{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "066d4f2e-5eba-4304-b6ac-7a5c53f98832",
   "metadata": {},
   "source": [
    "Notebook Jupyter      UTC MT12 \n",
    "$$  \\text{UTC MT12} \\quad \\quad  \\text{TP} 2 $$\n",
    "###### Cette cellule est une cellule Markdown"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa2bf806-cdc1-4a32-aa38-77d951f4ff25",
   "metadata": {},
   "source": [
    "Dans ce TP, on considère l'espace des fonctions continues sur $[-1,1]$ à valeurs dans $\\mathbb{R},$ noté $\\mathcal{H} = C^0([-1,1];\\mathbb{R})$, muni du produit scalaire $$\\langle f,g \\rangle  = \\int_{-1}^1 f(t) g(t)\\, dt,\\qquad f,g\\in \\mathcal{H},$$  et la norme associée $\\|f\\|=\\sqrt{\\langle f,f \\rangle}$.\n",
    "\n",
    "Le but de cette séance est d'introduire une famille de polynôme orthogonaux, les polynômes de Legendre notés $(P_k)_{k\\ge 0}$, qui forme une famille totale de $\\mathcal{H}$, i.e., $(P_k)_{k\\ge 0}$ engendre un sous-espace vectoriel dense dans $\\mathcal{H}$. Plus précisément, pour toute fonction $f \\in \\mathcal{H}$, pour tout $\\varepsilon > 0$, il existe $n \\in \\mathbb{N}$ et $a_{f,0}, \\ldots, a_{f,n} \\in \\mathbb{R}$ tels que \n",
    "$$ \\left|\\left|f - \\sum_{k=0}^n a_{f,k} P_k \\right|\\right| \\leq \\varepsilon.$$ \n",
    "\n",
    "Intuitivement, on peut voir les polynômes $(P_k)_{k \\geq 0}$ comme une ``base'' de $\\mathcal{H}$. Il faut faire cependant attention, car ici $\\mathcal{H}$ est de dimension infinie. La notion de famille totale généralise la notion de base algébrique d'un espace vectoriel de dimension finie. Nous allons voir dans cette séance des applications pratiques de cette notion de famille totale. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82ac1981-08cf-4965-a2a0-938580b9172a",
   "metadata": {},
   "source": [
    "#### Plan \n",
    "[1. Exercice préliminaire : récursivité](#1.-Exercice-préliminaire-récursivité)\n",
    "\n",
    "[2. Polynômes de Legendre](#2.-Polynômes-de-Legendre)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6245769-e438-448d-b2f1-f8fae9850ac5",
   "metadata": {},
   "source": [
    "# 1. Préliminaire : récursivité"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfc1bad9-413c-42d9-83ac-7690a4f0dadc",
   "metadata": {},
   "source": [
    "## 1.1 Suite récurrente"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e082528b-7e0a-4aee-a8ab-834cb74a2fc5",
   "metadata": {},
   "source": [
    "On a vu dans le TP1 comment coder une suite définie par un terme général. Lorsqu'une suite est définie à partir d'une formule de récurrence, pour la coder, il faut utiliser *la récursivité*, c'est à dire,   \n",
    "\n",
    "     * (a) définir un terme de départ. \n",
    "     * (b) définir un terme en fonction du précédent. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe9fb0dd-82b9-4fec-989d-1872aba34661",
   "metadata": {},
   "source": [
    "Exemple : fonction \"SUITE\" qui implémente la suite $(U_n)_{n \\geq 1}$  définie par récurrence comme suit : $$ \\left\\lbrace \\begin{array}{l} U_1 = 1,\\\\ U_{n+1} = \\frac{U_n}{2}. \\end{array} \\right.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1d4f8009-607e-4548-ac25-50a80f67540e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def SUITE (n):\n",
    "    if n < 1:\n",
    "         return('la valeur de n est incorrecte') \n",
    "    elif n == 1:\n",
    "         return(1)\n",
    "    else:\n",
    "        return(SUITE(n-1)/2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d1bced5-68be-47ad-b425-6bf5da14cdc2",
   "metadata": {},
   "source": [
    "**Note importante**\n",
    "\n",
    "Si l'argument d'entrée (\"input\") de la fonction est un nombre négatif, par exemple  $-3$, il faut s'assurer que votre fonction va renvoyer un message d'erreur. Sinon, la machine va chercher à calculer SUITE(-4), qui elle-même va chercher à calculer SUITE(-5), etc, et ne va jamais s'arrêter. Il faut dont s'assurer que la condition d'arrêt (calcul de $U_1$) est bien satisfaite à un moment donné quand on écrit une fonction récursive."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dad6ebca-9d0c-4d90-abce-06add9d0ee70",
   "metadata": {},
   "source": [
    "## 1.2 Questions \n",
    "\n",
    "###### Cette cellule est une cellule Markdown "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47791b15-89f3-4f38-b66d-9ecc696f2f0b",
   "metadata": {},
   "source": [
    "### Q1 Ecrire une fonction qui code \n",
    "\n",
    "$$\\left\\{ \\begin{array}{l} U_0 = 1,\\\\ U_{n+1} = U_n + 1. \\end{array} \\right. $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8b55cf7b-4de0-4b9e-aa54-7c700055db25",
   "metadata": {},
   "outputs": [],
   "source": [
    "def suite1 (n):\n",
    "    if n<0:\n",
    "        return(print(\"la valeur de n est incorrecte\"))\n",
    "    elif n==0:\n",
    "        return(1)\n",
    "    else:\n",
    "        return(suite1(n-1)+1)    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "811dd969-ce48-4883-95c1-50061e31e207",
   "metadata": {},
   "source": [
    "### Q2 Écrire une fonction qui code la suite de Fibonacci \n",
    "\n",
    "$$\\left\\lbrace \\begin{array}{l} U_0 = 0,\\\\ U_1 = 1,\\\\ U_{n+2} = U_{n+1} + U_n. \\end{array} \\right.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "309fe117-c72e-45f1-824c-12696541b1a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def Fibo (n):\n",
    "    if n < 0:\n",
    "         return('la valeur de n est incorrecte') \n",
    "    elif n==0:\n",
    "         return(0)\n",
    "    elif n==1:\n",
    "         return(1)\n",
    "    else:\n",
    "        return(Fibo(n-1)+ Fibo(n-2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9fc5bed-c706-4d6d-ab89-86724645f39d",
   "metadata": {},
   "source": [
    "### Q3 Écrire une fonction qui code la suite de fonctions \n",
    "\n",
    "$$\\left\\lbrace \\begin{array}{l} f_0(x) = x,\\\\ f_{n+1}(x) = x \\cdot f_n(x) \\end{array} \\right.$$\n",
    "L' argument d'entrée de votre fonction est donc la paire $(n,x)$ ou $(x,n)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "037e7f41-3941-47a8-afa6-5abbf25836a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def SuiteF (n,x):\n",
    "    if n < 0:\n",
    "         return('la valeur de n est incorrecte') \n",
    "    elif n ==0:\n",
    "         return(x)\n",
    "    else:\n",
    "        return(x*SuiteF(n-1,x))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f01ce21-a297-4d8a-bd7e-c7ff93665368",
   "metadata": {},
   "source": [
    "### Q4 \n",
    "\n",
    "* Quelle est cette suite de fonctions ? \n",
    "* Représenter graphiquement les trois premiers termes de cette suite de fonctions sur l'intervalle $[-1,1]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f1bc7eb8-de85-4890-bf92-83bfe2175cac",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "N = 100\n",
    "X = np.linspace(-1, 1, N)\n",
    "Y0= SuiteF(0,X)\n",
    "Y1= SuiteF(1,X)\n",
    "Y2= SuiteF(2,X)\n",
    "plt.plot(X, Y0, '.-r', linewidth = 3,label='n=0')\n",
    "plt.plot(X, Y1, '.-b', linewidth = 3,label='n=1')\n",
    "plt.plot(X, Y2, '.-g', linewidth = 3,label='n=2')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid(); \n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f4f3754-37ae-4b3a-9793-dba2515dfd90",
   "metadata": {},
   "source": [
    "# 2. Polynômes de Legendre"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a2eb135-a8f5-41d5-810f-13891f36bb1b",
   "metadata": {},
   "source": [
    "## 2.1. Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7119b2b2-ba63-4dcb-892b-765a437ff675",
   "metadata": {},
   "source": [
    "Les polynômes de Legendre sont des polynômes  solutions sur l'intervalle  $[-1,1]$ de l'équation différentielle suivante :\n",
    "\n",
    "$${\\frac {\\textrm {d}}{{\\textrm {d}}x}}\\left[(1-x^{2}){\\frac {{\\textrm {d}}P_{n}(x)}{{\\textrm {d}}x}}\\right]+n(n+1)\\,P_{n}(x)=0,\\qquad P_{n}(1)=1.$$ \n",
    "\n",
    "Pour tout entier $n\\geq 1$ et pour $x\\in [-1,1]$, partant de $P_0(x)=1$, $P_1(x)=x$, on peut démontrer la formule de récurrence $$(n+1)\\,P_{n+1}(x)=(2n+1)\\,x\\,P_{n}(x)-n\\,P_{n-1}(x)\\qquad (2)$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9547516e-147f-41d9-9f06-44898df11101",
   "metadata": {},
   "source": [
    "Les polynômes de Legendre sont deux à deux orthogonaux (mais pas orthonormés) pour le produit scalaire dans $\\mathcal{H}$, et on montre que $$\\begin{array}{l} \\langle  P_n,P_m\\rangle = {\\displaystyle \\int _{-1}^{1}P_{m}(x)P_{n}(x)\\,dx={2 \\over {2n+1}}\\,\\delta _{mn}},\\qquad (3)\\end{array}$$\n",
    "où\n",
    "$\\delta$ désigne le symbole de Kronecker."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89ce7b84-167a-400b-9394-ad2e04e1da47",
   "metadata": {},
   "source": [
    "**Remarques**\n",
    "\n",
    "* La famille $(P_k/\\|P_k \\|)_k$ est donc orthonormée dans $\\mathcal{H}$. \n",
    "\n",
    "* On peut montrer que c'est une \"base\" (famille totale ) de $\\mathcal{H}$. \n",
    "\n",
    "* Les polynômes $P_{2p}$ sont des fonctions paires tandis que les polynômes $P_{2p+1}$ sont des fonctions impaires. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07889d4a-48fc-4c6d-a76d-7d5257c662e3",
   "metadata": {},
   "source": [
    "## 2.2 Questions \"Polynômes de Legendre\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a60a8e0f-7c1e-4ff4-8cba-4691f02bcbb4",
   "metadata": {},
   "source": [
    "### Q5 Calculer à la main les six premiers polynômes de Legendre et vérifier que \n",
    "$$\\begin{array}{l}P_2(x) = \\frac{3}{2}x^2-\\frac{1}{2},\\\\ P_3(x) = \\frac{5}{2}x^3 - \\frac{3}{2}x, \\\\ P_{{4}}(x)={\\frac  {1}{8}}\\left( 35x^{{4}}-30x^{{2}}+3 \\right),\\\\ P_{{5}}(x)={\\frac  {1}{8}} \\left( 63x^{{5}}-70x^{{3}}+15x \\right),\\\\ P_{{6}}(x)={\\frac  {1}{16}}\\left( 231x^{{6}}-315x^{{4}}+105x^{{2}}-5 \\right)\\end{array}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd8e3b4b-c97b-4d7b-b15b-73592e23ed2d",
   "metadata": {},
   "source": [
    "### Q6 Écrire une fonction qui code les polynômes de Legendre de degré $n$ au moyen de la formule de récurrence (2). \n",
    "\n",
    "Cette fonction a pour argument d'entrée le couple $(n,x)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f7613764-12ce-43fb-a270-75e00cf3bbad",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def Legendre (n,x):\n",
    "    if n < 0:\n",
    "         return('la valeur de n est incorrecte') \n",
    "    elif n == 0:\n",
    "         pn= np.ones(np.size(x))\n",
    "    elif n == 1:\n",
    "        pn = x\n",
    "    else:\n",
    "        pn = (1/n)*( (((2*n)-1)*x*Legendre(n-1,x))-((n-1)*Legendre(n-2,x)))\n",
    "    return(pn)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07a2cf69-cf51-451f-b1af-788dd17c13af",
   "metadata": {},
   "source": [
    "## 2.3 Questions  \"Meilleure approximation de la fonction $f :x \\in [-1,1] \\mapsto \\exp(-x)$\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acdbc6e7-2852-434a-b198-9b99dc20adf3",
   "metadata": {},
   "source": [
    "Dans cette section, on cherche à détemriner la meilleure approximation de la fonction $f :x  \\in [-1,1] \\mapsto \\exp(-x)$ sur le sous-espace vectoriel engendré par les polynômes de Legendre de degré inférieur à $n$.  Remarquons que $f \\in \\mathcal{H}$. \n",
    "\n",
    "Plus précisément, en reprenant les notations du Chapitre $2$, si on note $\\mathcal{P}_n = \\operatorname{Vect}\\left\\langle P_0,\\ldots,P_n \\right\\rangle \\subset \\mathcal{H}$, on cherche un polynôme $P$ de $\\mathcal{P}_n$ réalisant la meilleure approximation de $f$ dans $\\mathcal{P}_n$. Autrement dit, on cherche un polynôme $P \\in \\mathcal{P}_n$ solution du problème de minimisation suivant $$\\|f-P\\| = \\min \\lbrace \\|f - Q \\|, \\, \\, Q \\in \\mathcal{P}_n \\rbrace$$ En reprenant les calculs du Chapitre $2$, on montre que l'unique polynôme, noté $\\pi_n f$, solution de ce problème est donné par la formule $$\\pi_n f(x) = \\sum_{k=0}^n a_{f,k}\\, \\dfrac{P_k(x)}{\\|P_k\\|},\\qquad \\text{avec} \\quad a_k:= a_{f,k}= \\langle f,\\dfrac{P_k}{\\|P_k\\|}\\rangle \n",
    "\\quad \\text{et}\\quad \\|P_k\\|=\\sqrt{\\langle P_k,P_k\\rangle}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b95bf91e-dde3-4d31-8826-9428298204ee",
   "metadata": {},
   "source": [
    "####   On liste ci-dessous la valeur de $a=(a_0,a_1,a_2,a_3,a_4,a_5,a_6)$, \n",
    "$$\\begin{array}{lcl} a_0& =& \\sqrt{2}*\\sinh(1)\\\\ a_1& =& -\\frac{\\sqrt{6}}{\\exp(1)} \\\\ a_2& =& \\frac{\\exp(2)-7}{\\exp(1)}*\\sqrt{\\frac{5}{2}} \\\\ a_3 &=& \\frac{5*\\exp(2)-37}{\\exp(1)}*\\sqrt{\\frac{7}{2}}\\\\ a_4 &=& 3*\\sqrt{2}*\\frac{18*\\exp(2)-133}{\\exp(1)}\\\\ a_5 &=& \\frac{329*\\exp(2)-2431}{\\exp(1)}*\\sqrt{\\frac{11}{2}}\\\\ a_6 &=& \\frac{3655*\\exp(2)-27007}{\\exp(1)}*\\sqrt{\\frac{13}{2}}\\end{array}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "640ae29f-3162-46a9-ae65-425abf5ba2d1",
   "metadata": {},
   "source": [
    "### Q7 Écrire une fonction \"approx\" qui, prend en entrée  le triplet $(x,n,a)$ et qui renvoie $\\pi_n f(x)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2b5fb4fb-9614-4cd5-856c-2a8b52399a19",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # on définit d'abord la vecteur a\n",
    "a0 = np.sqrt(2)*np.sinh(1)\n",
    "a1 = -np.sqrt(6)/np.exp(1) \n",
    "a2 = ((np.exp(2)-7)/np.exp(1))*np.sqrt(5/2) \n",
    "a3 = ((5*np.exp(2)-37)/np.exp(1))*np.sqrt(7/2)\n",
    "a4 = (3*np.sqrt(2))*((18*np.exp(2)-133)/np.exp(1))\n",
    "a5 = ((329*np.exp(2)-2431)/np.exp(1))*np.sqrt(11/2)\n",
    "a6 = ((3655*np.exp(2)-27007)/np.exp(1))*np.sqrt(13/2)\n",
    "a=np.array([a0,a1,a2,a3,a4,a5,a6], dtype=np.float64)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a9f09fc1-c049-4ad6-a47c-0ebbb38db600",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "# Approximation de f sur les 7 premières fonctions de base\n",
    "def approx (x,n,a):\n",
    "    sX=np.size(x)\n",
    "    pk=np.ones(sX*(n+1)).reshape(sX,n+1) #matrice de dimension : dim(x)*(n+1)\n",
    "    pi_k=np.ones(sX*(n+1)).reshape(sX,n+1) #matrice de dimension : dim(x)*(n+1)\n",
    "    for k in range(n+1):\n",
    "        pk_nor = np.sqrt(2/((2*k)+1)) #la normalisation\n",
    "        pk[:,k] = Legendre (k,x)\n",
    "        pi_k[:,k]= (a[k]*pk[:,k])/pk_nor\n",
    "    return(np.sum(pi_k,1))  # on somme sur les colonnes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0315f8e6-10fa-43ba-b33a-c1387c06ede3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "# Code alternatif à la la précédente fonction \"approx\" \n",
    "def approxAlt (x,n,a):\n",
    "    y=0\n",
    "    for k in range(n+1):\n",
    "        y+= (a[k]/np.sqrt(2/((2*k)+1)))*Legendre(k,x)\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1735b98a-bd97-426c-93d8-25d812a5dc18",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "# Code alternatif  aux précédentes fonctions  \"approx\"  et \"approxAlt\"\n",
    "def approxAlt1 (x,n,a):\n",
    "    ap = [ ((a[k]/np.sqrt(2/((2*k)+1)))*Legendre(k,x)) for k in range(n+1)]\n",
    "    app =sum(ap)\n",
    "    return app   "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45003e35-3fbd-49e6-a1c2-d22e488824dd",
   "metadata": {},
   "source": [
    "### Q8 Écrire un script qui propose une vérification de l'inégalité de Bessel, à savoir  $$\\|\\pi_6 f\\|^2 = \\sum_{k=0}^6 a_k^2 \\leq \\|f\\|^2.$$ \n",
    "\n",
    "Pour ce faire on calculera la valeur exacte de $\\|f\\|^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17a22846-c1c6-4a87-8efe-7dd04463bd76",
   "metadata": {},
   "source": [
    "#### Remarquons que $\\|f\\|^2=\\sinh(2)=(1/2)(\\exp(2) - \\exp(-2))$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "dcb270bc-6064-4c6d-aa65-906596e9dbe7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.6268604078392452\n",
      "3.6268604078470186\n",
      "3.626860407847019\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "print(np.sum(a**2))\n",
    "print(np.sinh(2))\n",
    "print((1/2)*(np.exp(2)-np.exp(-2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "81e0a543-8311-40e4-9702-033cc7df77a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def I_bessel (n,a): #Vérification de l'inégalité de Bessel\n",
    "    a_tronq=a[range(n+1)]\n",
    "    z=np.sum(a_tronq**2)\n",
    "    f_no2=np.sinh(2)\n",
    "    return(f_no2-z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "18f62bb7-8606-4cfc-98f1-237c4291891d",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(I_bessel(6,a))\n",
    "# print(np.sinh(2)-np.sum(a**2)) Alternative sans définir de fonction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a47bed42-6671-48b5-ac8a-869e8c152a0c",
   "metadata": {},
   "source": [
    "###  Q9  Considérer une discrétisation uniforme de l'intervalle $[-1,1]$ avec $400$ points, représenter graphiquement sur 3 graphiques distincts :\n",
    "1) les $7$ premiers polynômes de Legendre $P_k$,\n",
    "2)  la fonction $x\\mapsto f(x)$ ainsi que $\\pi_6 f (x)$, la meilleure approximation de $f$ sur le sous-espace vectoriel engendré par les polynômes de Legendre de degré inférieur ou égal à $6$,\n",
    "3)  la fonction d'erreur d'approximation définie ci-après,\n",
    "   $$\\varepsilon(x) = f(x) - \\pi_6 f(x)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8e7aff6f-e99b-4572-a834-4b6a17a5d370",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "N = 400\n",
    "X = np.linspace(-1, 1, N)\n",
    "Y=np.exp(-X)\n",
    "Z=approx(X,6,a)\n",
    "eps=Y-Z\n",
    "P0= Legendre(0,X)\n",
    "P1= Legendre(1,X)\n",
    "P2= Legendre(2,X)\n",
    "P3= Legendre(3,X)\n",
    "P4= Legendre(4,X)\n",
    "P5= Legendre(5,X)\n",
    "P6= Legendre(6,X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "62c80f4c-f72c-4b81-8df0-405292134310",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "#plt.subplot(3, 1, 1)\n",
    "plt.plot(X, P0, '.-r', linewidth = 1,label='0')\n",
    "plt.plot(X, P1, '.-b', linewidth = 1,label='1')\n",
    "plt.plot(X, P2, '.-g', linewidth = 1,label='2')\n",
    "plt.plot(X, P3, '.-y', linewidth = 1,label='3')\n",
    "plt.plot(X, P4, '.-m', linewidth = 1,label='4')\n",
    "plt.plot(X, P5, '.-c', linewidth = 1,label='5')\n",
    "plt.plot(X, P6, '.-k', linewidth = 1,label='6')\n",
    "\n",
    "plt.title(\"7 premiers polynomes de Legendre\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid(); \n",
    "plt.legend()\n",
    "\n",
    "plt.tight_layout()      # Sans cette ligne, il y a des chevauchements dans les étiquettes\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3a24e7df-ad60-4d9b-9114-da52668685c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(X, Y, '*-r', linewidth = 1,label='f')\n",
    "plt.plot(X, Z, '-b', linewidth = 1,label='Approx')\n",
    "\n",
    "plt.title(\"la fonction f et sa projection\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid(); \n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(X, eps, '.-g', linewidth = 1,label='Erreur')\n",
    "plt.title(\"erreur d'approximation\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid(); \n",
    "plt.legend()\n",
    "\n",
    "plt.tight_layout()      # Sans cette ligne, il y a des chevauchements dans les étiquettes\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2aff8e3f-cf22-425e-aa23-06a48f6a8319",
   "metadata": {},
   "source": [
    "## 2.4 Questions \"Meilleure approximation de la fonction $g :x \\in[-1,1] \\mapsto |x|$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "804c1138-f2f5-45e7-8f8a-9f7c03d98d6c",
   "metadata": {},
   "source": [
    "### Q10 On cherche désormais à déterminer la meilleurs approximation de la fonction $g :x \\in [-1,1] \\mapsto |x|$ sur le sous-espace vectoriel engendré par les polynômes de Legendre de degré inférieur à $n$. Remarquons que $g \\in \\mathcal{H}$. \n",
    "\n",
    "1) Déterminer à la main l'expression des $a_k$ pour cette fonction;\n",
    "\n",
    "2) Prouver que ces $a_k$ sont nuls pour k impair et simplifier l'expression pour les k pairs."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b02d9d6-58a1-4c2f-bc36-bfdaa6c4173a",
   "metadata": {},
   "source": [
    "#### Remarquons que $a_{2k+1}=0$ car une fonction impaire intégrée sur un intervalle symétrique autour de 0; en revanche \n",
    "\n",
    "$$a_{2k}=2 \\int_0^1 x P_{2k}(x) \\frac{ \\sqrt{ 2(2k)+1}}{\\sqrt{2}}dx$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c9202cf-9e0d-45c7-951c-759a85943763",
   "metadata": {},
   "source": [
    "### Q11 Importer la librairie \"scipy.integrate\" \n",
    "1) utiliser la fonction fonction \"scipy.integrate.quad\" qui permet le calcul d'une integrale\n",
    "2) Créer une fonction \"$g_{coeff}$' qui, à partir de l'ordre $k$, retourne le coefficient $a_k$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d8287ce",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12431332-3030-47f3-8128-478d5f5ea909",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.integrate as integrate\n",
    "f = lambda x, k: 2*x*Legendre(k,x)*np.sqrt(2*k+1)/np.sqrt(2)\n",
    "z,err=integrate.quad(f, 0, 1, args=(2,)) #integrale + erreur k=2\n",
    "print('z=',z)\n",
    "print('err',err)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "1350905c-eb66-4f14-b6e6-91fc093ac9da",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.integrate as integrate\n",
    "def g_coeff (k):\n",
    "    if k % 2 == 0:\n",
    "        a,err= integrate.quad(f, 0, 1, args=(k,))\n",
    "    else:\n",
    "        a = 0\n",
    "    return(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffec3af1-ebda-4070-8f50-7629941819ca",
   "metadata": {},
   "source": [
    "### Q12 \n",
    "Sachant que $a_0 = 1/\\sqrt{2}$, $a_2 = \\sqrt{10}/8$ et $a_4 = -\\sqrt{2}/16$, vérifier que l'application \"$g_{coeff}$\" est correcte."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8dc2841e-0ddb-4d45-bab6-417c76d2ec03",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(1/np.sqrt(2),g_coeff(0))\n",
    "print(np.sqrt(10)/8,g_coeff(2))\n",
    "print(-np.sqrt(2)/16,g_coeff(4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f150204-6f0e-4e67-a8b0-f1113362f970",
   "metadata": {},
   "source": [
    "### Q13 Représenter sur une même fenêtre graphique\n",
    "1) les polynômes $\\pi_n g$ pour $n=2$, $n=4$ et $n=6$,\n",
    "2) l'erreur d'approximation pour $n=2$, $n=4$ et $n=6$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "08d9d013-ae3d-4226-98d1-8671d2618801",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "N = 400\n",
    "X = np.linspace(-1, 1, N)\n",
    "Y=np.abs(X)\n",
    "a0 = g_coeff (0)\n",
    "a1 = g_coeff (1)\n",
    "a2 = g_coeff (2) \n",
    "a3 =  g_coeff (3) \n",
    "a4 =  g_coeff (4) \n",
    "a5 =  g_coeff (5) \n",
    "a6 =  g_coeff (6) \n",
    "a=np.array([a0,a1,a2,a3,a4,a5,a6], dtype=np.float64)\n",
    "\n",
    "Z2=approx(X,2,a)\n",
    "Z4=approx(X,4,a)\n",
    "Z6=approx(X,6,a)\n",
    "eps2=Y-Z2\n",
    "eps4=Y-Z4\n",
    "eps6=Y-Z6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1699ac02-8324-4b7a-9caf-af4c628d167e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(X, Y, '*-r', linewidth = 1,label='g')\n",
    "plt.plot(X, Z2, '-b', linewidth = 1,label='2')\n",
    "plt.plot(X, Z4, '-g', linewidth = 1,label='4')\n",
    "plt.plot(X, Z6, '-c', linewidth = 1,label='6')\n",
    "\n",
    "plt.title(\"la fonction f et sa projection\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid(); \n",
    "plt.legend()\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(X, eps2, '-b', linewidth = 1,label='2')\n",
    "plt.plot(X, eps4, '-g', linewidth = 1,label='4')\n",
    "plt.plot(X, eps6, '-c', linewidth = 1,label='6')\n",
    "plt.title(\"erreur d'approximation\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid(); \n",
    "plt.legend()\n",
    "\n",
    "plt.tight_layout()      # Sans cette ligne, il y a des chevauchements dans les étiquettes\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72f7228b-a3ba-4720-b621-6748c58a8977",
   "metadata": {},
   "source": [
    "### Q14 Commenter la figure obtenue. Cette méthode d'approximation semble-t-elle converger rapidement ?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc0d2ddb-6c38-4397-86f7-b02134d2c40a",
   "metadata": {},
   "source": [
    "La fonction $g$ est continue et dérivable par morceaux sur $[-1,1]$; en particulier elle n'est pas dérivable en $x=0$. Empiriquement convergence en moyenne quadratique semble valide tandis que la convergence ponctuelle n'est pas valide pour tout $x$ dans $[-1,1]$ et en particulier pour $x=0$."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}