{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ddffdd27-761b-44a7-996f-02b579be697c",
   "metadata": {},
   "source": [
    "# Mallows 3 last "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a8c66522-09e5-43c0-bd69-ee62874b5b27",
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import prod\n",
    "import sympy\n",
    "import numpy as np\n",
    "from actinvoting import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "376b0b6f-31dd-48d1-b905-0ff145822489",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.6931471805599453)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 3\n",
    "phi = sympy.Rational(50, 100)\n",
    "rho = - np.log(float(phi))\n",
    "rho"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ee967e60-96d4-4a9f-96a0-032b55591740",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.840802583309334$"
      ],
      "text/plain": [
       "0.840802583309334"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "culture = CultureMallows(m=m, phi=phi)\n",
    "session = WorkSession(culture=culture, c=m-1)\n",
    "rate = session.p_of_zeta / prod([session.zeta[j]**(1/2) for j in session.adversaries])\n",
    "rate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c45cb8a-1714-4f16-a12f-baa077b6801e",
   "metadata": {},
   "source": [
    "## Runtimes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d6d3cf05-d538-46c7-a4f1-9a0f5c000ffa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "run_time_str='0s'\n",
      "run_time_str='0s'\n",
      "run_time_str='0s'\n",
      "run_time_str='0s'\n",
      "run_time_str='0s'\n",
      "run_time_str='0s'\n",
      "run_time_str='0s'\n",
      "run_time_str='0s'\n",
      "run_time_str='0s'\n",
      "run_time_str='0s'\n",
      "run_time_str='0s'\n",
      "run_time_str='0s'\n",
      "354 μs ± 10.6 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "equivalent_probas = equivalent_batch(session=session, ns=[100], n_jobs=1, force_recompute=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c67484ea-1163-4e8c-8e63-89883a982372",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run_time_str='17s'\n"
     ]
    }
   ],
   "source": [
    "exact_probas = exact_batch(session=session, ns=[100], n_jobs=1, force_recompute=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "38bd4142-cf17-48d2-b113-1273de56603b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run_time_str='46s'\n"
     ]
    }
   ],
   "source": [
    "monte_carlo_probas = monte_carlo_batch(session=session, ns=[100], n_samples=10000, n_jobs=1, force_recompute=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "851de865-ae75-4791-8833-581bfd56183a",
   "metadata": {},
   "source": [
    "## Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e855bb3f-acb2-4ed6-99b7-80e551e90e62",
   "metadata": {},
   "outputs": [],
   "source": [
    "ns_equivalent_probas = list(range(2, 101))\n",
    "ns_exact_probas = list(range(2, 101))\n",
    "ns_monte_carlo_probas = list(range(2, 31))\n",
    "n_samples = 10000\n",
    "n_jobs = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b3342443-bdcc-432d-8de9-2e7130d44b9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading Mallows_m=3_phi=1_2_c=2_hash(ns)=-7142264137129868933_equiv.pkl\n"
     ]
    }
   ],
   "source": [
    "equivalent_probas = equivalent_batch(session=session, ns=ns_equivalent_probas, n_jobs=n_jobs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0a22021e-0ec3-4278-a9cc-57ba3af32ac3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading Mallows_m=3_phi=1_2_c=2_ns=[2,_3,_4,_5,_6,_7,_8,_9,_10,_11,_12,_13,_14,_15,_16,_17,_18,_19,_20,_21,_22,_23,_24,_25,_26,_27,_28,_29,_30]_n_samples=10000_mc.pkl\n"
     ]
    }
   ],
   "source": [
    "monte_carlo_probas = monte_carlo_batch(session=session, ns=ns_monte_carlo_probas, n_samples=n_samples, n_jobs=n_jobs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f3b2da43-30b7-4f50-8558-dc99752f3d56",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading Mallows_m=3_phi=1_2_c=2_hash(ns)=-7142264137129868933_exact.pkl\n"
     ]
    }
   ],
   "source": [
    "exact_probas = exact_batch(session=session, ns=ns_exact_probas, n_jobs=n_jobs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e39fc91b-62f5-4920-b48a-4356b164d378",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_simu_and_theo(\n",
    "    equivalent_probas=equivalent_probas, monte_carlo_probas=monte_carlo_probas, exact_probas=exact_probas,\n",
    "    ns_equivalent_probas=ns_equivalent_probas, ns_monte_carlo_probas=ns_monte_carlo_probas, ns_exact_probas=ns_exact_probas,\n",
    "    log_scale=True, file_name='mallows_3_last.tex', y_label=r\"$\\mathbb{P}(3 \\text{ is CW})$\", verbose=False\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ab925be6-f3ed-4ad8-88c6-2c464c6c3759",
   "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": "3.12.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}