{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Equality Constraints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "is_executing": true
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import hopsy\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic example without qquality constraints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# create 3D rectangle\n",
    "A = np.array(\n",
    "    [\n",
    "        [1.0, 0.0, 0.0],\n",
    "        [0.0, 1.0, 0.0],\n",
    "        [0.0, 0.0, 1.0],\n",
    "        [-1.0, 0.0, 0.0],\n",
    "        [0.0, -1.0, 0.0],\n",
    "        [0.0, 0.0, -1.0],\n",
    "    ]\n",
    ")\n",
    "b = np.array([1.0, 2.0, 3.0, 1.0, 2.0, 3.0])\n",
    "\n",
    "\n",
    "rectangle = hopsy.Problem(A=A, b=b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mc = hopsy.MarkovChain(rectangle)\n",
    "rng = hopsy.RandomNumberGenerator(42)\n",
    "_, samples = hopsy.sample(mc, rng, n_samples=20000, thinning=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[-0.43426088  0.42225266  0.10534782]\n",
      "  [-0.06525985  0.06436831 -2.46131662]\n",
      "  [-0.05369373  1.80750632  0.80462979]\n",
      "  ...\n",
      "  [ 0.21379724 -1.72031362 -2.44581382]\n",
      "  [ 0.98883212 -0.25319745  2.33836859]\n",
      "  [-0.71434968 -0.06717306  1.55590868]]]\n"
     ]
    }
   ],
   "source": [
    "print(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZGRnq0KGDMjIyFBUV5XFJKT4+XiNGjFBOTo7atm2rjIwMj31cGDNmzJiL1lJYWKjCwkJz3e12/56pAUCF49IGUHHKfRNvcXGxxowZo9tuu0233HKLJMnlcslmsykgIMBjbEhIiFwulznm1+HlQv+FvkuNcbvd+vnnn0utJzU1VQ6Hw1zCw8PLOzUAAFDNlfsMTFJSknbs2KENGzZUZD3llpKSouTkZHPd7XYTYlAl+L9s1CRW/PeMa0O5AsyoUaO0dOlSrV+/XjfccIPZ7nQ6dfbsWR0/ftzjLEx+fr6cTqc55quvvvLYX35+vtl34b8X2n49xm63q06dOqXW5OvrK19f3/JMB9UYvzwBXAus+Luuqv/Hp0wBxjAMjR49WosXL9batWsVGRnp0R8dHa3atWtr1apV6tevnyQpNzdXBw4cUGxsrCQpNjZWL7zwgo4cOaLg4GBJUnp6uux2u1q0aGGO+eyzzzz2nZ6ebu4DQMWy4i9PANe2MgWYpKQkzZs3T5988onq169v3rPicDhUp04dORwODR06VMnJyQoMDJTdbtfo0aMVGxurDh06SJLi4uLUokULDRo0SGlpaXK5XHr22WeVlJRknkF57LHH9Pe//11PP/20HnnkEa1evVofffSRli3jlywAACjjTbzvvPOOCgoK1LVrV4WGhprLggULzDGvvfaa/vSnP6lfv37q3LmznE6nFi1aZPb7+Pho6dKl8vHxUWxsrB588EENHjxYU6ZMMcdERkZq2bJlSk9PV+vWrfXKK6/ovffe4yPUAABAkuRlGIZR1UVUBrfbLYfDoYKCAtnt9qoup8pxiQAAUJEq6x6YK33/5m8hAQAAyyHAAAAAyyHAAAAAyyHAAAAAy/ldfwvpWsUNsQAAVC3OwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMshwAAAAMspc4BZv369+vTpo7CwMHl5eWnJkiUe/V5eXqUu06ZNM8c0atSoRP/UqVM99rNt2zZ16tRJfn5+Cg8PV1paWvlmCAAAapwyB5hTp06pdevWmj59eqn9hw8f9lhmzZolLy8v9evXz2PclClTPMaNHj3a7HO73YqLi1NERISysrI0bdo0TZo0STNnzixruQAAoAaqVdYNEhISlJCQcNF+p9Ppsf7JJ5+oW7duaty4sUd7/fr1S4y9YO7cuTp79qxmzZolm82mli1bKjs7W6+++qoSExPLWjIAAKhhKvUemPz8fC1btkxDhw4t0Td16lQ1aNBAbdu21bRp03T+/HmzLyMjQ507d5bNZjPb4uPjlZubq59++qnUYxUWFsrtdnssAACgZirzGZiy+OCDD1S/fn3de++9Hu2PP/64br31VgUGBmrjxo1KSUnR4cOH9eqrr0qSXC6XIiMjPbYJCQkx+6677roSx0pNTdXkyZMraSYAAKA6qdQAM2vWLA0cOFB+fn4e7cnJyebPrVq1ks1m0/Dhw5WamipfX99yHSslJcVjv263W+Hh4eUrHAAAVGuVFmC++OIL5ebmasGCBZcdGxMTo/Pnz2vfvn1q2rSpnE6n8vPzPcZcWL/YfTO+vr7lDj8AAMBaKu0emPfff1/R0dFq3br1ZcdmZ2fL29tbwcHBkqTY2FitX79e586dM8ekp6eradOmpV4+AgAA15YyB5iTJ08qOztb2dnZkqS8vDxlZ2frwIED5hi3262FCxfq0UcfLbF9RkaGXn/9df3nP//Rt99+q7lz52rs2LF68MEHzXAyYMAA2Ww2DR06VDk5OVqwYIHeeOMNj0tEAADg2lXmS0hbtmxRt27dzPULoWLIkCGaM2eOJGn+/PkyDEP9+/cvsb2vr6/mz5+vSZMmqbCwUJGRkRo7dqxHOHE4HFqxYoWSkpIUHR2thg0basKECXyEGgAASJK8DMMwqrqIyuB2u+VwOFRQUCC73V6h+240flmF7g8AAKvZN7V3pez3St+/+VtIAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcggwAADAcsocYNavX68+ffooLCxMXl5eWrJkiUf/Qw89JC8vL4+lZ8+eHmOOHTumgQMHym63KyAgQEOHDtXJkyc9xmzbtk2dOnWSn5+fwsPDlZaWVvbZAQCAGqnMAebUqVNq3bq1pk+fftExPXv21OHDh83lww8/9OgfOHCgcnJylJ6erqVLl2r9+vVKTEw0+91ut+Li4hQREaGsrCxNmzZNkyZN0syZM8taLgAAqIFqlXWDhIQEJSQkXHKMr6+vnE5nqX3ffPONli9frs2bN6tdu3aSpLfeeku9evXSyy+/rLCwMM2dO1dnz57VrFmzZLPZ1LJlS2VnZ+vVV1/1CDoAAODaVCn3wKxdu1bBwcFq2rSpRowYoaNHj5p9GRkZCggIMMOLJPXo0UPe3t7KzMw0x3Tu3Fk2m80cEx8fr9zcXP3000+lHrOwsFBut9tjAQAANVOFB5iePXvqH//4h1atWqWXXnpJ69atU0JCgoqKiiRJLpdLwcHBHtvUqlVLgYGBcrlc5piQkBCPMRfWL4z5rdTUVDkcDnMJDw+v6KkBAIBqosyXkC7ngQceMH+OiopSq1at1KRJE61du1bdu3ev6MOZUlJSlJycbK673W5CDAAANVSlf4y6cePGatiwofbs2SNJcjqdOnLkiMeY8+fP69ixY+Z9M06nU/n5+R5jLqxf7N4aX19f2e12jwUAANRMlR5gDh48qKNHjyo0NFSSFBsbq+PHjysrK8scs3r1ahUXFysmJsYcs379ep07d84ck56erqZNm+q6666r7JIBAEA1V+YAc/LkSWVnZys7O1uSlJeXp+zsbB04cEAnT57UU089pU2bNmnfvn1atWqV7r77bt10002Kj4+XJDVv3lw9e/bUsGHD9NVXX+nLL7/UqFGj9MADDygsLEySNGDAANlsNg0dOlQ5OTlasGCB3njjDY9LRAAA4NpV5gCzZcsWtW3bVm3btpUkJScnq23btpowYYJ8fHy0bds23XXXXfrDH/6goUOHKjo6Wl988YV8fX3NfcydO1fNmjVT9+7d1atXL91+++0e3/HicDi0YsUK5eXlKTo6Wk888YQmTJjAR6gBAIAkycswDKOqi6gMbrdbDodDBQUFFX4/TKPxyyp0fwAAWM2+qb0rZb9X+v7N30ICAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWQ4ABAACWU+YAs379evXp00dhYWHy8vLSkiVLzL5z585p3LhxioqKUt26dRUWFqbBgwfr0KFDHvto1KiRvLy8PJapU6d6jNm2bZs6deokPz8/hYeHKy0trXwzBAAANU6ZA8ypU6fUunVrTZ8+vUTf6dOntXXrVj333HPaunWrFi1apNzcXN11110lxk6ZMkWHDx82l9GjR5t9brdbcXFxioiIUFZWlqZNm6ZJkyZp5syZZS0XAADUQLXKukFCQoISEhJK7XM4HEpPT/do+/vf/6727dvrwIEDuvHGG832+vXry+l0lrqfuXPn6uzZs5o1a5ZsNptatmyp7Oxsvfrqq0pMTCxryQAAoIap9HtgCgoK5OXlpYCAAI/2qVOnqkGDBmrbtq2mTZum8+fPm30ZGRnq3LmzbDab2RYfH6/c3Fz99NNPpR6nsLBQbrfbYwEAADVTmc/AlMWZM2c0btw49e/fX3a73Wx//PHHdeuttyowMFAbN25USkqKDh8+rFdffVWS5HK5FBkZ6bGvkJAQs++6664rcazU1FRNnjy5EmcDAACqi0oLMOfOndP9998vwzD0zjvvePQlJyebP7dq1Uo2m03Dhw9XamqqfH19y3W8lJQUj/263W6Fh4eXr3gAAFCtVUqAuRBe9u/fr9WrV3ucfSlNTEyMzp8/r3379qlp06ZyOp3Kz8/3GHNh/WL3zfj6+pY7/AAAAGup8HtgLoSX3bt3a+XKlWrQoMFlt8nOzpa3t7eCg4MlSbGxsVq/fr3OnTtnjklPT1fTpk1LvXwEAACuLWU+A3Py5Ent2bPHXM/Ly1N2drYCAwMVGhqqP//5z9q6dauWLl2qoqIiuVwuSVJgYKBsNpsyMjKUmZmpbt26qX79+srIyNDYsWP14IMPmuFkwIABmjx5soYOHapx48Zpx44deuONN/Taa69V0LQBAICVeRmGYZRlg7Vr16pbt24l2ocMGaJJkyaVuPn2gjVr1qhr167aunWrRo4cqV27dqmwsFCRkZEaNGiQkpOTPS4Bbdu2TUlJSdq8ebMaNmyo0aNHa9y4cVdcp9vtlsPhUEFBwWUvYZVVo/HLKnR/AABYzb6pvStlv1f6/l3mAGMVBBgAACpPVQcY/hYSAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwHAIMAACwnDIHmPXr16tPnz4KCwuTl5eXlixZ4tFvGIYmTJig0NBQ1alTRz169NDu3bs9xhw7dkwDBw6U3W5XQECAhg4dqpMnT3qM2bZtmzp16iQ/Pz+Fh4crLS2t7LMDAAA1UpkDzKlTp9S6dWtNnz691P60tDS9+eabmjFjhjIzM1W3bl3Fx8frzJkz5piBAwcqJydH6enpWrp0qdavX6/ExESz3+12Ky4uThEREcrKytK0adM0adIkzZw5sxxTBAAANY2XYRhGuTf28tLixYvVt29fSb+cfQkLC9MTTzyhJ598UpJUUFCgkJAQzZkzRw888IC++eYbtWjRQps3b1a7du0kScuXL1evXr108OBBhYWF6Z133tH//M//yOVyyWazSZLGjx+vJUuWaNeuXVdUm9vtlsPhUEFBgex2e3mnWKpG45dV6P4AALCafVN7V8p+r/T9u0LvgcnLy5PL5VKPHj3MNofDoZiYGGVkZEiSMjIyFBAQYIYXSerRo4e8vb2VmZlpjuncubMZXiQpPj5eubm5+umnn0o9dmFhodxut8cCAABqpgoNMC6XS5IUEhLi0R4SEmL2uVwuBQcHe/TXqlVLgYGBHmNK28evj/Fbqampcjgc5hIeHv77JwQAAKqlGvMppJSUFBUUFJjLd999V9UlAQCASlKhAcbpdEqS8vPzPdrz8/PNPqfTqSNHjnj0nz9/XseOHfMYU9o+fn2M3/L19ZXdbvdYAABAzVShASYyMlJOp1OrVq0y29xutzIzMxUbGytJio2N1fHjx5WVlWWOWb16tYqLixUTE2OOWb9+vc6dO2eOSU9PV9OmTXXddddVZMkAAMCCyhxgTp48qezsbGVnZ0v65cbd7OxsHThwQF5eXhozZoz+9re/6d///re2b9+uwYMHKywszPykUvPmzdWzZ08NGzZMX331lb788kuNGjVKDzzwgMLCwiRJAwYMkM1m09ChQ5WTk6MFCxbojTfeUHJycoVNHAAAWFetsm6wZcsWdevWzVy/ECqGDBmiOXPm6Omnn9apU6eUmJio48eP6/bbb9fy5cvl5+dnbjN37lyNGjVK3bt3l7e3t/r166c333zT7Hc4HFqxYoWSkpIUHR2thg0basKECR7fFQMAAK5dv+t7YKozvgcGAIDKU6O+BwYAAOBqIMAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLIcAAAADLqfAA06hRI3l5eZVYkpKSJEldu3Yt0ffYY4957OPAgQPq3bu3/P39FRwcrKeeekrnz5+v6FIBAIBF1aroHW7evFlFRUXm+o4dO3TnnXfqvvvuM9uGDRumKVOmmOv+/v7mz0VFRerdu7ecTqc2btyow4cPa/Dgwapdu7ZefPHFii4XAABYUIUHmKCgII/1qVOnqkmTJurSpYvZ5u/vL6fTWer2K1as0M6dO7Vy5UqFhISoTZs2ev755zVu3DhNmjRJNput1O0KCwtVWFhorrvd7gqYDQAAqI4q9R6Ys2fP6p///KceeeQReXl5me1z585Vw4YNdcsttyglJUWnT582+zIyMhQVFaWQkBCzLT4+Xm63Wzk5ORc9VmpqqhwOh7mEh4dXzqQAAECVq/AzML+2ZMkSHT9+XA899JDZNmDAAEVERCgsLEzbtm3TuHHjlJubq0WLFkmSXC6XR3iRZK67XK6LHislJUXJycnmutvtJsQAAFBDVWqAef/995WQkKCwsDCzLTEx0fw5KipKoaGh6t69u/bu3asmTZqU+1i+vr7y9fX9XfUCAABrqLRLSPv379fKlSv16KOPXnJcTEyMJGnPnj2SJKfTqfz8fI8xF9Yvdt8MAAC4tlRagJk9e7aCg4PVu3fvS47Lzs6WJIWGhkqSYmNjtX37dh05csQck56eLrvdrhYtWlRWuQAAwEIq5RJScXGxZs+erSFDhqhWrf8eYu/evZo3b5569eqlBg0aaNu2bRo7dqw6d+6sVq1aSZLi4uLUokULDRo0SGlpaXK5XHr22WeVlJTEJSIAACCpkgLMypUrdeDAAT3yyCMe7TabTStXrtTrr7+uU6dOKTw8XP369dOzzz5rjvHx8dHSpUs1YsQIxcbGqm7duhoyZIjH98YAAIBrW6UEmLi4OBmGUaI9PDxc69atu+z2ERER+uyzzyqjNAAAUAPwt5AAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlEGAAAIDlVHiAmTRpkry8vDyWZs2amf1nzpxRUlKSGjRooHr16qlfv37Kz8/32MeBAwfUu3dv+fv7Kzg4WE899ZTOnz9f0aUCAACLqlUZO23ZsqVWrlz534PU+u9hxo4dq2XLlmnhwoVyOBwaNWqU7r33Xn355ZeSpKKiIvXu3VtOp1MbN27U4cOHNXjwYNWuXVsvvvhiZZQLAAAsplICTK1ateR0Oku0FxQU6P3339e8efN0xx13SJJmz56t5s2ba9OmTerQoYNWrFihnTt3auXKlQoJCVGbNm30/PPPa9y4cZo0aZJsNlupxywsLFRhYaG57na7K2NqAACgGqiUe2B2796tsLAwNW7cWAMHDtSBAwckSVlZWTp37px69Ohhjm3WrJluvPFGZWRkSJIyMjIUFRWlkJAQc0x8fLzcbrdycnIueszU1FQ5HA5zCQ8Pr4ypAQCAaqDCA0xMTIzmzJmj5cuX65133lFeXp46deqkEydOyOVyyWazKSAgwGObkJAQuVwuSZLL5fIILxf6L/RdTEpKigoKCszlu+++q9iJAQCAaqPCLyElJCSYP7dq1UoxMTGKiIjQRx99pDp16lT04Uy+vr7y9fWttP0DAIDqo9I/Rh0QEKA//OEP2rNnj5xOp86ePavjx497jMnPzzfvmXE6nSU+lXRhvbT7agAAwLWn0gPMyZMntXfvXoWGhio6Olq1a9fWqlWrzP7c3FwdOHBAsbGxkqTY2Fht375dR44cMcekp6fLbrerRYsWlV0uAACwgAq/hPTkk0+qT58+ioiI0KFDhzRx4kT5+Piof//+cjgcGjp0qJKTkxUYGCi73a7Ro0crNjZWHTp0kCTFxcWpRYsWGjRokNLS0uRyufTss88qKSmJS0QAAEBSJQSYgwcPqn///jp69KiCgoJ0++23a9OmTQoKCpIkvfbaa/L29la/fv1UWFio+Ph4vf322+b2Pj4+Wrp0qUaMGKHY2FjVrVtXQ4YM0ZQpUyq6VAAAYFFehmEYVV1EZXC73XI4HCooKJDdbq/QfTcav6xC9wcAgNXsm9q7UvZ7pe/f/C0kAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgOQQYAABgORUeYFJTU/XHP/5R9evXV3BwsPr27avc3FyPMV27dpWXl5fH8thjj3mMOXDggHr37i1/f38FBwfrqaee0vnz5yu6XAAAYEG1KnqH69atU1JSkv74xz/q/PnzeuaZZxQXF6edO3eqbt265rhhw4ZpypQp5rq/v7/5c1FRkXr37i2n06mNGzfq8OHDGjx4sGrXrq0XX3yxoksGAAAWU+EBZvny5R7rc+bMUXBwsLKystS5c2ez3d/fX06ns9R9rFixQjt37tTKlSsVEhKiNm3a6Pnnn9e4ceM0adIk2Wy2EtsUFhaqsLDQXHe73RU0IwAAUN1U+j0wBQUFkqTAwECP9rlz56phw4a65ZZblJKSotOnT5t9GRkZioqKUkhIiNkWHx8vt9utnJycUo+Tmpoqh8NhLuHh4ZUwGwAAUB1U+BmYXysuLtaYMWN022236ZZbbjHbBwwYoIiICIWFhWnbtm0aN26ccnNztWjRIkmSy+XyCC+SzHWXy1XqsVJSUpScnGyuu91uQgwAADVUpQaYpKQk7dixQxs2bPBoT0xMNH+OiopSaGiounfvrr1796pJkyblOpavr698fX1/V70AAMAaKu0S0qhRo7R06VKtWbNGN9xwwyXHxsTESJL27NkjSXI6ncrPz/cYc2H9YvfNAACAa0eFBxjDMDRq1CgtXrxYq1evVmRk5GW3yc7OliSFhoZKkmJjY7V9+3YdOXLEHJOeni673a4WLVpUdMkAAMBiKvwSUlJSkubNm6dPPvlE9evXN+9ZcTgcqlOnjvbu3at58+apV69eatCggbZt26axY8eqc+fOatWqlSQpLi5OLVq00KBBg5SWliaXy6Vnn31WSUlJXCYCAAAVfwbmnXfeUUFBgbp27arQ0FBzWbBggSTJZrNp5cqViouLU7NmzfTEE0+oX79++vTTT819+Pj4aOnSpfLx8VFsbKwefPBBDR482ON7YwAAwLWrws/AGIZxyf7w8HCtW7fusvuJiIjQZ599VlFlAQCAGoS/hQQAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACyHAAMAACynWgeY6dOnq1GjRvLz81NMTIy++uqrqi4JAABUA9U2wCxYsEDJycmaOHGitm7dqtatWys+Pl5Hjhyp6tIAAEAVq7YB5tVXX9WwYcP08MMPq0WLFpoxY4b8/f01a9asqi4NAABUsVpVXUBpzp49q6ysLKWkpJht3t7e6tGjhzIyMkrdprCwUIWFheZ6QUGBJMntdld4fcWFpyt8nwAAWEllvL/+er+GYVxyXLUMMD/++KOKiooUEhLi0R4SEqJdu3aVuk1qaqomT55coj08PLxSagQA4FrmeL1y93/ixAk5HI6L9lfLAFMeKSkpSk5ONteLi4t17NgxNWjQQF5eXhV2HLfbrfDwcH333Xey2+0Vtt/qpKbPkflZX02fY02fn1Tz58j8ys8wDJ04cUJhYWGXHFctA0zDhg3l4+Oj/Px8j/b8/Hw5nc5St/H19ZWvr69HW0BAQGWVKLvdXiP/Uf5aTZ8j87O+mj7Hmj4/qebPkfmVz6XOvFxQLW/itdlsio6O1qpVq8y24uJirVq1SrGxsVVYGQAAqA6q5RkYSUpOTtaQIUPUrl07tW/fXq+//rpOnTqlhx9+uKpLAwAAVazaBpi//OUv+uGHHzRhwgS5XC61adNGy5cvL3Fj79Xm6+uriRMnlrhcVZPU9DkyP+ur6XOs6fOTav4cmV/l8zIu9zklAACAaqZa3gMDAABwKQQYAABgOQQYAABgOQQYAABgOQQYAABgOQSYy9i3b5+GDh2qyMhI1alTR02aNNHEiRN19uzZS2535swZJSUlqUGDBqpXr5769etX4puFq4sXXnhBHTt2lL+//xV/e/FDDz0kLy8vj6Vnz56VW+jvUJ45GoahCRMmKDQ0VHXq1FGPHj20e/fuyi20nI4dO6aBAwfKbrcrICBAQ4cO1cmTJy+5TdeuXUs8h4899thVqvjypk+frkaNGsnPz08xMTH66quvLjl+4cKFatasmfz8/BQVFaXPPvvsKlVaPmWZ35w5c0o8V35+flex2rJZv369+vTpo7CwMHl5eWnJkiWX3Wbt2rW69dZb5evrq5tuuklz5syp9Dp/j7LOce3atSWeQy8vL7lcrqtTcBmkpqbqj3/8o+rXr6/g4GD17dtXubm5l93uar8GCTCXsWvXLhUXF+vdd99VTk6OXnvtNc2YMUPPPPPMJbcbO3asPv30Uy1cuFDr1q3ToUOHdO+9916lqsvm7Nmzuu+++zRixIgybdezZ08dPnzYXD788MNKqvD3K88c09LS9Oabb2rGjBnKzMxU3bp1FR8frzNnzlRipeUzcOBA5eTkKD09XUuXLtX69euVmJh42e2GDRvm8RympaVdhWovb8GCBUpOTtbEiRO1detWtW7dWvHx8Tpy5Eip4zdu3Kj+/ftr6NCh+vrrr9W3b1/17dtXO3bsuMqVX5myzk/65Svbf/1c7d+//ypWXDanTp1S69atNX369Csan5eXp969e6tbt27Kzs7WmDFj9Oijj+rzzz+v5ErLr6xzvCA3N9fjeQwODq6kCstv3bp1SkpK0qZNm5Senq5z584pLi5Op06duug2VfIaNFBmaWlpRmRk5EX7jx8/btSuXdtYuHCh2fbNN98YkoyMjIyrUWK5zJ4923A4HFc0dsiQIcbdd99dqfVUhiudY3FxseF0Oo1p06aZbcePHzd8fX2NDz/8sBIrLLudO3cakozNmzebbf/3f/9neHl5Gd9///1Ft+vSpYvx17/+9SpUWHbt27c3kpKSzPWioiIjLCzMSE1NLXX8/fffb/Tu3dujLSYmxhg+fHil1lleZZ1fWV6b1Y0kY/HixZcc8/TTTxstW7b0aPvLX/5ixMfHV2JlFedK5rhmzRpDkvHTTz9dlZoq0pEjRwxJxrp16y46pipeg5yBKYeCggIFBgZetD8rK0vnzp1Tjx49zLZmzZrpxhtvVEZGxtUo8apYu3atgoOD1bRpU40YMUJHjx6t6pIqTF5enlwul8dz6HA4FBMTU+2ew4yMDAUEBKhdu3ZmW48ePeTt7a3MzMxLbjt37lw1bNhQt9xyi1JSUnT69OnKLveyzp49q6ysLI/H3tvbWz169LjoY5+RkeExXpLi4+Or3XMllW9+knTy5ElFREQoPDxcd999t3Jycq5GuVeFlZ6/36tNmzYKDQ3VnXfeqS+//LKqy7kiBQUFknTJ972qeA6r7Z8SqK727Nmjt956Sy+//PJFx7hcLtlsthL3WoSEhFTL653l0bNnT917772KjIzU3r179cwzzyghIUEZGRny8fGp6vJ+twvP02//dEV1fA5dLleJ09C1atVSYGDgJWsdMGCAIiIiFBYWpm3btmncuHHKzc3VokWLKrvkS/rxxx9VVFRU6mO/a9euUrdxuVyWeK6k8s2vadOmmjVrllq1aqWCggK9/PLL6tixo3JycnTDDTdcjbIr1cWeP7fbrZ9//ll16tSposoqTmhoqGbMmKF27dqpsLBQ7733nrp27arMzEzdeuutVV3eRRUXF2vMmDG67bbbdMstt1x0XFW8Bq/ZMzDjx48v9YaqXy+//WXy/fffq2fPnrrvvvs0bNiwKqr8ypRnfmXxwAMP6K677lJUVJT69u2rpUuXavPmzVq7dm3FTeIyKnuOVa2y55eYmKj4+HhFRUVp4MCB+sc//qHFixdr7969FTgLVITY2FgNHjxYbdq0UZcuXbRo0SIFBQXp3XffrerScIWaNm2q4cOHKzo6Wh07dtSsWbPUsWNHvfbaa1Vd2iUlJSVpx44dmj9/flWXUsI1ewbmiSee0EMPPXTJMY0bNzZ/PnTokLp166aOHTtq5syZl9zO6XTq7NmzOn78uMdZmPz8fDmdzt9T9hUr6/x+r8aNG6thw4bas2ePunfvXmH7vZTKnOOF5yk/P1+hoaFme35+vtq0aVOufZbVlc7P6XSWuPnz/PnzOnbsWJn+vcXExEj65SxjkyZNylxvRWnYsKF8fHxKfGrvUq8fp9NZpvFVqTzz+63atWurbdu22rNnT2WUeNVd7Pmz2+014uzLxbRv314bNmyo6jIuatSoUeaHAi53pq8qXoPXbIAJCgpSUFDQFY39/vvv1a1bN0VHR2v27Nny9r70iavo6GjVrl1bq1atUr9+/ST9cuf5gQMHFBsb+7trvxJlmV9FOHjwoI4ePerxZl/ZKnOOkZGRcjqdWrVqlRlY3G63MjMzy/xprfK60vnFxsbq+PHjysrKUnR0tCRp9erVKi4uNkPJlcjOzpakq/oclsZmsyk6OlqrVq1S3759Jf1yGnvVqlUaNWpUqdvExsZq1apVGjNmjNmWnp5+1V5vZVGe+f1WUVGRtm/frl69elVipVdPbGxsiY/cVtfnryJlZ2dX+eutNIZhaPTo0Vq8eLHWrl2ryMjIy25TJa/BSrs9uIY4ePCgcdNNNxndu3c3Dh48aBw+fNhcfj2madOmRmZmptn22GOPGTfeeKOxevVqY8uWLUZsbKwRGxtbFVO4rP379xtff/21MXnyZKNevXrG119/bXz99dfGiRMnzDFNmzY1Fi1aZBiGYZw4ccJ48sknjYyMDCMvL89YuXKlceuttxo333yzcebMmaqaxiWVdY6GYRhTp041AgICjE8++cTYtm2bcffddxuRkZHGzz//XBVTuKSePXsabdu2NTIzM40NGzYYN998s9G/f3+z/7f/Rvfs2WNMmTLF2LJli5GXl2d88sknRuPGjY3OnTtX1RQ8zJ8/3/D19TXmzJlj7Ny500hMTDQCAgIMl8tlGIZhDBo0yBg/frw5/ssvvzRq1aplvPzyy8Y333xjTJw40ahdu7axffv2qprCJZV1fpMnTzY+//xzY+/evUZWVpbxwAMPGH5+fkZOTk5VTeGSTpw4Yb7GJBmvvvqq8fXXXxv79+83DMMwxo8fbwwaNMgc/+233xr+/v7GU089ZXzzzTfG9OnTDR8fH2P58uVVNYXLKuscX3vtNWPJkiXG7t27je3btxt//etfDW9vb2PlypVVNYWLGjFihOFwOIy1a9d6vOedPn3aHFMdXoMEmMuYPXu2IanU5YK8vDxDkrFmzRqz7eeffzZGjhxpXHfddYa/v79xzz33eISe6mTIkCGlzu/X85FkzJ492zAMwzh9+rQRFxdnBAUFGbVr1zYiIiKMYcOGmb98q6OyztEwfvko9XPPPWeEhIQYvr6+Rvfu3Y3c3NyrX/wVOHr0qNG/f3+jXr16ht1uNx5++GGPcPbbf6MHDhwwOnfubAQGBhq+vr7GTTfdZDz11FNGQUFBFc2gpLfeesu48cYbDZvNZrRv397YtGmT2delSxdjyJAhHuM/+ugj4w9/+INhs9mMli1bGsuWLbvKFZdNWeY3ZswYc2xISIjRq1cvY+vWrVVQ9ZW58JHh3y4X5jRkyBCjS5cuJbZp06aNYbPZjMaNG3u8Fqujss7xpZdeMpo0aWL4+fkZgYGBRteuXY3Vq1dXTfGXcbH3vF8/J9XhNej1/4sFAACwjGv2U0gAAMC6CDAAAMByCDAAAMByCDAAAMByCDAAAMByCDAAAMByCDAAAMByCDAAAMByCDAAAMByCDAAAMByCDAAAMBy/h+ZXGznIm0PDgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GAAAYhwADAACMQ4ABAADGIcAAAADjsIj3Gpi42AoAgIaEJzAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxDgAEAAMYhwAAAAOMQYAAAgHEIMAAAwDgEGAAAYBwCDAAAMA4BBgAAGIcAAwAAjEOAAQAAxiHAAAAA4xBgAACAcQgwAADAOAQYAABgHAIMAAAwDgEGAAAYhwADAACMQ4ABAADGIcAAAADjEGAAAIBxCDAAAMA4NQ4wWVlZGjhwoCIiImSz2bR27VqvfpvNVu02Z84ca0ybNm2q9M+aNctrngMHDqhHjx7y9/dXZGSkZs+efW1XCAAAGpwaB5jz58+rS5cuWrhwYbX9p0+f9tqWLl0qm82mwYMHe42bOXOm17gJEyZYfW63W/Hx8YqKilJOTo7mzJmj9PR0LVmypKblAgCABqhxTQ/o37+/+vfvf8l+l8vltb9u3Tr17t1bt9xyi1d78+bNq4y9aMWKFSorK9PSpUtlt9vVoUMH5ebmau7cuRo9enRNSwYAAA1Mna6BKSoq0oYNG5ScnFylb9asWWrZsqXuvPNOzZkzR+Xl5VZfdna2evbsKbvdbrUlJCQoPz9f33zzTbXnKi0tldvt9toAAEDDVOMnMDXx1ltvqXnz5nr44Ye92p955hn9/Oc/V3BwsHbv3q20tDSdPn1ac+fOlSQVFhYqOjra65iwsDCrr0WLFlXOlZGRoRkzZtTRlQAAgPqkTgPM0qVLNWzYMPn7+3u1p6amWj937txZdrtdY8aMUUZGhhwOxzWdKy0tzWtet9utyMjIayscAADUa3UWYD744APl5+dr1apVVxzbvXt3lZeX6+TJk2rfvr1cLpeKioq8xlzcv9S6GYfDcc3hBwAAmKXO1sC8+eabio2NVZcuXa44Njc3V40aNVJoaKgkKS4uTllZWbpw4YI1JjMzU+3bt6/25SMAAHBjqXGAOXfunHJzc5WbmytJOnHihHJzc1VQUGCNcbvdevfdd/XUU09VOT47O1vz58/XP/7xD/3zn//UihUrNHHiRD3++ONWOBk6dKjsdruSk5OVl5enVatW6ZVXXvF6iQgAANy4avwS0r59+9S7d29r/2KoSEpK0vLlyyVJb7/9tjwejx577LEqxzscDr399ttKT09XaWmpoqOjNXHiRK9w4nQ6tXnzZqWkpCg2NlatWrXStGnTeAs1AACQJNk8Ho/H10XUBbfbLafTqZKSEgUGBtbq3G1e2FCr8wEAYJqTsxLrZN6r/fvNdyEBAADjEGAAAIBxCDAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxDgAEAAMYhwAAAAOMQYAAAgHEIMAAAwDgEGAAAYBwCDAAAMA4BBgAAGIcAAwAAjEOAAQAAxiHAAAAA4xBgAACAcQgwAADAOAQYAABgHAIMAAAwDgEGAAAYhwADAACMQ4ABAADGIcAAAADjEGAAAIBxCDAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxT4wCTlZWlgQMHKiIiQjabTWvXrvXqf+KJJ2Sz2by2fv36eY05e/ashg0bpsDAQAUFBSk5OVnnzp3zGnPgwAH16NFD/v7+ioyM1OzZs2t+dQAAoEGqcYA5f/68unTpooULF15yTL9+/XT69Glr+8tf/uLVP2zYMOXl5SkzM1Pr169XVlaWRo8ebfW73W7Fx8crKipKOTk5mjNnjtLT07VkyZKalgsAABqgxjU9oH///urfv/9lxzgcDrlcrmr7PvnkE23atEkff/yxunbtKklasGCBBgwYoD/84Q+KiIjQihUrVFZWpqVLl8put6tDhw7Kzc3V3LlzvYIOAAC4MdXJGpgdO3YoNDRU7du317hx4/T1119bfdnZ2QoKCrLCiyT17dtXjRo10p49e6wxPXv2lN1ut8YkJCQoPz9f33zzTbXnLC0tldvt9toAAEDDVOsBpl+/fvrTn/6krVu36ve//7127typ/v37q6KiQpJUWFio0NBQr2MaN26s4OBgFRYWWmPCwsK8xlzcvzjm32VkZMjpdFpbZGRkbV8aAACoJ2r8EtKVDBkyxPq5U6dO6ty5s9q2basdO3aoT58+tX06S1pamlJTU619t9tNiAEAoIGq87dR33LLLWrVqpWOHTsmSXK5XDpz5ozXmPLycp09e9ZaN+NyuVRUVOQ15uL+pdbWOBwOBQYGem0AAKBhqvMA8/nnn+vrr79WeHi4JCkuLk7FxcXKycmxxmzbtk2VlZXq3r27NSYrK0sXLlywxmRmZqp9+/Zq0aJFXZcMAADquRoHmHPnzik3N1e5ubmSpBMnTig3N1cFBQU6d+6cJk+erI8++kgnT57U1q1b9ctf/lLt2rVTQkKCJOn2229Xv379NGrUKO3du1cffvihxo8fryFDhigiIkKSNHToUNntdiUnJysvL0+rVq3SK6+84vUSEQAAuHHVOMDs27dPd955p+68805JUmpqqu68805NmzZNfn5+OnDggB566CHdeuutSk5OVmxsrD744AM5HA5rjhUrVui2225Tnz59NGDAAN13331en/HidDq1efNmnThxQrGxsZo0aZKmTZvGW6gBAIAkyebxeDy+LqIuuN1uOZ1OlZSU1Pp6mDYvbKjV+QAAMM3JWYl1Mu/V/v3mu5AAAIBxCDAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxDgAEAAMYhwAAAAOMQYAAAgHEIMAAAwDgEGAAAYBwCDAAAMA4BBgAAGIcAAwAAjEOAAQAAxiHAAAAA4xBgAACAcQgwAADAOAQYAABgHAIMAAAwDgEGAAAYhwADAACMQ4ABAADGIcAAAADjEGAAAIBxCDAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxDgAEAAMYhwAAAAOPUOMBkZWVp4MCBioiIkM1m09q1a62+CxcuaMqUKerUqZOaNWumiIgIjRgxQqdOnfKao02bNrLZbF7brFmzvMYcOHBAPXr0kL+/vyIjIzV79uxru0IAANDg1DjAnD9/Xl26dNHChQur9H333Xfav3+/fvOb32j//v1avXq18vPz9dBDD1UZO3PmTJ0+fdraJkyYYPW53W7Fx8crKipKOTk5mjNnjtLT07VkyZKalgsAABqgxjU9oH///urfv3+1fU6nU5mZmV5tr732mrp166aCggK1bt3aam/evLlcLle186xYsUJlZWVaunSp7Ha7OnTooNzcXM2dO1ejR4+uackAAKCBqfM1MCUlJbLZbAoKCvJqnzVrllq2bKk777xTc+bMUXl5udWXnZ2tnj17ym63W20JCQnKz8/XN998U+15SktL5Xa7vTYAANAw1fgJTE388MMPmjJlih577DEFBgZa7c8884x+/vOfKzg4WLt371ZaWppOnz6tuXPnSpIKCwsVHR3tNVdYWJjV16JFiyrnysjI0IwZM+rwagAAQH1RZwHmwoUL+tWvfiWPx6NFixZ59aWmplo/d+7cWXa7XWPGjFFGRoYcDsc1nS8tLc1rXrfbrcjIyGsrHgAA1Gt1EmAuhpdPP/1U27Zt83r6Up3u3burvLxcJ0+eVPv27eVyuVRUVOQ15uL+pdbNOByOaw4/AADALLW+BuZieDl69Ki2bNmili1bXvGY3NxcNWrUSKGhoZKkuLg4ZWVl6cKFC9aYzMxMtW/fvtqXjwAAwI2lxk9gzp07p2PHjln7J06cUG5uroKDgxUeHq5HHnlE+/fv1/r161VRUaHCwkJJUnBwsOx2u7Kzs7Vnzx717t1bzZs3V3Z2tiZOnKjHH3/cCidDhw7VjBkzlJycrClTpujQoUN65ZVXNG/evFq6bAAAYDKbx+Px1OSAHTt2qHfv3lXak5KSlJ6eXmXx7UXbt29Xr169tH//fj399NM6cuSISktLFR0dreHDhys1NdXrJaADBw4oJSVFH3/8sVq1aqUJEyZoypQpV12n2+2W0+lUSUnJFV/Cqqk2L2yo1fkAADDNyVmJdTLv1f79rnGAMQUBBgCAuuPrAMN3IQEAAOMQYAAAgHEIMAAAwDgEGAAAYBwCDAAAMA4BBgAAGIcAAwAAjEOAAQAAxiHAAAAA4xBgAACAcQgwAADAOAQYAABgHAIMAAAwDgEGAAAYhwADAACMQ4ABAADGIcAAAADjEGAAAIBxCDAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxDgAEAAMYhwAAAAOMQYAAAgHEIMAAAwDgEGAAAYBwCDAAAMA4BBgAAGIcAAwAAjFPjAJOVlaWBAwcqIiJCNptNa9eu9er3eDyaNm2awsPD1bRpU/Xt21dHjx71GnP27FkNGzZMgYGBCgoKUnJyss6dO+c15sCBA+rRo4f8/f0VGRmp2bNn1/zqAABAg1TjAHP+/Hl16dJFCxcurLZ/9uzZevXVV7V48WLt2bNHzZo1U0JCgn744QdrzLBhw5SXl6fMzEytX79eWVlZGj16tNXvdrsVHx+vqKgo5eTkaM6cOUpPT9eSJUuu4RIBAEBDY/N4PJ5rPthm05o1azRo0CBJ//f0JSIiQpMmTdJzzz0nSSopKVFYWJiWL1+uIUOG6JNPPlFMTIw+/vhjde3aVZK0adMmDRgwQJ9//rkiIiK0aNEi/frXv1ZhYaHsdrsk6YUXXtDatWt15MiRq6rN7XbL6XSqpKREgYGB13qJ1WrzwoZanQ8AANOcnJVYJ/Ne7d/vWl0Dc+LECRUWFqpv375Wm9PpVPfu3ZWdnS1Jys7OVlBQkBVeJKlv375q1KiR9uzZY43p2bOnFV4kKSEhQfn5+frmm2+qPXdpaancbrfXBgAAGqZaDTCFhYWSpLCwMK/2sLAwq6+wsFChoaFe/Y0bN1ZwcLDXmOrm+PE5/l1GRoacTqe1RUZG/vQLAgAA9VKDeRdSWlqaSkpKrO2zzz7zdUkAAKCO1GqAcblckqSioiKv9qKiIqvP5XLpzJkzXv3l5eU6e/as15jq5vjxOf6dw+FQYGCg1wYAABqmWg0w0dHRcrlc2rp1q9Xmdru1Z88excXFSZLi4uJUXFysnJwca8y2bdtUWVmp7t27W2OysrJ04cIFa0xmZqbat2+vFi1a1GbJAADAQDUOMOfOnVNubq5yc3Ml/d/C3dzcXBUUFMhms+nZZ5/Vb3/7W/31r3/VwYMHNWLECEVERFjvVLr99tvVr18/jRo1Snv37tWHH36o8ePHa8iQIYqIiJAkDR06VHa7XcnJycrLy9OqVav0yiuvKDU1tdYuHAAAmKtxTQ/Yt2+fevfube1fDBVJSUlavny5nn/+eZ0/f16jR49WcXGx7rvvPm3atEn+/v7WMStWrND48ePVp08fNWrUSIMHD9arr75q9TudTm3evFkpKSmKjY1Vq1atNG3aNK/PigEAADeun/Q5MPUZnwMDAEDdaVCfAwMAAHA9EGAAAIBxCDAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxDgAEAAMYhwAAAAOMQYAAAgHEIMAAAwDgEGAAAYBwCDAAAMA4BBgAAGIcAAwAAjEOAAQAAxiHAAAAA4xBgAACAcQgwAADAOAQYAABgHAIMAAAwDgEGAAAYhwADAACMQ4ABAADGIcAAAADjEGAAAIBxCDAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxDgAEAAMap9QDTpk0b2Wy2KltKSookqVevXlX6xo4d6zVHQUGBEhMTFRAQoNDQUE2ePFnl5eW1XSoAADBU49qe8OOPP1ZFRYW1f+jQIT3wwAN69NFHrbZRo0Zp5syZ1n5AQID1c0VFhRITE+VyubR7926dPn1aI0aMUJMmTfTyyy/XdrkAAMBAtR5gQkJCvPZnzZqltm3b6v7777faAgIC5HK5qj1+8+bNOnz4sLZs2aKwsDDdcccdeumllzRlyhSlp6fLbrfXdskAAMAwdboGpqysTP/93/+tJ598UjabzWpfsWKFWrVqpY4dOyotLU3fffed1Zedna1OnTopLCzMaktISJDb7VZeXt4lz1VaWiq32+21AQCAhqnWn8D82Nq1a1VcXKwnnnjCahs6dKiioqIUERGhAwcOaMqUKcrPz9fq1aslSYWFhV7hRZK1X1hYeMlzZWRkaMaMGbV/EQAAoN6p0wDz5ptvqn///oqIiLDaRo8ebf3cqVMnhYeHq0+fPjp+/Ljatm17zedKS0tTamqqte92uxUZGXnN8wEAgPqrzgLMp59+qi1btlhPVi6le/fukqRjx46pbdu2crlc2rt3r9eYoqIiSbrkuhlJcjgccjgcP7FqAABggjpbA7Ns2TKFhoYqMTHxsuNyc3MlSeHh4ZKkuLg4HTx4UGfOnLHGZGZmKjAwUDExMXVVLgAAMEidPIGprKzUsmXLlJSUpMaN/3WK48ePa+XKlRowYIBatmypAwcOaOLEierZs6c6d+4sSYqPj1dMTIyGDx+u2bNnq7CwUFOnTlVKSgpPWAAAgKQ6CjBbtmxRQUGBnnzySa92u92uLVu2aP78+Tp//rwiIyM1ePBgTZ061Rrj5+en9evXa9y4cYqLi1OzZs2UlJTk9bkxAADgxlYnASY+Pl4ej6dKe2RkpHbu3HnF46OiorRx48a6KA0AADQAfBcSAAAwDgEGAAAYhwADAACMQ4ABAADGIcAAAADjEGAAAIBxCDAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxDgAEAAMYhwAAAAOMQYAAAgHEIMAAAwDgEGAAAYBwCDAAAMA4BBgAAGIcAAwAAjEOAAQAAxiHAAAAA4xBgAACAcQgwAADAOAQYAABgHAIMAAAwDgEGAAAYhwADAACMQ4ABAADGIcAAAADjEGAAAIBxCDAAAMA4tR5g0tPTZbPZvLbbbrvN6v/hhx+UkpKili1b6qabbtLgwYNVVFTkNUdBQYESExMVEBCg0NBQTZ48WeXl5bVdKgAAMFTjupi0Q4cO2rJly79O0vhfp5k4caI2bNigd999V06nU+PHj9fDDz+sDz/8UJJUUVGhxMREuVwu7d69W6dPn9aIESPUpEkTvfzyy3VRLgAAMEydBJjGjRvL5XJVaS8pKdGbb76plStX6he/+IUkadmyZbr99tv10Ucf6e6779bmzZt1+PBhbdmyRWFhYbrjjjv00ksvacqUKUpPT5fdbq+LkgEAgEHqZA3M0aNHFRERoVtuuUXDhg1TQUGBJCknJ0cXLlxQ3759rbG33XabWrdurezsbElSdna2OnXqpLCwMGtMQkKC3G638vLyLnnO0tJSud1urw0AADRMtR5gunfvruXLl2vTpk1atGiRTpw4oR49eujbb79VYWGh7Ha7goKCvI4JCwtTYWGhJKmwsNArvFzsv9h3KRkZGXI6ndYWGRlZuxcGAADqjVp/Cal///7Wz507d1b37t0VFRWld955R02bNq3t01nS0tKUmppq7bvdbkIMAAANVJ2/jTooKEi33nqrjh07JpfLpbKyMhUXF3uNKSoqstbMuFyuKu9Kurhf3bqaixwOhwIDA702AADQMNV5gDl37pyOHz+u8PBwxcbGqkmTJtq6davVn5+fr4KCAsXFxUmS4uLidPDgQZ05c8Yak5mZqcDAQMXExNR1uQAAwAC1/hLSc889p4EDByoqKkqnTp3S9OnT5efnp8cee0xOp1PJyclKTU1VcHCwAgMDNWHCBMXFxenuu++WJMXHxysmJkbDhw/X7NmzVVhYqKlTpyolJUUOh6O2ywUAAAaq9QDz+eef67HHHtPXX3+tkJAQ3Xffffroo48UEhIiSZo3b54aNWqkwYMHq7S0VAkJCfrjH/9oHe/n56f169dr3LhxiouLU7NmzZSUlKSZM2fWdqkAAMBQNo/H4/F1EXXB7XbL6XSqpKSk1tfDtHlhQ63OBwCAaU7OSqyTea/27zffhQQAAIxDgAEAAMYhwAAAAOMQYAAAgHEIMAAAwDgEGAAAYBwCDAAAMA4BBgAAGIcAAwAAjEOAAQAAxiHAAAAA4xBgAACAcQgwAADAOAQYAABgHAIMAAAwDgEGAAAYhwADAACMQ4ABAADGIcAAAADjEGAAAIBxCDAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxDgAEAAMYhwAAAAOMQYAAAgHEIMAAAwDgEGAAAYBwCDAAAMA4BBgAAGKfWA0xGRobuuusuNW/eXKGhoRo0aJDy8/O9xvTq1Us2m81rGzt2rNeYgoICJSYmKiAgQKGhoZo8ebLKy8tru1wAAGCgxrU94c6dO5WSkqK77rpL5eXlevHFFxUfH6/Dhw+rWbNm1rhRo0Zp5syZ1n5AQID1c0VFhRITE+VyubR7926dPn1aI0aMUJMmTfTyyy/XdskAAMAwtR5gNm3a5LW/fPlyhYaGKicnRz179rTaAwIC5HK5qp1j8+bNOnz4sLZs2aKwsDDdcccdeumllzRlyhSlp6fLbrfXdtkAAMAgdb4GpqSkRJIUHBzs1b5ixQq1atVKHTt2VFpamr777jurLzs7W506dVJYWJjVlpCQILfbrby8vGrPU1paKrfb7bUBAICGqdafwPxYZWWlnn32Wd17773q2LGj1T506FBFRUUpIiJCBw4c0JQpU5Sfn6/Vq1dLkgoLC73CiyRrv7CwsNpzZWRkaMaMGXV0JQAAoD6p0wCTkpKiQ4cOadeuXV7to0ePtn7u1KmTwsPD1adPHx0/flxt27a9pnOlpaUpNTXV2ne73YqMjLy2wgEAQL1WZy8hjR8/XuvXr9f27dt18803X3Zs9+7dJUnHjh2TJLlcLhUVFXmNubh/qXUzDodDgYGBXhsAAGiYaj3AeDwejR8/XmvWrNG2bdsUHR19xWNyc3MlSeHh4ZKkuLg4HTx4UGfOnLHGZGZmKjAwUDExMbVdMgAAMEytv4SUkpKilStXat26dWrevLm1ZsXpdKpp06Y6fvy4Vq5cqQEDBqhly5Y6cOCAJk6cqJ49e6pz586SpPj4eMXExGj48OGaPXu2CgsLNXXqVKWkpMjhcNR2yQAAwDC1/gRm0aJFKikpUa9evRQeHm5tq1atkiTZ7XZt2bJF8fHxuu222zRp0iQNHjxY//u//2vN4efnp/Xr18vPz09xcXF6/PHHNWLECK/PjQEAADeuWn8C4/F4LtsfGRmpnTt3XnGeqKgobdy4sbbKAgAADQjfhQQAAIxDgAEAAMYhwAAAAOMQYAAAgHEIMAAAwDgEGAAAYBwCDAAAMA4BBgAAGIcAAwAAjEOAAQAAxiHAAAAA4xBgAACAcQgwAADAOAQYAABgHAIMAAAwDgEGAAAYhwADAACMQ4ABAADGIcAAAADjEGAAAIBxCDAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxDgAEAAMYhwAAAAOMQYAAAgHEIMAAAwDgEGAAAYBwCDAAAME69DjALFy5UmzZt5O/vr+7du2vv3r2+LgkAANQD9TbArFq1SqmpqZo+fbr279+vLl26KCEhQWfOnPF1aQAAwMfqbYCZO3euRo0apZEjRyomJkaLFy9WQECAli5d6uvSAACAjzX2dQHVKSsrU05OjtLS0qy2Ro0aqW/fvsrOzq72mNLSUpWWllr7JSUlkiS3213r9VWWflfrcwIAYJK6+Pv643k9Hs9lx9XLAPPVV1+poqJCYWFhXu1hYWE6cuRItcdkZGRoxowZVdojIyPrpEYAAG5kzvl1O/+3334rp9N5yf56GWCuRVpamlJTU639yspKnT17Vi1btpTNZqu187jdbkVGRuqzzz5TYGBgrc3bUHG/rh736upxr64e9+rqca+uXl3eK4/Ho2+//VYRERGXHVcvA0yrVq3k5+enoqIir/aioiK5XK5qj3E4HHI4HF5tQUFBdVWiAgMD+QWvAe7X1eNeXT3u1dXjXl097tXVq6t7dbknLxfVy0W8drtdsbGx2rp1q9VWWVmprVu3Ki4uzoeVAQCA+qBePoGRpNTUVCUlJalr167q1q2b5s+fr/Pnz2vkyJG+Lg0AAPhYvQ0w//Ef/6Evv/xS06ZNU2Fhoe644w5t2rSpysLe683hcGj69OlVXq5C9bhfV497dfW4V1ePe3X1uFdXrz7cK5vnSu9TAgAAqGfq5RoYAACAyyHAAAAA4xBgAACAcQgwAADAOAQYAABgHALMT/TQQw+pdevW8vf3V3h4uIYPH65Tp075uqx65+TJk0pOTlZ0dLSaNm2qtm3bavr06SorK/N1afXS7373O91zzz0KCAio00+UNtHChQvVpk0b+fv7q3v37tq7d6+vS6qXsrKyNHDgQEVERMhms2nt2rW+LqneysjI0F133aXmzZsrNDRUgwYNUn5+vq/LqpcWLVqkzp07W5/AGxcXp7/97W8+qYUA8xP17t1b77zzjvLz8/U///M/On78uB555BFfl1XvHDlyRJWVlXr99deVl5enefPmafHixXrxxRd9XVq9VFZWpkcffVTjxo3zdSn1yqpVq5Samqrp06dr//796tKlixISEnTmzBlfl1bvnD9/Xl26dNHChQt9XUq9t3PnTqWkpOijjz5SZmamLly4oPj4eJ0/f97XpdU7N998s2bNmqWcnBzt27dPv/jFL/TLX/5SeXl5178YD2rVunXrPDabzVNWVubrUuq92bNne6Kjo31dRr22bNkyj9Pp9HUZ9Ua3bt08KSkp1n5FRYUnIiLCk5GR4cOq6j9JnjVr1vi6DGOcOXPGI8mzc+dOX5dihBYtWnjeeOON635ensDUorNnz2rFihW655571KRJE1+XU++VlJQoODjY12XAEGVlZcrJyVHfvn2ttkaNGqlv377Kzs72YWVoaEpKSiSJf5+uoKKiQm+//bbOnz/vk+8pJMDUgilTpqhZs2Zq2bKlCgoKtG7dOl+XVO8dO3ZMCxYs0JgxY3xdCgzx1VdfqaKiosrXiYSFhamwsNBHVaGhqays1LPPPqt7771XHTt29HU59dLBgwd10003yeFwaOzYsVqzZo1iYmKuex0EmGq88MILstlsl92OHDlijZ88ebL+/ve/a/PmzfLz89OIESPkuUG+oaGm90qSvvjiC/Xr10+PPvqoRo0a5aPKr79ruVcArq+UlBQdOnRIb7/9tq9Lqbfat2+v3Nxc7dmzR+PGjVNSUpIOHz583evgu5Cq8eWXX+rrr7++7JhbbrlFdru9Svvnn3+uyMhI7d692yeP1K63mt6rU6dOqVevXrr77ru1fPlyNWp042Toa/m9Wr58uZ599lkVFxfXcXX1X1lZmQICAvTee+9p0KBBVntSUpKKi4t58nkZNptNa9as8bpvqGr8+PFat26dsrKyFB0d7etyjNG3b1+1bdtWr7/++nU9b739NmpfCgkJUUhIyDUdW1lZKUkqLS2tzZLqrZrcqy+++EK9e/dWbGysli1bdkOFF+mn/V5Bstvtio2N1datW60/xJWVldq6davGjx/v2+JgNI/HowkTJmjNmjXasWMH4aWGKisrffI3jwDzE+zZs0cff/yx7rvvPrVo0ULHjx/Xb37zG7Vt2/aGePpSE1988YV69eqlqKgo/eEPf9CXX35p9blcLh9WVj8VFBTo7NmzKigoUEVFhXJzcyVJ7dq100033eTb4nwoNTVVSUlJ6tq1q7p166b58+fr/PnzGjlypK9Lq3fOnTunY8eOWfsnTpxQbm6ugoOD1bp1ax9WVv+kpKRo5cqVWrdunZo3b26tqXI6nWratKmPq6tf0tLS1L9/f7Vu3VrffvutVq5cqR07duj999+//sVc9/c9NSAHDhzw9O7d2xMcHOxxOByeNm3aeMaOHev5/PPPfV1avbNs2TKPpGo3VJWUlFTtvdq+fbuvS/O5BQsWeFq3bu2x2+2ebt26eT766CNfl1Qvbd++vdrfoaSkJF+XVu9c6t+mZcuW+bq0eufJJ5/0REVFeex2uyckJMTTp08fz+bNm31SC2tgAACAcW6sRQgAAKBBIMAAAADjEGAAAIBxCDAAAMA4BBgAAGAcAgwAADAOAQYAABiHAAMAAIxDgAEAAMYhwAAAAOMQYAAAgHH+P2PHJNzGLkxzAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.title(\"first dimension\")\n",
    "plt.hist(samples[0, :, 0])\n",
    "plt.figure()\n",
    "plt.title(\"second dimension\")\n",
    "plt.hist(samples[0, :, 1])\n",
    "plt.figure()\n",
    "plt.title(\"third dimension\")\n",
    "plt.hist(samples[0, :, 2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now constraint rectangle to 2D by fixing third dimension at 2.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_eq = np.array(\n",
    "    [\n",
    "        [0.0, 0.0, 1.0]\n",
    "    ]\n",
    ")\n",
    "b_eq = np.array([2.5])\n",
    "\n",
    "constrained_rectangle = hopsy.add_equality_constraints(rectangle, A_eq=A_eq, b_eq=b_eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "mc = hopsy.MarkovChain(constrained_rectangle)\n",
    "rng = hopsy.RandomNumberGenerator(43)\n",
    "_, constrained_samples = hopsy.sample(mc, rng, n_samples=20000, thinning=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.title(\"first dimension constrained\")\n",
    "plt.hist(constrained_samples[0, :, 0])\n",
    "plt.figure()\n",
    "plt.title(\"second dimension constrained\")\n",
    "plt.hist(constrained_samples[0, :, 1])\n",
    "plt.figure()\n",
    "plt.title(\"third dimension constrained (=2.5)\")\n",
    "plt.hist(constrained_samples[0, :, 2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}