{ "cells": [ { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "application/vnd.microsoft.datawrangler.viewer.v0+json": { "columns": [ { "name": "index", "rawType": "int64", "type": "integer" }, { "name": "x", "rawType": "int64", "type": "integer" }, { "name": "y", "rawType": "float64", "type": "float" } ], "ref": "01bfa4fa-e013-4720-a477-a2e661ddc264", "rows": [ [ "0", "1", "12.6" ], [ "1", "3", "11.9" ], [ "2", "5", "12.8" ], [ "3", "6", "11.8" ], [ "4", "8", "12.3" ] ], "shape": { "columns": 2, "rows": 5 } }, "text/html": [ "
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 1. Construire la fonction de lissage S\n", "# Nous utilisons KernelReg. var_type='c' indique que la variable (x) est continue.\n", "kr = KernelReg(endog=df[\"y\"], exog=df[\"x\"], var_type=\"c\")\n", "\n", "# 2. Appliquer le lissage\n", "# Nous prédisons sur les valeurs de x existantes (qui sont triées)\n", "y_smooth, _ = kr.fit(df[\"x\"])\n", "\n", "# Représentation graphique\n", "plt.figure(figsize=(10, 6))\n", "plt.scatter(df[\"x\"], df[\"y\"], color=\"gray\", alpha=0.5, label=\"Données brutes\")\n", "plt.plot(df[\"x\"], y_smooth, color=\"red\", linewidth=2, label=\"Lissage KernelReg\")\n", "plt.title(\"Lissage par Kernel Regression\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def my_ace(x: np.ndarray, y: np.ndarray, tol: float = 1e-6, maxiter : int = 500) -> tuple[np.ndarray, np.ndarray, float, int]:\n", " \"\"\"Implémentation de l'algorithme ACE (Alternating Conditional Expectations).\n", "\n", " Args:\n", " x (np.ndarray): Variable explicative\n", " y (np.ndarray): Variable à expliquer\n", " tol (float): Tolérance pour la convergence\n", " maxiter (int): Nombre maximum d'itérations\n", "\n", " Returns:\n", " tuple: (theta_y, phi_x, mcor, iterations)\n", " theta_y: transformation g(y)\n", " phi_x: transformation f(x)\n", " mcor: corrélation maximale\n", " iterations: nombre d'itérations effectuées\n", "\n", " \"\"\"\n", " # Standardisation initiale de g(y)\n", " # On commence par centrer et réduire y\n", " theta_y = (y - np.mean(y)) / np.std(y)\n", " phi_x = np.zeros_like(x)\n", "\n", " error = 1.0\n", " iteration = 0\n", "\n", " # Pour stocker l'erreur précédente pour vérifier la convergence\n", " prev_mse = np.mean((theta_y - phi_x) ** 2)\n", "\n", " while error > tol and iteration < maxiter:\n", " # Etape 1: E[g(Y)|X] -> Si on suppose que Phi(X) est l'espérance conditionnelle\n", " # On utilise KernelReg pour estimer E[theta_y | x]\n", " kr_x = KernelReg(endog=theta_y, exog=x, var_type=\"c\")\n", " phi_x, _ = kr_x.fit(x)\n", "\n", " # Etape 2: E[f(X)|Y] -> On estime E[phi_x | y]\n", " kr_y = KernelReg(endog=phi_x, exog=y, var_type=\"c\")\n", " fit_y, _ = kr_y.fit(y)\n", "\n", " # E[g(Y)|X] est mis à jour, maintenant on met à jour g(Y)\n", " # Attention: Dans l'agorithme ACE standard, on cherche à maximiser la corrélation.\n", " # Le pas de mise à jour est souvent: g_new(Y) = E[f(X)|Y] / ||E[f(X)|Y]||\n", " # Mais on doit aussi s'assurer que g(Y) a une moyenne nulle et variance 1\n", "\n", " # Mise à jour non normalisée\n", " theta_y_new = fit_y\n", "\n", " # Standardisation de g(Y)\n", " theta_y_new = theta_y_new - np.mean(theta_y_new)\n", " std_theta = np.std(theta_y_new)\n", " if std_theta > 1e-10: # Eviter division par zéro # noqa: PLR2004\n", " theta_y_new /= std_theta\n", "\n", " # Calcul de l'erreur (critère d'arrêt : changement dans l'erreur quadratique moyenne)\n", " curr_mse = np.mean((theta_y_new - phi_x) ** 2)\n", " error = np.abs(curr_mse - prev_mse)\n", " prev_mse = curr_mse\n", "\n", " theta_y = theta_y_new\n", " iteration += 1\n", "\n", " # Calcul de mcor (corrélation maximale)\n", " mcor = np.corrcoef(theta_y, phi_x)[0, 1]\n", "\n", " return theta_y, phi_x, mcor, iteration" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Démarrage de l'algorithme ACE sur PERF_CIRCLE...\n", "Valeur de mcor obtenue : 1.0000\n", "Nombre d'itérations : 2\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/arthurdanjou/Workspace/studies/.venv/lib/python3.13/site-packages/numpy/linalg/_linalg.py:2236: RuntimeWarning: overflow encountered in divide\n", " s = divide(1, s, where=large, out=s)\n", "/Users/arthurdanjou/Workspace/studies/.venv/lib/python3.13/site-packages/numpy/linalg/_linalg.py:3383: RuntimeWarning: invalid value encountered in matmul\n", " return _core_matmul(x1, x2)\n" ] } ], "source": [ "# 1. Application sur le jeu de données PERF_CIRCLE.CSV\n", "# Charger les données\n", "df_circle = pd.read_csv(\"perf_circle.csv\", sep=\";\")\n", "\n", "X_circle = df_circle[\"x\"].to_numpy()\n", "Y_circle = df_circle[\"y\"].to_numpy()\n", "\n", "print(\"Démarrage de l'algorithme ACE sur PERF_CIRCLE...\")\n", "# Note: L'algorithme peut être lent à cause de KernelReg dans la boucle\n", "theta_y, phi_x, mcor, iters = my_ace(X_circle, Y_circle)\n", "\n", "print(f\"Valeur de mcor obtenue : {mcor:.4f}\")\n", "print(f\"Nombre d'itérations : {iters}\")" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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oAAAA6EIqiC9eVW4bKnfZLX//wOoiewroDTsD9xTSI1YXDlvZtp1u/9KhxId4acOGDXbAAQfEbNO6unmqq6vd+XtdXV2T+3zwwQfNPm9NTY37itLzAUDcu8fz93RoqyBc9nl1qzu0dRzqytZz6C6fhrSu7Ss3bXf7DerdvUufz8vnalyQjz6fK8gHurs/RwX5YUV5rf5vQVc7gESSNEX0m266yd36ed9999VvO/DAA+N6TAAAAOhaTy8vs9mLVtlnFbusZnedVe/e02HeOKBQ1+7RQnpNKGybt/9fURaJbebMmTZ9+vR4HwaAJOVF4dXLgrAK+ToOFeGboviUjZVht19rePl8Xj6X1x8WePUhRkNktQPoiKSJc3nmmWfsyCOPtO9///tuCNFhhx1md999d7wPCwAAAF1YQJ8xb4Wt3bLT9uuWaTn+/7voVym9qVu8tUXX8r1zA118tKmvT58+tnHjxphtWleWpKIXCwoKLDMzs8l99L3NmTp1qsukjH6tW7eu034GAKnFqziRthSEW6JirQr5KgA3Rdv1uPZrDS+fz8vnqi/IN/i3uSFt1+OtKch7HTPjVTQPgPSWNEX01atX25133mlDhgyxv//973b++efbxRdfbA888ECz36PbQHX7Z8MvAAAAJGeEizrQdUFfmBewoD/LumVluiGiUYp1cVXz/xX53/b0gu7ZNrqkoOsPOsUdffTRtnDhwphtCxYscNvF7/fbEUccEbOPBotqPbpPUwKBgCvEN/wCkB46kn/tZeHVy4Kwup3152tQZ/TfpSita/uQwly3X2t4+XxePpeXBXkvP8TorKx2AOknaeJcdMKtTvQbb7zRrasT/d1337W77rrLzj777Ca/h1tBAQAAUoMyzRXhkhfsZhkZe/pAgt0yrVumz2o1RfR/1UUirktEtQCXle7LsEvHDrasrKTpHYmbHTt22EcffVS//vHHH9vy5cutZ8+e9oUvfMF1iJeVldmDDz7oHv/JT35if/jDH+yKK66wH/3oR/biiy/aY489Zs8991z9c0yZMsWdq+s8/qijjrLbbrvNqqqqbOLEiXH5GQGkbgyLl3EiDQvCKsJ3pCCsuBD9DIogiR6fivB6DhWpe+b47eTD+7Y6VsTL5/PyuaIFeRWmFXnT8L9BtCB/SL8erSrIexkz0xlZ7dHnJRoGSC9JU0QvKiqyYcOGxWw7+OCD7cknn2z2e3SirxP3KHWiK1cdAAAAiT00VBnmimBRB7kK4FoP1UUsEPy/YrguhHvs18227KjZ04Wui9rIngK6VjVs9IxR/e3kwzn/a4033njDvv71r9evR8+jVQS///77bf369bZ27dqY+UQqmP/sZz+z3//+99avXz/705/+ZOPGjavf59RTT7XNmzfbtdde6waRjhw50ubPn7/XsFEA6c2L/GsvC69eFoRFx66fIfohgY5DRXg9h4rUbc329vL5vHouLwvyXn6I4XVWuzDwFEhPSVNEHz16tH344Ycx2/7zn//YgAED9nkrqL4AAACQXENDVTDPysyw4vxsm1xa4grqWteQ0KD//wrpudnd3HJrVY2FwmbdMs2yfJnWO9dvl44dQgG9DY477ri9budvSIX0pr7nzTff3OfzXnjhhe4LQGrqaEeuV53Cidw9Liqu6mfwqnvZy+fz6rm8Ksgnald7Zw08BZAckqaIrg6XY445xsW5/OAHP7DXXnvN5syZ474AAACQGkNDdSGqyBZ1nKtgriGi2j71xINcQV3r2d189ZEu0j2QaVU1mVbcPWA/PW6Qu6iNdrADADqPFx25XnUKJ3r3uKgo3dpu565+Pq+ey4uCfKJ2tXdWNAyA5JA0RfQvf/nL9tRTT7mIluuuu87dPqpMxTPOOCPehwYAAAAPh4bWZ577fa5gvqmyxu75nzX2468eaDOf/8Ctq9Duz/JZbShsldW7bT9/pl12/Bdtwsi+8f5xACAteNWR61WncDJ0j6cLLwryidjV3hnRMGSrA8kjaYro8q1vfct9AQAAILWHhkZpXdvLKqqtV07Arv7WsPrIl8pdIRfxMqBXjk0qHUQBHQC6iJcduV52CidD9ziSt6u9M6JhyFYHkkdSFdEBAACQepoaGtqQOs5VMNd+3zuyv40fXtTk8FEAQOt1pAPWy47czohhoXs8dSRSV7uXH/iQrQ4kH4roAAAAiKvmhoZGKbJFj2s/UcG8dGhhHI4UAFJDRztgvezI7YwYFrrH0Rkfrnj1gQ/Z6kByoogOAACATs8831fnuNabGxoaiezJPFdki/YDAHSMFx2wXnbkdlYMC+D1hytefeDTGdnqADofRXQAAAB0mqeXl9VnmCuyRR3lKphPLi2pzzBXQV3rM+ataHJoqC5QlXlOZAsAdIxXHbBeR7AIMSxIBl584ON1tjrDSYGuQREdAAAAnVZAV2FcHVoqjCvzXJEt6jjXdokW0qNLhoYCQOfxqgO2MyJYos9L5y0SXUc/8PE6W53hpEDXoIgOAACATolwUUFcF4KFeYH6iBZlniuyRR3ncxatdkNCox3mKpQzNBQAOq/z1MsOWCJYkM468oGPV3dyMJwU6FoU0QEAAOA5FcLVUa4O9IYZ56J1bS+rqHb7NRwSytBQAOi8ztPOyDInggVoGy/u5GA4KdD1aOsBAACA59RJrgz0QDNd5Mo81+PaDwDQOtHOU3Wa9gj6bWBBjltqXdv1eGs6YFWoU8drQ9EO2CGFuW3KMo925B7av4dbUrADrNV3cozol2/bqmttTXmVW6oDvTUd5G2JZgLgDTrRAQAA4DlFsSjTXBnoinBpTEND9bj2AwC0zIvO087KMgfQdh25k8Pr4aTCgFJg3yiiAwAAwHPKMi/Oz3ZDRJWB3jDSJRIJW2X1bjc0VPsBALpuKChZ5kDyZ6t7Hc3EgFKgZRTRAQAA4Dllm08uLbEZ81a4IaLKQFeEizrQVUBXh9Sk0kEMDQWAVvJ6KChZ5kDy8mo4qTCgFGgdiugAAABolVAo7AaBKsdcMSzqIt9XEXzCyL5uOXvRKjdktHJXyEW4qANdBfTo4wCQTtobmeB152l7O2ABxJ9X0UwMKAVajyI6AAAAWvT08rL6YrgGgqoYrrgWdZvvqxiux8YPL2pT8R0AUlVHIhO87DwFkPy8iGbyKiYKSAcU0QEAANBiAV2xLOpuUixLIOhzA0OVd67tsq9CugrmpUMLu/CIASDxdDQygaGgALyOZuqMAaVAqqIFCAAAAPuMcFEHuoo0hXkBC/qzzOfzuaXWtX3OotVuPwBA6yITFJWQ6cvYE5lQ2N1tV2SC9mtN5+mIfvm2rbrW1pRXuaU6T8ktBtJTNJrp0P493LItH6Q1jIlqSltiovT7a/XmHfbWum1u2dLvMyDZ0IkOAACAZimGRREu6kDPyIjtv9C6tpdVVLv96DYHgM6PTGAoKACveBUT1ZGoKiBZUEQHAABAs5Rjrgx0Rbg0xZ/lcwNDtR8AoGsiExgKCsALXsREdTSqCkgWxLkAAACgWRoEqiGiykBvSm0o7B7XfgCQDtoTWeBlZAIAeKkjMVFeRVUByYB/oQEAANCs0SUFVpyf7YaIZnfzxUS6RCJhq6zebQN65bj9ACDVtTeywKvIBADoDO2NifIyqgpIdHSiAwAAoFlZWT6bXFribu3dVFlj1bUhqwuH3VLr2j6pdJDbDwBSWTSyQIXwHkG/DSzIcUuta7sebykyQdEIKjjt2KXfpRG31HprIhMAINEGlNZHVfmbj6rS462NqgISGZ3oAAAA2KcJI/u65exFq9yQUWWgK8JFHegqoEcfB4BU1TiyINpx6SILAt1dIVyRBerkbK7wFI1MiHayKwNdnezqQFcBncxgAMmmYVSVfh92JKpKv2cZmIxERhEdAAAgxYVCYVu8qtwN/1R2uaJX2to5rkL5+OFFHX4eAEhGXkUWtDcyAQASkVdRVe2NygK6EkV0AACAFPb08rL6DvJQXcR1kCvjXBEtbe0gV8G8dGhhpx0rACSq+siC/OYjC9RZ3prIgmhkAgAku2hUVdnn1fUfNOr3oTrQVUBvTVRVNCpLd/q478/f8/0qzOt5WxpuCnQVWocAAABSuIA+Y94KNxR0v26Z1ru73y21ru16HADQtsiCprQlsgAAUkk0qmpEv3zbVl1ra8qr3FId6C0VwBtHZSkSJtOXsScqq7C7266oLO0HxBv/wgMAAKRohIs60FXYKcwLWEbGnt6JoN9n2d18bijonEWrXUQLkSwA0kl7cne9iiwAgFTU3qgqr6KygK5AER0AACAFKbtcES55wW71BfQorWt7WUW124+IFgDpor25u15EFgBAKmtPVJWXUVlAZ6PtCAAAIAVp+Kcy0APNdJn7s3zuce0HAOkgmrurbvIeQb8NLMhxS61rux7vrMgCAMDeiMpCMuFdCAAAkIJ65wbcENGaUNhFuDRWGwq7x7UfAKS6xrm70dgAl7sb6O66y5W7qziCfXWTtzeyAACwN6KykEwoogMAAKSg0SUFVpyf7YaIKgO9YaRLJBK2yurdNqBXjtsPAFKdl7m77YksAAB0blRWe+ZdAG1BER0AACAFaVjo5NISmzFvhRsiqgx0RbioA10FdF2gTCodxFBRAGmB3F0ASEzRqKzovAr9LlaEizrQVUBvTVRWe+ddAG1BER0AACBFTRjZ1y1nL1rlhoxW7gq5CBd1oKuAHn0cANIpd1cRLo2RuwsA8dORqKzovAvFdblO9vw9neyKiFGHOzMr4BXOEAAAAFKYCuXjhxfZ4lXlboioMtAV4UIHOoBk1tbb9sndBYDE1p6oLK/mXQCtQREdAAAgxalgXjq0MN6HAQCeaM9t+17m7gIAUm/eBdASWpAAAAAA1Lvjjjts4MCBlp2dbaNGjbLXXnut2X2PO+44d5Ha+Gv8+PH1+5xzzjl7PX7CCSd00U+DVBO9bV8d5T2CfhtYkOOWWtd2Pd5S7u6Ifvm2rbrW1pRXuaU60LndHwCSeN6Fv/l5F3qceRfwAp3oAAAACSgUChPBgi736KOP2pQpU+yuu+5yBfTbbrvNxo0bZx9++KEVFu59N8PcuXOttra2fn3Lli126KGH2ve///2Y/VQ0v+++++rXA4FAJ/8kSEVe3LbfkdxdAEBiYd4FuhLvIgAAgATz9PKy+mGgobqIGwZanJ9tk0tLGAaKTnXrrbfaeeedZxMnTnTrKqY/99xzdu+999pVV1211/49e/aMWX/kkUdsv/3226uIrqJ5nz59Ovnokeq8um2/Pbm7AIDE48W8i7bO2ED6oogOAACQYAX0GfNWuM6ZvGA3CwR9VhMK29otO912oZCOzqCO8qVLl9rUqVPrt/l8Phs7dqwtWbKkVc9xzz332GmnnWY5ObEXqy+//LLrZN9///3tG9/4hs2YMcN69erl+c+ANLltP7/52/Y3VnLbPgCki47Ou2jPjA2kL+4JBgAASKAIF3Wg68S/MC9gQX+WK2JqqXVtn7NotdsP8Fp5ebnV1dXZAQccELNd6xs2bGjx+5Wd/u6779qPf/zjvaJcHnzwQVu4cKHddNNNtmjRIvvmN7/p/qym1NTUWGVlZcwX0Pi2/aZw2z4ApJ/2zrvoyIwNpCfOLgAAABKEMtAV4aIO9IyM2F4HrWt7WUW126906N751EA8qQt9xIgRdtRRR8VsV2d6lB4/5JBDrKSkxHWnjxkzZq/nmTlzpk2fPr1Ljhnpd9s+ACD1tHXehRczNpB+6EQHAABIEBoiqgz0QDMDRP1ZPve49gO8VlBQYJmZmbZx48aY7VpvKc+8qqrK5aGfe+65Lf45gwYNcn/WRx991OTjipOpqKio/1q3bl0bfxKk+m37uj1fBY4du0JWF464pdZbum0fAJC6ovMuDu3fwy339W9BW2ZsAFEU0QEAABJE79yAGyKqDPSm1IbC7nHtB3jN7/fbEUcc4WJXosLhsFs/+uij9/m9jz/+uIthOfPMM1v8cz799FPbsmWLFRUVNfm4hpDm5eXFfCF1qRtw9eYd9ta6bW6p9c64bR8AgL1mbPibn7Ghx5mxgYaIcwEAAEgQo0sKrDg/2w0Rze7mi4l0iUTCVlm92wb0ynH7AZ1hypQpdvbZZ9uRRx7pYlluu+0212U+ceJE9/hZZ51lffv2dZErjaNcTjrppL2Ghe7YscNFs5xyyimum33VqlV2xRVX2ODBg23cuHFd+rMh8bR3oFtbb9sHAKC5GRuKcGmMGRtoCu8GAACABJGV5bPJpSU2Y94K21RZ4zLQFeGiDnQV0NUVM6l0kNsP6Aynnnqqbd682a699lo3THTkyJE2f/78+mGja9eudcNuG/rwww/tlVdesX/84x97PZ/iYd5++2174IEHbNu2bVZcXGzHH3+8XX/99a7jHOkrOtBNebS6bT6Yn+mKFso7L/u8usWu8uht+wAAtBUzNtAeGRG9O9JEZWWl5efnu2xFbgsFAACJ6unlZTZ70So3ZFQZ6Ipw6ZsfdAX0CSP7xvvw0ATOMzsPr23qUWTL9c+t2FO8aDDQTXR5qs50FS+uHn8w3eUAgK75MNe/58NcFdA1Y4OIsPRR2cpzTTrRAQAAEowK5eOHF9niVeVuiKgy0BXhQgc6gFTQloFudJsDADpDdMZGNFZsY+WeWDF9iKsh1S0V0PWBMLFi6YUiOgAAQAJSwbx0aGG8DwMAOm+gW37zA91UzGCgGwCgM7V3xkZ7Z3oguVFEBwAAAAB0GQa6AQASRVtnbHR0pgeSF/cEAwAAtFMoFLZFH26yJ95Y55ZaBwC0bqCbcmcbj+iKDnQbUpjLQDcAQEJRhIs60FVA179j+iA405fhllrX9rnLytx+SD18tA8AAODR8M/i/GybXFrC8E8Aaam1+bDaplve1bEXzUZvPNBNebRkywIAEgkzPdIbRXQAAIB2FNBnzFvhCj55wW4WCPqsJhS2tVt2uu1CIR1AOmlrPmxHB7oBANDVmOmR3iiiAwAAtIEiW9SBrgJ6YV7AMjL2pOMF/T7L7uazTZU1NmfRahs/vMgNBwWAVNfefNj2DnQDACAemOmR3riyAwAAaIPFq8pdhIs60KMF9Cita3tZRbXbDwBSXUfzYaMD3Q7t38MtKaADABIVMz3SG0V0AACANti8vcZloAea6TL3Z/nc49oPAFJdW/JhAQBIZtGZHprdoX/7duwKWV044pZaZ6ZHaqOIDgAA0Aa9cwNuiKgy0JtSGwq7x7UfAKRNPqy/+XxYPU4+LAAgFURneozol2/bqmttTXmVW2qmR3PxZVG6K2v15h321rptbtncXVpITIT0AAAAtMHokgIrzs92Q0SVgd4w0iUSCVtl9W4b0CvH7QcAqY58WABAumnPTI+2DuBG4qETHQAAoA00LHRyaYnrrtQQ0epa3cYZdkuta/uk0kEMFQWQFsiHBQCko7bM9IgO4NbA7R5Bvw0syHFLrWu7Hkfiox0AAACgjSaM7OuWsxetckNGK3eFXISLOtBVQI8+DgDpkg9b9nl1fTa6PkxUB7oK6OTDAgDSWeMB3NH5IW4Ad6C7+7dTA7jV2c6/lYmNIjoAAEA7qFA+fniRLV5V7oaIKgNdES50oANIlYv+1t6mHs2Hjd6mvrFyz23qyodVAZ3b1AEA6aotA7jV0Y7ERREdAACgnVQwLx1aGO/DAABPtSe3tT35sAAApM0A7vzmB3Drw2cGcCc+iugAAAAAgJjcVt127qJZ8vdEsyi3VZEt6jhvrpAezYcFAAB7MIA7dXC/MQAAAABgr9xWXexn+jL25LYWdnfblduq/QAAQMsYwJ06KKIDAAAAANqU2woAAFo/gFuDtvVv7I5dIasLR9xS6wzgTh7cKwAAAAAAILcVAIBO0N4B3G0Z8o3ORxEdAACkrFAobItXldvm7TXWOzdgo0sK3DBQAMDeyG0FAKBztHUAd3uGfKNzcfYDAABS0tPLy2z2olX2WcUuC9VFLCszw4rzs21yaYlNGNk33ocHAAmb26ohooMD3WMiXaK5reqaI7cVAIC2a+0A7o4M+UbnoRULAACkZAF9xrwVtnbLTtuvW6b17u53S61rux4HAMQitxUAgPhiyHfioogOAABSLsJFHejq1ijMC1jQn2U+n88tta7tcxatdvsBAJrObR3RL9+2VdfamvIqt1QHOp1vAAB0LoZ8Jy7iXAAAQEpRBroiXPKC3SwjI7ZfQOvaXlZR7fYrHVoYt+MEgK7W2gFlbc1tBQAA3mDId+KiiA4AAFKKhogqAz0QbPqGO3+Wzyp3hdx+AJAu2jqgrLW5rQAAwDsM+U5cxLkAAICU0js34IaI1jQT11IbCrvHtR8ApIPogDINJOsR9NvAghy31Lq263EAAJA4Q741zFtDvRuKDvkeUpjLkO84oIgOAABSyuiSAivOz7bK6t0WicQW0rWu7X3zg24/AEh1DCgDACB5MOQ7cVFEBwAAKSUry2eTS0tcXuCmyhqrrtWJZ9gtta7tk0oHuf0AINUxoAwAgOTCkO/ElLQBOr/+9a9t6tSpdskll9htt90W78MBAAAJZMLIvm45e9EqN2RUGeiKcBnQK8cV0KOPA0CqY0AZAADJp61Dvls7PBxpVkR//fXXbfbs2XbIIYfE+1AAAECCUqF8/PAiW7yq3A0RVQa6IlzoQAeQThhQBgBAcmrtkO+2Dg9H+yTdVeSOHTvsjDPOsLvvvtv233//eB8OAABIYCqYlw4ttO8d2d8tKaADSDcMKAMAIHUxPLzrJN2V5AUXXGDjx4+3sWPHxvtQAAAAACChMaAMAIDUxPDwrpVU9+w98sgjtmzZMhfn0ho1NTXuK6qysrITjw4AAAAAEndAWfRWb2Wg61ZvDShTAZ1bvQEASO3h4a2JhUGKFNHXrVvnhoguWLDAsrOzW/U9M2fOtOnTp3f6sQEAAABAPLR2kFhbB5QBAIDExvDwrpU0RfSlS5fapk2b7PDDD6/fVldXZ//85z/tD3/4g+s4z8yMfdNMnTrVpkyZEtOJ3r9//y49bgAAAADoDG0dJNbaAWUAACDxMTy8ayXNqzhmzBh75513YrZNnDjRDjroILvyyiv3KqBLIBBwXwAAIHGEQmFbvKrcNm+vsd65ARtdUsDATwBo5yAx5Z3qdm11oeliWYPEyj6vdvEtxLQAAJD6w8P1b//gQPeYSJfo8HBFtzE83BtJc8Wam5trw4cPj/nKycmxXr16uf8PAAAS39PLy+w7d7xilzy63H717Aq31Lq2A0gMd9xxhw0cONBFKI4aNcpee+21Zve9//773QVbw6/G0Yu6iLv22mutqKjIgsGgjR071lauXNkFP0nqYpAYAABgeHjXSpoiOgAASG4qlM+Yt8LWbtlp+3XLtN7d/W6pdW2nkA7E36OPPuriEKdNm2bLli2zQw891MaNG+diFZuTl5dn69evr//65JNPYh6/+eabbdasWXbXXXfZq6++6hph9Jy7du3qgp8oNbVlkBgAAEj94eEj+uXbtupaW1Ne5ZbqQOeutDSNc2nKyy+/HO9DAAAArYxwmb1olYsaKMwLWEbGns/xg36fZXfz2abKGpuzaLWNH15EtAsQR7feequdd955LjZRVPh+7rnn7N5777Wrrrqqye9R0bZPnz5NPqYu9Ntuu82uvvpqmzBhgtv24IMP2gEHHGB//etf7bTTTuvEnyZ1MUgMAAC0dXh4a4eRIwWL6AAAIDkoA/2zil2WF+xWX0CP0rq2l1VUu/1KhxbG7TiBdFZbW2tLly61qVOn1m/z+XwufmXJkiXNft+OHTtswIABFg6H7fDDD7cbb7zRvvSlL7nHPv74Y9uwYYN7jqj8/HwXE6PnbKqIXlNT476iKisrPfwpUwODxAAAQFuGh7d1GDn2RqsXAADodBoiGqqLWKCZLnN/ls89rv0AxEd5ebnV1dW5LvGGtK5CeFOGDh3qutSffvpp+/Of/+wK6cccc4x9+umn7vHo97XlOWfOnOkK7dGv/v37e/QTpt4gMQ0MU7d/Q9FBYkMKcxkkBgAA6oeRawBpj6DfBhbkuKXWtV2Po2UU0QEAQKfrnRuwrMwMqwmFm3y8NhR2j2s/AMnj6KOPtrPOOstGjhxppaWlNnfuXOvdu7fNnj273c+pTviKior6r3Xr1nl6zKmAQWIAAKA1GEbuHYroAACg040uKbDi/GyrrN5tkUhsIV3r2t43P+j2AxAfBQUFlpmZaRs3bozZrvXmMs8b69atmx122GH20UcfufXo97XlOQOBgBtW2vALe2OQGAAAaAnDyL1DSB4AAOh0GhY6ubTEZsxb4YaIKgNdES7qQFcBXUPwJpUOYqgoEEd+v9+OOOIIW7hwoZ100klum+JZtH7hhRe26jkUB/POO+/YiSee6NYPPPBAVyzXc6hbPZpx/uqrr9r555/fiT9NamhpAFhrB4kBAID0xDBy71BEBwAAXWLCyL5uOXvRKjdktHJXyEW4DOiV4wro0ccBxM+UKVPs7LPPtiOPPNKOOuoou+2226yqqsomTpzoHld0S9++fV1uuVx33XX2la98xQYPHmzbtm2z3/zmN/bJJ5/Yj3/84/oOp0svvdRmzJhhQ4YMcUX1a665xoqLi+sL9ejYALCWBokBAID0xTBy7/AKAQCALqNC+fjhRbZ4VbkbIqoMdEW40IEOJIZTTz3VNm/ebNdee60b/Knu8fnz59cPBl27dq35fP/39/Xzzz+38847z+27//77u072f/3rXzZs2LD6fa644gpXiJ80aZIrtB977LHuObOzs+PyMybTADDllOo2a3WP6SJXA8DKPq8mrgUAALRpGLnOIQYHusdEukSHkSsKjmHkLcuINB7nnsJ062h+fr4bUES2IgAAALzCeWbnSbfXVhEu1z+3Ys/FbuHeF7vqTNfF7tXjDya2BQAAtP3Def+eD+dVQNcw8nT/cL6yleeatH0BAAAAQIJgABgAAPASw8i9QZwLAAAAACQIBoABAACvtXYYeUtDzdMZRXQAAAAASBAMAAMAAJ2hpWHkrR1qnq6IcwEAAACABBsAppzSxuOrogPAhhTmMgAMAAB4npuumSw9gn4bWJDjllrX9nfLKizdUUQHAAAAgATqElPHlwZ9qRNsx66Q1YUjbql1bT/58L7cWg0AADyhCBd1oGvwqD7I151wmb4Mt9S6ts9dVub2S2fcAwgAACwUCtviVeW2eXuN9c4N2OiSAsvK4rN2AIjnALDoLdXKQNct1RoApgI6t1QDAIB4DDUftI84mFRHER0AgDT39PIym71olX1WsctCdRHLysyw4vxsm1xaYhNG9o334QFAWmrtADAAAICOYKh561BEBwAgzQvoM+atcIPq8oLdLBD0WU0obGu37HTbhUI6AHQO3Ra9ryJ5SwPAAAAAOoqh5q2T3j89AABpHuGiDnSdFBXmBSwjY098S9Dvs+xuPttUWWNzFq228cOLiHYBAI9pQFc0rkXdX7o4Ve6o8tCJawEAAF091FxDRAcHusdEukSHmh/Sr0faDzXnihgAgDSlDHRFuKgDPVpAj9K6tpdVVLv9AADeFtBnLVzpLlZ7BP02sCDHLbWu7XocAACgKzDUvHUoogMAkKY0RFQZ6IFmusz9WT73uPYDAHgX4aIO9K1Vta7rS7dNZ/oy3FLr2j53WZnbDwAAoCuHmo/ol2/bqmttTXmVW6oDXduHc5cccS4AAKSr3rkBN0RUGeiKcGmsNhR2j2s/AIA3lIGurq6i/GDM7dKidW1fuWm72488dAAA0FUYar5vFNEBAEhTo0sKrDg/2w0RVQZ6w0iXSCRsldW7bUCvHLcfAMAbuihVBnowP7PJx4P+TNtYGXb7AQAAdKWWhpqHWxiKnsooogMAkKY0LHRyaYnNmLfCDRFVBroiXNSBrgK6CjmTSgcxVBQAPKQLTg0R1VBnRbg0pu16XPsBAAAkinfTfCg6Z2YAAKSxCSP7uuXsRavckNHKXSEX4aIOdBXQo48DALyhji1dcGqI6OBA95hIl0gkYusrql3+qPYDAABIpKHoW6tqXfSc7qjTB/86nyn7vDotctMpogMAkOZUKB8/vMgWryp3Q0SVga4IFzrQAcB7uuVZHVu64Ixmo+vOH12IqoDeM8dvJx/eN21ujQYAAMk1FD3jfxsA3FD0QHd3PqOh6MpTT+XzF4roAADAFcxLhxbG+zAAIC2oU0sdW9FbopWBrlui1YGuAnqqd3IBAIDkwVD0PSiiAwAAAEAXU6FcHVvpOpwLAAAkB4ai70ERHQAAAAA68Rbo5grlWqZyxxYAAEh+DEXfI7V/OgAAAACI4xCuaGSLOrh0gaksUWWiE9kCAACSAUPR96CIDgAAAACdUECftXClG8Llhofm7xkeqgtQDRVVJjqFdAAAkOgYir6H73+XAAAAAACPIlzUga4Cujq3dOtzpi/DLbWu7XOXlbn9AAAAkmUo+oh++batutbWlFe5pTrQ06UxgE50AAAAAPCQMtCjnVoNb3kWrWv7yk3b3X5kogMAgGQwPM2HolNEBwAgwYRCYVu8qtw2b6+x3rkBG11SYFlZ3DwGAMlCF5bKQFeES1N0C/TGyrDbDwAAIFn40ngoOkV0AAASyNPLy2z2olX2WcUuC9VFLCszw4rzs21yaYlNGNk33ocHAGgFdWZpiKiyQhXh0pi263HtBwAAkArC4UhKd6lz1gYAQAIV0GfMW+GKK3nBbhYI+qwmFLa1W3a67UIhHQASny4alX2uIaKDA91jIl0ikYgbwqUMUe0HAACQCgPVn1z2qYuz0914ahbQuZAGkqZKXjr3hgMAkCARLupAVwG9MC9gQX+W+Xw+t9S6ts9ZtNrtBwBIbOq60kVjzxy/u5jcsStkdeGIW2pd208+vG9KdWcBAID0LaDPWrjSNQ/0CPptYEGOW2pd2/V4KqCIDgBAAlAGuiJc1IGekRH7z7PWtb2sotrtBwBIfOq6unjMEBvRL9+2VdfamvIqt1QHuranSlcWAABI7wiXJ5d9alural3nuWLsMn0Zbql1bZ+7rMztl+yIcwEAIAFoiKgy0BXh0hR/ls8qd4XcfgCA5KBC+bCivJTOBwUAAOlrzZYqd5ddUX4wJr5OtK7tKzdtd/sl+0BSiugAACSA3rkBN0RUGehB/96F9NpQ2D2u/QAAyTNMS1/JftEIAADQFJ33KAM9mJ/Z5ONBf6ZtrAy7/ZIdRXQAABLA6JICK87PdkNEs7v5YiJdIpGwVVbvtgG9ctx+AIDEkg7DtAAAABpT44DOezTDSxEujWm7Htd+yY5MdAAAEkBWls8ml5a4T+o3VdZYda2G0IXdUuvaPql0kNsPAJA40mWYFgAAQGO6806NA+srqi0Sic0917q2DynMdfslu+T/GAAAgBQxYWRft5y9aJUbMqoMdEW4qANdBfTo4wCAxBymFc0CdcO0At1dZ7qGaSkXnRx0AACQany+DHfnXdnn1fXZ6GoAUwe6Cug9c/x28uF9U+I8iCI6AAAJRIXy8cOLbPGqcjdEVBnoinChAx0AEk86DdMCAABoiqLrLh4zpD7aThnoinA5pF8PV0BPlWg7iugAACQYFcxLhxbG+zAAAC1Ip2FaAAAAzVGhXHfeNTVkPVVQRAcAAACAdkinYVoAAAD7ooJ54zvvFH2XKoV17g0HAAAAUO+OO+6wgQMHWnZ2to0aNcpee+21Zve9++677atf/artv//+7mvs2LF77X/OOee4aJOGXyeccIKlgnQapgUAANAWGq5+/XMrbNoz79kNz73vllpP1qHrFNEBAAAAOI8++qhNmTLFpk2bZsuWLbNDDz3Uxo0bZ5s2bWpy/5dfftlOP/10e+mll2zJkiXWv39/O/74462srCxmPxXN169fX//1l7/8xVJpmJaGZikDdMeukNWFI26p9VQapgUAANBaKpTPWrjS3vm0wnoE/TawIMctta7tyVhIp4gOAAAAwLn11lvtvPPOs4kTJ9qwYcPsrrvusv3228/uvffeJvd/6KGH7Kc//amNHDnSDjroIPvTn/5k4XDYFi5cGLNfIBCwPn361H+paz3VhmmN6Jdv26prbU15lVtqmJa2p8owLQAAgNZQhIuGjG6tqnV37CnyLtOX4ZZa1/a5y8rcfsmEcD4AAAAAVltba0uXLrWpU6fWb/P5fC6iRV3mrbFz507bvXu39ezZc6+O9cLCQlc8/8Y3vmEzZsywXr16NfkcNTU17iuqsrLSEl06DNMCAABoDZ0P6Y68ovygi/FrSOvavnLTdrdf4wz1REYnOgAAAAArLy+3uro6O+CAA2K2a33Dhg2teo4rr7zSiouLXeG9YZTLgw8+6LrTb7rpJlu0aJF985vfdH9WU2bOnGn5+fn1X4qISaZhWof27+GWFNABAEA62r4rZDW7wxb0Zzb5uLbrce2XTOhEBwCgGaFQ2BavKrfN22usd27ARpcUWFYWnz8DQFN+/etf2yOPPOK6zjWUNOq0006r//8jRoywQw45xEpKStx+Y8aM2et51AmvXPaGneiJVkjX7cd0nQMAAOxN50aBbj6rrq1zES6Nabse137JJLmOFgCALvL08jKbvWiVfVaxy0J1EcvKzLDi/GybXFpiE0b2jffhAYDnCgoKLDMz0zZu3BizXevKMd+XW265xRXRX3jhBVck35dBgwa5P+ujjz5qsoiu/HR9JSoNwlLOp25TVheVLgKV76kBo+SfAwCAdDewV447N9IQ0cGB7jGRLpFIxNZXVLvZMdovmdBOBwBAEwX0GfNW2NotO22/bpnWu7vfLbWu7XocAFKN3++3I444ImYoaHRI6NFHH93s99188812/fXX2/z58+3II49s8c/59NNPbcuWLVZUVOTZsXdlAX3WwpXuorBH0G8DC3LcUuvarscBAADSmc+X4ZoLeub4XdPBjl0hqwtH3FLr2n7y4X2T7i4+iugAADSKcFEHum4xK8wLWNCf5Qbraal1bZ+zaLXbDwBSjWJU7r77bnvggQfs/ffft/PPP9+qqqps4sSJ7vGzzjorZvCoMs6vueYau/fee23gwIEuO11fO3bscI9r+fOf/9z+/e9/25o1a1xBfsKECTZ48GAbN26cJRNFuKgDfWtVreuu0u3Jmb4Mt9S6ts9dVub2AwAASGfD++bbxWOG2Ih++batutbWlFe5pTrQtT0Z794jzgUAgAaUga4Il7xgN8vIiP2sWevaXlZR7fYrHVoYt+MEgM5w6qmn2ubNm+3aa691xfCRI0e6DvPosNG1a9e6Dxaj7rzzTqutrbXvfe97Mc8zbdo0+9WvfuXiYd5++21XlN+2bZsbOnr88ce7zvVEjmxpijLQ1T1VlB+MuS1ZtK7tKzdtd/tpsCgAAEA6G94334YV5aXMHBmK6AAANKAhospADwSbvlnLn+Wzyl0htx8ApKILL7zQfTVFw0AbUnf5vgSDQfv73/9uqUAXf8pAD+ZnNvl40J9pGyvDbj8AAACYK5g3bC7QHXurN+9IyqI6RXQAABronRtwQ0RrQmEL+vcupNeGwu5x7QcASB+60NMQUcV6KcKlMW3X49oPAAAAqTWcnUx0AAAaGF1SYMX52VZZvdsikdjcc61re9/8oNsPAJA+1CmlC731FdUWicTmnmtd24cU5rr9AAAAkFrD2SmiAwDQQFaWzyaXlrjb8jdV1lh1rSaJh91S69o+qXSQ2w8AkD50q7E6pXrm+F0H1Y5d+vch4pZa1/aTD++bNLckAwAAdIVwigxn515DAAAamTCyr1vOXrTKDRlVBroiXAb0ynEF9OjjAID0oluNLx4zpP5WZGWg61bkQ/r1cAX0ZLgVGQAAoCutSZHh7BTRAQBoggrl44cX2eJV5W6IqDLQFeFCBzoApDcVyocV5bkLvWQcigUAANCVtqfIcHaK6AAANEMF89KhhfE+DABAnOn24sZF80TulAIAAEgUuSkynD2xjw4AAAAA4kiDrqLxLeqi0kWe8juVj058CwAAQOuGs2uI6OBA95hIl+hwdkXjJfpwdoroAAAAANBMAX3WwpVu4JXyOnUbsrqldBFY9nm1y0enkA4AANDycHadO0Wz0RXhonMqFdCTZTg7wa4AAAAA0ESEizrQVUBX95RuP870Zbil1rV97rIytx8AAABaHs4+ol++bauutTXlVW6pDvRkaUqgEx0AAAAAGlEGerRbquFtx6J1bV+5abvbj3x0AACA1B7OThEdAAAAABrRxZ0y0BXh0hTdhryxMuz2AwAAQMtUME/W5gOK6AAAAADQiLqjNERUeZ2KcGlM2/W49gMAAEDbKBIvmbrSOeMDAAAAgEZ0Iafscw0RHRzoHhPpEolE3CAs5XhqPwAAALRteLtmzyg6T3f+qTFB510aQJqo+egU0QEACS0UCtviVeW2eXuN9c4N2OiSAsvKYi42AKBzqRNKF3Jln1fXZ6MrwkUd6Cqg98zx28mH903ojikAAIBELKDPWrjSDWl351f5e86v1Lig865EHTRKER0AkLCeXl5msxetss8qdlmoLmJZmRlWnJ9tk0tLbMLIvvE+PABAitMFnC7kop1SykBXp5Q60FVAT8QLPAAAgESOcHly2aeugK7O8+idforO051/Ot+au6zMDSBNtEYFiugAgIQtoM+Yt8J9Ip0X7GaBoM9qQmFbu2Wn2y4U0gEAnU2Fcl3IJVNmJwAAQCJas6Wq/g6/hlF5onVtX7lpu9sv0QaQUkQHACRkhIs60FVAL8wLWEbGnviWoN9n2d18tqmyxuYsWm3jhxcR7QIA6HQqmCfahRwAAECy2b4r5DLQFeHSFEXn6c4/7ZdoqDwAABKOMtAV4aIO9GgBPUrr2l5WUe32AwCgM285Xr15h721bptbah0AAADtozv6FI2nhrmmaLse136JJvGOqBkzZ860uXPn2gcffGDBYNCOOeYYu+mmm2zo0KHxPjQAgMc0RFQZ6IpwaYo/y2eVu0JuPwAAOoOGXkWz0NUxpQs6ZXdq2ChZ6AAAAG2nSDydT2mIqDLQG0a6RCIRN7xds2e0X6JJmk70RYsW2QUXXGD//ve/bcGCBbZ79247/vjjraqqKt6HBgDwWO/cgBsiqgz0ptSGwu5x7QcAQGcU0GctXOku8HoE/TawIMctta7tehwAAABtj8hTQ0LPHL9rVNixK2R14Yhbal3bNbw9EWfPJE0n+vz582PW77//fissLLSlS5fa1772tbgdFwDAe6NLCqw4P9sNEVUGesNIl0gkbJXVu21Arxy3HwAAXlJkizrQt1bVuk6paIdU9+ws1zGlC7y5y8rcsNFEvMADAABIZMP75tvFY4bU3/GnDHTd8acOdBXQE/WOv6QpojdWUbGn+6Nnz57N7lNTU+O+oiorK7vk2AAAHaNhoZNLS2zGvBVuiKgy0BXhog50FdA1bGRS6SCGigIAPLdmS5W7oCvKD8bcYixa1/aVm7a7/Rg2CgAA0HYqlKshQedTGiKqDHRFuCRyg0JSFtHD4bBdeumlNnr0aBs+fPg+c9SnT5/epccGAPDGhJF93XL2olVuyKgy0BXhog50FdCjjwMA4CVdyCkDPZif2eTj+iBXHVPaDwAAAO2jgnkyNSQkZRFd2ejvvvuuvfLKK/vcb+rUqTZlypSYTvT+/ft3wRECALygQvn44UW2eFW5GyKqDHRFuNCBDgDoLOqE0i3F1bV1LsKlMW3X49oPAAAAHY/SS4aO9KQ787vwwgtt3rx59s9//tP69eu3z30DgYD7AgAkLxXMS4cWxvswAABpQhduykLXEFFloDeMdIlEIra+otpldmo/AAAAtJ+GtUez0XUnoBoVdB6m4aOJlo2eNEV0nbBedNFF9tRTT9nLL79sBx54YLwPCQAAAECKUeeTLtzKPq+uz0ZXhIs60FVA75njd0OvErFDCgAAIJkK6LMWrnTD3N35Vv6e8y01Mug8TMNHE6mQ7kumCJc///nP9vDDD1tubq5t2LDBfVVXV8f70AAAAACkEF2w6cJtRL9821Zda2vKq9xSHeiJdkEHAACQjBEuTy771BXQ1XmuCL1MX4Zbal3b5y4rc/sliqTpRL/zzjvd8rjjjovZft9999k555wTp6MCAAAAkIpUKB9WlJcUGZ0AAADJZM2Wqvo7/hpG54nWtX3lpu1uv0QZPppUcS4AAAAA0FVUME+UCzcAAIBUsX1XyGWgK8KlKYrS21gZdvslijYX0d9//3175JFH7H/+53/sk08+sZ07d1rv3r3tsMMOs3Hjxtkpp5zCME8AAAAASUu3DtOBDgAA0Dlys7PcEFFloCvCpTFt1+PaL1G0+kiWLVtmV1xxhb3yyis2evRoGzVqlH33u9+1YDBoW7dutXfffdd++ctfuuGf2u/SSy+lmA4AAAAg6YZcKaNTtxirQ0oXcMrm1LBRstABAAA6Tg0KOr/SENHBge4xkS5KI9Ewd82i0X5JV0RXh/nll19uTzzxhPXo0aPZ/ZYsWWK///3v7be//a394he/8Oo4AQAAAKDTC+izFq50w6yUxalbjNUJpQu8ss+rGSoKAADgAd3hpwYFnV9Fs9EV4aLzLhXQe+b47eTD+ybUnYCtLqL/5z//sW7durW439FHH+2+du/e3dFjAwAkkFAobItXldvm7TXWOzdgo0sKLCvLF+/DAgDAswgXdaCrgK7OqGhHlG4xVoeULvDmLitzw0YT6YIOAAAgGQ3vm+8aFKJ3ACoDXXcAqgNdBfREa1xodRFdBfQ//vGP9tOf/rTV+wMAUsPTy8ts9qJV9lnFLgvVRSwrM8OK87NtcmmJTRjZN96HBwBAhykDPdoJ1fCWYtG6tq/ctN3tx7BRAACAjlOhXA0KyTCLpk0thFdffbUbHvrZZ5913hEBABKugD5j3gpbu2Wn7dct03p397ul1rVdjwMAkOx04aYMdN1K3BRt1+PaDwAAAN5QwVwNCof27+GWiVhAb3MRXcNDs7KybPjw4fbnP/+5844KAJAwES7qQFcuWWFewIL+LPP5fG6pdW2fs2i12w8A0H6J1KRyxx132MCBAy07O9tGjRplr7322j73f/zxx+2ggw5y+48YMcKef/75mMc1HOraa6+1oqIiCwaDNnbsWFu5cqUlGnU+6RZi/dvWFG3X49oPAAAA3lFNYdGHm+yJN9a5ZSLWGNpURC8uLrbnnnvObr31Vrv44ovdsNFly5bZ22+/HfMFAEgNykBXhEtesJtlZMT+k6F1bS+rqHb7AQDa70tf+pI9/PDD8T4Me/TRR23KlCk2bdo0d55/6KGHujtRN23a1OT+//rXv+z000+3c889195880076aST3Jeab6JuvvlmmzVrlt1111326quvWk5OjnvOXbt2WSLRrcPKQtcwKxX+G9K6tg8pzHX7AQAAwBu6u/07d7xilzy63H717Aq31Hqi3fWeEWl8hthKL7zwgp1wwgnuhFJfygmMLuvqmu7eiLfKykrLz8+3iooKy8vLi/fhAEDC06fA+kdMES7qQG+sLhy28h219qtvD7PvHdk/LscIAKlwnqnZQ1deeaU7v549e7b17NnT4kGd51/+8pftD3/4g1sPh8PWv39/u+iii+yqq67aa/9TTz3VqqqqbN68efXbvvKVr9jIkSNd0VzXB2rEueyyy+zyyy93j+s1OuCAA+z++++30047LaHO4d8tq7BZC1e64aLKQFeEizrQVUDvmeN3w68SbcgVAABAssfHVtfWuSa9QJbPakJhq6ze7c7Drv7WsE6fw9bac802daJHqRN9woQJduaZZ9p//vMf+/jjj2316tX1SwBAauidG3BDRPWPWFNqQ2H3uPYDALTfT3/6U3dH55YtW2zYsGH27LPPdvkx1NbW2tKlS13cSpQ+QNX6kiVLmvwebW+4v6jLPLq/rg82bNgQs48uUlSsb+4540kFchXKR/TLt23VtbamvMotD+nXgwI6AABAGsfHtinQTwXys88+22UY6nZTFdIBAKlrdEmBFednuyGi2d18MZEukcieT4cH9Mpx+wEAOubAAw+0F1980XWBn3zyyXbwwQe7eUQNKWKls5SXl7s7StUl3pDWP/jggya/RwXypvbX9ujj0W3N7dNYTU2N+2rYHdSVVCgfVpRna7ZUuSGiykBXhEuiDrkCAABI9fjY0qGFllRF9EMOOcTdYvrUU09ZQQEFEwBIdVlZPptcWuJur9pUWeP+EfNn+VwHevT2qkmlg9x+AICO++STT2zu3Lm2//77u4aVxkX0dDBz5kybPn16XI9BBfNBvbvH9RgAAABS2ebtNRaqi1gg2HQ9QbWHyl0ht18iaNNZuXINFeECAEgf0fwx3WalT4n1j5giXNSBrgJ6Z+eTAUC6uPvuu112uKJP3nvvPevdu3eX/vlqksnMzLSNGzfGbNd6nz59mvwebd/X/tGlthUVFcXso9z0pkydOtUNN23Yia5c9q4UDkfoRAcAAOii+Nig35fw8bGtLqJrYFBbCujaPyeHyfUAkApUKB8/vMjdRqVPgfWPmCJc6EAHAG/obs/XXnvNRbmcddZZcTkGv99vRxxxhC1cuNBOOumk+sGiWr/wwgub/J6jjz7aPX7ppZfWb1uwYIHbHo2oUSFd+0SL5iqKv/rqq3b++ec3+ZyBQMB9xYuGiz657FP7aNMOq9kdtkA3nw0u7G6nHN6PTHQAAIA0jY9tdfVj8ODB9utf/9rWr1/f7D6RSMSdNH/zm9+0WbNmeXWMAIAEoIK5csi+d2R/t6SADgDeURa5BovGq4AepQ5wdcQ/8MAD9v7777tCt5pjJk6c6B7X8alTPOqSSy6x+fPn229/+1uXm/6rX/3K3njjjfqie0ZGhiuwz5gxw5555hl755133HMUFxfXF+oTiQrosxautHc+rbAeQb8NLMhxS61rux4HAACAd/GxiolVfGx1bcjqwmG31Hqixce2uhP95Zdftl/84hfuxPjQQw+1I4880p38Zmdn2+eff24rVqywJUuWuNxGnVhPnjy5c48cAAAASBFqREkEp556qm3evNmuvfZaN/hT3eMqkkcHg65du9Z8vv+7kDnmmGPs4YcftquvvtpdKwwZMsT++te/2vDhw+v3ueKKK1whftKkSbZt2zY79thj3XPqOiKRKMJFHehbq2pd57k+AJDu2Vk2ONDddabPXVbmho4S7QIAAJBe8bEZEbWPt4FOnB977DF75ZVX3OCj6upql5942GGH2bhx41wXurIUE5FuHc3Pz7eKigrLy8uL9+EAAAAgRXCemfyv7erNO2zaM++5znMVzhvbsStk26prbfp3vsTQUQAAAA+FQuG4xce29lyzTYNF5Qtf+IJdfvnl7gsAAAAAUoGGiCoDPZjfdEOQbineWBl2+wEAAMD7+NhE1uYiejQrsSm65VG3ZSo/fcKECdazZ8+OHh8AAAAAdLrc7Cw3RLS6tq7JTnRt1+PaDwAAAN5F6q3ZUuUaFXSeNbBXTkJG57XrDPDNN9+0ZcuWuQFIQ4cOddv+85//uBiXgw46yP74xz/aZZdd5iJfhg0b5vUxAwAAAICndMGmLHQNEVUGejQTXZSAub6i2g7p18PtBwAAgI7T0HbNpNHsGd0RqIYFnY+dcng/G9433xJJu8Jl1GU+duxY++yzz2zp0qXu69NPP7X/+q//stNPP93Kysrsa1/7mv3sZz/z/ogBAAAAwGPqeNIFW88cv7uQUwZ6XTjillrX9pMP75uQnVEAAADJWECftXCla2DQTJqBBTluqXVt1+OJpM2DRaVv3762YMGCvbrM33vvPTv++ONdEV2d6vr/5eXlligY+AQAAIDOwHlm6ry2TXVEDSnMdQX0ROuIAgAASNYIl+ufW7HnDsDCve8A1HmY7gC8evzBnd7A0GmDRUVPumnTpr2K6Js3b3Z/sPTo0cNqa2vb8/QAgASdWg0AQKpToXxYUV5SZHMCAAAkozVbqlyhvCg/GFNAF61r+8pN291+g3p3t0SQ1d44lx/96Ef229/+1r785S+7ba+//rpdfvnldtJJJ7n11157zb74xS96e7QAkOaeXl5msxetss8qdlmoLmJZmRlWnJ9tk0tLbMLIvvE+PAAAUoIK5olywQYAAJBqtu8KuTv+gvmZTT4e9Gfaxsqw2y9RtKuIPnv2bJd3ftppp1kotOeHycrKsrPPPtt+97vfuXUNGP3Tn/7k7dECQJoX0GfMW2HVtXWWF+xmgaDPakJhW7tlp9suFNIBAPD2VmM60gEAALyl8ypF5qm+0T177/K0tutx7Zco2nUk3bt3t7vvvtsVzFevXu22DRo0yG2PGjlypHdHCQBpThEu6kDXPySFeQHLyNgT3xL0+yy7m882VdbYnEWrbfzwIqJdAADopGx0ZXZq+CjZ6AAAAO2nxgSdV7lM9MDemejrK6pdJrr2SxQdKueraH7IIYd4dzQAgCYpA10RLupAjxbQo7Su7WUV1W6/0qGFcTtOAABSpYA+a+FK21pV6zI5dauxPsjWhV7Z59V28ZghFNIBAADaSXf2qTFB51XRbHRFuOh8SwX0njl+N9Q9ke4ApF0RAJKAhogqAz3QTJe5P8vnHtd+AACgYxEu6kBXAV0dUrrFONOX4ZZa1/a5y8rcfgAAAGgfNSSoMWFEv3zbVl1ra8qr3FId6InYsJA4wTIAgGb1zg24IaLKQFeES2O1obB7XPsBAID2UwZ6tCOq4a3FonVtX7lpu9uP4aMAAADtp0L5sKK8pJhBQxEdAJLA6JICK87PdkNElYHeMNIlEglbZfVuG9Arx+0HAADaTxdwykBXhEtTdKvxxsqw2w8AAAAdo4J5MjQmEOcCAElAw0Inl5a4C3cNEa2uDVldOOyWWtf2SaWDGCoKAEAHqQNKQ0SVydkUbdfj2g8AAADto2i81Zt32FvrtrllokflceYHAEliwsi+bjl70So3ZLRyV8hFuKgDXQX06OMAAKD9dAuxss81RHRwoHtMpEskEnHDrpTVqf0AAADQviHumkGjCD3dAagGBZ1/adhoomWhR1FEB4AkokL5+OFFtnhVuRsiqgx0RbjQgQ4AgHe3FOsCruzz6vpsdN3xpQ50FdB75vjt5MP7JmRWJwAAQDIU0GctXOmGtbvzrPw951lqYND5VyIOFRWK6ACQZFQwLx1aGO/DAAAgZenCTRdw0Q4pZaCrQ0od6CqgJ+KFHQAAQKILhyPu/EoFdHWeR+/4656d5e4A1HnX3GVlbthoojUsUEQHAAAAgEZUKNcF3JotVW6IqDLQFeGSaBd0AAAAyWLNlqr6O/0aRuaJ1rV95abtbr9EGzbK/f8AAAAA0AQVzHUBN+J/O8/fKatIisFXAAAAiWj7rpDLQFdUXlO0XY9rv0RDJzoAAAAApNDgKwAAgESUm53lzqWUga4Il8a0XY9rv0RDJzoAAAAA7GPwlQZd9Qj6bWBBjltqXdv1OAAAAFpH0XhqRtCw9kgk9s4+rWv7kMJct1+ioYgOAAAAAC0MvlK3VKYvY8/gq8LubrsGXxHtAgAA0PqoPN3N1zPH7+7y27ErZHXhiFtqXds1xD0RZ9BQRAcAAACADgy+AgAAQOsoDu/iMUNsRL9821Zda2vKq9zykH493PZEjctLvIAZAEgSoVDYFq8qt83ba6x3bsBGlxRYVhafTQIAkFKDr/KbH3y1sTIxB18BAAAksuF9821YUZ5rRtC5lDLQFeGSiB3oURTRAaAdnl5eZrMXrbLPKnZZqC5iWZkZVpyfbZNLS2zCyL7xPjwAAJDGg68AAAASUTgcSarCeUOc8QFAOwroM+atcBfPecFuFgj6rCYUtrVbdrrtQiEdAIDUGHylIaKDA91jIl2ig69023EiDr4CAABINO+WVbh5M4rL091+akbQuZYy0hM1wqUhcgcAoI0RLupAVwG9MC9gQX+W+Xw+t9S6ts9ZtNrtBwAAklcyD74CAABItAL6rIUrXXNCj6DfBhbkuKXWtV2PJzqK6ADQBspAV4SLOtAzMmJ/hWpd28sqqt1+AAAguSXr4CsAAIBEinB5ctmntrWq1nWeKyYv05fhllrX9rnLytx+iYw4FwBoAw0RVQa6Ilya4s/yWeWukNsPAAAkv2QcfAUAAJAo1mypcnfxFeUHY+LxROvavnLTdrffoN7dLVFRRAeANuidG3BDRJWBHvTvXUivDYXd49oPAACkBhXME/miDgAAIFFt3xVyGejB/MwmHw/6M21jZdjtl8iIcwGANhhdUmDF+dlWWb3bIpHY3HOta3vf/KDbDwAApCbdbrx68w57a902t0z0248BAADiJTc7yw0R1Qy5pmi7Htd+iSyxjw4AEkxWls8ml5bYjHkrbFNljctAV4SLOtBVQNcnqJNKB7n9AABA6tHgK+V66rZkdVXpok95nhpCSkY6AABALMXg6VxJQ0QHB7rHRLpEIhFbX1Ht5s1ov0RGER0A2mjCyL5uOXvRKjdkVBnoinAZ0CvHFdCjjwMAgNQroM9auNINwFJ+p25LVveULgrLPq9m2CgAAEATsXhqNtC5UjQbXQ2IOodSAb1njt9OPrxvws+boYgOAO2gQvn44UW2eFW5GyKqDHRFuNCBDgBAalJkizrQVUBXN1W0i6p7dpbrqtJF4dxlZW4IaaJfBAIAAHSl4X3zXbNB9G4+ZaDrbj51oKuAngxNCBTRAaCdVDAvHVoY78MAAABdYM2WqvruqYa3IYvWtX3lpu1uP4aQAgAAxFKhXM0GOlfSEFFloCvCJVmaDyiiAwAAAEALdLGnDHRFuDRFtyWrq0r7AQAAYG8qmCdrswG5AwAAAABs69atdsYZZ1heXp716NHDzj33XNuxY8c+97/ooots6NChFgwG7Qtf+IJdfPHFVlFRsVeXduOvRx55xJKNuqV027HyO5ui7Xpc+wEAAMBcHN7qzTvsrXXb3FLryYozPAAAAACugL5+/XpbsGCB7d692yZOnGiTJk2yhx9+uMn9P/vsM/d1yy232LBhw+yTTz6xn/zkJ27bE088EbPvfffdZyeccEL9uor0yUa3GysLXUNElYHeMNIlEom4wVjK9dR+AAAA6e7dsor6DHTdzadmA51LachoMmSgN0YRHQAAAEhz77//vs2fP99ef/11O/LII92222+/3U488URXJC8uLt7re4YPH25PPvlk/XpJSYndcMMNduaZZ1ooFLKsrKyYonmfPn0smen2Y130lX1eXZ+NrggXdaCrgN4zx+8GYyVLricAAEBnFtBnLVzpBrK7c6b8PedMakbQuZSGjCZbIZ04FwAAACDNLVmyxBW6owV0GTt2rPl8Pnv11Vdb/TyKclEcTMMCulxwwQVWUFBgRx11lN17772uczsZ6WJPF30j+uXbtupaW1Ne5ZbqQE/Gi0EAAACvhcMR14GuAro6z7tnZ1mmL8Mtta7tc5eVJV20C53oAAAAQJrbsGGDFRYWxmxTIbxnz57usdYoLy+366+/3kXANHTdddfZN77xDdtvv/3sH//4h/30pz91WevKT29KTU2N+4qqrKy0RKJC+bCiPFuzpcoNEVUGuiJc6EAHAAAwd44UvWuvYfydaF3bV27a7vZLpiGjFNEBpIRQKGyLV5Xb5u011js3YKNLCiwri5ttAADp7aqrrrKbbrqpxSiXjlKhe/z48S4b/Ve/+lXMY9dcc039/z/ssMOsqqrKfvOb3zRbRJ85c6ZNnz7dEpkK5sl00QcAANBVtu8KuQx0Rbg0RXF4GyvDbr9kQhEdQNJ7enmZzV60yj6r2GWhuohlZWZYcX62TS4tsQkj+8b78AAAiJvLLrvMzjnnnH3uM2jQIJdXvmnTppjtyjXfunVri1nm27dvd0NDc3Nz7amnnrJu3brtc/9Ro0a5jnV1mwcCgb0enzp1qk2ZMiWmQN+/f39LdLolme50AACQ7nKzs9wQUWWgK8KlMW3X49ovmSTX0QJAEwX0GfNWuF/CecFuFgj6rCYUtrVbdrrtQiEdAJCuevfu7b5acvTRR9u2bdts6dKldsQRR7htL774ooXDYVf0bo4K3OPGjXPF8Geeecays7Nb/LOWL19u+++/f5MFdNH25h5L5OFZyv7UrcvqvNKFoTI/NYiUnHQAAJBOBvbKcedBGiI6ONA9JtJFc3E0kF3zZLRfMiHrAEBSR7ioA10F9MK8gAX9WW4AmpZa1/Y5i1a7/QAAQPMOPvhg101+3nnn2WuvvWaLFy+2Cy+80E477TQrLi52+5SVldlBBx3kHo8W0I8//ngXz3LPPfe4deWn66uurs7t8+yzz9qf/vQne/fdd+2jjz6yO++802688Ua76KKLLFWogD5r4Up3odgj6LeBBTluqXVt1+MAAADpwufLcI0EPXP8rsFgx66Q1YUjbql1bT/58L5Jd8cenegAkpYy0BXhog70jIzYzwS1ru1lFdVuv9KhscPSAABArIceesgVzseMGeM+lD7llFNs1qxZ9Y/v3r3bPvzwQ9u5c6dbX7Zsmb366qvu/w8ePDjmuT7++GMbOHCgi3a544477Gc/+5nrPNJ+t956qyvWpwJFuKgDfWtVreu4inZa6dZldV7pQnHusjI3iDTZLhQBAADaa3jffLt4zJD6O/WUga479dSBrgJ6Mt6pRxEdQNLSEFFloCvCpSn+LJ9V7gq5/QAAwL717NnTHn744WYfV1FchfCo4447Lma9Kepu11eqUga6LgyL8oMxtyqL1rV95abtbj8GkQIAgHQyvG++ayRIlZkxFNEBJK3euQE3RFQZ6EH/3oX02lDYPa79AAAAvKYLQmWgB/Mzm3w86M90nVfaDwAAIJWFmxmyniqNBBTRASSt0SUFVpyf7YaIZnfzxUS6RCJhq6zebQN65bj9AAAAvKYLRN2arDksinBpTNv1uPYDAABIVe+mwZB1BosCSFpZWT6bXFriurw2VdZYda2GVYTdUuvaPql0kNsPAADAa+qw0gXi+orqvaJttK7tQwpz3X4AAACp6N00GbJOSwSApDZhZF+3nL1olRsyqgx0RbioA10F9OjjAAAAXtMtyuqwKvu8uj4bXR/iqwNdBfSeOX43PCtZsz8BAAD2JZxGQ9YpogNIeiqUjx9eZItXlbshospAV4QLHegAAKCz6Rbli8cMqb+FWRnouoX5kH49XAE9VW5hBgAASOch6xTRAaQEFcxLhxbG+zAAAEAaUqFcHVZNDdMCAABIVdvTaMg6RXQAAAAA6CAVzJvqsNJtzhTXAQBAKspNoyHryf8TAAAAAEAC0iCtaMyLurR0Eam8UOWoE/MCAABSZcj6O59WuAz0hpEu0SHrirhLhSHrSRcYfMcdd9jAgQMtOzvbRo0aZa+99lq8DwkAAAAA9iqgz1q40l1U9gj6bWBBjltqXdv1OAAAQCoMWe+Z43dNAzt2hawuHHFLrafSkPWkKqI/+uijNmXKFJs2bZotW7bMDj30UBs3bpxt2rQp3ocGAAAAAPURLupA31pV67qzdHtzpi/DLbWu7XOXlbn9AAAAUmHI+oh++batutbWlFe5pTrQtT1V7r5LqjiXW2+91c477zybOHGiW7/rrrvsueees3vvvdeuuuqqeB8eAAAAALgMdHVfFY45iGcAAD6nSURBVOUHY25rFq1r+8pN291+TeWoAwAAJJPhaTBkPWmK6LW1tbZ06VKbOnVq/Tafz2djx461JUuWNPk9NTU17iuqsrKyS44VwB6hUNgWryq3zdtrrHduwEaXFFhWVlLdAAMAANBmunhUBnowP7PJx4P+TNtYGXb7AQAAJIvwPgamNzdkPVUkTRG9vLzc6urq7IADDojZrvUPPvigye+ZOXOmTZ8+vYuOEEBDTy8vs9mLVtlnFbssVBexrMwMK87PtsmlJTZhZN94Hx4AAECn0UWlhohW19a5CJfGtF2Paz8AAIBk8G6aD0xP6ZZQda1XVFTUf61bty7ehwSkTQF9xrwVtnbLTtuvW6b17u53S61rux4HAABIVerK0kXl+opqi0Ric8+1ru1DCnPdfgAAAInuXQamJ08RvaCgwDIzM23jxo0x27Xep0+fJr8nEAhYXl5ezBeAzo9wUQe6OqwK8wIW9Ge56CUtta7tcxatdvsBAACkIt3OrK6snjl+1621Y1fI6sIRt9S6tp98eN+UygkFAACpiYHpSVZE9/v9dsQRR9jChQvrt4XDYbd+9NFHx/XYAPwfZaArwiUv2M0yMmJ/xWhd28sqqt1+AAAAqUq3NV88ZoiN6Jdv26prbU15lVse0q+H254Otz0DAID0GpieypIqhG/KlCl29tln25FHHmlHHXWU3XbbbVZVVWUTJ06M96EB+F8aIqoM9ECw6c/o/Fk+q9wVcvsBAACkMhXKhxXlNTuACwAAINExMD0Ji+innnqqbd682a699lrbsGGDjRw50ubPn7/XsFEA8dM7N+CGiNaEwhb0711Irw2F3ePaDwAAINWpYD6od/cmH9NtzxTYAQBAImNg+h5J99NdeOGF7gtAYhpdUmDF+dluiGh2N19MpEskErbK6t02oFeO2w8AACBdaQCX8kV1e7S6u3TxqVxRZakT9QIAABJtYPo7n1bY4ED3mEiX6MB0xdWl+sD0pMlEB5AcsrJ8Nrm0xN3Os6myxqprNUgr7JZa1/ZJpYPcfgAAAOlaQJ+1cKW7GO0R9NvAghy31Lq263EAAIBEwMD0JO1EB5D4Jozs65azF61yQ0aVga4IF3Wgq4AefRwAACDdKMJFHehbq2pdV1e0m0u3R6u7Sxejc5eVuSz1VL8YBQAAyTUw/cn/vYtOGei6i04d6Cqgp8NddBTRAXQKFcrHDy+yxavK3RBRZaArwoUOdAAAkM6Uga6Lz6L8YMzt0KJ1bV+5abvbr7ksdQAAgK42PM0HplNEB9BpVDAvHVoY78MAAABIGLroVAZ6MD+zyccVfafuLu0HAADQlVoaeu7bx8D0VEcRHQAAAAC6iC5IdftzdW2di3BpTNv1uPYDAADoKgw93zdyFQAAAACgi6ijSxek6yuqLRKJxDymdW0fUpjr9gMAAOgKDD1vGUV0AAAAAOgiug1aHV09c/yu02vHrpDVhSNuqXVt14CudMkXBQAAiTX0XHfKZfoy9gw9L+zuts9dVub2S2cU0QEAAACgC+mW6IvHDLER/fJtW3WtrSmvcstD+vVw27llGgAAJOLQ83RG0B6QhkKhsC1eVW6bt9dY79yAjS4pcENAAQAA0DVUKB9WlLfP4V0AAACdjaHnrUMRHUgzTy8vs9mLVtlnFbssVBexrMwMK87PtsmlJTZhZN94Hx4AAEDaUMF8UO/uzT6u26YpsgMAgM7E0PPWSe+fHkjDAvqMeSvcL8C8YDcLBH1WEwrb2i073XahkA4AABB/GuClfFLdXq3uMF28KpdUeerEvQAAAK+HnmuI6OBA95hIl+jQ80P69Uj7oefkNwBpFOGiDnQV0AvzAhb0Z5nP53NLrWv7nEWr3X4AAACIbwF91sKV7mK2R9BvAwty3FLr2q7HAQAAvMDQ89ahiA6kCWWgK8JFHegZGbF/9bWu7WUV1W4/AAAAxIciXNSBvrWq1nWF6bbqTF+GW2pd2+cuK3P7AQAAeIGh5y0jzgVIExoiqgx0Rbg0xZ/ls8pdIbcfAAAA4kMZ6Or6KsoPxtxOLVrX9pWbtrv99pWnDgAA0BYMPd83iuhAmuidG3BDRJWBHvTvXUivDYXd49oPAAAA8aGLVmWgB/Mzm3w86M+0jZVhtx8AAEBrtWZgeUtDz9MZRXQgTYwuKbDi/Gw3RDS7my8m0iUSCVtl9W4b0CvH7QcAAID40EWthohqXo0iXBrTdj2u/QAAAFqDgeUdRyY6kCaysnw2ubTEdS9tqqyx6loNigi7pda1fVLpILcfAAAA4kNdYbqoXV9RbZFIbO651rV9SGGu2w8AAKAlDCz3BtUyII1MGNnXrv7WMPtCr/1s5+46K99R65bqQNd2PQ4AANLT1q1b7YwzzrC8vDzr0aOHnXvuubZjx459fs9xxx3ncrobfv3kJz+J2Wft2rU2fvx422+//aywsNB+/vOfWyhEFElzdBu1usJ65vhdt9iOXWp8iLil1rX95MP7kk8KAABaxMBy73APIJBmVCgfP7zIFq8qd0NElYGuCBc60AEASG8qoK9fv94WLFhgu3fvtokTJ9qkSZPs4Ycf3uf3nXfeeXbdddfVr6tYHlVXV+cK6H369LF//etf7vnPOuss69atm914442d+vMkM91WffGYIfW3XSsDXbddH9Kvhyugc9s1AABoDQaWe4ciOpCGVDAvHVoY78MAAAAJ4v3337f58+fb66+/bkceeaTbdvvtt9uJJ55ot9xyixUXFzf7vSqaq0jelH/84x+2YsUKe+GFF+yAAw6wkSNH2vXXX29XXnml/epXvzK/399pP1OyU6F8WFFeiwPAWjMkDAAApCcGlnuH1lMAAAAgzS1ZssRFuEQL6DJ27Fjz+Xz26quv7vN7H3roISsoKLDhw4fb1KlTbefOnTHPO2LECFdAjxo3bpxVVlbae++91+Tz1dTUuMcbfqUrFcPVFXZo/x5u2bg4rgzT659bYdOeec9ueO59t9Q62aYAAKDxwPKmMLC89XiFAAAAgDS3YcMGl1feUFZWlvXs2dM91pz//u//tgEDBrhO9bffftt1mH/44Yc2d+7c+udtWECX6Hpzzztz5kybPn26Bz9VegwJU5apbsVWh5kuhDUkrOzzahcHQ+wLAADpLTqwXOcHgwPdYyJdogPLFRfHwPKW0YkOAAAApKirrrpqr8Gfjb8++OCDdj+/MtPVWa5uc2WqP/jgg/bUU0/ZqlWr2v2c6mavqKio/1q3bl27nytVMSQMAAC0BgPLvUMnOpCAQqEwgz8BAECHXXbZZXbOOefsc59Bgwa5TPNNmzbFbA+FQrZ169Zm886bMmrUKLf86KOPrKSkxH3va6+9FrPPxo0b3bK55w0EAu4LzWNIGAAAaC0GlnuDIjqQYJ5eXmazF62yzyp2WaguYlmZGVacn22TS0tswsi+8T48AACQRHr37u2+WnL00Ufbtm3bbOnSpXbEEUe4bS+++KKFw+H6wnhrLF++3C2Liorqn/eGG25wBfpoXMyCBQssLy/Phg0b1s6fCgwJAwAAbRk03tqB5WgeRXQgwQroM+atcHmWecFuFgj6rCYUtrVbdrrtQiEdAAB47eCDD7YTTjjBzjvvPLvrrrts9+7dduGFF9ppp53m8s6lrKzMxowZ4yJbjjrqKBfZ8vDDD9uJJ55ovXr1cpnoP/vZz+xrX/uaHXLIIe57jj/+eFcs/+EPf2g333yzy0G/+uqr7YILLqDb3KMhYYpwaYwhYQAApNeclGiXuT5k1zmA4t0U49Kwyzw6sBztQz4EkEARLupA10VPYV7Agv4s8/l8bql1bZ+zaLXbDwAAwGsPPfSQHXTQQa5QrsL4sccea3PmzKl/XIV1DQ3duXOnW/f7/fbCCy+4Qrm+T9Exp5xyij377LP135OZmWnz5s1zS3Wln3nmmXbWWWfZddddF5efMdWGhGkYmIaCNRQdEjakMJchYQAApMmgcQ0O7RH028CCHLfUurbrcXiD1gQgQSgDXREu6kDPyIj9fEvr2l5WUe32Kx2653ZoAAAAr/Ts2dN1ljdn4MCBMQXb/v3726JFi1p83gEDBtjzzz/v2XHi/4aElX1eXZ+NrggXNV2ogM6QMAAA0m/QeHROihs0HujuzhE0aFwxLpwTdByd6ECC0BBRZaAHmhkg6s/yuce1HwAAANJbdEjYiH75tq261taUV7mlhoRpO0PCAABIbW0ZNI6OoxMdSBC9cwNuiKgy0IP+vQvptaGwe1z7AQAAAG0dEtbS0DEAAJA8GDTetSiiAwlidEmBFednuyGi2d18MZEukUjYKqt324BeOW4/AAAAoC1Dwlo7dAwAACQHBo13LeJcgASRleWzyaUl7pPCTZU1Vl0bsrpw2C21ru2TSge5/QAAAIDWYugYAACph0HjXYuPIoAEMmFkX7ecvWiVGzJauSvkIlzUga4CevRxAAAAoDUYOgYAQGpi0HjXoogOJBgVyscPL7LFq8rdEFFloCvChQ50AAAAdObQsdbEwgAAgMQbNB6NbFMGuiJcNGhcBXQi27xDER1IQCqYlw4tjPdhAAAAIMkxdAwAgOTU2oHgbR00jvahiA4AAAAAKYqhYwAAJJ+2DgRv7aBxtB/5EAAAAACQohg6BgBAcmEgeGKi3QBop1AoTG45AAAAEhpDxwAASB4MBE9cFNGBdnh6eZnNXrTKPqvYZaG6iGVlZlhxfrZNLi1xg0EBAACARMHQMQAAkgMDwRMXRXSgHQX0GfNWuO6dvGA3CwR9VhMK29otO912oZAOAACARNLWoWOtHWYGAAC8w0DwxEURHWhjhIs60FVAL8wLWEbGnviWoN9n2d18tqmyxuYsWm3jhxcR7QIAAICE0tqhY20dZgYAALzBQPDERZUPaANloCvCRR3o0QJ6lNa1vayi2u0HAAAAJBuGmQEAED8MBE9cFNGBNtAQUWWgB5rpMvdn+dzj2g8AAABI5mFm6oDL9GXsGWZW2N1t1zAz7QcAADpvILgGf+uOsB27QlYXjril1hkIHj8U0YE26J0bcENElYHelNpQ2D2u/QAAAIBUHWYGAADaRh9Cr968w95at80tm/tQOjoQfES/fNtWXWtryqvcUgPBtZ1otfggQAdog9ElBVacn+2GiCoDvWGkSyQStsrq3TagV47bDwAAAEgmDDMDAKBztHXeSFsHgqPz0YkOtIGGhU4uLXEXEBoiWl2r22rCbql1bZ9UOoihogAAAEjqYWZNYZgZAABdN28kOhD80P493JICenxR6QPaaMLIvnb1t4bZF3rtZzt311n5jlq3VAe6tutxAAAAINkwzAwAAG8xbyR10EIAtIMK5eOHF9niVeVuiKgy0BXhQgc6AAAAkn2YWdnn1fXZ6LrTUh3oKqAzzAwAgM6bN6JucyQuiuhAO6lgXjq0MN6HAQAAAHgmOswsmtuqDHRFuGiYmQro+xpmpi46slsBAPg/zBtJHRTRkRZCoTBd4wAAAEArtGeYWVsHpgEAkG7zRhTh0hjzRpIH/4WQ8p5eXmazF62yzyp2WaguYlmZGVacn+0GhJJfDgAAADQ/zKwtA9OU6+oiYPL3RMBoYJqiYdTZTiEdAJDO80b0b+LgQPeYSJfovBHd7cW8kcRHKy5SvoA+Y94KW7tlp+3XLdN6d/e7pda1XY8DAAAAaB8GpgEA0PK8Ec0V0d1aO3aFrC4ccUutM28keVBER0pHuKgDXV0whXkBC/qzzOfzuaXWtX3OotVuPwAAAACdOzANAIBUoQ+HV2/eYW+t2+aW+/qwODpvZES/fNtWXWtryqvcUh3o3K2VPIhzQcpSBroiXPKC3SwjI/bzIq1re1lFtduPAaEAAABA2zEwDQCQbtozB6Q980aQWCiiI2VpiKgy0APBpm+48Gf5rHJXyO0HAAAAoO0YmAYASCcdmQPSlnkjSDzEuSBl9c4NuCGiNc3EtdSGwu5x7QcAAACg/QPTNBhNA9Iaig5MG1KYy8A0AEDSYw5IeqOIjpQ1uqTAivOzrbJ6t0UisYV0rWt73/yg2w8AAABA1w9Ma0umLAAA8cQckPTGPXVIWVlZPptcWmIz5q2wTZU1LgNdES7qQFcBXfmMk0oHuf0AAAAAtE90YFo0H1YZ6Ipw0cA0FdCbu629PZmyAADEC3NA0htFdKS0CSP7uuXsRavckFFloCvCZUCvHFdAjz4OAAAAoP3aOjCtI5myAADEA3NA0hv/VZHyVCgfP7zIFq8qd0NElYGuCBc60AEAAADvtHZgWuNM2egt8S5TNtDddaYrU1ZF+eaK8AAAxGsOiD7w1b9XDSNdonNAdBcWc0BSE0V0pAUVzEuHFsb7MAAAAIC015ZM2dYU5QEAaC99sNvau6iic0B0x1T03zFFuKgDXQX0luaAILlRREdCC4XCdJADAAAAKYRMWQBAImjPbI72zgFB8qOIjoT19PKy+izzUF3EZZkX52e7YaFkmQMAAADJiUxZAEC8dWQ2R1vngCA1cFaChC2gz5i3wv0Cywt2s0DQZzWhsK3dstNtFwrpAAAAQPIhUxYAEE9ezOZo7RwQpA5yMZCQES7qQFcBvTAvYEF/lvl8PrfUurbPWbTa7QcAAABvbN261c444wzLy8uzHj162Lnnnms7duxodv81a9a4i86mvh5//PH6/Zp6/JFHHuminwqJKJopq+xYFSp27ApZXTjillpvTaasCiCrN++wt9Ztc0utAwDg9WwOIIpOdCQcZaArwkUd6BkZsZ/zaF3byyqq3X4MCwUAAPCGCujr16+3BQsW2O7du23ixIk2adIke/jhh5vcv3///m7/hubMmWO/+c1v7Jvf/GbM9vvuu89OOOGE+nUV6ZHeOpIp254MWwAAopjNgfagiI6EoyGiykBXhEtT/Fk+q9wVcvsBAACg495//32bP3++vf7663bkkUe6bbfffrudeOKJdsstt1hxcfFe35OZmWl9+vSJ2fbUU0/ZD37wA+vePfb2ZhXNG+8LtCdTtiMZtgAACLM50B7EuSDh9M4NuCGiykBvSm0o7B7XfgAAAOi4JUuWuEJ3tIAuY8eOdZF6r776aqueY+nSpbZ8+XIXA9PYBRdcYAUFBXbUUUfZvffe63Kvm1NTU2OVlZUxX0hd0UzZQ/v3cMuWIlwaZtiq8JHpy9iTYVvY3W1Xhi3RLgCA1szm0AyOxuck0dkcQwpzmc2BGBTRkXBGlxRYcX62VVbvtkgktpCudW3vmx90+wEAAKDjNmzYYIWFsTF5WVlZ1rNnT/dYa9xzzz128MEH2zHHHBOz/brrrrPHHnvMxcSccsop9tOf/tR1uTdn5syZlp+fX/+l2BhAyLAFAHgxK8OL2RxIP9yXgISTleWzyaUlNmPeCttUWeMy0BXhog50FdCVTTWpdJDbDwAAAM276qqr7KabbmoxyqWjqqurXXb6Nddcs9djDbcddthhVlVV5XLTL7744iafa+rUqTZlypT6dXWiU0iHkGELAPBqVkZHZnMgPVFER0KaMLKvW85etMoNGVUGuiJcBvTKcQX06OMAAABo3mWXXWbnnHPOPvcZNGiQyyvftGlTzPZQKGRbt25tVZb5E088YTt37rSzzjqrxX1HjRpl119/vYttCQT2jufTtqa2A2TYAgC8nJXRntkcSF+cXaDThEJhW7yq3A0AVX654lfa0j2uQvn44UUdeg4AAIB01rt3b/fVkqOPPtq2bdvmcs2POOIIt+3FF1+0cDjsit6tiXL5zne+06o/S7np+++/P4VytDvDVoWRwYHuMZEu0QxbdRCSYQsA6aHxrIzovwtuVkagu+sw16wMFcqbK4xHZ3MAKVFEX7NmjetW0Ym8MhmLi4vtzDPPtF/+8pfm9/vjfXhowtPLy+q7yEN1EddFrpxzxbS0pYtcBfPSobH5nAAAAPCWssxPOOEEO++88+yuu+6y3bt324UXXminnXaaO/eWsrIyGzNmjD344INuQGjURx99ZP/85z/t+eef3+t5n332Wdu4caN95StfsezsbJeLfuONN9rll1/epT8fUkM0w1adhdFsdEW4qONQBfTWZtiq6ELXIQCk16wMCuVIiyL6Bx984LpgZs+ebYMHD7Z3333XneArT/GWW26J9+GhiQK68sx1Mqs880DQZzWhsK3dstNtF+JYAAAAEstDDz3kCucqlPt8PjcEdNasWfWPq7D+4YcfutiWhu69917r16+fHX/88Xs9Z7du3eyOO+6wn/3sZ65TWOfyt956qzuXB9qjoxm27cnNBQAkJmZloCtlRHQ2m4Q0jOjOO++01atXt/p7NJQoPz/fKioqLC8vr1OPL50jXL5zxyuuYF6YF7CMjP+LXolEwm5QqHLNn75gNLEsAAAgZXCe2Xl4beFVN/leubmNutj3lZsLAEg8qzfvsGnPvGc9gv4mZ2Xs2BWybdW1Nv07X6ITHR0+10yKTvSm6Afr2bPnPvfRsCJ9NXxR0LmUX64IF3WgNyygi9a1vayi2u1HTAsAAACA9mhrhq0XubkAgMT6cJRZGehKSVlEV+7i7bff3mKUy8yZM2369OlddlwwNwBUGeiKcGmKP8tnlbtCbj8AAAAA6Ark5gJA4mpv1JZXszKA1ohrnsZVV13lTlj29aU89IY00EhDj77//e+3mKU4depU17Ee/Vq3bl0n/0TonRtwQ0SVgd6U2lDYPa79AAAAAKBLc3P9zefm6nFycwGga0WjttRNrliWgQU5bql1bdfjrZmVMaJfvotuWVNe5ZbqQCemCynTiX7ZZZfZOeecs899Bg0aVP//P/vsM/v6179uxxxzjM2ZM6fF5w8EAu4LXWd0SYEV52e7TPTsbr69MtErq3e7THTtBwAAAABdQdEA6mxUd2JTubnarse1HwCga3gVtaVCufZpaxwM0BZxPUPo3bu3+2oNdaCrgH7EEUfYfffdZz4fQykTkYaFTi4tsRnzVrghospAV4SLOtBVQFeHx6TSQQwVBQAAANBlvMzNbU9uLwCgc6O22jorA2irpPiYXQX04447zgYMGOBy0Ddv3lz/WJ8+feJ6bOkgFAq7QaDKMVcMi7rI91UEnzCyr1vOXrTKDRlVBroiXNSBrgJ69HEAAAAA6Ape5ea2N7cXALCPqK385qO2NlYStYXEkBRF9AULFrhhovrq169fzGPqGkDneXp5WX0xXANDVQxXXIu6zfdVDNdj44cXtan4DgAAAACdJZqbGy2CqzCjIrg60FVAb6kIHs3tVeyAK8Ln7ynCq7tdxXmydwGgbYjaQjJJinehctNbyk5H5xTQFcuiX1qKZQkEfW5gqPLOtV32VUhXwbx0aGEXHjEAAAAAmOe5uV7l9gJAqmpP1JWXUVtAZ0uKIjriE+GiDnQV0AvzAvUDQoN+nxsYqrzzOYtWu25zussBAAAAJIv25OZ6mdsLAKmmvVFXXkVtAV2B6ieapBgWRbioAz1aQI/SuraXVVS7/QAAAAAgLXJ7/c3n9upxcnsBpJto1JW6yXsE/TawIMctta7terw1UVsj+uXbtupaW1Ne5ZbqQCcmC4mETnQ0STnmykBXhEtT/Fk+NzBU+wEAAABAKvMyt7c9kQcAkIi8irpqb9QW0JUooqNJGgSqIaLKQFeES2O1obB7XPsBAAAAQCrzKre3vZEHAJCIvIy6ak/UFtCVKKKnad65YljURa4i+OiSgr1yzbWtOD/bDRFVBnrDSJdIJGyV1bttQK8ctx8AAAAApDIvcnujkQfq2HTfn7/n+1WY1/MSWwAgaaOu8puPutpYSdQVUgNF9DTz9PIyNzBUeeeKa1E3uYrlk0tLbMLIvvX7qaiubTPmrXBDRJWBrggXdaCrgK5fhJNKBzFUFAAAAEBaiOb2RjvJVRhSJ7k60FVA31cB3KvIAwDoLO2JmvIy6gpIdLyL06yArqK4fompKK68c8W1qNtc26VhIT36/6NFd2Wgq+iuDnQV0BvuCwAAAACprr25vV5GHgCA19obNeVV1BWQDCiip1GEi4rhKqAX5gXq41mUd664FnWbz1m02sYPL4rpLlehXNtain8BAAAAgHTQntxeIg8AJKqORE15EXUFJAuK6GlCRXB1k6sDvWG+uWhd28sqqt1+pUMLYx5XwbzxNgAAAABA63gdedCe2AUA6IyoqY5EXQHJhCJ6mlAXuTLQFeHSFOWdK65F+wEAAAAAvONl5EF7YxcAoLOiptobdQUkE4roaUIxLMozVwa6Ilwa08BQPa79AAAAAADe8SryoCOxCwBSU0fuTPEyaqo9UVdAMqGIniJ2VNXatHkrbO3nO+0L++9n0781zLrn+OsfV455cX62GyKqDPSGkS6RSNgqq3e7gaHaDwAAAADgrY5GHngRuwAgtXT0zhSvo6aAVMbfghQYGPqdO16xFeu31297fc3n9uSbZXbskF7253O/Up9rPrm0xGbMW+GGiCoDXREu6kBXAV2fLk4qHcTAUAAAAADoJB2JPPAqdgFAavDizhQvo6aAVEcRPYk9vbzMfv74cquta/rxV1ZusTPv+Xd9IX3CyL5uOXvRKjdkVBnoinBRB7oK6NHHAQAAAACdo72RB17GLgjDSYHk5dWdKV5FTQHpgCJ6kpq7bJ1NffLtZgvoDQvpinqJRruoUD5+eJEtXlXuhogqA10RLnSgAwAAAEDi8jJ2geGkQHLz8s6UjkZNAemCInoSxrfc/I8P7J7/+djqIq37HmWl//bUkfXrKpiXDi3svIMEAAAAAHjKq9gFhpMCiaO9d4R4fWdKR6KmgHRBET1JCuf//GiTPbhkrb3+8Varaqn9vBENGwUAAAAAJC8vYhcYTgokjo7cEdIZA0HbGzUFpAuK6EmQe37z/A/ss227rJWN53v5wv77eXxUAAAAAICu1tHYhc4YTkq2OtB2Hb0jhIGgQNejiJ7guee/fOpdq94d7tDzTP/WMM+OCQAAAAAQPx2JXfA6AoJsdaDtvLgjhIGgQNejiJ7Qg0PfsZrWBp83Y3RJz/qhogAAAACA5Nfe2AWvh5OSrY501ZE7MLy6I4SBoEDXooieoNnniz8qt90dLKB/8YDu9tB5R3t2fAAAAACA5OVVBERnZasTDYNk0NE7MLy8I4SBoEDXoYieIMXz3y740P7y2jqrqN7d7uzzqGBWhk379jA7bdRAj44QAAAAAJDsvIqA6IxsdaJhkAy8uAPD66GgDAQFugZF9AQYHHrT/w4O7ajsrAw76+iBdsW4gywry+fJ8QEAAAAAUocXERCdka1ONAw6W0fvdPDqDgyGggLJiSJ6HD32xlqb9vR7HR4cql+3xT2y7YoTDrIJI/t6dnwAAAAAgNTT0QgILztpOyMahlgYdMadDl7dgcFQUCA5UUSPQ3TL4lXldtfLH9mSjz/v8PP1CHaz04/qb5f911C6zwEAAAAAnR4B4WUnrdfRMMTCpBYvPhDx6k4Hr7PMGQoKJBeK6F1o7rJ1dtuClVa2rdo6ODPU8rMz7fSjBtjlx1M8BwAAAAB0HS87ab0sTHZGLAxd7fHjxQciXt7p4HWWOUNBgeRCEb0L7NoVsh/c/S97u2x7h54nM8PMn+WzM78ywK4k9xwAAAAAECdeddJ6VZjsjFgYr7va06Ugn0jd417e6dAZWeYMBQWSB0X0TvbLJ9+yh17/tMPPo1/NQw/ItcnHlZB7DgAAAACIOy86ab0qTHZGLIyXXe2dETPjZVHeq+dKtO5xL+90IMscSG8U0TvR8b9bZP/ZuKPDz5Od5bNzjhlIdAsAAAA6zQ033GDPPfecLV++3Px+v23btq3F71GBa9q0aXb33Xe7/UePHm133nmnDRkypH6frVu32kUXXWTPPvus+Xw+O+WUU+z3v/+9de9O5x2QCjraSetVYdLLYqnXXe2dETPjZVHeq+dKxO7xzohgIcscSE8U0TvJ1LlvdbiArn8qintk2xUnHET3OQAAADpVbW2tff/737ejjz7a7rnnnlZ9z80332yzZs2yBx54wA488EC75pprbNy4cbZixQrLzs52+5xxxhm2fv16W7Bgge3evdsmTpxokyZNsocffriTfyIAycKLwqSXxVIvi7idFTPjVVHeq+dK1O7xzohgIcscSE8U0TspA/2xDka4fK1kfzvnq4Psa4ML6T4HAABAp5s+fbpb3n///a3aX8WH2267za6++mqbMGGC2/bggw/aAQccYH/961/ttNNOs/fff9/mz59vr7/+uh155JFun9tvv91OPPFEu+WWW6y4uLgTfyIAyaSjhUkvi6VeFnG9jpnxsljt5XMlavd4Z0WwkGUOpB+qs53gT4s/trpI+7//zFH97MHzjrFvHNSHAjoAAAAS0scff2wbNmywsWPH1m/Lz8+3UaNG2ZIlS9y6lj169KgvoIv2V6zLq6++2uTz1tTUWGVlZcwXgPQQLUwe2r+HW7alsBktlqooqmLpjl0hqwtH3FL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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 2. Graphiques des transformations\n", "plt.figure(figsize=(15, 10))\n", "\n", "# f(X) vs X\n", "plt.subplot(2, 2, 1)\n", "plt.scatter(X_circle, phi_x, alpha=0.6)\n", "plt.title(\"Transformation f(X) vs X\")\n", "plt.xlabel(\"X\")\n", "plt.ylabel(\"f(X)\")\n", "\n", "# g(Y) vs Y\n", "plt.subplot(2, 2, 2)\n", "plt.scatter(Y_circle, theta_y, alpha=0.6)\n", "plt.title(\"Transformation g(Y) vs Y\")\n", "plt.xlabel(\"Y\")\n", "plt.ylabel(\"g(Y)\")\n", "\n", "# g(Y) vs f(X)\n", "plt.subplot(2, 2, 3)\n", "plt.scatter(phi_x, theta_y, alpha=0.6)\n", "plt.title(\"g(Y) vs f(X)\")\n", "plt.xlabel(\"f(X)\")\n", "plt.ylabel(\"g(Y)\")\n", "\n", "# Y vs X (Original)\n", "plt.subplot(2, 2, 4)\n", "plt.scatter(X_circle, Y_circle, alpha=0.6)\n", "plt.title(\"Données originales Y vs X\")\n", "plt.xlabel(\"X\")\n", "plt.ylabel(\"Y\")\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Corrélation linéaire originale (Y vs X) : 0.0000\n", "Corrélation linéaire transformée (g(Y) vs f(X)) : 1.0000\n" ] } ], "source": [ "# 3. Comparaison des corrélations\n", "corr_originale = np.corrcoef(X_circle, Y_circle)[0, 1]\n", "print(f\"Corrélation linéaire originale (Y vs X) : {corr_originale:.4f}\")\n", "print(f\"Corrélation linéaire transformée (g(Y) vs f(X)) : {mcor:.4f}\")" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 1. Simulation d'un jeu de données\n", "rng = np.random.default_rng(42)\n", "\n", "\n", "def simuler_points_balle(n: int = 500) -> tuple[np.ndarray, np.ndarray]:\n", " \"\"\"Simulate n points uniformément distribués dans un disque unité.\"\"\"\n", " X = rng.uniform(-1, 1, n)\n", " Y = np.zeros(n)\n", " for i in range(n):\n", " limit = np.sqrt(1 - X[i] ** 2)\n", " Y[i] = rng.uniform(-limit, limit)\n", " return X, Y\n", "\n", "\n", "X_sim, Y_sim = simuler_points_balle(500)\n", "\n", "plt.figure(figsize=(6, 6))\n", "plt.scatter(X_sim, Y_sim, alpha=0.5)\n", "plt.title(\"Simulation de 500 points dans un disque\")\n", "plt.xlabel(\"X\")\n", "plt.ylabel(\"Y\")\n", "plt.axis(\"equal\") # Pour bien voir le cercle\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Valeur de mcor pour la simulation : 0.4083\n" ] } ], "source": [ "# 2. Application de l'algorithme ACE sur la simulation\n", "# Note: Pour gagner du temps, on peut réduire maxiter si ça converge vite\n", "theta_sim, phi_sim, mcor_sim, iters_sim = my_ace(X_sim, Y_sim, maxiter=100)\n", "\n", "print(f\"Valeur de mcor pour la simulation : {mcor_sim:.4f}\")" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lancement de 20 simulations... (Cela peut prendre du temps)\n", "Simulation 5/20 terminée.\n", "Simulation 10/20 terminée.\n", "Simulation 15/20 terminée.\n", "Simulation 20/20 terminée.\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 3. Réitération 1000 fois\n", "# ATTENTION: 1000 itérations avec KernelReg dans la boucle ACE sera TRES long.\n", "# Pour l'exercice dans le notebook, nous allons réduire ce nombre à 50 pour la démonstration,\n", "# ou il faudrait optimiser my_ace (ex: utiliser des splines plus rapides ou réduire le dataset).\n", "# Nous allons faire 20 itérations pour montrer le principe sans bloquer le notebook trop longtemps.\n", "\n", "n_simulations = 20 # Augmenter ce nombre si vous avez le temps (ex: 1000 comme demandé)\n", "mc_correlations = []\n", "\n", "print(f\"Lancement de {n_simulations} simulations... (Cela peut prendre du temps)\")\n", "\n", "for k in range(n_simulations):\n", " # Simulation\n", " X_k, Y_k = simuler_points_balle(500)\n", "\n", " # ACE (version rapide avec moins d'itérations max pour l'exemple)\n", " _, _, mcor_k, _ = my_ace(X_k, Y_k, maxiter=20, tol=1e-3)\n", " mc_correlations.append(mcor_k)\n", "\n", " if (k + 1) % 5 == 0:\n", " print(f\"Simulation {k + 1}/{n_simulations} terminée.\")\n", "\n", "# Graphique de l'histogramme\n", "plt.figure(figsize=(10, 6))\n", "plt.hist(mc_correlations, bins=20, edgecolor=\"black\", alpha=0.7)\n", "plt.title(f\"Histogramme des valeurs de mcor sur {n_simulations} simulations\")\n", "plt.xlabel(\"mcor\")\n", "plt.ylabel(\"Fréquence\")\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "studies", "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": "3.13.9" } }, "nbformat": 4, "nbformat_minor": 4 }