{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b05a0b08-8d46-4964-8ce2-42ce6de5b7bf",
   "metadata": {},
   "source": [
    "# Demo for Multiphase Monte Carlo in hopsy\n",
    "\n",
    "Multiphase Monte Carlo works well for some uniform sampling problems. Here is a short demo on how to use it from hopsy.\n",
    "In contrast to the BenchmarkingMultiphaseMonteCarloSampling.ipynb, which writes a custom implementation of the algorithm to demonstrate hopsys flexibility, this notebook uses the preimplemented variant in hopsy.\n",
    "\n",
    "For everyday sampling this preimplemented variant is convenient.\n",
    "Reference: https://drops.dagstuhl.de/opus/volltexte/2021/13820/pdf/LIPIcs-SoCG-2021-21.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "74de923a-0c62-4c4c-85e9-00e3c4e36e6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import hopsy\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8abaac4c-b7c3-44a0-8997-39704e191d76",
   "metadata": {},
   "source": [
    "## define problem and run sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7e252552-4816-4c1a-8a24-bb93caf1bbd1",
   "metadata": {},
   "outputs": [],
   "source": [
    "bp = hopsy.BirkhoffPolytope(5)\n",
    "problem =  hopsy.Problem(bp.A, bp.b)\n",
    "# gurobi can find the chebyshev center at 0, but glpk can not. For CI, the start is hardcoded, because we don't have gurobi licenses on CI servers\n",
    "start = np.zeros(problem.A.shape[1])\n",
    "seeds = [42, 43, 44, 45]\n",
    "samples, iterations, ess, runtime = hopsy.run_multiphase_sampling(problem=problem, seeds=seeds, steps_per_phase=100, starting_points=[start for s in seeds], n_procs=len(seeds))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ec22a7a-4627-47fd-9009-1c8b7c2b77ca",
   "metadata": {},
   "source": [
    "## visualize samples "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "41be9690-9947-4699-b048-b389b104dfca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/rqysrAKfLykpKU+/qampeuqpp9SiRQtVrlw5z3vmrXnz5qljx46qUqWKKlasqMsvv1xPPPGETpw4UWTb2bNnu+pydymZjh07yuFwuM7s/eWXXzR8+HA1bNhQ5cqVU/369TV48GDt27cvT7sff/xRAwcOVMOGDVW2bFnFxsZqxIgR+u9//+vRmD755BP17t1b9erVU9myZVW5cmW1atVKEydO1J9//llguwEDBsjhcKh+/fqSpBMnTuif//ynLrvsMlWoUEGVK1fWtddeq/fff7/IGhYvXqyePXvqoosuUlRUlCpVqqSGDRuqffv2mjBhgtsz2op6PZ2OHDmixx9/3PX+ly1bVvXr11e/fv20du3aQuu68DO2Y8cO3Xvvvapfv76ioqJUq1Yt3XbbbSV6PwxvfPLJJ5Kk6Oho3X777W7Xueiii9S1a1dJ0urVq3Xy5MnSKs9vkRvkBrlBbuQWSrkBa8gNcoPcIDdyIzfy6tSpk+vfu3fv9mEl/oPcIDfIDXIjN3Ijr9xXHDlz5owPK/Ef5Aa5QW6QG7mFam6kpaXpH//4h6TzJ/tVq1at5J7M+LEvv/zSSDKSzBNPPOFxu+uvv97V7ptvvnG7znvvvWcqVKjgWs/dz+DBg012dna+tnv27HGtM2vWLDN+/PgC+6hRo4b56aef3Nbw9ddfm+jo6EJrkGSSk5PztY2LizOSTP/+/fM8XlRfuV/L1157zfXYunXrCn1Np06d6lp348aNha7rbT25HTt2zLRt27bQ9S+99FKzd+9et8/3xBNPuNbbuXOnqV+/fr72s2bN8rh+Y4zJzs42vXv3LrCehg0bml9//bXQv9VZs2a5lu/Zsyff8g4dOhhJpkOHDmblypWmUqVKbp+rZs2a5ueffzbGGDNv3jwTGRnpdr24uDjz+++/Fzim48ePm86dOxf6OtesWbPAv4v+/fu7nmf79u1uX2fnz3333ee2j7Nnzxb6ujp/rrzySq9fT2OMWb58eZGfr/vuu8/k5OS4bZ/7M/bxxx+b8uXLu+0jPDzcfPjhhwW+1lY5++/QoUOR62ZmZprw8HAjydxwww2Frjtp0iRX31988YVN1foPcoPcIDfIDXKjg+U+cr9O3v7dBypyg9wgN8gNcqODbX0uWrTI1e8LL7xgW7/+hNwgN8gNcoPc6GBbn++8846r33HjxtnWrz8hN8gNcoPcIDc6eN12xIgRRpK59tprXY85/8Yu/MwVV1BOkj/77LOudlOmTMm3/KOPPjIOh8O1AXjxxRfNsmXLzObNm82iRYtM9+7dXe1Hjx6dr33uELnmmmtcb/S8efPMpk2bzKpVq0xCQoJrnb///e/5+jhz5oz5y1/+YiSZSpUqmYcffth8/vnnZvPmzWbdunVm3rx55v777zd169b1KkR++OEHs3z5ctdz/+tf/zI//PBDnp/Dhw8bY4w5ceKEKVeunJFkhg4dWuhresUVVxhJ5m9/+1uh613I+Zy33nqrkWT+8pe/5KvH6ezZs+bqq6/O8+FZsGCB2bRpk/n0009Nz549XcsaNWpkTp48me/5cofI3/72NxMREWH+8Y9/mJUrV5pNmzaZDz74wHz77bdejWHUqFGuPps0aWJmzJhhNm7caFatWmWGDRtmwsLCTOvWrW0JkYsvvthUqVLFxMbGmldffdWsX7/epKSkmAcffND1N9u2bVuzYcMGU6ZMGXPppZead955x2zYsMF8+eWXpl+/fq7n6dOnj9vxnDlzxrRs2dK1AezXr5/54IMPzL///W+TkpJinn76aVOtWjUjyVSpUsVtYDtDpEaNGubiiy82lSpVMo8//rj56quvzKZNm8zbb79tLrroIlcty5Yty9fHq6++6lrerl07M3v2bJOSkmK2bNliVq5caV544QVz3XXXmTZt2nj9em7dutUVsBEREWb06NHmyy+/NBs2bDDTp083DRo0cLV/+OGH3b5Ozs9Yy5YtTdmyZU2DBg3MtGnTzL///W+zbt06k5SUZMqWLWskmejoaPPf//7XbT9WeRMiP/zwg2v9UaNGFbruxx9/7Fr3tddes6dYP0JukBvkBrlBbnSw3AeT5E943I7cIDfIDXKD3MjvgQcecPX72Wef2davPyE3yA1yg9wgNzoUq5/jx4+bLVu2mNGjR5uIiAgjyURGRprdu3fbU6ifITfIDXKD3CA3OnjV7ttvvzUOh8NERESYbdu2uR5nktyLEFm1apWr3aBBg/IsO3LkiImJiXEtc3cklTHGPProo0aSCQsLM9u3b8+zLHeISDL33nuvOXfuXL4+hgwZ4lpny5YteZatXr3atcxdSDhlZ2eb1NTUfI8XFCIX1lfUF5zOjU5MTIzJyMhwu86WLVtc/b300kuF9leQ3EfmFGTatGmu50lISHD7mjrfl4I+/LlDJCwszCxfvtxSvU7ff/+9CQsLc21M3AXXu+++m+fvoTgh4gwSdxukcePGudapUaOGueaaa0x6enq+9ZxHL5UpU8ZtP87XsHLlymbTpk1ux713715Tp04dI8n07ds333Ln++n82/nxxx/zrbNr1y7XRvaWW27Jt7x9+/ZGkrnqqqsK/Bwac/7ouwsV9Xo6Qz08PNzt38Dx48fNX//6V9ffibv6nZ8x6fzRXu4+h++9955rnRdffLHAMVjhTYh8/vnnrvWfe+65QtfduHGja93x48fbVK3/IDfIjQuRG+SGMeSGp5gkf8LjduQGuUFukBvkRl4HDx50nTFUo0YNc/r0aVv69TfkBrlxIXKD3DCG3ChK7vfnwp/y5cubRYsW2VqrPyE3yI0LkRvkhjHkRkGysrLMZZddZiSZxMTEPMtKapI8qO5J7pT7+vQX3nfgjTfeUGpqqurWravXX39dZcqUcdvHxIkTVbduXZ07d05z5swp8Lnq1KmjV1991e29J8aNG+f6d0pKSp5lf/zxh+vf1157bYH9lylTRtHR0QUuL64hQ4ZIOn9vi48//tjtOrNmzZIkRUZG6p577imxWl577TVJUo0aNTRt2jS3r+nEiRPVtGlTSdLbb7+tzMzMAvsbMGCArr/++mLV9Oabb+rcuXOSpLfeeksVK1bMt05CQoJuvPHGYj1Pbq+88opq1KiR7/Hc90o5evSo3nnnHZUvXz7feiNGjJAknT17VuvWrcuz7NSpU67X+amnntKVV17ptoa4uDhNmDBBkrRgwQKlp6cXWO9TTz2lyy67LN/jjRs3Vs+ePSXJ7f0xnJ+Ba665psDPoSRVrVq1wGXubNiwQRs3bpQk3XvvvW7/BqpUqaK33npL0vl7xLz++uuF9jlz5ky3n8O+ffvqL3/5i6T8n/HSlPve4u7+RnOrUKGC69+nTp0qsZoCDbnhOXKjcOQGuSH5f26g+MgNz5EbhSM3yA0p8HPDGKNhw4a59ksmTJigsmXL+rgq/0JueI7cKBy5QW5IgZ8bTnfeeae2b9+u22+/3del+B1yw3PkRuHIDXJDCpzceOaZZ7Rt2zY1aNDA9f6VtKCcJM/9Qc89eSRJn376qSSpR48eioqKKrCPMmXK6Oqrr5akfB/E3Hr16lVgP02aNHHV8uuvv+ZZVqdOHde/nRtpX7j22mt1ySWXFFhHVlaW5s2bJ0m6+eabVb169RKp4+DBg/r5558lSXfccYcqVarkdr0yZcpo4MCBks7/D8KWLVsK7PPuu+8udl2rVq2SJDVr1qzADa4kDRo0qNjPJUmVK1fWDTfc4HZZgwYNXK/L3/72N1166aVu12vevLnr3xf+3a1Zs0apqamSzv/tFsb5PzfZ2dnavHmz23UcDof69u1bYB/O1+z48eM6ceJEnmXOz0BycrKOHj1aaC3ecL5nkjR48OAC12vbtq3rNczd5kLNmjXT3/72N7fLHA6HWrRoISn/a12azpw54/p3ZGRkoevm3l6dPn26xGoKNOSG58iNwpEb5EYg5AaKj9zwHLlROHKD3AiG3Jg0aZKSk5MlSZ06ddJ9993n44r8D7nhOXKjcOQGuRGIufH000/rhx9+0A8//KBvvvlGb7zxhlq2bKkPP/xQffv21a5du3xdot8hNzxHbhSO3CA3AiU3du3apaefflqSNG3aNJUrV65UnjcoJ8lzB0fuoyNycnL0n//8R5I0ffp0ORyOQn8WLlwoKe9RURdyHvVTkCpVquSrSZLatWunhg0bSpIefPBBtWnTRpMnT9Y333yjrKwszwdrA+cH7YsvvtC+ffvyLPv000917NgxSfZtKN358ccfXf++6qqrCl039/Lc7S5U0AffU5mZma7/SWvdunWh67Zp06ZYz+V08cUXuz3CzKly5cqS5Ar+wtaR8v/dbdq0yfXvOnXqFPr3f/nll7vWLegzUL169TxHNl4o91FSF9bSv39/SdIvv/yixo0ba9CgQfrggw904MCBAvvzhPNvIjIyUldccUWh6zr/lnbt2lXg566oz7hzjBeOrzTlPkujqO1H7qMTSytoAgG54R1ywz1yg9yQAiM3UHzkhnfIDffIDXJDCvzceP/9911neTRo0EDz5s1TWFhQftVULOSGd8gN98gNckMKzNyoW7euLr/8cl1++eW65pprNHz4cG3YsEHDhg3T2rVrddVVV+m7777zdZl+hdzwDrnhHrlBbkiBkxvDhg3TmTNnFB8fr+7du5fa8wblnkvuozZy/xEfP35cZ8+e9bq/jIyMApe5uxxEbs6dw5ycnDyPR0REKDk52XWkx8aNG/Xoo4+qXbt2qly5srp166Z58+bla1cS+vfvr4iICBlj9O677+ZZNnPmTEnn/2emoCOA7HD8+HHXv2vWrFnourVr13bb7kLOALfqzz//lDHGo5pq1apVrOdy8vTvqbD1cn8hceHfz3//+19LdRX0GfC0Xne1DBo0SI8++qjKlCmj1NRUzZo1S3379lVsbKwaN26ssWPHWjp6yfk3UbVq1UIvcyL972/JGJPv0kVOVj/jpSn3kYlFXUI996Vliro0eyghN7xDbrhHbvwPuVEwf8gNFB+54R1ywz1y43/IjYL5c24sXbpUAwcOlDFGtWvX1sqVK/N8fvA/5IZ3yA33yI3/ITcK5s+5kVt4eLheeeUVxcbG6s8//3RdXhnnkRveITfcIzf+h9womD/kxsyZM/Xll1+qUqVKmjp1aqk+d+GvcIDaunWr699NmjRx/Tv3mzxkyBCNGjXKo/6KunyxVX/961/1ww8/KDk5WcnJyfr666/1yy+/6PTp01q+fLmWL1+uF198UZ999lmRG7HiqFWrlnr06KHFixdr9uzZmjBhghwOhw4ePKgVK1ZIOn9fivDw8BKrIbfCjjTyhp312lWTr+X+DGzZskUREREetbvoootKpJ6nn35aQ4cO1fvvv6/Vq1fr3//+tzIyMrR79269+OKLevXVV/XKK69o+PDhXvcdLO+ZJ3K/P0UdqbZ//37Xv2NjY0uspkBDbniH3ChasGyDyA3APXLDO+RG0YJlG0RuhI6vvvpKvXr1UnZ2tqpUqaLly5erUaNGvi7Lb5Eb3iE3ihYs2yByI7RFRkaqW7duevvtt7Vu3Tr9/vvvqlu3rq/L8gvkhnfIjaIFyzaI3AhOzzzzjCSpQ4cOBd4bPfcBEh9++KEkqUKFCrr55puL9dxBOUm+cuVK17/btWvn+nfuo66MMXkut+Ar4eHh6tmzp3r27ClJOnTokJYtW6bXXntNmzdv1ubNmzVs2DAtXry4ROsYMmSIFi9erD179mjNmjXq2LGj5syZ49roOO+TUVJyvzeHDx8udN3cl8bI3c5uuS/rUVRNRS33F7kvHVKjRo0SCwdvxMXF6dFHH9Wjjz6q7Oxsbdy4UfPnz9f06dN15swZjRw5UldddZXr3hhFcf5NHDt2TGfPni30aCvn35LD4Sj2kXm+dMkllyg8PFw5OTnavn17oevmXl7QfV9CEbnhPXIjP3KjdJAb8AfkhvfIjfzIjdJBbthvw4YNuvnmm3XmzBlVrFhRn3/+ebEvBxrsyA3vkRv5kRulg9woXTVq1HD9+7fffmOS/P8jN7xHbuRHbpQOcqP4nLeIXbJkiZYsWVLk+nfddZek8699cSfJg+5y6z/++KNWr14t6fxZkq1atXIti4yM1GWXXSZJ+uabb3xSX1Hq1KmjgQMHat26dWrZsqWk838Yp0+f9rgPK0eYdOvWzbVBmTVrVp7/tm/fXhdffLHXfXojd6CvX7++0HU3bNjgtp3dypYt6xr3xo0bC123qOX+IveG2B8/AxEREbrmmmv08ssva968eZLO/w+f8/45nnD+TWRlZbnu0VMQ59/SxRdfXGJHVJaGyMhI131j1q1bV+h9f9asWSNJioqKyrN9DGXkBrlhF3Kj9JEb8AVyg9ywC7lR+siN4vv+++/VrVs3nTp1SmXLllVycnKR990MdeQGuWEXcqP0kRsl7/fff3f9m9sCnkdukBt2ITdKH7kReIJqkvz06dNKSEhw3Wdh3Lhx+Y6yuOWWWySdP5ty+fLlpV6jpyIiItShQwdJ0tmzZ3XixAmP25YtW9b1b+cRGEUJCwtzHU21cOFCLVu2TDt37pR0/t4KJe0vf/mL66zW+fPnF3hf5ZycHM2ePVvS+XtyOIO2pHTt2lWS9MMPP+S5zM2FnPc28Xddu3Z13YPilVdecX1W/FGXLl1c/859H56iON8zqfD3Zd26dfrpp5/ytQlUzqM109LS9PHHH7td58CBA1q1apWk869v7nuZhypy4zxywz7khu+QGygN5MZ55IZ9yA3fITe8t3PnTl1//fX6888/FRERoUWLFqljx46+LsuvkRvnkRv2ITd8h9ywX3p6uj7//HNJUrly5dS4cWMfV+R75MZ55IZ9yA3fITc8t3fvXhljCv1xbk8kuR7bu3dvsZ87aCbJf/rpJ7Vr1871Qe/QoYNGjBiRb71Ro0a5jkobOHCgtm3bVmi/S5cu1ffff297vSkpKfrll18KXJ6VleU647NixYp5Lj1TlGrVqrmOGtm9e7fH7QYNGiSHw6GMjAxXoFSqVEm9e/f2uI/iuO+++yRJR44c0QMPPOB2nYkTJ7o++Pfee6+ioqJKtKZhw4a5jlwbOnSo0tPT863z/vvv67PPPivROuxSuXJl3X///ZKkb7/9VqNHj9a5c+cKXP/w4cN65513SqSW9957T2fPni1wufN+MZLUoEEDj/tt06aN6wjLt99+23XkZW6pqakaNmyYpPP/A+VuWxFohgwZopiYGEnS+PHjdezYsTzLc3JyNHLkSNclhh566KFSr9HfkBv/Q27Yh9wgNxC8yI3/ITfsQ26QG4Hit99+U9euXXX48GGFh4dr3rx56t69u6/L8mvkxv+QG/YhN8iNQHD06FEtWrSo0HXOnDmjQYMGue4x26tXL5UrV640yvNb5Mb/kBv2ITfIDRQuYO5J/t///lc//vij6/f09HT9+eef+v7777V69WqtXLnSddTI3//+dy1cuFARERH5+qlVq5beffdd9erVS4cOHVKrVq00YMAA3XjjjbrooouUnZ2tAwcOaMOGDVq4cKF+/fVXJScn235/rdWrV+upp55S+/btddNNN+lvf/ubatSoodOnT2vnzp168803tWXLFknS4MGDC73vwIXKlCmj1q1b65tvvtHMmTPVokULXXHFFa7Xo2rVqm7vdVG/fn117dpVK1eudN3L4I477lCFChVsGHHRhg8frvfff1/r1q3TrFmztG/fPo0cOVINGjTQoUOHNHPmTNcZso0aNdKECRNKvKbmzZvrvvvu07Rp07Rp0ya1atVKjzzyiJo1a6bU1FQtWLBAb731llq1aqVNmzaVeD12ePLJJ7VmzRqtX79eU6dO1VdffaV7771XV1xxhSpUqKA///xT27Zt06pVq/T555+rWbNmGjJkiO119OvXT+PGjdPtt9+ua665Ro0aNVLZsmV1+PBhrVy5Um+88Yak8/8Tdffdd3vV99tvv62rrrpKWVlZ6t69u/7xj3/o5ptvVoUKFbR161ZNmTJFv/76q6TzR2T6+v49//nPfwq8dMoff/zhOrrQqVevXvkuQVW1alU988wzGj58uPbt26errrpKjz32mJo1a6aDBw/q5Zdf1pdffinp/D07QuGMD3KD3CA37EFuBGduSOePrs99dPvatWvd/luSateurW7dulkvOgCQG+QGuWEPciP4cuPYsWPq2rWr9u/fL0kaO3asmjZtmmebeaEqVaoE/X1lyQ1yg9ywB7kRfLlx6tQp9erVS40bN1Z8fLzatGmjunXrKioqSkePHtWGDRs0Y8YM15jr1q2rZ555pqSG4zfIDXKD3LAHuRF8ueFTxo99+eWXRpLHPzVq1DBPP/20yc7OLrLvTz/91FStWrXIPsPCwswXX3yRp+2ePXtcy2fNmlXo88TFxRlJpn///nkef+KJJzwa06233moyMjI87tdpyZIlxuFwuO3ziSeeKLDejz76KM+633zzTaHj81T//v2NJBMXF1foeseOHTNt27Yt9DW59NJLzd69e922z/262iUrK8vcfvvtBdbToEEDs3v37kJf31mzZrmW79mzJ9/yDh06GEmmQ4cOhdZS1PvuVNR7nZaWVuiYcv906tQpX3tP38/Cxu3Jc8fExJjPP//cq36dli9fbqKjowvt/7777jM5OTlu23v6Wnv6WhTG0+1BUWM2xph//vOfBX72JZnu3bub06dPW67V35Eb5Aa5kRe5UXS/TqGYG86aPfkp6m8tUJEb5Aa5kRe5UXS/TqGUG95uKz0ZV6AiN8gNciMvcqPofp1CKTdyb5OK+rn66qvN7t27Ldfq78gNcoPcyIvcKLpfp1DKDU84/8bs/GwYY0zAnEmeW1hYmCpVqqSYmBjFxcXpyiuvVPv27dWjRw+Pb05/8803a8+ePXr77bf12Wefadu2bTp+/LjKlCmj2rVr67LLLlPnzp3Vq1cvxcbG2j6GcePG6W9/+5tWrVqlrVu36uDBg67Ly9SuXVtt2rRRQkKCbrrpJkv933TTTVq9erWmTp2qjRs36siRI8rOzi6yXc+ePVWxYkWdOnVKTZs21TXXXGPp+a2qWrWqvv76a73//vuaN2+etm7dquPHjys6OlrNmjVTr169dO+993r8PtvBea+19957T2+99Za+//57ZWdnKy4uTrfddpvGjRunKlWqlFo9dqhUqZIWLVqktWvX6t1331VKSooOHjyo06dPKzo6Wo0aNVKbNm1000036frrry+RGn788UctXbpUa9eu1e7du3X48GGdOHFClSpVUtOmTXXDDTdoxIgRqlWrlqX+r7/+ev3yyy96+eWX9dlnn+nXX39VZmamatWqpfbt22v48OFq166dzaPyvYkTJ+qGG27Qa6+9ppSUFB0+fFiVK1dW8+bNNXDgQN11112+LtEnyI2ikRv2ITfIDQQ+cqNo5IZ9yA1yA4GP3CgauWEfcoPc8Hf16tVTSkqKVqxYoQ0bNmjfvn06fPiwTp48qYoVK6pevXpq1aqVevfurRtuuMF1KehQQm4UjdywD7lBbqBgDmP8+M72KHW7du3SJZdcIkl65pln9PDDD/u4IgCAPyM3AADeIDcAAN4gNwAA3iA3AHgjzNcFwL/MnDlT0vn7fiQkJPi4GgCAvyM3AADeIDcAAN4gNwAA3iA3AHiDSXK4nDhxQm+99Zak85clqV27to8rAgD4M3IDAOANcgMA4A1yAwDgDXIDgLcC8p7ksM9///tfpaWl6eDBg0pKStLx48flcDiUmJjo69IAAH6I3AAAeIPcAAB4g9wAAHiD3ABQHEySh7iHH35Y7777bp7HRo4cqZYtW/qoIgCAPyM3AADeIDcAAN4gNwAA3iA3ABQHk+SQJEVGRqpRo0a699579Y9//MPX5QAA/By5AQDwBrkBAPAGuQEA8Aa5AcAKhzHG+LoIAAAAAAAAAAAAAABKQ9CeSX7u3DkdPHhQlSpVksPh8HU5AGArY4xOnjypv/zlLwoLC/N1OUGB3AA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      "text/plain": [
       "<Figure size 2000x1600 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## visualization settings\n",
    "title_fs = 24\n",
    "label_fs = 16\n",
    "tick_fs = 16\n",
    "legend_fs = 16\n",
    "img_format = \"pdf\"\n",
    "##\n",
    "\n",
    "\n",
    "n_dims = samples.shape[2]\n",
    "n_cols = 5\n",
    "n_rows = int(n_dims / n_cols) + 1\n",
    "\n",
    "plt.figure(figsize=(n_cols * 4, n_rows * 4))\n",
    "plt.subplot(n_rows, n_cols, 1)\n",
    "plt.suptitle(\n",
    "    \"Marginal densities for BP(5)\", y=1.0, fontsize=title_fs\n",
    ")\n",
    "\n",
    "for dim in range(n_dims):\n",
    "    plt.subplot(n_rows, n_cols, dim + 1)\n",
    "    plt.title(f\"Density for dimension {dim}\", fontsize=title_fs - 4)\n",
    "    _, bins, _ = plt.hist(\n",
    "        samples[0,:, dim],\n",
    "        bins=20,\n",
    "        density=True,\n",
    "        label=\"chain 1\" if dim == 0 else None,\n",
    "        alpha=0.75,\n",
    "    )\n",
    "    plt.hist(\n",
    "        samples[1,:, dim],\n",
    "        bins=bins,\n",
    "        density=True,\n",
    "        label=\"chain 2\" if dim == 0 else None,\n",
    "        alpha=0.75,\n",
    "    )\n",
    "    plt.hist(\n",
    "        samples[2,:, dim],\n",
    "        bins=bins,\n",
    "        density=True,\n",
    "        label=\"chain 3\" if dim == 0 else None,\n",
    "        alpha=0.75,\n",
    "    )\n",
    "    plt.hist(\n",
    "        samples[3,:, dim],\n",
    "        bins=bins,\n",
    "        density=True,\n",
    "        label=\"chain 3\" if dim == 0 else None,\n",
    "        alpha=0.75,\n",
    "    )\n",
    "    plt.xticks(fontsize=tick_fs)\n",
    "    plt.yticks(fontsize=tick_fs)\n",
    "\n",
    "plt.figlegend(fontsize=legend_fs)\n",
    "plt.tight_layout(rect=[0, 0.03, 1, 0.95])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1ada9abf-80e3-4c3c-be2d-b4781ff167e5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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