{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supreme court: Analysis in the original basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports\n",
    "from mcmpy import Data, MCM, MCMSearch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The dataset contains 895 datapoints, of which 128 different ones.\n"
     ]
    }
   ],
   "source": [
    "# Data object\n",
    "\n",
    "n = 9   # Number of variables\n",
    "q = 2   # Number of states\n",
    "data = Data('../../input/US_SupremeCourt_n9_N895.dat', n, q)\n",
    "\n",
    "print(\"The dataset contains %i datapoints, of which %i different ones.\" %(data.N, data.N_unique))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# MCMSearch object\n",
    "searcher = MCMSearch()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Search for the optimal MCM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MCM contains 9 variables divided into 2 components\n",
      "Total log-evidence: -3300.4\n",
      "Component 0 : \t101110100\t Size: 5\t Log-evidence: -1754.41\n",
      "Component 1 : \t010001011\t Size: 4\t Log-evidence: -1545.98\n"
     ]
    }
   ],
   "source": [
    "# The system is small enough to perform an exhaustive search\n",
    "opt_mcm = searcher.exhaustive(data)\n",
    "opt_mcm.print_details()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analysis\n",
    "\n",
    "##### Log-evidence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The log-evidence of the complete model:  -3305.546575913696\n",
      "The log-evidence of the independent model:  -5258.100240438084\n",
      "The log-evidence of the optimal MCM:  -3300.395469673639\n"
     ]
    }
   ],
   "source": [
    "# Writing the partition as a 1D gray code array\n",
    "print(\"The log-evidence of the complete model: \", data.log_evidence([0,0,0,0,0,0,0,0,0]))       # All variables in component 0\n",
    "print(\"The log-evidence of the independent model: \", data.log_evidence([0,1,2,3,4,5,6,7,8]))    # All variables in a different component\n",
    "\n",
    "print(\"The log-evidence of the optimal MCM: \", data.log_evidence(opt_mcm))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note** that it is advised to used MCM objects as input parameters as there is no check if a given array is a valid partition.<br>\n",
    "The same results can be obtained in the following way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The log-evidence of the complete model:  -3305.546575913696\n",
      "The log-evidence of the independent model:  -5258.100240438084\n",
      "The log-evidence of the optimal MCM:  -3300.395469673639\n"
     ]
    }
   ],
   "source": [
    "print(\"The log-evidence of the complete model: \", data.log_evidence(MCM(n, \"complete\")))\n",
    "print(\"The log-evidence of the independent model: \", data.log_evidence(MCM(n, \"independent\")))\n",
    "\n",
    "print(\"The log-evidence of the optimal MCM: \", data.log_evidence(opt_mcm))"
   ]
  }
 ],
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