{ "cells": [ { "cell_type": "markdown", "id": "48a3d38b", "metadata": {}, "source": [ "# Performance" ] }, { "cell_type": "code", "execution_count": 1, "id": "f8cffbab", "metadata": { "tags": [ "nbval-ignore-output" ] }, "outputs": [], "source": [ "import bdms\n", "import time\n", "import numpy as np\n", "import scipy\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import seaborn as sns" ] }, { "cell_type": "markdown", "id": "f1463497", "metadata": {}, "source": [ "## Runtime\n", "\n", "Runtime analysis of a two-state process run for 4 simulation time units with 1000 different seeds.\n", "For each seed we record the median of 5 repeated runtimes, as well as the number of nodes in the simulated tree.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "de22d0e6", "metadata": {}, "outputs": [], "source": [ "birth = bdms.poisson.DiscreteProcess([0.1, 1.0])\n", "mutation = bdms.poisson.ConstantProcess(1.0)\n", "mutator = bdms.mutators.DiscreteMutator((0, 1), np.array([[0, 1], [1, 0]]))" ] }, { "cell_type": "code", "execution_count": 3, "id": "70731773", "metadata": {}, "outputs": [], "source": [ "runtimes = []\n", "n_nodes = []\n", "\n", "for seed in range(1000):\n", " repeats = []\n", " for _ in range(5):\n", " tree = bdms.Tree(state=0)\n", " runtime = time.time()\n", " tree.evolve(\n", " 4.0,\n", " birth_process=birth,\n", " mutation_process=mutation,\n", " mutator=mutator,\n", " seed=seed,\n", " )\n", " repeats.append(time.time() - runtime)\n", " runtimes.append(np.median(repeats))\n", " n_nodes.append(sum(1 for node in tree.traverse()))" ] }, { "cell_type": "markdown", "id": "85a59c74", "metadata": {}, "source": [ "Plotting the runtime against the number of nodes in the tree, we see that the runtime scales linearly with the number of nodes in the tree." ] }, { "cell_type": "code", "execution_count": 4, "id": "186b258b", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(n_nodes, runtimes, s=10, alpha=0.5)\n", "plt.xlabel(\"number of nodes\")\n", "plt.ylabel(\"runtime (seconds)\")\n", "plt.xscale(\"log\")\n", "plt.yscale(\"log\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "b5262a87", "metadata": {}, "source": [ "## Growth rate" ] }, { "cell_type": "markdown", "id": "27e532a0", "metadata": {}, "source": [ "To assess how population size grows with time, we'll perform 1000 simulations with 1000 different seeds for each of several simulation times." ] }, { "cell_type": "code", "execution_count": 5, "id": "ef482c61", "metadata": {}, "outputs": [], "source": [ "sim_times = [1, 2, 3, 4]" ] }, { "cell_type": "code", "execution_count": 6, "id": "4e88b23e", "metadata": {}, "outputs": [], "source": [ "rng = np.random.default_rng(0)\n", "dat = []\n", "\n", "for i, sim_time in enumerate(sim_times):\n", " for _ in range(1000):\n", " tree = bdms.Tree()\n", " try:\n", " tree.evolve(sim_time, seed=rng)\n", " finally:\n", " dat.append([sim_time, len(tree)])\n", "\n", "df = pd.DataFrame(dat, columns=[\"time\", \"population size\"])" ] }, { "cell_type": "markdown", "id": "1aa9a74c", "metadata": {}, "source": [ "For a Yule process with unit per-particle birth rate (our default simulation), the population size at time $t$ is a geometric random variable with parameter $p=e^{-t}$.\n", "The plot below shows the empirical cumulative distribution function of population sizes at time $t$ for $t=1,2,3,4$, along with the theoretical cumulative distribution function of a geometric random variable with parameter $p=e^{-t}$." ] }, { "cell_type": "code", "execution_count": 7, "id": "3fdcdfba", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.displot(\n", " df,\n", " row=\"time\",\n", " x=\"population size\",\n", " aspect=3,\n", " height=2,\n", " log_scale=(True, False),\n", " kind=\"ecdf\",\n", ")\n", "for sim_time, ax in zip(sim_times, plt.gcf().axes):\n", " ax.get_lines()[0].set_label(\"simulated ECDF\")\n", " p = np.exp(-sim_time)\n", " ax.plot(\n", " scipy.stats.geom.cdf(range(1000), p),\n", " \"r.\",\n", " ds=\"steps-post\",\n", " label=\"theoretical CDF\",\n", " )\n", " ax.legend(loc=\"lower right\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "81a26674", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "bdms", "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": "3.12.1" } }, "nbformat": 4, "nbformat_minor": 5 }