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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "TP 2 -- Informatique CM3 -- Septembre 2015 "
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Python @ Polytech'Lille"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Le texte de cette sessions de travaux pratiques est \u00e9galement disponible ici\n",
      "http://nbviewer.ipython.org/github/ecalzavarini/python-at-polytech-lille/blob/master/Python-TP2-2015.ipynb\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "Nous vous rappelons que les modalit\u00e9s pour accomplir ce TP sont les m\u00eames de la premi\u00e8re s\u00e9ance :\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "Vous aurez \u00e0 \u00e9crire plusieurs scripts (script1.py , script2.py , ...). Les scripts doivent \u00eatre accompagn\u00e9s par un document descriptif unique (README.txt). Dans ce fichier, vous devrez d\u00e9crire le mode de fonctionnement des scripts et, si besoin, mettre vos commentaires. Merci d'y \u00e9crire aussi vos noms et prenoms complets.\n",
      "Tous les fichiers doivent \u00eatre mis dans un dossier appel\u00e9 TP2-nom1-nom2 et ensuite \u00eatre compress\u00e9s dans un fichier archive TP2-nom1-nom2.tgz .\n",
      "Enfin vous allez envoyer ce fichier par email \u00e0 l'enseignant: soit Enrico (enrico.calzavarini@polytech-lille.fr) ou Stefano (stefano.berti@polytech-lille.fr).\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "Vous avez une semaine de temps pour compl\u00e9ter le TP, c'est-\u00e0-dire que la date limite pour envoyer vos travaux c'est dans 7 jours \u00e0 partir d'aujourd'hui.\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Gestion des accents en Python"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Dans la premi\u00e8re s\u00e9ance de TP, vous avez souvent rencontr\u00e9 un message d'erreure issue de  l'utilisation des caract\u00e8res accentu\u00e9s dans les scripts en Python.\n",
      "Voici une solution  \u00e0  ce probl\u00e8me. \n",
      "En premi\u00e8re ligne d\u2019un script, il faut ins\u00e9rer la ligne :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# -*- coding: utf-8 -*-"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "ou bien"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# -*- coding: latin-1 -*-"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Il s\u2019agit d\u2019un pseudo-commentaire indiquant \u00e0 Python le syst\u00e8me de codage utilis\u00e9, ici l\u2019utf-8 (ou le latin-1) qui comprend les caract\u00e8res sp\u00e9ciaux comme les caract\u00e8res accentu\u00e9s, les apostrophes, les c\u00e9dilles , etc ."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Utiliser les fonctions en Python"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Vous savez d\u00e9j\u00e0 ce qu'est une fonction math\u00e9matique d'une variable r\u00e9elle.\n",
      "Consid\u00e9rons par exemple la fonction f(x) suivante :\n",
      "\n",
      "f : x ---> 2 x + 1\n",
      "\n",
      "pour la d\u00e9finir en Python :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#definition d'une fonction\n",
      "def f(x):\n",
      "    return 2 * x + 1\n",
      "\n",
      "#utilisation de la fonction\n",
      "\n",
      "print(f(4))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "9\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Avez-vous remarqu\u00e9 qu\u2019\u00e0 la deuxi\u00e8me ligne, on n\u2019a pas commenc\u00e9 \u00e0 \u00e9crire au d\u00e9but de la ligne? De la m\u00eame fa\u00e7on que pour les structures de contr\u00f4le 'if' ou 'for', nous devons appliquer la r\u00e8gle d'indentation.\n",
      "Cette indentation est indispensable pour que l'interpr\u00e9teur Python comprenne la fin d'un bloc de d\u00e9finition d'une fonction."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Le principe de d\u00e9finition de fonctions est int\u00e9ressant pour deux raisons :\n",
      "\n",
      "1) cela nous permet de ne pas r\u00e9p\u00e9ter un calcul long \u00e0 taper,\n",
      "\n",
      "2) Python poss\u00e8de un type sp\u00e9cial d\u00e9di\u00e9 au fonctions, que l\u2019on peut donc manipuler, mettre dans des listes pour les \u00e9tudier les unes \u00e0 la suite des autres. \n",
      "\n",
      "Par exemple :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print( f(1) , f(2) , f(3) , f(4) , f(5) , f(6))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(3, 5, 7, 9, 11, 13)\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print( type(f))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<type 'function'>\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# definition d'une seconde fonction\n",
      "def hi(name):\n",
      "    print(\"hello \" + name + \" from Python!!!\")\n",
      "\n",
      "#exemple d'utilisation    \n",
      "hi(\"Mark\")    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "hello Mark from Python!!!\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#definition  d'une trosieme fonction\n",
      "from random import choice\n",
      "def lettre():\n",
      "    return choice('abcdefghijklmnopqrstuvwxyz')\n",
      "\n",
      "#exemple d'utilisation \n",
      "lettre()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "'j'"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#definition d'une liste de fonctions\n",
      "mes_fonctions = [f,hi,lettre]\n",
      "\n",
      "#utilisation\n",
      "mes_fonctions[1](\"Dominique\")\n",
      "\n",
      "mes_fonctions[2]()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "hello Dominique from Python!!!\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "'e'"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Script 1 : calcul des forces sur un ballon de football"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Image\n",
      "Image(filename='kick.jpg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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+wT4IuZWL2V7ofwG+GNz+0F451ewZrSAo958TP2sdc8M6nBFdahaLN4Gtp47i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\n",
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "<IPython.core.display.Image at 0x113af0750>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Les forces sur un ballon de football en vol suite \u00e0 un coup de pied d'un joueur sont deux: la force de la pesanteur (le poids $F_P$) et la force de  tra\u00een\u00e9e exerc\u00e9e par le frottement de l'air sur le ballon ($F_T$). Leurs expressions sont les suivantes : "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$F_P = M\\ g$$\n",
      "\n",
      "$$F_T = 0.5 \\ C_D \\ \\rho \\ u^2\\ S $$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "O\u00f9 $M$ est la masse du ballon, $g$ l'acc\u00e9l\u00e9ration de gravit\u00e9, $C_D$ le coefficient de tra\u00een\u00e9e, $\\rho$ la masse volumique de l'air, $u$ la vitesse du ballon et enfin $S$ la section du ballon $S=\\pi\\ R^2$ (avec R le rayon)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Nous demandons d'\u00e9crire un script qui tout d'abord demande \u00e0 l'utilisateur d'entrer les valeurs du rayon du ballon (en m\u00e8tres), de la masse du ballon (en kg) et de la vitesse du ballon ainsi que l'unit\u00e9 de mesure pour cette derni\u00e8re (soit \"m/s\" ou \"km/h\").\n",
      "Ensuite le script devra calculer les forces $F_P$ et $F_T$, afficher les deux valeurs ainsi que leur rapport $F_T/F_P$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On demande de faire tout cela  \u00e0 l'aide de quatre fonctions :\n",
      "\n",
      "1) une fonction qui convertit  la vitesse de \"km/h\" en \"m/s\" si besoin\n",
      "\n",
      "2) une fonction qui calcule la surface $S$ du ballon  \u00e0 partir du rayon $R$\n",
      "\n",
      "3) une fonction qui calcule $F_T$\n",
      "\n",
      "4) une fonction qui calcule $F_P$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Les donn\u00e9es du probl\u00e8me sont l'acc\u00e9l\u00e9ration de gravit\u00e9 $g=9.81 \\, m /s^2$, la masse volumique de l'air $\\rho = 1.2 \\, kg/m^{-3}$,  le coefficient de train\u00e9e $C_D=0.2$. \n",
      "Tourner le script plusieurs fois et dire ce qui change dans le rapport $F_T/F_P$ pour des valeurs de vitesse croissante (p.ex. $u=10 \\, km/h$, $u=120 \\, km/h$) et \u00e0 masse et rayon fixes."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Script 2 : \u00e9tude de la fonction de transfert du syst\u00e8me ressort - amortisseur (suspension) d\u2019un  automobile"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "L\u2019objet de ce script est d'illustrer \u00e0 l'aide de Python les r\u00f4les respectifs jou\u00e9s par le ressort et l\u2019amortisseur d\u2019un syst\u00e8me automobile. \n",
      "Pour ce faire, nous \u00e9tudions un ressort coupl\u00e9 \u00e0 un amortisseur en parall\u00e8le. \n",
      "\n",
      "Comme dans la figure ci-dessous:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Image\n",
      "Image(filename='masse-ressort-amortisseur.jpg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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R4Ee1WeXXJdHtFjwAPf4PaJd+CpZ/FHiH40eMfAV/a291o37QP7N37SHx+uNb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\n",
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "<IPython.core.display.Image at 0x1139f8850>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "L'\u00e9quation v\u00e9rifi\u00e9e par le syst\u00e8me est la suivante :\n",
      "\n",
      "$$ \\ddot{x} + \\frac{\\omega_0}{Q} \\dot{x} + \\omega_0^2\\ x = \\frac{F}{m} \\cos( \\omega t) $$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Ici $m$ est la masse de la roue, $F$ et $\\omega$ sont respectivement l'intensit\u00e9 de la force appliqu\u00e9e (qui mod\u00e9lise l'effet des ondulations du sol sur la roue) et sa pulsation , $\\omega_0$ la pulsation caract\u00e9ristique du ressort ($\\omega_0=\\sqrt{k/m}$) et enfin $Q$ est un coefficient appel\u00e9 coefficient de qualit\u00e9. Ici on n\u00e9gligera le poids de la roue. \n",
      "\n",
      "Un syst\u00e8me tr\u00e8s amorti a un $Q$ faible. \u00c0 l'inverse, un $Q$ \u00e9lev\u00e9 correspond \u00e0 un syst\u00e8me peu amorti. Pour fixer les id\u00e9es, le $Q$ d'une voiture avec des amortisseurs en bon \u00e9tat est l\u00e9g\u00e8rement sup\u00e9rieur \u00e0 1."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "De la solution de l'\u00e9quation du syst\u00e8me ressort-amortisseur on trouve la fonction de transfert qui d\u00e9crit la r\u00e9ponse du syst\u00e8me en fonction de la pulsation $\\omega$. \n",
      "\n",
      "En particulier la fonction de transfert (le module de cette fonction pour la pr\u00e9cision) s'\u00e9crit :"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$ T(\\omega) = \\frac{F}{m \\ \\omega_0^2} \\frac{1}{\\sqrt{ \\left( 1 - \\omega^2/\\omega_0^2 \\right)^2 +  Q^{-2} \\ \\omega^2/\\omega_0^2 }} $$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "ou en utilisant la pulsation adimensionn\u00e9e u = \u03c9/\u03c90 :"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$ T(u) = \\frac{F}{m \\ \\omega_0^2} \\frac{1}{\\sqrt{ \\left( 1 - u^2 \\right)^2 +  u^{2}/ \\      Q^2}} $$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Nous demandons d'\u00e9crire un script qui trace un graphique du module de la fonction de transfert $T(u)$ en fonction de la pulsation adimensionn\u00e9e $u$ (dans l'intervalle $[0,2]$) pour toutes les valeurs de $Q$ dans l'intervalle $[0,10]$ avec rapport entre une valeur de $Q$ et la valeur pr\u00e9c\u00e9dente de $\\delta Q = 2.0$ (facteur de redoublement)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Prendre la valeur suivante pour l'amplitude de la fonction de transfert  $$ \\frac{F}{m \\omega_0^2} = 2 $$ "
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "\u00c7a pourrait \u00eatre utile : "
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "La boucle while "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Le but de la boucle \"while\" est de r\u00e9p\u00e9ter certaines instructions tant qu\u2019une condition est respect\u00e9e. On n\u2019est pas donc oblig\u00e9 de savoir au d\u00e9part le nombre de r\u00e9p\u00e9titions \u00e0 faire."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nb_repetitions = 3\n",
      "i = 1\n",
      "\n",
      "while i <= nb_repetitions :\n",
      "    print \"Et \"+str(i)+\"!\"\n",
      "    i = i+1\n",
      "print \"Z\u00e9ro!\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Et 1!\n",
        "Et 2!\n",
        "Et 3!\n",
        "Z\u00e9ro!\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "L\u2019instruction \"break\" sert, non pas \u00e0 interrompre le programme, mais \u00e0 sortir de la boucle."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nb_repetitions = 3\n",
      "i = 1\n",
      "\n",
      "while i <= nb_repetitions :\n",
      "    print \"Et \"+str(i)+\"!\"\n",
      "    i = i+1\n",
      "    if i==3: \n",
      "        break\n",
      "print \"Z\u00e9ro!\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Et 1!\n",
        "Et 2!\n",
        "Z\u00e9ro!\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Cr\u00e9ation d'une l\u00e9gende sur un graphique"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "% matplotlib inline  \n",
      "\n",
      "from math import *\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "t = np.linspace(0,10,400)   # Cr\u00e9ation d'une array numpy : Temps = Abscisses \n",
      "\n",
      "def U(t,Q):\n",
      "    return np.exp(-2/Q*t)*np.cos(2*pi*t)  # Fonction U d\u00e9pendant d'un param\u00e8tre Q\n",
      "\n",
      "# Plot1 avec Q = 2 et \u00e9dition du label correspondant\n",
      "Q=2.0\n",
      "plt.plot(t,U(t,Q),label=\"Q=\" + str(Q)) \n",
      "\n",
      "# Plot2 avec Q = 10 et \u00e9dition du label correspondant\n",
      "Q=10.0\n",
      "plt.plot(t,U(t,Q),label=\"Q=\" + str(Q)) \n",
      "\n",
      "plt.legend(loc='upper right')        # Appel de la l\u00e9gende\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ne3e7Ir2TwfupYJBEf1/9PkXmd7Ph5AauLLiSqIioEfdSNalMT5nO1sqtiq7B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\niIiIiIiIlf4P6bbveZA4AbYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113a171d0>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Script 3 : Calcul de la valeur critique du coefficient de qualit\u00e9 d'une suspension"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u00c9crire un script qui calcule la valeur critique de $Q$, c'est-\u00e0-dire la valeur pour laquelle on observe une transition entre le r\u00e9gime de vibrations sur-amorties ($T(u)$ non croissante) et celui de r\u00e9sonance ($T(u)$ non monotone, avec un maximum pour $0< u < 1$)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pour cela faire, on peut par exemple calculer la valeur maximale $T_{max}$ de $T(u)$ pour des valeurs croissantes de $Q$, et arr\u00eater le calcul lorsque $T_{max}$ est sup\u00e9rieur \u00e0 $F / (m \\omega_0^2)$. \n",
      "\n",
      "Dans ce cas on vous sugg\u00e8re de prendre $Q=0.5$ comme valeur de d\u00e9part et de l'incr\u00e9menter  pas \u00e0 pas d'une valeur $\\delta Q = 10^{-6}$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Utiliser encore : $F /(m \\omega_0^2) = 2$  "
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Calcul de la valeur maximale avec numpy"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pour ce script, il peut \u00eatre utile d'utiliser la fonction numpy pour calculer le maximum d'une liste :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      " import numpy as np\n",
      " \n",
      " val=np.linspace(0,7,500)\n",
      " \n",
      " val_max = np.amax(val)\n",
      "    \n",
      " print(val_max)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "7.0\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Script 4 : Pr\u00e9paration des donn\u00e9es d'entr\u00e9e pour une machine-outil \u00e0 contr\u00f4le num\u00e9rique"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Les machines-outil d'usinage \u00e0 contr\u00f4le num\u00e9rique peuvent \u00eatre contr\u00f4l\u00e9es \u00e0 travers un fichier de donn\u00e9es d'entr\u00e9e. Ce fichier contient toutes les sp\u00e9cifications g\u00e9om\u00e9triques de l'objet \u00e0 usiner et il a souvent la forme d'une matrice en deux dimensions, dans laquelle chaque \u00e9l\u00e9ment identifie une coordonn\u00e9e spatiale (x, y) alors que la valeur de l'\u00e9l\u00e9ment contient l'information sur l'usinage (par exemple dans une fraiseuse \"$0$\" signifie couper et \"$1$\" signifie  garder tel qu'il est). \n",
      "\n",
      "Nous consid\u00e9rons ici une machine-outil fraiseuse avec r\u00e9solution du dixi\u00e8me de millim\u00e8tre, et une surface de travail de $(10 \\times 10) cm^2$. Nous voulons d\u00e9couper de la pi\u00e8ce brute une bielle \u00e0 partir d'un bloc de m\u00e9tal de dimensions $(10 \\times 10) cm^2$ (l'\u00e9paisseur du bloc n'a pas d' importance ici).\n",
      "\n",
      "La g\u00e9om\u00e9trie de la bielle est montr\u00e9e dans la figure ci-dessous :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Image\n",
      "Image(filename='bielle.jpg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "jpeg": 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Glvfu3jG4utJbxzrNp/ZHibS9UvwD+o6gAoAKACgAoAKACgAoAKACgAoAKACg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\nCgAoAKACgAoAKACgAoAKACgAoAKACgD/2Q==\n",
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "<IPython.core.display.Image at 0x117d6c950>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "D\u00e9tails de la g\u00e9om\u00e9trie de la bielle:\n",
      "\n",
      "- le grand anneau a rayon interne $r_1 = 10.0\\ mm$, rayon externe $r_2 = 16.0\\ mm$ , position du centre $x_1 = 50.0 \\ mm$ , $y_1 = 20.0 \\ mm$.\n",
      "\n",
      "- le petit anneau a rayon interne $r_3 = 3.0\\ mm$ , rayon externe $r_4 = 11.2\\ mm$ , position du centre $x_2 = 50.0 \\ mm$ , $y_2 = 75.0 \\ mm$.\n",
      "\n",
      "- la barre de liaison a longueur $l=30.0\\ mm$ , hauteur $h = 10.0\\ mm$ et centre g\u00e9om\u00e9trique en $x_3 = 50.0 \\ mm$, $y_3 = 50.0 \\ mm$. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On demande d'\u00e9crire un script qui cr\u00e9e la matrice pour usiner la bielle en figure.\n",
      "\n",
      "Cette matrice devra avoir $1000$ x $1000$ \u00e9l\u00e9ments, chaque \u00e9l\u00e9ment correspondant \u00e0 $(0.1 \\times 0.1) mm^2$, et la valeur des \u00e9l\u00e9ments doit \u00eatre soit $0$ si le mat\u00e9riau doit \u00eatre enlev\u00e9 (ou bien compl\u00e8tement frais\u00e9 dans ce cas) et $1$ s'il doit \u00eatre gard\u00e9 comme il est.\n",
      "\n",
      "a) Montrer \u00e0 travers un graphique la matrice que vous avez obtenu\n",
      "\n",
      "b) Tracer aussi un graphique de la section longitudinale centrale de la bielle."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Cela pourrait vous \u00eatre utile :"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Cr\u00e9er et manipuler un tableau multidimensionnel avec numpy"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "#d\u00e9finition d'une matrice avec numpy\n",
      "tableau = np.array ([[0 ,1 ,2] ,[1,2,3], [4,6,12], [44 ,55 ,56]]) \n",
      "\n",
      "print(tableau)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0  1  2]\n",
        " [ 1  2  3]\n",
        " [ 4  6 12]\n",
        " [44 55 56]]\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n=tableau[3,0] # copier un element du tableau  ,  tableau[num. ligne][num. colonne]\n",
      "\n",
      "print(n) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "44\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Noter que l'indice de gauche indique toujours le nombre de la ligne tandis que l'indice de droite indique le num\u00e9ro de la colonne. \n",
      "\n",
      "Ce syst\u00e8me d'indexage (dite convention \"row-major order\" ou \"ligne par ligne\") n'est pas toujours intuitif :\n",
      "dans le cas d'une matrice $A[i, j]$ qui contient des informations spatiales l'indice \u00e0 gauche ( $i$ ) identifie la coordonn\u00e9e verticale $y$ et l'indice de droite ( $j$ ) identifie la coordonn\u00e9e horizontale $x$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c=tableau[:,0] # copier une colonne du tableau\n",
      "\n",
      "print(c)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0  1  4 44]\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d=tableau[:2,:2] # copier une colonne du tableau\n",
      "\n",
      "print(d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[0 1]\n",
        " [1 2]]\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tableau = tableau + 2  #ajouter 2 aux \u00e9l\u00e9ments du tableau\n",
      "print(tableau)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 2  3  4]\n",
        " [ 3  4  5]\n",
        " [ 6  8 14]\n",
        " [46 57 58]]\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tableau2 = np.zeros((4,3))  #d\u00e9finition d'une matrice compos\u00e9e de z\u00e9ros\n",
      "\n",
      "print(tableau2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.  0.  0.]\n",
        " [ 0.  0.  0.]\n",
        " [ 0.  0.  0.]\n",
        " [ 0.  0.  0.]]\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Repr\u00e9senter graphiquement une matrice"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "my_mat = np.random.random((50, 80)) #cr\u00e9ation d'une matrice al\u00e9atoire de 80x50 elements\n",
      "\n",
      "plt.matshow(my_mat) # repr\u00e9sentation graphique\n",
      "\n",
      "plt.xticks(range(0,80,10)) # d\u00e9finition des marqueurs en x\n",
      "plt.yticks(range(0,50,10)) # d\u00e9finition des marqueurs en y\n",
      "\n",
      "plt.colorbar()\n",
      "\n",
      "plt.show()        "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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U+2lpaxupRD4FrJM3d1yy7UL/2hUf9Y2Ws1C8V+rv3B8p/STnPE7e+VwWx5WV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\nJbL53XOxaifnY0Z7DtOe7BRBnR7DUoebWa/LtKF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UYj4Sfgdirgz6uzbKF+9GAQJAPXwS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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1138dcf90>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.matshow(my_mat,cmap='Greys') # repr\u00e9sentation graphique en blanc et noir\n",
      "plt.colorbar()\n",
      "plt.show()        "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10d5c7310>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.core.display import HTML\n",
      "def css_styling():\n",
      "    styles = open('custom.css', 'r').read()\n",
      "    return HTML(styles)\n",
      "css_styling()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "IOError",
       "evalue": "[Errno 2] No such file or directory: 'custom.css'",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mIOError\u001b[0m                                   Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-36-6e0370214c4d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mstyles\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'custom.css'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mHTML\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstyles\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mcss_styling\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[0;32m<ipython-input-36-6e0370214c4d>\u001b[0m in \u001b[0;36mcss_styling\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mIPython\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdisplay\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mHTML\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mcss_styling\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mstyles\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'custom.css'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mHTML\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstyles\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mcss_styling\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mIOError\u001b[0m: [Errno 2] No such file or directory: 'custom.css'"
       ]
      }
     ],
     "prompt_number": 36
    }
   ],
   "metadata": {}
  }
 ]
}