Cours GSON du 27 novembre 2018

Introduction-NumPy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "hide_input": false
   },
   "source": [
    "# NumPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Bibliothèque pour le calcul scientifique en Python\n",
    "- Ne fait pas partie de Python, doit être installé séparément\n",
    "\n",
    "**Trois usages principaux :**\n",
    " - Gestion **efficace** de données homogènes et volumineuses\n",
    " - Gestion de données **multidimensionnelles**\n",
    " - **Interfaçage** avec du code en C / C++ / Fortran *(hors sujet dans ce cours)*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Une structure de données compacte : le tableau"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Liste | Tableau |\n",
    "| --- | --- |\n",
    "| taille variable | taille fixe |\n",
    "| éléments arbitraires | éléments d'un même type |\n",
    "| unidimensionnelle | multidimensionnel |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Par convention, on rénomme `numpy` en `np` à l'importation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les tableaux ont beaucoup en commun avec les listes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
      "[ 1  2  3  4  5  6  7  8  9 10]\n"
     ]
    }
   ],
   "source": [
    "liste = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
    "print(liste)\n",
    "tableau = np.array(liste)\n",
    "print(tableau)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 1\n",
      "[4, 5, 6] [4 5 6]\n",
      "[10, 9, 8, 7, 6, 5, 4, 3, 2, 1] [10  9  8  7  6  5  4  3  2  1]\n"
     ]
    }
   ],
   "source": [
    "print(liste[0], tableau[0])\n",
    "print(liste[3:6], tableau[3:6])\n",
    "print(liste[::-1], tableau[::-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un tableau a pourtant quelques attributs en plus: le type des éléments (`dtype`) et la forme (`shape`), une généralisation de la longueur au cas multi-dimensionnel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "1\n",
      "(10,)\n",
      "int64\n"
     ]
    }
   ],
   "source": [
    "print(len(tableau))\n",
    "print(tableau.ndim)\n",
    "print(tableau.shape)\n",
    "print(tableau.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tableaux multidimensionnels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les tableaux multidimensionnels ressemblent aux listes de listes (de listes ...)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1, 2], [3, 4], [5, 6]]\n",
      "[[1 2]\n",
      " [3 4]\n",
      " [5 6]]\n"
     ]
    }
   ],
   "source": [
    "liste_de_listes = [[1, 2], [3, 4], [5, 6]]\n",
    "print(liste_de_listes)\n",
    "tableau_2d = np.array(liste_de_listes)\n",
    "print(tableau_2d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "3\n",
      "2\n",
      "(3, 2)\n",
      "int64\n"
     ]
    }
   ],
   "source": [
    "print(len(liste_de_listes))\n",
    "print(len(tableau_2d))\n",
    "print(tableau_2d.ndim)\n",
    "print(tableau_2d.shape)\n",
    "print(tableau_2d.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'indexation se fait par dimension, mais autrement c'est exactement comme pour les listes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tableau_2d[0, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tableau_2d[:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 5])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tableau_2d[1:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 5],\n",
       "       [4, 3],\n",
       "       [2, 1]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tableau_2d[::-1, ::-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quelques fonctions préfabriquées pour créer des tableaux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2, 3, 4]\n",
      "[0 1 2 3 4]\n"
     ]
    }
   ],
   "source": [
    "print(list(range(5)))\n",
    "print(np.arange(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0. ,  0.1,  0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8,  0.9,  1. ,\n",
       "        1.1,  1.2,  1.3,  1.4,  1.5,  1.6,  1.7,  1.8,  1.9,  2. ])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(0., 2.1, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0. ,  0.1,  0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8,  0.9,  1. ,\n",
       "        1.1,  1.2,  1.3,  1.4,  1.5,  1.6,  1.7,  1.8,  1.9,  2. ])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(0, 2., 21)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.],\n",
       "       [ 0.,  3.,  0.],\n",
       "       [ 0.,  0.,  5.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag([1., 3., 5.])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((2, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0],\n",
       "       [0, 0, 0]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((2, 3), dtype=np.int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.,  0.],\n",
       "       [ 0.,  0.,  1.,  0.],\n",
       "       [ 0.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0],\n",
       "       [0, 1, 0, 0],\n",
       "       [0, 0, 1, 0],\n",
       "       [0, 0, 0, 1]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(4, dtype=np.int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(4, dtype=np.int32).dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Arithmétique"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le principe à retenir : toutes les opérations sont faites élément par élément."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tableau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  4,  6,  8, 10, 12, 14, 16, 18, 20])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tableau + tableau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3,  4,  5,  6,  7,  8,  9, 10, 11, 12])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tableau + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  4,  6,  8, 10, 12, 14, 16, 18, 20])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*tableau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  4],\n",
       "       [ 9, 16],\n",
       "       [25, 36]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tableau_2d ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  1.41421356,  1.73205081,  2.        ,  2.23606798,\n",
       "        2.44948974,  2.64575131,  2.82842712,  3.        ,  3.16227766])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(tableau)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice : créez les tableaux suivants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1., -1., -1.],\n",
       "       [-1.,  1., -1.],\n",
       "       [-1., -1.,  1.]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*np.eye(3)-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  0,  0,  0],\n",
       "       [ 0,  4,  0,  0],\n",
       "       [ 0,  0,  9,  0],\n",
       "       [ 0,  0,  0, 16]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag(np.arange(1, 5)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  0,  0,  0],\n",
       "       [ 0,  4,  0,  0],\n",
       "       [ 0,  0,  9,  0],\n",
       "       [ 0,  0,  0, 16]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag(np.arange(5)**2)[1:, 1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 3, 2, 1, 0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.abs(np.arange(9)-4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La ligne qui commence avec % n'est pas du Python, mais une instruction pour Jupyter. Elle doit être tel qu'écrite ci-dessous, on n'a même pas droit à un commentaire après !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x112178cc0>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ERA+Fu0iUONzo48evfsJLhWXaJyYKKNxFokDNwQZmLCjk4y17+P7XB/OvFw3WdgIRTuEu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\nEoH+HxQnrTjZ6F3ZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed88470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0., 1., 20)\n",
    "y = x**2\n",
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1122ade80>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nVgzG+Jh7Lk0mt7CUWUsynY5iPOCZLzNQlDtGdXM6Sp1ZMRjjY3rHRXFZ31hm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\nqcaKwRhjTDX/D3CiHmf/czn3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1121d9a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0., 2.*np.pi, 50)\n",
    "y = np.sin(x)\n",
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.plot?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice : refaites le plot suivant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1122b6f60>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0Dq9dk0BGxjThszXJuq/BXo5uhMQlxlK1vgFmp3ErujBYZOUV8ukqN2gtlCrt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\nwQ8RzAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1122b6c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 2.*np.pi, 50)\n",
    "plt.plot(x, np.sin(x))\n",
    "plt.plot(x, np.cos(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour tout savoir sur les plots, consultez la documentation :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.plot?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Efficacité : mémoire et temps CPU"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Combien de mémoire occupe une liste ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "def liste_de_nombres_aleatoires(n):\n",
    "    return [random.uniform(0, 1) for _ in range(n)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.45746533964959313,\n",
       " 0.595769007781765,\n",
       " 0.626199638230877,\n",
       " 0.7063634990393685,\n",
       " 0.4353474973701733,\n",
       " 0.29776452050739255,\n",
       " 0.31325815381725475,\n",
       " 0.516490107822669,\n",
       " 0.062355047756414206,\n",
       " 0.9344328762660984]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "liste_de_nombres_aleatoires(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python propose la fonction `sys.getsizeof` pour trouver la taille en mémoire d'un objet. On peut l'appliquer à un tableau sans complications :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "def memoire_occupee_par_un_tableau(t):\n",
    "    return sys.getsizeof(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "120"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "memoire_occupee_par_un_tableau(np.array([1, 2, 3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: La valeur obtenu indique le nombre d'octets que le tableau occupe. A titre de comparaison, la mémoire vive d'un ordinateur moderne se mesure en gigaoctets (GO), donc des milliards d'octets. Comptez 1 GO pour un smartphone entrée de gamme et 64 GO pour un ordinateur de bureau haut de gamme."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour une liste, cette fonction n'évalue pas la mémoire occupée par ses éléments, car il s'agit d'objets indépendants. Il faut les compter séparément :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "172"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sys\n",
    "sys.getsizeof([1, 2, 3]) + sys.getsizeof(1) + sys.getsizeof(2) + sys.getsizeof(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice : écrivez une fonction qui calcule la mémoire totale occupée par une liste et ses éléments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def memoire_occupee_par_une_liste(l):\n",
    "    m = sys.getsizeof(l)\n",
    "    for element in l:\n",
    "        m += sys.getsizeof(element)\n",
    "    return m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "172"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "memoire_occupee_par_une_liste([1, 2, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice : faites un plot de la mémoire nécessaire pour stocker une liste et un tableau en fonction du nombre d'éléments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x112969d30>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZL90xkomDu9vqbT84o3h2LxuNwBkpAPxIRL4UkTkiUrNKphewz+e0XLesl3tct/yUc1S1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\nYxrMQsMYY0yDWWgYY4xpsP8PdFuwoMBPyoUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112810e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.linspace(0, 10000, 1000, dtype=np.int)\n",
    "m_liste = []\n",
    "m_tableau = []\n",
    "for nn in n:\n",
    "    l = liste_de_nombres_aleatoires(nn)\n",
    "    m_liste.append(memoire_occupee_par_une_liste(l))\n",
    "    m_tableau.append(memoire_occupee_par_un_tableau(np.array(l)))\n",
    "plt.plot(n, m_liste, label='liste')\n",
    "plt.plot(n, m_tableau, label='tableau')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice : modifiez ce plot pour montrer la mémoire utilisée par élément"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x112a80f98>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZZZjZe/sjmP4UPOPacTVLiIhEFTdJuHs78ON+iKWfqSYhIhJPopebFpvZx2yQXbw3XP2b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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1121cd860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.linspace(1, 10000, 1000, dtype=np.int)\n",
    "m_liste = []\n",
    "m_tableau = []\n",
    "for nn in n:\n",
    "    l = liste_de_nombres_aleatoires(nn)\n",
    "    m_liste.append(memoire_occupee_par_une_liste(l)/nn)\n",
    "    m_tableau.append(memoire_occupee_par_un_tableau(np.array(l))/nn)\n",
    "plt.plot(n, m_liste, label='liste')\n",
    "plt.plot(n, m_tableau, label='tableau')\n",
    "plt.xlabel(\"nombre d'éléments\")\n",
    "plt.ylabel(\"octets par élément\")\n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}