From 4e7e615987ece12152b3d9a1c30003046a40713a Mon Sep 17 00:00:00 2001 From: 12cc772fde428a92a737775c5b8ea0f8 <12cc772fde428a92a737775c5b8ea0f8@app-learninglab.inria.fr> Date: Tue, 3 Oct 2023 15:46:56 +0000 Subject: [PATCH] module2_exo1 --- module2/exo1/toy_notebook_fr.ipynb | 147 ++++++++++++++++++++++++++++- 1 file changed, 144 insertions(+), 3 deletions(-) diff --git a/module2/exo1/toy_notebook_fr.ipynb b/module2/exo1/toy_notebook_fr.ipynb index 0bbbe37..7592f4d 100644 --- a/module2/exo1/toy_notebook_fr.ipynb +++ b/module2/exo1/toy_notebook_fr.ipynb @@ -1,5 +1,147 @@ { - "cells": [], + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 1 On the computation of π\n", + "1.1 Asking the maths library\n", + "My computer tells me that π is approximatively\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.141592653589793\n" + ] + } + ], + "source": [ + "from math import *\n", + "print(pi)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 1.2 Buffon’s needle\n", + "Applying the method of Buffon’s needle, we get the approximation\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.128911138923655" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "np.random.seed(seed=42)\n", + "N = 10000\n", + "x = np.random.uniform(size=N, low=0, high=1)\n", + "theta = np.random.uniform(size=N, low=0, high=pi/2)\n", + "2/(sum((x+np.sin(theta))>1)/N)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 1.3 Using a surface fraction argument\n", + "A method that is easier to understand and does not make use of the sin function is based on the\n", + "fact that if X ∼ U(0, 1) and Y ∼ U(0, 1), then P[X2 + Y2 ≤ 1] = π/4 .\n", + "The following code uses this approach:\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "np.random.seed(seed=30)\n", + "N = 2000\n", + "x = np.random.uniform(size=N, low=0, high=1)\n", + "y = np.random.uniform(size=N, low=0, high=1)\n", + "accept = (x*x+y*y) <= 1\n", + "reject = np.logical_not(accept)\n", + "fig, ax = plt.subplots(1)\n", + "ax.scatter(x[accept], y[accept], c='b', alpha=0.2, edgecolor=None)\n", + "ax.scatter(x[reject], y[reject], c='r', alpha=0.2, edgecolor=None)\n", + "ax.set_aspect('equal')\n" + ] + }, + { + "cell_type": "raw", + "metadata": {}, + "source": [ + "It is then straightforward to obtain a (not really good) approximation to π by counting how\n", + "many times, on average, X\n", + "2 + Y\n", + "2\n", + "is smaller than 1:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.122" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "4*np.mean(accept)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], "metadata": { "kernelspec": { "display_name": "Python 3", @@ -16,10 +158,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 } - -- 2.18.1