{ "cells": [ { "cell_type": "markdown", "id": "ef674ab4-d343-474a-9b6e-a3888c353796", "metadata": {}, "source": [ "## MT09 - TP6 - Automne 2024\n", "## Interpolation polynomiale\n" ] }, { "cell_type": "markdown", "id": "f2e7f71c-6313-4917-a489-9cea671cfcc7", "metadata": { "tags": [] }, "source": [ "#### 1. Algorithme de Horner de calcul des polynômes\n", "Ecrire une fonction\n", "```\n", "p = horn(a, t, theta)\n", "```\n", "qui, étant donné le tableau $a$ de coefficients $(a_0, a_1, ...,a_n)$, le tableau $t$\n", "de valeurs $(t_0,t_1,...,t_{n-1})$ et le point courant $\\theta$, calcule\n", "\n", "$$\n", "P(\\theta) = a_0 + a_1(\\theta-t_0)\n", "+a_2(\\theta-t_0)(\\theta-t_1)\n", "+...+ a_n (\\theta-t_0)(\\theta-t_1)...(\\theta-t_{n-1})\n", "$$\n", "\n", "à l'aide de l'algorithme de Horner vu en cours (attention : appliqué ici à la base de Newton)." ] }, { "cell_type": "code", "execution_count": 7, "id": "c7cd03d2-5a55-4f48-acf6-7b68281d11c0", "metadata": { "tags": [] }, "outputs": [], "source": [ "def horn(a, t, theta):\n", " # Algo : \n", " # p = a_n\n", " # pour k= n-1 à 0 par pas de -1 faire:\n", " # p = a_k + (t-t_k)*p\n", " # fin pour\n", " # \n", " #\n", " n = a.size - 1\n", " p = a[n]\n", " for k in range(n-1, -1, -1):\n", " p = a[k] + (theta-t[k]) * p\n", " return p" ] }, { "cell_type": "markdown", "id": "1ecd2cd7-4b7b-4f9f-9673-685a5d8d85e2", "metadata": {}, "source": [ "Vérification. - Appliquez l'algorithme au calcul du polynôme $p(x) = -1+2x-x^2+x^3$ et vérifiez que vous obtenez les bonnes valeurs de $p$ en $x=0$, $x=1$ et $x=2$." ] }, { "cell_type": "code", "execution_count": 10, "id": "7db1ce79-55e3-4dd5-85b6-6b8287674928", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-1.0\n", "1.0\n", "7.0\n", "23.0\n" ] } ], "source": [ "import numpy as np\n", "t = np.zeros(3)\n", "a = np.array([-1, 2, -1, 1])\n", "x=0; px = horn(a, t, x); print(px)\n", "x=1; px = horn(a, t, x); print(px)\n", "x=2; px = horn(a, t, x); print(px)\n", "x=3; px = horn(a, t, x); print(px)" ] }, { "cell_type": "markdown", "id": "ed96cd06-4950-4810-a0c7-75279d2ccb08", "metadata": { "tags": [] }, "source": [ "### 2. Polynômes d'interpolation, forme de Newton\n", "#### Différences divisées\n", "Ecrire une fonction\n", "```\n", "d = diffdiv(y, t)\n", "```\n", "qui, étant donné le tableau $t=(t_0, t_1, .. t_{n})$, le tableau\n", "$y=(y_0,...,y_n)$ avec\n", "$y_0=f(t_0), \\ y_1=f(t_1), ..., y_{n}=f(t_{n})$, calcule les différences divisées $f_0=f[t_0]$, $f_1=f[t_0,t_1]$, ..., $f_{n} = f[t_0, ..., t_n]$\n", "(on suppose que les $t_i$ sont distincts deux à deux)." ] }, { "cell_type": "code", "execution_count": 13, "id": "2af5cf8a-1729-4aa1-91d4-f40219b80ab8", "metadata": { "tags": [] }, "outputs": [], "source": [ "def diffdiv(y,t):\n", " n = y.size - 1\n", " # Algorithme : voir polycopié\n", " # Init\n", " # d = y\n", " # boucle pour k de 1 à n\n", " # boucle pour i de n à (k-1) par pas de (-1)\n", " # d_i = (d_i - d_{i-1)} / (t_i - t_{i-k}}\n", " # fin pour\n", " # fin pour\n", " #\n", " d = np.copy(y)\n", " for k in range(1, n+1):\n", " for i in range(n, k-1, -1):\n", " d[i] = (d[i]-d[i-1]) / (t[i]-t[i-k])\n", " return d" ] }, { "cell_type": "markdown", "id": "aacdf36a-e3e8-40b9-ae4c-e722b4b015a4", "metadata": {}, "source": [ "Application numérique et vérification : considérer\n", "$t=(1,\\ 3,\\ 4.5,\\ 5,\\ 6)$ et $y=(1,\\ 5,\\ 3,\\ 7,\\ -1)$.\n", "Vous devez obtenir : \n", "\n", "`\n", "d = [ 1. 2. -0.95238095 1.4047619 -1.3031746 ]\n", "`" ] }, { "cell_type": "code", "execution_count": 16, "id": "314b4d91-82c8-46ac-a420-c47af5835430", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "d = [ 1. 2. -0.95238095 1.4047619 -1.3031746 ]\n" ] } ], "source": [ "t = np.array([1, 3, 4.5, 5, 6], dtype=np.float64) \n", "#!! : ATTENTION : bug si le type n'est pas mis en float64 (divisions entieres !!!)\n", "y = np.array([1, 5, 3, 7, -1], dtype=np.float64)\n", "#!! : ATTENTION : bug si le type n'est pas mis en float64 (divisions entieres !!!)\n", "d = diffdiv(y, t)\n", "print(\"d = \", d)" ] }, { "cell_type": "markdown", "id": "3e72642c-57e4-4ccf-85a7-40cfa465c866", "metadata": { "tags": [] }, "source": [ "#### Interpolation polynomiale\n", "En utilisant ```diffdiv()``` et ```horn()```, écrire une fonction\n", "```\n", "p = interpol(y, t, theta)\n", "```\n", "qui, étant donné $(y_0, y_1, ..., y_n)$, $(t_0, t_1, ..., t_n)$,\n", "$\\theta$ réels, calcule $p=P(\\theta)$ où $P$ est le polynôme de degré inférieur ou égal à $n$ tel que $P(t_i)=y_i$. " ] }, { "cell_type": "markdown", "id": "f264a8e4-23d3-4161-92a5-2fbe56872798", "metadata": {}, "source": [ "Application numérique : considérer $t=(1, \\ 3, \\ 4.5, \\ 5, \\ 6)$, $y=(1, \\ 5, \\ 3, \\ 7, \\ -1)$. Calculer $p$ dans le cas $\\theta=3$ puis\n", "$\\theta=4$." ] }, { "cell_type": "code", "execution_count": 20, "id": "f06a963a-cf76-4c70-b353-538470415f35", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.0\n", "0.08095238095238155\n" ] } ], "source": [ "def interpol(y, t, theta):\n", " a = diffdiv(y, t)\n", " p = horn(a, t, theta)\n", " return p\n", "\n", "t = np.array([1, 3, 4.5, 5, 6], dtype=np.float64)\n", "y = np.array([1, 5, 3, 7, -1], dtype=np.float64)\n", "theta = 3\n", "print( interpol(y,t,theta) )\n", "theta = 4\n", "print( interpol(y,t,theta) )" ] }, { "cell_type": "markdown", "id": "f09384e8-cde5-4968-bd8c-b48897080db3", "metadata": { "tags": [] }, "source": [ "#### Tracé du polynôme d'interpolation\n", "En considérant le tableau de valeurs de $\\theta$\n", "```\n", "theta = np.linspace(1, 6, 200)\n", "```\n", "dans un graphique, tracez le polynôme d'interpolation $p$ pour les tableaux $t$ et $y$ ci-dessus. Sur le même graphique, affichez d'une autre couleur les points d'interpolationn $(t_i, y_i)$ ainsi que la fonction $f$ en ligne continue." ] }, { "cell_type": "code", "execution_count": 23, "id": "f78b3bcb-72bc-4cae-9818-7dc9736ca1c7", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = np.linspace(1, 6, 200)\n", "p = np.zeros(200)\n", "for i in range(0, 200):\n", " p[i] = interpol(y, t, theta[i])\n", "\n", "import matplotlib.pyplot as plt\n", "plt.plot(theta, p, '.-'); plt.grid();\n", "plt.plot(t, y, 'or')" ] }, { "cell_type": "markdown", "id": "a9acf430-dc23-4ad6-929f-6f8a6642b854", "metadata": { "tags": [] }, "source": [ "#### Phénomène de Runge\n", "On considère maintenant la fonction \n", "\n", "$$\n", "f(x) = \\frac{1}{1+x^2}\n", "$$\n", "\n", "sur l'intervalle $[-5, 5]$. Considérez les tableaux de $t$, $y$ et $\\theta$ définis par\n", "\n", "```\n", "t = np.linspace(-5, 5, N)\n", "y = f(t)\n", "theta = np.linspace(-5, 5, 200)\n", "```\n", "\n", "pour les valeurs de $N$ respectives : $N=5,\\ 7,\\ 10, 12, 13, 24$. Est-ce satisfaisant ?\n", "\n", "ps : le phénomène observé se nomme le phénomène de Runge." ] }, { "cell_type": "code", "execution_count": 34, "id": "8090d816-ffe2-452e-bf27-457214b356e7", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(x):\n", " y = 1.0 / (1.0+x**2)\n", " return y\n", "\n", "N = 11\n", "t = np.linspace(-5, 5, N, dtype=np.float64)\n", "y = f(t)\n", "theta = np.linspace(-5, 5, 200)\n", "p = np.zeros(200)\n", "for i in range(0, 200):\n", " p[i] = interpol(y, t, theta[i])\n", " \n", "plt.plot(theta, p, '.-'); plt.grid();\n", "plt.plot(theta, f(theta), '-g')\n", "plt.plot(t, 0*y, '+b')\n", "plt.plot(t, y, 'or')" ] }, { "cell_type": "code", "execution_count": 36, "id": "d065861f-8ab1-419e-93d8-8e3b052665c6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#\n", "# TEST HORS TP : en faisant l'interpolation sur g(x) = log(f(x))\n", "# p = interpolation polynomiale(g)\n", "# puis en considérant l'interpolée non polynomiale exp(p(x)) pour f\n", "#\n", "theta = np.linspace(-5, 5, 200)\n", "p = np.zeros(200)\n", "for i in range(0, 200):\n", " p[i] = interpol(np.log(y), t, theta[i])\n", " \n", "plt.plot(theta, np.exp(p), '.-'); plt.grid();\n", "plt.plot(theta, f(theta), '-g')\n", "plt.plot(t, y, 'or')\n", "plt.plot(t, 0*y, 'om')" ] }, { "cell_type": "markdown", "id": "c5e7182e-6aab-4d2f-bbb1-b69e525bc088", "metadata": { "tags": [] }, "source": [ "#### Points de Tchebychev\n", "Refaire la même tâche mais en considérant cette fois-ci les points d'interpolation donnés par le tableau `tcheb` (points de Tchebychev) :\n", "\n", "```\n", "tcheb = np.cos( np.linspace(np.pi/(2*N) , (2*N-1)*np.pi/(2*N), N) ) # dans [-1, 1]\n", "t = 5 * tcheb # dans [-5, 5]\n", "y = f(t)\n", "theta = np.linspace(-5, 5, 200)\n", "```" ] }, { "cell_type": "code", "execution_count": 39, "id": "1337dd31-d4d3-46da-8bf4-b28ee8df6a76", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#%matplotlib inline \n", "# ipympl\n", "# N=24 donne de bons resultats\n", "N = 17\n", "tcheb = np.cos( np.linspace(np.pi/(2*N) , (2*N-1)*np.pi/(2*N), N) ) # dans [-1, 1]\n", "t = 5 * tcheb # dans [-5, 5]\n", "y = f(t)\n", "theta = np.linspace(-5, 5, 200)\n", "\n", "p = np.zeros(200)\n", "for i in range(0, 200):\n", " p[i] = interpol(y, t, theta[i])\n", "\n", "plt.figure()\n", "plt.plot(theta, p, '.-'); plt.grid();\n", "plt.plot(theta, f(theta), '-g')\n", "plt.plot(t, y, 'or')\n", "plt.plot(t, 0*y, '+b')\n", "plt.show()\n", "#" ] }, { "cell_type": "markdown", "id": "7db2c28d-0b9f-4023-a4c0-b9d5e9138a63", "metadata": {}, "source": [ "### 3. Polynômes de Hermite\n", "\n", "Sur le même graphique, tracer les 4 polynômes suivants sur l'intervalle $[0,1]$:\n", "\n", "\\begin{align*}\n", "& p_1(x) = (1-x)^2(2x+1), \\\\\n", "& p_2(x) = x^2(3-2x), \\\\\n", "& p_3(x) = x(1-x)^2, \\\\\n", "& p_4(x) = -(1-x)x^2.\n", "\\end{align*}\n", "\n", "Quelles sont les propriétés de $p_1$, $p_2$, $p_3$, $p_4$~?" ] }, { "cell_type": "code", "execution_count": 42, "id": "337951ff-e9c5-4fc8-baaf-405d9bf742db", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "N=200\n", "x = np.linspace(0, 1, N)\n", "p1 = (1-x)**2*(2*x+1)\n", "p2 = x**2*(3-2*x)\n", "p3 = x*(1-x)**2\n", "p4 = -(1-x)*x**2\n", "plt.plot(x, p1, '.-', label=\"p1\")\n", "plt.plot(x, p2, '.-', label=\"p2\")\n", "plt.plot(x, p3, '.-', label=\"p3\")\n", "plt.plot(x, p4, '.-', label=\"p4\")\n", "plt.legend();\n", "plt.axis('equal')\n", "plt.grid()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1a13139e-09bc-4196-b547-c4f034e66b97", "metadata": {}, "source": [ "À partir de $(p_1,p_2,p_3,p_4)$, construire le polynôme d'interpolation $p$ de degré inférieur ou égal à 3 tel que\n", "\n", "$$\n", "p(0) = y_0, \\quad p'(0) = d_0, \\quad p(1) = y_1, \\quad p'(1)= d_1.\n", "$$\n", "Application : on prendra les valeurs $y_0 = 3$, $d_0 = 0$, $y_1 = 2$, $d_1=1$." ] }, { "cell_type": "code", "execution_count": 45, "id": "90623c89-3794-4680-abf8-f6a6f997657d", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y = np.array([3, 2], dtype=np.float64)\n", "d = np.array([0, 1], dtype=np.float64)\n", "p = y[0]*p1 + y[1]*p2 + d[0]*p3 + d[1]*p4\n", "plt.plot(x, p, '.-'); plt.grid()\n", "plt.axis('equal')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "990b1808-3925-4c28-b547-592da9561708", "metadata": {}, "source": [ "Dans une fonction python, définir une fonction $q$ polynomiale de degré 3 par morceaux telle que\n", "* $q(x) = p_1(x)$ sur l'intervalle $[0,1]$\n", "* $q(x) = p_2(x+1)$ sur l'intervalle $[-1,0]$\n", "* $q(x) = 0$ ailleurs\n", "\n", "Tracer $q$ sur l'intervalle $[-2,2]$. Quelles sont les propriétés de $q$ autres que les conditions données ?" ] }, { "cell_type": "code", "execution_count": 48, "id": "2ac9bf2f-09f6-49f8-8c9b-5a28f1ea89d4", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def q(x):\n", " if abs(x-0.5)<=0.5:\n", " y = (1-x)**2*(2*x+1)\n", " elif abs(x+0.5)<0.5:\n", " y = (x+1)**2*(3-2*(x+1))\n", " else:\n", " y = 0\n", " return y\n", "\n", "# !! version vectorisee :\n", "def qvec(x):\n", " y = (1-x)**2*(2*x+1) * (abs(x-0.5)<=0.5) \\\n", " + (x+1)**2*(3-2*(x+1)) * (abs(x+0.5)<0.5)\n", " return y\n", "\n", "N=400\n", "x = np.linspace(-2, 2, N)\n", "y = np.zeros(N)\n", "for i in range(0, N):\n", " y[i] = q(x[i])\n", "plt.plot(x, y, '-')\n", "plt.grid(); \n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "id": "49d95f17-da70-4d0f-b611-65eb5668d98d", "metadata": {}, "source": [ "Dans une fonction python, définir une fonction $r$ polynomiale de degré 3 par morceaux telle que\n", "* $r(x) = p_3(x)$ sur l'intervalle $[0,1]$\n", "* $r(x) = p_3(x+1)$ sur l'intervalle $[-1,0]$\n", "* $r(x) = 0$ ailleurs\n", "\n", "Tracer $r$ sur l'intervalle $[-2,2]$. Quelles sont les propriétés de $r$ autres que les conditions données ?" ] }, { "cell_type": "code", "execution_count": 51, "id": "795379e2-6acd-4c4b-ab63-3216c780fe86", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def r(x):\n", " if abs(x-0.5)<=0.5:\n", " y = x*(1-x)**2\n", " elif abs(x+0.5)<=0.5:\n", " y = -(x+1)**2*(1-(x+1))\n", " else:\n", " y = 0\n", " return y\n", "\n", "# !! Version vectorisee :\n", "def rvec(x):\n", " y = x*(1-x)**2*(abs(x-0.5)<=0.5) - (x+1)**2*(1-(x+1))*(abs(x+0.5)<=0.5)\n", " return y\n", "\n", "N = 400\n", "x = np.linspace(-2, 2, N)\n", "y = rvec(x)\n", "plt.plot(x, y, '-')\n", "plt.ylim(-0.5,0.5)\n", "plt.grid();" ] }, { "cell_type": "markdown", "id": "ffdab76d-260e-42c4-814c-32ff52cb1c1b", "metadata": {}, "source": [ "À partir de $q$ et $r$, on va pouvoir définir une fonction d'interpolation polynomaile par morceaux. On considère le tableau de points d'interpolation\n", "\n", "$$\n", "t = [-5, -4, ..., 0, ..., 4, 5]\n", "$$\n", "\n", "et la fonction $s(\\theta)$ définie par\n", "\n", "$$\n", "s(\\theta) = \\sum_{i=0}^N \\left\\{ f(t_i)\\, q(\\theta-t_i)\n", "+ f'(t_i)\\, r(\\theta-t_i) \\right\\}\n", "$$\n", "\n", "Définir d'abord une fonction ```fprim(theta)``` qui calcule la dérivée de $f$ en $\\theta$.\n", "Définir ensuite une fonction ```interpol(y, z, t, theta)``` qui calcule $s(\\theta)$\n", "étant donné les tableaux $t$ (```t = np.arange(-5.0, 6.0, 1.0)```),\n", "$y=(f(t_0), f(t_1), ... , f(t_N)$, \n", "$z=(f'(t_0), f'(t_1), ... , f'(t_N))$. \n", "\n", "Tracer enfin la fonction $s(\\theta)$ sur l'intervalle $[-5,5]$ et comparer à la fonction $f$." ] }, { "cell_type": "code", "execution_count": 58, "id": "ca1e4379-bd07-40be-ad3b-1ec1ba115cda", "metadata": { "tags": [] }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "3f32d88c622a484c99ef02f1bf6e6ebd", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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