\n",
            "        0.0699, 0.0943, 0.0806, 0.0808, 0.0320, 0.0279], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118026.04529302816; tensor([0.1392, 0.8608], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3288, 0.0111, 0.0960, 0.0443, 0.0242, 0.0138, 0.0068, 0.0436, 0.0457,\n",
            "        0.0717, 0.0942, 0.0797, 0.0816, 0.0312, 0.0271], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118052.26026838107; tensor([0.1360, 0.8640], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3330, 0.0105, 0.0963, 0.0421, 0.0223, 0.0132, 0.0066, 0.0444, 0.0464,\n",
            "        0.0733, 0.0943, 0.0781, 0.0828, 0.0303, 0.0263], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118072.15833471471; tensor([0.1328, 0.8672], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3375, 0.0099, 0.0967, 0.0399, 0.0207, 0.0127, 0.0064, 0.0453, 0.0473,\n",
            "        0.0751, 0.0945, 0.0745, 0.0848, 0.0295, 0.0254], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118090.19432878484; tensor([0.1300, 0.8700], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3418, 0.0093, 0.0972, 0.0380, 0.0193, 0.0121, 0.0062, 0.0461, 0.0480,\n",
            "        0.0766, 0.0946, 0.0712, 0.0862, 0.0286, 0.0246], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118107.68520119955; tensor([0.1274, 0.8726], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3458, 0.0088, 0.0977, 0.0363, 0.0181, 0.0117, 0.0060, 0.0468, 0.0486,\n",
            "        0.0778, 0.0948, 0.0685, 0.0874, 0.0278, 0.0238], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118132.49004767358; tensor([0.1251, 0.8749], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3494, 0.0084, 0.0981, 0.0348, 0.0170, 0.0112, 0.0059, 0.0475, 0.0495,\n",
            "        0.0790, 0.0947, 0.0661, 0.0883, 0.0269, 0.0230], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118149.72928983661; tensor([0.1230, 0.8770], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3529, 0.0080, 0.0988, 0.0336, 0.0160, 0.0108, 0.0057, 0.0482, 0.0505,\n",
            "        0.0802, 0.0946, 0.0634, 0.0891, 0.0260, 0.0223], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118162.28264765444; tensor([0.1211, 0.8789], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3562, 0.0076, 0.0995, 0.0324, 0.0150, 0.0105, 0.0055, 0.0489, 0.0512,\n",
            "        0.0814, 0.0945, 0.0608, 0.0900, 0.0251, 0.0216], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118174.77810855117; tensor([0.1192, 0.8808], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3594, 0.0072, 0.1001, 0.0312, 0.0141, 0.0101, 0.0053, 0.0495, 0.0517,\n",
            "        0.0825, 0.0945, 0.0583, 0.0909, 0.0241, 0.0209], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118185.59944600437; tensor([0.1176, 0.8824], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3626, 0.0068, 0.1006, 0.0301, 0.0133, 0.0098, 0.0052, 0.0501, 0.0523,\n",
            "        0.0836, 0.0946, 0.0559, 0.0918, 0.0232, 0.0202], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118195.77553443855; tensor([0.1161, 0.8839], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3656, 0.0064, 0.1011, 0.0290, 0.0126, 0.0095, 0.0050, 0.0507, 0.0529,\n",
            "        0.0846, 0.0947, 0.0536, 0.0926, 0.0223, 0.0195], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118205.52054960113; tensor([0.1147, 0.8853], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3684, 0.0061, 0.1017, 0.0280, 0.0119, 0.0092, 0.0048, 0.0513, 0.0533,\n",
            "        0.0855, 0.0948, 0.0514, 0.0933, 0.0214, 0.0188], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118215.551314115; tensor([0.1134, 0.8866], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3713, 0.0058, 0.1023, 0.0270, 0.0113, 0.0089, 0.0047, 0.0518, 0.0534,\n",
            "        0.0864, 0.0950, 0.0493, 0.0941, 0.0205, 0.0182], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118232.37914324527; tensor([0.1123, 0.8877], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3739, 0.0055, 0.1027, 0.0260, 0.0107, 0.0087, 0.0045, 0.0522, 0.0535,\n",
            "        0.0871, 0.0957, 0.0474, 0.0947, 0.0197, 0.0176], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118250.25922160057; tensor([0.1113, 0.8887], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3759, 0.0052, 0.1032, 0.0250, 0.0102, 0.0084, 0.0044, 0.0526, 0.0538,\n",
            "        0.0879, 0.0967, 0.0456, 0.0953, 0.0189, 0.0170], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118260.09798606916; tensor([0.1104, 0.8896], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3773, 0.0048, 0.1038, 0.0239, 0.0097, 0.0082, 0.0043, 0.0530, 0.0543,\n",
            "        0.0887, 0.0977, 0.0439, 0.0958, 0.0181, 0.0164], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118271.71563340985; tensor([0.1094, 0.8906], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3796, 0.0045, 0.1047, 0.0221, 0.0092, 0.0080, 0.0041, 0.0535, 0.0545,\n",
            "        0.0897, 0.0978, 0.0424, 0.0969, 0.0173, 0.0158], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118282.60803836922; tensor([0.1082, 0.8918], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3816, 0.0042, 0.1058, 0.0189, 0.0087, 0.0078, 0.0040, 0.0542, 0.0543,\n",
            "        0.0907, 0.0993, 0.0407, 0.0983, 0.0164, 0.0151], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118294.81613384333; tensor([0.1071, 0.8929], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3820, 0.0039, 0.1071, 0.0166, 0.0082, 0.0075, 0.0038, 0.0547, 0.0547,\n",
            "        0.0916, 0.1017, 0.0392, 0.0989, 0.0156, 0.0145], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118301.89459979474; tensor([0.1061, 0.8939], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3839, 0.0036, 0.1084, 0.0148, 0.0078, 0.0073, 0.0037, 0.0552, 0.0554,\n",
            "        0.0925, 0.1045, 0.0377, 0.0964, 0.0149, 0.0138], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118308.2051672618; tensor([0.1052, 0.8948], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3851, 0.0034, 0.1095, 0.0134, 0.0074, 0.0072, 0.0036, 0.0556, 0.0558,\n",
            "        0.0932, 0.1063, 0.0364, 0.0958, 0.0142, 0.0133], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118314.11931256864; tensor([0.1045, 0.8955], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3862, 0.0031, 0.1105, 0.0121, 0.0071, 0.0070, 0.0035, 0.0559, 0.0561,\n",
            "        0.0937, 0.1074, 0.0351, 0.0959, 0.0136, 0.0127], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118319.72788745818; tensor([0.1039, 0.8961], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3874, 0.0029, 0.1113, 0.0111, 0.0068, 0.0068, 0.0034, 0.0563, 0.0564,\n",
            "        0.0943, 0.1082, 0.0339, 0.0962, 0.0129, 0.0121], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118325.05998860548; tensor([0.1034, 0.8966], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3886, 0.0027, 0.1121, 0.0102, 0.0065, 0.0066, 0.0033, 0.0566, 0.0566,\n",
            "        0.0948, 0.1088, 0.0328, 0.0965, 0.0123, 0.0116], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118330.13566138703; tensor([0.1029, 0.8971], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3897, 0.0026, 0.1129, 0.0095, 0.0062, 0.0065, 0.0032, 0.0568, 0.0568,\n",
            "        0.0952, 0.1092, 0.0317, 0.0968, 0.0117, 0.0112], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118334.97572420618; tensor([0.1025, 0.8975], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3908, 0.0024, 0.1136, 0.0088, 0.0059, 0.0063, 0.0031, 0.0571, 0.0570,\n",
            "        0.0956, 0.1096, 0.0307, 0.0971, 0.0112, 0.0107], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118339.60376744211; tensor([0.1022, 0.8978], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3917, 0.0023, 0.1142, 0.0082, 0.0057, 0.0062, 0.0030, 0.0573, 0.0573,\n",
            "        0.0961, 0.1099, 0.0298, 0.0974, 0.0107, 0.0103], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118344.01361049918; tensor([0.1018, 0.8982], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3925, 0.0021, 0.1149, 0.0076, 0.0054, 0.0061, 0.0029, 0.0576, 0.0575,\n",
            "        0.0965, 0.1102, 0.0290, 0.0977, 0.0102, 0.0098], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118349.80214852741; tensor([0.1015, 0.8985], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3931, 0.0020, 0.1154, 0.0071, 0.0052, 0.0060, 0.0028, 0.0578, 0.0577,\n",
            "        0.0969, 0.1103, 0.0282, 0.0982, 0.0097, 0.0095], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118354.11411247181; tensor([0.1010, 0.8990], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3919, 0.0019, 0.1162, 0.0067, 0.0050, 0.0059, 0.0027, 0.0583, 0.0583,\n",
            "        0.0976, 0.1107, 0.0275, 0.0991, 0.0093, 0.0091], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118357.9407217762; tensor([0.1005, 0.8995], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3915, 0.0018, 0.1170, 0.0063, 0.0048, 0.0058, 0.0026, 0.0586, 0.0585,\n",
            "        0.0981, 0.1111, 0.0268, 0.0994, 0.0089, 0.0087], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118361.58986286668; tensor([0.1002, 0.8998], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3917, 0.0017, 0.1176, 0.0059, 0.0047, 0.0057, 0.0026, 0.0588, 0.0587,\n",
            "        0.0984, 0.1114, 0.0262, 0.0996, 0.0085, 0.0084], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118365.07165572919; tensor([0.0999, 0.9001], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3922, 0.0016, 0.1180, 0.0056, 0.0045, 0.0056, 0.0025, 0.0590, 0.0588,\n",
            "        0.0988, 0.1117, 0.0257, 0.0998, 0.0081, 0.0081], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118368.40183079721; tensor([0.0997, 0.9003], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3928, 0.0015, 0.1184, 0.0053, 0.0043, 0.0056, 0.0024, 0.0592, 0.0589,\n",
            "        0.0990, 0.1119, 0.0251, 0.1000, 0.0077, 0.0078], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118371.58217587465; tensor([0.0995, 0.9005], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3934, 0.0015, 0.1188, 0.0050, 0.0042, 0.0055, 0.0023, 0.0593, 0.0590,\n",
            "        0.0993, 0.1121, 0.0246, 0.1002, 0.0074, 0.0075], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118374.62317633427; tensor([0.0993, 0.9007], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3940, 0.0014, 0.1191, 0.0047, 0.0041, 0.0054, 0.0023, 0.0594, 0.0591,\n",
            "        0.0995, 0.1123, 0.0241, 0.1003, 0.0071, 0.0072], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118377.53051380013; tensor([0.0992, 0.9008], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3946, 0.0013, 0.1193, 0.0045, 0.0039, 0.0054, 0.0022, 0.0595, 0.0592,\n",
            "        0.0997, 0.1126, 0.0237, 0.1004, 0.0068, 0.0069], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118380.31093372853; tensor([0.0991, 0.9009], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3951, 0.0012, 0.1196, 0.0042, 0.0038, 0.0053, 0.0021, 0.0596, 0.0593,\n",
            "        0.0999, 0.1128, 0.0233, 0.1005, 0.0065, 0.0067], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118382.9684612923; tensor([0.0990, 0.9010], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3957, 0.0012, 0.1199, 0.0040, 0.0037, 0.0053, 0.0021, 0.0597, 0.0594,\n",
            "        0.1001, 0.1130, 0.0229, 0.1006, 0.0062, 0.0064], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118385.51220962813; tensor([0.0989, 0.9011], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3962, 0.0011, 0.1201, 0.0038, 0.0035, 0.0052, 0.0020, 0.0598, 0.0595,\n",
            "        0.1002, 0.1132, 0.0225, 0.1007, 0.0059, 0.0062], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118387.93874292371; tensor([0.0988, 0.9012], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3967, 0.0011, 0.1203, 0.0036, 0.0034, 0.0052, 0.0020, 0.0599, 0.0595,\n",
            "        0.1004, 0.1133, 0.0222, 0.1008, 0.0057, 0.0060], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118390.27244010876; tensor([0.0987, 0.9013], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3971, 0.0010, 0.1205, 0.0035, 0.0033, 0.0051, 0.0019, 0.0600, 0.0596,\n",
            "        0.1005, 0.1135, 0.0219, 0.1009, 0.0054, 0.0057], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118392.49859979618; tensor([0.0987, 0.9013], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3976, 0.0010, 0.1207, 0.0033, 0.0032, 0.0051, 0.0019, 0.0601, 0.0597,\n",
            "        0.1007, 0.1137, 0.0216, 0.1010, 0.0052, 0.0055], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118394.63081777762; tensor([0.0986, 0.9014], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3980, 0.0009, 0.1209, 0.0031, 0.0031, 0.0051, 0.0018, 0.0601, 0.0597,\n",
            "        0.1008, 0.1138, 0.0213, 0.1011, 0.0049, 0.0053], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118396.67074146966; tensor([0.0985, 0.9015], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3984, 0.0009, 0.1210, 0.0030, 0.0030, 0.0051, 0.0018, 0.0602, 0.0598,\n",
            "        0.1009, 0.1140, 0.0210, 0.1011, 0.0047, 0.0051], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118398.61252224467; tensor([0.0985, 0.9015], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3987, 0.0008, 0.1212, 0.0028, 0.0029, 0.0051, 0.0017, 0.0603, 0.0598,\n",
            "        0.1010, 0.1141, 0.0208, 0.1012, 0.0045, 0.0049], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118400.49374185604; tensor([0.0984, 0.9016], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3991, 0.0008, 0.1213, 0.0027, 0.0028, 0.0050, 0.0017, 0.0603, 0.0599,\n",
            "        0.1011, 0.1142, 0.0206, 0.1013, 0.0043, 0.0048], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118402.28391522568; tensor([0.0984, 0.9016], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3994, 0.0008, 0.1215, 0.0026, 0.0027, 0.0050, 0.0016, 0.0604, 0.0599,\n",
            "        0.1013, 0.1144, 0.0204, 0.1013, 0.0041, 0.0046], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118403.99738552244; tensor([0.0983, 0.9017], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.3997, 0.0007, 0.1216, 0.0025, 0.0026, 0.0050, 0.0016, 0.0605, 0.0600,\n",
            "        0.1014, 0.1145, 0.0203, 0.1014, 0.0040, 0.0044], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118405.6386095564; tensor([0.0983, 0.9017], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4000, 0.0007, 0.1217, 0.0023, 0.0025, 0.0050, 0.0016, 0.0605, 0.0600,\n",
            "        0.1015, 0.1146, 0.0201, 0.1014, 0.0038, 0.0042], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118407.21125770769; tensor([0.0982, 0.9018], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4002, 0.0007, 0.1219, 0.0022, 0.0025, 0.0050, 0.0015, 0.0606, 0.0600,\n",
            "        0.1015, 0.1147, 0.0200, 0.1015, 0.0036, 0.0041], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118408.71463187542; tensor([0.0982, 0.9018], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4005, 0.0006, 0.1220, 0.0021, 0.0024, 0.0050, 0.0015, 0.0606, 0.0601,\n",
            "        0.1016, 0.1148, 0.0199, 0.1015, 0.0035, 0.0039], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118410.15772272841; tensor([0.0982, 0.9018], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4007, 0.0006, 0.1221, 0.0020, 0.0023, 0.0051, 0.0015, 0.0606, 0.0601,\n",
            "        0.1017, 0.1149, 0.0198, 0.1016, 0.0033, 0.0038], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118411.53957454397; tensor([0.0981, 0.9019], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4009, 0.0006, 0.1222, 0.0019, 0.0022, 0.0051, 0.0014, 0.0607, 0.0601,\n",
            "        0.1018, 0.1149, 0.0197, 0.1016, 0.0032, 0.0037], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118412.8399911903; tensor([0.0981, 0.9019], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4011, 0.0005, 0.1222, 0.0019, 0.0022, 0.0051, 0.0014, 0.0607, 0.0602,\n",
            "        0.1019, 0.1150, 0.0197, 0.1016, 0.0030, 0.0035], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118414.12998802395; tensor([0.0981, 0.9019], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4013, 0.0005, 0.1223, 0.0018, 0.0021, 0.0051, 0.0014, 0.0608, 0.0602,\n",
            "        0.1019, 0.1151, 0.0197, 0.1017, 0.0029, 0.0034], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118415.34317385207; tensor([0.0981, 0.9019], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4014, 0.0005, 0.1224, 0.0017, 0.0020, 0.0051, 0.0013, 0.0608, 0.0602,\n",
            "        0.1020, 0.1151, 0.0196, 0.1017, 0.0028, 0.0033], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118416.5047523647; tensor([0.0981, 0.9019], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4016, 0.0005, 0.1225, 0.0016, 0.0020, 0.0052, 0.0013, 0.0608, 0.0602,\n",
            "        0.1020, 0.1152, 0.0196, 0.1017, 0.0027, 0.0031], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118417.62120767529; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4017, 0.0004, 0.1225, 0.0015, 0.0019, 0.0052, 0.0013, 0.0608, 0.0603,\n",
            "        0.1021, 0.1152, 0.0196, 0.1017, 0.0025, 0.0030], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118418.68985560973; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4018, 0.0004, 0.1226, 0.0015, 0.0018, 0.0052, 0.0012, 0.0609, 0.0603,\n",
            "        0.1021, 0.1153, 0.0197, 0.1018, 0.0024, 0.0029], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118419.7138074335; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([0.4020, 0.0004, 0.1226, 0.0014, 0.0018, 0.0053, 0.0012, 0.0609, 0.0603,\n",
            "        0.1022, 0.1153, 0.0197, 0.1018, 0.0023, 0.0028], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118420.69542146407; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0205e-01, 3.8957e-04, 1.2267e-01, 1.3508e-03, 1.7241e-03, 5.3240e-03,\n",
            "        1.1793e-03, 6.0910e-02, 6.0311e-02, 1.0224e-01, 1.1536e-01, 1.9769e-02,\n",
            "        1.0179e-01, 2.2346e-03, 2.7005e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118421.63546512477; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0214e-01, 3.7206e-04, 1.2271e-01, 1.2916e-03, 1.6686e-03, 5.3656e-03,\n",
            "        1.1532e-03, 6.0929e-02, 6.0324e-02, 1.0228e-01, 1.1539e-01, 1.9836e-02,\n",
            "        1.0181e-01, 2.1383e-03, 2.5993e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118422.5283021414; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0222e-01, 3.5536e-04, 1.2274e-01, 1.2350e-03, 1.6148e-03, 5.4081e-03,\n",
            "        1.1278e-03, 6.0947e-02, 6.0337e-02, 1.0231e-01, 1.1542e-01, 1.9915e-02,\n",
            "        1.0182e-01, 2.0461e-03, 2.5016e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118423.39852024283; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0228e-01, 3.3942e-04, 1.2278e-01, 1.1809e-03, 1.5625e-03, 5.4512e-03,\n",
            "        1.1031e-03, 6.0963e-02, 6.0348e-02, 1.0235e-01, 1.1544e-01, 2.0003e-02,\n",
            "        1.0183e-01, 1.9578e-03, 2.4073e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118424.22669954851; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0235e-01, 3.2421e-04, 1.2281e-01, 1.1293e-03, 1.5117e-03, 5.4943e-03,\n",
            "        1.0790e-03, 6.0978e-02, 6.0358e-02, 1.0238e-01, 1.1546e-01, 2.0100e-02,\n",
            "        1.0184e-01, 1.8732e-03, 2.3162e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118425.02124804622; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0240e-01, 3.0968e-04, 1.2284e-01, 1.0799e-03, 1.4624e-03, 5.5370e-03,\n",
            "        1.0556e-03, 6.0991e-02, 6.0367e-02, 1.0241e-01, 1.1548e-01, 2.0205e-02,\n",
            "        1.0185e-01, 1.7921e-03, 2.2282e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118425.7734244749; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0245e-01, 2.9580e-04, 1.2286e-01, 1.0327e-03, 1.4145e-03, 5.5788e-03,\n",
            "        1.0328e-03, 6.1003e-02, 6.0376e-02, 1.0244e-01, 1.1550e-01, 2.0316e-02,\n",
            "        1.0185e-01, 1.7143e-03, 2.1432e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118426.51144567922; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0249e-01, 2.8254e-04, 1.2288e-01, 9.8754e-04, 1.3679e-03, 5.6194e-03,\n",
            "        1.0106e-03, 6.1015e-02, 6.0383e-02, 1.0246e-01, 1.1551e-01, 2.0432e-02,\n",
            "        1.0186e-01, 1.6398e-03, 2.0610e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118427.21015234516; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0253e-01, 2.6987e-04, 1.2290e-01, 9.4433e-04, 1.3227e-03, 5.6584e-03,\n",
            "        9.8893e-04, 6.1025e-02, 6.0390e-02, 1.0249e-01, 1.1552e-01, 2.0550e-02,\n",
            "        1.0186e-01, 1.5684e-03, 1.9817e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118427.88205247524; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0256e-01, 2.5776e-04, 1.2292e-01, 9.0297e-04, 1.2787e-03, 5.6955e-03,\n",
            "        9.6781e-04, 6.1035e-02, 6.0396e-02, 1.0251e-01, 1.1553e-01, 2.0671e-02,\n",
            "        1.0187e-01, 1.4999e-03, 1.9051e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118428.52409684978; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0259e-01, 2.4618e-04, 1.2294e-01, 8.6338e-04, 1.2359e-03, 5.7305e-03,\n",
            "        9.4722e-04, 6.1044e-02, 6.0402e-02, 1.0253e-01, 1.1554e-01, 2.0793e-02,\n",
            "        1.0187e-01, 1.4343e-03, 1.8311e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118429.13840179733; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0262e-01, 2.3512e-04, 1.2295e-01, 8.2549e-04, 1.1943e-03, 5.7632e-03,\n",
            "        9.2714e-04, 6.1053e-02, 6.0407e-02, 1.0255e-01, 1.1555e-01, 2.0913e-02,\n",
            "        1.0187e-01, 1.3714e-03, 1.7596e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118429.72954999108; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0265e-01, 2.2453e-04, 1.2297e-01, 7.8921e-04, 1.1539e-03, 5.7936e-03,\n",
            "        9.0755e-04, 6.1061e-02, 6.0413e-02, 1.0257e-01, 1.1556e-01, 2.1032e-02,\n",
            "        1.0188e-01, 1.3111e-03, 1.6906e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118430.29601649479; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0267e-01, 2.1442e-04, 1.2298e-01, 7.5448e-04, 1.1146e-03, 5.8217e-03,\n",
            "        8.8845e-04, 6.1069e-02, 6.0418e-02, 1.0259e-01, 1.1557e-01, 2.1148e-02,\n",
            "        1.0188e-01, 1.2533e-03, 1.6239e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118430.83638790259; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0270e-01, 2.0475e-04, 1.2300e-01, 7.2122e-04, 1.0764e-03, 5.8475e-03,\n",
            "        8.6982e-04, 6.1076e-02, 6.0423e-02, 1.0261e-01, 1.1557e-01, 2.1261e-02,\n",
            "        1.0188e-01, 1.1979e-03, 1.5596e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118431.35706983662; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0273e-01, 1.9550e-04, 1.2301e-01, 6.8939e-04, 1.0394e-03, 5.8711e-03,\n",
            "        8.5165e-04, 6.1084e-02, 6.0427e-02, 1.0263e-01, 1.1558e-01, 2.1369e-02,\n",
            "        1.0189e-01, 1.1449e-03, 1.4975e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118431.8586197854; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0275e-01, 1.8666e-04, 1.2302e-01, 6.5891e-04, 1.0034e-03, 5.8927e-03,\n",
            "        8.3394e-04, 6.1091e-02, 6.0432e-02, 1.0264e-01, 1.1559e-01, 2.1472e-02,\n",
            "        1.0189e-01, 1.0941e-03, 1.4376e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118432.31732782471; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0278e-01, 1.7821e-04, 1.2304e-01, 6.2975e-04, 9.6840e-04, 5.9125e-03,\n",
            "        8.1667e-04, 6.1098e-02, 6.0437e-02, 1.0266e-01, 1.1560e-01, 2.1570e-02,\n",
            "        1.0189e-01, 1.0454e-03, 1.3799e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n",
            "L: -118432.79786038595; tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>); tensor([4.0280e-01, 1.7014e-04, 1.2305e-01, 6.0183e-04, 9.3446e-04, 5.9305e-03,\n",
            "        7.9985e-04, 6.1105e-02, 6.0442e-02, 1.0268e-01, 1.1560e-01, 2.1662e-02,\n",
            "        1.0190e-01, 9.9879e-04, 1.3242e-03], dtype=torch.float64,\n",
            "       grad_fn=<ExpBackward>)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CDrwOA9ZEBa2",
        "outputId": "b795e75d-efc1-48aa-d287-5ca343300f48"
      },
      "source": [
        "F.log_softmax(Theta1['is_delta'], 0).exp()"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0.0980, 0.9020], dtype=torch.float64, grad_fn=<ExpBackward>)"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mkA7haAeS97o",
        "outputId": "67b5a648-1267-47f1-cc01-65736779e3f0"
      },
      "source": [
        "with torch.no_grad():\n",
        "  r, v, L, p_singlet_mle = compute_r_v_2(Y,S,Theta1)\n",
        "\n",
        "p_singlet_mle = p_singlet_mle.numpy()"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:59: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:60: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:61: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "id": "d20-ru-fKPUL",
        "outputId": "b3456465-f95d-4bbf-dce9-28e90b87e96f"
      },
      "source": [
        "adata.obs['p_singlet_mle'] = p_singlet_mle\n",
        "adata.obs['probability_single_cell_mle'] = adata.obs.p_singlet_mle\n",
        "sc.pl.scatter(adata, x = 'ECadherin', y = 'Vimentin', color = 'probability_single_cell_mle')"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 541.714x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "id": "R-cmPY7YKSOH",
        "outputId": "ef29cb7f-2750-4b44-943b-1062e8890053"
      },
      "source": [
        "p_doublet_mle = 1 - p_singlet_mle\n",
        "adata.obs['p_doublet_mle'] = p_doublet_mle\n",
        "adata.obs['probability_doublet_cell_mle'] = adata.obs.p_doublet_mle\n",
        "sc.pl.scatter(adata, x = 'ECadherin', y = 'Vimentin', color = 'probability_doublet_cell_mle')"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 541.714x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "f1e-j_AHKeYa",
        "outputId": "f7f07faf-5025-46ec-a104-0edc29593bd9"
      },
      "source": [
        "plt.plot(torch.tensor(psi_init), label=\"before\")\n",
        "plt.plot(Theta1['log_psi'].exp().detach().numpy(), label=\"after\")\n",
        "plt.legend()\n",
        "plt.xlabel(\"cluster number\")\n",
        "plt.ylabel(\"cell size\")"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'cell size')"
            ]
          },
          "metadata": {},
          "execution_count": 31
        },
        {
          "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": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "t87HI8ipKkEH",
        "outputId": "9155f81e-df4d-4a51-86ef-6391886606f5"
      },
      "source": [
        "plt.plot(loss)\n",
        "plt.xlabel(\"iter\")\n",
        "plt.ylabel(\"nll\")"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'nll')"
            ]
          },
          "metadata": {},
          "execution_count": 32
        },
        {
          "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": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "id": "TE-KF36oSjQs",
        "outputId": "3c4043e2-db60-4d5e-fe52-ffc613e81176"
      },
      "source": [
        "sc.pl.scatter(adata, x = 'ECadherin', y = 'Vimentin', color = 'Area')"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 541.714x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "6X_JIYs2Sly9",
        "outputId": "2f71f0b1-56d8-43bd-a8e2-fffd9624feb8"
      },
      "source": [
        "plt.hist(adata.obs['Area'], bins = 100)\n",
        "plt.xlabel(\"Size\")\n",
        "plt.ylabel(\"Count\")"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Count')"
            ]
          },
          "metadata": {},
          "execution_count": 34
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}