{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supreme court: Analysis in the best basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports\n",
    "import numpy as np\n",
    "from mcmpy import Data, MCM, MCMSearch, Basis, BasisSearch"
   ]
  },
  {
   "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": [
    "# Search objects\n",
    "basis_searcher = BasisSearch()\n",
    "mcm_searcher = MCMSearch()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Search for the best basis representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Operator 1: \t000100100\t Indices: 3\t6\t\n",
      "Operator 2: \t000001010\t Indices: 5\t7\t\n",
      "Operator 3: \t000000011\t Indices: 7\t8\t\n",
      "Operator 4: \t100010000\t Indices: 0\t4\t\n",
      "Operator 5: \t100000100\t Indices: 0\t6\t\n",
      "Operator 6: \t101000000\t Indices: 0\t2\t\n",
      "Operator 7: \t010000010\t Indices: 1\t7\t\n",
      "Operator 8: \t001000001\t Indices: 2\t8\t\n",
      "Operator 9: \t000000100\t Indices: 6\t\n"
     ]
    }
   ],
   "source": [
    "# The system is small enough to perform an exhaustive search\n",
    "opt_basis = basis_searcher.exhaustive(data)\n",
    "opt_basis.print_details()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entropy of operator 0 :\t 0.25176\n",
      "Entropy of operator 1 :\t 0.32138\n",
      "Entropy of operator 2 :\t 0.37267\n",
      "Entropy of operator 3 :\t 0.37486\n",
      "Entropy of operator 4 :\t 0.38776\n",
      "Entropy of operator 5 :\t 0.41832\n",
      "Entropy of operator 6 :\t 0.44482\n",
      "Entropy of operator 7 :\t 0.52134\n",
      "Entropy of operator 8 :\t 0.58803\n"
     ]
    }
   ],
   "source": [
    "# These operators are ranked from low to high entropy\n",
    "for i in range(n):\n",
    "    # Take the ith column of the matrix\n",
    "    spin_op_i = opt_basis.matrix[:,i]\n",
    "    print(\"Entropy of operator\", i, \":\\t\", np.round(data.entropy_of_spin_operator(spin_op_i), 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Basis transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "transformed_data = opt_basis.gauge_transform_data(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Search for the optimal MCM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MCM contains 9 variables divided into 3 components\n",
      "Total log-evidence: -3154.42\n",
      "Component 0 : \t100000000\t Size: 1\t Log-evidence: -228.947\n",
      "Component 1 : \t011000100\t Size: 3\t Log-evidence: -970.39\n",
      "Component 2 : \t000111011\t Size: 5\t Log-evidence: -1955.08\n"
     ]
    }
   ],
   "source": [
    "# The system is small enough to perform an exhaustive search\n",
    "opt_mcm = mcm_searcher.exhaustive(transformed_data)\n",
    "opt_mcm.print_details()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analysis\n",
    "\n",
    "##### Log-evidence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The log-evidence of the complete model:  -3305.546575913697\n",
      "The log-evidence of the independent model:  -3327.0799458467227\n",
      "The log-evidence of the optimal MCM:  -3154.421230299753\n"
     ]
    }
   ],
   "source": [
    "print(\"The log-evidence of the complete model: \", transformed_data.log_evidence(MCM(n, \"complete\")))\n",
    "print(\"The log-evidence of the independent model: \", transformed_data.log_evidence(MCM(n, \"independent\")))\n",
    "\n",
    "print(\"The log-evidence of the optimal MCM: \", transformed_data.log_evidence(opt_mcm))"
   ]
  }
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