{ "cells": [ { "cell_type": "markdown", "id": "ef674ab4-d343-474a-9b6e-a3888c353796", "metadata": {}, "source": [ "## MT09 - TP6 - Automne 2025\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": 2, "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": 3, "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": 4, "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 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": 5, "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": 6, "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": 7, "id": "f78b3bcb-72bc-4cae-9818-7dc9736ca1c7", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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 : $N=5,\\ 7,\\ 10, 12, 13, 24$. \n", "\n", "Sur le même graphique, tracez la fonction d'origine et son interpolée polynomiale. \n", "Sur un 2è graphique, on tracera la fonction d'erreur\n", "\n", "$$\n", "E_N(x) = f(x) - p_N(x).\n", "$$\n", "\n", "Le résultat est-il satisfaisant ?\n", "\n", "ps : le phénomène d'instabilité observé se nomme le **phénomène de Runge**." ] }, { "cell_type": "code", "execution_count": 8, "id": "8090d816-ffe2-452e-bf27-457214b356e7", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 8, "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 = 12\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": 19, "id": "b2f91ce9-dfaa-4291-9acb-16fc6ae3c850", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 17\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')\n", "plt.ylim([-1.5, 1.5])\n", "plt.legend(['p(x)', 'f(x)', 'pts interp', '(t_i, y_i)'])" ] }, { "cell_type": "code", "execution_count": 20, "id": "d065861f-8ab1-419e-93d8-8e3b052665c6", "metadata": {}, "outputs": [], "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": "code", "execution_count": 25, "id": "18a9599e-09af-41c9-9962-2163be3d6d1e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Tracé de la fonction d'erreur\n", "plt.plot(theta, f(theta) - p, '-g'); plt.grid()\n", "plt.plot(t, 0*y, '+b')\n", "plt.ylim([-0.3, 0.3])\n", "plt.show()" ] }, { "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": 11, "id": "1337dd31-d4d3-46da-8bf4-b28ee8df6a76", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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": "code", "execution_count": 12, "id": "69d6b92a-4cc9-4697-9cbe-6746e09904b3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Tracé de la fonction d'erreur\n", "plt.plot(theta, f(theta) - p, '-g'); plt.grid()\n", "plt.plot(t, 0*y, '+b')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "id": "54b950f1-d59f-443d-8f8e-d52193ea0bb7", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 34\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": "code", "execution_count": 14, "id": "62cd2c27-3e29-4a51-bc13-5befb19e1d6e", "metadata": {}, "outputs": [ { "data": { "image/png": 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jxYi9ObZgUVw3oOZ6coQYkfIYBBGR2/bn7gdgy/7EhMbIj/tbEGS/vaczQftz96PaUo3okGh0bNlRflxk1v48yxFiREpjEEREbju/HkgQ3Tq7snd5vE2uBkHeGiYvrlFqYio0Go38uLimzAQRKY9BEBG5TQyPF1kLoXNsZwBAZnGmx9skMjnOrCIPeG+YvOhO7BzTudbj4pr+nf83qs3VHm0TUXPHIIiI3Hb+8HghMTwRAFBqLPV4UOFv3WE5ZTkAgMSIxFqPJ0UkoWVIS1gkizwjNxEpg0EQEblFkiS5q+b87rDw4HA5qDhTfsaj7fK37jARBCWEJ9R6XKPR1HSJcYQYkaIYBBGRW0qNpcivzAcAdInrUus5jUYjf6hnl2Z7tF0uB0Fe6g7LLrNdn/ODIADoGtcVAHCk4IhH20TU3DEIIiK3nC45DQCIMkQhPDi8zvOiS0xkOjzF3UyQ17rDwhPrPNcmog0AIKs0y6NtImruGAQRkVtOl9qCoKSIpHqfF5kNfwmC5JogD2aCrJIVZ8ps3YX1ZYLEtRXXmoiU4ZEgaO7cuUhJSUFISAhSU1Oxfv36Rrdfu3YtUlNTERISgo4dO2LevHl1tlm6dCm6d+8Og8GA7t27Y9myZbWeX7duHf7xj38gKSkJGo0Gy5cvV/IlEdE5IjvRJrJNvc/L3WFlftId5oWaoILKApistmU6WrdoXed5cW2ZCSJSlupB0JIlSzBlyhQ888wz2L17NwYPHozRo0cjM7P+IbPHjh3DmDFjMHjwYOzevRtPP/00HnnkESxdulTeZvPmzRg3bhzGjx+PvXv3Yvz48Rg7diy2bt0qb1NeXo5LLrkEc+bMUfslEgU00R3mS5kgSZLcrwnyYHeYuDYxoTEw6Ax1nmcmiEgdOrVP8Oabb+Kee+7BvffeCwCYPXs2fvnlF7z//vuYOXNmne3nzZuHdu3aYfbs2QCAbt26YceOHZg1axZuuukm+RjDhw/H9OnTAQDTp0/H2rVrMXv2bHz55ZcAgNGjR2P06NFqvzyigCdngiLqzwSJGhdPZoKMFqO86ro/dIc1Vg8E1Fzb3PJcmCwm6IP0HmsbUXOmahBkNBqxc+dOPPXUU7UeHzFiBDZt2lTvPps3b8aIESNqPTZy5EjMnz8fJpMJer0emzdvxtSpU+tsIwInV1RXV6O6umYispKSEgCAyWSCyeT51aR9jbgGvBbq8sfrfLL4JAAgISyh3nbHhcYBsI0O89TrKq4slv+th77OeRu7ziFBIQCAMmOZx9p7qvgUACC+RXy954zSR0Gv1cNkNSGzMBPtotp5pF3u8sf72V/xWtdw5hqoGgTl5eXBYrEgPj6+1uPx8fHIyak/NZ6Tk1Pv9mazGXl5eUhMTGxwm4aO6YiZM2dixowZdR5ftWoVwsKc+ybZnK1evdrbTQgI/nSdD5w6AADI/jsbK3NX1nn+cMVhAMCJ/BNYubLu82rIN9qG7AchCKt/afha1nedT+TaZm4+dPyQx9q7JncNAMBSbGnwnNFB0ThrPYulq5aiS4su9W7jq/zpfvZ3vNZARYXj9Xyqd4cBqLUODmDrrz//saa2P/9xZ4/ZlOnTp2PatGnyzyUlJUhOTsaIESMQGRnp8nGbC5PJhNWrV2P48OHQ65mKV4s/XufJRyYDAP4x9B/ol9SvzvNZpVl4/O/HUWwuxshRIxGkDVK9TYcKDgF/AS0MLTBmzJg6zzd2nbN3Z+PjrI8R1Sqq3n3VsObXNUAWkHphKsYMq/+cF+RdgLOnzqJ9z/YY09Uz7XKXP97P/orXuoboyXGEqkFQXFwcgoKC6mRocnNz62RyhISEhHq31+l0iI2NbXSbho7pCIPBAIOhbkGiXq8P+BvKHq+HZ/jLdbZKVrnWp13LdvW2OSkqCRpoYJEsKDGX1Dv6SWkmyZYOD9OHNXod67vOESERAIBKc6XHfge5lbkAgKTIpAbPKUaInak44xf3hj1/uZ+bA15rOPX6VR0dFhwcjNTU1DrpudWrV2PgwIH17jNgwIA6269atQp9+/aVX1hD2zR0TCJSR255LiySBRpo6p3fBgD0QXrEhdnqgjw1QszVkWFAzegwTw6RF7NpN3QNAU6YSKQG1YfIT5s2DR999BE+/vhjHDhwAFOnTkVmZiYmTZoEwNYNddddd8nbT5o0CSdOnMC0adNw4MABfPzxx5g/fz4ef/xxeZtHH30Uq1atwquvvoqDBw/i1Vdfxa+//oopU6bI25SVlWHPnj3Ys2cPANvQ+z179jQ4NJ+InCc+kOPD46HTNpxYFouCemrpDFdXkLffxxtD5M9fPNUeh8kTKU/1mqBx48YhPz8fL7zwArKzs9GjRw+sXLkS7du3BwBkZ2fXCkxSUlKwcuVKTJ06Fe+99x6SkpLwzjvvyMPjAWDgwIFYvHgx/v3vf+PZZ59Fp06dsGTJEqSlpcnb7NixA1dccYX8s6j3+ec//4kFCxao/KqJAoOYI6ih4fFCQngC9p3Z5xeZIG8OkWcmiMizPFIY/eCDD+LBBx+s97n6ApIhQ4Zg165djR7z5ptvxs0339zg80OHDpULqolIHeIDuaGJEgVPT5ioRHeYpzJBVeYqFFYVAmg8CJIzQSXMBBEphWuHEZHLRNdMk5mgFp5dOsOtIMjDy2aINcOCg4LRMqRlg9tx6Qwi5TEIIiKXNbVumCBqXfwhE2TfHeaJbLJ9V1hj03yITFCpsRSl1aWqt4soEDAIIiKXNbWCvOCP3WEWyQKjxahou+rjSD0QAIQHhyPSYJuzjMXRRMpgEERELmtq3TDB0yvJK9EdZn8cNYlr0lQQBLA4mkhpDIKIyGVNrSAviIVB/SETpA/SQ6+1zUnmieLophZPtcfiaCJlMQgiIpdUm6uRX2lbo6upmiCR5SipLvFIdsWdIMh+P08Mk3e0OwxgcTSR0hgEEZFLxAexIcjQ6KgmAIg0RCJEZ1udXYyGUpO7QZAnh8mLICi+RdPL/iSFc8JEIiUxCCIil9iPDGtq8WKNRoPYUNvafwWVBaq3TalMUKWpUrE2NURcD7G0SGNEJohBEJEyGAQRkUuc6cYBgOiQaACQJwZUk1JBkCe67sT1ENenMeJaeyKbRhQIGAQRkUvOVpwFALQKa+XQ9i1DbV1mhZUMguyJ6yGuT2PEtRbXnojcwyCIiFxyttzJIOhc3VBRVZFaTZK5GwSF6kIBAJVm9bvDxPVoqq4KAFq1OBcElTMIIlICgyAicomcCWrhZCbIA91hoqDZ1zNBJotJbqszmaDCqkKYLCZV20YUCBgEEZFLRBDUukVrh7aPNkQD8Gx3mP3Eh87wVBBkHxBGGaKa3D4mNAYa2IrQxfQEROQ6BkFE5JLc8lwALtQEsTBaJgLCSEMkgrRBTW4fpA2SR5GJ609ErmMQREQukWuCHO0O86OaIE8FQc7UAwmsCyJSDoMgInKJy6PD/CATJBdGqzxPkLgWjtQDCRwhRqQcBkFE5DRJkpBXkQfA8UyQPE+QyjVBZqtZXv3d1zNB4lo4MkeQwEwQkXIYBBGR04qqimC2mgE4P0Re7UyQffbG54MgkQlypjuMmSAixTAIIiKniQ/gSEMkDDqDQ/uILh+1a4LsAxexXpmz5CDI7IM1QWHMBBEphUEQETnN2ZFhgF0mqLIQkiSp0i6gdj1QU2uaNSRU76GaICdmixbElAS5FRwdRuQuBkFE5DRnR4YBNXUvFsmCMmOZGs0C4H5RtP2+nuoOY00QkXcwCCIipzk7MgywBRZ6rR6Aul1i/hQEudUdxpogIrcxCCIip4kshKOzRQOARqPxyDB5fwqCXBoiz0wQkWIYBBGR01zJBAG164LU4ldBUKXro8MKKgtgsVpUaRdRoGAQREROc3bxVEGeK8jHM0GeWkXelZqg2LBYAIAEieuHEbmJQRAROc2V0WGAZ4bJ+1MmSK4JcqI7TKfVISY0BgDXDyNyF4MgInKaK6PDAM90h5WbygG4voI84JkgyCpZUVxVDMC57jCgphaLdUFE7mEQRORnJEnCttPbUFBZ4LU2iO4wZwqjAc/MGq10JkitOY2Kq4ohwXZsZ7rDAO+PEJMkCRszN8pBHJG/YhBE5EckScKTvz6JtI/S0P+j/qgyV3mlDXImyMnuME+sH6ZITdC5yRIBqHaNRSAYqgt1eNZtwdsjxN7e+jYGfTIIfT7sg+NFx73SBiIlMAgi8hNWyYoHf3wQr296HQBwqOAQXtv4msfbUVJdApPVBMCF7jBRE1RdpHSzZEoWRgPqFUe7Ug8keDMTdLrkNJ79/VkAwNHCoxj8yWBk5GV4vB1ESmAQROQn3tv2HubtnAcNNLjz4jsBADM3zMTRwqMebYf44A0PDnd6bS5/GSKvD9LLEzuqVRfkyvB4wZvrhz2++nGUGcvQN6kvusV1w6mSUxjzxRhYJavH20LkLgZBRH7iiz+/AAD856r/4NPrP8WwlGGoMlfh0Z8f9Wg7XB0ZBsBvJku031+1IMiFiRIFkYHz9Pphvx37DYv/XAytRosPr/kQayesRaQhEkcLj2Lb6W0ebQuREhgEEfmBnLIcbD21FQBw58V3QqPRYM6YOQjSBOGHv3/waDbI1ZFhQE1NkK8PkbffX60gSFwDZ4uiAe+NDntn6zsAgEmpk9A7sTdatWiFMZ3HAAC+O/idR9tCpAQGQUR+YEXGCkiQcGmbS5EUkQQA6BrXFZe2uRQAsCFzg8fa4urIMMB/usMA9VeSV6Q7zIM1QVbJKt9nd11yl/z4tRdeCwD4LoNBEPkfBkFEfuD7v78HUPOBIwxqNwiAh4MgF0eGAewOsyd3h7kSBHlhdFhGXgbyK/MRqgtF78Te8uOjO4+GTqvDgbwDOJR/yGPtIVICgyAiH1duLMevR38FAFzX9bpazw1uNxgAsD5zvcfaI7IPcWFxTu8rPvCrzFWqDT33myCo0o2aoHMBaH5lvsfWDxP3WP+2/REcFCw/Hh0SjaEdhgIAvs/43iNtIVIKgyAiH7fqyCpUmavQsWVHXNTqolrPDUweCAA4mHfQY1mBvIo8AK5lgiIMEdBAA0C9uiB/CYLENAGu1ASJ9cOsklXV+ip7Itsoso/22CVG/opBEJGPs+8K02g0tZ6LDYtF91bdAQCbTm7ySHvEop2uZIK0Gq3qEyb6SxDkTk1QcFAwIg2RAOCxRVQbDYK62IKgjSc3ykEykT9gEETk49YcXwMAuPrCq+t93tNdYuJDzpUgCFC/LkixwmiVV5J3Z4g8UHP9PRF0nC45jWNFx6DVaDGg7YA6z7ePbo+LWl0Eq2TF+hOe65olcheDICIfll+RLy9L0C+pX73beLo42u0gSOURYoGQCQI8GwSJe6tXQi9EGCLq3SatTRoAYGf2TtXbQ6QUBkFEPkx8oHSO6YyokKh6txFB0M7snaquei64GwSpPVeQEqvIA749TxDgnSBoUHLdrjAhNSkVAIMg8i8Mgoh82I6sHQBqPmDq0z6qPdpEtIHZapYnVFSL0WJESXUJgJriXGep2R0mSZJfZIIkSfKvIOhkw/VAQt+kvgBs96wkSaq3iUgJDIKIfJj4Vt03sW+D22g0GqS1tXVF7D2zV9X25FfYinDtC5ydFRlsK+gtrS5Vqlky+2H3itUEqTBZYrWlWl6EtqEMX1PiQj0TBJksJvyZ+ycAyPdZfS6Ovxg6rQ55FXk4WXJS1TYRKYVBEJEPcyQTBABdY7sCgOqreYsP3NjQWGg1rr19iFFNIqOkJPusjZjx2VVqZoLsX3t4cLhLxxCZOLWDoGNFx2C2mhGmD0PbyLYNbheiC5GncBD3LZGvYxBE5KPyKvKQWZwJAOid0LvRbbvG2YKgg/kHVW2TO8PjBVFYW2pUPhMkApbgoGDotDq3jiUHQWblgyCRBQsPDnc5mBS/A7WHyB/Ms91TXWK7NNlW0SW2M4t1QeQfGAQR+SjxQXJh7IVNdpnIQVCeukGQu0XRgGcyQe52hdkfQ81MkLgWrvBUTZC4p8Q91pjURBZHk39hEETko+SusMTGu8IAoEtcFwC21eaLq4pVaxODIGX4UxAkuli7xHZpclsWR5O/YRBE5KPEt2lHgqBIQyQSwxMBABn56tUFBVIQpOYq8v4UBIkuVkcyQT3je0Kn1SG/Ml/uyiXyZQyCiBowd/tcXP7J5Xj2t2ex7fQ2j59fZILEt+umiGyQmsXRgRQE+UsmqLCyEGarWZF21UfOBMU1nQkK0YWgZ+ueADxfHJ1XkYePd3+Mm7+6Gdctvg4FlQUePT/5JwZBRPVYfWQ1Jq+cjPWZ6/HS+peQ9lEaZm2a5bHz51fky8OMeyc2XhQtiBFiatYF2Y8Oc1VEsPqF0f4SBIlr4YqY0BgAgARJtdm38yry5MLrC2MvdGgfkbncnbNblTbVJ6s0CxfNvQj3fH8Plh5Yiu8zvseE5RPYJUdNYhBEdJ6s0izc8e0dkCDh2i7X4rou1wEAZqyd4bHFIf/K+wuAbSJER7MFciaI3WE+HwSJANCdTJBOq5OX3FDrvhRZoHZR7Ry+pj1a9wAA7D+7X5U21efldS8jtzwX7aPa418D/wVDkAEr/l6BNza/4bE2kH9iEERkR5Ik3PHtHThbcRaXxF+CxTctxrfjvkXvhN4oM5bhtY2veaQdB/IOAAAuan2Rw/t4YoRYIAVBYrJEX+0OA9SvC3JmZJgg7tm/zv6lSpvOd7zoOP67678AgAXXL8Brw1/D26PeBgA89etTXunKJv/BIIjIzpZTW7Dm+BqE6kLx9S1fI1QfCq1GixeveBEAMGfbHGSXZqveDvEBIiafc4T4oDpUcAgWq0WVdikxT5D44K8wVShey6JGJkiNVeSVDoLUmitIDoJinQiCzt2zhwsO15rBWy0vrn0RJqsJw1KGYWiHoQCA+1Pvx9iLxsIiWTzajU3+h0EQkZ0FexYAAG656BZ0ju0sPz6m8xj0b9sfleZKzNwwU/V2iO6w7q26O7xPu6h2CNGFwGgxyivPK02JTJD9KuRKL52hVneY0rUlSgVBas8aLbpWHSmKFhLCExAdEg2rZFW1axYADuUfwsK9CwFA/qIC2JaSmT5oOgDgu4zvWCRNDWIQRHROpakSi/cvBgBMuGRCrec0Gg1mDJ0BAPhs32cwWUyqtkXuDnMiE6TVaOXiVTW6xKrMVSgzlgFwLwgKDgqGIcgAQPniaKVWkAdqgiCrZIXRYnT7ePaUKIwGfLM7TKPRyPetuI/V8tm+z2CRLBjZaSQGJA+o9VyvhF64JP4SGC1GLP5zsartIP/FIIjonOUHl6OkugTto9pjSIchdZ4fljIMcWFxKKoqwqaTm1RrR4m5BGfKzwAAurXq5tS+YkI7Nb6Bi8VTdVqd2xkMteqC1MgE2R9XKUoURgPqLqJqtBhxtPAoAMcmSrQnMphq1wX98PcPAIDbetxW7/MTek0AUJPhJTofgyDyScVVxdiVvQs/H/4Z1eZqj5xzwd4FAIB/XvLPetdICtIGYUznMQCAFX+vUK0dJ6tsQ+PbR7V3enFNNYuj7YfHazQat47lD0GQPkiPIE0QAOXrgvyhMPpo4VFYJAvCg8ORFJHk1L6eyASdKjmF3Tm7oYFG/rs83+09b4dOq8P2rO3Yn+uZ0Wp/nPkDvx/7HZnFmarV5pFyGASRz3l81eOIfjUaqR+mYvTno3HL17fAKllVPeepklNYfWQ1AOCfvf7Z4HbXdL4GQM03UDWIIMiZkWFCp5adAECVmiAl6oEEfwiC7I+jdCbIH4KgY4XHANjuKWeDXnmEWJ56maAf//4RANC/bX+0atGq3m1at2iNqztfDcAz2aDVR1aj1we9cOWnV6L97PboMqeLavV5pAwGQeRTlh1YJs/t0bpFa+i1eqz4ewVeWPuCquddfnA5JEgY1G4QOrbs2OB2IzqNgE6rQ0Z+Bg7lH1KlLZlVtuUGusc5XhQtdIjuAMB/giBfLoy2P04gBkHiHhL3lDNEd9iRwiMwWpWtpxJ+OGT7InLNhdc0ut1dl9wFAFh6YKmqkyceLTyKcd+Mg1Wyyu9dRwqPYMLyCap/iSPXMQgin5FbnouJP0wEADx52ZM48/gZ/Pcftvk/Zqydge8OfqfauX86/BMA4B8X/qPR7aJCojCkva1eSK1skDuZIPGBdaL4hOJvvEoMjxfECLFAzwTZj5RzhZpD5N0JghLDE+URYlnVWco2DLbfx69HfwXQ9N/siE4joNfqcazoGA4VqPPFpdxYjusXX4/CqkJc2uZSnJhyAgceOoAW+hZYe2It3tn6jirnJfcxCCKHbM/ajq3FW1Vdo2jSD5NwtuIserbuKY/E+mevf+LhSx8GADzw4wOqjMqqMlfh92O/AwBGXTCqye3FN0/xTVRpIghyZni80CayDYI0QTBajMgpy1G0XewOU4ZVssqj7Hw6E1R8HIBrQZBGo5HvX5HZVNJvx35DlbkK7aLayTNUNyQ8OByD2w8GAPx06CfF2wIA72x9B3/k/oH4FvH4duy3CNGFoFNMJ7wxwpbVfurXp1SdxDQjLwNf/PkFTFZ1R602RwyCqEnLDy7HkE+HYOaxmbj4w4vx+b7PFU8r78nZg2UHl0Gn1eGzGz6DQWeQn5s1YhbiW8Qjuywbyw8uV/S8ALDuxDpUmivRJqKNvPhjY0QQtO7EOsU/xPMr8lFkLgLgWhCk0+qQHJUMQPkuMUWDoGD/CILUWEleBECAckFQUVWR4l8Q3MkEATXF0SKoV5KoB7qm8zUO1SuNvmA0AODnIz8r3haL1YJ5O+cBAF696lW0iWwjP3d/6v0Y2Wkkqi3V+M+G/yh+7qOFR3Hnt3ei+9zumPD9BPzn+H88NpCkuWAQRI1akbECY78eC7PVDJ1Gh8MFh3Hnsjvx4c4PFT3PBzs+AADc2O1GXJJwSa3ngoOCcV+f+wAAc3fMVfS8QM23w1EXjHLoDfWCmAuQEp0Cs9WMzSc3K9oWMZrGlZFhglp1QcwEKUO8Zr1WL8+X5KrokGh5JKPSEwL6chC09sRaALauLkeIIGjN8TWKBrSArVs8szgTMaExGNdjXK3nNBoN0oemAwCW7F+i6O+opLoEl318GT7/43NYJSt0Wh12luzErctuVXxeq+aMQVAzsu7EOgz7dBjGfD4Gd357p9tz2fyd/zdu/vpmmKwm3NLtFiy4aAEe6fcIAOC5Nc8pVtRaWl2KRX8sAgBMSp1U7zb3p94PrUaLNcfXKD7UVXw7dKQrTLis3WUAgI0nNyraFhEEdYtzbn4ge2oHQe6sIC/IhdEKT5boT0FQpCHS7akGgrRBqiyiWmGqQG55LgDXgyCRyVQ6CCqoLJD/TgYmD3S4LW0j26LKXCUHUEoRX8zu6X0PQnQhdZ5Pa5OGS+IvQZW5Cp/u/VSx87628TXklOWgU8tO2Hn/TqwYtwLBmmD8eOhHPLH6CbeOXWWuwr9W/Qs3LLkBVyy8AtN+maZqUbk3MQjyQadKTqHbe90wccVEh/exWC2Y+MNE/HbsN/x0+Cd8/sfnuG3pbW59I3hj0xswWowYljIMC69biHBdOGZeOROdYzojtzxXsRWav/jjC5QZy9Altou89s/5kqOS5dXc39/xviLnBWyBwsG8gwjSBOGqjlc5vN+g5EEAlA+C5OUyXBgZJnSI6gDAtzNBgVwYrVRRtCB+H2crzipyPAA4UXQCABBliEJ0SLRLxxCF/dnV2Yp20Ygvd11iuzQ4NP58Go1GzgYpWRf0d/7fWHVkFTTQ4IG+DzR4bvHcvB3zFAkmskqz8ObmNwHYygX6JPbBsJRheKzDYwCAD3Z+4FZQ/PaWtzFr8ywsP7gca46vwVtb3sLPhx3vStx2ehsSZiVgzrY5LrfBUxgE+aCpv0zFwbyD+O+u/yKz2LGiwqUHluJg3kFEh0Rj/rXzkRieiMziTHy8+2OX2nC2/Cw+3Wf71vL8kOeh0+oA2CaQe2XYKwCAWZtmuV18K0mSHNRM6jup0W/GD/V7CADw6d5PUW4sd+u8gnhDHJA8wKk3e5EJ2npK2WJxMcOuEpmgY0XHlGiSTHzIOvrB0xh/6Q4TK8krOVmiUsPjBfH7UDITJO4dV7NAgG2EWJQhClZYkVGg3AzmGzNtXzwuS77Mqf1EpleMBFWC6MYf03kMUlqmNLjd7T1vR3hwODLyMxTJRKWvSUeluRIDkwfKXw4B4NLIS9EnoQ+qzFV4f7trXxZLq0vx+qbXAQBT0qZg3EW2Lr4X173ocAD3+qbXcab8DB5f9TiOFBxxqR2ewiDIx6w6sgrf/PUNAECChEX7FjW5j1Wy4qV1LwEAHk17FP/X+//kxQNfXv+yS9/C5m6fiypzFfol9cOgdoNqPXdTt5uQ1iYN5aZyzFzv3mKi27O2Y++ZvQjRhcjzeTTkypQr0bFlR5QaS536VtKYVUdXAQBGdXK8KwywpdejQ6JRbirH3py9irQFqOkOc6UoWlCjO0ySJLl7pFVY4ARBamSCRDeyYkHQud+H+P0owd16IKD2CLEDZ5WbOVpkX8UXEUdd1fEqBGmCcKjgkCJ/G5Ik4eu/vgYA3Nvn3ka3jTBE4M6edwKwZWnccaTgCObvng8AeH3467W+OGo0GkxJmwIAmLN9DqrMVU4f/73t7yG/Mh+dYzrj9RGvY/ao2QjRhWDzqc347dhvTe5fWFmI7zO+BwBUW6rx8E8P+3RXGoMgH1JtrsbklZMBQF4I89O9nzZ5A63IWIE/cv9ARHAEHkmz1ezcl3of2kS0wamSU/IfjKMqTZWYs92WxnxswGN1sjP2xX6f7fvMpT804Ys/vgBgK4iOCY1pdFuNRoMbut4AAFh2cJnL5xQsVos8NH54p+FO7avVaDGgrW3BRqW6xAoqC5BTbsusdY11fMHK88lzBRUpN1dQqbFU7lr11UyQyWKShwj7chCkeCboXBB0tly57jAlgiCgpltXqZmjq83V2J61HQDqfDlrSqQhEmlt0wAA/zv6P7fbsjN7J06WnEQLfQuM7DSyye1FoPTdwe9qjRB01se7P4ZVsmJEpxH11kTd1PUmJEcmI7c816Ev0fbss0DPXv4sdFodEsIT5IEpL61/qcljfLX/KxgtRrSPag+9Vo+fDv+E7zLUm+PNXR4JgubOnYuUlBSEhIQgNTUV69evb3T7tWvXIjU1FSEhIejYsSPmzZtXZ5ulS5eie/fuMBgM6N69O5Ytq/uh6Ox5vW3BngU4VHAICeEJ+N9d/0OoLhQZ+RnYdnpbo/v9Z6Nt6OVD/R6SA4kQXYicDZq5YaZTa9h88ccXyKvIQ/uo9rip+031bjO843C0jWyLwqqaqN9ZFqsFS/YvAQDc3uN2h/YRQdAPf//g9giIndk7UVxdjChDFFITU53eX6TjN2RucKsdgugKa6Vv5Va9iJgryGQ1Ibs0W5G2iQ/YMH2YIgGGGoXR9oGKEqvIA34SBJ0LSpWsCVIqCBLdukqtIbYrexeqzFVoFdYKnWM6O73/sJRhAIBfj/3qdluWHbB95oy6YJQ8lUJj+iT2QeeYzqg0V7r1ninKFO7pfU+92+iD9Hg07VEAwFtb3nIqCzNvxzwUVBbgwtgLcVvPmkVp/zXwX9Br9VhzfA22nNrS6DFE+x6+9GE8PvBxALZ5knyV6kHQkiVLMGXKFDzzzDPYvXs3Bg8ejNGjRyMzs/5al2PHjmHMmDEYPHgwdu/ejaeffhqPPPIIli5dKm+zefNmjBs3DuPHj8fevXsxfvx4jB07Flu3bnX5vJ6UnQ2kpwN79tj+n33uc+rH3buA35/HPzs+hbaRbXFjtxuB0gRMfiJP3uZ8Ww9kYstnI6EpS8Kj/R+t9dy9fe5FbGgsTp02Y8KU4w0eo07bZgAoTcCD/R6Ua4HOF6QNwj8vsa2xNe/372q9Dkct274FOSsmIsrY1eFMzIDkAUgIT0BxXij+b2qm0+e09+22zcDvz2NA9I0I0gY5vb9Ix6/bfwjPPy+51RYA2PTXMeD355Fg7O3WceS5gkoT8OzzFrfbBZz7gC1NgH7dy4ocLyI4AihNQM4PkxQ5HnAuUClNANakIz83WJFjhunDgNIErF84TLF2ns6yAr8/j6Cytoocr3WL1kBpAn5fMESxNv59vBT4/XlEGp1bPf583Vt1B0oTsG7hlYq07afde4Dfn0ef8KtdGlknBj+s2vOHW3+z2dnAh28kAaUJtvdpB2g0Gtza41YAwIL1v7j0nvnV1vU49d09iDJ2xbVdrm1wu3v73ItQXSj+OlqA+x/Lcug8WVkSXnvFdr//a+C/ar33J0cl24b/lybg0ScLGzzexv1HsenT4dCUJeGOi+/AU4OeglajRcbxYkybXiLvl50NPPaY7T+l7lmXSSq79NJLpUmTJtV6rGvXrtJTTz1V7/ZPPPGE1LVr11qPTZw4Uerfv7/889ixY6VRo0bV2mbkyJHSrbfe6vJ5z1dcXCwBkIqLix3a3hk7d0oSIEmLFtn+v3On7fHW00ZJgCR9sGK7JEmS9MvhXyTc31sCJGnz1up6jzXl408lQJL6pt9f7/MP/PCAfAxxnsYs/y1TAiRJMzFVyirJkh83Go3S8uXLJaPRKD92KP+QhHRImompDh/f3o1vvSgBknT9my84td/EFROdek0N6TdjogRI0pMLF7u0f7mxXNK9oFOkLZIkSePeeVUCJGnok9NqXWdXDF0wVLF2SZIkfX/we0WPd6r4lHy8HTus7h9QkqTD+YcdbmN993N9Zm2cpejrliRJGj/nLQmQpDvnvKnI8b7Y94XibYx+5EoJkKQvfjno1nGO5x9v8j3MGUNnTpMASXpk/gKX9q82V0thL4e5fb2++fWoBEiSblI/qaiyyOH99uful5AOSTepn0vnH/nadAmQpLFvz6zz3Pn39O1Lb3fqdX7xy0EJkCT9A2n1vib794DtOyz1HuPeeXMlQJIGvjhZfuyS9y+p0w7xGajkPWvPmc9vVTNBRqMRO3fuxIgRtSe0GjFiBDZtqn8Om82bN9fZfuTIkdixYwdMJlOj24hjunJebztZfBK5ZWcA1EwyNixlGGLPDX/dkb2j3v3+dy6tOyzlynqfv6PnHfK/HRnhItbD6t+2PxIjEhvd9oKYCzCo3SBILtSdmCwm/HrM1i/vSH+6PdElBsDlmpdKUyX25OwBAFzaJs2lY4Tpw9A7wb2sjb2jhUcBAPGGeLeP5W43xvmU7GoBancFVVuUGT6t9PpegHK1RfbKTbZ6kBbBynTZKVGjZa/cWI6iqkIAQFJEklvHSgxPRIjW1lV0oviEW8eSJEkehNAroZdLxwgOCpbX/nOHqCXs1+ZSRIVEObxf91bd0bN1T5dGlBZVFeH347bz/qORLJAgMvUAHJpNfOWhlQCAy9tfXu9rGt5pOELP/T00NFeb6GYc3Xm0/Jijczl5S/19HQrJy8uDxWJBfHztN/X4+Hjk5NQ/tDonJ6fe7c1mM/Ly8pCYmNjgNuKYrpy3uroa1dU1b8YlJbZ+e5PJJAdf7sjOBnJygLNngU2bNAB0eOfzgwC6Ys4cM6zx2cCB6wEAG9bocSTDds5ORfciH8A3vx7FpYn9AAAajS2GPlOWiz/26AEALQuvwrZttn0SEmznzMkBdNKliC0egXwAn/y4F3qkytskJtZum1WSsOx32xtVN+MdtY4XF2eSr4f9PkP0U7Eh2/bHs22bGWazVOf49V2HTSc3o+RYJwCAdLp3rXPVt5/9vuGWyxGadxkqAXy1+jCslpQm9z3/GNtO74bplG3NodxDbbEtounz13eclIqbsD3btijj9u1Nv/6GjgMAGX/YPhTNWRdj2zYz9HrHj3P+8XTZlwLZQS636/zj7dwnAdl9FDueVTIA2bZ7cePmCugQ5NLx7I/5Z67F4TaK+7ihv21xzOxDiYq+bgDIPGgLWgqOdHDovm/qmDn5SYq28Wjhafl4B/eFIjTI+TaKY5lMFkTnXYkcAKvX5yPl3BxWrhzrdGkWCo/a9i8/3sXpayeO07lqHH7KttWHOnO97H+HP6yzLQqbUnGTw+0Q+18W9DD+yN7q8PnFft8eWAXjSdsX5LJjF9Y5r7iXMzNNyM8HIqxDEFV4JYoBLFi5FxrpkjrnEce2WK1YsfY0AKBz1dh6P0uAIFxkHo8dAD7/5QC6nRu8IT6PTpacwvG/bBN3tjg7GD/+aGtHaMl1QLatfnPBAjM+WpKD33YfBXA5AGDpUjP+/FNCXBzQo4fzfwf1ceYzWyNJ6o1dy8rKQps2bbBp0yYMGDBAfvzll1/GZ599hoMH6y4od+GFF+Luu+/G9OnT5cc2btyIQYMGITs7GwkJCQgODsbChQtx2201hVuff/457rnnHlRVVbl03vT0dMyYMaPO41988QXCwtz/Nvjll12wZInrI37sXXRRHvbvb3jCunHjbK+vsfONG3cQt92W4VDb7LcVXNnHnf3c3VfJY/jicQL1eP5yzEBroy8ey93jeGt/Z/dzZntHtgUa/yxp6vPIGa78HdSnoqICt99+O4qLixEZ2fgABFWDIKPRiLCwMHz99de44YaaLoxHH30Ue/bswdq1dSeNuvzyy9G7d2+8/fbb8mPLli3D2LFjUVFRAb1ej3bt2mHq1KmYOnWqvM1bb72F2bNn48SJEy6dt75MUHJyMvLy8pq8iI44PxP0yis64OKFwL5/4oJhv6O61VacPG0E1j+H//zHjMRE268l87QJzz4dBvzjXnz2wDRcGNtZjrwn/fgAdu8GsOIjzJtnRu/eNd8ogJpvLSvXncGMf7WF9rqJWDn1JbQMja7328CL617CD+tO13u8uDgTVq9ejeHDh0Ov19f6VvTIgoXY+v69GPTQQrxx1+3yPg19qzmcWY4xX45B9cnu9Z6rqUwQAHy0cjf+O+NStLr1aayYMgMajXOZoLu++ycy/ghz6vz1HedkySnc/M7LwIqP8O57Vbi0r3MZDXGcPTl7MfGjecCKj/DQQ7tx221dodfrXP42vyt7Nx6Y/6HLr+/846WvnYGf1ucodjwAGDnraRR9/TqefvUYrhva1qXj2R9zw8mNeGzhIofaaDLVvp8bOub6zA14/NPPFX3dd8x9E4cXPon7nt+Ke8f0cft1myxmDJr5MLDiI8x6pxiD08LcauM3B5bi9aW/uvWaazJBZjz5wRJs/GwCet33Hj64936XjzV769v4cvVBt/9mrZKE4a8/ibKlb+Gxlw9i7FWdHDqO2P+rv77GG9/+5nQ77O+B2957HUc/fRo3PvETnrzpqkb3z84GNh84jlu/HQdNTl9I339Y73nFPd2jx3Dk59vu6R/WZuPFJ9oh6LqJ+NHF936gpt1btpvw6GTb59HCSVPQNa6L/Hn04MqHsHOXVT5G27YS8vOB2Fjg1k+eQNnStzBk3G6szf0aKOoA7LbdC08/bUaXLspmgkpKShAXF+dQEOSRwugHHnig1mPdunVrtDC6W7dutR6bNGlSncLo0aNH19pm1KhRdQqjnTnv+dQsjN6xw2orCrvxNgmQpOAH+0v6F/T1FrHJBWT395ZeXPui/HhmUaakSdc4VPhmf4zXNrxW7za5ZblSyEshDR6vsULSed9vkwBJajF5sFRuLG/y9c/fNV9COqT2T9zgcmHc+i3l8mval7PPqX2zSrIkpEORYlKr1SoXkS786Q+XjzNv+zy5PW+88bvbhdFHC442WcTojFGLRilefNvhyRtrDQRw11d/fqV4YfT/jv5P8dfdefo4CZCkd5dvVOaAkiSFT75cAmwFu+56cvWTir1mo9Eo3f/iPAmQpPZP3ODWsQbOH6hYu0a9/rQESNKEue84ve+VC690ux1Pf/aNBEhSp6dukazWpgcGPLHqCQnpkAa//GiD563vnrZ/739p7Uv1HrugosDhYnH74z3+y+Py44WVhY0OEhnyylT5M8L+vbfZF0YDwLRp0/DRRx/h448/xoEDBzB16lRkZmZi0qRJAIDp06fjrrtqZgqeNGkSTpw4gWnTpuHAgQP4+OOPMX/+fDz++OPyNo8++ihWrVqFV199FQcPHsSrr76KX3/9FVOmTHH4vN508NycGbogW7RuNFfDZDXJRdANWfH3Cvnfr218DRIkpCb1derc7257t96ivHk75qHKXIVuLsxUnJpkq+0oN5Zh+cHlTW4vFhG8pvM1Tp9LsC9Y/fbAt07tK2abduW1nk+j0chrJP155k+Xj7P/rLKLwraJbAPANoS4sLLQ7eMpORGfEK4PBwDFlkDxm8Loc69XvH4lRIdGAwAKq9z/XTu6VI+jEvS2dMLJ4pMuryFmspiwK3uXYm0Sa/85O8dXfkU+1h53f9mL4R1tU4IcKTgsD9BoiNlqlufeaWxYfFPmbJ9T7/X/aNdHqDBV4IJY5+Zd+mDnByioLABge081W83o0MDSIRe3vhiA7TMCALq1cn1ZIKWpHgSNGzcOs2fPxgsvvIBevXph3bp1WLlyJdq3bw8AyM7OrjV3T0pKClauXIk1a9agV69eePHFF/HOO+/gpptqJu0bOHAgFi9ejE8++QQXX3wxFixYgCVLliAtLc3h83rT2vwlwJB0XNkvHlfftwOIsE2UcGmXZDz/fO10YGIiMO2pUiAiG9tOb0NOWQ6ySrPw313/BQA8OequOvucLzEReOZZM2JaG3Gy5KQ8yZdQba7Ge9vfAwA8dOWNTR7vfG2StBjyzzVARDY+2fNJo9seKzyGtSfWQgMN7r58lNPnEhITgesm7gEisp2ePfrHQz8CAEb37uXy+e3179oeGJKOI2bXJ03cd2YfEJGNa+/fjZYtq9xrEGyjYOITrcCQdJjD3F/F+2zFWSAiG/dOPa1IuhoAYlpXA0PSoY9SZs2rClMFEJGNrjcvUayNYfowICIbLYbPUuyYVaHHgCHp6JBsUOaAABISJGBIOjQROW4fK7M4E4jIxs0P7FfkNbdvFYyQq16FNfyUPCGos/ad2YcqcxWi4irx3HOS2+26oV9/YOgMHDatcyro++HvH2CRLOjWsaVb7x1dUiLR/eavgYhsLNy7sNFtVx1ZhZyyHMSFxeGWtEFOnTcxEfj3sxYkJAI5ZTlY/OfiWs+brWa8u+1dAMCDQ29w6LPkueckdO8Yg1JjKd7eYitbEV/Qr+7dp95jXHFxV2BIuu3vM64rXrthGjBgFoIuexuRscp8CXKZ8omo5kGt7jCzxSwlzEqQkA7p+4PfS6XVpVLEKxES0tFgV5UkSVK/D/tJSIc04rMR0t3L75aQDumy+Zc5lEoVnvvtOQnpkAbOH1jr8U92fyIhHVKbN9pIRnP93QNNdR8cLThqmzMoXSMdKTjSYBtmrJkhIR3SVZ9e5XC7G5JXnicFzQiSkA7paIFj3QDV5mr5em87tc3tNkiSJP106CcJ6ZA6v9PZpf2tVqsUNTNKQjqk7Se3O9RN44j+H/WXkA5p6V9L3TqO1WqVQl8Kdeo6O+KmJTdJSIc0d9tcRY43a+MsCemQ7vz2zia3dbQ7TMyFFfFKhCJtlCRJCn4xWEI6pMyiTMWOed2X10lIhzRv+zy3j9XurXYS0iFtPrnZ7WOJ6zz0k6ES0iF9vOtjl44zd9tcCemQRn420u02CZfNv0xCOqT3t7/v8D7iOj//+/Nun/+HjB8kpENq9VqrBt93JUmSrl98vYR0SI/+9Gijx2vsnv7P+v9ISId08fsX1/rM+OrPr+Q2VJoqHW77N/u/kZAOKWpmlPTOlnfke3rDiQ31bl9hrLB1l6VDmr15tmS1WqUL3rlAQjqkRXsXOXxeR/lUdxjV9tux35BTloPY0FiMvGAkwoPD8cqwV3BJ/CW1pik/34tXvIhQXShWHVklZ1ueG/KcU7OmPtDvAei1emw6uQmbTtrmSyozlslrxTyS9gj0QXWLRB2R0jIFoy4YBQkSXln/Sr3bVJmr5AyW/RwWrooNi8Xl7W3DLB3NBm3I3IBSYylat2gtd+O569I2lwIADhUcktPDzsgszkRxdTH0Wr1bq8efr11UO/n47ig3lctzTCk5J41YGkSp9cPkxVN1ynVhKb2KfLW5Wl7uxZ2lUc6n1CKqZqsZp0tsQ6XF/aOES+Jtw7P3nnFtseGtp21DytNcnNOrPmM6jwFQkxluSrmxHL8c+QVA7bnKXDXygpGIbxGPsxVn5eWDzvfHmT+w/OByaKDB/an3u3yu+1PvR5g+DPvO7JPfKy1WC97c8iYAYFLfSQjRhTh8vBu63YAerXuguLoYj/z8CIwWI27qdhMGJA+od/tQfSim9p+KoR2G4u7ed0Oj0chz2C36w7n1zZTGIMjDwoPDcXXnq3FHzzsQHGSb2n/ypZOxZ9IetI1seBr9kReMxJZ7t6BTS9tIhv5t+8v9yo5KCE+QA62rv7gaX+3/CsM+HYa/zv6F6JBoeZE8Vz13+XMAgIV7F8oT/9l7b9t7OFVyCm0j2+Lm7je7dS5BTFl/fpq3IT/+fa4r7ILR0GqUuf1jQmPkdYyaWuetPqImoHur7vI9oYTkyGQA7gdBoh4oRBei2JpcABAZrOwiqkqvIG9/LLPV7NCEc02xf60RwQoGQQqtH5Zdmg2LZIFOq0N8C/cn7RR6tu4JAE3WvzREBEHiC4cSru58NQDbYqqVpqaD3O8zvkeVuQodW3bExfEXu31+nVYnr/H13O/P1bsW4gvrXgAA3HLRLbYlSFzUMrQlJqZOBADc+s2tWLBnAa5bfB22nNqC4KBgPND3AaeOp9Vo8ezlzwIANNDgpStewle3fNXoe+prw1/D7//8XZ4o9Y6ed6BTy064LPkyr64yzyDIwwYkD8APt/+A2aNmO73vxfEXY8f9O/D+1e9j2bhlLq2dM2v4LPRv2x9FVUUY9804bDu9DbGhsVh15yq0DG3p9PHsDUgegJGdRsJsNdfJBhVXFeOVDbbHZgyd4dS3jsaMu2gcdFodtmdtx4GzTS/SKL71iTdApYjVqbee2trElnWJb8euzoLbEKUyQeKDtVVYK5fuuYYovZK8mkGQ/fHdIV5rC30Ll9ara4i8krybQZC4V9pGtlW0ffaZIGc/8IqqinAwzzZfjZJB0MXxF6NtZFtUmiux5viaJrcXtTt39rxTsb+DR9IeQUJ4Ao4VHcMHOz6o9dwfZ/7AN399Aw00csDhjv9c9R/c0v0WmKwm3P3d3fjx0I8I0YXgsxs+a3J1gPrc0v0WfHnTl9h0zyY8c/kzTn+p7BzbGYcePoR/X/5vRd9XnMUgyEtc/aVHh0RjUt9JSAhPcGn/Vi1aYc0/1+D/ev0fAKBNRBusu3sd+rXp59Lxzvf8kOcBAAv2LEBGXs2kV69tfA0FlQXoFtcNd11yV0O7O61Vi1ZyWrupAsP9ufuRkZ8BnVaHEZ1GNLqts/q36Q8A2Hxqs9P7im/H4oNCKYoFQecyQUovzyAHQUbfDYKCg4LlN3clgyClVpAX5EyQm6P4xL2iZFcYYFtNXq/Vo6iqyOn7UXyx6Niyo6L3oEajwZgLbO8dSw8sbXTbrNIsrD66GgAUff9qEdxCfs98cd2LKK0uBWBbIuTZ322Bzy0X3YIerXu4fa7goGB8edOXcsY/OTIZG+7egLEXjXXpeGJB2P5t+7vcJm8GPwKDoABk0Bnw0bUfYcs9W7DvgX1upVnPJ7JBFsmCQZ8Mws+Hf8aLa1/ErM2zAAAvX/lygyvTu+qui21vSov2LYLFamlwuw93fggAuObCa5xa78cRYn2czac2N9qG+oggSK1M0MkS90aH2WeClKR0TVC5yTbKRKk1uQDbm7QIqpQIgkqNtg85JeuBAOUyQeJeUToICg4Klt9nnO0S23hyIwDgsuTLFG0TANxxsa0uZfGfixu9DxftWwSrZMVlyZehU0wnRdtwT+97cEHMBThbcRajPx+NzSc346avbsJ3Gd8plgUSgrRB+OCaD7Dp/zZh3wP7FKuL9GcMggKURqNBWts0xITGKH7sj679CH0S+yCvIg+jPx+N59bY+rtv7n4zru96veLnu+bCa9AypCVOl57Gb8d+q3ebSlOlPNeG6BtXUs/4nggPDkdJdYlTc/4UVxXjWNExAMAlCepkgnLKclyenwVQLxMkamLEt193qZEJApQtjhYftErWAwEqZIIilQ2CgJog39niaDWDoMHtBqNbXDeUm8rx+b7P691GkiQ5y6zEgI7z6YP0mDtmLsL0Ydh4ciMGfjwQyw4uQ3BQMOZfO1+RLJA9jUaDAckDEB0Srehx/RWDIFJc28i22HD3BjltnBieiMU3LcZXN3+lSvrToDPgth62gu+GusS+2v8ViqqK0CG6g+JdYYCtyFGkhTdmbnR4v31n9gGwpaaVDkhjQ2Pl2qtTJadcPo7ILrQOa61IuwSRDRHZEXepFQQpmgmqVicT1LqF7XdztuKsW0WmIghKjkpWpF32RHevM5kgk8Ukd4dd1k75IEijqRl19cHOD+q9druyd+Gvs38hRBfictdRU4Z3Go4DDx2QvyS2iWiDdRPW4e7ed6tyPqrBIIhUEaoPxYLrFmDPxD34++G/Ma7HOFX7f//Zy/YN7av9X9WqRRI+3GXrCruvz32KjQo7nzwL7UnHJ01UqygasL3BK1EXJIZdq5UJKjs3i6y7/CEIEq9V8UzQue4ws9WMoqoil4+jVk0Q4FomaO+ZvSg3lSM6JFrRbnt7d11yFwxBBuw9sxfbs7bXeV6M0Lq+6/WKd6PbaxfVDsvGLcO+Sfuw/8H98mALUheDIFKNRqPBJQmXIDxYueUBGnJpm0txdeerYbKa8PBPD9f6Rrczayc2ndwEnVaHu3up981KfFN1JhOkVlG0oEQQpHZNkK93h/lDTZBBZ5ADK3fqgtQMgkR379HCow7XgYm/pYHJA1X78hITGoNbLroFAPDO1ndqPffj3z/i+4zvodPqFK3NaUzP+J6qBltUG4MgajbeHvU2DEEGrD66Wh7tcbb8LG752vYGd2O3G10aCuqotDZp0Gq0OFF8Qp5wrilqFUULorbDneJo1WuCfLw7LFQfWuv47pC7wxTOBAHu1wWVGcvktcfUCIJiQmPkuav25jiWDVKzHsjeQ/0eAgB8/sfn+GjXRwBsk7s+8vMjAIApaVNUy0SRdzEIomajU0wnPHnZkwCAySsn45X1r+D6JdfjWNExdGzZEe+NeU/V80cYIuSMjnjzbkyZsUwOgpSaouB8/pIJUmKyNLUzQY5MqNcUOROkRhDk5gixk8W2QDnKEKX4EH5B3OeO/H1IkuSxIKh/2/7yUPUHfnwAr218DTcuuRFHC48iKSIJzw15TtXzk/cwCKJm5alBT+HC2AtxpvwMnvntGWw6uQnRIdH48fYfERcWp/r5xZu1I6tTb8zcCItkQUp0iirfvIGaAle3giCVM0EWyYIqs/uLxvpFd5hKhdGA+5kgNYuihaHthwKAQ5MTHi86jqzSLOi0OtW+JNh7fsjzuK3HbTBbzXjy1yfx0+GfAACzR85W5fdFvkHZCVuIvCxUH4ot92zBV/u/wg+HfsDf+X9j3tXz0DWuq0fOf1m7yzBn+xyHgiDxQTCkwxDV2uNuJqjSVCnPv6N0Jsh+Pp9SY6nc7eQqvwiCPJAJcnX9MDXrgQRxr2/I3ACTxdToWoUiC9QnsY/iv9P6aDQafHzdx6g0V+JY4TGMumAUbup2k0cCMPIeBkHU7LQMbYmJfSdiYl/l5wNqypD2tjf5PTl7cKbsDOLDG15/ae2JtQBqvh2rwT4IkiTJ6RF6OWU5AGzrhindRaLVaBEeHI4yYxlKq0vlYd6usEpWeR4fxYMgne8XRgOQZ5E/U37Gpf3VnCNI6NG6B2JCY1BQWYBd2bsaHQH18+GfAdT8TXlCiC4Ey8Y5thgzNQ/sDiNSUGJEIlITUyFBanR16jJjmTwcV81MkChELTeVuzR0Oqs0CwCQFJGkyhQHShVH23enqVUYrcRkiWoWRidFJAGo+Z05S63Zou1pNVpc3v5yAI13iZmtZqw8tBIA8I8L/6Fae4gYBBEp7Nou1wKwrTrdkE0nN8FsNaN9VHt0iO6gWltC9aFyN8mJ4hNO759dlg3ANuGlGpQaJm+fpREzPCvFH4bIAzW/I/E7c5a4P9SsCQLs6oJOrGlwm42ZG1FYVYjY0FgMSB6gansosDEIIlKY+Oa6+ujqBgt+xbfgoR2Gqt6e9tHtAQAnipwPguwzQWpQKhMkAhRDkEHR1c8BlQqjfTATJO4PNYNyoOae35C5AWarud5tVvy9AgAwpvMYxdcaJLLHIIhIYb0SeqFtZFtUmCoaXMtM1AN5ot5BfKgdLzru9L6qB0EKZ4LUKKD1l0yQfRDk7JQDZqtZ7g5TOwjqGd8TLUNaosxYhl3Zu+rdRmRRRVaVSC0MgogUptFo5GxQfV1ipdWl2HZ6GwAPZYKibJkgV4Ig1bvDFMoElRuVX0FeEN1rvp4JEoXRRotRnvTQUVmlWTBbzdBpdar9rgX7uqD/Hf1fnecz8jJwqOAQ9Fq9Kuv8EdljEESkAvENdsXfK+p8K/9498cwW83oEttF9W/dQM03e1dqgpgJspss0c3CaKtklacbUCMTZNAZEBsaC8D5LjHRFdYuqp3i3Yn1GdN5DADgo90fwWK11HpOfHG4IuUK1SZtJBIYBBGp4IoOVyA8OBxZpVlyfQNg63Z4a8tbAICp/aequqis4NPdYQrXBPlyd5j9QrFqZIIA1+uCxL3hiaAcAO68+E7EhsbiaOFRLD+4XH7cZDFh/u75ADgqjDyDQRCRCgw6Ayb3mwwAeGzVYzBajACApX8txYniE4gLi8Ndl9zlkbaI7jCXRoeVnusOU2nNNTkI8oNMkLtBkHiNQZoghOhC3G5XfcTvSfzeHCXuDXGvqC1MH4YH+z0IAHh90+tytvS97e8hIz8DrcJaYfzF4z3SFgpsDIKIVPL04KeREJ6AwwWH8c7WdyBJEl7f9DoAYHK/yW7PkOwoMTqsoLLA4dW7Adts0aK2RPXusADIBNkXRauVAfSXTBBgW7TUEGTA1tNbsenkJpwtP4v0NekAgJevfJkrqZNHMAgiUkmEIQIzh80EAMxYOwN9PuyDndk7EaILkb8Fe0KkIRIxoTEAnBsmL4qiQ3WhiDKo84HkD91h8mSJbi6gqmZRtJAU7j9BUHx4vJwNvW7xdbh8weUori5Gr4Re+L/e/+exdlBgYxBEpKK7LrkL/ZL61Vox/tG0RxVfjLQprnSJ2XeFqZW58KfCaCUzQWqRu8OcnDDR091hwr8G/gsRwRHIr8zHwbyDAIC3R73tkeJsIoBrhxGpSqvR4pux32DJn0twQcwF6J3Y26PftoUO0R2wO2e3U8XRahdFAypkgnQ+HAR5IhPkQneYVbLK64Z5+t7sHNsZ2Y9lY0/OHuzO2Y22kW3l4fNEnsAgiEhl7aLa4V+X/curbZCHyTvRHeaRIIiZIEW5EgTllOXAaDEiSBOENpFt1Gpag1oEt8Bl7S7DZe0u8/i5idgdRhQA5AkTi487vI/aEyUC/lETJI5pspoaXObBEZ7IBNmvH+borNEiO9g2si2XqKCAwyCIKAC4MleQJzJB4cHhAHw7E2S/IKs7xdEi0BOvWQ32s0YXVBY4tI83iqKJfAWDIKIA4PPdYe5mgszqBUH2c/q40yXmiUyQQWdAXFgcAMe7xDy1cCqRL2IQRBQAxFxBZyvOyutsNcWT3WFlxjJYJavLx1EzE6TRaBSpC/JETRBQu0vMESIT5OmRYUS+gEEQUQCIDomW5/oRI4Ga4slMEACHg7P6qBkE2R/X1zNBgPPF0WJ4PDNBFIgYBBEFCGfqgipNlSiqKgKgbhAUqguFVmN7G3KnS0zNVeQBZVaS91QmyNkgiDVBFMgYBBEFCNEldqzoWJPb2s8WreZK3hqNRpH1wzyVCXJnJXk5CFI5EyR3hzmwfphVstZMlBjN7jAKPAyCiAJE55jOAIC/8/9uclv7rjC1V7pXojjar7rDPJUJKms6E3Sy+CSqzFXQa/VoF9VO1XYR+SIGQUQBomtcVwCQlydozOmS0wDU7QoT/CkTpEh3mIdqgk6VnGpyW3EvdI7tzDmCKCAxCCIKEF1iuwAAMvIzmtz2UMEhAECnmE6qtglgJkhp4nd2uOBwk9uKe0HcG0SBhkEQUYAQmaATRSeanPRPBEGiC01N/pAJUmIleU9lgi6IuQAAUFBZ0OSEiSITJO4NokDDIIgoQMSFxaFlSEtIkOQgpyGibsgjQZCbmSBJkpgJshOmD0ObCNsaYIfyG/89MxNEgY5BEFGA0Gg0DtcFiQ/PC2MvVL1d7maCTFYTLJIFgIpBkM69IMhkMaHaUg1A/UwQUPN7a6oInpkgCnQMgogCSJe4c3VBeQ3XBRVUFiC/Mh9ATdeKmuxnjXaFfWDiq5kg+9emdiYIqMngNZbxK60ulUcBivuCKNAwCCIKIF1jz2WC8hvOBIksUFJEkmqTD9pztztMBCZBmiDotXrF2mVP1AS5GgSJ1xYcFIzgoGDF2tWQzrFNB0GiKyy+RTyiQ6JVbxORL2IQRBRAHMkEiQ9OT3SFAe53h9nXA6k1p5G7kyV6askMwZHuMHEPMAtEgYxBEFEAEbUfGfkZkCSp3m08WRQNKJcJUqsrzP7Y7maCPNEVBth1h+UfavD3LNcDxbIeiAIXgyCiANKxZUcEaYJQZixrcG0pTw6PB+wyQc05CPJwJqhjy47QarQoNZYitzy33m3kkWHMBFEAYxBEFECCg4LlyfQaGiHmyZFhgF0mSIHuMLX4WybIoDOgfZRtLbCGusQ4MoyIQRBRwGls5mhJkmq6w2L9IxMkVpD3RBBUbip3aX9PZ4KAxoujLVaL/DjnCKJAxiCIKMA0NldQbnkuSo2l0ECDji07eqQ97maCxPBzNbMs4cHhAGoCLmd5OhME1K4LOl9mcSaqzFUIDgpGh+gOHmsTka9hEEQUYLq36g4A2JW9q85zIgvUPro9QnQhHmmPu5kgEQS10Ks3nF8c29W5jLyRCZJHiBXU7Q7bnbMbgC0LFKQN8libiHwNgyCiAHN5+8sBAFtPb62T2fB0UTQARBoiAQAl1SUu7S8CE5GtUYM4tstBkIfWDbPXWCbot2O/AQCGtB/isfYQ+SIGQUQBJiU6Be2j2sNsNWND5oZaz3l6eDxQ00VUZa6CyWJyen9Rp+OJIMjVmiAR4ImAzxNETdDhgsOwStZaz4kg6MqUKz3WHiJfxCCIKMBoNBr5w098GAprjq8BAFyScInH2mOfHXGlS8wfMkHeCII6RHdApCESleZKbDu9TX48uzQbB/IOQAMNhnRgJogCG4MgogAkB0HHa4KgrNIsbD29FQBwzYXXeKwt+iA9QnW2ZSlc6RLzZBBktBhhtBid3t8bQZBOq8OYzmMAAMsPLpcf//347wCA3om9ERMa47H2EPkiBkFEAeiKDlcAsBVHF1YWAgC+z/geAJDWJg1JEUkebY87dUEeKYy2W0PNlRFi3giCAOD6LtcDqB0EyV1hHdgVRsQgiCgAtYlsgy6xXWCVrFh3Yh2Amg/KG7re4PH2uBMEeaImKDgoWF6c1ZW6IG8FQaM7j0ZwUDAy8jPkKRFYD0RUg0EQUYCyrwsqriqWPxyv73q9x9siggNX5gryRHeY/fFdqQsStU6eDoIiDZEYljIMgC3IPV50HMeKjkGn1WFQu0EebQuRL2IQRBSgRBC07OAyvLbxNZisJnSN6+qVtaSU6A7z5SDIW5kgoCao/Wr/V5i5fiYA4NI2l3p04kYiX8UgiChADUsZhtYtWuNkyUm8suEVADU1JJ4mPpDdqgkKVq8myP747gRB3gg8ru1yLTTQYHfObny460MAwO09bvd4O4h8EYMgogDVMrQltt27DRN6TYBWo4VWo8XYi8Z6pS1u1QQZ1a8Jsj++s4XRZqtZXnjVG5mghPAEXJFiK4S/MPZCfH3L13iw34MebweRL9J5uwFE5D3to9vjk+s+wdODnkZxdTF6J/b2Sjsig5tvd5h9nZMnZ4y2t/imxfgz908Mbj8YOi3f9okE/jUQkcdWjG9Ic64JEq/JEGSAQWdQvF2OaNWilZwNIqIa7A4jIq9zNQiSJMkj8wTZH9/VIMgbXWFE1DgGQUTkdfIQeSeXzag0V0KCBMB3M0HeGh5PRE1jEEREXudqJsi+SDlMH6Zom87n6iKqzAQR+S4GQUTkda4OkRdZmTB9GIK0QYq3y567NUGcl4fI9zAIIiKvczUT5Kl6IPtzsCaIqPlgEEREXuduEKR2PZD9ORgEETUfDIKIyOtcrgnywOKpgts1QcEMgoh8DYMgIvI6+9FhkiQ5vB8zQUTkDlWDoMLCQowfPx5RUVGIiorC+PHjUVRU1Og+kiQhPT0dSUlJCA0NxdChQ7F///5a21RXV+Phhx9GXFwcWrRogWuvvRanTp2qtc3LL7+MgQMHIiwsDNHR0Qq/MiJSkggQrJJVXmLCEf4QBIkZoxkEEfkeVYOg22+/HXv27MHPP/+Mn3/+GXv27MH48eMb3ee1117Dm2++iTlz5mD79u1ISEjA8OHDUVpaM3/IlClTsGzZMixevBgbNmxAWVkZrrnmGlgsFnkbo9GIW265BQ888IBqr4+IlBGqC4VWY3s7cqZLzFOLp9qfw+lMkJGjw4h8lWrLZhw4cAA///wztmzZgrS0NADAf//7XwwYMAAZGRno0qVLnX0kScLs2bPxzDPP4MYbbwQALFy4EPHx8fjiiy8wceJEFBcXY/78+fjss89w1VVXAQAWLVqE5ORk/Prrrxg5ciQAYMaMGQCABQsWqPUSiUghGo0GkYZIFFUVoaS6BIkRiQ7t56nFU+3P4ewCquwOI/JdqgVBmzdvRlRUlBwAAUD//v0RFRWFTZs21RsEHTt2DDk5ORgxYoT8mMFgwJAhQ7Bp0yZMnDgRO3fuhMlkqrVNUlISevTogU2bNslBkLOqq6tRXV0t/1xSYnvjMplMMJlMLh2zORHXgNdCXYF8nSODbUFQQXkBTFGOvf7iqmIAQFhQmFPXzJXrbNDY1v0qM5Y5tZ+rbWwOAvl+9jRe6xrOXAPVgqCcnBy0bt26zuOtW7dGTk5Og/sAQHx8fK3H4+PjceLECXmb4OBgtGzZss42DR3XETNnzpSzR/ZWrVqFsDB1Z6L1J6tXr/Z2EwJCQF5no+1/q9evRm5ErkO7/HH6DwBA7qlcrFy50ulTOnOdC0wFAGw1Pj/++CM0Go1D+53OOw0AOLj3IFYedb6NzUFA3s9ewmsNVFQ4XlfodBCUnp5eb7Bgb/v27QBQ75uEJElNvnmc/7wj+ziyTWOmT5+OadOmyT+XlJQgOTkZI0aMQGQk09gmkwmrV6/G8OHDodfrvd2cZiuQr/Orea8i81QmuvXqhjFdxji0z8qfVgJngR5demDM5Y7tA7h2nYurioH9gBVWDBs5DCG6EIf2e+ToI0AVcNXgq9AvqZ/DbWwOAvl+9jRe6xqiJ8cRTgdBkydPxq233troNh06dMC+fftw5syZOs+dPXu2TqZHSEhIAGDL9iQm1tQE5ObmyvskJCTAaDSisLCwVjYoNzcXAwcOdPblyAwGAwwGQ53H9Xp9wN9Q9ng9PCMQr3NUSBQAoMJc4fBrr7DYvvFFhUa5dL2cuc7RQdHyv6ulakToHSt0FoXRMS1iAu53KgTi/ewtvNZw6vU7PTosLi4OXbt2bfS/kJAQDBgwAMXFxdi2bZu879atW1FcXNxgsJKSkoKEhIRa6Tyj0Yi1a9fK+6SmpkKv19faJjs7G3/++adbQRAReZcrK8l7sjBap9XJ2R9Hi6MlSeIQeSIfplpNULdu3TBq1Cjcd999+OCDDwAA999/P6655ppaRdFdu3bFzJkzccMNN0Cj0WDKlCl45ZVX0LlzZ3Tu3BmvvPIKwsLCcPvttwMAoqKicM899+Cxxx5DbGwsYmJi8Pjjj6Nnz57yaDEAyMzMREFBATIzM2GxWLBnzx4AwAUXXIDwcPXfMInIORHBzi+i6sl5gsR5qsxVDg+TrzRXwiLZpu4Qr4+IfIdqQRAAfP7553jkkUfkkVzXXnst5syZU2ubjIwMFBcXyz8/8cQTqKysxIMPPojCwkKkpaVh1apViIioeQN56623oNPpMHbsWFRWVmLYsGFYsGABgoJqVpF+7rnnsHDhQvnn3r17AwB+//13DB06VI2XS0RucGXpDE8uoCrOk4c8h4Mg8Vo00HhkLiMico6qQVBMTAwWLVrU6DbnT5Gv0WiQnp6O9PT0BvcJCQnBu+++i3fffbfBbRYsWMA5goj8iDtBkCczQfbnbYp4LRGGCHkySCLyHfyrJCKf4EoQ5MkFVO3P4+giqpwokci3MQgiIp/QnDNBDIKIfBODICLyCW7VBHmo3sbZ9cMYBBH5NgZBROQTxOgpR4fI268476uZIDE8niPDiHwTgyAi8gnOZoJEAAR4MAjSO7eIKjNBRL6NQRAR+QRngyCRjdFAg1BdqGrtsseaIKLmhUEQEfkEV4Og8OBwt9YNdAaDIKLmhUEQEfkEEShUmatgtBib3N7TRdH25yozMQgiag4YBBGRT4gw1BQPi4Lixnh6eLz9uRzOBBkZBBH5MgZBROQTdFodwvRhABzrEvPk4qmCPFkiC6OJmgUGQUTkM5xZRNUfMkEcIk/k2xgEEZHPiA6JBgAUVRU1ua2nF0+1P5ejQVBhVSEAICokSrU2EZHrGAQRkc9oGdoSQE3w0Bh/yAQVVtpeR0xojGptIiLXMQgiIp8hgoWCyoImt/X04qn253J0AVURzDEIIvJNDIKIyGe0DDmXCar0/0yQ2WqWa5vE6yIi38IgiIh8hhwEOdAdJoqOvRUEWSVro9va1zWJWici8i0MgojIZzjTHSYCJU8GGPbnKq4qbnRb8RoigiOgD9Kr2SwichGDICLyGc4URotMiye7mgw6g7xOWVMj2ESXnnhNROR7GAQRkc/w9UyQ/fmaCtRYFE3k+xgEEZHPcKYw2luZFjlb1UQbRSDHomgi38UgiIh8hsiaONIdJrbxdJDhaPE25wgi8n0MgojIZ4gsiyPdYXJNkJcyQU3VBDETROT7GAQRkc8QAUNRVVGjQ9BNFpM8V4/XMkFNdIfJmSoWRhP5LAZBROQzRMBglayNLqJqn4Xx9LpcLIwmaj4YBBGRzwjRhchD0BvLtIgAIyI4AjqtziNtExzNBLE7jMj3MQgiIp/iSHG0N+fgcXQuIxZGE/k+BkFE5FMcKY72xkSJgn3dUmNYE0Tk+xgEEZFPcaS7yZsBhqOZIHaHEfk+BkFE5FMcmTVaBEjeWJhULoxuanQYu8OIfB6DICLyKY5kWrw1UaL9ORtrX5W5CpXmStv27A4j8lkMgojIp8SENJ0J8mpNkN1kiZIk1buNyAJpNVpEGiI91jYicg6DICLyKY6szeXV0WHnAi+z1YxyU3m929gv7qrV8G2WyFfxr5OIfIpDQ+S9tII8AITpw+S5iRoK1EQWi/VARL6NQRAR+RSRaWm0MNqLNUEajabJuiA5U8WRYUQ+jUEQEfkURwqjvbV4qtDUIqqcI4jIPzAIIiKf4swQeW9lWpqay4jdYUT+gUEQEfkUX58s0f687A4j8m8MgojIp4jsSamxFCaLqc7zVsmK4qpiAN4pjLY/LzNBRP6NQRAR+RT7wKa+mpviqmJIsM3P4/XusIYyQV4s3CYixzEIIiKfEqQNkicYrC/IEIFRqC4UBp3Bk02TNbWIqre764jIMQyCiMjnNFYc7QsBRlM1QewOI/IPDIKIyOc0VhztzcVThaZqglgYTeQfGAQRkc9pbNZoX6i3aaomiJkgIv/AIIiIfI7obqqvO8zbEyXan7u+miBJknyiy46ImsYgiIh8TlxoHAAgtzy3znO+0NXUWHddcXUxzFYzACA2NNaj7SIi5zAIIiKf0zayLQDgVMmpOs/5RHdYI4XRmcWZAGwBUKg+1KPtIiLnMAgiIp/TLqodgJqAwp4vFUZXmatQZa6q9dzJ4pMAal4DEfkuBkFE5HOSo5IBACdLTtZ5zhfqbSINkdBAY2vPeV1ios3iNRCR72IQREQ+JznSFkBkFmdCkqRaz8mF0V7sDtNqtHI26PziaJG9ahfJTBCRr2MQREQ+R9QEVZmrkF+ZX+s5X8gE2Z///LogZoKI/AeDICLyOQadAfEt4gHU1NgIolg6ITzB4+2yJ85/fvG2yASJbBYR+S4GQUTkk0Qmxb44utJUiazSLABAp5advNIuQZz/SMGRWo+zMJrIfzAIIiKfJIII++Loo4VHAQBRhiivz8YsB0GFNUGQVbLKmSF2hxH5PgZBROSTRHeSfXfY4YLDAIBOMZ2g0Wi80i6hU0zdIOhM2RmYrCZoNVokRSR5q2lE5CAGQUTkk+QRYiU13WEi4PB2V5h9G0RgBtRkrZIikqDT6rzSLiJyHIMgIvJJcneYXSZI1N9cEHOBV9pkT7ThdMlpecJEFkUT+RcGQUTkk+qbMNGXMkFxYXGICI6ABAnHCo8BYFE0kb9hEEREPklkU06XnIbFagFQuybI2zQaTZ26IHmOIGaCiPwCgyAi8kkJ4QnQaXWwSBZkl2XDbDXjRPEJAL6RCQLqDpOXZ4tmJojILzAIIiKfFKQNQpuINgBswUVmcSbMVjMMQQa0iWzj5dbZnD9MnrNFE/kXBkFE5LPkuqDik3K2pWPLjtBqfOOtSxRHi246FkYT+ReO4SQin2U/YWJBZQEA36gHEuxrgqrN1cgpywHA7jAif8EgiIh8lv1q8sFBwQB8px4IqGnLscJjcldYiC4EcWFx3mwWETmIQRAR+SwRBO3J2SMvk+FLQVDbyLbQa/UwWU1YkbFCfszbs1kTkWMYBBGRzxrSYQiCNEFYn7keGtgCC1/qDgvSBiGlZQr+zv8bj616DABwZYcrvdwqInKUb1QXEhHVo0frHvjkuk8AABIkAL4xW7Q90R4JEga1G4S3Rr3l5RYRkaMYBBGRTxt/yXi8NdIWWITpw9AhuoN3G3Sei1pdBAC4OP5irLhtBcL0YV5uERE5it1hROTzpvSfgvZR7RFpiJQLpH3FE5c9gXZR7XBrj1sRHRLt7eYQkRMYBBGRX7ih2w3ebkK94sLiMPnSyd5uBhG5QNXusMLCQowfPx5RUVGIiorC+PHjUVRU1Og+kiQhPT0dSUlJCA0NxdChQ7F///5a21RXV+Phhx9GXFwcWrRogWuvvRanTp2Snz9+/DjuuecepKSkIDQ0FJ06dcLzzz8Po9GoxsskIiIiP6RqEHT77bdjz549+Pnnn/Hzzz9jz549GD9+fKP7vPbaa3jzzTcxZ84cbN++HQkJCRg+fDhKS0vlbaZMmYJly5Zh8eLF2LBhA8rKynDNNdfAYrEtsnjw4EFYrVZ88MEH2L9/P9566y3MmzcPTz/9tJovl4iIiPyIat1hBw4cwM8//4wtW7YgLS0NAPDf//4XAwYMQEZGBrp06VJnH0mSMHv2bDzzzDO48cYbAQALFy5EfHw8vvjiC0ycOBHFxcWYP38+PvvsM1x11VUAgEWLFiE5ORm//vorRo4ciVGjRmHUqFHycTt27IiMjAy8//77mDVrllovmYiIiPyIakHQ5s2bERUVJQdAANC/f39ERUVh06ZN9QZBx44dQ05ODkaMGCE/ZjAYMGTIEGzatAkTJ07Ezp07YTKZam2TlJSEHj16YNOmTRg5cmS97SkuLkZMTEyD7a2urkZ1dbX8c0lJCQDAZDLBZDI5/sKbKXENeC3UxevsGbzOnsHr7Dm81jWcuQaqBUE5OTlo3bp1ncdbt26NnJycBvcBgPj4+FqPx8fH48SJE/I2wcHBaNmyZZ1tGjrukSNH8O677+KNN95osL0zZ87EjBkz6jy+atUqhIVxyKuwevVqbzchIPA6ewavs2fwOnsOrzVQUVHh8LZOB0Hp6en1Bgv2tm/fDgD1Th0vSVKTU8qf/7wj+zS0TVZWFkaNGoVbbrkF9957b4P7T58+HdOmTZN/LikpQXJyMkaMGIHIyMhGzx0ITCYTVq9ejeHDh0Ov13u7Oc0Wr7Nn8Dp7Bq+z5/Ba1xA9OY5wOgiaPHkybr311ka36dChA/bt24czZ87Uee7s2bN1Mj1CQkICAFu2JzExUX48NzdX3ichIQFGoxGFhYW1skG5ubkYOHBgreNlZWXhiiuuwIABA/Dhhx822maDwQCDwVDncb1eH/A3lD1eD8/gdfYMXmfP4HX2HF5rOPX6nR4dFhcXh65duzb6X0hICAYMGIDi4mJs27ZN3nfr1q0oLi6uE6wIKSkpSEhIqJXOMxqNWLt2rbxPamoq9Hp9rW2ys7Px559/1jru6dOnMXToUPTp0weffPIJtFpOjk1EREQ1VIsMunXrhlGjRuG+++7Dli1bsGXLFtx333245pprahVFd+3aFcuWLQNg6wabMmUKXnnlFSxbtgx//vknJkyYgLCwMNx+++0AgKioKNxzzz147LHH8L///Q+7d+/GnXfeiZ49e8qjxbKysjB06FAkJydj1qxZOHv2LHJychqsGSIiIqLAo+qM0Z9//jkeeeQReSTXtddeizlz5tTaJiMjA8XFxfLPTzzxBCorK/Hggw+isLAQaWlpWLVqFSIiIuRt3nrrLeh0OowdOxaVlZUYNmwYFixYgKCgIAC2YubDhw/j8OHDaNu2ba3zSZKk1sslIiIiP6JqEBQTE4NFixY1us35QYlGo0F6ejrS09Mb3CckJATvvvsu3n333XqfnzBhAiZMmOBsc4mIiCiAsFCGiIiIAhKDICIiIgpIXEW+AaKbzpn5Bpozk8mEiooKlJSUBPzwSzXxOnsGr7Nn8Dp7Dq91DfG57UgNMIOgBogFW5OTk73cEiIiInJWaWkpoqKiGt1GI3G4VL2sViuysrIQERHR5GzVgUDMoH3y5EnOoK0iXmfP4HX2DF5nz+G1riFJEkpLS5GUlNTkHIHMBDVAq9XWGV5PQGRkZMD/gXkCr7Nn8Dp7Bq+z5/Ba2zSVARJYGE1EREQBiUEQERERBSQGQeQQg8GA559/vt5FZkk5vM6ewevsGbzOnsNr7RoWRhMREVFAYiaIiIiIAhKDICIiIgpIDIKIiIgoIDEIIiIiooDEIIhcVl1djV69ekGj0WDPnj3ebk6zcvz4cdxzzz1ISUlBaGgoOnXqhOeffx5Go9HbTWsW5s6di5SUFISEhCA1NRXr16/3dpOalZkzZ6Jfv36IiIhA69atcf311yMjI8PbzWr2Zs6cCY1GgylTpni7KX6DQRC57IknnkBSUpK3m9EsHTx4EFarFR988AH279+Pt956C/PmzcPTTz/t7ab5vSVLlmDKlCl45plnsHv3bgwePBijR49GZmamt5vWbKxduxYPPfQQtmzZgtWrV8NsNmPEiBEoLy/3dtOare3bt+PDDz/ExRdf7O2m+BUOkSeX/PTTT5g2bRqWLl2Kiy66CLt370avXr283axm7fXXX8f777+Po0ePerspfi0tLQ19+vTB+++/Lz/WrVs3XH/99Zg5c6YXW9Z8nT17Fq1bt8batWtx+eWXe7s5zU5ZWRn69OmDuXPn4qWXXkKvXr0we/ZsbzfLLzATRE47c+YM7rvvPnz22WcICwvzdnMCRnFxMWJiYrzdDL9mNBqxc+dOjBgxotbjI0aMwKZNm7zUquavuLgYAHj/quShhx7C1VdfjauuusrbTfE7XECVnCJJEiZMmIBJkyahb9++OH78uLebFBCOHDmCd999F2+88Ya3m+LX8vLyYLFYEB8fX+vx+Ph45OTkeKlVzZskSZg2bRoGDRqEHj16eLs5zc7ixYuxa9cubN++3dtN8UvMBBEAID09HRqNptH/duzYgXfffRclJSWYPn26t5vslxy9zvaysrIwatQo3HLLLbj33nu91PLmRaPR1PpZkqQ6j5EyJk+ejH379uHLL7/0dlOanZMnT+LRRx/FokWLEBIS4u3m+CXWBBEA2zfkvLy8Rrfp0KEDbr31VqxYsaLWB4bFYkFQUBDuuOMOLFy4UO2m+jVHr7N4Q8vKysIVV1yBtLQ0LFiwAFotv7e4w2g0IiwsDF9//TVuuOEG+fFHH30Ue/bswdq1a73Yuubn4YcfxvLly7Fu3TqkpKR4uznNzvLly3HDDTcgKChIfsxisUCj0UCr1aK6urrWc1QXgyBySmZmJkpKSuSfs7KyMHLkSHzzzTdIS0tD27Ztvdi65uX06dO44oorkJqaikWLFvHNTCFpaWlITU3F3Llz5ce6d++O6667joXRCpEkCQ8//DCWLVuGNWvWoHPnzt5uUrNUWlqKEydO1Hrs7rvvRteuXfHkk0+y+9EBrAkip7Rr167Wz+Hh4QCATp06MQBSUFZWFoYOHYp27dph1qxZOHv2rPxcQkKCF1vm/6ZNm4bx48ejb9++GDBgAD788ENkZmZi0qRJ3m5as/HQQw/hiy++wHfffYeIiAi53ioqKgqhoaFebl3zERERUSfQadGiBWJjYxkAOYhBEJEPWrVqFQ4fPozDhw/XCS6ZvHXPuHHjkJ+fjxdeeAHZ2dno0aMHVq5cifbt23u7ac2GmH5g6NChtR7/5JNPMGHCBM83iKgB7A4jIiKigMQqSyIiIgpIDIKIiIgoIDEIIiIiooDEIIiIiIgCEoMgIiIiCkgMgoiIiCggMQgiIiKigMQgiIiIiAISgyAiIiIKSAyCiIiIKCAxCCIiIqKAxCCIiIiIAtL/A618AR59zOCYAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Tracé de la fonction d'erreur\n", "plt.plot(theta, f(theta) - p, '-g'); plt.grid()\n", "plt.plot(t, 0*y, '+b')\n", "plt.show()" ] }, { "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": 13, "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", "import matplotlib.pyplot as plt\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.clf()\n", "plt.plot(x, p1, '.-', label=\"p1\"); plt.plot([0,0.2], [1.0,1.0], '-k.')\n", "plt.plot(x, p2, '.-', label=\"p2\");plt.plot([0.8,1.0], [1.0,1.0], '-k.')\n", "plt.plot(x, p3, '.-', label=\"p3\"); plt.plot([0,0.2], [0,0.2], '-k.')\n", "plt.plot(x, p4, '.-', label=\"p4\"); plt.plot([0.8,1.0], [-0.2,0], '-k.')\n", "plt.plot([0.0,0.2], [0.0,0], '-k.')\n", "plt.plot([0.8,1.0], [0.0,0], '-k.')\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": 18, "id": "90623c89-3794-4680-abf8-f6a6f997657d", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "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.plot([0,0.2], [3.0,3.0], '-k')\n", "plt.plot([0.8, 1.0], [1.8, 2.0], '-k')\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": 27, "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) + (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": 28, "id": "795379e2-6acd-4c4b-ab63-3216c780fe86", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.125\n", "0.125 0.09600000000000002\n" ] } ], "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", "print(r(0.5))\n", "\n", "xx = np.array([0.5, 0.6])\n", "print(*[r(xx[i]) for i in range(2)])" ] }, { "cell_type": "code", "execution_count": 29, "id": "5464f2e8-5b1d-467c-b2a7-28601bd9ecfa", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# !! 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": 35, "id": "ca1e4379-bd07-40be-ad3b-1ec1ba115cda", "metadata": { "tags": [] }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "96932020978a424db8db10b9ca2c9748", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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"91e93136-8f2c-4fce-a47f-e9ba889000c1", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Tracé de la fonction d'erreur\n", "plt.plot(theta, f(theta) - s, '-g'); plt.grid()\n", "plt.plot(t, 0*y, '+b')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "e639892f-ebc8-4d20-81ff-0d28f91cbe8c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 32, "id": "6c46c184-08ff-4e4c-8fb0-a023e0283af8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]\n" ] } ], "source": [ "print(np.arange(0, 1, 0.1))" ] }, { "cell_type": "code", "execution_count": null, "id": "177ea273-19b3-4bcc-82db-1a44035a20b1", "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": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 5 }