From d84068d18d33465866c4bb0f1016b1bd4483f1b6 Mon Sep 17 00:00:00 2001 From: adf52b78a1975b5ac63bbd1f3ffc1b59 Date: Wed, 19 Jul 2023 10:43:55 +0000 Subject: [PATCH] Jupyter test. Help. --- module2/exo1/Untitled.ipynb | 34 +++++++ module2/exo1/Untitled1.ipynb | 157 +++++++++++++++++++++++++++++ module2/exo1/toy_notebook_fr.ipynb | 48 ++++++++- 3 files changed, 236 insertions(+), 3 deletions(-) create mode 100644 module2/exo1/Untitled.ipynb create mode 100644 module2/exo1/Untitled1.ipynb diff --git a/module2/exo1/Untitled.ipynb b/module2/exo1/Untitled.ipynb new file mode 100644 index 0000000..f00390e --- /dev/null +++ b/module2/exo1/Untitled.ipynb @@ -0,0 +1,34 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext rpy2.ipython" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.6.4" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/module2/exo1/Untitled1.ipynb b/module2/exo1/Untitled1.ipynb new file mode 100644 index 0000000..db1a1c6 --- /dev/null +++ b/module2/exo1/Untitled1.ipynb @@ -0,0 +1,157 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# À propos du calcul de $\\pi$\n", + "## En demandant à la lib maths\n", + "Mon ordinateur m’indique que $\\pi$ vaut *approximativement* " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.141592653589793\n" + ] + } + ], + "source": [ + "from math import *\n", + "print (pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## En utilisant la méthode des aiguilles de Buffon \n", + "Mais calculé avec la **méthode** des [https://fr.wikipedia.org/wiki/Aiguille_de_Buffon], on obtiendrait comme **approximation** :" + ] + }, + { + "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)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Avec un argument \"fréquentiel\" de surface\n", + "Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d’appel à la fonction sinus se base sur le fait que si $X\\sim U(0,1)$ et $Y\\sim U(0,1)$ alors $P[X^2+Y^2\\leq1]=\\pi/4$ (voir [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": 4, + "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "EOL while scanning string literal (, line 13)", + "output_type": "error", + "traceback": [ + "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m13\u001b[0m\n\u001b[0;31m ax.scatter(x[reject],y[reject], c='r’, alpha=0.2, edgecolor=None)\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m EOL while scanning string literal\n" + ] + } + ], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "\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", + "\n", + "accept=(x*x+y*y)<=1 \n", + "reject=np.logical_not(accept)\n", + "\n", + "fig, ax=plt.subplots(1) \n", + "ax.scatter(x[reject],y[reject], c='r’, 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 alor saisé d’obtenir une approximation (pas terrible) de $\\pi$ en comptant combien de fois, en moyenne, $X^2 + Y^2$ est inferoeir à 1 :" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "invalid syntax (, line 1)", + "output_type": "error", + "traceback": [ + "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m 4.np.mean(accept)\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" + ] + } + ], + "source": [ + "4.np.mean(accept)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.6.4" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/module2/exo1/toy_notebook_fr.ipynb b/module2/exo1/toy_notebook_fr.ipynb index 0bbbe37..39a724e 100644 --- a/module2/exo1/toy_notebook_fr.ipynb +++ b/module2/exo1/toy_notebook_fr.ipynb @@ -1,5 +1,48 @@ { - "cells": [], + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# À propos du calcul de $\\pi$\n", + "## En demandant à la lib maths\n", + "Mon ordinateur m’indique que $\\pi$ vaut *approximativement*" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.141592653589793\n" + ] + } + ], + "source": [ + "from math import *\n", + "print(pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## En utilisant la méthode des aiguilles de Buffon\n", + "Mais calculé avec la **méthode** des [https://fr.wikipedia.org/wiki/Aiguille_de_Buffon], on obtiendrait comme **approximation** :" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], "metadata": { "kernelspec": { "display_name": "Python 3", @@ -16,10 +59,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 } - -- 2.18.1