From 6de3309d1af0985da74197defc90f617b351ffee Mon Sep 17 00:00:00 2001 From: 08665f0d5a3cef5a146df356c344b7b3 <08665f0d5a3cef5a146df356c344b7b3@app-learninglab.inria.fr> Date: Mon, 8 Jul 2024 12:40:50 +0000 Subject: [PATCH] excercice02_1stpart --- module2/exo1/toy_notebook_en.ipynb | 209 ++++++++++++++++++++++++++++- 1 file changed, 206 insertions(+), 3 deletions(-) diff --git a/module2/exo1/toy_notebook_en.ipynb b/module2/exo1/toy_notebook_en.ipynb index 0bbbe37..9572568 100644 --- a/module2/exo1/toy_notebook_en.ipynb +++ b/module2/exo1/toy_notebook_en.ipynb @@ -1,5 +1,209 @@ { - "cells": [], + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# toy_notebook_en " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## March 28, 2019" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### **1. On the computation of $\\pi$**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### **1.1 Asking the maths library**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "My computer tells me that $\\pi$ is *approximatively*" + ] + }, + { + "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": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### **1.2 Buffon's needle**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Applying the method of __[Buffon's needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem)__, we get the **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": [ + "### **1.3 Using a surface fraction argument**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A method that is easier to understand and does not make use of the sin function is based on the fact that if $X\\sim U(0,1)$ and $Y\\sim U(0,1)$, then $P[X^2+Y^2 \\leq 1] = \\pi/4$ (see __[\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)__). The following code uses this approach:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "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", + "accept = (x*x+y*y) <= 1\n", + "reject = np.logical_not(accept)\n", + "\n", + "fig, ax = plt.subplots(1)\n", + "ax.scatter(x[accept], y[accept], c='b', alpha=0.2, edgecolor = None)\n", + "ax.scatter(x[accept], y[accept], c='r', alpha=0.2, edgecolor = None)\n", + "ax.set_aspect('equal')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is then straightforward to obtain a (not really good) approximation to $\\pi$ by counting how many times, on average, $X^2+Y^2$ is smaller than 1:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.112" + ] + }, + "execution_count": 6, + "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 +220,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 } - -- 2.18.1