From 90ac2a51d53b51915640f99a96ac557853a2b1a2 Mon Sep 17 00:00:00 2001 From: 8c82b2701c130ec4af8160ecac35027a <8c82b2701c130ec4af8160ecac35027a@app-learninglab.inria.fr> Date: Wed, 4 Jun 2025 14:01:10 +0000 Subject: [PATCH] fulfilled first version of module 2 exo1 --- module2/exo1/toy_notebook_fr.ipynb | 167 ++++++++++++++++++++++------- 1 file changed, 127 insertions(+), 40 deletions(-) diff --git a/module2/exo1/toy_notebook_fr.ipynb b/module2/exo1/toy_notebook_fr.ipynb index b1958bd..91b44ad 100644 --- a/module2/exo1/toy_notebook_fr.ipynb +++ b/module2/exo1/toy_notebook_fr.ipynb @@ -1,92 +1,179 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# À propos du calcul de $\\pi$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## En demandant à la lib math" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Mon ordinateur m’indique que $\\pi$ vaut *approximativement*" + ] + }, { "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.141592653589793\n" + ] + } + ], "source": [ - "variable = 10" + "from math import *\n", + "print(pi)" ] }, { - "cell_type": "code", - "execution_count": 2, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - " my_function <- function() { # create a function with the name my_function\n", - " print(\"Hello World!\")\n", - "} " + "## En utilisant la méthode des aiguilles de Buffon" ] }, { - "cell_type": "code", - "execution_count": 3, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "# Create some variables\n", - "x <- 1:10\n", - "y1 <- x*x\n", - "y2 <- 2*y1" + "Mais calculé avec la **méthode** des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon), on obtiendrait comme **approximation** :" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "metadata": {}, "outputs": [ { "data": { - "image/png": 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J+tuPln5s0ZjoPtts86++c/fuuy7I7Ugzww9miZvXDs5OnO4YuzK25+z8jrnq9/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\nAAAAAElFTkSuQmCC", "text/plain": [ - "plot without title" + "3.128911138923655" ] }, + "execution_count": 2, "metadata": {}, - "output_type": "display_data" - }, + "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)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Avec un argument \"fréquentiel\" de surface" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d’appel à la fonction\n", + "sinus se base sur le fait que si $X \\sim \\mathcal{U}(0, 1)$ et $Y \\sim \\mathcal{U}(0, 1)$ alors $P[X2 + Y2 \\leq 1] = \\pi/4$ (voir\n", + "[méthode de Monte Carlo sur Wikipedia](https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80)). Le code suivant illustre ce fait :" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ { "data": { - "image/png": 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PBw52cDANhERoYiIvTyy3r4YdNRgIrwcDgcpjNckl9++aVjx47btm2rXbt269at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\nKHYAAACKoNgBAAAo4v8AwdYrG5PbiT8AAAAASUVORK5CYII=", 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\n", "text/plain": [ - "plot without title" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "# Create a basic stair steps plot \n", - "plot(x, y1, type = \"S\")\n", - "# Show both points and line\n", - "plot(x, y1, type = \"b\", pch = 19, \n", - " col = \"red\", xlab = \"x\", ylab = \"y\")" + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "np.random.seed(seed=42)\n", + "N = 1000\n", + "x = np.random.uniform(size=N, low=0, high=1)\n", + "y = np.random.uniform(size=N, low=0, high=1)\n", + "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')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Il est alors aisé d’obtenir une approximation (pas terrible) de $\\pi$ en comptant combien de fois,\n", + "en moyenne, $X^2 + Y^2$ est inférieur à $1$ :" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "text/plain": [ + "3.112" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "4*np.mean(accept)" + ] } ], "metadata": { "kernelspec": { - "display_name": "R", - "language": "R", - "name": "ir" + "display_name": "Python 3", + "language": "python", + "name": "python3" }, "language_info": { - "codemirror_mode": "r", - "file_extension": ".r", - "mimetype": "text/x-r-source", - "name": "R", - "pygments_lexer": "r", - "version": "3.4.1" + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.4" } }, "nbformat": 4, -- 2.18.1