experiments/manifold/coil.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from utils import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = PRNG(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "rc = {\n",
    "    'axes.axisbelow': True,\n",
    "    'axes.linewidth': 1.0,\n",
    "    'figure.dpi': 150,\n",
    "    'font.size': 12.0,\n",
    "    'legend.fontsize': 'xx-small',\n",
    "    'lines.linewidth': 1.0,\n",
    "    'savefig.transparent': True,\n",
    "    'xtick.labelsize': 'x-small',\n",
    "    'xtick.major.width': 1.0,\n",
    "    'ytick.labelsize': 'x-small',\n",
    "    'ytick.major.width': 1.0,\n",
    "    'font.family': ['serif'],\n",
    "    'text.usetex': True,\n",
    "    'text.latex.preamble': r'\\usepackage{amsfonts}',\n",
    "}\n",
    "\n",
    "plt.rcParams.update(rc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = jnp.linspace(0, 2 * jnp.pi, 256)\n",
    "radius = 2.0\n",
    "depth = jnp.linspace(-2.0, 2.0, 256)\n",
    "\n",
    "mu_i = jnp.stack((radius * jnp.sin(theta), radius * jnp.cos(theta), depth), axis=-1)\n",
    "sigma_i = 1e-2 * jnp.ones_like(mu_i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = jnp.array([[1.0, 0.0, 2.0]])\n",
    "\n",
    "def A(x):\n",
    "    return jnp.einsum('...ij,...j', W, x)\n",
    "\n",
    "cov_y = 1e-2 ** 2 * jnp.eye(1)\n",
    "\n",
    "y = jnp.array([0.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prior(n):\n",
    "    i = rng.randint((n,), minval=0, maxval=len(mu_i))\n",
    "\n",
    "    x = mu_i[i]\n",
    "    x = x + sigma_i[i] * rng.normal(x.shape)\n",
    "\n",
    "    return x\n",
    "\n",
    "def posterior(n):\n",
    "    p_x = prior(n)\n",
    "    log_p_y_x = jax.scipy.stats.multivariate_normal.logpdf(y, A(p_x), cov_y)\n",
    "    p_x_y = rng.choice(p_x, (n,), p=jnp.exp(log_p_y_x))\n",
    "\n",
    "    return p_x_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_x = prior(65536)\n",
    "cov_x = jnp.cov(p_x.T)\n",
    "fig = show_corner(p_x, height=1.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xhAO1sbGR0dHRJA/PWuEFetA/vrj3IB9e/hdJkhNvH831G5tJko+nfztfOjLY74P0vNv+yIm3j+bsqZo4BobCvn3Hn5mZyfe///0XXufMmTNZXl7eryEA8AoOJXnjte7/Fq7f2Mzd+/uyfgLQc/ZtK8WpU6eSJB9++GHm5+e7XnCXJGfPns34+HjGx8f3awgAvIpK8pvVL6dI8qDIltVjgEG3r78jPHXqVD7++OOsr69v+dzVq1ezsLCQmze9WxtAr6hUKjlUqeSQnRPAENq3FeMnPXrx3ZOWl5dz7dq1vPvuuwcxBAAAeKFSX1UiigEA6BWD/XJrAADYJmEMAAARxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkCQ5UvYADlqz2czq6mqSpNVqZWZmJnNzcyWPCgCAsg1VGNfr9czOznZCuN1u5/jx41ldXU2j0Sh5dOzWL+7ce+bxd0aH6mkOAOzQUG2laDabuXr1aufjarWaubm5NJvNEkcFAEAvGKqltLGxsbTb7a5j4+PjSR5uq6jVatv6dzY2NrZ1DACA/jFUYby+vv7cY9uN4iQZHR3dszGxPU9uk7h1527n8jf+zsLjKx17/Bj+5M+e3Df+5c4l2yoAgOcZqq0UT2u322k2m1lcXCx7KAAAlGyol8/OnDmT6enpLCwsvPzKT7hz586WYxsbGzl27NheDQ0AgAPWl2G8srKSer2+revOzs4+M3wvXLiQJFlaWnrlrz8yMvLKf4fdeXILxJOXf3XtT8sYDgAwgPoyjKempjrnIt6Jy5cvZ319vRPF7XY71Wp1j0YHAEA/Gro9xmtra1leXu46b3Gz2dxytgoAAIZLX64Y79Sjd7qr1+td5y6+dOnSK+8zBgBgsAxVGJ88eTLtdjvz8/NdxycnJ0saEQAAvWKowvj27dtlDwEAgB41dHuMAQDgWYQxAABEGAMAQBJhDAAASYQxAAAkEcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJBEGAMAQJLkSNkDAODgFUWRu/eLfHHvQdlDAegZwhhgyBRFkXNXWrl+Y3Nb138Uz68frqRSqezn0ABKJYwBnmNQg/Du/WJLFL/x2qE87xZ+50d/mSQ58fbRnD1VG6j7AuBJwniPFEXRubyxsVHiSKAcR48e3XUwFUWRzc3N/PKL+3s0qu354v7j7QT37t3rXH4UhO+MvJbv/M5vpPLcdOwvT97e36q+nkqlkkOV5N797vv9S4cr+eL+4+9t129s5v+98Vm+dNjLU/bLyOuHMjoy4ocPKEmleLLo2LGf//znOXbsWNnDgNLcuXMnIyMju/o3NjY2Mjo6mj/8J/98j0YF/ecf/W5t13MJ2Bk/9gMAQKwY75kHDx7kxo0bSfbmV8qvYmNjo7Na/emnnw7dSoPb3xu3fy+3UpSlV+7Lsgzz7e+l237Q/4cAj9ljvEcOHTqUr33ta2UPIyMjI0P1n9nT3P7+vv2VSqVnxt/v9+VuDfPtH+bbDsPOVgoAAIgwBgCAJMIYAACSCGMAAEjirBQAAJDEijEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkCQ5UvYABkVRFNnc3EySHD16NJVKpeQRQf8xjwAokxXjPbK5uZnR0dGMjo52/mMHXo15BECZhDEAAEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJkiNlD6AszWYzq6urSZJWq5WZmZnMzc2VPCoAAMoylGFcr9czOzvbCeF2u53jx49ndXU1jUaj5NEBAFCGodxK0Ww2c/Xq1c7H1Wo1c3NzaTabJY4KAIAyDeWK8djYWNrtdtex8fHxJA+3VdRqtRf+/Y2NjW0dA57PPAKg1wxlGK+vrz/32MuiOElGR0f3fEwwbMwjAHrNUG6leFq73U6z2czi4mLZQwEAoCSVoiiKsgdRtpmZmSTJ0tLStq7/vF8BHzt2LEly586djIyM7N0AYQCZRwD0mqHcSvGkCxcuJNl+FCfxnzXsAfMIgF4z1FspLl++nPX19U4UP/2CPAAAhsfQhvHa2lqWl5e7zlvcbDbFMQDAkBrKPcatViunT59OvV7vOt5oNDrvhveqNjY2Oq+ytzcSdsY8AqBMQ7nH+OTJk2m325mfn+86Pjk5WdKIAAAo21CG8e3bt8seAgAAPWZo9xgDAMCThDEAAEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJkiNlD4Dde/Pv/vedy5/9479X4kiAfvKLO/c6l//wf7jWufxv/xtvdi7/5//h8c7lr33ltYMZGEBJrBgDAECEMQAAJEkqRVEUZQ9iEGxsbGR0dDRJcufOnYyMjJQ8Iug/5hEAZbJiDAAAEcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJDEO98BAAOqKIrcvf/4rLSvH66kUqmUOCJ6nTAGAAZOURQ5d6WV6zc2O8dOvH00Z0/VxDHPZSsFADBw7t4vuqI4Sa7f2OxaQYanCWMAYKDVxt8oewj0CWEMAAy0Q7ZOsE3CGAAAIowBACCJMAYAgCTCGAAAkghjAABIIowBACCJMAYAgCTCGAAAkhxgGP/4xz/Oe++9l69//ev5gz/4g/zyl7/sfO6P//iPMzs7m+9973sHNRwAAOhyIGF85cqVTE1N5ebNmzl+/Hg++eST/NZv/Vb++q//Okny0Ucf5dSpU1lcXDyI4QAAwBZHDuKLLC4uZnl5OadOneocazabmZqaytraWr7yla9kfHz8IIYCAADPdCArxrVarSuKk2Rubi6XLl3K9PT0QQwBAABe6EBWjCuVyjOPT05O5uOPP86HH36YqampgxhKx8rKSpaWllKtVtNut3Py5MnMzc0d6BgAAOgdBxLGtVotP/vZz9JqtdJqtfLBBx90fW5hYSEzMzMHMZQkD6O4Xq9ndXW1c+z06dMZGxuzgg0AMKQOZCvFRx99lB/84AeZm5t75gvsjh8/nj//8z/Pm2++eRDDyeLiYmZnZ7uOzc/Pp16vH8jXBwCg91SKoijKHsRBq1QqWV5e7tq+0Wq1MjExkdXV1UxOTr7yv7mxsZHR0dEkyZ07dzIyMrJn46Vb6xf/X+fy3/n+/9K5/L/+F9/qXD721dcOdEzsjbLn0Rvv/oPO5V9d+9MD/drA3vri3oN8ePlfJElOvH00129sJkk+nv7tfOnI4LyNQ1EUuXv/ccq9frjy3C2svNyBbKXoJWtra888PjY2luRhIL8sjDc2NrZ1DHg+8whgd4qiyLkrrU70Jw9/CDh7qiaOd2jffmS6du1a3nvvvfzwhz/cry+xI7du3UryOISf9/kXGR0d3fLn2LFjezpOGHTmEcDu3L1fdEVxkly/sdm1gsyr2bcV40ajkfX19XzwwQf5vd/7va7Pffe7382JEye6XoQH21V758udy//bf/l4+8R/+t/8H53L/91/9s3O5X/rbx09mIHR/6qPw/wXv7zXufzOV4bul2vALpSxvaE2/kZaN3+1r19jGOzbd/uJiYksLi4+cwX2/PnzuXbtWs6ePZtz587t1xCe6dFK8dPjetlK8pPu3Lmz5djGxobVLngF5hEwiMra3nDI1ok9sW9hfPPmzVQqlRw/fvyZn3/33XdTq9UOPI5rtVqSpN1udx1/9PF2XnjnhXWwe+YRMIhetL3hS0fEa6/btzA+f/58Pvzww5w4cSJnzpzJV7/61S3XOajTsz2pWq1mamoqrVar63ir1Uq1Wu2EM/3ha195fPaJ//O7/1GJI2EQ/Oqf/sOyhwAMENsb+s++vfju888/z82bN/PRRx/lrbfeyje/+c1873vfy09/+tOu6z0dqAehXq+n0Wh0HWs0Gs88xzIAwE7Y3tB/9m3F+IMPPkitVsvS0lJ+8pOf5MqVKzl//nwnPmu1Wlqt1pZAPQhTU1NZXFzM/Px8JiYmcvPmzczMzHhLaABgRx694O6Lew/KHgq7sG9hXKvVcv78+STJ+++/nyT57LPPsrKykk8++SQXL15Ms9ks7cwU09PT3v4ZANi1Z73gjv60b1spnn5xW/JwT/H777+fRqORBw8epCiK/PjHP96vIQAA7LtnveDujdcO7V9ksW/27TGbmZnJ97///Rde58yZM1leXt6vIQAAHKgTbx/Nv/nO0fxm9cuJLcZ9Z9+2Upw6dSpJ8uGHH2Z+fj7f+MY3uj5/9uzZjI+PZ3x8fL+GAABwoA5VHr/orii8A12/2ddV/lOnTuXjjz/O+vr6ls9dvXo1CwsLuXnz5n4OAQAAtuVA3uf00YvvnrS8vJxr167l3XffPYghAADAC5W6L1wUAwDQK7xgEgAAIowBACCJMAYAgCTCGAAAkghjAABIIowBACCJMAYAgCTCGAAAkghjAABIIowBACCJMAYAgCTCGAAAkghjAABIIowBACCJMAYAgCTCGAAAkghjAABIkhwpewDA7r3x7j/oXP7VtT8tcST0k7/57Nedy99a/Kedy//+v/MbncuL/8nf7lx+Z9R/GcBgs2IMAAARxgAAkMRWChgItk+wE3/rzdc6l/+f/+o/LnEkAL3BijEAAEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkEQYAwBAEmEMAABJhDEAACQRxgAAkCQ5UvYADlqz2czq6mqSpNVqZWZmJnNzcyWPCgCAsg1VGNfr9czOznZCuN1u5/jx41ldXU2j0Sh5dAAAlGmotlI0m81cvXq183G1Ws3c3FyazWaJowIAoBcM1Yrx2NhY2u1217Hx8fEkD7dV1Gq1bf07Gxsb2zoGPJ95BECvGaowXl9ff+6x7UZxkoyOju7ZmGBYmUcA9Jqh2krxtHa7nWazmcXFxbKHAgBAyYZqxfhpZ86cyfT0dBYWFl7p7925c2fLsY2NjRw7dmyvhgYDzzwCoNf0ZRivrKykXq9v67qzs7PPDN8LFy4kSZaWll7564+MjLzy3wG6mUcA9Jq+DOOpqanOuYh34vLly1lfX+9EcbvdTrVa3aPRAQDQj4Zuj/Ha2lqWl5e7zlvcbDa3nK0CAIDh0pcrxjv16J3u6vV617mLL1269Mr7jAEAGCxDFcYnT55Mu93O/Px81/HJycmSRgQAQK8YqjC+fft22UMAAKBHDd0eYwAAeBZhDAAAEcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJBEGAMAQBJhDAAASYQxAAAkSY6UPQAAgH5VFEW+uPfgpdd7dJ3XD1dSqVT2e1jskDDeI0VRdC5vbGyUOBIox9GjR3f9zd48gr2bS5ubmy+8zoOiyMbdlwddv/ri/uPbdu/evc7lv7n9eb50eG9+YV6kyH/9v/+r/GLj151jv753P4f+9cP34PG3tHznR3+ZJHln5LV853d+I5XsPo4P4jb2opHXD+XQNubITuZSpXjyfyJ27Oc//3mOHTtW9jCgNHfu3MnIyMiu/g3zCPZmLm1sbGR0dPT5V6hU8of/+P/a1deAMv23f/ffTV6SsDuZS4P74wQAALwCK8Z75MGDB7lx40aSvfk12KvY2NjorLJ9+umnu15p6Dduf2/c/r143pc5j5LeuS/LMsy3v5du+0FtpdipXrqvepH758UO8v7ZyVyyx3iPHDp0KF/72tfKHkZGRkaGehK6/f19+3tlHiX9f1/u1jDf/kG47ZVK5UBuwyDcV/vJ/fNivXj/2EoBAAARxgAAkEQYAwBAEmEMAABJnJUCAACSWDEGAIAkwhgAAJIIYwAASCKMAQAgiTAGAIAkwhgAAJIIYwAASJIcKXsA7J9ms5nV1dUkSavVyszMTObm5koe1d5aWVnJ0tJSqtVq2u12Tp48OXC38UWG4TEu27Dcx+bScDzOu7GT++jR9c6ePZupqam0Wq00Go2cPn0609PTBzHsPbfTuTJMc6yvnysFA2lhYaFYXV3tfHz79u2iWq0Wc3NzJY5qby0vLxeTk5Ndx6ampoqlpaWSRnSwhuExLtuw3Mfm0nA8zrux0/tofX29SNL1p5/v153OlWGaY/3+XBHGA6parRaNRqPr2MLCQjFIPwtNTU0Vi4uLXceWlpaKWq1W0ogO1jA8xmUblvvYXBqOx3k3dnofra+vF3Nzc0Wj0SgajUaxvr6+n8PcdzudK8M0x/r9uWKP8YAaGxtLu93uOjY+Pp7k4a8rBsHKykomJye7jk1OTqbVamVtba2kUR2cYXiMyzYs97G5NByP827s5j56tGVgbm4utVptv4Z4IHY6V4ZpjvX7c8Ue4wG1vr7+3GP9/o0pyXO/kYyNjSV5OPme/iY0aAb9Me4Fw3Afm0vD8Tjv1m7vo7W1tVy9ejW1Wi1TU1N7Pr6DsNO5MmxzrN+fK1aMh0S73U6z2czi4mLZQ9kTt27dSvL4G8vzPj9MBu0x7kWDeB+bS1sN4uO8117lPmo0Grl161bm5ubSbrczMTHRlyvxO50rwz7H+u25IoyHxJkzZzI9PZ2FhYWyh8I+8RjvP/fxcPA4v9x276NarZYrV650Vv6mp6czNTWVmZmZgxgmPaDfniu2UvS4lZWV1Ov1bV13dnb2mU+8CxcuJEmWlpb2dGxlevST99M/ab/sJ/NBNYiP8V4yj57PXOo2qI/zI2XMhWq12vXxyZMn02w20263t3yul+10rgzzHOvH54ow7nFTU1OdcwHuxOXLl7O+vt55UvbbN6LnebRP6ekN/o8+HqT9Wi8zqI/xXjKPns9cemyQH+dHDnouTExMpF6vP/Mctrdu3eqr+3enc2VY51i/PldspRhga2trWV5eTqPR6Bx79JNXv6tWq50TgD+p1WqlWq0OzQtmBvkx7hWDfh+bSw8N+uO8F3Z6Hz39HFpfX+/L59ZO58owzrF+fq5UiqIoDuyrcWBarVZOnz695VdmjUZjV6sFvWRlZSXz8/Ndr4A9ffr00Lxj1TA8xmUblvvYXBqOx3k3tnMfPXrnsosXL3ZWQev1emZnZzsft9vtHD9+PBcvXuzLd77bzlx51v0wTHOs358rwnhAvfXWW8/8yWxycnKgvtFfvnw5y8vLmZiYyM2bNzMxMTFw32SeZ1ge4zIN031sLrW3HB/Ex3mntnMfra2t5dSpU1laWuo6zdaFCxc6K3+tVivz8/N9e8q25OVz5Xn3w7DMsX5/rghjAACIPcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJBEGAMAQBJhDAAASYQxAAAkEcYAAJAkOVL2AGC7VlZWsrS0lGq1mlarlYsXL6ZaraZer2d8fDzr6+uZn5/P5ORk2UOFnmUewd4wlwZTpSiKouxBwMusrKxkbW0tCwsLSZJ6vZ5Wq5WxsbEsLi4mSU6ePJlarZbl5eUyhwo9yzyCvWEuDS5bKegLS0tLnW9ASfLNb34zly9fzsTERKrVam7dupVbt25lfn6+xFFCbzOPYG+YS4PLVgp63uXLl7d8c/mLv/iLJMnc3FySpFar5fbt21v+brPZzOrqaiYmJrK+vp6ZmZlMTU3t/6Chx+xmHrXb7aysrKRer2d5eTm1Wm3/Bww9ajdz6cKFC1lfX0+StFqt1Ot1/yf1GFsp6EsnT55Mkqyurj73Os1mM8vLy1laWuocm5iYyNLSkj1fkO3No7W1taysrKRWq2VmZiarq6vmDzxlO3OpXq9nfn6+84PlyspKTp8+neXlZXHcQ2yloO+02+2sra299BvJ4uJiZmdnu45NT0/n3Llz+zk86AvbnUeTk5NZWFjwHzc8x3bn0uXLl9NqtTofT01NZXJysrMnmd4gjOk7KysrSbIlep/UbrfTarVSrVa7jk9MTOTy5cv7OTzoC9uZR8DLvcpcejKMk2RsbGzLMcoljOk7j17h+/Svc+v1eufy1atXkzz8pvOkpz+GYbWdeQS83Hbn0vr6emcP8iNXr161NanHCGN63unTp7u+wTSbzS0v/llbW8vExETn43a7nSRbVoyf/jwMi53MI2CrvZpLzWYzSXLx4sW9HyQ7JozpaY9e+DM+Pp7k4TeSRqPR9aundrudS5cudf0k/rwgvnXr1r6OF3rRTucR0G2v5tLa2loWFxezurr63P+vKIfTtdHTHr3wJ3n4a6nTp093XuAwMzPT+Sn96RcvPDr+9Mrwy1aSYRDtdB4B3fZiLj06TZso7k1O18bAmpiYyOLiYqanpzvH5ufnc+vWra5TuAEv126389ZbbzldG+xCq9XK4uJiGo1G59iFCxe63iyEclkxZmDV6/U0Go2uMH703vbAq7ENCXan1WplZmYmZ8+e7Zwd6datW503B6E3WDFmoHnnO9idVquVRqPR2Vv56Nyrs7OzVo7hFbz11lvPfOH3wsKCbUw9RBgDAECclQIAAJIIYwAASCKMAQAgiTAGAIAkwhgAAJIIYwAASCKMAQAgiTAGAIAkwhgAAJIIYwAASCKMAQAgiTAGAIAkwhgAAJIIYwAASCKMAQAgSfL/A1GEox0JmUaTAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 720x720 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_x_y = posterior(65536)\n",
    "fig = show_corner(p_x_y, height=1.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_xt_y = p_x_y + 0.25 * rng.normal(p_x_y.shape)\n",
    "fig = show_corner(p_xt_y, height=1.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Heuristics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def log_prior(xt, sigma_t):\n",
    "    log_pi = jax.vmap(jax.scipy.stats.norm.logpdf, in_axes=(None, 0, 0))(xt, mu_i, jnp.sqrt(sigma_i**2 + sigma_t**2))\n",
    "    log_pi = jnp.sum(log_pi, axis=-1)\n",
    "\n",
    "    return jax.scipy.special.logsumexp(log_pi, axis=0)\n",
    "\n",
    "def log_likelihood(xt, sigma_t, method):\n",
    "        J = jnp.vectorize(jax.jacobian(log_prior), signature='(n),()->(n)')(xt, sigma_t)\n",
    "        E_x_xt = xt + sigma_t**2 * J\n",
    "        E_y_xt = A(E_x_xt)\n",
    "\n",
    "        if method == 'zero':\n",
    "            V_x_xt = 0.0 * jnp.eye(3)\n",
    "        elif method == 'cov_t':\n",
    "            V_x_xt = sigma_t**2 * jnp.eye(3)\n",
    "        else:\n",
    "            if method == 'cov_x':\n",
    "                H = -jnp.linalg.inv(cov_x + sigma_t**2 * jnp.eye(3))\n",
    "            elif method == 'hessian':\n",
    "                H = jnp.vectorize(jax.hessian(log_prior), signature='(n),()->(n,n)')(xt, sigma_t)\n",
    "\n",
    "            V_x_xt = sigma_t**2 * jnp.eye(3) + sigma_t ** 4 * H\n",
    "\n",
    "        V_y_xt = cov_y + A(A(V_x_xt).mT)\n",
    "\n",
    "        return jax.scipy.stats.multivariate_normal.logpdf(y, E_y_xt, V_y_xt)\n",
    "\n",
    "def approx_posterior(n, sigma_t, method):\n",
    "    p_x = prior(n)\n",
    "    p_xt = p_x + sigma_t * rng.normal(p_x.shape)\n",
    "\n",
    "    log_q_y_xt = log_likelihood(p_xt, sigma_t, method)\n",
    "\n",
    "    q_xt_y = rng.choice(p_xt, (n,), p=jnp.exp(log_q_y_xt))\n",
    "\n",
    "    return q_xt_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YAAAAkJTgJaGnp6c1NzcnScrlcjp//rzGxsZC7hUAAADCksjAeGJiQhcuXAgC4Xw+r9OnT2tubk5TU1Mh9w4AAABhSGQqxfT0tO7cuRP8nMlkNDY2punp6RB7BSBMvu9rfXOr4n++74fdPQBAAyRyxLivr0/5fL5sW39/v6TttIpsNvvS319ZWalpG4B48H1fV2/ndG9xteK/Dw2kdWUkK8/zGtwzAEAjJTIwXlhYqLptt6BYknp6eg69TwDCUyj6VYNiSbq3uKpC0VdHK4ExADSzRAbGL8rn85qentbk5GTYXQEQsqGBtFLP498tXy8NmAEAzYXAWNLFixd17tw5Xb58uab9l5eXd2xbWVnRyZMnD7trABos5UmpIGWC3GIASJLEB8bXr1+XJM3MzNT8O93d3fXqDgAAAEKSyKoUJTdu3NDCwkIQFL94Qx4AAACSI7GB8fz8vG7dulVWt3h6eprgGAAAIKESmUpRWuluYmKirHbxe++9V3OeMQAAAJpLIgPjM2fOKJ/Pa3x8vGz78PBwSD0CAABA2BIZGD9+/DjsLgAAACBiEptjDAAAAFgExgAAAIAIjAEAAABJBMYAAACAJAJjAAAAQFJCq1IAQBL5vq9C0df65lbYXQGASCIwBoAE8H1fV2/ndG9xNeyuAEBkERgDSKwkjaAWiv6OoLirLSUvpP4AQBQRGANIpCSPoA4NpJXyJE+S5xEaA0AJgTGAREryCGrKk1IExACwA4ExgMRjBBUAIBEYAwAjqAAASdQxBgAAACQRGAMAAACSCIwBAAAASeQYAwB2Uarz3N7icXMigKZGYAwAeKlLN+9K2q7ecWUkS3AMoGmRSgEA2MHTdl1n697iqgpFP5wOAUADMGIMANjB8zydynTKl7TlK5ErBAJIHgJjAEBFnuc9XwmQUWIAyUAqBQAAACACYwAAAEASgTEAAAAgicAYAAAAkERgDAAAAEgiMAYAAAAkUa4tVh4sbwbt4z3urXuw5LbLLEhl90FzqHYOAACAg+MvKwDUYH1zS5LU3uKxJDIANCkCYwCowaWbdyVJQwNpXRnJEhwDQBMiMI6paukTdoEqO+1ulaVhMDUfSbx30eBJ6mpLaW1jK9h2b3FVhaKvjlYCYwBoNvw1BYAqPM/TqUynfElb/nZQDABoXgTGAPASnuc9n5Txd9kTABB3BMYRVG0avdrf5eKW+4ct025tcVO9nsm3qJaGwdR8hNj32rxHny5tBG3zVuuTp257yuxv3/fjvbynAAC8DHWMAQAAABEYAwAAAJJIpYgmM0Ve9CvnT/hmu90lZebR7VS7VyUPI0XJqciwqSxl7/uW2ana2+VXbGrL/FSWQlMBqRYAgKRjxBgAAAAQgTEAAAAgiVSKUFWtPlFlwY6NTTen3mJSJlYLxaDd3uq+67SZqhQbRb/iPraKhUeFirqppdJItbSZLbO9YM4Bu3t5Oo1rt9ofWp7/n1dWtqJiH1lIBACQRIwYAwAAACIwBgAAACSRShGuKtPodsEOO3VuK0gsrdqFHipPwW8UzQ+2QoV5HLsYRFsr35PqpVpqQplazocNU6LCvHcbm5UXdil4bv90+3YfNk2Zi47WloqPV63vAAA0MyIhAAAAQATGAAAAgCRSKRqu7A5/s6DCJ09dasS6mS7f3HLttfWi2V453cJOuxdNJYpMd3vQfmZyLDrb3Hcj+7vV1pGgQsHB2eNm3/eN4lal3bVmqo6srLvjb6uRdLe7xyxuuXdv3bzXpQoV9nls1QpbwKJaugfvOQCgmTFiDAAAAChigfEPfvCDsLsAAACAhIrUvOh7772nN954I+xuHDo7Xf7KkTa3/YnbblMj/CoVCezUufW0YKbjTeqFXcih5ZnZx1QwONbt+mMTKDqoUFE3ZWkKVaqF2BSIZ+Z9//DpatBOt7rL154Di2vrQfvNV465x3n+mF3trhJF2aIivnv+V3orfzSQSgMAaGYN+cv2wQcfKJ/P77rf/Px8/TsDAAAAVNCQwHh0dFQ//vGPy0ZCK7EjZgBQD77vq1D0tb5Z+WZHAEByNSQwnpyclLQdIFfz8OFD/d7v/V4jutNwNn3i0yU35W1LP9jKEjZlosWswGEX8vjBp0+C9v1l95ivmecazPS4xym4x+lqM4s6GPZ7iW/m+Jk+P1z2C6KtELH8zB3nFrNIx5pJq1gquH3uPlgJ2ul2l/pism/0ydKzoH28u0OS1Gnef5uq095SOX2m6oIkMeT7vq7ezune4uruOwMAEqdhI8bvvvuujh49WnWfo0ePanh4uBHdkSTNzs5qZmZGmUxG+XxeZ86c0djYWMOeH0DjFYr+jqC4qy1VtTwhdiqNtLe3eMzyAWg6DQmMjx49qpGRkV33Gx8fb0BvtoPiiYkJzc3NBdvOnj2rvr4+nTt3riF9ABCuoYG0Ut72xA0BXu0u3bwrafv4XRnJcuwANJWGzYu/+eabu+5z+vTpBvRkO7XjwoULZdvGx8c1MTFR98B4q0qadauZOrdVCB6uFYL29z926RNLZrGPHlNlYGndTc1/76N80P7l4y6t4nSmO2jbKftUlb9vpE/UrlrayYMlt92m2pedD+b4P1p277utMvHpitv+Fz9fCtpHzQIuBbNAzEDapda0Pn+D7QIv/T0dQdsu9mL7e7xKhYq4S3lSiqCuJp62R9bXzLl1b3FVhaKvjlaOIYDmkciaXLOzszvSNoaHh5XL5WqqjLGyslLxPwBoRp7n6VSmU184ntbQQDrs7gBA3dQtMH7//ff1la98Rd/+9rfr9RT7Ui3w7evrkyTlcrldH6Onp2fHfydPnjzUfgJAlHiep5TnVZ1ZAoBmULc50qmpKS0sLOjtt9/WV7/61bJ/+/rXv66hoSG9/fbb9Xr6qh49eiTJBcLV/r0RNk1Fgs2im1NvNdUB7AIMrx1x0+U//MjdQJTy3OP8xc+fBu1//KsngvbRDjelbitgrJupUc/M5Xe1u3YSptUPS7W0E1tR5KSpHPKzxy5Nwk7rr2y4Y/6TJ2tB+xNT1eSXX+sN2g9X3f4DZtGWJ6bSxbGO7RQK+z7b9ImCWfjl9WN24RfEGeXpAKB2dYtyBgcHNTk5WTHQvHbtmt5//31duXJFV69erVcX6mZ5eXnHtpWVFUaNAUQK5ekAYG/qFhg/fPhQnudVvaHuzTffVDabbXhwXBopfjFg320k2eru7t51HwDNKy4lyyhPBwB7U7fA+Nq1a3rnnXc0NDSkixcv6siRIzv2eVld43rJZrOStGOJ6tLPjaylDCCe4liyjPJ0ALC7ugXGT58+1cOHDzU1NaXLly9reHhYZ8+e1W//9m/rjTfeCPar5Wa3w5TJZDQ6OrrjeXO5nDKZTBA4H4ZS6S670lmL+YO0acZt7GJ0djWyjMkNXnzm8lFPmlxfk6qsPlN+K/fIrXr2i8dcPqr9o9hhckztwme2pJhdBQ/7c7LK6od2ZUMbqrR47s14/Uhn0P43P3Yl+3686cquHTf72JujTprz4Umh8PzxuoJt9p21ZbdY7XCnuJcsozwdAOyublUp3n77bWWzWc3MzOj3f//35fu+rl27pjNnzqilpUWf//zn1dLSorNnz9arC1VNTExoamqqbNvU1FSwdDUAvIiSZQDQ/Oo2FJTNZnXt2jVJ0ltvvSVJevLkiWZnZ/Wd73xH7777rqanp0OpTDE6OqrJyUmNj49rcHBQDx8+1Pnz51kSGsBLeV6ppgezKADQjOoWGL+Ywytt5xS/9dZbeuuttzQ1NaV3331X3/3ud/Vbv/Vb9epGVefOnav/8s/P/3ba1AWbVtFq5ryXntlpcTf9/ZOHbuGQ/k5Xrm3FrI5n2XSILpMmsW7yLTJmNTRbuqu9NVVxO3fqNIYt0zfQ497rnoK7TP+jX3I3hz4z5bfuL7v0DJuKY1N3Pp95nk5j3k9bus9Os6c8Aj8AQPLULZXi/Pnz+sM//MOX7nPx4kXdunWrXl0AAAAAala3EeORkRFJ0jvvvKPx8fGyG+4k6cqVK+rv71d/f3+9ugAAAADUrK63m4+MjGhkZETf+ta3dgTGd+7c0e3btzUxMVHPLoSq0ipx9m7/srSHdleWYn3DpUn0d7u0il5ToaKr1e2/VHCP+aXjbn+r31QnaGsxqR0mV9KmT1Tbjv2x77s9nhsmxaW91abcuPe3YKog/FKfK3u4uOaqlPxyv9tuz4djJv0m9Tx1J93uzkt73tkKGa8cYeU7AEDyNKQOU+nmO+vWrVt6//339eabbzaiCwAAAMBLhVqglKAYQCP4vq9C0Q9WrAMAoBIq9zeYXSzhwZKb8u5orbzQRrrDTXWvmkoU3Z1u+5b5W79uFn3oMOkWvV3uee3iHdXSKk70MpV+mMred5NWcarPpbh88sRVlvDa3ftSLKtk4k6OI13uPbLpN5m0S5+w6RE9na3Pt7l+2UoUdhES28dqryMufN/X1du5HUsjAwDworpVpQCAKCgU/R1BcVdbisx5AMAO8Rv+AYB9GhpIK+Vtl3L2WB4ZAPACAuMGK5uiNn+X7cIfrx51U+Ef5QtBu7PNpUbYagYdZQtz7J4C8UqGNIkwVUtHaDFpLS3m5GhJmffLpMGk2+354No24LOLyJRSZexCItUWcItjykQtUl55+ggAABapFAAAAIAIjAEAAABJpFI0XLUpaptiYdutZnrdTpG32+lwZoabQrXKFbayRLXUh5aUS6WwC8uUV5fYeaJUWoQGAICkYsQYAAAAEIExAAAAIIlUisjYaxUAO0XerBUEkuwg7ynnBgAA+8OIMQBgX9Y3t8pKTQJA3BEYAwD25dLNu7p6O0dwDKBpMM8aU0yRoxrODdSTp+0ltdc2thcZure4qkLRV0cr5XEAxB8jxgCAmnmep1OZTg0NpMPuCgAcOgJjAMCeeJ6nFAPEAJoQgTEAAAAgAmMAAABAEoExAAAAIImqFABwIOub29UZ2ls8eR6JtwAQZwTGAHAAl27elSQNDaR1ZSRLcAwAMUYqBQDsUamWr1Wq5wsAiC9GjAFgj0q1fH1JW/52UAwAiD8CYwDYB8/ztJ00wSgxADQLUikAAAAAMWKMJvJgadP9YO5/Ot7DaQ4AAHbHiDEAAAAgAmMAAABAEqkUiIkHyyZNwt7rZFMmet3pbNMqPnm6EbRfOdJWj+4BAIAmwIgxAAAAIAJjAAAAQBKpFIgYmzLh+y5nYsumT5j2ltnn4yeFoO2p8rK8ny65tIoTvaRVAAAAhxFjAAAAQATGAAAAgCRSKRABNn1iy+RMmCwJbW7ZtIrKS/CuPHOP097qvvOlUl7F7bZyhW/yMzzP7c/iIAAAJAcjxgAAAIAYMQbQpHzfV6Hoa31zK+yuAABigsAYobDpE5tFF7iYpoomfWLp2UbF7WvrxaB9rKfdPabZx/NtmoR7fJu20driVWwjnnzf19XbOd1bXA27KwCAGCGVAkDTKRT9HUFxV1uqShE/AAC2MWIMoKkNDaSV8rZXD7c3VjYz0kgAYH8IjBGKra0qi3eY6hD5FbdgxwdPVoJ2T5s7bf/sw3zQzvZ1Bu11k5PxxolM0E6ZwKin0z1OOtVSqQtoAimv/H1vdmGkkZQC8PYWLzFfPgA0JwJjAGgiYaSRXLp5V9L26PyVkSzBMYDYIjAGgCZVzzQST9sB99qGm525t7iqQtFXRyuBMYB4IjBGw3y65CpL2KltW5Viac3ts7i6HrR/tOhSKT5zpCNoPzN/lP+Xf/uzoP1f/Z3PBO3/78OHQfuL/T1Bu621K2i3mEVAWkzfbPUMFvtA3NQzjcTzPJ3KdMrXdjoUFUAANAP+0gMA9sXzvOcpGiTmA2gOlGsDAAAAxIgxQlIw6RMFU1JqbcMt2PFk3aVV2MoV/8N3fxy0HzxwKRZD2b6g/a3377vtr/QG7eNpl55xssdVsfDtiBfpkQAAJBIjxgAAAIASOGI8PT2tubk5SVIul9P58+c1NjYWcq8AAAAQtkQFxhMTE7pw4UIQCOfzeZ0+fVpzc3OampoKuXfNzyvLUXCpC/ameVsdIl9wqRR/9YlLmbDpE0t51/6X/+O/cI+T/VLQ/vBXTgXtzxz9XNB+rcctIJJuNwt8GFtb3FQEAEBSJCqVYnp6Wnfu3Al+zmQyGhsb0/T0dIi9AgAAQBQkasS4r69P+Xy+bFt/f7+k7bSKbDZb0+OsrKzUtA0AAADxkajAeGFhoeq2WoNiSerp6dl9J+xUpdrDU7OoR8Es2NHT5k5P33cpDR0dLu3hw+//y4qP+ca/P+ge/6mrRNFqUjW6Wt3j2BSOsi6bzSz2AQBAc0tUKsWL8vm8pqenNTk5GXZXAAAAELJED3tdvHhR586d0+XLl/f0e8vLyzu2rays6OTJk4fVNQD74Pu+CkVf66Y2diOVnre9xZNXp6WYAQD1E8vAeHZ2VhMTEzXte+HChYqB7/Xr1yVJMzMze37+7u7uPf8OytMPPnzk0huOdrUF7QebbvtfmEoUpwfSbnuLm+j4zMh/GrTvf/hp0C4U3EIhv/ml14J2ptP1wVbJ2DTVJzZMUNXZ5tItSJ+INt/3dfV2TvcWV0Prw6WbdyVJQwNpXRnJEhwDQMzE8i/96OhoUIt4P27cuKGFhYUgKM7n88pkMofUOwBhKBT9HUFxV1uq7gsZes+fZ83kx99bXFWh6KujlcAYAOIkcTnG8/PzunXrVlnd4unp6R3VKgDE19BAWl84ntapTGfdR209z9OpTKe+cDytITOzAQCIn1iOGO9XaaW7iYmJstrF77333p7zjFEbW8nBrOmhNpMOsbbh0h56OtwpOXK6P2j/bNmNBI6ceT1o22ISi8tue1kVi1b3XH2d7UHbVqJoN/u0mbaoShFLKU9KNTCNwfNKiTksCAMAcZaov+5nzpxRPp/X+Ph42fbh4eGQegQAzYUbEAHEWaIC48ePH4fdBQBoatyACCDOEhUYo/FsysH9p24hjy2T6tCacqkLvjkjj5i0iu511/6lE51B++79taBt0yGOpV2li7//2UzQfv1IuuL+tj82DcPmUpA+AVTGDYgAmgV/6QEAB1K6AdGXtOUr1JJ5AHAQBMYAgAPjBkQAzYDAGA2TMlUgbLZCut0torFacNu7Otz2XxzoDdpHn7o0iV/pPxq0f/T4adD+TI9LmTjZ41IvujvdY9qqFHYhDzvxS/oEAADJkbg6xgAAAEAlBMYAAACASKVAI5n0CZvG4Jt/aG2xi26403Pd3O2ePd4dtFfX3eIgb7QfC9or624xDvtctm0XgNgsmgVB2vi+CABAEhEYA0AdNHqhC9/3VSj6wfMCAPaOwBgA6qCRC134vq+rt3OUSQOAAyIwRsMc7939dPso78pS2KJPaVOhorDp/qW30z2mTZNYLbjtR7tcFYuiKYdhwxRbMYNKFNivsBa6KBT9HUFxV1tKLK0BAHtDBAAAhyQKC10MDaSV8raDdJZjBoC9ITAGEGtRy60Ne6GLlFd+Y2mYGp1nDQAHRWCMSGlrcRUhbNqDZXZRW0vlRUO6zKIhdj55y1SfaGs1D2R+98Gyq2hBWkW0kVsbbY3MswaAw0BdKgCxRW5t9JTyrK1SnjUARB3DYQCaArm10RCFPGsA2C8CY0SKrVzxYMmlNNhFQF4/1l5xn+NHdj+dy/Y3aRKkT8RLpbziKOXWJl2lPGvyjQHEAREAgFiJY14xQSH5xgDigcAYQKzEMa84qUFhWHWdAWC/CIwRWX4N5a5qWTSklv1Jn4inKOcVNyIojFqpuheRbwwgbogGAMRWlPOK6x0UxiWlhHxjAHFCYAwAdVLPxT7imFJSktTUEgDRR2CMyDrR2xZ2FxCyUqqAFdW0gVoddLS0UvpElFNKSqqlliytF9XRmmL0GEAkeL5fZXkx7Mny8rJ6e3slSffv31d3d3fIPQIaK51OHziw8X1fq6vbwZIvX3/0Zx/rwcpG1f1PH+tQKgax1JYv/fjxetm2491tuvSbr8rbwxhvtWMSl+MgbR8L3/f1Qb5Qtn0/x6MZdben1NPdzZcEICQExofk008/1cmTJ8PuBhCa5eXlA38hXFlZUU9Pj373n/35IfUKiJ9/+o+yDK4AIWFJaAAAAECMGB+ara0tLS4uSjqcKeW9WFlZCUark5jGweuPxus/zFSKsETlWIYlya8/Sq+90X9DADjcfHdIUqmUTpw4EXY31N3dnag/Zi/i9cf79XueF5n+x/1YHlSSX3+SXzuQdKRSAAAAACIwBgAAACQRGAMAAACSCIwBAAAASVSlAAAAACQxYgwAAABIIjAGAAAAJBEYAwAAAJIIjAEAAABJBMYAAACAJAJjAAAAQBKBMQAAACCJwBgAAACQRGAMAAAASCIwBgAAACRJrWF3oFn4vq/V1VVJUjqdlud5IfcIiB+uIwBAmBgxPiSrq6vq6elRT09P8IcdwN5wHQEAwkRgDAAAAIjAGAAAAJBEYAwAAABIIjAGAAAAJBEYAwAAAJIIjAEAAABJBMYAAACAJAJjAAAAQBKBMQAAACCJwBgAAACQRGAMAAAASCIwBgAAACQRGAMAAACSCIwBAAAASQTGAAAAgCQCYwAAAEASgTEAAAAgicAYAAAAkERgDAAAAEgiMAYAAAAkERgDAAAAkgiMAQAAAEkExgAAAIAkAmMAAABAEoExAAAAIInAGAAAAJBEYAwAAABIklrD7kBYpqenNTc3J0nK5XI6f/68xsbGQu4VAAAAwpLIwHhiYkIXLlwIAuF8Pq/Tp09rbm5OU1NTIfcOAAAAYUhkKsX09LTu3LkT/JzJZDQ2Nqbp6ekQewUAAIAwJXLEuK+vT/l8vmxbf3+/pO20imw2+9LfX1lZqWnbYXiwvBm0j/ck8u1Ck2rkdYTK+HwBgHKJ/CRcWFioum23oFiSenp6Dr1PQNJwHQFoJr7vq1D0g5/bWzx5nhdij7AfiQyMX5TP5zU9Pa3JycmwuwIAAGLG931dvZ3TvcXVYNvQQFpXRrIExzFDYCzp4sWLOnfunC5fvlzT/svLyzu2rays6OTJk4fdtQNNb1abJmX6FFHQyOsIu+NzAdi/QtEvC4ol6d7iqgpFXx2tBMZxkvhPv+vXr0uSZmZmav6d7u7uenUHSAyuIwDNKNvfpdzDtbC7gX1KZFWKkhs3bmhhYSEIil+8IQ8AAGAvUqROxFpiR4zn5+d169atsrrF09PTGhsbUyaTCa9jL1HLVGct+zBNCuBFfC4AQEID49JKdxMTE2W1i997772a84wBAABeZn1zSxIVKuIkkYHxmTNnlM/nNT4+XrZ9eHg4pB4BAIBmc+nmXUlUqIiTRAbGjx8/DrsLL/VgyaVDbPmuJuLJI227/7LbXZ8ubQTtE73ud7n7HGhOVSvRVPlMqZYLuZfPCPvYx3v5PAFSkrraUlrb2Aq2UaEiPvgUAwAAOCyedCrTKV/Slq8dZdwQbQTGAAAAh8jzPG2PDfu77ImoITCOCDt16ZsLKZVy0y73n26YfZytLfdTi9m/WioTi30AzalqJRqT4mBTrIrms+OTJ257S4v78Pj4SSFot6Zchc9SSgalqQA0k0TXMQYAAABKCIwBAAAAkUoRGZtFd/eqna60bPpEsUr6hLnhXBvmMT8xaRjVkFYBNA97PdvPC/tBUjQfGH6VVMjyX62wv8mksGkatiwVnycA4oIRYwAAAEAExgAAAIAkUikiw6ZPrG0Ug7a939tOe265LInyVApVLt7/zDxmd7t72+0Ua9l0K4DIsmkSZaqmSbj2WsF9eKTsB4xpm4+Lss8g33efU63Pf3nTfBi1pHZfMMQixQJA1DBiDAAAAIgRYwAAgLpb39yeXWlv8cpuTkW0EBjXUWn6sNqCGmXTniaNYbNopz3dnObqeuW7zO2UaXeHe66u9hb3VGVZEu5xWs3UZ0dbiyqhWgUQLVUX6TELeXzw8FnQfrzsqkVsmQ+D9lY3abi4sh60063ucY51twXtpWfuuY6mt7eXL/DhHttubrEVKnr5DEEyXbp5V5I0NJDWlZEswXFEkUoBAABQB56krrbyUOve4qoKRe7piSq+ugMAANSB53k6lemUr+2a4PcWV8PuEnZBYFxHu6Ud2BSIQrHynd3r5vZwu8/yRuV0iH+dexy0f+1Eb9A+lUkH7aU197t2mnRj0z1+1bveAUTWzx67dIjChruebfrE/RWXYtHT5j6jfvRoKWgPpDuCdm/XkaBt07xW103pitLjdbrHM1ka2lLl0THStJAEnuc9r+7CKHEckEoBAACwT77vBzfWIf74ig4AALAPvu/r6u0cKRJNhBFjAACAfSgU/bKguKstJWpNxBsjxnX0YGk7f86uRmcXl1s3OYBtLe5S+vnjtaBtV8F7su5KLj145nIJP11y29tb3eP85Km7WE90dwZtu1LV6rr7bmTzA7eqrIJHTiAQLXZVO3MbQlkpKFsVypZu/FcfunsS7KJ1/+4ni0H70VohaJ8+2h20T6a2P1PazGeOLSPZ2mJX5HT4DEGzGhpIq8UTZdhijhFjAACAA0oRFDcFAmMAAABApFLUVWmFp0+eulQH+12yw9QzWjar2vlVKrpsmBSIj5+66U37+CvmcX79lCvXVlb2zTxOb6cr12af1n7pPdHbJgDRZEeobErW0jN3zX+85Eq0/Z9//SBo/+KJrqD98yfuc+R0v9ueN+UdCz1bZvv2Z9CrR92+qcqL4JV98NnUD9IqAEQNI8YAAACACIwBAAAASaRSNMQrR1wqQqlShST5nptStDOQtm0rUXzwxFWr+PkTl0rRaVIyNs1d4Ysr7rmemdvVu9tagra9i9y221v4zgTEga0gY69/lTXdD/8gezRo/x9/4dIqOsznwtqG+9NwxFSrsZ8LTwvbn03Hi26VvKKpUGETsMo+30zqB+kTAKKG6AcAAAAQgTEAAAAgiVSKhrB3Xm/5fsV2q5miHDjipibb29z2v3m0ErRbzHRkd7ubAn31tZ6g3dnm9nlkFgRJt6WDdm+XOwU6ylIyXOqFXUCEChVAtKRMKYh2cw3b1AjPJDPce+gqVPza665yzU8fu88Im+7wH37uWNAumJSsV3u2q1G0mEoYrSkz1mLyJ7xq1SoAIGIYMQYAAABEYAwAAABIIpWiIardef1R3lWWsIXx7Y3ltlLEUJ9LgbBshYrudvdd5zM9rvD+iXRn0O41d5lXu6O9rCpFBFa4tOkcdprXLhZgF0Y5eYSUD9TGVoopLcrzsn2sWvavts9hsZ8vdrGfVpPicCLt0rPefMWlT/zpT/JB+8zrLg1ro+gupnuPXQrXl064iha7rXxrP1tSpi/1Ph4AcBCMGAMAAAAiMAYAAAAkkUrRcPfNVGebSVfwPHe399pGMWjbu8x/odelUnS2uDvOf/WEe/z+Ljdlah+np8O91fYu9m6z3S4CYCtmnGxgJQpbwcOy1TDK0ipMnoetpGGPM2kVkKqfE3Zqv1oKxIapxmCv21oes5FstRr72XE07fr2eN2lXv1DU3HCpk/Zz5dN3732tKl00dfdLqk8ZcO2bXoY1WwAxAUjxgAAAIAIjAEAAABJpFI0XMpMddqKE1baLNjRZaYu19vclObRbjc1ubTmpn/tNG+HWRyko7Wl4vb1TfeYrWbusyVV+ZZzm+pQrdrGXlW749+mdti77dc3XJ83zRS3TRE5PeCqcFg/N5VAyipvGNw135xsatEnT912m37w9Jk5z8y1YS8Hu8hFtWs4CuzrsgsIfe5Yd9C2r9Gmi9g0DKvTLhry/PH9KoeA9AkAccSIMQAAACACYwAAAEASqRSNZ6ZkW1psWoXb3t7qttu0Abswx8q6mxbu7XLbbSqFrSzRYaZGbTqHvZO+WkUI6yDpE9XSMGzqwsdmsRJ7TApmytey2+3CH39zfzVop7zKd823mbYXhVVMsG+fPLELwLjt1a4Be97YfVaeuevK66yc9mRTfGw6ju2DPZ1eaWBVlGoVNmx61qq7xMquGVuhxupss9Vz3PbSdWWvL/u665F2BQD1xogxAAAAIAJjAAAAQBKpFA1Xy5SinQK1d4HbKd90hynAX3TbbXqAvVvcznba9Am7QIGt6qAG3mxvp6Dta1lccnO+bSa95P7SM7c95b7bLa6tB+3PHXV33hfNgXg146pV2IICvlnEwFbAaOQ0OA7HhjmH8jZvwLzfNo3pk6fufGr13Pn0s6cuHaevsz1op9vNYjkdlSu52NQLe36/cjSktIrlymkVZRlE5vjYa8Z+LvgVSlBUex7SJ9DMfN9XoeiXVXZBc+CTCwAAoEa+7+vq7ZzuLa7uvjNih1QKAACAGhWK/o6guKsttadbuNc3tyrOwCB8jBhHULUFJj5dclOy9nqyd9vbdAs7XWynSe1058mQUgXK0ie23FTUs43Kiyc8W3PVAj41KRPLBfdabIWAx8/cFPqxLjcN/ulT97t28ZRj3W6faoubIFrKK5iY8968fz2m0sJTsxDOx/m1oP3omTsnPl52j2lTMs5mj7v9TXrG6ro75+wCObb6SYc5z8Ji0xrs9W//MNs/0a0m98qmYdkfKi3gUS19ghQLNKuhgbRS3nZWkufV/rfj0s27GhpI68pIdk+/h/pjxBgAAGAfUt52ycJagltP2yPLJfcWV1UoMmocNQ0LjL/73e/qK1/5ij7/+c/rd37nd7S0tBT82x/8wR/owoUL+sY3vtGo7gAAADSM53k6lenU0EA67K7gJTy/AUkut2/f1tmzZzU8PKy+vj7duXNHnudpfn5en/3sZyVJ09PTeuedd1QsFnd5tGhaWVlRT0+PJGl5eVnd3d27/EZjhTWVWW3RkM1i5fSJVbNwyYNlN8X9b3/+OGj/q799FLTbTRrJY7P/m6f7gradQv+vhz8TtPtM+kSXuVPf3rVftnaB+YHp4PqodB3ZFKJK0/dSeZpRfsW1Hyy5c+KBScF5WnD7/G/f+yho/+29h0H79dePBu1fNedTtq8jaI+cdikWdryov9edW/Ycrdb/qCH1AahufXNL79z4S0nSF46nyxe5qcGW7+tvHmznKH/z3C+XpUMifA35xJucnNStW7c0MjISbJuentbo6Kjm5+fV29ur/v7+RnQFAAAAqKghX1Oy2WxZUCxJY2Njeu+993Tu3LlGdAEAAAB4qYaMGFdLSh8eHtY3v/lNvfPOOxodHW1EVwKzs7OamZlRJpNRPp/XmTNnNDY21tA+NFJY06HV7oa3VQTWTSrFY3PH/0+XVoL2w1X3u69kuoL2/337R0F7y1S3+Ju/vh+0f+VXXwva//pnLg3DToPbigJFM63VWqWyBxrHM0kKNmXCWn5mUrDMW2YrmPzzH7k0iYdmkZiPPn4atH1zXn7/X/yboP3xr/1K0L587otB+ydP3Dn6hf7eoG0XqvG8+J04pE8ASKqGfPpls1l98MEHyuVyyuVyevvtt8v+7fLlyzp//nwjuiJpOyiemJjQ3NxcsO3s2bPq6+tjBBsAACChGpJK8bWvfU1//Md/rLGxMU1OTu7499OnT+tP/uRPdPTo0Qq/ffgmJyd14cKFsm3j4+OamJhoyPMDAAAgeho2X3bt2jVdu3at6r9ns1k9evSo6r8fptKIsTU8PKxcLqf5+XkNDw83pB+NFImqFGZG2d7FaxdkKJhqFasbbnr8z/7KpUZ0p90d//mf/Ng96KcfBM2Tf/8/Dtr/wRfcjZ2vHXEVBRZX3TR7tbuC7TR+tYVXUF/VjvvP8y7txhbXsVUpjrS737UZXW1mMZi1tcoLXnQefzVoPzMpGX96Lx+07bn73/zddMXttipF3Ks9xL3/ALCbxH2yzc/PV9ze17ddjimXy+0aGK+srNS0DUB1XEcAgKipWyrF+++/r6985Sv69re/Xa+n2JfSqHQpEK727y/T09Oz47+TJ08eaj+BZsd1BACImrqNGE9NTWlhYUFvv/22vvrVr5b929e//nUNDQ2V3YSH+opCVQpbUcDc/K/1TZcyYae7N8xOv3LapUPc/Od/6R7/C18I2g863KIqrW1ukY7/9Tv3gvaF3xoM2ulX3T4dZn9bMeO1TOImVSLNTuWbbAW1tOxeYH+wvzNo/z8fuUoUP//T226nDVetouXzvx60s4MDQXt13fXhP/+1E7s+b8pWPNmKX4UKi/QJAM2ubiPGg4ODmpub0507d3b827Vr13TmzBlduXKlXk9fVWmk+MWR4d1Gkq3l5eUd/92/f3/X3wPgcB0BqDff97W+uRX814DFfhFzdfv6//DhQ3mep9OnT1f89zfffFPZbFZXrlzR1atX69WNHbLZrCQpn8+XbS/9XMuNd1Fb7hmII64jAPXk+76u3s7p3uJqsG1oIK0rI9mq6ysAdQuMr127pnfeeUdDQ0O6ePGijhw5smOfRpVnszKZjEZHR5XL5cq253I5ZTKZIHDG4bPTyFvmW3u7qRDwmaNu8Y5PV9209taWuynry3/nc0H7hz/8KGi3pV2g9e99wU19W0MDbjr91BG3/2rBTY/3drl9yqpqGEwpN061Sgj3n7rUHFtlwlY8yXS6CiafmFSeX3rdffb87B+6xYU6OlxKzYc5N3r97Jnrw9/7dTer1NXq9i+rumLSJ+xiHx1NVKECiLpC0S8LiiXp3uKqCkVfHa3NExj7vq9C0f5N9Qj8D6BuqRRPnz7Vw4cP9bWvfU3Hjh3Tl7/8ZX3jG9/QD37wg7L9XgxQG2FiYkJTU1Nl26ampirWWAYAAPFSSqEoyfZ3vWTv+CqNir9z4y+D/67ezpEycgB1G6Z4++23lc1mNTMzo+9973u6ffu2rl27FgSf2WxWuVxuR4DaCKOjo5qcnNT4+LgGBwf18OFDnT9/vqmXhAYAIAkqpVCkmnQENSmj4o1Ut8A4m80GC3q89dZbkqQnT55odnZW3/nOd/Tuu+9qeno6tMoU586dY/nnBmttsRMU7pv8ivlmu2QWW+htbwvav/YZl/aw9MxNiX/pS68F7XTHqaA90OvSIT57zC3qYae+bWrHyW63j6p80Q5ruruWdI5mnpYve51L7nXa989WqOhqd++xTdn5e5/LBO3/+d/9zD3+cXdudXS45zpl0i1+Y9ClT9jnHeh0501Pl/vdtOmDTauwovA+VTtvmvl8QvN7MVjsaks1ZpnfkGX7u5R7uBZ2N2KvbufKize3Sds5xW+99Zampqa0tbV9d+h3v/vdenUBAAAk2NBAWqcynVICBk+bdVS80eoWGJ8/f15/+Id/+NJ9Ll68qFu3btWrCwAAIMFSnrgRDXtStzmykZERSdI777yj8fFxvfHGG2X/fuXKFfX396u/v7/Cb6MZ2SnZT0xFgd5Ot73LLLRxpMulUvSZ6gK/1N8TtH94fyloDx5zN1d8689dRYEvDB1z+/S53z1qHt9+brZUmfoOS7UpbtveLLrUFHts7Ss5eWT79dqFVk70tmk3UZpWP97rnv9njwtBu8Ok6bSZvLrlZ27xmNMZlzIx/ndd2k1nizvnvvdRvuLzDva5c2ugy6VP9HW587I15frQahYcsce4WlpMvdkUFKtoUk2qnTe1pFtU+ncAiKO6pt2MjIzom9/8phYWFnb82507d3T58mU9fPiwnl0AAABIFBY02b+GfL0v3Xxn3bp1S++//77efPPNRnQBAAAgES7dvCuJBU32I9R5L4LiZLFTr+XpCm7iwvPct9uCSQ/o73HT153rbur7PxlyU9zLZhGG/+LNV4P2UH9v0PZtyQnThbKbFkyzkVPDZRUXzLf8V464qXhbEeHZhksTsIuk2EoM9jCXUg/aWvb2ARml6XE73W/ZFIvNLXfe2OoQK+vueA2ZdJxPl9aD9hdNhYo2kxpxus9ttwMw/T0ulcKOy1T7I1Stwobt/2Gx15s9b2zXtqosurNp97cXhD0X/GCHgE3TsccgSucQ0KxS2q7AsbbhPgMp3bZ3fFoBAIDEKC380XQrxHnSqUynfElbvnbUN0ZtCIwBAEDslZZGtiveVdLMaQaeV5rjIbd4vwiM0TDVppFtqoCtNNBm0gPaW127o821V9bd43SaafNs2k2VW7YChl1wJAqFKDZM6oiZydZHeXdM7BR3i/kwt38IWs2LKZj9SxU/7JR5lCpO1MKeK7WwaQ8Fc4yOdbvH+YW2dNDuL7jUiGKx8h8We17aPWxaQi39rEf6RBnTOZteYo+JTdmxKRM29aLdpN58/KRg9tn+f1uBw15GJ+r9+gCj0mp3lqfmSzN4cdlrHA4+uQAAQKxVWhq5qy0VfFnzPK+p0gx2+yKA/SMwBgAATWNoIL29sIfKbwJtpjSDSstex3PcO3oIjBEKO41831QaaDdTWq1m4YVVU1HA7tPb2Wa2u31s1YtOs2hIS5XqE/Zzst4pBWXVAsx0/WsZN43/4SNXKcHM/Cm/aqeyd6ZJvMgeh/XnD9TT6fZd3zSLNFT5W1H3Kf9D9upRdxw/eeLOrYFekyZhjmmrOXS2ukd7h2vbNIzuDnc8bAqOF4F8HHtu2dScTXOe2ddip2FtKog9t+w5dNSkoJQep8ceD7NvvatuANWkvGQtjzw0kFYLK/wdmrou8AEAAID6Ydnrw0VgDAAA0KRYAW9vmN9C6E7WVGnA7VOtkoJNybBTumUfCCEt3mHZ57ULVvzt/bWgbWfl7XT3/eVnQftpwR2H3jb3mGubLqXkcxm3MEWpesCzDffgdho8CsfmsNk0gOO9lc8ze94c6XL72On/2FTvMKe6rT7ydM31f63gzo+Hz9Yr7n9/1W0/mXaL6xS33II6/b0dz3/PPadnHsM351Nsjh8SZ31zq/nqGb/g0s27TVmarl4YMQYAAIl06eZdXb2da7oR1VJ5upJSaTrsjsAYAAAkRhKCxlJ5uqGB9O47owxzWoisT5fcFPcJMw1ebeGFaikZZXfHhzSNa/tgp6w3TJqEnfZfNQuXLK64ShQ/+ORp0LYLKyyaqepuU02ht9293uPdnZKkZ2YqPW0WRfGb7A+DVFs1BJt2Yysz2BSL2tJ9wuebXIpV8z7bKhN/+ehJ0H5mSp789acuTSfT5c6LR6vu3LJ3+pcW3eky51C6o3J1FIu0CoStFDQWY1jPuNbV/aTt15lqgtJ0jcanEgAASJQ4Bo0s6tEYBMYAAAC72MtobT3strofDgeBMSLrRJUqAq8c3b1CRdn2Bi4uUK0/ZRUOTFqFTYew1QI2TFrDUsFN6feYqeq7porFsbR7/Pxa5cd5sLI9VX6ss73iv9uFU2y1jLLKDk049b3X17TXVIBGpg4UqyzS8WjNVZnImwoV/++PHgXtM5/LBO2BbtfPVvP+L2+43918/vib5nnWCi5gsGkVdmSOu+IRR1Ebra22uh8Orvn+ygEAAByiqI3WJm11v0YiMAYAAKgRo7XNjcAYsVZtajoKi3dYdjrdVg6w0932A7asusCm+92f5l2FCpt6YdMdHi67afN5U8XizKtHJJWnT2wW3dR3W4ub+rYpHii313Or3ueiPbfsYhsbm+Y8M5VQvv+BOyf6et3iHXd+/Dhot7W6yiZnv9gftI+2uzSmUnWTdrNvV7s7bziD0KwYrW1uBMYAAAAhKN3I1+yr78UJgTEAAEAILt28K0ks2RwhBMZAI1Qpl2mnvu2SpMtmgY+WVMrsb1Mv3O/a8kG9XW66+1SmY8f+vV3usrfPb6fPrWasRNGs7Dlk02GeFtz59PmT3UH79p9/ErT/8a+/FrR/+LOloN1jFol5VnTpO0fVtuN57PlZdq6axAqydJB0pZX31swCO6XV9zpauUDCxl88AACABimtvOdre3AiKiXgsI3AGAAAoIE8rzSPEq/V95KAwBgIkV08wVao6Gp1FSI6W1yKQ6dJd8ikXcrEF092BW2bEPFozS3U8dne7Sn0ZxtuOryvxy32UTDpGLbSQCMXqMBBufPJpji0mfPsl0+kg/bHnz0WtP/io+Wg/auf6Q3ax7tcOk6HqVxSeip73rS12LQftyvpEwDionJSIQAAAJAwBMYAAACASKUAGuJ4r7vUHiy51ATPc/PN6Y5Ws93NPW+aOenfeP1o0D5iFlv4+bK7eWNl06VK/MZrfW5/U62iZMs8dpuZ7yZlItpseotNwTEZE2Xbs8d6gvbPn6wF7f/siwNB++Ezt3jMa2mXmmPTek70dgbt0iI0XW12YRg31tLieRXbnFsAoowRYwAAAECMGAMAgJjyfV+Fol9Wyx2VscpebQiMgUYzn0dlC2yYVIaWTndp2uoCx4quisSSqThxqtct2mArXfR02sU8nk99t7eYbZX7Ug0VKqLBHnv7ntgFPrpNas7jFZcm8ZmjLk1iwwQTPW1u/6Md7jw71u1ScGx6RvvzFItqC8O01FCKgvMJB+H7vq7ezlEHuEasslcbUikAAEDsFIr+jqC4qy0lwj2ntMqeVVplD5XxFR0AAMTa0EBaKW87EGQk1GGVvb0jMAYawE4ZWy22jID5Al/cclPcHWaqOmWqWAwccQsvbBTN4hymMoCtaNH5vHpA2aIiZur9lSM7q1Yg+mz6RGvKvff2HOrvcefKulngpdMs8HKk4N7/ZwW3j02xSXe4NJzS09oQxC7wYVVLkyB9Aocl5UmpAwTEzZx/yyp7e8OnEgAASLQo5N82c3AeJwTGAAAgcUr5t2sbbnallH/b0dr4wDQKwTkIjIGGqGXK+P5TV2Wiw9wsUTCVA+xUtq0QYD8+7SILne3ejn1SNn1jjxWOmPqOnhO9lVNgqi0C0t7q3sPVdZcycdQsAGOnpNOmiolNzSllbdj0ibKFbKqkDwFREYX821qCc0rSNRZ/5QAAQCKFnX+7W3BOSbrGIzAGAACowvfrO1r7suCcknSNR2AMRMRJUxXiwZKbhrZT1XaKO+VmuGVLkrdVWVihlK9WSzqEfX47PY4Y8Su3bd6iXQTEplt0m5Qde87ZlMdSSk61xUZIu0EziNKILSXpGoNPLgAAgApeHLENc7T2oCXpUBsCYwAAgF0MDaTV4jFa2+wIjIGIO1nDwhvVKgDsdzqb9In4q+U9tCkzrxzd/3kWPCfpE2hiKYLiRKi8TBEAAACQMHy9BwAAeM6uQIfkITAGIuggqQxMZ6NW1c6zatUlOLeQBHYFuv/2H3wu3M6g4UilAAAAiVZagc4qrUCHZEnc1//p6WnNzc1JknK5nM6fP6+xsbGQewUAAMISheWhrdKiIvVaWMSmi3BDYblEBcYTExO6cOFCEAjn83mdPn1ac3NzmpqaCrl3wP7tddGO4PeoPpEItSzYwqIuiJN6rEZXaQW6eq549zJXb+f0Yf5Z3R7fpotcGckSHBuJSqWYnp7WnTt3gp8zmYzGxsY0PT0dYq8AAECtSqvRlYK7epr4v35U9+eo5MWg+DAWFiFdpDaJGhbo6+tTPp8v29bf3y9pO60im83W9DgrKys1bQNQHdcRgP2o92p0pQBybcONFoe14t1hLgMdtXSRqEpUYLywsFB1W61BsST19PQcWp+ARona9DjXUePU8t5H7fwAalGP1ehsABlsUziLexz2MtCV0kVQLlGpFC/K5/Oanp7W5ORk2F0BAAB7VK/V6DzPU8r814ig+MVUh7BGqZMu0UMEFy9e1Llz53T58uU9/d7y8vKObSsrKzp58uRhdQ1oelxHAOC8OFId1ih10sUyMJ6dndXExERN+164cKFi4Hv9+nVJ0szMzJ6fv7u7e8+/A6Ac1xEAlHOpDghLLAPj0dHRoBbxfty4cUMLCwtBUJzP55XJZA6pdwAAAIijxOUYz8/P69atW2V1i6enp3dUqwAAAECyxHLEeL9KK91NTEyU1S5+77339pxnDAAAgOaSqMD4zJkzyufzGh8fL9s+PDwcUo8AAAAQFYkKjB8/fhx2FwAAABBRicsxBgAAACohMAYAAABEYAwAAABIIjAGAAAAJCXs5jsAABBPvu+rUPS1vrkVdlfQxAiMAQBApPm+r6u3c7q3uBp2V9DkSKUAAACRVij6O4LirraUvJD6g+bFiDEAAIiNoYG0Up7kSfI8QuODKqWmtLd4HE8RGAMAgBhJeVKKAO7QXLp5V9L2F44rI9nEB8ekUgAAACSIp+1UFOve4qoKRT+cDkUII8YAAAAJ4nmeTmU65Uva8sVNjQaBMQAAQMJ4nvf85kVGiS1SKQAAAAARGAMAAACSSKUAAAARxWp3aDQCYwAAEDmsdtd465tbia9nTCoFAACIHFa7a7xLN+/q6u2cfD+5N+QxYgwAACKN1e7qp1TTeG1jO12lVM+4ozWZx5kRYwAAEGml1e4Iig9fqabx0EA67K5EAiPGAAAgMrjhrvE8z1PK1DMuHfsk5hsTGAMAgEjghrtouHTzrqTtFJYrI9lEBcekUgAAgEjghrvwlHKNrXuLq1paL2p9cysxN+QxYgwAABqmlCpRiU2f4Ia7xirlGvuStnwFX1BKo8enMp36+ktGj5sl7YLA+JDYb1IrKysh9gQIRzqdPvCHItcRcHjX0urqy9MRtnxfK4XG5vH68vVHf/axHqxs7LpvsViUH/84K7Y6Wjytmy8wP80/0z/51l9V3f94d5su/ear8howvt/dnlKqhmtkP9eS5ydlbLzOPv30U508eTLsbgChWV5eVnd394Eeg+sIOJxraWVlRT09PdV38Dz97v/+wwM9BxCm/+m//JK0Swi7n2uJHGMAAABAjBgfmq2tLS0uLko6nGmwvVhZWQlG2e7fv3/gkYa44fVH4/Ufxnkf5nUkRedYhiXJrz9Kr71RqRT7FaVjFUUcn5dr5PHZz7VEjvEhSaVSOnHiRNjdUHd3d6IvQl5/vF9/VK4jKf7H8qCS/Pqb4bV7nteQ19AMx6qeOD4vF8XjQyoFAAAAIAJjAAAAQBKBMQAAACCJwBgAAACQRFUKAAAAQBIjxgAAAIAkAmMAAABAEoExAAAAIInAGAAAAJBEYAwAAABIIjAGAAAAJBEYAwAAAJKk1rA7gPqZnp7W3NycJCmXy+n8+fMaGxsLuVeHa3Z2VjMzM8pkMsrn8zpz5kzTvcaXScJ7HLakHGOupWS8zwexn2NU2u/KlSsaHR1VLpfT1NSUzp49q3PnzjWi24duv9dKkq6xWJ8rPprS5cuX/bm5ueDnx48f+5lMxh8bGwuxV4fr1q1b/vDwcNm20dFRf2ZmJqQeNVYS3uOwJeUYcy0l430+iP0eo4WFBV9S2X9xPq77vVaSdI3F/VwhMG5SmUzGn5qaKtt2+fJlv5m+C42OjvqTk5Nl22ZmZvxsNhtSjxorCe9x2JJyjLmWkvE+H8R+j9HCwoI/NjbmT01N+VNTU/7CwkI9u1l3+71WknSNxf1cIce4SfX19Smfz5dt6+/vl7Q9XdEMZmdnNTw8XLZteHhYuVxO8/PzIfWqcZLwHoctKceYaykZ7/NBHOQYlVIGxsbGlM1m69XFhtjvtZKkayzu5wo5xk1qYWGh6ra4fzBJqvpB0tfXJ2n74nvxQ6jZNPt7HAVJOMZcS8l4nw/qoMdofn5ed+7cUTab1ejo6KH3rxH2e60k7RqL+7nCiHFC5PN5TU9Pa3JyMuyuHIpHjx5Jch8s1f49SZrtPY6iZjzGXEs7NeP7fNj2coympqb06NEjjY2NKZ/Pa3BwMJYj8fu9VpJ+jcXtXCEwToiLFy/q3Llzunz5cthdQZ3wHtcfxzgZeJ93V+sxymazun37djDyd+7cOY2Ojur8+fON6CYiIG7nCqkUETc7O6uJiYma9r1w4ULFE+/69euSpJmZmUPtW5hK37xf/Ka92zfzZtWM7/Fh4jqqjmupXLO+zyVhXAuZTKbs5zNnzmh6elr5fH7Hv0XZfq+VJF9jcTxXCIwjbnR0NKgFuB83btzQwsJCcFLG7YOomlKe0osJ/qWfmylfazfN+h4fJq6j6riWnGZ+n0safS0MDg5qYmKiYg3bR48exer47vdaSeo1FtdzhVSKJjY/P69bt25pamoq2Fb65hV3mUwmKABu5XI5ZTKZxNww08zvcVQ0+zHmWtrW7O/zYdjvMXrxHFpYWIjlubXfayWJ11iczxXP932/Yc+Ghsnlcjp79uyOKbOpqakDjRZEyezsrMbHx8vugD179mxiVqxKwnsctqQcY66lZLzPB1HLMSqtXPbuu+8Go6ATExO6cOFC8HM+n9fp06f17rvvxnLlu1qulUrHIUnXWNzPFQLjJnXs2LGK38yGh4eb6oP+xo0bunXrlgYHB/Xw4UMNDg423YdMNUl5j8OUpGPMtZTfsb0Z3+f9quUYzc/Pa2RkRDMzM2Vltq5fvx6M/OVyOY2Pj8e2ZJu0+7VS7Tgk5RqL+7lCYAwAAACIHGMAAABAEoExAAAAIInAGAAAAJBEYAwAAABIIjAGAAAAJBEYAwAAAJIIjAEAAABJBMYAAACAJAJjAAAAQBKBMQAAACCJwBgAAACQRGAMAAAASCIwBgAAACQRGAMAAACSCIwBAAAASQTGAAAAgCQCYwAAAECS1Bp2B4Bazc7OamZmRplMRrlcTu+++64ymYwmJibU39+vhYUFjY+Pa3h4OOyuApHFdQQcDq6l5uT5vu+H3QlgN7Ozs5qfn9fly5clSRMTE8rlcurr69Pk5KQk6cyZM8pms7p161aYXQUii+sIOBxcS82LVArEwszMTPABJElf/vKXdePGDQ0ODiqTyejRo0d69OiRxsfHQ+wlEG1cR8Dh4FpqXqRSIPJu3Lix48Pl+9//viRpbGxMkpTNZvX48eMdvzs9Pa25uTkNDg5qYWFB58+f1+joaP07DUTMQa6jfD6v2dlZTUxM6NatW8pms/XvMBBRB7mWrl+/roWFBUlSLpfTxMQEf5MihlQKxNKZM2ckSXNzc1X3mZ6e1q1btzQzMxNsGxwc1MzMDDlfgGq7jubn5zU7O6tsNqvz589rbm6O6wd4QS3X0sTEhMbHx4MvlrOzszp79qxu3bpFcBwhpFIgdvL5vObn53f9IJmcnNSFCxfKtp07d05Xr16tZ/eAWKj1OhoeHtbly5f5ww1UUeu1dOPGDeVyueDn0dFRDQ8PBznJiAYCY8TO7OysJO0Ieq18Pq9cLqdMJlO2fXBwUDdu3Khn94BYqOU6ArC7vVxLNjCWpL6+vh3bEC4CY8RO6Q7fF6dzJyYmgvadO3ckbX/oWC/+DCRVLdcRgN3Vei0tLCwEOcgld+7cITUpYgiMEXlnz54t+4CZnp7ecfPP/Py8BgcHg5/z+bwk7RgxfvHfgaTYz3UEYKfDupamp6clSe++++7hdxL7RmCMSCvd+NPf3y9p+4NkamqqbOopn8/rvffeK/smXi0gfvToUV37C0TRfq8jAOUO61qan5/X5OSk5ubmqv69Qjgo14ZIK934I21PS509eza4weH8+fPBt/QXb14obX9xZHi3kWSgGe33OgJQ7jCupVKZNoLiaKJcG5rW4OCgJicnde7cuWDb+Pi4Hj16VFbCDcDu8vm8jh07Rrk24AByuZwmJyc1NTUVbLt+/XrZYiEIFyPGaFoTExOampoqC4xLa9sD2BvSkICDyeVyOn/+vK5cuRJUR3r06FGwOAiigRFjNDVWvgMOJpfLaWpqKsitLNVevXDhAiPHwB4cO3as4o3fly9fJo0pQgiMAQAAAFGVAgAAAJBEYAwAAABIIjAGAAAAJBEYAwAAAJIIjAEAAABJBMYAAACAJAJjAAAAQBKBMQAAACCJwBgAAACQRGAMAAAASCIwBgAAACQRGAMAAACSCIwBAAAASQTGAAAAgCQCYwAAAECS9P8DIfAqBFe26OAAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 720x720 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_xt_y = approx_posterior(65536, sigma_t=0.25, method='hessian')\n",
    "fig = show_corner(q_xt_y, height=1.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_xt_y = approx_posterior(65536, sigma_t=0.25, method='zero')\n",
    "fig = show_corner(q_xt_y, height=1.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_xt_y = approx_posterior(65536, sigma_t=0.25, method='cov_t')\n",
    "fig = show_corner(q_xt_y, height=1.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_xt_y = approx_posterior(65536, sigma_t=0.25, method='cov_x')\n",
    "fig = show_corner(q_xt_y, height=1.6)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}