NumPy - mesures du temps CPU

numpy-performance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy 2 : exercices d'échauffement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Combien gagne-t-on en temps CPU avec NumPy ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python propose un module pour mesurer la durée d'exécution d'une commande, qui prend certaines précautions pour assurer des résultats fiables. Notamment, la commande est exécutée plusieurs fois afin d'obtenir un temps moyen qui est beaucoup moins sensible aux aléas de l'environnement qu'une mesure unique.\n",
    "\n",
    "Voici comment l'utiliser :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0038431570001193904\n"
     ]
    }
   ],
   "source": [
    "import timeit\n",
    "\n",
    "print(timeit.timeit(\"len(range(10))\", number=10000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le principe est simple: on fournit la commande sous forme d'une chaîne de caractères, et le nombre de répétition, et on obtient le temps d'exécution moyen en secondes.\n",
    "\n",
    "A la place d'une chaîne de caractères, on peut donner une fonction *sans arguments* :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.005144783000105235\n"
     ]
    }
   ],
   "source": [
    "def test():\n",
    "    return len(range(10))\n",
    "\n",
    "print(timeit.timeit(test, number=10000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le temps est plus long dans ce cas, parce que l'appel à la fonction a aussi un coût, qui est en fait de la même ordre de grandeur que le coût de la simple fonction `len`. Mais ce petit surcoût devient négligeable quand on mesure des calculs plus substantiels, ce que nous allons faire par la suite."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice : temps d'exécution pour additioner deux listes ou deux tableaux\n",
    "\n",
    "Nous reprenons la génération de listes de nombres aléatoires de la semaine dernière :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": "markdown",
   "metadata": {},
   "source": [
    "A vous de faire :\n",
    "\n",
    " 1. Ecrivez une fonction qui additionne deux listes élément par élément.\n",
    " 2. Vérifiez que votre fonction donne le même résultat pour deux listes aléatoires que l'addition des deux listes converties en tableaux.\n",
    " 3. Mesurez le temps d'exécution de votre fonction pour des listes aléatoires de tailles entre 10 et 1000.\n",
    " 4. Mesures également le temps d'exécution de la somme après conversion en tableaux.\n",
    " 5. Faites un plot des deux temps d'exécutions en fonction du nombre d'éléments.\n",
    " 6. Faites un plot des deux temps d'exécutions *par élément* en fonction du nombre d'éléments."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour vous aider avec les deux premières étapes, voici le code qui fait la vérification. Il vous reste à compléter la définition de la fonction `somme_de_listes`. Si tout va bien, le test produit `True` pour chaque itération de la boucle.\n",
    "\n",
    "Cet exemple illustre qu'un tableau peut aussi contenir de booléens, donc des valeurs `True` ou `False`. La comparaison `t1 == t2` compare `t1` et `t2` élément par élément et retourne un tel tableau de booléens. Avec `.all()` on teste si tous les éléments ont la valeur `True`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hide_input": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "def somme_de_listes(l1, l2):\n",
    "    return [x + y for x, y in zip(l1, l2)]\n",
    "\n",
    "for i in range(5):\n",
    "    l1 = liste_de_nombres_aleatoires(10)\n",
    "    l2 = liste_de_nombres_aleatoires(10)\n",
    "    somme_listes = somme_de_listes(l1, l2)\n",
    "    t1 = np.array(l1)\n",
    "    t2 = np.array(l2)\n",
    "    somme_tableaux = t1 + t2\n",
    "    print((np.array(somme_listes) == somme_tableaux).all())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour ceux qui n'ont pas vu la fonction `zip` avant, voici comment elle fonctionne :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 'a'), (2, 'b'), (3, 'c')]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(zip([1, 2, 3], ['a', 'b', 'c'])) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour les mesures des étapes 4 à 6, il reste un astuce à connaître. Il faut contourner la contrainte de `timeit.timeit`, qui n'accepte qu'une fonction sans argument. Impossible donc de faire quelque chose comme\n",
    "`timeit.timeit(somme_de_listes(l1, l2))`. L'astuce est de définir une fonction supplémentaire rien que pour mesurer le temps d'exécution. Voici un exemple :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00013218300045991782\n"
     ]
    }
   ],
   "source": [
    "l1 = liste_de_nombres_aleatoires(10)\n",
    "l2 = liste_de_nombres_aleatoires(10)\n",
    "def temps():\n",
    "    return somme_de_listes(l1, l2)\n",
    "print(timeit.timeit(temps, number=100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vous pouvez faire cela même dans une boucle :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50 0.003870102998916991\n",
      "100 0.0073099260007438716\n",
      "500 0.0457768300002499\n"
     ]
    }
   ],
   "source": [
    "for n in [50, 100, 500]:\n",
    "    l1 = liste_de_nombres_aleatoires(n)\n",
    "    l2 = liste_de_nombres_aleatoires(n)\n",
    "    def temps():\n",
    "        return somme_de_listes(l1, l2)\n",
    "    print(n, timeit.timeit(temps, number=1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A vous de jouer ! N'hésitez pas à consulter le notebook de la semaine dernière comme source d'inspiration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10f70da20>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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CAcP/vLCD1RuPMCI5jh9/biZXzc/tsMY20GlAUCqKdbR8ZlCqy6oh6EijvvHbNwtYvfEI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\nKaWUTQOCUkopQAOCUkopmwYEpZRSAPz/ln9d/uN1q+UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f327470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.linspace(0, 1000, 100, dtype=np.int)\n",
    "t_liste = []\n",
    "t_tableau = []\n",
    "for nn in n:\n",
    "    l1 = liste_de_nombres_aleatoires(nn)\n",
    "    l2 = liste_de_nombres_aleatoires(nn)\n",
    "    t1 = np.array(l1)\n",
    "    t2 = np.array(l2)\n",
    "    def somme_listes():\n",
    "        return [x + y for x, y in zip(l1, l2)]\n",
    "    def somme_tableaux():\n",
    "        return t1 + t2\n",
    "    t_liste.append(timeit.timeit(somme_listes, number=100))\n",
    "    t_tableau.append(timeit.timeit(somme_tableaux, number=100))\n",
    "plt.plot(n, t_liste, label='liste')\n",
    "plt.plot(n, t_tableau, label='tableau')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10f8f6940>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bf9D0a8LNXcdbuPi//pfKhvaEjxnJtlQ2MT4njYn2ZxZWmOWhTttc1Cil4TJE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\n7zOR5BAaHq4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b74d240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.linspace(10, 1000, 100, dtype=np.int)\n",
    "t_liste = []\n",
    "t_tableau = []\n",
    "for nn in n:\n",
    "    l1 = liste_de_nombres_aleatoires(nn)\n",
    "    l2 = liste_de_nombres_aleatoires(nn)\n",
    "    t1 = np.array(l1)\n",
    "    t2 = np.array(l2)\n",
    "    def somme_listes():\n",
    "        return [x + y for x, y in zip(l1, l2)]\n",
    "    def somme_tableaux():\n",
    "        return t1 + t2\n",
    "    t_liste.append(timeit.timeit(somme_listes, number=100)/nn)\n",
    "    t_tableau.append(timeit.timeit(somme_tableaux, number=100)/nn)\n",
    "plt.plot(n, t_liste, label='liste')\n",
    "plt.plot(n, t_tableau, label='tableau')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Enfin, on peut s'intéresser à la performance *relative* de listes et de tableaux. On divise donc, pour une taille donnée, la temps obtenu pour les listes par le temps obtenu pour les tableaux :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x119c529b0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4HMOHzfL8LH5w6wqONnt44q2hUzSbuvrijrIeL5n1Nysm1P6GLv7mkXc40d5L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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119439e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.linspace(10, 10000, 100, dtype=np.int)\n",
    "t_rel = []\n",
    "for nn in n:\n",
    "    l1 = liste_de_nombres_aleatoires(nn)\n",
    "    l2 = liste_de_nombres_aleatoires(nn)\n",
    "    t1 = np.array(l1)\n",
    "    t2 = np.array(l2)\n",
    "    def somme_listes():\n",
    "        return [x + y for x, y in zip(l1, l2)]\n",
    "    def somme_tableaux():\n",
    "        return t1 + t2\n",
    "    t_liste = timeit.timeit(somme_listes, number=100)\n",
    "    t_tableau = timeit.timeit(somme_tableaux, number=100)\n",
    "    t_rel.append(t_liste / t_tableau)\n",
    "plt.plot(n, t_rel)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sur mon ordinateur, je gagne donc environ un facteur 100 en utilisant les tableaux. Ceci ne vaut que pour mon ordinateur, et que pour l'addition, bien sûr !"
   ]
  }
 ],
 "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
}