{ "cells": [ { "cell_type": "markdown", "id": "ddffdd27-761b-44a7-996f-02b579be697c", "metadata": {}, "source": [ "# Mallows 4 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 = 4\n", "phi = sympy.Rational(50, 100)\n", "rho = - np.log(float(phi))\n", "rho" ] }, { "cell_type": "code", "execution_count": 3, "id": "e6060822-3fbe-4038-8090-c93ce1b31df4", "metadata": {}, "outputs": [], "source": [ "tau = [-2*rho, -rho, 0, 0]" ] }, { "cell_type": "code", "execution_count": 4, "id": "ee967e60-96d4-4a9f-96a0-032b55591740", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.7003724308895327" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "culture = CultureMallows(m=m, phi=phi)\n", "session = WorkSession(culture=culture, c=m-1, tau=tau)\n", "rate = session.p_of_zeta / prod([session.zeta[j]**(1/2) for j in session.adversaries])\n", "float(rate)" ] }, { "cell_type": "markdown", "id": "3153071d-b0bc-4880-aeb8-3bc0b88475c7", "metadata": {}, "source": [ "## Runtimes" ] }, { "cell_type": "code", "execution_count": 5, "id": "65490980-6a1e-4b83-8a8b-616c1cd80a5c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "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", "run_time_str='0s'\n", 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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", "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", "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", "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", "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", "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", "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", "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", "run_time_str='0s'\n", "run_time_str='0s'\n", "run_time_str='0s'\n", "run_time_str='0s'\n", "361 μs ± 8.82 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n" ] } ], "source": [ "%%timeit\n", "equivalent_probas = equivalent_batch(session=session, ns=[25], n_jobs=1, force_recompute=True)" ] }, { "cell_type": "code", "execution_count": 6, "id": "77aba142-5146-4fe9-a023-7b7adb9e1a16", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "run_time_str='4m34s'\n" ] } ], "source": [ "exact_probas = exact_batch(session=session, ns=[25], n_jobs=1, force_recompute=True)" ] }, { "cell_type": "code", "execution_count": 7, "id": "ef011c44-14cd-4c2f-9f53-d2f27838ed64", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "run_time_str='16s'\n" ] } ], "source": [ "monte_carlo_probas = monte_carlo_batch(session=session, ns=[25], n_samples=10000, n_jobs=1, force_recompute=True)" ] }, { "cell_type": "markdown", "id": "eb8c92b7-33a9-4993-8070-311bc0938ddb", "metadata": {}, "source": [ "## Plot" ] }, { "cell_type": "code", "execution_count": 8, "id": "e855bb3f-acb2-4ed6-99b7-80e551e90e62", "metadata": {}, "outputs": [], "source": [ "ns_equivalent_probas = list(range(2, 51))\n", "ns_exact_probas = list(range(2, 26))\n", "ns_monte_carlo_probas = list(range(2, 21))\n", "n_samples = 10000\n", "n_jobs = -1" ] }, { "cell_type": "code", "execution_count": 9, "id": "1480c7e8-dc7e-460d-aea3-7ae376142e25", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loading Mallows_m=4_phi=1_2_c=3_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,_31,_32,_33,_34,_35,_36,_37,_38,_39,_40,_41,_42,_43,_44,_45,_46,_47,_48,_49,_50]_equiv.pkl\n" ] } ], "source": [ "equivalent_probas = equivalent_batch(session=session, ns=ns_equivalent_probas, n_jobs=n_jobs)" ] }, { "cell_type": "code", "execution_count": 10, "id": "0a22021e-0ec3-4278-a9cc-57ba3af32ac3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loading Mallows_m=4_phi=1_2_c=3_ns=[2,_3,_4,_5,_6,_7,_8,_9,_10,_11,_12,_13,_14,_15,_16,_17,_18,_19,_20]_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": 11, "id": "f3b2da43-30b7-4f50-8558-dc99752f3d56", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loading Mallows_m=4_phi=1_2_c=3_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]_exact.pkl\n" ] } ], "source": [ "exact_probas = exact_batch(session=session, ns=ns_exact_probas, n_jobs=n_jobs)" ] }, { "cell_type": "code", "execution_count": 12, "id": "e39fc91b-62f5-4920-b48a-4356b164d378", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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_4_last.tex', y_label=r\"$\\mathbb{P}(4 \\text{ is CW})$\", verbose=False\n", ")" ] }, { "cell_type": "code", "execution_count": null, "id": "7355e052-c33f-4924-8d6f-7c01881ca68c", "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 }