Files
opti-non-lin/cours3.ipynb
2026-01-18 17:29:00 +01:00

611 lines
185 KiB
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{
"cells": [
{
"cell_type": "code",
"execution_count": 138,
"id": "c03a657e",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import time"
]
},
{
"cell_type": "markdown",
"id": "a462ed55",
"metadata": {},
"source": [
"Méthode Newton $\\mathbb{R}$"
]
},
{
"cell_type": "code",
"execution_count": 139,
"id": "e90827f2",
"metadata": {},
"outputs": [],
"source": [
"def f1(x):\n",
" f = 2*x-np.log(x)\n",
" g = 2 - 1/x\n",
" h = 1/(x**2)\n",
" return f, g, h"
]
},
{
"cell_type": "code",
"execution_count": 140,
"id": "ca26160d",
"metadata": {},
"outputs": [],
"source": [
"def f2(x):\n",
" f = x**3 - 6*x**2 + 4*x + 2\n",
" g = 3*x**2 - 12*x + 4\n",
" h = 6*x - 12\n",
" return f, g, h"
]
},
{
"cell_type": "code",
"execution_count": 141,
"id": "1f6bfe41",
"metadata": {},
"outputs": [],
"source": [
"def NewtonR(fct, x0, maxiter, tol=1e-9):\n",
" x = np.zeros(maxiter)\n",
" x[0] = x0\n",
"\n",
" for k in range(maxiter-1):\n",
" f, g, h = fct(x[k])\n",
" x[k+1] = x[k] - g/h\n",
"\n",
" if abs(g) < tol:\n",
" return x[:k+1]\n",
"\n",
" return x"
]
},
{
"cell_type": "code",
"execution_count": 142,
"id": "c012277d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1eec176bb10>]"
]
},
"execution_count": 142,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Ici ça marche super bien\n",
"\n",
"absc = np.linspace(0.01, 1.5, 1000)\n",
"oord = f1(absc)[0]\n",
"\n",
"x0 = 0.1\n",
"\n",
"x = NewtonR(f1, x0, 1000)\n",
"for k in range(len(x)):\n",
" f, g, h = f1(x[k])\n",
" plt.plot(x[k], f, 'ob')\n",
"\n",
"plt.plot(absc, oord, 'g')"
]
},
{
"cell_type": "code",
"execution_count": 143,
"id": "087255d2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1eec408c050>]"
]
},
"execution_count": 143,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Ici ça dépend du point initial\n",
"\n",
"absc = np.linspace(-2, 5, 1000)\n",
"oord = f2(absc)[0]\n",
"\n",
"x0 = [3,0]\n",
"c = ['b', 'r']\n",
"\n",
"for i, x0 in enumerate(x0):\n",
" x = NewtonR(f2, x0, 1000)\n",
" for k in range(len(x)):\n",
" f, g, h = f2(x[k])\n",
" plt.plot(x[k], f, 'o' + c[i])\n",
"\n",
"plt.plot(absc, oord, 'g')"
]
},
{
"cell_type": "markdown",
"id": "f68a7951",
"metadata": {},
"source": [
"Examen d'implémentation | Gradient et Newton"
]
},
{
"cell_type": "markdown",
"id": "06964cdd",
"metadata": {},
"source": [
"$f(x_1,x_2)=2x_1^2-1.05x_1^4+x_1^6/6+x_1x_2+x_2^2$\n",
"\n",
"$\\nabla f(x_1,x_2)=\n",
"\\begin{pmatrix}\n",
"4x_1 - 4.2x_1^3 + x_1^5 + x_2 & x_1 + 2x_2 \\\\\n",
"\\end{pmatrix}$\n",
"\n",
"$\\nabla^2 f(x_1,x_2)=\n",
"\\begin{pmatrix}\n",
"4 - 12.6x_1^2 + 5x_1^4 & 1 \\\\\n",
"1 & 2 \\\\\n",
"\\end{pmatrix}$"
]
},
{
"cell_type": "code",
"execution_count": 144,
"id": "7ba5e5c4",
"metadata": {},
"outputs": [],
"source": [
"def fexamen(x, nargout=2):\n",
" x1 = x[0]\n",
" x2 = x[1]\n",
" f = 2*x1**2 - 1.05*x1**4 + x1**6/6 + x1*x2 + x2**2 \n",
"\n",
" g = np.array([4*x1 - 4*1.05*x1**3 + x1**5 + x2, x1 + 2*x2])\n",
"\n",
" if nargout==3:\n",
" H = np.array([[4 - 12*1.05*x1**2 + 5*x1**4, 1],\n",
" [ 1 , 2]])\n",
" return f, g, H\n",
"\n",
" return f, g"
]
},
{
"cell_type": "code",
"execution_count": 145,
"id": "7fb63347",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(np.float64(1.0), array([1., 2.]))\n"
]
}
],
"source": [
"# Vérification de fexamen: OK\n",
"x = np.array([0,1])\n",
"print(fexamen(x))"
]
},
{
"cell_type": "code",
"execution_count": 146,
"id": "449e09c6",
"metadata": {},
"outputs": [],
"source": [
"def w1(f,x,d,alpha,beta1):\n",
" f0, g0 = f(x) # à l'itéré courant\n",
" f1, g1 = f(x+alpha*d) # à l'itéré potentiel\n",
" return f1 <= f0 + alpha*beta1 * np.dot(d, g0)\n",
"\n",
"def w2(f,x,d,alpha,beta2):\n",
" f0, g0 = f(x) # à l'itéré courant\n",
" f1, g1 = f(x+alpha*d) # à l'itéré potentiel \n",
" return np.dot(d, g1) >= beta2*np.dot(d, g0)\n",
"\n",
"def wolfebissection(f,x,d,alpha,beta1=1e-3,beta2=0.9):\n",
" aleft = 0\n",
" aright = np.inf\n",
"\n",
" while True:\n",
" w_1 = w1(f,x,d,alpha,beta1)\n",
" w_2 = w2(f,x,d,alpha,beta2)\n",
"\n",
" if w_1 and w_2:\n",
" break\n",
"\n",
" elif not w_1:\n",
" aright = alpha\n",
" alpha = (aleft+aright)/2\n",
"\n",
" elif not w_2:\n",
" aleft = alpha\n",
" if aright<np.inf:\n",
" alpha = (aleft+aright)/2\n",
" else:\n",
" alpha *= 2 # 2 est arbitraire\n",
"\n",
" return alpha"
]
},
{
"cell_type": "code",
"execution_count": 147,
"id": "3d5c52c7",
"metadata": {},
"outputs": [],
"source": [
"def methgradient(f,x0,maxiter=300,tol=1e-6):\n",
" x = x0.copy()\n",
" fobj = np.zeros(maxiter)\n",
" ngrad = np.zeros(maxiter)\n",
"\n",
" for k in range(maxiter):\n",
" fx, g = f(x)\n",
" d = -g\n",
" alpha = wolfebissection(f,x,d,1)\n",
"\n",
" x = x+alpha*d # calcul nouvel itéré\n",
"\n",
" # sauvegarde des f et g\n",
" fx, g = f(x)\n",
" fobj[k] = fx\n",
" ngrad[k] = np.linalg.norm(g)\n",
"\n",
" # critère d'arrêt\n",
" if np.linalg.norm(g) <= tol:\n",
" break\n",
"\n",
" return x, fobj[:k+1], ngrad[:k+1]"
]
},
{
"cell_type": "code",
"execution_count": 148,
"id": "c2a657c7",
"metadata": {},
"outputs": [],
"source": [
"def methNewton(f,x0,maxiter=300,tol=1e-6):\n",
" x = x0.copy()\n",
" fobj = np.zeros(maxiter)\n",
" ngrad = np.zeros(maxiter)\n",
"\n",
" for k in range(maxiter):\n",
" fx, g, H = f(x, nargout=3) # besoin de H\n",
" z = np.linalg.solve(H,g)\n",
"\n",
" x = x-z # calcul nouvel itéré\n",
"\n",
" # sauvegarde des f et g\n",
" fx, g = f(x)\n",
" fobj[k] = fx\n",
" ngrad[k] = np.linalg.norm(g)\n",
"\n",
" # critère d'arrêt\n",
" if np.linalg.norm(g) <= tol:\n",
" break\n",
"\n",
" return x, fobj[:k+1], ngrad[:k+1]"
]
},
{
"cell_type": "code",
"execution_count": 149,
"id": "274c9c44",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x0 = np.array([0.1, 0.1])\n",
"\n",
"xg, fg, ngg = methgradient(fexamen,x0)\n",
"xn, fn, ngn = methNewton(fexamen,x0)\n",
"\n",
"plt.semilogy(fg, label=\"gradient\")\n",
"plt.semilogy(fn, label=\"Newton\")\n",
"plt.title(\"Evolution de la fonction objectif\")\n",
"plt.legend()\n",
"plt.show()\n",
"\n",
"plt.semilogy(ngg, label=\"gradient\")\n",
"plt.semilogy(ngn, label=\"Newton\")\n",
"plt.title(\"Evolution de la norme du gradient\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 150,
"id": "1016c4ec",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Avec la méthode du gradient : x=[-9.13230123e-08 9.55910628e-08]\n",
"fobj=1.7087772621488852e-14 | grad=[-2.69700986e-07 9.98591133e-08] | H=[[4. 1.]\n",
" [1. 2.]]\n",
"EigResult(eigenvalues=array([4.41421356, 1.58578644]), eigenvectors=array([[ 0.92387953, -0.38268343],\n",
" [ 0.38268343, 0.92387953]]))\n",
"Avec la méthode de Newton : x=[ 3.64930450e-08 -1.82465225e-08]\n",
"fobj=2.3305490890415854e-15 | grad=[1.27725658e-07 4.33680869e-19] | H=[[4. 1.]\n",
" [1. 2.]]\n",
"EigResult(eigenvalues=array([4.41421356, 1.58578644]), eigenvectors=array([[ 0.92387953, -0.38268343],\n",
" [ 0.38268343, 0.92387953]]))\n"
]
}
],
"source": [
"print(f\"Avec la méthode du gradient : x={xg}\")\n",
"f, g, H = fexamen(xg, nargout=3)\n",
"print(f\"fobj={f} | grad={g} | H={H}\")\n",
"print(np.linalg.eig(H))\n",
"# On a un point ou le gradient vaut 0 et la matrice hessienne est definie positive\n",
"# => on a un minimum local\n",
"\n",
"print(f\"Avec la méthode de Newton : x={xn}\")\n",
"f, g, H = fexamen(xn, nargout=3)\n",
"print(f\"fobj={f} | grad={g} | H={H}\")\n",
"print(np.linalg.eig(H))\n",
"# On a un point ou le gradient vaut 0 et la matrice hessienne est indéfinie\n",
"# => on a un point selle"
]
},
{
"cell_type": "markdown",
"id": "bf54a678",
"metadata": {},
"source": [
"$f(x)=(x_1-2x_2)^4 + (x_2-3x_3)^4 + (x_3-4x_4)^4 + \\ldots + (x_n-(x_1+1))^4$\n",
"\n",
"$x_1 = 2x_2 = 2*3*4(x_1+1) => -23x_1=24 => x_1=-24/23$\n",
"\n",
"$x_2 = 3x_3 = 3*4(x_1+1) => x_2 = \\ldots$\n",
"\n",
"$\\ldots$\n",
"\n",
"$x_i = \\frac{-n!}{i(n!-1)}$"
]
},
{
"cell_type": "code",
"execution_count": 151,
"id": "1a83735f",
"metadata": {},
"outputs": [],
"source": [
"def fsize(x,nargout=2):\n",
" n = len(x)\n",
"\n",
" #Calcul de f\n",
" v = 1.0*x\n",
" v[:-1] = v[:-1]-x[1:]*np.arange(2,1+len(x))\n",
" v[-1] = x[-1]-x[0]-1\n",
" f = np.sum(v**4)\n",
"\n",
" #Calcul du gradient uniquement s'il est demandé\n",
" g = 4*v**3\n",
" g[1:] = g[1:]-4*(v[:-1]**3)*np.arange(2,1+len(x))\n",
" g[0] = g[0]-4*v[-1]**3\n",
"\n",
" #Calcul de la hessienne uniquement si elle est demandée\n",
" if nargout==3:\n",
" H = np.zeros((n,n))\n",
" for i in range(1,n):\n",
" H[i-1:i+1,i-1:i+1] = H[i-1:i+1,i-1:i+1]+ 12*v[i-1]**2*np.array([[1,-(i+1)],[-(i+1),(i+1)**2]])\n",
" H[0,0] += 12*v[-1]**2\n",
" H[0,-1] -= 12*v[-1]**2\n",
" H[-1,0] -= 12*v[-1]**2\n",
" H[-1,-1] += 12*v[-1]**2\n",
" if nargout==3:\n",
" return f, g, H\n",
" else:\n",
" return f, g"
]
},
{
"cell_type": "code",
"execution_count": 152,
"id": "1f5737dc",
"metadata": {},
"outputs": [],
"source": [
"def methgradientTime(f,x0,maxtime,maxiter=300):\n",
" start_time = time.time()\n",
" x = x0.copy()\n",
" fobj = np.zeros(maxiter)\n",
" temps = np.zeros(maxiter)\n",
"\n",
" for k in range(maxiter):\n",
" fx, g = f(x)\n",
" d = -g\n",
" alpha = wolfebissection(f,x,d,1)\n",
"\n",
" x = x+alpha*d # calcul nouvel itéré\n",
"\n",
" # sauvegarde des f et g\n",
" fx, g = f(x)\n",
" fobj[k] = fx\n",
" temps[k] = time.time() - start_time\n",
"\n",
" if temps[k] > maxtime:\n",
" break\n",
"\n",
" if np.linalg.norm(g) <= 1e-6:\n",
" break\n",
"\n",
" return x, fobj[:k+1], temps[:k+1]"
]
},
{
"cell_type": "code",
"execution_count": 153,
"id": "0ee9c336",
"metadata": {},
"outputs": [],
"source": [
"def methNewtonTime(f,x0,maxtime,maxiter=300):\n",
" start_time = time.time()\n",
" x = x0.copy()\n",
" fobj = np.zeros(maxiter)\n",
" temps = np.zeros(maxiter)\n",
"\n",
" for k in range(maxiter):\n",
" fx, g, H = f(x, nargout=3) # besoin de H\n",
" z = np.linalg.solve(H,g)\n",
"\n",
" x = x-z # calcul nouvel itéré\n",
"\n",
" # sauvegarde des f et g\n",
" fx, g = f(x)\n",
" fobj[k] = fx\n",
" temps[k] = time.time() - start_time\n",
"\n",
" if temps[k] > maxtime:\n",
" break\n",
"\n",
" # critère d'arrêt\n",
" if np.linalg.norm(g) <= 1e-6:\n",
" break\n",
"\n",
" return x, fobj[:k+1], temps[:k+1]"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f4b1b445",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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2EwKW999/3+Xr1V1wGtLZ7LtG57nRn1+bhujpiO2G0gIMIOlKhw4d1CP2P5Q24AKNczymt99+W5UcutORwt204DyP93b13Z3bnLhqA4bAGW10EBg89dRT6ocigj+U8qEdmbec85B2lGKh9AglbGhzhpoK1Fqgkbentj2DlhqgoRSKuZHxKCpHlKs3TLPv/46oHjuOfTSpF9nVNEAUIlVXgxG5Kp1xt+hW/zw0vkXJig5FqyiV8NS4FPgcfGf8crOP1vG59vSeRQjEPPXZaAyKngP/+c9/HJYjL/VGcGfzfVAEjaJX+9IWd7ajK/jeOMlgzISa1KVI/lz2tbrA+zhvx5o+B78mnU9iaIBXUzCKEy/yG43+amqsq5fkIR9rGkOpPqqK6mPfrQv7Y9nVtsC+XtdB8ZCf2H9QxYfG5tU5m/MNLk72sMyT+6S+r9mf11Aa5lxKg++I6lJ3thlKNVD9hwn5gtIX/FDFj6K6jNlVXX4hLTge0IBVD5bqCj21UA2Dkv7BgwfbluN87m46GmLfApyXUMKCaebMmeoHJq6ZCGQ8dQwFbJsWdzcAira+/PJL1esEw7/bVw0BWrFnZGQ4tH3BemiFjSha78pY3Q6Noj37qhjUNS5cuLDKutiB3BlqHDsGDkT0SLH/dYULPD7LVe+es6H3LMLn2HMejRHRNarZ0DbA1QUcJ526wns6/3JEPbZzF8u6wHbExQm9V+yhFT5OBLX1pHKm3x4A+w7q/Z3p6ddPDO5s23PZ1+oCn7N27VpZvXq1bRmKilFFgh4FzlUL8+fPV8GefVCJ/bimPEMxPPIbJWXO8J30/ECRPQIH9FgoLi52WM9+H0A+nk0xeU3qY9+tC/xgQmCBX/32+wfSgl+u2E51hX0S+yZ+sTv/QnfOT3f2SVSxo8Rizpw5qhpdh5IF9MTx1PkG5zVUpWBft0+nq9FfsW9h30UJijN8J+xfgEDAHvJFD7Ttv4s7qjuOUT2C/Qg9tpzPWZh3ToMregmF/d+Xlpaq6nFX6XDnOKiPfQtDUTjTA+O65mdNArakBQeVqwZM6AZoH8kjSMGBMm3aNNUN2Lk7KhonIjJHgyb0r8dJHSdtdPPCAeXcRsK5+gnFe+hCisaUaFSFrsmIyJ0b+KGBIn6ZInpF2wtE7q7aHeDXIbr24SBB3Sy6qSKaxg6OLon2jW7PBXZGNAjF++IgQb4tW7bM5ZgU6AaKSBvpRYNgXPSwg+M74ju52tlrgm51OOmiwRo+d/PmzaqawX671RV+aaH0Br8K0BYDVYA4eNGoDNVONXWLrQ5+ZeA9EExgP8G+g4s5AizU9aPhGvIRJyV0G0Q+ou0UfrG6autxLvtaXaA+Gt03EXRgv0T1G05u+GWHC7hz/TReR0kktge6uyIt+JWKbV0d5Am6oyIYQRE9ghNclPBLGvmDNkv4wYDSKgSOqCfH/osuziihxJg8OF70YnwcHwjm0CUU6yGIwzY9V57ed+sK3VmxHQYOHKi6WevdUtGI+WzufYPtgn0cwSIaUuKiin0OwyHgvKIPA4D8xLkIXYzxN9gfnUtSANsM+y62PbYpzgl6l2fsn566RYY+ngvSh+MfF1V0F8Z53Ll0FcMUfPHFF2o9HCv4Lgi6cZ7A8YLjG3+DfQrbD98LbftQwo28xTFZ3bAD1cFnAPIW53XkC/Y/nDeQhzgn43MRNOI4xbGEH6c4pu3H/HIF5zjs86iivP/++9WPKPyIdlXlV5fjwNP7Fs7JqB5CoIqSHLQdwvUBeWvfqP+caQGmpi7Pzl3CAN3rUlJSXHaH1WVmZmrjx4/XEhISVLe87t27V3kfV93k4Ntvv1XdBfF3HTt2VN1ZXXV53rFjhzZ48GAtPDzcoYufc5dn+y7OnTp10oKDg7XExETtnnvu0U6cOFFr19+aumI7QxfH+++/X3V7QxfDUaNGaQcPHnT5PZFH9913n8pLpAndqi+55BLtzTffrPVzXHV5fuihh1RXVOTHBRdcoK1evbpKF+HqVPe90a33wQcf1JKTk1Ua27dvr7oy2nexBHw/fJfa0gn79+9X3QebNGmiumSjuzz+1r5b7FtvvaWWo2ukfXdSV9/HnX1N796ItDtztW1c2bNnj+ruHRcXp4WFhWn9+vVT3VhddX/98MMPtSlTpqjuk9ge6HaJ7+3OPoXtj+6u+Dt0bcb3+ctf/qIdOXLEYb0vvvhCGzRokFoP3VSRHnyurqCgQHW3R3qRJv2zzrXLs7v7bnVdll19vivV/T0sXbpU7eP6d8dxtm3bNod19HOGc3fT6s4PGPoAXY2xTzZq1EjtZ999953t9YyMDLUdsU3w9/p+6NzlWbdgwQLb+8XHx2u33HKLdujQoSr7AM4Tzlyd71xBF+0nn3zSdtwPHTpU27Jli8vjDscy9sl27dqp4wTHC/afF154QXXThk8//VQNDYH9Fuu0bNlSdSM+evRorWlxdRyhqzW6/6PLsHOe//e//9UuvPBC9f0x4dyMfWrnzp21npfg559/1gYMGKC+N85POEb0YTnst0VdjgNP71vLli3TrrnmGpU+5Cceb7rppipdz8+VCf94LgQiIqoK98hCkX1to8MSEdWEbVqIqN6hWuxsG0kTEekYtBBRvUEjc72uGz0KiIjORcA2xCWi+odummjch8aJaIxIRHQuDGnTgt4y6HuOX15oza1DLwGMqIckoYsbWqDX91DdRERE5BsMqR7CHTQxtoPzmAcYIwNdOdE1DY9r1qwxInlERETkhQwJWoYOHepyTAkM+oMBpHB/H0zV3ZeEiIiIAk+dgxY0qMNgNRiICFU3uGuoqzsoY2Ah3B8BgzJhdE13Bw/CTZnw3s530SUiIqLAVueGuBhZEKOF4mZ1GE3RmT4aH4Z1RsCC0TFxG3eMylpTyQnuH7F48WI1aiDuRYKR+hAg2d9roSYYkvrIkSOqBIftYIiIiHwD2rHiViAosKjtjtB1DloQTNR0TxEMM4/hrjGsMyB4wR0f586dq4YHrw6GxMZw0RgSHDAUMNq0VBe04F4G9vczwH1nPHW7dSIiImpYBw8eVMP+N1iXZ9zECQ1o7bs2ImpCVY/9zddcSUlJkVWrVqk2LbhvA3oX4b4M1cE9KHB/HVdfGvcrISIiIu+Xl5enYgB37p/m0aAlJydH3bk1MTHRYTnm7W9OiCAGNzxDVROiKtwgDTdtwk2wevfubbu9NW72Vx0ERqiGcv7SCFgYtBAREfkWd5p2GDK4HKqCXJk+fbqa3IE7k2IiIiKiwODRLs+4t4jFYlG3JreH+aSkJE9+FBEREQUYjwYtISEhkpqaKsuWLXPo1YN5VP8QERERna06Vw8VFBQ43F4+PT1dNm7cqHr9YIwVtDMZO3as9OnTR/r166e6PKPtit6biIiIyFPQjhKDkZJ3Qwcb1MQ0eNCybt06GTZsmG1ebwyLQGXevHkyZswYNST/1KlTJSMjQ3r16iVLliyp0jiXiIjoXOBH9KFDh9Q4H+T9jWzR8SYqKsr3bphYH9B7KDY2VnJzc9l7iIgoAEpYdu/eLREREWpEdQ4q6r0QZqAwo6ioSNq3b1+lxKUu129Deg8RERGdC1QJ4WKIgAWjqJN3w3bCiPfYbudSTWTIDROJiIg8gSUsgbWdGLQQERGRT2DQQkRE5KeeeOIJ1SFGN27cOLn22mvFV7FNCxERUYB4+eWXPd7bCoHRokWL1PAn9Y1BCxERkRfDzYgxeKsnoJeOL2P1UC32ZhfIs19vl1eX7TY6KURE5Afy8/PllltukcjISGnWrJm89NJLMnToUHnggQfU661bt5ann35abrvtNtUF+M4771TLH330UenQoYPq5t22bVt5/PHHqwys99xzz6lx0XDH5DvuuEOKi4sdXneuHsKo9TNmzJA2bdqoXlg9e/aUTz/91Pb68uXLVSNajGyPQWPx2YMGDZKdO3eq1zE+25NPPqlugoz1MGFZfWFJSy1yCkrlzRV7pU1CpPz5kvZGJ4eIiFxAlcepsgpDPjs82FKn3jEYlPXnn3+WL774QgUYGIx1w4YNDm1PXnjhBbV82rRptmXR0dEqIEhOTpbNmzfLhAkT1LK//OUv6vWPP/5YVdXMnj1bLrzwQnn33XfllVdeUQFOdRCwvPfeezJnzhw1hsqKFSvkT3/6k+qiPGTIENt6f/vb3+TFF19Uy++++265/fbb1XfAgLJbtmxRg8jqN0Ouz9IcBi21aBJdeSfp7PwSo5NCRETVQMDSZeo3hnz2tqdGSERIkNulLO+884588MEHcskll6hlb7/9tgpE7F188cXy0EMPOSz7+9//bnuO0piHH35YPvroI1vQgtvmoHQFEzzzzDMqkHAubdGVlJTIs88+q9bR7w+IAGflypXyxhtvOAQt06dPt80/9thjcuWVV6r3RekMRrkNCgpqkBsjM2hxM2gpKCmXotJyt3dMIiIiZ3v37lVVOrg3nw4lEx07dnRYD1UxzhYsWKBKTvbs2aNuYVBeXu4wguz27dtVKYg9BCM//PCDy7TgPoIYpfbSSy+t0oamd+/eDst69Ohhe44qLcjKylL3HGxIvALXIjLEoor+EMXn5JdKy8bMMiIib4PzNEo8jPpsT0N7F3urV69W7WDQfmTEiBEq0EEpC6pszhYCH/jqq6+kefPmDq+Fhlb+YLe/4aFOrwpDe5iGxitwLbBxUNpy4HiRZBcUS8vGEUYniYiIXJyrfaEkHNUvCAB+/fVXWykF7rmza9cuGTx4cLV/t2rVKmnVqpVqW6Lbv3+/wzqdO3eWX375RTXg1a1Zs6ba9+zSpYsKTg4cOOBQFVRX6NmEe0E1BO/fwkbL3CZTra/LnqAgyc4/3+jUEBGRD0PD2bFjx8ojjzwi8fHx0rRpU9XY1mw219iYF41kDxw4oEpX+vbtq0pHFi5c6LDOpEmTVO8gVC1dcMEF8v7778vWrVurbYiLtKBdzIMPPqhKTdB4FwEUGtii2gnpdAfa16Snp6txWnAnZ7yvc0mNp7DLc22KT8rw4m9khHkdG+MSEdE5mzlzpmprctVVV8nw4cNVgIFSkrCwsGr/5uqrr1bBxcSJE1UvI5S8oMuzPfTkwTI0zE1NTVUlMffcc0+NaUHXavwNehEhDZdffrkKiNAF2l3XXXed+rthw4ap3kUffvih1BeT5umh8QxSl1tb18nxdJFXekmxFiz/GrRSJo/o5Ln3JiKis4KeK/h1j4trTRd7X1BYWKjalKB9it7zJ5C2V14drt+sHqpNdGUXrjBTmeTnHjM6NURE5ON+++032bFjh+pBhAv1U089pZZfc801RifN6zFoqU1wuJQEx0poWa5U5B42OjVEROQHMHgcRpVFI1ZU5fz000+SkJBgdLK8HoMWN5RFJEpobq5IfobRSSEiIh+HMVDWr19vdDJ8EhviusEaVTmQTkgRgxYiIiKjMGhxQ1BsZdASUZItVqtftFsmIiLyOQxa3BAa30I9NtGOS+4pxztqEhERUcNg0OIGS2zljawSTScku4BjtRARERmBQYs7opudCVo4wBwREZEhGLS4I4ZBCxERkdEYtNShpKWJnJSc3EKjU0NERBSQGLS4I7KJWMUiFpMmJ3I4wBwREZ0d3NAQN0Z87rnnHJYvWrSoxhsmnosnnnhC3a/IHzBocYfZIqXhlSMVrvt9q+SwMS4REZ0l3HvnH//4h5w4ccLopPgcBi117PYcU35MXlm22+jkEBGRj8KdnZOSktSdlauzcuVKueiiiyQ8PFxSUlLk/vvvVzdWhNdee026detWpZRmzpw5Dp/x97//XebNmydPPvmkbNq0Sa2DCcvgwIED6n5HUVFR6kaFf/zjHyUzM7NKCc27774rrVu3Vjc1vPHGGyU/P1+MwqDFTSa7HkQf/HJA9mYXGJ0kIiLSaZpIaaExEz67DiwWizz77LPy6quvyqFDh6q8vmfPHrn88svluuuuk99//10WLFiggpiJEyeq14cMGSLbtm2T7OxsNf/jjz+q+xYtX75czZeVlcnq1atl6NChMmbMGHnooYeka9eucvToUTVhmdVqVQHL8ePH1d9/9913snfvXvWac1oQFC1evFhNWNe5aqsh8d5D7jodtAxIKJH3MjWZ9sVWmX97v3qrgyQiojooKxJ5tnJMrQb31yMiIZF1+pPRo0erUoxp06bJf/7zH4fXUAJzyy23yAMPPKDm27dvL6+88ooKVl5//XVVyhIfH68CiOuvv14FKwhMXn75ZbX+2rVrVeAyaNAgVVKDkpSgoCBVuqNDkLJ582ZJT09XJTkwf/58Fdz8+uuv0rdvX7UMwQ1KZqKjo9X8rbfeKsuWLZPp06eLEVjS4q7oyo09pFm5hFjM8tPuHFmyhfciIiKis4N2Le+8845s377dYTmqchAoINjQpxEjRqgAAkEGfiwPHjxYBSsnT55UpS733nuvlJSUyI4dO1Qwg6AjIiKi2s/GZyJY0QMW6NKli8TFxTmkB9VCesACzZo1k6ysLDEKS1rcFVMZwUeX5cjdQ9rKK9+nydOLt8klnRMlJIixHxGRoYIjKks8jPrss4DAA8HIlClTVK8iXUFBgdx1112qHYuzli1bqkdU/bz55pvy008/qbtGo02KHsggaEGpjCcEBwc7zCNgQvBkFAYtdSxpkbyjcu+N7eSDtQflSG6xLN+ZJZd1PVPkRkREBkBVfR2raLwB2oegmqhjx462Zeeff74qPWnXrl21fzdkyBBVffTJJ5+oAAbwuHTpUvn5559VdZEuJCREKioqHP6+c+fOcvDgQTXppS34TJTcoMTFWxlSRIC6vEaNGqm6OHso9ho2bJjKsO7du9taSnuF6NN1pflHJSzYIqN7V87/d0PVRlRERETuwLUO7VfQZkX36KOPyqpVq1TD240bN8ru3bvl888/tzXEhR49eqjr6AcffOAQtKDRLKqJLrjgAocqHlxf8V45OTnqdfQu0j97w4YNqh3MbbfdpoKhPn36iLcyJGiZNGmSavDjDMVjTz31lIr2ULwVGhoqXlfSUnxSpOyUXJda2QX6+x1ZcqKw1Ni0ERGRz8J1z77KBQEJroG7du1S3Z5R/TN16lRJTk52qKbBa3i88MILbX+HaiIEHZGRZ0qd0AsJvZFQKNCkSRP58MMP1d8hEELgg2olBDFt27ZVPZW8mUnT6thXy0NQ74a+5p9++qma37p1qwpmULR1NvLy8lQf8tzcXLXRPA7ZhJbpaKF+/28i8W3lqld/ki2H8+TJq7vK2EGtPf+ZRETkUnFxsSo9aNOmjRqsjXx3e9Xl+l3nkpYVK1bIqFGjVMSHSA1FUc5mz56tiqOQsP79+6tip9qg+AstpPHeqM9DH3avqy+1a9cC151fWdoya+kuWb//uJGpIyIi8nt1DlrQzqRnz54qMHEFRUuTJ09Wfc9RT4Z10Tq6ti5S5eXlqhX0v/71LzUoDvqQY/Iqdu1a4I99UqRHi1g5UVQmN731i3y37cxIgkRERGRw0DJy5Eh55plnVGNaV2bOnCkTJkyQ8ePHqwa1GFYYfcXnzp1b4/s2b95c1cOhFTPaslxxxRWq0VB10JAIRUr2U73TS1pOBy2RoUHy0Z0DZHjnplJabpW731svX24yqMsdERGRn/NoQ9zS0lJZv369atBj+wCzWc2j9KQmGAgHpTG4gRQaJKEaCl2yqoMRA1EHpk/2A+TUm5jKUXEl/8ygchEhQTLnT6kyundzqbBqMumj32R3pnH3ZSAiIvJXHg1a0JUKfcETExMdlmM+I+PMhR5BzA033CBff/21tGjRQgU0GGIY7VjQihktoDFs8VVXXVXtZ2EwHjTa0Sf0NW+oofwlz7E0Jchilhdv6CkXtksQqyby1ebKkhgiIiLy8cHlqushhKonTO5AFVKDd4mOrlrSojObTXJ1r2RZmZYjS7dnygPDOzRs2oiIApBBHWDJoO3k0ZIW3GUSd6+0v7U1YN7+Rk0+yxa0uG63cnGnpqqTEbpBH8091bBpIyIKILjW6M0SyPvp20nfbl5R0oKhglNTU9UdIK+99lq1DO1TMG8/kp/Psm/TgqjR6Q7PCVGh0jslTjYcOCnLtmfJnwa0MiadRER+Dk0K0MkjOztb3R8H7SfJOyEOwHbC9sJ2Oxd1/mvcyCktLc02rw8NjNtk40ZO6O48duxY1ROoX79+MmvWLNVNGr2JfF7U6dKi8mKRUydEIuKrrDK8S+LpoCWTQQsRUT3BOGG44zCuQfv37zc6OVQLBJWIEbDdGjRoWbdunRoKWIcgBRCo4FbaY8aMUREVhhxG41vcCGrJkiVVGuf6pOAwkfB4kVPHK0tbXAQtl3RKlH8u2Smr9hxTvYks5nPbQEREVH3pPjptsIrIN7aVJ0rD6hy04IZMtTWoQVWQX1QHVdeuRQUtR0QSq94J87wmkSpQKSm3SnZ+iSTFcnhpIqL6ggshh/EPHKwE9MBYLc7dn5NiKg+gwyfZGJeIiMhTGLTUldP9h1xpHheuHhm0EBEReQ6DlnO8/5AryXGVJS1HGLQQERF5DIOWc7z/kCvNG50uaTnBoIWIiMhTGLTUVYw7JS2VQQtLWoiIiDyHQUtdsU0LERGRIRi0nG2blsIskYpyl6swaCEiIvI8Bi11FZkgYrKIaNbKwKWG6qH84nLJKy5r4AQSERH5JwYtdWW21NoYNzI0SOIigtVztmshIiLyDAYt9dyuhUELERGRZzBoOduh/N3sQcRuz0RERJ7BoKWegpYzjXGLGypVREREfo1BSz3cf8g+aEnLKmioVBEREfk1Bi3nUtKSd6TaVXq1jFOPS7dnyvu/7G+olBEREfktBi3nVD1UfUlL39bxcv/F7dTzxxdtkV/3HW+o1BEREfklBi3nFLRUX9ICD17aQUZ2SxKrJvLlpprXJSIiopoxaDmXNi3FuSKlRdWuZjKZ5Moeleuu23eioVJHRETklxi0nI3QGJHgiFp7EEGfVvHqcUdGnhSUuB72n4iIiGrHoOVsmExutWuBpNgw1ZMIVUQbD5xsmPQRERH5IQYt9ThWi65P60bqcd1+NsYlIiI6WwxaznmsltqDltRWlUHL+v1s10JERHS2GLTU4/2HnIOW3w6clArUExEREVGdMWg5W9HJbpe0dEqKkajQINUQ940Ve+o/bURERH6IQcu5lrS4EbRYzCaZdEl79fyfS3bK7B/SRNNY4kJERFQXDFrOVoz7JS0wYXBbeWB4ZeDy/Dc75fZ5v0p2fkl9ppCIiMivMGjxRJsWN0tNHhjeQZ6+pquEBJnlh53ZcsmLy+W9NftZ6kJEROQGBi3n2uW5okTklPu9gm4d2Fq+mHiBdE2Okbzicvn7oi3yzdaax3ohIiIiBi1nLyhUJDy+TlVE9g1zv5h4odyQ2kLNf7s1sz5SSERE5FcYtHiiXYsb3Z5dNc4d3bu5er4yLYdVRERERLVg0NJAPYhcOb9VIwkNMktWfomkZRV4Nm1ERER+hkFLAw3l70pYsEX6tYm3lbYQERFR9Ri0GBi0wAXtEtTjz2nHPJUqIiIiv8SgxRP3HzqLNi26C08HLWv2HpPyCqunUkZEROR3GLQYXNLSpVmMxIRVDvG/MzPfc2kjIiLyM4YELaNHj5ZGjRrJ9ddfX+W1oqIiadWqlTz88MPi9RK7igz9q8igP5/1W5jNJuncLEY933GUQQsREZFXBS2TJk2S+fPnu3xt+vTpMmDAAPEJcS1Fhj4q0r1q8FUXetCy/WiehxJGRETkfwwJWoYOHSrR0dFVlu/evVt27NghI0eOlEDSuVllXuzIYEkLERGRx4KWFStWyKhRoyQ5OVlMJpMsWrSoyjqzZ8+W1q1bS1hYmPTv31/Wrl3r1nujSmjGjBkSaDBCrl7SwkHmiIiIPBS0FBYWSs+ePVVg4sqCBQtk8uTJMm3aNNmwYYNad8SIEZKVlVXj+37++efSoUMHNQWaDonRYjaJHCss5Z2fiYiIqhEkdYSqm5qqb2bOnCkTJkyQ8ePHq/k5c+bIV199JXPnzpXHHnus2r9bs2aNfPTRR/LJJ59IQUGBlJWVSUxMjEydOtXl+iUlJWrS5eX5bnuQ8BCLtE6IlL3ZhbI9I1+axoQZnSQiIiL/btNSWloq69evl+HDh5/5ALNZza9evbrGv0W10MGDB2Xfvn3ywgsvqMCnuoBFXz82NtY2paSkiC9jY1wiIqIGDFpycnKkoqJCEhMTHZZjPiMjwzaPIOaGG26Qr7/+Wlq0aFFrQOPKlClTJDc31zYh4PFlGK8FGLQQERF5qHrIE5YuXVrj6+PGjav1PUJDQ9XkLzolVfYg2naEQQsREVG9l7QkJCSIxWKRzMxMh+WYT0o6fUdkcqlnSpx63J1VICcKS41ODhERkX8HLSEhIZKamirLli2zLbNarWp+4MCBnvwov5MQFSrtmkap57+kHzc6OURERL5fPYSePWlpabb59PR02bhxo8THx0vLli1Vd+exY8dKnz59pF+/fjJr1izVTVrvTUTVG9A2XtKyCuSX9GNyeTeWTBEREZ1T0LJu3ToZNmyYbR5BCiBQmTdvnowZM0ays7NVzx80vu3Vq5csWbKkSuNcqqp/m8by3poDsmYvS1qIiIicmTQ/GYIV47Sg6zN6EmF8F1+UlV8s/aYvE5NJZOPjl0lsRLDRSSIiIvKa67ch9x4i15pGh0nbJpGCMHLtPpa2EBER2WPQ4mUGtG2sHn9l0EJEROSAQYuXaZsQqR4zcouNTgoREZFXYdDiZWLDK9ux5J4qMzopREREXoVBi5eJiwhRjycZtBARETlg0OKtJS1FHBWXiIjIHoMWLxN3upszq4eIiIgcMWjxMnF2bVqsVr8YQoeIiMgjGLR4mZjTQQvilfyScqOTQ0RE5DUYtHiZsGCLhAVXbpY8VhERERHZMGjxQnHhp3sQFTFoISIi0jFo8UJsjEtERFQVgxYvbtdy8hS7PRMREekYtHhxDyJWDxEREZ3BoMULsXqIiIioKgYtXoj3HyIiIqqKQYs333+IQ/kTERHZMGjxQixpISIiqopBixcHLWyIS0REdAaDFi/EhrhERERVMWjx4hFxGbQQERGdwaDFi0taWD1ERER0BoMWLx4R91RZhZSUVxidHCIiIq/AoMULRYcGidlU+ZxVRERERJUYtHghs9l0ptszq4iIiIgUBi3e3u2ZJS1EREQKgxYvFXt6VNwjJ08ZnRQiIiKvwKDFS/VvE68eZ/+QJuUVVqOTQ0REZDgGLV7qvqHtpFFEsOzKLJD3fzlgdHKIiIgMx6DFS8VGBMvkyzqq509+uVX++MZqmfntTlmyJUOKy9gNmoiIAk+Q0Qmg6t3UN0VW7MqW77Zlytr042oClMCMv6CN3DesnVj0vtFERER+jkGLFwuymOWt2/rIweNFsnxnlmw+nCs/px2TwydPyczvdklMWJCMu6CN0ckkIiJqEAxafEBKfITcOrC1el5h1WTOj3vk+W92yktLd8s1vZpLo8jKnkZERET+zJA2LaNHj5ZGjRrJ9ddfb1t28OBBGTp0qHTp0kV69Oghn3zyiRFJ83qoDrprcFvplBStRsudtXSX0UkiIiLy36Bl0qRJMn/+fIdlQUFBMmvWLNm2bZt8++238sADD0hhYaERyfOJaqOpV3VRz9GzKKegxOgkERER+WfQghKV6Ohoh2XNmjWTXr16qedJSUmSkJAgx49XNjylqga1S5CeKXFSbtVk0W+HjU4OERGR9wUtK1askFGjRklycrKYTCZZtGhRlXVmz54trVu3lrCwMOnfv7+sXbu2Tp+xfv16qaiokJSUlLomL6DckNpCPX687qBommZ0coiIiLwraEGVTc+ePVVg4sqCBQtk8uTJMm3aNNmwYYNad8SIEZKVleXW+6N05bbbbpM333yzrkkLOKN6JktokFkNQPf7oVyjk0NERORdQcvIkSPlmWeeUY1pXZk5c6ZMmDBBxo8frxrVzpkzRyIiImTu3Lm1vndJSYlce+218thjj8mgQYPqmrSAvKniiK5J6vmn6w8ZnRwiIiLfadNSWlqqqnaGDx9+5gPMZjW/evXqGv8W1Rvjxo2Tiy++WG699Va3Apy8vDyHKRBd2iVRPe7ICMzvT0REgcOj47Tk5OSotiiJiZUXUh3md+zYYZtHELNp0yZV1dSiRQvVvRl/h6oldHfW28m8++670r17d5efNWPGDHnyyScl0MWfHqMF3Z+JiIj8mSGDyy1dutTlcqvV/bsZT5kyRbWd0aGkJRAb7qKKCE4WMWghIiL/5tGgBd2ULRaLZGZmOizHPLoxe1JoaKiaAp0etLCkhYiI/J1H27SEhIRIamqqLFu2zKH0BPMDBw705EeR3d2goaTcyrs/ExGRX6tzSUtBQYGkpaXZ5tPT02Xjxo0SHx8vLVu2VFU2Y8eOlT59+ki/fv3UKLdou4LeROR5USFBghs9WzWRvFNlEhZsMTpJRERE3hG0rFu3ToYNG2ab19uVIFCZN2+ejBkzRrKzs2Xq1KmSkZGhRrldsmRJlca55Blms0liwoNVmxZUETWNCTM6SURERN4RtGAI/tpGX504caKaqOHatehBCxERkb8y5N5D5Flx7EFEREQBgEGLH0D1ELCkhYiI/BmDFj/Abs9ERBQIGLT4AQYtREQUCBi0+AEGLUREFAgYtPhR0IJxWoiIiPwVgxZ/uv8QgxYiIvJjDFr8QNzpofxZPURERP6MQYsfYJdnIiIKBAxa/AAb4hIRUSBg0OIHGLQQEVEgYNDiR0FLablVissqjE4OERFRvWDQ4geiQoPEYjap57z/EBER+SsGLX7AZDJJTFjlDbtZRURERP6KQYufiIsIUY8MWoiIyF8xaPET7PZMRET+jkGLn2APIiIi8neVDSHIb4KW15enyf5jhdI8Lly6NY+Vrskxqs0LERGRr2PQ4ieGdWwiX/1+RPZkF8qr36fZlrdqHCFXdm8ml3VNklbxEWrIfwYxRETki0yapmniB/Ly8iQ2NlZyc3MlJiZGAlF2fol8ty1TNh8+KYdOnJJf9x2X4jKrwzrRYUFyfstG0iExSlrGR8j1qSkSHmIxLM1ERBTY8upw/WbQ4scKS8rlh51Z8tXvR2XN3mNywsUYLkM6NJF54/uy9IWIiLz++s3qIT8WGRokV/VIVhNgtNy0rALZcOCE7D9WJO+u3i8/7sqWrzdnyJU9mhmdXCIiohoxaAkgYcEW1TgXE0SGWOSV79PkqcVbpVfLONV4l4iIyFsxaAlg9w5rJ59vOqJKXYa9sFxGdE1SI+s2jgyRFvERMqpHMtu7EBGR12DQEuAlL3PH9ZW/Ldwsa/Yely83HXF4PSuvWCZe3N6w9BEREdlj0BLgzmsSJR9OGCAr03Jky+E8OVVWoRrtrk0/LnuzC41OHhERkQ2DFlI9hy5q30RN8NmGQypoycwvNjppRERENhzGn6pIjAlTj1l5JUYnhYiIyIZBC1XRNDpUPWbmsaSFiIi8B4MWqqLp6ZKWvOJyNbYLERGRN2DQQlWg23NoUOWuwSoiIiLyFgxayGXDXFu7FjbGJSIiL8GghWpp18KSFiIi8g4MWsgllrQQEZG3MSRoGT16tDRq1Eiuv/56h+WLFy+Wjh07Svv27eXf//63EUmj05qwpIWIiLyMIUHLpEmTZP78+Q7LysvLZfLkyfL999/Lb7/9Js8//7wcO3bMiOQRS1qIiMgLGRK0DB06VKKjox2WrV27Vrp27SrNmzeXqKgoGTlypHz77bdGJI/s2rSw9xAREfls0LJixQoZNWqUJCcnq14mixYtqrLO7NmzpXXr1hIWFib9+/dXAUltjhw5ogIWHZ4fPny4rskjD2FJCxER+XzQUlhYKD179lSBiSsLFixQ1TzTpk2TDRs2qHVHjBghWVlZnkgvNZCmMWzTQkREPh60oNrmmWeeUY1pXZk5c6ZMmDBBxo8fL126dJE5c+ZIRESEzJ07t8b3RcmNfckKnmNZdUpKSiQvL89hIs9JjK4sack9VcZRcYmIyP/atJSWlsr69etl+PDhZz7AbFbzq1evrvFv+/XrJ1u2bFHBSkFBgfzvf/9TJTTVmTFjhsTGxtqmlJQUT36VgBcTfmZU3Ox8lrYQEZGfBS05OTlSUVEhiYmJDssxn5GRYZtHEHPDDTfI119/LS1atFABTVBQkLz44osybNgw6dWrlzz00EPSuHHjaj9rypQpkpuba5sOHjzoya8S8NBeSa8iWr6TVXtERGS8ICM+dOnSpS6XX3311WpyR2hoqJqo/lzUvol88MsBefzzrfJL+nF5+ppu0igyxOhkERFRgPJoSUtCQoJYLBbJzMx0WI75pKQkT34UNYAnRnWV+y9pLxazSRb/flQufWmFfLfNcdsSERH5ZNASEhIiqampsmzZMtsyq9Wq5gcOHOjJj6IGEBJklsmXdpCF9w6S9k2jJKegRCbMXycPfbxJCkvKjU4eEREFmDoHLWgku3HjRjVBenq6en7gwAE1j+7Ob731lrzzzjuyfft2ueeee1Q3afQmIt/Uo0WcfPnnC+WuIW3FZBL574ZDct8HG6S8wmp00oiIKICYNE3T6vIHy5cvV41lnY0dO1bmzZunnr/22mtqGH40vkWj2ldeeUUNMlef0OUZvYjQKDcmJqZePyuQrdl7TMa9vVaKy6xyU78UuaV/K2nbJFIiQgxpHkVERD6uLtfvOgct3opBS8P5evNRuff9DQ7LmseFq+DlvCZRcl7TKOnRPFZ6tIhVvZCIiIiqw6CFQUu9W/jbIXl/zQHZm1MoxwtLXa7TNTlGLuuSJC0ahUuHxGjpkBQloUGWBk8rERF5LwYtDFoaFIKWvdkFskdNhbI7M19W7TkmJeXWKg17h3RoIhe1T5Dk2HBJig1TU3xEiJjNLJEhIgpEeQxaGLQY7URhqXz222HZlZEvB44XyfaMPDlZVOZyXXSpbhwZIk2iQ2XQeY3l4REdWSJDRBQg8hi0MGjxNtjNdmTky/+2ZMj2o3mSkVssR3OL5VhhiTjvgf3bxKuu1mHBFjUqb9PoMBXYEBGR/2HQwqDFZ5RVWFX1Eu5vtDMjX6Z9sVUKnMaAQSPfeeP7SvvEaMPSSURExl+/PTq4HFFdBVvMkhgTJt2ax8p1qS3kk7sHyoC28dImIVKSY8MkyGySwydPqUHtcqupXiIiosDAkhbyascKSuTq135WgUu/NvHy+i3nS+Mo3nOKiMhfsKSF/AYClLdu6yMRIRZZm35crnjlJ3nx253y+cbDqmqJiIgCB4cxJa/XJTlGPrt3kNz3/gbVpfrV79PU8tJyq9zQJ8Xo5BERUQNhSQv5hE5JMfLFxAvl8au6SM8WsWrZrsx8o5NFREQNiCUt5DMiQ4PkjgvbiMUksulQrhw6ccroJBERUQNiSQv5nBaNItQjgxYiosDCoIV8Tov4cPV46ESR0UkhIqIGxKCFfA4Gm4MTRWVVBqIjIiL/xaCFfE50WLDERQSr54dZRUREFDAYtJBPatGIVURERIGGQQv5pBZxbIxLRBRoGLSQT2JJCxFR4GHQQj4etLCkhYgoUDBoIZ/EsVqIiAIPgxbySRyrhYgo8DBoIZ8fqyW/uMzo5BARUQNg0EI+O1ZL0+hQ9XzC/HWSmVdsdJKIiKieMWghnzV9dHeJDLHImr3H5ZIXf5RZS3dJcVmF0ckiIqJ6wqCFfNalXRLliz9fKD1bxKrh/Gct3a0mIiLyTwxayKed1yRKFt57gTx6eSc1vzIt2+gkERFRPWHQQj7PbDbJVT2aqec7M/KltNxqdJKIiKgeMGghvxlsLjY8WMoqNNmVmW90coiIqB4waCG/YDKZpGtyjHq+7Uie0ckhIqJ6wKCF/Ea35rHqccuRXKOTQkRE9YBBC/kNvaRlK0taiIj8EoMW8htdk2Nt1UMVVs3o5BARkYcxaCG/0SYhUiJCLHKqrEJ+2JEl2fklaoj/sgr2JiIi8gdBRieAyFMsZpN0aRYj6/afkP+bv87htajQIHn4sg4y7oI2hqWPiIj8qKTlpZdekq5du0qXLl3k/vvvF01jET/VzYOXdpB+reOlcWSIw3KMmPvEl9tk9g9pklNQwn2LiMgHmTQvOXtnZ2fLgAEDZOvWrRIcHCyDBw+WF154QQYOHOjW3+fl5UlsbKzk5uZKTExlg0wKbFarJqUVVnU/orkr0+WV79McSmUigi0SFmJRVUrhwRYJP/2o5kOCpHvzGBnWsakadRcD2BERkefV5frtVdVD5eXlUlxcebfesrIyadq0qdFJIh+GQCPMbJGwYItMvqyjxIQHy9s/75MjuadUQ938knI1VefLTUfk2a93qEAmJT5cgi1mNYVYzBJkMam7TE8b1VUaOZXqEBFR/fBY0LJixQp5/vnnZf369XL06FFZuHChXHvttQ7rzJ49W62TkZEhPXv2lFdffVX69eunXmvSpIk8/PDD0rJlSwkKCpK7775bzjvvPE8lj0j+76K2akLJS+6pMikqrZBTmMrK5VSpVTXgLSotV6+fKCqTn9NyZG36cbV8V2aBy/fsmRIn49lOhojIt4KWwsJCFYjcfvvt8oc//KHK6wsWLJDJkyfLnDlzpH///jJr1iwZMWKE7Ny5U5WonDhxQhYvXiz79u2T8PBwGTlypAqEUE1E5EkoecFUm7uHnKdKZPYdK5SM3GLVCwm3CcDj15uPyuLfj3L0XSIiXwxaEGRgqs7MmTNlwoQJMn78eDWP4OWrr76SuXPnymOPPSZLly6Vdu3aSXx8vHr9yiuvlDVr1lQbtJSUlKjJvk6MyNPQ9gVtWjDZQxMXBC3bM7jfERH5Ve+h0tJSVW00fPjwMx9sNqv51atXq/mUlBRZtWqVatNSUVEhy5cvl44dO1b7njNmzFANd/QJf0/UULo0qxzIbldGAceBISLyp6AlJydHBSKJiYkOyzGP9i2AnkNXXHGF9O7dW3r06KHas1x99dXVvueUKVNUS2N9OnjwYL1/DyL7u0pj7Bf0TtqbXWh0coiIAoJX9R6aPn26mtwRGhqqJiKjeiZ1SopWA9ltP5onHZOijU4SEZHfa5CSloSEBLFYLJKZmemwHPNJSUkNkQQij+vcrHI8AQQtRETkJ0FLSEiIpKamyrJly2zLrFarmnd38Dgib9Pl9F2ltzFoISLyreqhgoICSUs7M+Joenq6bNy4UfUGwtgr6O48duxY6dOnjxqbBV2e0U1a701E5GtY0kJE5KNBy7p162TYsGG2eQQpgEBl3rx5MmbMGDVU/9SpU1Xj2169esmSJUuqNM4l8hUdE6NV1+ecglLJyi+WptFhRieJiMivec29h84V7z1ERrj4xeWq99A7t/eTIR2aGJ0cIiK/vn571V2eiXxNF1YRERE1GAYtRB5o18Lh/ImI6h+DFqJzwJIWIqKGw6CFyAPdnvfmFKq7QxMRUf1h0EJ0DppGh0p8ZIi6G/TuzAKjk0NE5NcYtBCdA5PJJJ2bVQ7hzyoiIqL6xaCF6Bx1TuLIuEREDYFBC5GH2rVsPZJrdFKIiPwagxaic5TaqpF6xB2f07LyjU4OEZHfYtBCdI5aNY6UEV0TBWNLv/b9mftvERGRZzFoIfKAP1/cXj1+semIpOcUGp0cIiK/xKCFyAO6NY+Vizs1FasmMv2rbeInt/QiIvIqDFqIPOQvl3eUEItZlm7Pkg/WHjA6OUREfodBC5GHdEqKUYELPL14m/x+6KTRSSIi8isMWog86PYL2shF7ROkuMwqt/z7F/ntwAmjk0RE5DcYtBB5kNlskn/dcr70bd1I8ovL5Y9vrJa/Ltwsmw/lqqH+iYjo7Jk0P2kxmJeXJ7GxsZKbmysxMZWDfREZpbCkXCZ9tFGWbs+0LYsOC5KrejSTm/q1lO7NY9UtAIiIAl1eHa7fDFqI6tGv+47Lmyv2ypo9xyS/pNy2vEuzGLl32HlyVY9kQ9NHRORL1++gBksVUQDq2zpeTagaWpt+XBb8ekC+3pKh7lM08YPf5Hhhqdw2sLXRySQi8gkMWogagMVskoHnNVbTE0Wl8vKy3fL2z/tk6udbJchslpv7tzQ6iUREXo8NcYkaWFxEiEy9qovcObitmkdD3Y/XHTQ6WUREXo9BC5EB0Ah3yshOMm5QZdXQo//9Xf6xZIecKq0wOmlERF6LQQuRgYHLtFFd5LaBrdTNFl9fvkdGvrxCThSWGp00IiKvxKCFyODA5cmru8qbt6ZKYkyo7DtWJG+s2Gt0soiIvBKDFiIvCFwu65okz47urubnrUqXrPxio5NFROR1GLQQeQncJbpXSpy6BcDURVtl/f7jYuUoukRENgxaiLyoxOWREZU3XFyyNUOue3213PzvNZJTUGJ00oiIvAKDFiIvckG7BHn9lvPl8q5JEhFikTV7j8tVr6yUDbzxIhERh/En8lZpWQVy17vrZE92oQRbTHL/xe2lV8s46ZAYLYkxYUYnj4jII3jvIQYt5CcKSsrl4Y83qeoie81iw+SFG3qqkhkiokC5frN6iMiLRYUGyet/Ol+evrabDOvYRM5rEilmk8jR3GL574ZDRiePiKhB8d5DRD7QQPfWAa3UBB+tPSCPfbZZThaVGZ00IqIGxZIWIh8THxmiHnGHaCKiQOJVQUt6eroMGzZMunTpIt27d5fCwkKjk0TktUHLiSIGLUQUWLyqemjcuHHyzDPPyEUXXSTHjx+X0NBQo5NE5HUasaSFiAKU1wQtW7duleDgYBWwQHx8vNFJIvJK8RGVQUt+cbmUVVgl2OJVBaZERPXGY2e7FStWyKhRoyQ5OVk1HFy0aFGVdWbPni2tW7eWsLAw6d+/v6xdu9b22u7duyUqKkq9x/nnny/PPvusp5JG5FdiwoNVDyJgFRERBRKPBS1of9KzZ08VmLiyYMECmTx5skybNk02bNig1h0xYoRkZWWp18vLy+Wnn36Sf/3rX7J69Wr57rvv1EREjixmk8SdLm05UcgeREQUODwWtIwcOVK1Rxk9erTL12fOnCkTJkyQ8ePHq4a2c+bMkYiICJk7d656vXnz5tKnTx9JSUlRbVmuuOIK2bhxY7WfV1JSogaksZ+IAkWjiGD1yHYtRBRIGqQyvLS0VNavXy/Dhw8/88Fms5pHqQr07dtXlbqcOHFCrFarqm7q3Llzte85Y8YMNYKePiHYIQoU7EFERIGoQYKWnJwcqaiokMTERIflmM/IqByePCgoSLVjGTx4sPTo0UPat28vV111VbXvOWXKFDXkrz4dPHiw3r8HkbdopFcPMWghogDiNb2H9ComTO5AFRK7RJMEekkLq4eIKIA0SElLQkKCWCwWyczMdFiO+aSkpIZIApGfjtXChrhEFDgaJGgJCQmR1NRUWbZsmW0Z2q1gfuDAgQ2RBCK/bIjL6iEiCiQeqx4qKCiQtLQ0hyH50fsHg8S1bNlSdXceO3as6iHUr18/mTVrluomjd5ERHR2bVrYe4iIAonHgpZ169ap+wbpEKQAApV58+bJmDFjJDs7W6ZOnaoa3/bq1UuWLFlSpXEuEdWOvYeIKBB5LGgZOnSoaJpW4zoTJ05UExGdG95/iIgCEW9aQuTD9x9i7yEiCiQMWoh8uKSlsLRCissqjE4OEVGDYNBC5INiwoLUPYjgZBG7PRNRYGDQQuSDcCd19iAiokDDoIXIR8VHVo7VcpI9iIgoQDBoIfJRTaIrb2Ox4cAJo5NCRNQgGLQQ+ajrU1uoxzdX7JVctmshogDAoIXIR13ds7l0TIyWvOJyeWnpLlVNVNtYSUREvsyk+clZLi8vT2JjYyU3N1diYmKMTg5Rg/huW6ZMmL/ONh8dFiStGkdIy/gI6d48Tu4c3NbWy4iIyNev3yxpIfJhwzs3lZv7t7S1b8kvLpcth/Pk680Z8o8lO2TZdsc7qxMR+TKPDeNPRMZ0fX52dHc1FZWWy6ETp+TAsSJ5/5f98sPObFm+K1su65pkdDKJiDyCQQuRn4gICZIOidFqQpUQgpYfd2ardi4IboiIfB2rh4j8UP+28RJiMcvhk6dkT3ah0ckhIvIIBi1Eflrq0q9NvHq+Yle20ckhIvIIBi1EfmpwhwT1+CODFiLyEwxaiPzU4A5N1OOavcekrMJqdHKIiM4ZgxYiP9WhabREhwZJSblV0rIKjE4OEdE5Y9BC5KfMZpN0Tq4cqGnrkTyjk0NEdM4YtBD5sa62oCXX6KQQEZ0zBi1Efqxrcqx6ZEkLEfkDBi1EAVDSsv1IHm+mSEQ+j0ELkR9r1zRKDTKXX1IuB4+fMjo5RETnhEELkR8LtpilQ1KUes52LUTk6xi0EPm5rs0q27Ws239CyjleCxH5MN4wkcjPdW0eI7JO5D8r0+Xd1fulbZNINcT/1Ku6SJCFv1uIyHfwjEXk50Z2ayb928RLeLBFSiussiMjX+av3q/uAk1E5EtY0kLk55pEh8qCuwaK1aqpuz7/85ud8uWmI/L9jky5tEui0ckjInIbS1qIAmiE3JT4CLk+tYWaX7Y9i92gicinMGghCjCoKooIsUhWfolsOcxB54jIdzBoIQowYcEWuah9gnq+dHum0ckhInIb27QQBaBLOifKN1sz5Y0Ve2Thb4clNMisxnSxmE2qGinIbBKLyaTmo8KCJCEqRM5rEiWJMWESbDGJ2WRSwU9qq0YSGcrTCBE1DJ5tiALQ8M6JEh0WJPnF5XLgeNFZvw96JF3YPkESY0KlUUSIxGEKD5ZGkcHqeUxYkAqGMAVZTGp0XnSzRuATbDarAImIyF0mzU9a4uXl5UlsbKzk5uZKTEzl/VaIqHoni0rl0IlTUlJeISXlViktt4pV0wTjz1VYNfW8rMIqBSXlkplXInuyCiSnoEQtL7dqkp1fov7+XFhOl+pUBjMmW4CDkp/wEItqexMeEiQRwRYJC64MclDKg1Igs1nEhEeTqPnK56fnzfq8VC4zm6RDYpQK1lBCRES+ef1mSQtRgFKlIhEhZ/33+L2z6VCu/HbghJwoKlNB0JnHUjlRWKYCHozCW1ahqTFinCE4woSgqSGgdOmqHslyZfdmEhMedDrIqawGwzh7+rzJJJIQFcqqLyIv43UlLUVFRdK5c2e54YYb5IUXXnD771jSQuTdcKpBgIJSGgQw5RWVJTllDs8rHxHEFJWWS1FphZpOlZZLcZlVNKksCUJpD97PqlU+xxg0tufamc/Sl+H9VuzKVuPUuAtVWH1bx6u2PBjr5pb+LaVxVGi95hFRIMrz5ZKW6dOny4ABA4xOBhF5GKprUAUUZKnswdTQENis2XtMPt1wSNar+zBVBjYVp4MePGJeOx3oIFhateeYmuCLTUfkwwkDVABDRMbwqqBl9+7dsmPHDhk1apRs2bLF6OQQkR9Bu5ZB7RLU5I70nEJZuTtbsgtK5ZN1ByUtq0DGvLla7riwjXRNjj3djgbBWGW1ku3xdICG9jT27Wr0NKjlcuZ1vIR2PedSVUcUKDwWtKxYsUKef/55Wb9+vRw9elQWLlwo1157rcM6s2fPVutkZGRIz5495dVXX5V+/frZXn/44YfV66tWrfJUsoiIzkqbhEg1wejezWXMG6tlb3ah/G1h/fygum1gK3nqmm718t5E/sJjg8sVFhaqQASBiSsLFiyQyZMny7Rp02TDhg1q3REjRkhWVpZ6/fPPP5cOHTqoiYjImyB4WXz/hfKXyztK75Zx0jwuXJJjwyQpJkyaRoeqKiOMZRMfGSKNIoIlNjxYdfeODg2SyNO9oND7KSTIXNlTSi9xsevx/fXmDCO/IlHgNsRFkadzSUv//v2lb9++8tprr6l5q9UqKSkp8uc//1kee+wxmTJlirz33ntisVikoKBAysrK5KGHHpKpU6e6/IySkhI12TfkwfuxIS4R+RI0OO467RvVlubXvw1nmxkKOHl1aIjbIMP4l5aWqmqj4cOHn/lgs1nNr169Ws3PmDFDDh48KPv27VO9hiZMmFBtwKKvjy+pTwhYiIh8TURIkLRuXFkNtTMj3+jkEHm1BglacnJypKKiQhITEx2WYx7tW84GSmYQlekTAh4iIl/UMTFaPe7I4A0siXym95Bu3Lhxta4TGhqqJiIiX9epWbQs2ZohO1jSQmR8SUtCQoJqq5KZ6XhHWcwnJSU1RBKIiLxWp6TKenyWtBB5QdASEhIiqampsmzZMtsyNMTF/MCBAxsiCUREXqtzs8rqod2ZBeq2B0RUz9VD6PGTlpZmm09PT5eNGzdKfHy8tGzZUnV3Hjt2rPTp00eNzTJr1izVTXr8+PGeSgIRkU9KaRShukVjFN59x4qkXdMoo5NE5N9By7p162TYsGG2eQQpgEBl3rx5MmbMGMnOzlY9gtD4tlevXrJkyZIqjXOJiAJN5V2oo2XjwZOqiohBC5GP3DDxbPGGiUTky6Z89rt8uPag3DWkrUwZ2dno5BAF7jgtRERUs/5tGqvHH3dmG50UIq/FoIWIyAsM6dBEDe2Pbs9HTp4yOjlEXolBCxGRF2gUGSK9WzZSz3/YWXlPNiJyxKCFiMhLXNypqXr8fjuDFiKfGRGXiChQg5bnv9kpP+/JkX//tFfdFTrYok8mdYdo9VwtN6nnuGO0vg66TeNO03jEjWuJ/A2DFiIiL9EpKVqax4XL4ZOn5Jmvtp/1+4QGmaVxZIjER4VI48hQ9Twi1CIm/GcSQTijBzWV8/bLK19Tr9q9hvY2Fiw3mcRsMonFLLbn6jWz/prjc7yO9DSLDZdGkcGVAZYZgZepynMEYAy2qCYMWoiIvAQu2C/c0FM+23BISiusUlZhldJyTT1iKq/QbMsrJ822vNxqlYKScikus0pJuVWO5BarydfYB1W2IKoyenKYd1ivmucojQoNsqigCUFRZUBWGUhhHSxLig2TJtGhKmCymCsDJwRd6tFS+Yj1K+edXlePZmkWFybnNYmS8GBL5fqI1qheMGghIvIiA89rrKazVVRaLscKSuVYYakcLyyRHDwvKJVTZRUimiYYmAujc+FZ5eOZ+dP/C4bvcn4Nj1ZNOz1VrlNhrXyOZXi9cv7MupjXTqfp6MliySsuswVaetDlTP9c9eTMUvE1evCighvTmee2RwRClsrXEPxY7JbpQZLt7/XJVPV9HP7e/r3NJhnQtrEM7+JfA7gyaCEi8iMRIUESER8kKfER4u0Q+JRb9SCm8hHBzpngyTG4siJCchl02QVjds/xfih1KimvUO+vv4Z/8DmqROrkKRXg4b2RlorTU+Vzq22ZelQlWpWBmf56ablV9h8rkqz8EofvhtcR0ZWKcf69Ml1u7Jsij4zoKI2jQsUfcERcIiKic4TSJARGetCjJpQ2YdnpUqcqr1mtgvtjul52+tHVMisezwRQVV7TNMnJL5WP1x+0FVihrVRUaJCEBptVg+7Kdkenq8pOP4LeFglz+muYCw+xSFx4sLrFxNhBrQ27frOkhYiIyAMlXN7m6l7J8vTibWrAQjTu9oR+beI9HrTUhfflMhEREZ2zC9olyJIHBktuUZmkZeefbqRdISVllaUxetsj0J/bHtVCvR2TqDZRuafKJCkmzNDvxKCFiIjIj8VGBEtqq3jxBxwRl4iIiHwCgxYiIiLyCQxaiIiIyCcwaCEiIiKfwKCFiIiIfAKDFiIiIvIJDFqIiIjIJzBoISIiIp/AoIWIiIh8AoMWIiIi8gkMWoiIiMgnMGghIiIin8CghYiIiHyC39zlWTt9e+28vDyjk0JERERu0q/b+nU8IIKW/Px89ZiSkmJ0UoiIiOgsruOxsbE1rmPS3AltfIDVapUjR45IdHS0mEwmj0eBCIYOHjwoMTExHn3vQMe8rR/M1/rDvK0/zNvAzFdN01TAkpycLGazOTBKWvBFW7RoUa+fgY3tjRvcHzBv6wfztf4wb+sP8zbw8jW2lhIWHRviEhERkU9g0EJEREQ+gUGLG0JDQ2XatGnqkTyLeVs/mK/1h3lbf5i39SPUj/LVbxriEhERkX9jSQsRERH5BAYtRERE5BMYtBAREZFPYNBCREREPoFBSy1mz54trVu3lrCwMOnfv7+sXbvW6CT5nCeeeEKNUmw/derUyfZ6cXGx3HfffdK4cWOJioqS6667TjIzMw1Ns7dasWKFjBo1So0ciXxctGiRw+toVz916lRp1qyZhIeHy/Dhw2X37t0O6xw/flxuueUWNchUXFyc3HHHHVJQUCCBrLZ8HTduXJV9+PLLL3dYh/nq2owZM6Rv375qtPKmTZvKtddeKzt37nRYx51zwIEDB+TKK6+UiIgI9T6PPPKIlJeXS6Ca4Ua+Dh06tMp+e/fdd/t0vjJoqcGCBQtk8uTJqqvYhg0bpGfPnjJixAjJysoyOmk+p2vXrnL06FHbtHLlSttrDz74oHz55ZfyySefyI8//qhux/CHP/zB0PR6q8LCQrUfIph25Z///Ke88sorMmfOHPnll18kMjJS7bO4KOhwYd26dat89913snjxYnXBvvPOOyWQ1ZavgCDFfh/+8MMPHV5nvrqGYxoByZo1a1TelJWVyWWXXaby3N1zQEVFhbqwlpaWyqpVq+Sdd96RefPmqQA9UP3oRr7ChAkTHPZbnCN8Ol/R5Zlc69evn3bffffZ5isqKrTk5GRtxowZhqbL10ybNk3r2bOny9dOnjypBQcHa5988olt2fbt29ENX1u9enUDptL3II8WLlxom7darVpSUpL2/PPPO+RvaGio9uGHH6r5bdu2qb/79ddfbev873//00wmk3b48OEG/ga+ka8wduxY7Zprrqn2b5iv7svKylJ59eOPP7p9Dvj66681s9msZWRk2NZ5/fXXtZiYGK2kpMSAb+H9+QpDhgzRJk2apFXHF/OVJS3VQOS5fv16Vbxuf38jzK9evdrQtPkiVFGg6L1t27bqFymKJAF5jF8I9vmMqqOWLVsyn+soPT1dMjIyHPIS9/NAtaael3hE1UWfPn1s62B97NsomaHqLV++XBWfd+zYUe655x45duyY7TXmq/tyc3PVY3x8vNvnADx2795dEhMTbeugBBE3AkTpFkmVfNW9//77kpCQIN26dZMpU6ZIUVGR7TVfzFe/uWGip+Xk5KiiM/uNCZjfsWOHYenyRbhoosgRJ3sUTz755JNy0UUXyZYtW9RFNiQkRJ3wnfMZr5H79Pxytc/qr+ERF157QUFB6kTH/JYaq4ZQXdGmTRvZs2eP/PWvf5WRI0eqk77FYmG+uslqtcoDDzwgF1xwgbqIgjvnADy62q/11wKd1UW+ws033yytWrVSPxh///13efTRR1W7l88++8xn85VBC9U7nNx1PXr0UEEMDqSPP/5YNRYl8nY33nij7Tl+mWI/Pu+881TpyyWXXGJo2nwJ2mDgx4p9mzaqv3y9065NFfZbNNDH/orAG/uvL2L1UDVQnIZfUM4t2DGflJRkWLr8AX5RdejQQdLS0lReoiru5MmTDuswn+tOz6+a9lk8OjckR08B9HxhfrsP1Zw4R2AfBuZr7SZOnKgaKP/www/SokUL23J3zgF4dLVf668FsonV5Ksr+MEI9vutr+Urg5ZqoLgyNTVVli1b5lAEh/mBAwcamjZfh26giPQR9SOPg4ODHfIZxZdo88J8rhtUXeBEY5+XqJtGmwo9L/GIiwPaEei+//57tW/rJzSq3aFDh1SbFuzDwHytHto248K6cOFClSfYT+25cw7A4+bNmx0CQ/SYQffyLl26SCDSaslXVzZu3Kge7fdbn8tXo1sCe7OPPvpI9byYN2+e6h1w5513anFxcQ4tral2Dz30kLZ8+XItPT1d+/nnn7Xhw4drCQkJqrU73H333VrLli2177//Xlu3bp02cOBANVFV+fn52m+//aYmHL4zZ85Uz/fv369ef+6559Q++vnnn2u///676vHSpk0b7dSpU7b3uPzyy7XevXtrv/zyi7Zy5Uqtffv22k033aQFspryFa89/PDDqicL9uGlS5dq559/vsq34uJi23swX1275557tNjYWHUOOHr0qG0qKiqyrVPbOaC8vFzr1q2bdtlll2kbN27UlixZojVp0kSbMmWKFqjuqSVf09LStKeeekrlJ/ZbnBPatm2rDR482KfzlUFLLV599VV1MIWEhKgu0GvWrDE6ST5nzJgxWrNmzVQeNm/eXM3jgNLhgnrvvfdqjRo10iIiIrTRo0erg4+q+uGHH9RF1XlCl1y92/Pjjz+uJSYmqoD7kksu0Xbu3OnwHseOHVMX06ioKNW1cfz48erCHMhqyldcBHBSx8kcXXNbtWqlTZgwocqPF+ara67yFdPbb79dp3PAvn37tJEjR2rh4eHqRw9+DJWVlWmBSmrJ1wMHDqgAJT4+Xp0L2rVrpz3yyCNabm6uT+erCf8YXdpDREREVBu2aSEiIiKfwKCFiIiIfAKDFiIiIvIJDFqIiIjIJzBoISIiIp/AoIWIiIh8AoMWIiIi8gkMWoiIiMgnMGghIiIin8CghYiIiHwCgxYiIiLyCQxaiIiISHzB/wPx9VPMv1dnUQAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# La méthode de Newton a le temps de calculer moins d'itérés que le gradient\n",
"# à cause du coût de calcul plus élevé. En terme de temps, le gradient est meilleur.\n",
"\n",
"n = 5000\n",
"x0 = np.ones(n)\n",
"\n",
"maxtime = 15\n",
"xg, fg, tg = methgradientTime(fsize, x0, maxtime)\n",
"xn, fn, tn = methNewtonTime(fsize, x0, maxtime)\n",
"\n",
"plt.semilogy(fg, label=\"gradient\")\n",
"plt.semilogy(fn, label=\"Newton\")\n",
"plt.title(\"Evolution de la fonction objectif en fonction des itérations\")\n",
"plt.legend()\n",
"plt.show()\n",
"\n",
"plt.semilogy(tg, fg, label=\"gradient\")\n",
"plt.semilogy(tn, fn, label=\"Newton\")\n",
"plt.title(\"Evolution de la norme du gradient, en fonction du temps\")\n",
"plt.legend()\n",
"plt.show()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "optinonlin",
"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": "3.13.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}