notebooks/book1/03/gauss_infer_2d.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kV8dt83JzN1n"
   },
   "source": [
    "# Illustration of Bayesian inference for a 2d Gaussian random vector z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wB037kg4jb-F"
   },
   "source": [
    "### Importing probml_utils library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "hMylJdjIulS_",
    "outputId": "516cf220-e393-4301-b434-845774f45937"
   },
   "outputs": [],
   "source": [
    "try:\n",
    "    from probml_utils import savefig, latexify, is_latexify_enabled\n",
    "except ModuleNotFoundError:\n",
    "    %pip install -qq git+https://github.com/probml/probml-utils.git\n",
    "    from probml_utils import savefig, latexify, is_latexify_enabled"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Aj_ZHIYvjhlr"
   },
   "source": [
    "### Importing other libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "8fd_Z7xcdxmB"
   },
   "outputs": [],
   "source": [
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from jax.numpy.linalg import cholesky\n",
    "from jax.scipy.linalg import inv\n",
    "from scipy.stats import multivariate_normal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NsqugWFnjmVM"
   },
   "source": [
    "### Set latexify params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "g-gO9CA6xwnF",
    "outputId": "cdd89d4e-1e70-498e-85ae-379a39aa626c"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/patel_karm/probml-utils/probml_utils/plotting.py:26: UserWarning: LATEXIFY environment variable not set, not latexifying\n",
      "  warnings.warn(\"LATEXIFY environment variable not set, not latexifying\")\n"
     ]
    }
   ],
   "source": [
    "latexify(width_scale_factor=3, fig_height=1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "veI4lwHNjrPd"
   },
   "source": [
    "### Function declarations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "Ve8rzQiw4Eui"
   },
   "outputs": [],
   "source": [
    "def gaussSample(mu, sigma, n, key):\n",
    "    decomposition = cholesky(sigma)\n",
    "    normal_distribution = jax.random.normal(key, shape=(len(mu), n))\n",
    "    return jnp.dot(decomposition, normal_distribution).T + mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "7dnfhg7h31p1"
   },
   "outputs": [],
   "source": [
    "def plot_data(x, muTrue, savename, title, fig=None, ax=None):\n",
    "    marker_size = 4 if is_latexify_enabled() else None\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    ax.plot(x[:, 0], x[:, 1], \"o\", markerfacecolor=\"b\")\n",
    "    ax.set_ylim([-1, 1])\n",
    "    # ax.set_xlim([-1, 1])\n",
    "    ax.set_title(title)\n",
    "    ax.set_xlabel(\"$y_1$\")\n",
    "    ax.set_ylabel(\"$y_2$\")\n",
    "    ax.plot(muTrue[0], muTrue[1], \"x\", markerfacecolor=\"black\", color=\"k\")\n",
    "\n",
    "    sns.despine()\n",
    "    if len(savename) > 0:\n",
    "        savefig(savename)\n",
    "    return fig, ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "ATOm8injxRGb"
   },
   "outputs": [],
   "source": [
    "def make_contour_plot(x1, x2, p, savename, title, fig=None, ax=None):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    contour = ax.contourf(x1, x2, p)\n",
    "    cbar = fig.colorbar(contour, ax=ax)\n",
    "    cbar.set_ticks(jnp.linspace(p.min(), p.max(), 4))\n",
    "\n",
    "    ax.set_ylim([-1, 1])\n",
    "    ax.set_xlim([-1, 1])\n",
    "    ax.set_title(title)\n",
    "    ax.set_xlabel(\"$z_1$\")\n",
    "    ax.set_ylabel(\"$z_2$\")\n",
    "    plt.gca().set_aspect(\"equal\")\n",
    "    sns.despine()\n",
    "    if len(savename) > 0:\n",
    "        savefig(savename, tight_bbox=True)\n",
    "    return fig, ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 944
    },
    "id": "A-zIn0L_yaAj",
    "outputId": "4525792b-42c1-4f55-84c8-523645a2c9b6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 432x288 with 2 Axes>,\n",
       " <AxesSubplot:title={'center':'Posterior after 10 points'}, xlabel='$z_1$', ylabel='$z_2$'>)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEYCAYAAAB2qXBEAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAAceUlEQVR4nO3df5RcZZ3n8fcHMK3ZqEmMS2KaxjDJosFhEy1g0FkxDErQDcksbAyzjHFkTkZ29MzKURLkIJ44rglzdnFnhg1mAUV0wQjHkAwqE0LAsyPB9BpM6GhIE9jQbSKBJoyZOO1AvvtHPQ23m6r+kVtVtzr9eZ1Tp+597nNvffumOp++96l7SxGBmZnZsTqh6ALMzGx0c5CYmVkuDhIzM8vFQWJmZrk4SMzMLBcHiZmZ5eIgMTOzXBwkZnUi6WlJv5H0a0mHJP1Y0iclDfl7J+ntkkLSSY2o1SwPB4lZfS2IiDcCpwKrgOXArcWWZFZbDhKzBoiIFyNiA/BRYKmkd0n6iKTtkv5R0jOSvphZ5Ufp+ZCkw5LOlfQ7kh6U9Lyk5yR9W9LERv8sZgM5SMwaKCJ+AnQB/w74J+BjwETgI8CVkhalru9PzxMjYkJEPAII+ArwNuCdwCnAFxtVu1k1DhKzxvslMDkiHoqInRFxNCJ2AHcC51VbKSI6I2JTRPRGxEHgvw/W36xRPJBn1njTgR5J51AeN3kXMA5oAb5bbSVJJwP/g/LRzBsp/yH4Qt2rNRuCj0jMGkjSWZSD5P8A/xvYAJwSEW8GbqZ8+gqg0m25/2tq/92IeBNweaa/WWEcJGYNIOlNkv49cBfwrYjYSfmooici/lnS2cAfZVY5CBwFTsu0vRE4DLwoaTrwucZUbzY4+ftIzOpD0tPAycBLlENhF/At4OaIeFnSpcB/AyYDDwNPUx5cvzytvxK4EngdMB/4NfBN4HSgE7gD+ExEtDbupzJ7LQeJmZnl4lNbZmaWS1MEiaTbJD0r6fEqyyXpryV1Stoh6d2ZZUsl7UmPpY2r2szMoEmCBPgG5XPA1VwEzEqPZcAaAEmTgeuBc4CzgeslTaprpWZm1k9TBElE/AjoGaTLQuCbUbYVmChpGnAhsCkieiLiBWATgweSmZnV2Gi5IHE68Exmviu1VWt/DUnLKB/NMHv27Pd0dHTUp1Izs+NXxeuWmuKIpBEiYm1ElCKi9IY3vKHocszMjhujJUi6Kd+grk9raqvWbmZmDTJagmQD8LH06a3fA16MiP3A/cCHJE1Kg+wfSm1mZtYgTTFGIulO4APAFEldlD+J9TqAiLgZ+D7wYcpX8x4B/iQt65H0JWBb2tTKiBhs0N7MzGpsTF7ZXiqVor29vegyzMxGm7E92G5mZvXhIDEzs1wcJGZmlouDxMzMcnGQmJlZLg4SMzPLxUFiZma5OEjMzCwXB4mZmeXiIDEzs1wcJGZmlouDxMzMcnGQmJlZLk1xG3kzM6uf9du7Wb2xkwNHDjN1/ASWL5jJorkVv5X8mDhIzHKo9y+oWV7rt3dz9R272XfPmfR2TWZ/aw9XH9oBULP3qoPE7Bg14hfULK/VGzvL79F9UwDo3TeFffecyeqJHTV7n3qMxOwY9fsFPXrCq7+gGzuLLs3sFQeOHKa3a3K/tt6uyRw4crhmr+EgMTtGjfgFNctr6vgJtLT2/wbyltYepo6fULPXaIogkTRf0m5JnZJWVFh+o6TH0uMJSYcyy17OLNvQ0MJtTGvEL6hZXssXzKTtkh20tD0HJxylpe052i7ZwfIFM2v2GoWPkUg6EbgJ+CDQBWyTtCEidvX1iYjPZPp/Gpib2cRvImJOg8o1e8XyBTO5+tCOV8ZIWlp70i/o6UWXZvaKvnGQ1RM7Mh8KOf24+9TW2UBnROwFkHQXsBDYVaX/ZcD1DarNrKpG/IKa1cKiudPr+r5shiCZDjyTme8CzqnUUdKpwAzgwUzz6yW1Ay8BqyJifZ3qNHuNev+Cmo0GzRAkI7EEuDsiXs60nRoR3ZJOAx6UtDMinhy4oqRlwDKAtra2xlRrZjYGNMNgezdwSma+NbVVsgS4M9sQEd3peS/wEP3HT7L91kZEKSJKb33rW/PWbGZmSTMEyTZglqQZksZRDovXfPpK0juAScAjmbZJklrS9BTgfVQfWzEzszoo/NRWRLwk6VPA/cCJwG0R0SFpJdAeEX2hsgS4KyIis/o7ga9JOko5FFdlP+1lZmb1p/7/L48NpVIp2tvbiy7DzGy0UaXGZji1ZWZmo5iDxMzMcnGQmJlZLg4SMzPLxUFiZma5OEjMzCwXB4mZmeVS+AWJZtZ8/F30NhIOEjPrx99FbyPlU1tm1o+/i95GykFiZv34u+htpBwkZtaPv4veRspBYtZA67d3c+7Kh5mx4j7OXfkw67dX++qd4ixfMJO2S3bQ0vYcnHCUlrbn0nfRzyy6NGtSHmw3a5DRMojt76K3kfJt5M0a5NyVD7P91jPKg9hJS9tzzL2ig0e+cF6BlZkNW8XbyPuIxKxBaj2I7Ws9rFk4SMwaZOr4Cexv7el/RHKMg9ij5TTZ8c5hXuYgMWuQ5QtmcvWhHa/859/S2pMGsU8f8bb6XesBr17rMbFjTP5HVgSH+ascJGYNUstBbF/rUTyH+aua4uO/kuZL2i2pU9KKCss/LumgpMfS408zy5ZK2pMeSxtbuY0lN9xwA1u2bOnXtmXLFm644YZhb2PR3Ok88oXzeGrVR3jkC+cd8384vtajeA7zVxUeJJJOBG4CLgJmA5dJml2h63ciYk563JLWnQxcD5wDnA1cL2lSg0q3Meass85i8eLFr4TJli1bWLx4MWeddVbDa/G1HsVzmL+qGU5tnQ10RsReAEl3AQuBXcNY90JgU0T0pHU3AfOBO+tUq41h8+bNY926dSxevJgrr7ySNWvWsG7dOubNm9fwWnytR/FqOeY12jVDkEwHnsnMd1E+whjoEknvB54APhMRz1RZt+JvkqRlwDKAtra2GpRtY9G8efO48sor+dKXvsR1111XSIj0WTR3uoOjQA7zVzVDkAzHRuDOiOiV9GfA7cD5I9lARKwF1kL5gsTal2hjwZYtW1izZg3XXXcda9asYd68eYWGiRXLYV5W+BgJ0A2ckplvTW2viIjnI6I3zd4CvGe465rVSt+YyLp161i5cuUrp7kGDsCbjTXNECTbgFmSZkgaBywBNmQ7SJqWmb0Y+Hmavh/4kKRJaZD9Q6nNrOa2bdvWb0ykb8xk27ZtBVdmVqymuNeWpA8DXwVOBG6LiC9LWgm0R8QGSV+hHCAvAT3AlRHxi7TuJ4DPp019OSK+PtTr+V5bZmbHpOK9tpoiSBrNQWJmdkwqBkkznNoyM7NRzEFiZma5OEjMzCwXB4mZmeXiIDEzs1wcJGZmlouDxMzMcnGQmJlZLg4SMzPLxUFiZma5OEjMzCwXB4mZmeXiIDEzs1wcJGZmlouDxMzMchkt39luY8j67d2s3tjJgSOHmTp+AssXzPT3Yps1MQeJNZX127u5+o7d7LvnTHq7JrO/tYerD+0AcJiYNSmf2rKmsnpjZzlE9k2BoyfQu28K++45k9UbO4suzcyqaIogkTRf0m5JnZJWVFh+laRdknZI2izp1MyylyU9lh4bGlu51dqBI4fp7Zrcr623azIHjhwuqCIzG0rhQSLpROAm4CJgNnCZpNkDum0HShFxJnA3cENm2W8iYk56XNyQoq1upo6fQEtrT7+2ltYepo6fUFBFZjaUwoMEOBvojIi9EfFb4C5gYbZDRGyJiCNpdivQ2uAarUGWL5hJ2yU7aGl7Dk44Skvbc7RdsoPlC2YWXZqZVdEMg+3TgWcy813AOYP0vwL4QWb+9ZLagZeAVRGxvtJKkpYBywDa2try1Gt11DegvnpiR+ZTW6d7oN2siTVDkAybpMuBEnBepvnUiOiWdBrwoKSdEfHkwHUjYi2wFqBUKkVDCrZjsmjudAeH2SjSDKe2uoFTMvOtqa0fSRcA1wIXR0RvX3tEdKfnvcBDwNx6FmtmZv01wxHJNmCWpBmUA2QJ8EfZDpLmAl8D5kfEs5n2ScCRiOiVNAV4H/0H4s2ami++tONB4UESES9J+hRwP3AicFtEdEhaCbRHxAbgr4AJwHclAexLn9B6J/A1SUcpH12tiohdhfwgZiPkiy/teKGIsTdcUCqVor29vegybIw7d+XDbL/1jPLFl0lL23PMvaKDR75w3iBrmhVGlRqbYYzEbEzyxZd2vHCQmBXEF1/a8cJBYlYQX3xpx4vCB9vNxipffGnHCweJWYF88aUdD3xqy8zMcnGQmJlZLg4SMzPLxUFiZma5OEjMzCwXB4mZmeXiIDEzs1wcJGZmlouDxMzMcnGQmJlZLg4SMzPLxffasqbnr6M1a24OEmtq/jpas+Y37FNbkj4o6X9JmpPml9WqCEnzJe2W1ClpRYXlLZK+k5Y/KuntmWXXpPbdki6sVU3WHFZv7CyHyL4pcPQEevdNYd89Z7J6Y2fRpZlZMpIxkk8AnwMul3Q+MKcWBUg6EbgJuAiYDVwmafaAblcAL0TETOBGYHVadzawBDgDmA/8z7Q9O07462jNmt9IguTXEXEoIj4LfAg4q0Y1nA10RsTeiPgtcBewcECfhcDtafpu4A8kKbXfFRG9EfEU0Jm2Z8cJfx2tWfMbSZDc1zcRESuAb9aohunAM5n5rtRWsU9EvAS8CLxlmOsC5VNxktoltR88eLBGpVu9+etozZrfkIPtkjYBn42Ie7PtEfE3dauqDiJiLbAWoFQqRcHl2DD562jNmt9wPrW1HPiqpKeBz0fE/hrX0A2ckplvTW2V+nRJOgl4M/D8MNe1Uc5fR2vW3IY8tRURP42IecDfAT+UdL2kN9Swhm3ALEkzJI2jPHi+YUCfDcDSNH0p8GBERGpfkj7VNQOYBfykhrWZmdkQhjVGkga2dwNrgE8DeyT9cS0KSGMenwLuB34OrIuIDkkrJV2cut0KvEVSJ3AVsCKt2wGsA3YBPwT+PCJerkVdZmY2PCr/YT9IB+kfgBlAB7AVeBT4BfAXQEtE1Ox6kkYplUrR3t5edBlmZqONKjUOZ4xkGbArXps4n5b089xlmZnZqDZkkKTTR9V8pIa1mJnZKJTr7r8RsbdWhZiZ2ejk28ibmVkuDhIzM8vFQWJmZrk4SMzMLBcHiZmZ5eIgMTOzXBwkZmaWi4PEzMxycZCYmVkuDhIzM8vFQWJmZrk4SMzMLBcHiZmZ5eIgMTOzXBwkZmaWS6FBImmypE2S9qTnSRX6zJH0iKQOSTskfTSz7BuSnpL0WHrMaegPYGZmhR+RrAA2R8QsYHOaH+gI8LGIOAOYD3xV0sTM8s9FxJz0eKzeBZuZWX9FB8lC4PY0fTuwaGCHiHgiIvak6V8CzwJvbVSBZmY2uKKD5OSI2J+mDwAnD9ZZ0tnAOODJTPOX0ymvGyW1DLLuMkntktoPHjw44kLXb+/m3JUPM2PFfZy78mHWb+8e8TbMzI5HJ9X7BSQ9AEytsOja7ExEhKQYZDvTgDuApRFxNDVfQzmAxgFrgeXAykrrR8Ta1IdSqVT1dSpZv72bq+/Yzb57zqS3azL7W3u4+tAOABbNnT6STZmZHXfqHiQRcUG1ZZJ+JWlaROxPQfFslX5vAu4Dro2IrZlt9x3N9Er6OvDZGpb+itUbO8shsm9K+cX2TWHfPWeyemKHg8TMxryiT21tAJam6aXAvQM7SBoHfA/4ZkTcPWDZtPQsyuMrj9ejyANHDtPbNblfW2/XZA4cOVyPlzMzG1WKDpJVwAcl7QEuSPNIKkm6JfVZDLwf+HiFj/l+W9JOYCcwBfjLehQ5dfwEWlp7+rW1tPYwdfyEerycmdmooogRDRccF0qlUrS3tw+7/8AxkpbWHtou2cENf3y6T22Z2ViiSo11HyM5HvSFxeqJHRw4cpip4yewfIFDxMwMHCTDtmjudAeHmVkFRY+RmJnZKOcgMTOzXBwkZmaWi4PEzMxycZCYmVkuDhIzM8vFQWJmZrk4SMzMLBcHiZmZ5eIgMTOzXBwkZmaWi4PEzMxycZCYmVkuDhIzM8vFQWJmZrk4SMzMLJdCg0TSZEmbJO1Jz5Oq9Hs5833tGzLtMyQ9KqlT0nckjWtc9WZmBsUfkawANkfELGBzmq/kNxExJz0uzrSvBm6MiJnAC8AV9S3XzMwGKjpIFgK3p+nbgUXDXVGSgPOBu49lfTMzq42ig+TkiNifpg8AJ1fp93pJ7ZK2SlqU2t4CHIqIl9J8F1D1S9UlLUvbaD948GAtajczM+Cker+ApAeAqRUWXZudiYiQFFU2c2pEdEs6DXhQ0k7gxZHUERFrgbUApVKp2uuYmdkI1T1IIuKCassk/UrStIjYL2ka8GyVbXSn572SHgLmAvcAEyWdlI5KWoHumv8AZmY2qKJPbW0AlqbppcC9AztImiSpJU1PAd4H7IqIALYAlw62vpmZ1VfRQbIK+KCkPcAFaR5JJUm3pD7vBNol/YxycKyKiF1p2XLgKkmdlMdMbm1o9WZmhsp/2I8tpVIp2tvbiy7DzGy0UaXGoo9IzMxslHOQmJlZLg4SMzPLxUFiZma5OEjMzCwXB4mZmeXiIDEzs1wcJGZmlouDxMzMcnGQmJlZLg4SMzPLxUFiZma5OEjMzCwXB4mZmeXiIDEzs1wcJGZmlouDxMzMcnGQmJlZLoUGiaTJkjZJ2pOeJ1XoM0/SY5nHP0talJZ9Q9JTmWVzGv0zmJmNdUUfkawANkfELGBzmu8nIrZExJyImAOcDxwB/j7T5XN9yyPisQbUbGZmGUUHyULg9jR9O7BoiP6XAj+IiCP1LMrMzIav6CA5OSL2p+kDwMlD9F8C3Dmg7cuSdki6UVJLzSs0M7NBnVTvF5D0ADC1wqJrszMREZJikO1MA34XuD/TfA3lABoHrAWWAyurrL8MWAbQ1tY2gp/AzMwGU/cgiYgLqi2T9CtJ0yJifwqKZwfZ1GLgexHxL5lt9x3N9Er6OvDZQepYSzlsKJVKVQPLzMxGpuhTWxuApWl6KXDvIH0vY8BprRQ+SBLl8ZXHa1+imZkNpuggWQV8UNIe4II0j6SSpFv6Okl6O3AK8PCA9b8taSewE5gC/GUjijYzs1cpYuyd5SmVStHe3l50GWZmo40qNRZ9RGJmZqOcg8TMzHJxkJiZWS4OEjMzy8VBYmZmuThIzMwsFweJmZnl4iAxM7NcHCRmZpaLg8TMzHJxkJiZWS4OEjMzy8VBYmZmuThIzMwsFweJmZnl4iAxM7NcHCRmZpaLg8TMzHJxkJiZWS6FBomk/yipQ9JRSaVB+s2XtFtSp6QVmfYZkh5N7d+RNK4xlZuZWZ+ij0geB/4D8KNqHSSdCNwEXATMBi6TNDstXg3cGBEzgReAK+pbrpmZDVRokETEzyNi9xDdzgY6I2JvRPwWuAtYKEnA+cDdqd/twKK6FWtmZhWdVHQBwzAdeCYz3wWcA7wFOBQRL2Xap1fbiKRlwLI0e1jSUAFWyRTguWNYryijqd7RVCu43npzvfV1rPX+MCLmD2yse5BIegCYWmHRtRFxb71fv09ErAXW5tmGpPaIqDqW02xGU72jqVZwvfXmeuur1vXWPUgi4oKcm+gGTsnMt6a254GJkk5KRyV97WZm1kBFD7YPxzZgVvqE1jhgCbAhIgLYAlya+i0FGnaEY2ZmZUV//PcPJXUB5wL3Sbo/tb9N0vcB0tHGp4D7gZ8D6yKiI21iOXCVpE7KYya31rnkXKfGCjCa6h1NtYLrrTfXW181rVflP+zNzMyOzWg4tWVmZk3MQWJmZrk4SDIkTZa0SdKe9DypQp85kh5Jt3bZIemjmWXfkPSUpMfSY06d6qx4y5jM8pZ0y5jOdAuZt2eWXZPad0u6sB71HUO9V0nalfbnZkmnZpa9nNmfG5qk3o9LOpip608zy5am988eSUubpN4bM7U+IelQZllD96+k2yQ9K+nxKssl6a/Tz7JD0rszy4rYt0PV+59SnTsl/VjSv80sezq1PyapvUnq/YCkFzP/5l/ILBv0fTSoiPAjPYAbgBVpegWwukKffwPMStNvA/YDE9P8N4BL61zjicCTwGnAOOBnwOwBff4zcHOaXgJ8J03PTv1bgBlpOyc2Qb3zgPFp+sq+etP84Qa/B4ZT78eBv62w7mRgb3qelKYnFV3vgP6fBm4rcP++H3g38HiV5R8GfgAI+D3g0aL27TDrfW9fHZRv4/RoZtnTwJQm278fAP4u7/to4MNHJP0tpHyrFahyy5WIeCIi9qTpXwLPAm9tVIFUuWXMgD7Zn+Nu4A8kKbXfFRG9EfEU0Jm2V2i9EbElIo6k2a2UrwkqynD2bzUXApsioiciXgA2Aa+5CrjGRlrvZcCdda6pqoj4EdAzSJeFwDejbCvla8WmUcy+HbLeiPhxqgeKf+8OZ/9Wk+d97yAZ4OSI2J+mDwAnD9ZZ0tmU0/vJTPOX06HujZJa6lBjpVvGDLw1zCt9ovzx6Rcpfzx6OOvW2khf8wrKf5H2eb2kdklbJS2qQ30DDbfeS9K/892S+i6Yber9m04ZzgAezDQ3ev8OpdrPU8S+HamB790A/l7S/1X5Fk3N4lxJP5P0A0lnpLZc+3c03GurpjTILVuyMxERkqp+Njr9lXQHsDQijqbmaygH0DjKn9NeDqysRd1jgaTLgRJwXqb51IjolnQa8KCknRHxZOUtNMxG4M6I6JX0Z5SP/s4vuKbhWALcHREvZ9qacf+OOpLmUQ6S3880/37at/8a2CTpF+mIoUg/pfxvfljSh4H1wKy8Gx1zRyQRcUFEvKvC417gVykg+oLi2UrbkPQm4D7K9wvbmtn2/nRI3gt8nfqcNqp2y5iKfSSdBLyZ8i1lhrNurQ3rNSVdQDnML077D4CI6E7Pe4GHgLn1LJZh1BsRz2dqvAV4z3DXrYORvOYSBpzWKmD/DqXaz1PEvh0WSWdSfh8sjIjn+9oz+/ZZ4HvU/zTykCLiHyPicJr+PvA6SVPIu38bORDU7A/gr+g/2H5DhT7jgM3Af6mwbFp6FvBVYFUdajyJ8kDjDF4dFDtjQJ8/p/9g+7o0fQb9B9v3Uv/B9uHUO5fy6cFZA9onAS1pegqwhxEMANax3mmZ6T8EtqbpycBTqe5JaXpy0fWmfu+gPPirIvdveq23U30w+CP0H2z/SVH7dpj1tlEea3zvgPZ/BbwxM/1jYH4T1Du17z1AOdj2pX09rPdR1ddsxA82Wh6UxxE2p1+oB/reqJRPt9ySpi8H/gV4LPOYk5Y9COyk/IVd3wIm1KnODwNPpP98r01tKyn/NQ/weuC76Q3+E+C0zLrXpvV2Axc1aL8OVe8DwK8y+3NDan9v2p8/S89XNEm9XwE6Ul1bgHdk1v1E2u+dwJ80Q71p/osM+MOmiP1L+Yhof/od6qJ8OuiTwCfTclH+IrsnU02lgvftUPXeQvlL9freu+2p/bS0X3+W3ivXNkm9n8q8d7eSCcBK76PhPnyLFDMzy2XMjZGYmVltOUjMzCwXB4mZmeXiIDEzs1wcJGZmlouDxMzMcnGQmJlZLg4Ss4JIepekH2fm3y1pc5E1mR0LX5BoVhBJJwC/BKZHxMuSHgKuioifFluZ2ciMubv/mjWLiDgqqQM4Q9Is4P9FxE/TnXivBd4cEZcWW6XZ0Hxqy6xYW4H3Ub4X1uehfCfeiLiiyKLMRsJHJGbF2kr5K5pvinTbcbPRxkckZsX6BdALrC66ELNj5SAxK9ZfANdExD/1NUh6i6SbgbmSrimuNLPh8ae2zAog6Xcof8vmP3g8xEY7B4mZmeXiU1tmZpaLg8TMzHJxkJiZWS4OEjMzy8VBYmZmuThIzMwsFweJmZnl8v8BRyB4aIu1WhkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVYAAAEYCAYAAAAH/d6fAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAAjoklEQVR4nO3de7wdVX338c83kAsChoSYEJKQoKYgag2aB6vYyl2kSLAChtYSbGikLW0VL8TSR31Qa6y1PFVAPQIlqOUiiEZBINykVlECD5gLwYQIckIuJEBAgUCS3/PHrAOTnb33mX3OnH05+b5fr/06M2vWzKy9z8k3a6+5KSIwM7PyDGl1A8zMBhsHq5lZyRysZmYlc7CamZXMwWpmVjIHq5lZyRysVpOkv5B0cxP39zlJGyStbdY+W0HSP0m6uNXtsIHjYG0Tkh6W9Jyk30laJ+kySXv0Y3ufkfTt/rQpIr4TEcf0ZxtFSdoP+ChwUETsI+l0ST8teR/jJS2Q9JikkDSlYvlwSZdKelrSWklnl7n/HhHxLxFxRsE29/v3aM3nYG0v74mIPYA3A9OBf25VQyTt2o91JanRv639gI0Rsb6v+61oQ7X2bwNuBN5XY7XPAFOBycDhwCckHVtGe2wnExF+tcELeBg4Kjf/JeBHafoEYCnwFHAH8LpcvXOA1cAzwIPAkcCxwAvAi8DvgPtT3ZHAJcCatM7ngF3SstOB/wHOBzamZacDP83t6+3A3cCm9PPtuWV3AJ9P23gOeG2V9zgXeCi1dRnw3lR+VFpnW2rvVcDzwNY0/1SqNxz4N+C3wDrg68BuadlhQHf6PNYC36rzWe8KBDClovwx4Jjc/GeBK2tso+fzuiB9HsuBI3PL9wUWAE8AK4G/zi37DPDtND0ltWVWel8bgHPTslq/x9OBVelz/A3wF63++/Wr4u+j1Q3wK/0icsEKTCIL0s8CfwD8HjgaGAp8Iv1DHQYcADwK7JvWmwK8Jk2/9I83t4/rgG8AuwNjgV8CH0rLTge2AH+fgmc3csEKjAaeBP4yLT81ze+dlt+RguH1afnQKu/x5BQ4Q4D3p/c1Pi07DOjO1X1p37my81NYjQb2BH4IfCG3/hbgi2QBvFudz3qHYAVGpbJxubKTgMU1ttHzeX0k/V7eTxawo9PyO4GLgBHANOBx4IjK3w0vB+s302f+JmAz6T/Pyt9j+t09DRyQ5scDr2/1369f2788FNBevi/pKeCnwE+AfyH7B3t9RCyMiBfJemy7kfUet5KFyEGShkbEwxHxULUNSxoHHAd8OCJ+H9lX7vOBmblqj0XEVyNiS0Q8V7GJPwVWRMS30vIryHpp78nVuSwilqblL1a2ISK+GxGPRcS2iLgKWAEcUuSDkSRgDvCRiHgiIp5Jn0++/duAT0fE5irt703PePamXNkmsgCvZT3wfyPixfR+HgT+VNIk4FDgnIh4PiLuAy4GTquzrf8TEc9FxP3A/WQBW8s24A2SdouINRGxtO47s6ZzsLaXEyNir4iYHBF/m8JhX+CRngoRsY2slzohIlYCHybr1ayXdKWkfWtsezJZz2qNpKdSgH+DrOfa49E6bduuHckjwISC6yPpNEn35fb/BmBMvXVyXgW8Argnt/6NqbzH4xHxfMHtVfpd+vnKXNkryb5u17I6IvJ3MXqE7HPaF+gJ//yy/GdVKX8mxLO8HPTbiYjfk/1neybZ7/J6SQfW2a61gIO1/T1GForASz23SWRjpETEf0XEO1KdIPsqTJrOe5TsK+aYFN57RcQrI+L1uTr1bnW2XTuS/Xra0dv6kiaTfd09i2z4YC9gCaAaq1RuawPZOOzrc+0fGdnBviLtrysiniQbe873FN9ENiRTy4T0++ixH9nn9BgwWtKeFcvyn1XhplVp600RcTTZMMByss/V2oiDtf1dTfb18khJQ8lOSdoM/EzSAZKOkDSc7GBPzwEgyA7uTOk5Oh8Ra4CbgS9LeqWkIZJeI+mdBdtxA/AHkv5c0q6S3g8cBPyo4Pq7k4XE4wCSPkjWY61lHTBR0rDU/m1kAXK+pLFpGxMkvavg/knrjCAbPgEYnuZ7XA78s6RRqRf418BldTY3FvgHSUMlnQy8DrghIh4FfgZ8QdIISX8IzAb6ctrUdr9HSeMkzZC0O9nfwe94+XdubcLB2uYi4kHgA8BXyXpt7yE7LesFsoCYl8rXkv1D/2Ra9bvp50ZJ96bp08gOei0jO/B0DVmvp0g7NgLHkwX7RrKDaMdHxIaC6y8Dvgz8nCws3kh2VL2W28h6i2sl9ezjHLIDd3dJehq4hewAXiOe4+Wv/cvTfI9Pk5218AjZGPeXIuLGOtv6BdnpWRvIzog4KX1OkB3cm0LWe72ObOz3lgbbCjv+HocAZ6ftPgG8E/ibPmzXBpC2HyIysyIknQ6ckYZhzLbjHquZWcnaIljTZYTrJS2psVySviJppaRfSXpzbtksSSvSa1bzWm1mnUDSJEm3S1omaamkf0zloyUtTNmxUNKoGus3nDFtMRQg6U/Ixr0uj4gdDmhIOo7sxPXjgLcC/xERb5U0GlhEdvlnAPcAb0lHeM3MkDSe7EKUe9OZGvcAJ5Jd5PFERMyTNBcYFRHnVKzbp4xpix5rRNxJNhBfywyy0I2IuAvYK31Y7wIWphPGnwQWkl0GaGYGZGfERMS9afoZ4AGyc4pnAPNTtflkYVupTxnTFsFawAS2P/m8O5XVKjcz20G6o9nBZGd0jEunIUJ2Vs24Kqv0KWP6fAejTiNpDtklkeyxy6i3vONVp7a4RWaD14/XXFjrwo/CRo0eEhMmFouopYtfXEp2LneProjoytdJt+G8luyy7qfz13ZEREgqbVy0U4J1NdnVRj0mprLVZDffyJffUW0D6UPuAhg5dGzrB5bNrK7nn4drry92xfOB+615PiKm11qeLq65FvhORHwvFa+TND4i1qShxWq3rCycMXmdMhSwADgtnR3wR8Cm1IW/CTgmXSkzCjgmlZmZAS9dBn4J8EBE/Htu0QKy2zWSfv6gyup9ypi26LFKuoLsf4UxkrrJroAZChARXye7nPI4sqtungU+mJY9IemzZPcGBTgvIuodBDOznc+hZLe7XCzpvlT2T2RXLV4taTbZ1XanAEiaDpwZEWf0NWPa4nSrZhs5dGy8fczJrW6G2aBVxhjrbq8YEvc9uE+hugfut+aeekMBzdYpQwFmZh3DwWpmVjIHq5lZyRysZmYlc7CamZXMwWpmVjIHq5lZyRysZmYlc7CamZXMwWpmVjIHq5lZyRysZmYlc7CamZXMwWpmVjIHq5lZyRysZmYlc7CamZXMwWpmVrJ2eebVscB/ALsAF0fEvIrl5wOHp9lXAGMjYq+0bCuwOC37bUSc0JRGm1nHkHQpcDywPiLekMquAg5IVfYCnoqIaVXWfRh4BtgKbCnyCJiWB6ukXYALgaOBbuBuSQsiYllPnYj4SK7+3wMH5zbxXLUPw8ws5zLgAuDynoKIeH/PtKQvA5vqrH94RGwourN2GAo4BFgZEasi4gXgSmBGnfqnAlc0pWVmNihExJ1A1aerpsdjn0KJudIOwToBeDQ3353KdiBpMrA/cFuueISkRZLuknTigLXSzAarPwbWRcSKGssDuFnSPZLmFNlgy4cCGjQTuCYitubKJkfEakmvBm6TtDgiHqpcMX0gcwBGDNmjOa01sz7bGkO45uk3F6x9/RhJi3IFXRHRVXDl3r4FvyNlzFhgoaTlqQdcUzsE62pgUm5+YiqrZibwd/mCiFidfq6SdAfZ+OsOwZo+5C6AkUPHRr9bbWbtZEORg0qVJO0K/Bnwllp1chmzXtJ1ZMOXdYO1HYYC7gamStpf0jCy8FxQWUnSgcAo4Oe5slGShqfpMcChwLLKdc3MajgKWB4R3dUWStpd0p4908AxwJLeNtryYI2ILcBZwE3AA8DVEbFU0nmS8qdOzQSujIh8b/N1wCJJ9wO3A/PyZxOYmQFIuoKsU3aApG5Js9OimVQMA0jaV9INaXYc8NOUMb8Ero+IG3vbXzsMBRARNwA3VJR9qmL+M1XW+xnwxgFtnJl1vIg4tUb56VXKHgOOS9OrgDc1ur+W91jNzAYbB6uZWckcrGZmJXOwmpmVzMFqZlYyB6uZWckcrGZmJXOwmpmVzMFqZlYyB6uZWckcrGZmJXOwmpmVzMFqZlYyB6uZWckcrGZmJXOwmpmVzMFqZlYyB6uZWckcrGZmJWuLYJV0rKQHJa2UNLfK8tMlPS7pvvQ6I7dslqQV6TWruS03s04g6VJJ6yUtyZV9RtLqXK4cV2PduvlUTcsfJihpF+BC4GigG7hb0oIqT1u9KiLOqlh3NPBpYDoQwD1p3Seb0HQz6xyXARcAl1eUnx8R/1ZrpQbyaTstD1bgEGBlehoikq4EZgBFHmP9LmBhRDyR1l0IHEvF42zNBosXDpxYqN6w5d0D3JLOEhF3SprSh1X7lE/tEKwTgEdz893AW6vUe5+kPwF+DXwkIh6tse6EajuRNAeYAzBiyB4lNNts4BUN0nrrdWrIbg2xcO2BBWtfP0bSolxBV0R0FVjxLEmnAYuAj1b5tls0n7bTFmOsBfwQmBIRfwgsBOY3uoGI6IqI6RExfdiQ3UpvoFlZXjhw4kuvsra3E9jQ8+87vYqE6teA1wDTgDXAl8tqTDsE62pgUm5+Yip7SURsjIjNafZi4C1F1zXrBGWHabXt2/YiYl1EbI2IbcA3yb72V+pTxrTDUMDdwFRJ+5M1eCbw5/kKksZHxJo0ewLwQJq+CfgXSaPS/DHAJwe+yWbl6C3wNr1meOFtjXxoc++V7CUVufJeYEmVar3mUzUtD9aI2CLpLLKQ3AW4NCKWSjoPWBQRC4B/kHQCsAV4Ajg9rfuEpM+SvXmA83oOZJm1s3qB2kiYVlvPAbsjSVcAhwFjJHWTnU10mKRpZGcUPQx8KNXdF7g4Io6rlU+97i8iBuJ9tLWRQ8fG28ec3Opm2E6oVqD2NUyrqReszTqQ9eM1F6q/29hlxND44+v/sVDdnxz15XsiYnp/91mWlvdYzXYGjQTqM5OLZ9Kej+zYMdr0muHutbaYg9VsABUN1EbCtHK9auFqreVgNRsg1UK1SKBu3u+Futsd/tthO2yjSLh26vmsncjBalayvgRqb2FaWbcyXK29OFjNSlQZqvUCtVaYTpn4+A5lD3e/art5h2t7c7CalaReqNYL1GpBWmnKxMd3CNdGeBiguRysZv3U21f/WqFaJFDz+huu1jwOVrN+6EsvtTJQj95nec3tF78JycsqT7Vyb7X5HKxmfdRoqDYSqNbZHKxmfVAkVGv1UhsJ1KP3WV6115o/cJU/1cq91fbQDne3MusofQ3Vo/dZXjVUT3rlvYX229v4qq+2ah/usZo1oJFQrddLrQzTnvlrnn7zduWN9FYrubfaOu6xmhXUaE+1R2+hWkS13qqHANqXg9WsgP58/c+rF6q1eqv5UO3prTpU25uD1awX/TlQVZRDdXDxGKtZHUVPqerR6NH/ykAFh+pg4GA1q6Hoc6IauYFKtSDtkT9Q5VDtbA5Ws4Ia6a02qlqo+lzVztUWwSrpWOA/yJ4pc3FEzKtYfjZwBtkzrx4H/ioiHknLtgKLU9XfRsQJTWu4DVq93aWqRyO91Wp666WCQ7UMki4FjgfWR8QbUtmXgPcALwAPAR+MiKeqrPsw8AywFdhS5BEwLT94JWkX4ELg3cBBwKmSDqqo9v+A6RHxh8A1wL/mlj0XEdPSy6FqA67o3f5rXee/cO2BL7161Prq71AtzWXAsRVlC4E3pFz5NfWf8Hx4yphCz9Vqhx7rIcDKiFgFIOlKYAawrKdCRNyeq38X8IGmttB2KkXHVis93P2qHYYDeruJSl96qeBQbVRE3ClpSkXZzbnZu4CTytpfOwTrBODR3Hw38NY69WcDP87Nj5C0iGyYYF5EfL/aSpLmAHMARgzZoz/ttZ1MmU9QhR1P9q93JdXO3EuNUCO3SRyTcqBHV0R0NbC7vwKuqtUU4GZJAXyjyHbbIVgLk/QBYDrwzlzx5IhYLenVwG2SFkfEQ5Xrpg+jC7LHXzelwdZxGu2tDv/tsO3GWRu5X2rlEwDcS+2XDX19/LWkc8k6Zt+pUeUdKWPGAgslLY+IO+ttsx2CdTUwKTc/MZVtR9JRwLnAOyPipb+6iFidfq6SdAdwMNlAtFnbqfY4FfdSW0fS6WQHtY6MiKodrlzGrJd0HdnwZdsH693AVEn7kwXqTODP8xUkHQx8Azg2ItbnykcBz0bEZkljgEPZ/sCW2YDLh2XlWQL1nkvVW6CCQ3UgpbORPkHWWXu2Rp3dgSER8UyaPgY4r7dttzxYI2KLpLOAm8hOt7o0IpZKOg9YFBELgC8BewDflQQvn1b1OuAbkraRneEwLyKWVd2RWUn2fCRqnhnQ2wP+qt2NyoE68CRdARxGNhbbDXya7CyA4WRf7wHuiogzJe1LdtrnccA44Lq0fFfgvyLixt721/JgBYiIG4AbKso+lZs+qsZ6PwPeOLCts53dyIc273AAqycgi5x6VevWfrXun+pQLV9EnFql+JIadR8DjkvTq4A3Nbq/tghWs05V736o1dS7GbUDdfBwsJoVUK3X2uj6tThQBx8Hq1lB+XCsF7JFH5HiQB28HKxmOcOWdxc6l7Wvz5dymO4cWn6vALN2MxDhN2x5t0N1J+Ieq1kVRXuu9da3nZeD1ayGfDjWC1mHqFVysJoV4PC0RniM1cysZA5WM7OSOVjNzErmYDUzK5mD1cysZA5WM7OSOVjNzErmYDUzK5mD1cysZA5WM7OSFQ5WSUdL+qakaWl+TlmNkHSspAclrZQ0t8ry4ZKuSst/IWlKbtknU/mDkt5VVpvMbPCQdKmk9ZKW5MpGS1ooaUX6OarGurNSnRWSZhXZXyM91r8CPg58QNIRwLQG1q1J0i7AhcC7gYOAUyUdVFFtNvBkRLwWOB/4Ylr3ILKnur4eOBa4KG3PzCzvMrKMyJsL3BoRU4Fb0/x2JI0me/DgW8kee/3pWgGc10iwPhMRT0XEx8geAfu/Gli3nkOAlRGxKiJeAK4EZlTUmQHMT9PXAEcqe2ziDODKiNgcEb8BVqbtmZm9JCLuBJ6oKM7nynzgxCqrvgtYGBFPRMSTwEJ2DOgd9Hp3K0knAdcC1+caOVfS3/e2bkETgEdz891k/ztUrZMel70J2DuV31Wx7oRqO0lDF3MARgzZo5SGm9kAit4fJ54zRtKi3HxXRHT1ss64iFiTpteSPeq6UrV8qpoxeUVuG/gt4H3AB3oKJH0wIr5aYN22kT7kLoCRQ8c29mhNM2t3GyJiel9XjoiQVFouFBkKWA78BLhW0tBUVlZvFWA1MCk3PzGVVa0jaVdgJLCx4LpmZtWskzQeIP1cX6VOnzKmSLBGRHwd+B6wQNJugAqsV9TdwFRJ+0saRnYwakFFnQVAz9G4k4DbIiJS+cx01sD+wFTglyW2zcwGr3yuzAJ+UKXOTcAxkkalg1bHpLK6igwFPAkQEZdLepZsrPUVRVpdRBozPYussbsAl0bEUknnAYsiYgFwCfAtSSvJBqBnpnWXSroaWAZsAf4uIraW1TYzGxwkXQEcRjYW2012pH8ecLWk2cAjwCmp7nTgzIg4IyKekPRZsg4gwHkRUXkQbMf9ZR2/hhp4PHBZRIxpaMU2MnLo2Hj7mJNb3QyzQevHay7s97faIcOGxdT//cVCdX/9qbPv6c8Ya9kafuZVRPwI6NhQNTMbaL6k1cysZA5WM7OSOVjNzErmYDUzK5mD1cysZA5WM7OSOVjNzErmYDUzK5mD1cysZA5WM7OSOVjNzErmYDUzK5mD1cysZA5WM7OSOVjNzErmYDUzK5mD1cysZC0NVkmjJS2UtCL9HFWlzjRJP5e0VNKvJL0/t+wySb+RdF96TWvqGzCztifpgFxG3CfpaUkfrqhzmKRNuTqf6s8+G340S8nmArdGxDxJc9P8ORV1ngVOi4gVkvYF7pF0U0Q8lZZ/PCKuaV6TzayTRMSDwDQASbuQPb76uipV/zsiji9jn60eCpgBzE/T84ETKytExK8jYkWafozs2d+valYDzWxQORJ4KCIeGcidtLrHOi4i1qTptcC4epUlHQIMAx7KFX8+ddtvBeZGxOYa684B5gCMGLJHf9ttZgNMAXs+Uvgp0mMkLcrNd0VEV5V6M4EramzjbZLuBx4DPhYRS4u3dnsDHqySbgH2qbLo3PxMRISkmp+ipPHAt4BZEbEtFX+SLJCHAV1kwwjnVVs/fchdkD3+usG3YWbtbUNvj7+WNAw4gSw3Kt0LTI6I30k6Dvg+MLWvjRnwYI2Io2otk7RO0viIWJOCc32Neq8ErgfOjYi7ctvu6e1ulvSfwMdKbLqZDS7vBu6NiHWVCyLi6dz0DZIukjQmIjb0ZUetHmNdAMxK07OAH1RWSP/LXAdcXnmQKoUxkkQ2PrtkIBtrZh3tVGoMA0jaJ+VIz5DjEGBjX3fU6mCdBxwtaQVwVJpH0nRJF6c6pwB/Apxe5bSq70haDCwGxgCfa2rrzawjSNodOBr4Xq7sTElnptmTgCVpjPUrwMyI6POQYUsPXkXERrKjdJXli4Az0vS3gW/XWP+IAW2gmQ0KEfF7YO+Ksq/npi8ALihrf63usZqZDToOVjOzkjlYzcxK5mA1MyuZg9XMrGQOVjOzkjlYzcxK5mA1MyuZg9XMrGQOVjOzkjlYzcxK5mA1MyuZg9XMrGQOVjOzkjlYzcxK5mA1MyuZg9XMrGQOVjOzkrU0WCWNlrRQ0or0c1SNeltzz7takCvfX9IvJK2UdFV68KCZ2XYkPSxpccqQRVWWS9JXUpb8StKb+7O/VvdY5wK3RsRU4NY0X81zETEtvU7IlX8ROD8iXgs8Ccwe2OaaWQc7PGXI9CrL3g1MTa85wNf6s6NWB+sMYH6ank/2COtC0qNqjwB6Hond0PpmZjkzgMsjcxewl6Txfd1Yq4N1XESsSdNrgXE16o2QtEjSXZJOTGV7A09FxJY03w1MGLimmlkHC+BmSfdImlNl+QTg0dx8v/JkwB9/LekWYJ8qi87Nz0RESKr1HO/JEbFa0quB2yQtBjY12I45ZF18RgzZo5FVzawVtsHIhzYXrT2mYuy0KyK6cvPvSBkyFlgoaXlE3FlaWysMeLBGxFG1lklaJ2l8RKxJ3e71NbaxOv1cJekO4GDgWrLu+q6p1zoRWF2nHV1AF8DIoWNrBbiZdaYNNcZOge0yZL2k64BDgHywrgYm5ebr5klvWj0UsACYlaZnAT+orCBplKThaXoMcCiwLCICuB04qd76ZrZzk7S7pD17poFjgCUV1RYAp6WzA/4I2JQbpmxYq4N1HnC0pBXAUWkeSdMlXZzqvA5YJOl+siCdFxHL0rJzgLMlrSQbc72kqa03s04wDvhpypBfAtdHxI2SzpR0ZqpzA7AKWAl8E/jb/uxwwIcC6omIjcCRVcoXAWek6Z8Bb6yx/iqyLr2ZWVUpJ95UpfzruekA/q6sfba6x2pmNug4WM3MSuZgNTMrmYPVzKxkDlYzs5I5WM3MSuZgNTMrmYPVzKxkDlYzs5I5WM3MSuZgNTMrmYPVzKxkDlYzs5I5WM3MSuZgNTMrmYPVzKxkDlYzs5I5WM3MStbSYJU0WtJCSSvSz1FV6hwu6b7c63lJJ6Zll0n6TW7ZtGa/BzNrb5ImSbpd0jJJSyX9Y5U6h0nalMuST/Vnny195hUwF7g1IuZJmpvmz8lXiIjbgWmQBTHZw75uzlX5eERc05zmmlkH2gJ8NCLuTU9rvUfSwtxDSXv8d0QcX8YOWz0UMAOYn6bnAyf2Uv8k4McR8exANsrMBo+IWBMR96bpZ4AHgAkDuc9WB+u43LO715I9praemcAVFWWfl/QrSedLGl56C81s0JA0BTgY+EWVxW+TdL+kH0t6fX/2M+BDAZJuAfapsujc/ExEhKSos53xZI/BvilX/EmyQB4GdJENI5xXY/05wByAEUP2aOAdmFlLbAuGLe8uWnuMpEW5+a6I6MpXkLQHcC3w4Yh4umL9e4HJEfE7SccB3wem9q3hTQjWiDiq1jJJ6ySNj4g1KTjX19nUKcB1EfFibts9vd3Nkv4T+FiddnSRhS8jh46tGeBm1pE2RMT0WgslDSUL1e9ExPcql+eDNiJukHSRpDERsaEvjWn1UMACYFaangX8oE7dU6kYBkhhjCSRjc8uKb+JZtbJUj5cAjwQEf9eo84+qR6SDiHLxo193WerzwqYB1wtaTbwCFmvFEnTgTMj4ow0PwWYBPykYv3vSHoVIOA+4MzmNNvMOsihwF8CiyXdl8r+CdgPICK+TnZg/G8kbQGeA2ZGRJ+/2bY0WCNiI3BklfJFwBm5+YepchQvIo4YyPaZWeeLiJ+Sdb7q1bkAuKCsfbZ6KMDMbNBxsJqZlczBamZWMgermVnJHKxmZiVzsJqZlczBamZWMgermVnJHKxmZiVzsJqZlczBamZWMgermVnJHKxmZiVzsJqZlczBamZWMgermVnJHKxmZiVzsJqZlczBamZWspYGq6STJS2VtC09QLBWvWMlPShppaS5ufL9Jf0ilV8laVhzWm5mnaRWhuSWD08ZsjJlypT+7K/VPdYlwJ8Bd9aqIGkX4ELg3cBBwKmSDkqLvwicHxGvBZ4EZg9sc82s0/SSIT1mA0+mLDmfLFv6rKXBGhEPRMSDvVQ7BFgZEasi4gXgSmBGegb4EcA1qd584MQBa6yZdaqqGVJRZwZZhkCWKUemjOmTlj7+uqAJwKO5+W7grcDewFMRsSVXvsMjsntImgPMSbObb1x70ZIBaGurjQE2tLoRA2Cwvi8YpO9NumhJRLyhP9vYxpYXb1x70YsFqx8gaVFuvisiutJ0rQzJe6lORGyRtIksY/r0uxnwYJV0C7BPlUXnRsQPBnr/PdKH3JXatCgiao7pdiq/r84zWN9bRcj1SUR07DGTAQ/WiDiqn5tYDUzKzU9MZRuBvSTtmnqtPeVmZnm1MqRanW5JuwIjyTKmT1p98KqIu4Gp6QyAYcBMYEFEBHA7cFKqNwtoWg/YzDpG1QypqLOALEMgy5TbUsb0SatPt3qvpG7gbcD1km5K5ftKugGy8Q7gLOAm4AHg6ohYmjZxDnC2pJVk4yGXFNx1V+9VOpLfV+cZrO+tbd5XrQyRdJ6kE1K1S4C9U5acDexwSlYj1I9QNjOzKjphKMDMrKM4WM3MSrZTBGt/L51tV5JGS1ooaUX6OapGva2S7kuvykH7ttHsyw6bpcD7Ol3S47nf0RmtaGejJF0qab2kqueEK/OV9L5/JenNzW5jq+wUwUr/L51tV3OBWyNiKnArtQfcn4uIael1Qo06LdWKyw6boYG/q6tyv6OLm9rIvrsMOLbO8ncDU9NrDvC1JrSpLewUwdqfS2cHvnX9kr8Mr9Mv6W36ZYdN0ol/V4VExJ3AE3WqzAAuj8xdZOedj29O61prpwjWgqpd9lbzEtk2MS4i1qTptcC4GvVGSFok6S5JJzanaQ0r8vlvd9kh0HPZYTsr+nf1vvR1+RpJk6os70Sd+G+qFJ1wr4BC2uXS2bLVe1/5mYgISbXOnZscEaslvRq4TdLiiHio7LZan/0QuCIiNkv6EFmv/IgWt8n6YdAE6wBeOttS9d6XpHWSxkfEmvQVa32NbaxOP1dJugM4GGi3YG36ZYdN0uv7ioj8e7gY+NcmtKsZ2vLfVDN4KOBlRS57azf5y/CqXtIraZSk4Wl6DHAosKxpLSyu6ZcdNkmv76ti3PEEsquDBoMFwGnp7IA/Ajblhq4Gt4gY9C/gvWTjO5uBdcBNqXxf4IZcveOAX5P15s5tdbsLvK+9yc4GWAHcAoxO5dOBi9P024HFwP3p5+xWt7vO+9nh8wfOA05I0yOA7wIrgV8Cr251m0t6X18Alqbf0e3Aga1uc8H3dQWwBngx/fuaDZwJnJmWi+yMiIfS3970Vre5WS9f0mpmVjIPBZiZlczBamZWMgermVnJHKxmZiVzsJqZlczBamZWMgertSVJt+Vuo/e8pFNa3Sazonweq7U1SX8DHA6cGhFbW90esyLcY7W2Jek0snt6/gUwWdIlkq5pcbPMeuVgtbYk6WSyQD0lIl6M7H6ms1vdLrMiBs3drWzwkHQ88LfA8RHxfKvbY9Yo91itHc0nu8Xc/6SDV+6pWkfxwSvrCJL2Bj4PHE12564vtLhJZjU5WM3MSuahADOzkjlYzcxK5mA1MyuZg9XMrGQOVjOzkjlYzcxK5mA1MyuZg9XMrGQOVjOzkv1/ZuEbyyVXaA8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = {}\n",
    "prior = {}\n",
    "post = {}\n",
    "key = jax.random.PRNGKey(5)\n",
    "\n",
    "n_points = 10  # number of sample data points\n",
    "\n",
    "# Part A\n",
    "z = jnp.array([0.5, 0.5])\n",
    "sigma_data = 0.1 * jnp.array([[2, 1], [1, 1]])\n",
    "\n",
    "data[\"mu\"] = z\n",
    "data[\"Sigma\"] = sigma_data\n",
    "sample_points = gaussSample(data[\"mu\"], data[\"Sigma\"], n_points, key)\n",
    "plot_data(sample_points, z, \"gauss_2d_update_data\", \"Data\")\n",
    "\n",
    "# Part B\n",
    "xyrange = jnp.array([[-1, 1], [-1, 1]])\n",
    "npoints = 100j\n",
    "prior[\"mu\"] = jnp.array([0, 0])\n",
    "prior[\"Sigma\"] = 0.1 * jnp.eye(2)\n",
    "mesh = jnp.mgrid[xyrange[0, 0] : xyrange[0, 1] : npoints, xyrange[1, 0] : xyrange[1, 1] : npoints]\n",
    "x1, x2 = mesh[0], mesh[1]\n",
    "points = jnp.vstack([jnp.ravel(x1), jnp.ravel(x2)]).T\n",
    "prior_pdf = multivariate_normal.pdf(points, mean=prior[\"mu\"], cov=prior[\"Sigma\"]).reshape(x1.shape[0], x2.shape[0])\n",
    "\n",
    "make_contour_plot(x1, x2, prior_pdf, \"gauss_2d_update_prior\", \"Prior\")\n",
    "\n",
    "# Part C\n",
    "data_after_n = sample_points[:n_points, :]\n",
    "s0_inv = inv(prior[\"Sigma\"])\n",
    "s_inv = inv(sigma_data)\n",
    "post[\"Sigma\"] = inv(s0_inv + n_points * s_inv)\n",
    "mean = jnp.mean(data_after_n, 0)\n",
    "post[\"mu\"] = jnp.dot(post[\"Sigma\"], (jnp.dot(n_points, jnp.dot(s_inv, mean)) + jnp.dot(s0_inv, prior[\"mu\"])))\n",
    "post_pdf = multivariate_normal.pdf(points, mean=post[\"mu\"], cov=post[\"Sigma\"]).reshape(x1.shape[0], x2.shape[0])\n",
    "make_contour_plot(x1, x2, post_pdf, \"gauss_2d_update_post\", \"Posterior after \" + str(n_points) + \" points\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 352
    },
    "id": "j7lS5tD4byLk",
    "outputId": "3630e957-7942-4623-9d61-6dbe64457893"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1080x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(15, 5))\n",
    "plot_data(sample_points, z, \"\", \"Data \", fig=fig, ax=ax1)\n",
    "make_contour_plot(x1, x2, prior_pdf, \"\", \"Prior \", fig=fig, ax=ax2)\n",
    "make_contour_plot(x1, x2, post_pdf, \"\", \"Posterior after \" + str(n_points) + \" points\", fig=fig, ax=ax3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZGHdlkChkEOM"
   },
   "source": [
    "### Interactive plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 361,
     "referenced_widgets": [
      "6557b93cdba04cd8a210426662ff4ae5",
      "dfb2dded453b4e0cadb00030171dec81",
      "b6b8fc10566e4df198f60f14ae82b634",
      "7d1908c142a643289a2b0b2147cc99df",
      "d34d1219db274ed9a22ab773ec1f4f3d",
      "bab25a894ad24dfc860f7676c8103484",
      "ccb1d8424e674d3096d59761c601b27e",
      "8bb5443e3faf471f97014f29df4d25cc",
      "13362742f0b84c20b9e46dfdf1f6b5dc",
      "9388e86738644254b07e8984d685f5a8"
     ]
    },
    "id": "SV_IOj6wJRAq",
    "outputId": "16a73102-ed59-4ecf-93ae-9d7057f5b5ae"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6557b93cdba04cd8a210426662ff4ae5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=5, description='random_state', max=10, min=1), IntSlider(value=10, descr…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact\n",
    "\n",
    "\n",
    "@interact(random_state=(1, 10), n_=(1, 20))\n",
    "def generate_random(random_state, n_=10):\n",
    "    key = jax.random.PRNGKey(random_state)\n",
    "    sample_points = gaussSample(data[\"mu\"], data[\"Sigma\"], n_, key)\n",
    "    plot_data(sample_points, z, \"\", \"Data\")\n",
    "    plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "gauss_infer_2d.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3.7.13 ('py3713')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.13"
  },
  "vscode": {
   "interpreter": {
    "hash": "a787a6e8bcd3d3d3e4a766006c27db2c5a636d1b43e1d89cd16234e9a9c2591c"
   }
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "13362742f0b84c20b9e46dfdf1f6b5dc": {
     "model_module": "@jupyter-widgets/controls",
     "model_module_version": "1.5.0",
     "model_name": "SliderStyleModel",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "SliderStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "description_width": "",
      "handle_color": null
     }
    },
    "6557b93cdba04cd8a210426662ff4ae5": {
     "model_module": "@jupyter-widgets/controls",
     "model_module_version": "1.5.0",
     "model_name": "VBoxModel",
     "state": {
      "_dom_classes": [
       "widget-interact"
      ],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "VBoxModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "VBoxView",
      "box_style": "",
      "children": [
       "IPY_MODEL_dfb2dded453b4e0cadb00030171dec81",
       "IPY_MODEL_b6b8fc10566e4df198f60f14ae82b634",
       "IPY_MODEL_7d1908c142a643289a2b0b2147cc99df"
      ],
      "layout": "IPY_MODEL_d34d1219db274ed9a22ab773ec1f4f3d"
     }
    },
    "7d1908c142a643289a2b0b2147cc99df": {
     "model_module": "@jupyter-widgets/output",
     "model_module_version": "1.0.0",
     "model_name": "OutputModel",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/output",
      "_model_module_version": "1.0.0",
      "_model_name": "OutputModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/output",
      "_view_module_version": "1.0.0",
      "_view_name": "OutputView",
      "layout": "IPY_MODEL_9388e86738644254b07e8984d685f5a8",
      "msg_id": "",
      "outputs": [
       {
        "data": {
         "image/png": "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\n",
         "text/plain": "<Figure size 432x288 with 1 Axes>"
        },
        "metadata": {
         "needs_background": "light"
        },
        "output_type": "display_data"
       }
      ]
     }
    },
    "8bb5443e3faf471f97014f29df4d25cc": {
     "model_module": "@jupyter-widgets/base",
     "model_module_version": "1.2.0",
     "model_name": "LayoutModel",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "9388e86738644254b07e8984d685f5a8": {
     "model_module": "@jupyter-widgets/base",
     "model_module_version": "1.2.0",
     "model_name": "LayoutModel",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "b6b8fc10566e4df198f60f14ae82b634": {
     "model_module": "@jupyter-widgets/controls",
     "model_module_version": "1.5.0",
     "model_name": "IntSliderModel",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "IntSliderModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "IntSliderView",
      "continuous_update": true,
      "description": "n_",
      "description_tooltip": null,
      "disabled": false,
      "layout": "IPY_MODEL_8bb5443e3faf471f97014f29df4d25cc",
      "max": 20,
      "min": 1,
      "orientation": "horizontal",
      "readout": true,
      "readout_format": "d",
      "step": 1,
      "style": "IPY_MODEL_13362742f0b84c20b9e46dfdf1f6b5dc",
      "value": 10
     }
    },
    "bab25a894ad24dfc860f7676c8103484": {
     "model_module": "@jupyter-widgets/base",
     "model_module_version": "1.2.0",
     "model_name": "LayoutModel",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "ccb1d8424e674d3096d59761c601b27e": {
     "model_module": "@jupyter-widgets/controls",
     "model_module_version": "1.5.0",
     "model_name": "SliderStyleModel",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "SliderStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "description_width": "",
      "handle_color": null
     }
    },
    "d34d1219db274ed9a22ab773ec1f4f3d": {
     "model_module": "@jupyter-widgets/base",
     "model_module_version": "1.2.0",
     "model_name": "LayoutModel",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "dfb2dded453b4e0cadb00030171dec81": {
     "model_module": "@jupyter-widgets/controls",
     "model_module_version": "1.5.0",
     "model_name": "IntSliderModel",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "IntSliderModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "IntSliderView",
      "continuous_update": true,
      "description": "random_state",
      "description_tooltip": null,
      "disabled": false,
      "layout": "IPY_MODEL_bab25a894ad24dfc860f7676c8103484",
      "max": 10,
      "min": 1,
      "orientation": "horizontal",
      "readout": true,
      "readout_format": "d",
      "step": 1,
      "style": "IPY_MODEL_ccb1d8424e674d3096d59761c601b27e",
      "value": 5
     }
    }
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}