{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Les fonctions\n",
    "\n",
    "Définir des fonctions aide à alléger les programmes mais aussi permet une plus grande flexibilité afin de changer des paramètres, modèles. On peut définir une fonction en python en utilisant: "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "def myfunc(x,alpha):\n",
    "\treturn x**alpha"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Ici la fonction prend deux inputs, une valeur $x$ ainsi qu'un paramètre $\\alpha$. Elle retourne, $f(x) = x^{\\alpha}$.  "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "myfunc(2.0,0.5)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "On peut définir une valeur par défault pour certains paramètres. Mais tous les paramètres obligatoires doivent apparaître avant ceux qui sont optionnels et qui ont une valeur par défault. Par exemple:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "def myfunc(x,alpha=0.5):\n",
    "\treturn x**alpha"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "myfunc(2.0)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Variables globales et locales\n",
    "\n",
    "Les variables définies à l'intérieur d'une fonction sont locales à cette fonction. Elles ne sont pas accessibles en dehors de la fonction. Par exemple, "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "def myfunc(x,alpha=0.5):\n",
    "\tbeta = 4.0\n",
    "\treturn x**alpha"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "myfunc(2.0)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "beta"
   ],
   "outputs": [
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "name 'beta' is not defined",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-7-6c007a14875d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mbeta\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'beta' is not defined"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Que se passe-t-il quand une variable est à la fois assigné localement dans la fonction et existe en globale?"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "def myfunc(x,alpha=0.5):\n",
    "\tbeta = 4.0\n",
    "\treturn x**alpha"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "beta = 2.0\n",
    "myfunc(2.0)\n",
    "beta"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Sa valeur ne change pas globalement après un changement local dans la fonction. On peut utiliser une variable globale dans une fonction, "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "def myfunc(x,alpha=0.5):\n",
    "\treturn x**alpha + beta"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "source": [
    "myfunc(2.0)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "3.414213562373095"
      ]
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Mais ce n'est pas recommandé afin d'éviter les conflits et faciliter les appels répétés dans lesquels la valeur de `beta` change. Mieux vaut faire "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "source": [
    "def myfunc(x,beta=0.0,alpha=0.5):\n",
    "\treturn x**alpha + beta"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "source": [
    "myfunc(2.0)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "metadata": {},
     "execution_count": 16
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "source": [
    "myfunc(2.0,beta=2.0)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "3.414213562373095"
      ]
     },
     "metadata": {},
     "execution_count": 17
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Fonction partielle\n",
    "\n",
    "Certaines fonctions en Python demande comme argument une fonction d'une seule variable. Que faire si notre fonction en a plusieurs. On utilise alors la fonction `partial()` de `functools`:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "source": [
    "def myfunc(x,y,alpha,beta):\n",
    "\treturn x**alpha * y**beta "
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "source": [
    "from functools import partial"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "source": [
    "pfunc = partial(myfunc,y=1.0,alpha=0.5,beta=1.0)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "source": [
    "pfunc(2.0)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "metadata": {},
     "execution_count": 21
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "source": [
    "myfunc(2.0,1.0,0.5,1.0)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "metadata": {},
     "execution_count": 22
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Fonctions à plusieurs résultats\n",
    "\n",
    "Que faire si notre fonction retourne plusieurs réponses? On peut retourner ce qu'on appelle un tuple. Voyons voir, "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "source": [
    "def myfunc(x,y,alpha,beta):\n",
    "\treturn x**alpha,y**beta"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Cette fonction retourne deux nombres. "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "source": [
    "myfunc(2.0,0.0,0.5,1.0)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(1.4142135623730951, 0.0)"
      ]
     },
     "metadata": {},
     "execution_count": 28
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "On peut les assigner avec "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "source": [
    "xx,yy = myfunc(2.0,0.0,0.5,1.0)\n",
    "xx"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "metadata": {},
     "execution_count": 27
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Les fonctions `lambda`"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "On peut écrire des fonctions directement sur une ligne. Ceci est utile dans certaines circonstances:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "f = lambda x: x**0.5\n",
    "f(2.0)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "metadata": {},
     "execution_count": 1
    }
   ],
   "metadata": {}
  }
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