{ "cells": [ { "cell_type": "markdown", "id": "58db841f-7979-469a-8068-53d7106bbc4e", "metadata": { "editable": true, "panel-layout": { "height": 436.133, "visible": true, "width": 100 }, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Notebook Jupyter UTC MT12 \n", "$$ \\text{UTC MT12} \\quad \\quad \\text{TP} 3 $$\n", "###### Cette cellule est une cellule Markdown" ] }, { "cell_type": "markdown", "id": "6aa90e9f-ca03-4e8f-823c-e7126f17c88b", "metadata": { "editable": true, "panel-layout": { "height": 557.717, "visible": true, "width": 100 }, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Dans ce TP, on étudie la convergence des séries de Fourier de certaines fonctions. On commence dans un premier temps par une méthode permettant d'approcher la valeur de l'intégrale d'une fonction sur un intevalle.\n", "\n", "###### Cette cellule est une cellule Markdown" ] }, { "cell_type": "markdown", "id": "f8efffda-27f0-4e1b-8e8f-282ecf1e2376", "metadata": { "panel-layout": { "height": 3187.33, "visible": true, "width": 100 } }, "source": [ "#### Plan \n", "[1. Intégration d'une fonction continue sur un intervalle borné](#1.-Intégration-d-'-une-fonction-continue-sur-un-intervalle-borné)\n", "\n", "[2. Convergence ponctuelle de la série de Fourier d'une fonction périodique régulière](#2.-Convergence-ponctuelle-de-la-série-de-Fourier-d-'-une-fonction-périodique-régulière)\n", "\n", "[3. Phénomène de Gibbs pour une fonction périodique discontinue](#3.-Phénomène-de-Gibbs-pour-une-fonction-périodique-discontinue)" ] }, { "cell_type": "markdown", "id": "66f610d2-e32c-4019-ba00-996647530579", "metadata": { "panel-layout": { "height": 282.3, "visible": true, "width": 100 } }, "source": [ "# 1. Intégration d'une fonction continue sur un intervalle borné" ] }, { "cell_type": "markdown", "id": "2666429f-a7c0-40ba-adff-7e0f521c7c2a", "metadata": { "panel-layout": { "height": 3557.78, "visible": true, "width": 100 } }, "source": [ "Soit $[a,b]$ avec $a " ] }, { "cell_type": "markdown", "id": "4cab11bb-680d-4d16-b8d0-e2924dee695b", "metadata": {}, "source": [ "## 1.1 Questions" ] }, { "cell_type": "markdown", "id": "5463d09d-2ff1-4d21-b96b-fc4cce64546b", "metadata": { "panel-layout": { "height": 1089.37, "visible": true, "width": 100 } }, "source": [ "Dans un premier temps, on cherche à coder une fonction $$[N,I_-,I_+] = \\text{Riemann}(f, a, b, \\varepsilon),$$ qui retourne un entier $N=N(\\varepsilon)$ (idéalement le plus petit possible) et un encadrement de l'intégrale $I$ avec une précision $\\varepsilon$ imposée et garantissant la relation \n", "$$I_+(N)-I_-(N) \\leq \\varepsilon \\qquad (3)$$ \n", "\n", "Notons que l'inégalité suivante est toujours satisfaite : $0\\leq I_+(N)-I_-(N)$." ] }, { "cell_type": "markdown", "id": "6e796e89-7062-4f11-8829-586bc3d7607a", "metadata": { "panel-layout": { "height": 2461.37, "visible": true, "width": 100 } }, "source": [ "**Remarque** \n", "\n", "En pratique, le $\\min$ et le $\\max$ qui interviennent dans les formules (1) et (2) ci-dessus seront évalués (approchés) sur une grille plus fine (20 points par subdivision par exemple). \n", "\n", "En effet, pour évaluer le $\\max$ (ou le $\\min$) de $f$ sur les intervalles de la forme $[a+(k-1)h, a+kh[$ pour $1 \\leq k \\leq N$, on considère : $$f_k^{\\min} = \\min_{j\\in\\{0,19\\}} f(a+(k-1)h+j h/20),\\quad f_k^{\\max} = \\max_{j\\in\\{0,19\\}} f(a+(k-1)h+j h/20),$$ \n", "puis on définit $$ I_-(N) = h \\sum_{k=1}^N f_k^{\\min}\\quad \\text{et} \\quad I_+(N) = h \\sum_{k=1}^N f_k^{\\max}$$ \n", "\n", "Dans l'algorithme, on initialisera $N$ à une \"petite\" valeur (par exemple $N=1,2,3$), puis on si la condition (3) n'est pas satisfaite, on multipliera $N$ par $2$, et on répétera l'opération jusqu'à ce que la condition (3) soit satisfaite. " ] }, { "cell_type": "markdown", "id": "41a66df8-688d-48b6-b99e-6f4950568f48", "metadata": { "panel-layout": { "height": 231.867, "visible": true, "width": 100 } }, "source": [ "### Q1 Compléter le code suivant afin d'obtenir une valeur approchée de $I$ à $\\epsilon$ près et la valeur de $N(\\epsilon)$ associée." ] }, { "cell_type": "code", "execution_count": null, "id": "fbec7a5c-bedc-4ecd-841d-e10a4a6a62cf", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "def Riemann (f,a,b,epsilon):\n", " N=1\n", " done = bool(0) # booléen \"False\"\n", " nsubdiv=20\n", " while not done: #tant que 'not done == True\"\n", " N=2*N\n", " Iplus=0\n", " Imoins=0\n", " for k in range(N):\n", " Ik = [a+k*(b-a)/N, a+(k+1)*(b-a)/N]\n", " subdiv = np.linspace(float(Ik[0]), float(Ik[1]), nsubdiv)\n", " fmin= np.min(f(subdiv))\n", " fmax= np.max(f(subdiv))\n", " Imoins= Imoins + fmin*(b-a)/N\n", " Iplus= Iplus + fmax*(b-a)/N\n", " done = (Iplus-Imoins< epsilon)\n", " return [N,Imoins,Iplus]" ] }, { "cell_type": "raw", "id": "2c9c7150-de38-46cb-9372-119b5e94f0c1", "metadata": { "panel-layout": { "height": 932.65, "visible": true, "width": 100 } }, "source": [ "import numpy as np\n", "def Riemann (f,a,b,epsilon):\n", " N=1\n", " done = bool(0) # booléen \"False\"\n", " nsubdiv=20 # approximation du min et du max sur une grille de taille 20 dans chaque sous-intervalle\n", " while not done: #tant que 'not done == True\"\n", " N=2*N\n", " Iplus=0\n", " Imoins=0\n", " for k in range(N):\n", " Ik = [a+k*(b-a)/N, a+(k+1)*(b-a)/N]\n", " subdiv = np.linspace(float(Ik[0]), float(Ik[1]), nsubdiv)\n", " fmin= ...\n", " fmax= ...\n", " Imoins= ...\n", " Iplus= ...\n", " done = (Iplus-Imoins< epsilon)\n", " return [N,Imoins,Iplus]\n", "\n", "\n", "###### Cette cellule est une cellule Raw" ] }, { "cell_type": "markdown", "id": "91877d01-ae2c-4e0a-b675-0e7befa96ab8", "metadata": { "panel-layout": { "height": 900.717, "visible": true, "width": 100 } }, "source": [ "### Q2 Appliquer votre code précédent à la fonction $f(x)=\\sin(\\pi x)$ pour approcher $$ I=\\int_0^1 \\sin(\\pi x)\\, dx, \\quad \\text{ en prenant} \\; \\varepsilon=10^{-4}$$\n", "\n", "Pour cela,\n", "* calculer $I$ à la main\n", "* coder la fonction $f_{\\sin}$ qui à $x$ dans $[0,1]$ retourne $f(x)=\\sin(\\pi x)$\n", "* cxécuter \"Riemann$(f_{\\sin},0,1,0.0001)$\"\n", "* calculer cette même valeur en important la bibliothèque \"scipy integrate\" par la ligne de commande \"from scipy.integrate import quad\"\n", "* exécuter \"$I_{num}=quad(f_{\\sin},0,1)$\" qui retourne la valeur approchée nuùériquement de l'intégration de $f$ sur l'intervalle $(0,1)$ ainsi que son erreur\n", "* comparer $I_{num}$ et $I$ aux sorties $I_{-}(N)$ et $I_+(N)$ de la fonction Riemann." ] }, { "cell_type": "code", "execution_count": null, "id": "68867019-50d9-4e9c-8740-2dd58539399a", "metadata": { "panel-layout": { "height": 27.15, "visible": true, "width": 100 } }, "outputs": [ { "data": { "text/plain": [ "0.6366197723675814" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np \n", "2/np.pi" ] }, { "cell_type": "code", "execution_count": null, "id": "00983408-4797-47ad-9095-6dbf285b977f", "metadata": {}, "outputs": [], "source": [ "def f_sin (x):\n", " return(np.sin(np.pi*x))" ] }, { "cell_type": "code", "execution_count": null, "id": "07c76771-927c-4891-9006-08931c73e366", "metadata": {}, "outputs": [], "source": [ "## fonction x-->sin(pi x) alternative\n", "f_sin1 = lambda x: np.sin(np.pi*x)" ] }, { "cell_type": "code", "execution_count": null, "id": "3d71f758-0826-4d65-aa23-ca6ceaef63cb", "metadata": { "panel-layout": { "height": 117.8, "visible": true, "width": 100 } }, "outputs": [], "source": [ "[N,Im,Ip]=Riemann(f_sin,0,1,0.0001) \n", "#Riemann(lambda x : np.sin(np.pi*x),0,1,0.0001) # écriture alternative" ] }, { "cell_type": "code", "execution_count": null, "id": "36cb6054-2571-4610-b49c-52a3d8436260", "metadata": { "panel-layout": { "height": 27.15, "visible": true, "width": 100 } }, "outputs": [ { "data": { "text/plain": [ "(0.6366197723675814, 7.067899292141149e-15)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np \n", "from scipy.integrate import quad\n", "quad(f_sin,0,1)" ] }, { "cell_type": "markdown", "id": "49461119-e33b-4c6d-954b-f0a7568ad0d6", "metadata": { "panel-layout": { "height": 849.267, "visible": true, "width": 100 } }, "source": [ "### Q3 Comparaison avec la méthode des rectangles\n", "En reprenant le TD du Chapitre 1, coder la méthode des rectangles à gauche pour approcher la valeur de $I$ à une erreur d'approximation inférieure ou égale à $\\varepsilon=10^{-4};$ vérifier que cette erreur est bien inférieure à la valeur de sa majoration donnée en TD: \n", "\\begin{align*}\n", "I\\approx I_{app,rect}& =\\frac{b-a}{N} \\sum_{k=0}^{N-1}f(x_k), \\quad a=0=x_0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "N = 100\n", "X = np.linspace(0, 2, N)\n", "Z1=(X < 1)\n", "Z2=(X >= 1)\n", "Y=X*Z1+ (2-X)*Z2\n", "plt.plot(X, Y, '.-b', linewidth = 3)\n", "plt.title(\"Fonction $f$\")\n", "plt.show;" ] }, { "cell_type": "code", "execution_count": 2, "id": "a6eec745-447f-49fc-a23f-87a11c0e1b70", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "N=100\n", "X=np.linspace(-3,3,N)\n", "Z1=(np.floor(X)%2==0)\n", "Z2=(np.floor(X)%2==1)\n", "Y=(X-np.floor(X))*Z1+ (1-X+np.floor(X))*Z2\n", "plt.plot(X, Y, '.-b', linewidth = 3)\n", "plt.title(\"Fonction $f$\")\n", "plt.show;" ] }, { "cell_type": "markdown", "id": "385e29ac-c664-4cf0-9bf7-ce8545257b5c", "metadata": { "panel-layout": { "height": 729.217, "visible": true, "width": 100 } }, "source": [ "#### Q5 Calculer (à la main) les coefficients de Fourier de $f$ $$a_k(f) =\\frac2T \\int_{0}^T f(x)\\cos(2k\\pi \\frac{x}{T})\\, dx, \\quad k \\in \\mathbb{N}$$ et $$b_k(f) = \\frac2T \\int_0^T f(x)\\sin(2k\\pi \\frac{x}{T})\\, dx, \\quad k \\in \\mathbb{N}^*.$$" ] }, { "cell_type": "code", "execution_count": 1, "id": "722136f8-e5e2-4bba-96bf-c546c5d4ed94", "metadata": {}, "outputs": [], "source": [ "def ak (x,k):\n", " return(np.cos(k*np.pi*x))\n", "\n", "def bk (x,k):\n", " return(np.sin(k*np.pi*x))\n" ] }, { "cell_type": "markdown", "id": "ba74f451-a861-4367-b5c7-2b0e73d0a632", "metadata": {}, "source": [ "Par le calcul, on obtient: \n", "\\begin{align*}\n", "a_0 (f)& = 1 \\\\\n", "a_k (f)& = 2 \\int_0^1 x \\cos(k \\pi x) dx = -\\frac{4}{(\\pi k)^2}  \\quad \\forall k >0, \\; \\text{impair}\\\\\n", "a_k (f) & = 0, \\quad \\forall k >0, \\; \\text{pair}\\\\\\\\\n", "b_k (f) & = 0 \\quad \\forall k >0\n", "\\end{align*}" ] }, { "cell_type": "markdown", "id": "90ff1241-df71-4538-b6cb-1206416f6a7d", "metadata": { "panel-layout": { "height": 865.233, "visible": true, "width": 100 } }, "source": [ "#### Pour $N\\geq 1$ on définit la suite $(f_N)_{N\\geq 1}$, des sommes partielles de Fourier de $f$, par $$f_N(x) = \\frac{a_0(f)}{2} +\\sum_{k=1}^N \\left( a_k (f) \\, \\cos(k \\pi x) + b_k (f) \\, \\sin(k\\pi x) \\right) \\quad (4)$$" ] }, { "cell_type": "markdown", "id": "728acfd7-f0be-43b7-8d84-74450e548960", "metadata": { "panel-layout": { "height": 506.267, "visible": true, "width": 100 } }, "source": [ "#### Q6 Montrer (à la main) via un changement d'indice, que pour tout $N\\geq 0$ on a $$f_{2N+1}(x) = \\frac{1}{2} -\\frac{4}{\\pi^2} \\sum_{k=0}^N \\frac{\\cos((2k+1)\\pi x)}{(2k+1)^2}$$" ] }, { "cell_type": "markdown", "id": "dabdbce7-e09a-4e53-976a-7002a2ff8860", "metadata": {}, "source": [ "En reprenant la formule (4), nous avons\n", "\\begin{align*}\n", "f_{2N+1}(x) & = \\frac{a_0(f)}{2} +\\sum_{k=1}^{2N+1} a_k (f) \\, \\cos(k \\pi x) \\\\\n", "& = \\frac{1}{2} - \\frac{4}{\\pi^2} \\left( \\frac{\\cos (1\\pi x)}{1^2} +0 + \\frac{\\cos (3)\\pi x}{(3)^2}+0 +\\ldots+ \\frac{\\cos (2N+1)\\pi x}{(2N+1)^2}\\right) \\\\\n", "& = \\frac{1}{2} - \\frac{4}{\\pi^2} \\sum_{k=1}^N \\frac{\\cos (2k+1)\\pi x)}{(2k+1)^2} \n", "\\end{align*}" ] }, { "cell_type": "markdown", "id": "7eaacbbe-ea3f-4f2e-8ede-609efcf5badc", "metadata": { "panel-layout": { "height": 574.867, "visible": true, "width": 100 } }, "source": [ "#### Q7 Sur l'intervalle $[0,2]$ comparer graphiquement les fonctions $f_{2N+1}$ et $f$. On tracera ces courbes pour les différentes valeurs de $N$ suivantes : $N=2$, $4$, $8$, $16$, $32$, $64$, $128$ et $256$." ] }, { "cell_type": "code", "execution_count": 1, "id": "1750f6fe-3784-4859-b2f6-6e34dc237a08", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "def fN (x,N):\n", " y=1/2\n", " for k in range(N+1):\n", " y=y-(4/(np.pi*np.pi))*np.cos(((2*k)+1)*np.pi*x)/(((2*k)+1)*((2*k)+1))\n", " return(y)" ] }, { "cell_type": "code", "execution_count": 2, "id": "6ec527b9-9e5d-4e5d-94a2-55a075adfaca", "metadata": { "panel-layout": { "height": 701, "visible": true, "width": 100 } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "N = 100\n", "#X = np.array(np.linspace(0, 2, N))\n", "X = np.linspace(0, 2, N)\n", "Y1=fN(X,2)\n", "Y2=fN(X,4)\n", "Y3=fN(X,8)\n", "Y4=fN(X,16)\n", "Y5=fN(X,32)\n", "Y6=fN(X,64)\n", "Y7=fN(X,128)\n", "Y8=fN(X,256)\n", "plt.plot(X, Y1, '-r', linewidth = 0.50,label='N=2')\n", "plt.plot(X, Y2, '-b', linewidth = 0.50,label='N=4')\n", "plt.plot(X, Y3, '-g', linewidth = 0.50,label='N=8')\n", "plt.plot(X, Y4, '-y', linewidth = 0.50,label='N=16')\n", "plt.plot(X, Y5, '-c', linewidth = 0.50,label='N=32')\n", "plt.plot(X, Y6, '-m', linewidth = 0.50,label='N=64')\n", "plt.plot(X, Y7, '-k', linewidth = 0.50,label='N=128')\n", "plt.plot(X, Y8, '-g', linewidth = 0.50,label='N=256')\n", "plt.title(\"Series de fourier de $f$\")\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.grid(); \n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5acc49a6-ce13-44d2-b06b-636ad615f110", "metadata": { "panel-layout": { "height": 471.967, "visible": true, "width": 100 } }, "source": [ "#### Q8 Y a-t-il convergence ponctuelle (convergence normale) ? Si oui, ce résultat est-il conforme à un théorème vu en cours (lequel) ?" ] }, { "cell_type": "markdown", "id": "257e03ee-0a6d-4c83-a5f8-cea5674b9189", "metadata": {}, "source": [ "Oui la fonction $f$ est périodique continue (continue par morceaux, i.e. dans $\\mathcal{H}$) et dérivable par morceaux pour tout $x$ alors \n", "$f_N(x)$ converge simplement vers $\\frac{1}{2}(f(x^+)+f(x^-))$; ici comme la fonction est continue sur tout $\\mathbb{R}$, alors on a convergence ponctuelle en tout $x$. \n", "Ce résultat est conforme au Théorème de Dirichlet.\n", "\n", "Si $f$ est périodique continue et $C^1$ par morceaux, alors on a convergence normale de la série de Fourier de $f$. \n" ] }, { "cell_type": "code", "execution_count": null, "id": "d51e648e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "3bcf0a13-3a7c-41d8-9d33-85bc07f23d93", "metadata": { "panel-layout": { "height": 282.3, "visible": true, "width": 100 } }, "source": [ "# 3. Phénomène de Gibbs pour une fonction périodique discontinue" ] }, { "cell_type": "markdown", "id": "020fa8a0-b63e-4b32-8652-fbe7036a84a5", "metadata": {}, "source": [ "## 3.1 Questions" ] }, { "cell_type": "markdown", "id": "d3c628ed-5203-471f-ad30-2e908075126c", "metadata": { "panel-layout": { "height": 179.23333740234375, "visible": true, "width": 100 } }, "source": [ "#### On considère la fonction périodique $g$ de période $T=2$ définie sur l'intervalle $[-1,1]$ par:$$g(x) = \\left\\{\\begin{array}{ll}-1-x & \\text{si } x \\in [-1,0[,\\\\ 1-x & \\text{si } x \\in [0,1].\\end{array}\\right.$$ Cette fonction est étendue sur $\\mathbb{R}$ de manière périodique. " ] }, { "cell_type": "markdown", "id": "4d6cf267-d82b-4f29-a352-84408df6b496", "metadata": { "panel-layout": { "height": 60.36665344238281, "visible": true, "width": 100 } }, "source": [ "### Q9 Tracer la fonction $g$ sur l'intervalle $[-1,1]$, puis sur $[-4,4]$." ] }, { "cell_type": "code", "execution_count": 25, "id": "b0b4c1a4-ce45-45f1-96b1-c470ab32a180", "metadata": {}, "outputs": [], "source": [ "def g(x): #pour x dans [-1,1]\n", " z1=(x < 0)\n", " z2=(x >= 0)\n", " return((-1-x)*z1+ (1-x)*z2)" ] }, { "cell_type": "code", "execution_count": 27, "id": "04b1bdd9-1df1-4825-a14e-4da0d1101e4c", "metadata": { "panel-layout": { "height": 728.1500244140625, "visible": true, "width": 100 } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "N = 100\n", "X = np.linspace(-1, 1, N)\n", "Y=g(X)\n", "plt.plot(X, Y, '.-b', linewidth = 3)\n", "plt.title(\"Fonction $g$\")\n", "plt.show ;" ] }, { "cell_type": "code", "execution_count": 18, "id": "1e8d5c3d-8cae-4505-954d-e3e283e02280", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "N = 100\n", "#X = np.array(np.linspace(0, 2, N))\n", "X = np.linspace(-2, 2, N)\n", "Z1=(np.floor(X) % 2 == 0)\n", "Z2=(np.floor(X) % 2== 1)\n", "Y=(1-X+np.floor(X))*Z1+ (-1-X+np.floor(X))*Z2\n", "plt.plot(X, Y, '.-b', linewidth = 3)\n", "plt.title(\"Fonction $g$\")\n", "plt.show ;" ] }, { "cell_type": "markdown", "id": "23814e81-4300-428c-a1af-4a44c500b9e5", "metadata": { "panel-layout": { "height": 60.366668701171875, "visible": true, "width": 100 } }, "source": [ "### Q10 Calculer (à la main) les coefficients de Fourier de $g$." ] }, { "cell_type": "markdown", "id": "cc4839a1-ac38-401e-b94e-9a15774025cc", "metadata": { "panel-layout": { "height": 77.51667785644531, "visible": true, "width": 100 } }, "source": [ "$g$ est une fonction impaire donc $a_n(g)=0$ et le calcul de $b_n(g)$ donne $$b_n(g)=2/(\\pi n)$$ " ] }, { "cell_type": "markdown", "id": "edba18ea-68d8-48f1-9fbf-de758ce2fdca", "metadata": { "panel-layout": { "height": 163.26666259765625, "visible": true, "width": 100 } }, "source": [ "### Q11 Comme dans la section précédente on considère la suite $(g_N)_{N \\geq 1}$, où $g_N$ est donnée par (4). Sur l'intervalle $[-1,1]$, comparer graphiquement les fonctions $g_N$ et $g$. On tracera les courbes pour les valeurs de $N=2$, $4$, $8$, $16$, $32$ et $256$. " ] }, { "cell_type": "code", "execution_count": 19, "id": "6fa966f2-d7ee-4428-9c0d-ab5d8aecca37", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "def gN2 (x,N):\n", " y=0\n", " for k in range(N):\n", " y+= (2/((k+1)*np.pi))*np.sin((k+1)*np.pi*x)\n", " return(y)" ] }, { "cell_type": "code", "execution_count": 29, "id": "f5a83915-48bc-4510-bc28-8fa43293bf66", "metadata": { "panel-layout": { "height": 701, "visible": true, "width": 100 } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "N = 100\n", "#X = np.array(np.linspace(0, 2, N))\n", "X = np.linspace(-1, 1, N)\n", "Y1=gN2(X,2)\n", "Y2=gN2(X,4)\n", "Y3=gN2(X,8)\n", "Y4=gN2(X,16)\n", "Y5=gN2(X,32)\n", "Y6=gN2(X,256)\n", "plt.plot(X, Y1, '-r', linewidth = 0.50,label='N=2')\n", "plt.plot(X, Y2, '-b', linewidth = 0.50,label='N=4')\n", "plt.plot(X, Y3, '-g', linewidth = 0.50,label='N=8')\n", "plt.plot(X, Y4, '-y', linewidth = 0.50,label='N=16')\n", "plt.plot(X, Y5, '-c', linewidth = 0.50,label='N=32')\n", "plt.plot(X, Y6, '-m', linewidth = 0.50,label='N=256')\n", "plt.title(\"Series de fourier de $g$\")\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.grid(); \n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "83f9f8b9-a39b-4fba-9fed-4811f6550154", "metadata": { "panel-layout": { "height": 60.366668701171875, "visible": true, "width": 100 } }, "source": [ "### Q12 Que valent $g(0)$ et $g_N(0)$ pour tout $N \\geq 1$ ? " ] }, { "cell_type": "markdown", "id": "d1648ca8-30fa-4f9b-bba8-496a8ecb6a65", "metadata": {}, "source": [ "Pour tout $N\\geq 1$, on a \n", "\\begin{align*}\n", "\\forall N>0, \\quad g_N(0)&=0\\\\\n", "g(0) &= 1 \\\\\n", "\\Rightarrow g_N(0) - f(0) &= -1\n", "\\end{align*}" ] }, { "cell_type": "markdown", "id": "22da3e5b-800a-4b91-9248-25d46f5cb9d9", "metadata": { "panel-layout": { "height": 146.11666870117188, "visible": true, "width": 100 } }, "source": [ "### Q13 Convergence ponctuelle\n", "Y a-t-il visuellement convergence ponctuelle vers $g$ ? Si non, préciser (à la main) le(s) $x$ de $]-1,1[$ pour lesquels il n'y a pas de convergence ponctuelle ? Est-ce cohérent avec un théorème vu en cours ? Vers quelle valeur converge la suite $(g_N(0))_{N \\geq 1}$ ?" ] }, { "cell_type": "markdown", "id": "b56adf79-ba15-404f-a57f-a5885363b680", "metadata": { "panel-layout": { "height": 77.51666259765625, "visible": true, "width": 100 } }, "source": [ "Pas de convergence au point $x=0$. Cohérent car fonction non continue en $x=0$." ] }, { "cell_type": "markdown", "id": "6831c6bb-77d7-47d3-9f93-0102d5b72feb", "metadata": { "panel-layout": { "height": 282.13336181640625, "visible": true, "width": 100 } }, "source": [ "### Q14 Convergence en moyenne quadratique \n", "On veut illustrer la convergence de $(g_N)_{N \\geq 1}$ vers $g$ en norme $L^2([-1,1])$. \n", "\n", "Pour ce faire on approche la norme $L^2$ de la différence par la méthode des rectangles à gauche (voir question Q3 et le TD du chapitre $1$), à savoir, $$\\|g-g_N\\|^2_{L^2([-1,1])} \\approx \\frac{2}{K} \\sum_{i=0}^{K-1} \\left|g\\left(-1+i\\frac{2}{K}\\right) - g_N\\left(-1+i\\frac{2}{K}\\right)\\right|^2 = J_{K,N},$$ où $K \\in \\mathbb{N}^*$ est donné. " ] }, { "cell_type": "markdown", "id": "924170b0-959f-4bb9-9453-9305fb1f858e", "metadata": { "panel-layout": { "height": 231.86666870117188, "visible": true, "width": 100 } }, "source": [ "Fixons $K=600$, pour un $N$ donné, écrire un code permettant de calculer $J_{K,N}$ la valeur approchée de $||g-g_N||^2_{L^2([-1,1])}$. De plus afficher les valeurs de $J_{K,N}$ pour $N=64$, $128$, $256$, $512$, $1024$ et $2048$. En notant $\\alpha \\in \\mathbb{R}$ vérifiant $$J_{K,N} \\to \\alpha \\quad \\text{quand } N \\to +\\infty $$ Quelle valeur semble prendre $\\alpha$ ? Est-ce cohérent avec un résultat du cours ?" ] }, { "cell_type": "markdown", "id": "247a7870-61b9-4aee-9e4d-30c40b4bfe6e", "metadata": { "panel-layout": { "height": 94.66667175292969, "visible": true, "width": 100 } }, "source": [ "**Remarque.** \n", "\n", " * Pour toute fonction $f$ dans $\\mathcal{H}$ (fonction périodique et continue par morceaux), sa série de Fourier converge vers $f$ en moyenne quadratique. \n" ] }, { "cell_type": "code", "execution_count": 32, "id": "8eeca332-e733-4e30-818b-4f2f98f8b040", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "def JK (K,N):\n", " y=0\n", " for l in range(K):\n", " y=y+ (g(-1+(l*(2/K))) - gN2(-1+(l*(2/K)),N))*(g(-1+(l*(2/K))) - gN2(-1+(l*(2/K)),N))\n", " z=(2/K)*y\n", " return(z)" ] }, { "cell_type": "code", "execution_count": 33, "id": "8ead9879-860f-4ef6-9d2a-5d14a375ba2f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "64 0.006762355025493661\n", "128 0.00411563406317246\n", "256 0.003565242165563577\n", "512 0.0033773705296848\n", "1024 0.003344775259240126\n", "2048 0.003338577921581032\n" ] } ], "source": [ "import numpy as np\n", "vectN=[64,128,256,512,1024,2048]\n", "for N in vectN:\n", " print(N,JK(600,N))" ] }, { "cell_type": "code", "execution_count": null, "id": "a4fab4e9-52e4-4395-80eb-3bbcc387dd6c", "metadata": {}, "outputs": [], "source": [] } ], "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" }, "panel-cell-order": [ "58db841f-7979-469a-8068-53d7106bbc4e", "6aa90e9f-ca03-4e8f-823c-e7126f17c88b", "f8efffda-27f0-4e1b-8e8f-282ecf1e2376", "66f610d2-e32c-4019-ba00-996647530579", "2666429f-a7c0-40ba-adff-7e0f521c7c2a", "b6bf12bf-80fa-4b14-97b4-c0db8a08f899", "5463d09d-2ff1-4d21-b96b-fc4cce64546b", "41a66df8-688d-48b6-b99e-6f4950568f48", "554d9695-6029-44e0-83f5-653ea19803e7", "6e796e89-7062-4f11-8829-586bc3d7607a", "91877d01-ae2c-4e0a-b675-0e7befa96ab8", "3d71f758-0826-4d65-aa23-ca6ceaef63cb", "11842c15-000c-4010-9b0e-2e7895a7b2da", "68867019-50d9-4e9c-8740-2dd58539399a", "36cb6054-2571-4610-b49c-52a3d8436260", "49461119-e33b-4c6d-954b-f0a7568ad0d6", "b46b3267-f76c-40df-8bef-43770916ca11", "2d8667a4-a73d-4f2e-a8fe-b82ce917f142", "5098ec1e-db2a-442d-8f05-fd640051691c", "69dc26d8-b8d5-41eb-ba0f-5ef5785c49c0", "9a49ddf5-198d-4ad0-8eaf-630167f94b1e", "3bcf0a13-3a7c-41d8-9d33-85bc07f23d93", "f78c0529-11a0-41ec-924c-35def3b91ec8", "0ce4de48-c9f1-48cf-8841-1370fb3d78e4", "385e29ac-c664-4cf0-9bf7-ce8545257b5c", "90ff1241-df71-4538-b6cb-1206416f6a7d", "728acfd7-f0be-43b7-8d84-74450e548960", "7eaacbbe-ea3f-4f2e-8ede-609efcf5badc", "5acc49a6-ce13-44d2-b06b-636ad615f110", "6ec527b9-9e5d-4e5d-94a2-55a075adfaca", "d3c628ed-5203-471f-ad30-2e908075126c", "4d6cf267-d82b-4f29-a352-84408df6b496", "04b1bdd9-1df1-4825-a14e-4da0d1101e4c", "d74af3f1-4303-4861-9add-57d1f8fab36a", "23814e81-4300-428c-a1af-4a44c500b9e5", "cc4839a1-ac38-401e-b94e-9a15774025cc", "edba18ea-68d8-48f1-9fbf-de758ce2fdca", "f5a83915-48bc-4510-bc28-8fa43293bf66", "83f9f8b9-a39b-4fba-9fed-4811f6550154", "22da3e5b-800a-4b91-9248-25d46f5cb9d9", "b56adf79-ba15-404f-a57f-a5885363b680", "6831c6bb-77d7-47d3-9f93-0102d5b72feb", "924170b0-959f-4bb9-9453-9305fb1f858e", "247a7870-61b9-4aee-9e4d-30c40b4bfe6e" ] }, "nbformat": 4, "nbformat_minor": 5 }