S2_Objets_et_NumPy.ipynb

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 "metadata": {
  "name": "S2_Objets_et_NumPy"
 },
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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "S\u00e9ance 2 :  Objets et Calcul num\u00e9rique"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<img src='files/images/logo ENS Cachan Bretagne.png'>\n",
      "<strong>Formation Python du <a href='http://www.mecatronique.bretagne.ens-cachan.fr/'>d\u00e9partement M\u00e9catronique</a></strong>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "11h00 - 12h30\n",
      "\n",
      "Apr\u00e8s une S\u00e9ance 1 qui introduisait les bases du language Python g\u00e9n\u00e9raliste, voici deux sujets plus sp\u00e9cifiques\n",
      "\n",
      "*A) Python orient\u00e9 objet*\n",
      "\n",
      "* Introduction rapide aux objets avec l'exemple d'une classe \u00ab\u00a0Torseur\u00a0\u00bb.\n",
      "* M\u00e9thodes et surcharge d'op\u00e9rateurs (ou \"comment pouvoir additioner des torseurs\").\n",
      "\n",
      "*B) Python num\u00e9rique\u00a0avec NumPy*...\n",
      "\n",
      "* Calcul num\u00e9rique avec la biblioth\u00e8que NumPy.\n",
      "* Alg\u00e8bre lin\u00e9aire de base.\n",
      "* Lecture d'un fichier de donn\u00e9es exp\u00e9rimentales (fichier texte type CSV)\n",
      "\n",
      "*C) ...puis trac\u00e9 de graphiques avec Matplotlib*\n",
      "\n",
      "* aper\u00e7u des fonctions graphiques principales. D\u00e9placement/Zoom interactif.\n",
      "* exemple\u00a0: diagramme de Bode (avec la question de l'identification d'un mod\u00e8le)\n",
      "* bonus : diagrammes de Black, Nyquist"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "A) Python Orient\u00e9 Objet, par l'exemple"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Exemple de la cr\u00e9ation d'une Classe \"Torseur2D\", inspir\u00e9 de la m\u00e9canique du solide.\n",
      "\n",
      "Il existent d'autres tutoriels plus complets sur les objets en Python tel que http://docs.python.org/2/tutorial/classes.html#a-first-look-at-classes.\n",
      "\n",
      "\n",
      "### Cahier des charges de la Classe :\n",
      "\n",
      "L'objet math\u00e9matique Torseur peut se caract\u00e9riser par 3 param\u00e8tres :\n",
      "\n",
      "* une *r\u00e9sultante* (dim 2),\n",
      "* et un *moment* (dim 1)...\n",
      "* ...exprim\u00e9 en un *point* (dim 2).\n",
      "\n",
      "Pour manipuler ce type d'objet en Python, on cr\u00e9e donc une classe poss\u00e9dant ces trois champs.\n",
      "\n",
      "Dans un second temps, on va voir comment permettre l'addition des objets Torseur2D."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "A1) Construction de la classe, \u00e9tape par \u00e9tape"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Une classe se d\u00e9finit par le mot-cl\u00e9 `class` suivit du nom de la classe.\n",
      "\n",
      "On commence par une d\u00e9finition minimale qui inclue la *m\u00e9thode* `__init__` qui sert \u00e0 initialiser l'objet :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class Torseur2D(object):\n",
      "    def __init__(self, resul, mom_ref, ref):\n",
      "        '''torseur de r\u00e9sultante `resul` et de moment `mom_ref`\n",
      "        exprim\u00e9 au point de coordonn\u00e9es `ref`.\n",
      "        '''\n",
      "        # R\u00e9sultante\n",
      "        self.resul = resul\n",
      "        # Moment exprim\u00e9 en ref\n",
      "        self.mom_ref = mom_ref\n",
      "        # Point de r\u00e9f\u00e9rence\n",
      "        self.ref = ref\n",
      "        \n",
      "        print(\"Initialisation d'un Torseur\")\n",
      "    # end __init__()\n",
      "\n",
      "# Cr\u00e9ation (\"Instanciation\") d'un torseur\n",
      "T1 = Torseur2D((2,3), 1., (0,0))\n",
      "T1.mom_ref\n",
      "T1.ref\n",
      "T1.resul"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Initialisation d'un Torseur\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(2, 3)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Remarquons que la Docstring de init sert \u00e0 documnter la cr\u00e9ation de la classe :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Torseur2D?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Toutes les attributs d'un objet sont accessibles en lecture et en \u00e9criture :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "T1.resul = [4, 5]\n",
      "T1.resul"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[4, 5]"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Remarque : Par d\u00e9faut, aucune v\u00e9rification de la valeur assign\u00e9e n'est effectu\u00e9e, mais des v\u00e9rifications sont facilement impl\u00e9mentables (notion de *getter* et *setter*)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Formule du \"Changement de Point\""
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Une des formules essentielle pour travailler avec les torseurs est de calculer le moment en n'impore quel point (\"formule de changement de point\")\n",
      "\n",
      "On ajoute donc une nouvelle *m\u00e9thode* qui impl\u00e9mente de le changement de point :\n",
      "\n",
      "$$\\vec{M}(X) = \\vec{M}(O) + \\vec{R} \\times \\vec{OX} $$\n",
      "\n",
      "avec $\\vec{R}$ la r\u00e9sultante du torseur et $O$ le point de r\u00e9f\u00e9rence initial."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# m\u00e9thode \u00e0 ajouter dans la d\u00e9finition de la classe Torseur2D\n",
      "def calc_mom(self, pt):\n",
      "    '''calcule le moment du torseur en un point `pt` quelconque'''\n",
      "    # Formule du changement de point: M(X) = M(O) + R^OX\n",
      "    # 1) Vecteur d\u00e9placement OX = X-O:\n",
      "    delta_ref = (pt[0] - self.ref[0],\n",
      "                 pt[1] - self.ref[1])\n",
      "    # 2) Produit vectoriel R^OX\n",
      "    delta_mom = self.resul[0]*delta_ref[1] - self.resul[1]*delta_ref[0]\n",
      "    # 3) Nouveau moment:\n",
      "    mom = self.mom_ref + delta_mom\n",
      "    return mom\n",
      "# end calc_mom()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Souvent, les m\u00e9thodes servent \u00e0 **changer l'\u00e9tat de l'objet**. Ici, on propose par exemple de changer le point de r\u00e9f\u00e9rence (ce qui recalcule le moment au point de r\u00e9f\u00e9rence)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# m\u00e9thode \u00e0 ajouter dans la d\u00e9finition de la classe Torseur2D\n",
      "def set_ref(self, new_ref):\n",
      "    '''change le point de r\u00e9f\u00e9rence'''\n",
      "    # 1) Calcul du moment au nouveau point de r\u00e9f\u00e9rence\n",
      "    self.mom_ref = self.calc_mom(new_ref)\n",
      "    # 2) Mise \u00e0 jour du point de r\u00e9f\u00e9rence\n",
      "    self.ref = new_ref\n",
      "# end set_ref()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "M\u00e9thodes supl\u00e9mentaires"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On peut obtenir une belle repr\u00e9sentation textuelle en r\u00e9impl\u00e9mentant la m\u00e9thode sp\u00e9ciale `__str__` (celle-ci est appel\u00e9e par str(mon_torseur))"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def __str__(self):\n",
      "    res = 'Torseur 2D '\n",
      "    res += 'de R\u00e9sultante {0} et de Moment {1}'.format(str(self.resul),\n",
      "                                                        str(self.mom_ref))\n",
      "    res += ' exprim\u00e9 au point {0}'.format(str(self.ref))\n",
      "    \n",
      "    return res.encode('utf-8')\n",
      "# end __str__"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pour pouvoir additionner/soustraire des torseurs, il faut r\u00e9impl\u00e9menter les m\u00e9thodes correspondants \u00e0 ces op\u00e9rations :\n",
      "\n",
      "* `__add__` pour a + b\n",
      "* `__neg__` pour -a\n",
      "* `__sub__` pour a-b\n",
      "\n",
      "(cf. Emulating numeric types http://docs.python.org/2/reference/datamodel.html#emulating-numeric-types)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "### Op\u00e9ration arithm\u00e9tiques\n",
      "def __add__(self, other):\n",
      "    '''addition de 2 torseurs: T1 + T2\n",
      "    Le pt de r\u00e9f\u00e9rence utilis\u00e9 est celui de T1 (op\u00e9rande gauche)\n",
      "    '''\n",
      "    # 1) addition des R\u00e9sultantes:\n",
      "    resul = (self.resul[0] + other.resul[0],\n",
      "             self.resul[1] + other.resul[1])\n",
      "    # 2) addition des moments au point de r\u00e9f\u00e9rence de self:\n",
      "    mom_ref = self.mom_ref\n",
      "    other_mom = other.calc_mom(self.ref)\n",
      "    mom_ref = mom_ref + other_mom\n",
      "    # 3) Cr\u00e9ation de l'objet Torseur:\n",
      "    T = Torseur2D(resul, mom_ref, self.ref)\n",
      "    return T\n",
      "# end __add__\n",
      "\n",
      "def __neg__(self):\n",
      "    '''oppos\u00e9 du torseur'''\n",
      "    resul = (-self.resul[0], -self.resul[1])\n",
      "    mom_ref = -self.mom_ref\n",
      "    T = Torseur2D(resul, mom_ref, self.ref)\n",
      "    return T\n",
      "# end __neg__\n",
      "\n",
      "def __sub__(self, other):\n",
      "    '''soustraction de 2 torseurs: T1-T2'''\n",
      "    return self + (-other)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "D\u00e9finition compl\u00e8te de la classe Torseur2D"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class Torseur2D(object):\n",
      "    def __init__(self, resul, mom_ref, ref):\n",
      "        '''torseur de r\u00e9sultante `resul` et de moment `mom_ref`\n",
      "        exprim\u00e9 au point de coordonn\u00e9es `ref`.\n",
      "        '''\n",
      "        # R\u00e9sultante\n",
      "        self.resul = resul\n",
      "        # Moment exprim\u00e9 en ref\n",
      "        self.mom_ref = mom_ref\n",
      "        # Point de r\u00e9f\u00e9rence\n",
      "        self.ref = ref        \n",
      "        print(\"[Initialisation d'un nouveau Torseur]\")\n",
      "        #print(self)\n",
      "    # end __init__()\n",
      "    \n",
      "    def calc_mom(self, pt):\n",
      "        '''calcule le moment du torseur en un point `pt` quelconque'''\n",
      "        # Formule du changement de point: M(X) = M(O) + R^OX\n",
      "        # 1) Vecteur d\u00e9placement OX = X-O:\n",
      "        delta_ref = (pt[0] - self.ref[0],\n",
      "                     pt[1] - self.ref[1])\n",
      "        # 2) Produit vectoriel R^OX\n",
      "        delta_mom = self.resul[0]*delta_ref[1] - self.resul[1]*delta_ref[0]\n",
      "        # 3) Nouveau moment:\n",
      "        mom = self.mom_ref + delta_mom\n",
      "        return mom\n",
      "    # end calc_mom()\n",
      "\n",
      "    def set_ref(self, new_ref):\n",
      "        '''change le point de r\u00e9f\u00e9rence'''\n",
      "        # 1) Calcul du moment au nouveau point de r\u00e9f\u00e9rence\n",
      "        self.mom_ref = self.calc_mom(new_ref)\n",
      "        # 2) Mise \u00e0 jour du point de r\u00e9f\u00e9rence\n",
      "        self.ref = new_ref\n",
      "    # end set_ref()\n",
      "\n",
      "    def __str__(self):\n",
      "        res = u'Torseur 2D '\n",
      "        res += u'de R\u00e9sultante {0} et de Moment {1}'.format(str(self.resul),\n",
      "                                                            str(self.mom_ref))\n",
      "        res += u' exprim\u00e9 au point {0}'.format(str(self.ref))\n",
      "        \n",
      "        return res.encode('utf-8')\n",
      "    # end __str__\n",
      "    \n",
      "    ### Op\u00e9ration arithm\u00e9tiques\n",
      "    def __add__(self, other):\n",
      "        '''addition de 2 torseurs: T1 + T2\n",
      "        Le pt de r\u00e9f\u00e9rence utilis\u00e9 est celui de T1 (op\u00e9rande gauche)\n",
      "        '''\n",
      "        # 1) addition des R\u00e9sultantes:\n",
      "        resul = (self.resul[0] + other.resul[0],\n",
      "                 self.resul[1] + other.resul[1])\n",
      "        # 2) addition des moments au point de r\u00e9f\u00e9rence de self:\n",
      "        mom_ref = self.mom_ref\n",
      "        other_mom = other.calc_mom(self.ref)\n",
      "        mom_ref = mom_ref + other_mom\n",
      "        # 3) Cr\u00e9ation de l'objet Torseur:\n",
      "        T = Torseur2D(resul, mom_ref, self.ref)\n",
      "        return T\n",
      "    # end __add__\n",
      "    \n",
      "    def __neg__(self):\n",
      "        '''oppos\u00e9 du torseur'''\n",
      "        resul = (-self.resul[0], -self.resul[1])\n",
      "        mom_ref = -self.mom_ref\n",
      "        T = Torseur2D(resul, mom_ref, self.ref)\n",
      "        return T\n",
      "    # end __neg__\n",
      "    \n",
      "    def __sub__(self, other):\n",
      "        '''soustraction de 2 torseurs: T1-T2'''\n",
      "        return self + (-other)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Initialisation de 3 torseurs :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "T1 = Torseur2D((1,1),  0, (0,0))\n",
      "T2 = Torseur2D((1,1),  1, (0,0))\n",
      "T3 = Torseur2D((1,1), -1, (0,0))\n",
      "print(T3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[Initialisation d'un nouveau Torseur]\n",
        "[Initialisation d'un nouveau Torseur]\n",
        "[Initialisation d'un nouveau Torseur]\n",
        "Torseur 2D de R\u00e9sultante (1, 1) et de Moment -1 exprim\u00e9 au point (0, 0)\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Quelques op\u00e9rations de d\u00e9monstration :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Changer le point de r\u00e9f\u00e9rence :\n",
      "T3.set_ref((-1,0))\n",
      "print(T3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Torseur 2D de R\u00e9sultante (1, 1) et de Moment 0 exprim\u00e9 au point (-1, 0)\n"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(-T1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[Initialisation d'un nouveau Torseur]\n",
        "Torseur 2D de R\u00e9sultante (-1, -1) et de Moment 0 exprim\u00e9 au point (0, 0)\n"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(T1+T2) # torseurs d\u00e9j\u00e0 exprim\u00e9s au m\u00eame pt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[Initialisation d'un nouveau Torseur]\n",
        "Torseur 2D de R\u00e9sultante (2, 2) et de Moment 1 exprim\u00e9 au point (0, 0)\n"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(T1+T3) # torseurs exprim\u00e9s en des pts diff\u00e9rents"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[Initialisation d'un nouveau Torseur]\n",
        "Torseur 2D de R\u00e9sultante (2, 2) et de Moment -1 exprim\u00e9 au point (0, 0)\n"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pour compl\u00e9ter cette classe Torseur2D, on pourrait impl\u00e9menter les op\u00e9rations de comparaisons (== et !=) : http://docs.python.org/2/reference/datamodel.html#object.\\__eq\\__\n",
      "\n",
      "---"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "B) Python num\u00e9rique avec NumPy"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "B1) Pourquoi un module particulier (NumPy) ?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pour le calcul scientifique, on est souvent amen\u00e9 \u00e0 manipuler de *grands ensembles de nombres*.\n",
      "Les listes Python (`list`, vu \u00e0 la S\u00e9ance 1) sont des conteneurs *h\u00e9t\u00e9rog\u00e8nes* ne sont pas adapt\u00e9es pour cela car :\n",
      "\n",
      "* les op\u00e9rations arithm\u00e9tiques (addition, multiplication) ne sont pas r\u00e9alisable facilement (car le `+` pour les listes est une concat\u00e9nation)\n",
      "* une liste Python ne stocke par sont contenu de fa\u00e7on efficace (i.e. contigu\u00eb) en m\u00e9moire.\n",
      "\n",
      "Pour manipuler des tableau de nombres, il y a le module NumPy (http://docs.scipy.org/doc/numpy/user/) qui cr\u00e9e un nouveau type de tableau `array`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Importer le module numpy avec un nom raccourci :\n",
      "import numpy as np\n",
      "\n",
      "# Cr\u00e9er un \"array\" \u00e0 partir d'une liste\n",
      "l = np.array([10, 20, 30, 40]) # l n'est plus une liste mais un tableau NumPy\n",
      "\n",
      "print(type(l))\n",
      "l"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<type 'numpy.ndarray'>\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "array([10, 20, 30, 40])"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u00c0 premi\u00e8re vue, un tableau NumPy ressemble beaucoup \u00e0 une liste. En particulier on peut l'indexer comme une liste :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "10"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Grosse diff\u00e9rences, on r\u00e9alise facilement des *op\u00e9rations arithm\u00e9tiques terme \u00e0 terme* :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l+l"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "array([20, 40, 60, 80])"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l*10"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "array([100, 200, 300, 400])"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l**2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "array([ 100,  400,  900, 1600])"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On peut \u00e9galement utiliser des fonctions math\u00e9matiques usuelles (racine, exponentielle, ...) mais qui fonctionnent de fa\u00e7on *vectoris\u00e9e* :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.exp(l)\n",
      "np.sqrt(l)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "array([ 3.16227766,  4.47213595,  5.47722558,  6.32455532])"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Liste des ~60 fonctions vectoris\u00e9e : http://docs.scipy.org/doc/numpy/reference/ufuncs.html#available-ufuncs (appel\u00e9es \"ufuncs\" dans le jargon NumPy)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "B2) Fonctions de bases de NumPy"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* documentation de r\u00e9f\u00e9rence : http://docs.scipy.org/doc/ (en anglais)\n",
      "* Support de formation \"SciPy lectures\" : http://scipy-lectures.github.io/intro/numpy/array_object.html (en anglais)\n",
      "* Tutoriel de Nicolas Rougier http://www.loria.fr/~rougier/teaching/numpy/numpy.html (en anglais)\n",
      "* Autre support en fran\u00e7ais : http://python-prepa.github.io/edp_chaleur.html#introduction-rapide-a-numpy (formation Python ENS Paris)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Cr\u00e9ation de tableaux"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# On a d\u00e9j\u00e0 vu la fonction \"constructeur\" qui transforme tout type de listes (m\u00eame imbriqu\u00e9es) en tableau\n",
      "l = [1, 6, 10]\n",
      "np.array(l)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "array([ 1,  6, 10])"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# L'\u00e9quivalent de `range` :\n",
      "np.arange(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(np.zeros(5))\n",
      "print(np.ones(5))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.  0.  0.  0.  0.]\n",
        "[ 1.  1.  1.  1.  1.]\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Tableaux \u00e0 plusieurs dimensions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# avec des listes imbriqu\u00e9es\n",
      "np.array([[1,2,3], [4,5,6]])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "array([[1, 2, 3],\n",
        "       [4, 5, 6]])"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Matrice identit\u00e9 3x3 :\n",
      "np.eye(3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "array([[ 1.,  0.,  0.],\n",
        "       [ 0.,  1.,  0.],\n",
        "       [ 0.,  0.,  1.]])"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Question** : comment cr\u00e9er (avec `np.zeros`) un tableau \u00e0 plusieur dimensions ?  Une matrice 4x3 par exemple ?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.zeros( (4,3) )\n",
      "# attention aux parenth\u00e8ses pour que (3,3) soit bien *un seul argument*\n",
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 42,
       "text": [
        "array([[ 0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.]])"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "L'information sur le nombre de dimension est accessible avec l'attribut `.ndim`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(l.ndim)\n",
      "a.ndim"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
        "2"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sa dimension (sa \"forme\", cad shape en anglais) est accessbile avec `.shape` (qui est un tuple de longueur `ndim`)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "(4, 3)"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Trancher dans un tableau (\"slicing\")"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Un des grands int\u00e9r\u00eat des tableaux NumPy est la capacit\u00e9 d'acc\u00e9der s\u00e9lectivement \u00e0 des morceaux de tableau. Pour cela la syntaxe d'indexation (avec `[...]`) est \u00e9tendu pour permettre de selectionner chaque dimension"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([[1,2,3], [4,5,6], [7,8,9],[10,11,12]])\n",
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "array([[ 1,  2,  3],\n",
        "       [ 4,  5,  6],\n",
        "       [ 7,  8,  9],\n",
        "       [10, 11, 12]])"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# s\u00e9lectionner 1 \u00e9l\u00e9ment\n",
      "a[0,0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "1"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# s\u00e9lectionner la 1\u00e8re colonne \n",
      "a[:, 0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 61,
       "text": [
        "array([ 1,  4,  7, 10])"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pour s\u00e9lection plusieurs lignes/colonnes"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# M\u00e9thode 1 : indexer avec la syntaxe start:stop:step\n",
      "a[:, 0:2]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 73,
       "text": [
        "array([[ 1,  2],\n",
        "       [ 4,  5],\n",
        "       [ 7,  8],\n",
        "       [10, 11]])"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# M\u00e9thode 2 : indexer avec une liste (plus g\u00e9n\u00e9ral)\n",
      "a[:, [0, 1] ]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 74,
       "text": [
        "array([[ 1,  2],\n",
        "       [ 4,  5],\n",
        "       [ 7,  8],\n",
        "       [10, 11]])"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Mini-question :* comment s\u00e9lectionner la 2\u00e8me ligne ?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# s\u00e9lectionner la 2\u00e8me (-> index 1) ligne\n",
      "a[1, :]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 63,
       "text": [
        "array([4, 5, 6])"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Indexation logique** : pour s\u00e9lectioner des \u00e9l\u00e9ments *selon une condition*. Cela se fait en 2 \u00e9tapes :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \u00c9tape 1 : cr\u00e9\u00e9 le tableau bool\u00e9en qui va s\u00e9lectionner les \u00e9l\u00e9ments\n",
      "a5 = a > 5\n",
      "a5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 66,
       "text": [
        "array([[False, False, False],\n",
        "       [False, False,  True],\n",
        "       [ True,  True,  True],\n",
        "       [ True,  True,  True]], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \u00c9tape 2 : utiliser le tableau bool\u00e9en pour indexer :\n",
      "a[a5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 67,
       "text": [
        "array([ 6,  7,  8,  9, 10, 11, 12])"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \u00c9criture compacte (1 et 2 en une fois)\n",
      "a[a>5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 87,
       "text": [
        "array([ 6,  7,  8,  9, 10, 11, 12])"
       ]
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Typage de tableaux (\"dtype\")"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Les tableaux NumPy contiennent des types de donn\u00e9es homog\u00e8nes. L'attribut `.dtype` permet de conna\u00eetre ce type."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(np.array([1, 2, 3]).dtype) # tableau d'entier\n",
      "print(np.array([1., 2., 3.]).dtype) # tableau de flottants"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "int64\n",
        "float64\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Les fonctions de cr\u00e9ation de tableau ont \u00e9galement un argument `dtype` permettant d'indiquer le type souhait\u00e9"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([1, 2, 3])\n",
      "# le tableau cr\u00e9\u00e9 prend par d\u00e9faut le type des donnn\u00e9es d'entr\u00e9e : ici `int`\n",
      "a/2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 46,
       "text": [
        "array([0, 1, 1])"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([1, 2, 3], dtype=float)\n",
      "a/2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "array([ 0.5,  1. ,  1.5])"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "B3) Fonctions d'alg\u00e8bre lin\u00e9aire avec NumPy"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Produit matriciel : attention !"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Par d\u00e9faut, le produit (`*`) de 2 tableaux numpy se fait *terme \u00e0 terme*. Pour le produit matriciel, il y a `np.dot`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Fabrication d'une matrice diagonale \u00e0 partir d'une liste des \u00e9l\u00e9ments diagonaux\n",
      "A = np.diag([1,2])\n",
      "B = np.ones((2,2))*3\n",
      "print(A)\n",
      "print(B)\n",
      "A * B"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[1 0]\n",
        " [0 2]]\n",
        "[[ 3.  3.]\n",
        " [ 3.  3.]]\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 147,
       "text": [
        "array([[ 3.,  0.],\n",
        "       [ 0.,  6.]])"
       ]
      }
     ],
     "prompt_number": 147
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.dot(A,B)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 148,
       "text": [
        "array([[ 3.,  3.],\n",
        "       [ 6.,  6.]])"
       ]
      }
     ],
     "prompt_number": 148
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Remarque : dans la m\u00eame lign\u00e9e, on trouve le produit scalaire (i.e. produit interne `np.inner`) et le produit externe (`np.outer`)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.inner?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 150
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Alg\u00e8bre lin\u00e9aire"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Les fontions dites *d'alg\u00e8bre lin\u00e9aire* sont regroup\u00e9s dans le sous-module `numpy.linalg`. On y trouve :\n",
      "\n",
      "* calcul de d\u00e9terminant\n",
      "* inversion de matrice\n",
      "* calcul de valeurs propres\n",
      "* ...\n",
      "\n",
      "Documentation : http://docs.scipy.org/doc/numpy/reference/routines.linalg.html\n",
      "\n",
      "Certaines de ces fonctions seront mises en oeuvres lors de la S\u00e9ance 3. On illustre ici simplement le calcul num\u00e9rique d'un d\u00e9terminant"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Fabrication d'une matrice diagonale \u00e0 partir d'une liste des \u00e9l\u00e9ments diagonaux\n",
      "a = np.diag([1,2,3])\n",
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 143,
       "text": [
        "array([[1, 0, 0],\n",
        "       [0, 2, 0],\n",
        "       [0, 0, 3]])"
       ]
      }
     ],
     "prompt_number": 143
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.linalg.det(a) # det(a) vaut 1*2*3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 142,
       "text": [
        "6.0"
       ]
      }
     ],
     "prompt_number": 142
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "B4) Lecture/\u00e9criture de fichier de donn\u00e9es"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pour les fichiers texte du type CSV (nombres s\u00e9par\u00e9s par des virgules, ou autres), NumPy fournit des fonctions de lecture.\n",
      "\n",
      "La fonction `np.loadtxt`, assez flexible, permet de lire des fichiers avec diff\u00e9rents formats. Cependant, cette flexibilit\u00e9 aboutit \u00e0 une *signature* assez charg\u00e9e"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Consultons l'aide:\n",
      "np.loadtxt?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 136
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Lecture du fichier:\n",
      "conso = np.loadtxt('./S2_Objets_et_NumPy/RTE_conso_2010-08_2011-07.csv',\n",
      "                   delimiter=',', # les champs sont s\u00e9par\u00e9s par des virgules\n",
      "                   skiprows=4, # ne pas lire les 4 premi\u00e8res lignes (du blabla)\n",
      "                   usecols=[1]) # ne lire que la colonne *2* (comptage \u00e0 partir de 0 !)\n",
      "\n",
      "N = conso.shape[0]\n",
      "print(u'{} pts charg\u00e9s, soit {:.1f} jours'.format(N, N/24./4))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "35040 pts charg\u00e9s, soit 365.0 jours\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Conversion MW -> GW\n",
      "conso = conso/1000."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On peut faire quelques statistiques simples :\n",
      "\n",
      "(en utilisant les m\u00e9thodes de l'objet `ndarray`)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(conso.min())\n",
      "print(conso.max())\n",
      "print(conso.mean())\n",
      "print(conso.std())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "30.993\n",
        "96.35\n",
        "56.1964912386\n",
        "13.0847858651\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Petite question :* comment compter le nombre de jours pass\u00e9s au-dessus de 80 GW ?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# M\u00e9thode 1 : boucle for (tr\u00e8s d\u00e9conseill\u00e9e pour les grands tableaux)\n",
      "\n",
      "N80 = 0\n",
      "for c in conso:\n",
      "    if c >= 80:\n",
      "        # on incr\u00e9mente le compteur\n",
      "        N80 += 1\n",
      "N80"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 78,
       "text": [
        "1841"
       ]
      }
     ],
     "prompt_number": 78
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Solutions avec une *op\u00e9ration vectorielle de comparaison*"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "conso_80 = conso >= 80 # (GW)\n",
      "conso_80"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 86,
       "text": [
        "array([False, False, False, ..., False, False, False], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# M\u00e9thode 2 : indexaction logique pour ne s\u00e9lectionner que les \u00e9l\u00e9ments v\u00e9rifiant conso >= 80\n",
      "len(conso[conso_80])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 85,
       "text": [
        "1841"
       ]
      }
     ],
     "prompt_number": 85
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# M\u00e9thode 3 : jouer avec le transtypage implicite  (bool -> int)\n",
      "# On calcule la \"somme\"\n",
      "conso_80.sum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 83,
       "text": [
        "1841"
       ]
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "\u00c9criture de donn\u00e9es CSV"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Le pendant pour l'\u00e9criture de `np.loadtxt` est `np.savetxt`. On se r\u00e9ferera \u00e0 la documentation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.savetxt?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "C) Trac\u00e9 de graphiques avec Matplotlib"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "La biblioth\u00e8que Matplotlib ( http://matplotlib.org ) permet de r\u00e9aliser une grande palette de graphiques 2D (et m\u00eame un peu 3D) avec une syntaxe fortement calqu\u00e9e sur celle de Matlab.\n",
      "\n",
      "* trac\u00e9s temporels y = f(t)\n",
      "* nuages de points (x,y)\n",
      "* histogrammes\n",
      "* images\n",
      "* ...\n",
      "\n",
      "La gallerie ( http://matplotlib.org/gallery.html ) est une bonne fa\u00e7on d'avoir un aper\u00e7u des possibilit\u00e9s de Matplotlib.\n",
      "\n",
      "*Source de documentation :*\n",
      "\n",
      "* Documentation officielle http://matplotlib.org/contents.html (en anglais)\n",
      "* Tutoriel de Nicolas Rougier (INRIA) http://webloria.loria.fr/~rougier/teaching/matplotlib/ (en anglais)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Importer l'API de Matplotlib:\n",
      "import matplotlib.pyplot as plt\n",
      "# Remarques :\n",
      "# * cet import a d\u00e9j\u00e0 \u00e9t\u00e9 r\u00e9alis\u00e9 en mode \"Pylab\"\n",
      "# * il est par contre n\u00e9cessaire dans un script\n",
      "\n",
      "# Pour un travail interactif, on s'autorisera aussi\n",
      "from matplotlib.pyplot import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "C1) Aper\u00e7us de Matplotlib"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Un exemple de graphique minimal"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Cr\u00e9ation des \"donn\u00e9es\" : un sinus\n",
      "x = np.linspace(0, 4*np.pi)\n",
      "y = np.sin(x)\n",
      "\n",
      "# Trac\u00e9\n",
      "plt.plot(x,y) # ligne (bleue par d\u00e9faut)\n",
      "plt.plot(x,y, 'r+') # marqueurs \"+\" rouges\n",
      "\n",
      "# Annotations:\n",
      "plt.title('Un sinus')\n",
      "plt.xlabel('temps t')\n",
      "plt.grid(True);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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F/sr9nSQlwddfWyDIQ/T9ox5BYfqrVtk7zy8kJgauv15sbq2xOYZRtArX9m2xnU769i0o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\n2vQ1Go0mhPj/AWidhBZdXExmAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Exemple pour le d\u00e9placement et le zoom interactif: Consommation d'\u00e9lectricit\u00e9"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Lorsque qu'on travaille avec un grand nombre de points (ex : grande s\u00e9rie temporelle), l'exploration *interactive* des donn\u00e9es est particuli\u00e8rement utile.\n",
      "\n",
      "Remarque : pour manipuler des grandes s\u00e9ries de donn\u00e9es, il existe le puissant module `pandas` (Python Data Analysis Library http://pandas.pydata.org/) qui ne sera pas abord\u00e9 ici."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Vecteur temps en jours:\n",
      "t = np.arange(N)/24./4 # attention au '24.'\n",
      "t[:10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "array([ 0.        ,  0.01041667,  0.02083333,  0.03125   ,  0.04166667,\n",
        "        0.05208333,  0.0625    ,  0.07291667,  0.08333333,  0.09375   ])"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# %pylab qt # afficher la figure dans une fen\u00eatre interactive: n\u00e9cessite IPython 1.0 (pr\u00e9vu pour juillet 2014)\n",
      "plt.plot(t, conso)\n",
      "\n",
      "plt.xlabel('temps (j)')\n",
      "plt.ylabel(u'Puissance consomm\u00e9e (GW)');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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taRXW/Pncp7Byys115NeyzrOcoZByY6nh8ceB8HD6b4QAdeuq66Pg/y+lfAC9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\nhRkKBoPBYMjCDAWDwWAwZPl/1+UK6aq8IH4AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pour se d\u00e9placer et zoomer interactivement, utiliser la barre d'outils Matplotlib ou bien les raccourcis clavier ('p' et 'o').\n",
      "\n",
      "(ic\u00f4nes \n",
      " <img src='https://raw.github.com/matplotlib/matplotlib/master/lib/matplotlib/mpl-data/images/move.png'> et\n",
      " <img src='https://raw.github.com/matplotlib/matplotlib/master/lib/matplotlib/mpl-data/images/zoom_to_rect.png'>) \n",
      "\n",
      "* Les clic-gauche et clic-droit ont une action diff\u00e9rente !\n",
      "* Les touches 'x' et 'y' modifient \u00e9galement le comportement (d\u00e9placement/zoom horizontal ou vertical)\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Zoom \"programm\u00e9\"\n",
      "plt.plot(t, conso);\n",
      "plt.title('Zoom sur 2 semaines consommation')\n",
      "plt.xlabel('temps (j)')\n",
      "\n",
      "plt.xlim(99, 113);\n",
      "# il existe aussi plt.ylim"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 53,
       "text": [
        "(99, 113)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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QXa1Hv35AzU1Fl2vPkde1tXoEBwN+foabFwz7P3/jBvDyy/R66lQDKiuB48f1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\nAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Petite question : sur ce graphique de 14 jours, quels jours correspondent aux *weekends* ?"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Un histogramme"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.hist(conso, bins=50, normed=False)\n",
      "# (mettre normed=True pour tracer une densit\u00e9 de probabilit\u00e9)\n",
      "plt.xlabel(u'Puissance consomm\u00e9e (GW)');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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+OoiIiJzGRoCg9j5d5leaRekAsnj6mAAbASIiDzaoxgR6+i2y0n2erIN1sA57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\nMDYCREQe7P8DBkKcJJzxQUsAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 117
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "C2) Exemple Num\u00e9rique & Graphique plus complet : un diagramme de Bode"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "L'enjeu de cette partie :\n",
      "\n",
      "\n",
      "* *charger des donn\u00e9es* \"exp\u00e9rimentales\" issue du relev\u00e9 d'un diagramme de Bode\n",
      "* *tracer* un beau diagramme de Bode (gain et phase)\n",
      "* *mod\u00e9liser* une r\u00e9ponse fr\u00e9quentielle par une fonction de transfert (du 2\u00e8me ordre)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Chargement de donn\u00e9es  (pseudo relev\u00e9 exp\u00e9rimental d'un diagramme de Bode)\n",
      "data = np.loadtxt('./S2_Objets_et_NumPy/bode_data.csv', delimiter=',')\n",
      "data.shape # nombre de lignes, nombre de colonnes"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 89,
       "text": [
        "(100, 3)"
       ]
      }
     ],
     "prompt_number": 89
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Le fichier bode_data.csv contient 3 colonnes:\n",
      "\n",
      "* fr\u00e9quence (Hz)\n",
      "* gain (dB)\n",
      "* phase (\u00b0)\n",
      "\n",
      "**Question de slicing** : comment s\u00e9parer ces 3 colonnes dans 3 variables diff\u00e9rentes ?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# S\u00e9paration des donn\u00e9es\n",
      "f = data[:,0]\n",
      "gain = data[:,1]\n",
      "phase = data[:,2]\n",
      "\n",
      "# ou en abr\u00e9g\u00e9 :\n",
      "# f, gain, phase = data.T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 90
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Affichage (trac\u00e9 en \u00e9chelle lin\u00e9aire):\n",
      "plt.plot(f, gain);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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bFgMijUVGyrkCau6n4Okpb57h4XJyW2OWnS07cVeskCOw7t6prj5KS+XyE3Xp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\nEYHFgIiIwGJARERgMSAiIgD/D37XdbOm/NNTAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 91
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Avec une \u00e9chelle *lin\u00e9aire* en fr\u00e9quence, on ne reconnait pas grand chose...\n",
      "\n",
      "Une solution: le graphique *log/semilog* avec les fonctions `semilogx`, `semilogy` et `loglog`. (noms de fonction Matlab)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Trac\u00e9 en \u00e9chelle semilog pour les abscisses (la fr\u00e9quence)\n",
      "semilogx(f, gain)\n",
      "# Annotations:\n",
      "title('Diagramme de Bode')\n",
      "xlabel(u'fr\u00e9quence (Hz)')\n",
      "ylabel('gain (dB)');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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YK3jtaRach6GsPudhWI6pn0OjAT77TM7J2L/fese1Rpuch1Gq0nkYWnXq1MHU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\nREZhwCAiIqP8f7oxjasfFpSgAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 92
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Trac\u00e9 conjoint du gain et de la phase:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pour ce graphique plus compliqu\u00e9, on utilise l'approche *Orient\u00e9 Objet* (\"OO\" API). (Accessoirement, cela dispense d'utiliser `plt.semilogx`)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure('Bode', figsize=(6,6))\n",
      "ax1 = fig.add_subplot(2,1,1, xscale='log',\n",
      "                      title='Diagramme de Bode: gain (dB)')\n",
      "ax1.plot(f, gain)\n",
      "ax2 = fig.add_subplot(2,1,2, sharex=ax1,  # sharex -> synchronise les \u00e9chelles. Pratique pour zoomer !\n",
      "                      title=u'Phase (\u00b0)',\n",
      "                      xlabel=u'fr\u00e9quence (Hz)')\n",
      "ax2.plot(f, phase, 'g')\n",
      "# ajustement des \"ticks\"\n",
      "ax2.set_yticks([-180, -135, -90, -45, 0])\n",
      "# ou de fa\u00e7on plus automatique :\n",
      "# ax2.set_yticks(range(0,-181,-45)) # (de 0 \u00e0 -180\u00b0, tous les 45\u00b0)\n",
      "\n",
      "fig.tight_layout() # \"\u00e9tire\" les graphiques dans la fen\u00eatre"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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L5e7bpzqvF1+E114DPz/7xShsSyZdOCAj5C0kh1W88pLDKljFitC8OVy6lPsY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\n"
      }
     ],
     "prompt_number": 133
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On reconnait la fonction de tranfert d'un passe-bas du 2\u00e8me ordre\n",
      "\n",
      "$$ H(f) = \\frac{H_0}{1 + j \\frac{f}{Q f_0} - \\frac{f^2}{f_0^2}} $$ \n",
      "\n",
      "Les param\u00e8tres \u00e0 identifier sont :\n",
      "\n",
      "* le gain statique $H_0$\n",
      "* la fr\u00e9quence canonique $f_0$\n",
      "* le facteur de qualit\u00e9 $Q$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Identification des param\u00e8tres (exercice)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Cherchons le gain basse fr\u00e9quence $H_0$ dans les 5 premieres valeurs de gain :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Observation du gain \u00e0 basse fr\u00e9quence:\n",
      "print(f[:5])\n",
      "print(gain[:5])\n",
      "gain[:5].mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 100.      104.7616  109.7499  114.9757  120.4504]\n",
        "[ 6.155659  6.001112  5.810821  6.184953  6.278457]\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 94,
       "text": [
        "6.0862004000000001"
       ]
      }
     ],
     "prompt_number": 94
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# dB -> lin\u00e9aire\n",
      "H0_dB = 6 # dB\n",
      "print(10**(H0_dB/20.)) # Attention au point de \"20.\"\n",
      "H0 = 2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.99526231497\n"
       ]
      }
     ],
     "prompt_number": 95
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Cherchons la fr\u00e9quence canonique avec le maximum du gain"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gain.max()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 96,
       "text": [
        "14.366379999999999"
       ]
      }
     ],
     "prompt_number": 96
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Fr\u00e9quence canonique: c'est environ la fr\u00e9quence de r\u00e9sonance\n",
      "i_max = gain.argmax()\n",
      "f[i_max]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 97,
       "text": [
        "977.00999999999999"
       ]
      }
     ],
     "prompt_number": 97
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f0 = 1e3 "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 98
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pour le facteur de qualit\u00e9, on utilise la m\u00e9thode devinette (cf. S\u00e9ance 4 pour une identification par minimisation de l'erreur)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Facteur de qualit\u00e9 : devinette\n",
      "Q = 10"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 99
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Calcul de la fonction de transfert du passe-bas"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# On construit une fonction de transfert\n",
      "\n",
      "# Dans cet exemple, on a d\u00e9j\u00e0 un vecteur de fr\u00e9quence. \u00c0 d\u00e9faut, on pourrait utiliser :\n",
      "# f = np.logspace(2, 4, 100)# de 100 \u00e0 10 kHz\n",
      "\n",
      "# Tranfert du 2\u00e8 ordre:\n",
      "H_fit = H0/(1 + 2j*f/(f0*Q) - (f/f0)**2)\n",
      "H_fit[:5] # (tableau de nombres complexes)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 104,
       "text": [
        "array([ 2.01937787-0.04079551j,  2.02128641-0.0428206j ,\n",
        "        2.02338500-0.04495474j,  2.02569298-0.04720512j,\n",
        "        2.02823182-0.04957958j])"
       ]
      }
     ],
     "prompt_number": 104
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calcul du gain et de la phase\n",
      "Habs = np.abs(H_fit) # `abs` donne le module du nombre complexe\n",
      "\n",
      "gain_fit = 20*np.log10(Habs) # -> dB\n",
      "gain_fit[:5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 108,
       "text": [
        "array([ 6.10612393,  6.1145058 ,  6.12371376,  6.13383021,  6.14494616])"
       ]
      }
     ],
     "prompt_number": 108
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phase_fit = np.angle(H_fit) * 180 / np.pi\n",
      "phase_fit[:5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 109,
       "text": [
        "array([-1.15733307, -1.21361943, -1.27276485, -1.33493309, -1.40030107])"
       ]
      }
     ],
     "prompt_number": 109
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Comparaison donn\u00e9es/mod\u00e8les (et l\u00e9gende d'un graphique)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Par d\u00e9faut, les graphiques se superposent:\n",
      "semilogx(f, gain, '-+', label=u'donn\u00e9es')\n",
      "semilogx(f, gain_fit, label=u'mod\u00e8le')\n",
      "legend(loc='lower left');\n",
      "\n",
      "# Fabrication de la cha\u00eene de caract\u00e8re de titre:\n",
      "title_str = u'Mod\u00e9lisation du 2\u00e8 ordre: H0={:.1f}, f0={:.1f} kHz, Q={:.1f}'.format(H0, f0/1000, Q)\n",
      "# La syntaxe du \"string formatting\" : http://docs.python.org/2/library/string.html#formatstrings\n",
      "title(title_str);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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KS0ujjh070s6dOyktLU068CAvpalT9ne4du0amZmZUUBAQL40WWQ7cpcuXUpisZgyMzPz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\n9ImIXAiTPhGRC2HSJyJyIf8F8d58vMc6IQUAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 107
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Apparemment on a \u00e9t\u00e9 un peu optimiste pour le facteur de qualit\u00e9. $Q=5$ sera sans doute plus appropri\u00e9...\n",
      "(cf. script Bode_data_generator.py qui a fabriqu\u00e9 les donn\u00e9es)\n",
      "\n",
      "La S\u00e9ance 4 abordera l'identification des param\u00e8tres $H_0, Q, f_0$ par minimisation de l'erreur de gain et de phase."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Trac\u00e9s bonus"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* comment tracer un diagramme de Black ? (phase, gain dB) \n",
      "* comment tracer un diagramme de Nyquist ? (Re, Im)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Black :\n",
      "plot(phase, gain)\n",
      "plot(phase_fit, gain_fit)\n",
      "plot(-180,0, 'r*', markersize=15) # point critique\n",
      "\n",
      "# ajustement des \"ticks\"\n",
      "xticks([-180, -135, -90, -45, 0])\n",
      "\n",
      "xlabel(u'phase (\u00b0)')\n",
      "ylabel('Gain (dB)');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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4kIiICKysrHBzc6NLly5Ur659nP2D6PZ7IGix9+JeujfsjtWtRfTuJSsLpk6F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\nFAUhhBAGUhSEEEIY/D/lO3mOTp1CKQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 139
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Diagramme de Nyquist\n",
      "\n",
      "# \u00c9tape 1 : on reconstruit la r\u00e9ponse fr\u00e9quentielle complexe\n",
      "gain_lin = 10**(gain/20.) # dB -> lin\n",
      "H = gain_lin*np.exp(1j*phase/180*np.pi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 134
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \u00c9tape 2 : trac\u00e9 (utilisant les attributs .real et .image des tableaux de nombres complexes)\n",
      "plot(H.real, H.imag)\n",
      "plot(H_fit.real, H_fit.imag)\n",
      "plot(-1,0, 'r*', markersize=10) # point critique\n",
      "\n",
      "ax = gca()\n",
      "ax.set_aspect('equal') # M\u00eame \u00e9chelle en x et y\n",
      "ylim(-11,1);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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WagzqoFNeTnMO3EA1sUNITRHxEfC043ZtOjUHCqUaEJkYiY423I1UADpmDsVb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\nCzUHCoVSLtQcKBRKufw/CXfJWgxEtmQAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 137
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "*Fin de la session 2*\n",
      "\n",
      "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/3.0/fr/\">\n",
      "    <img alt=\"Licence Creative Commons\" style=\"border-width:0\" src=\"http://i.creativecommons.org/l/by/3.0/fr/88x31.png\" />\n",
      "</a>\n",
      "\n",
      "Ce <span xmlns:dct=\"http://purl.org/dc/terms/\" href=\"http://purl.org/dc/dcmitype/InteractiveResource\" rel=\"dct:type\">support de formation</span> cr\u00e9\u00e9 par\n",
      "<span xmlns:cc=\"http://creativecommons.org/ns#\" property=\"cc:attributionName\">Pierre Haessig</span>\n",
      "est mis \u00e0 disposition selon les termes de la\n",
      "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/3.0/fr/\">licence Creative Commons Attribution 3.0 France</a>."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}