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@olivierverdier
Created November 4, 2018 09:58
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as pl\n",
"import scipy.io as spi\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%run pca"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"%run femshape\n",
"\n",
"space = Space(order=4, meshsize=3,L=1)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"%run utils"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Saving and fetching data"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"import scipy.io as spi\n",
"ncurves = 200\n",
"npoints = 500\n",
"x,y = randshapes(ncurves,npoints)\n",
"x[0], y[0] = figure_of_eight(npoints)\n",
"spi.savemat('currents_data_200_500.mat',{'x':x,'y':y})"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def load_data(name, ncurves):\n",
" data = spi.loadmat(name)\n",
" x = data['x']\n",
" y = data['y']\n",
" x = x[:ncurves]\n",
" y = y[:ncurves]\n",
" return x, y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Separate a figure of 8"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"x,y = load_data('currents_data_200_500.mat', 20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Separate using the finite element representers"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"curves = np.stack([x,y], axis=-1)\n",
"currents = [Current(space, curve) for curve in curves]\n",
"reps = [Representer(current, scale=.3) for current in currents]"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"pe = pca_data(reps, 1)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"pca = PCA(pe, x, y)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(6,6))\n",
"pca.plot(scaling=.8, shift=(.1,0))\n",
"plt.axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Using the monomial representers"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<Figure size 432x288 with 0 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%run monomials.py"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"ncurves, npoints = x.shape\n",
"cl = (npoints-1)*np.ones((1,ncurves),dtype=int)\n",
"u = representer(x,y,ncurves,cl,npoints,10)\n",
"u1 = np.zeros((ncurves,np.shape(u)[1]*np.shape(u)[2]*2))\n",
"for i in range(ncurves):\n",
" u1[i,:] = np.matrix.flatten(u[i,:,:,:])"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"pca = PCA(u1, x, y)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pca.plot(scaling=.01)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Bigger data set"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"x_, y_ = load_data('currents_data_200_500.mat', 32)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Remove the figure eight:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"x, y = x[1:], y[1:]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## PCA on the FEM representer space"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"curves = np.stack([x,y], axis=-1)\n",
"reps = [Representer(Current(space, curve)) for curve in curves]"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"pe = pca_data(reps)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"pca = PCA(pe, x, y)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-2.4283318318291847, 2.1138948041950494, -2.508876668196168, 2.97113871705593)"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,8))\n",
"pca.plot(scaling=2, shift=(.1,0))\n",
"plt.axis('equal')"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.0321262950668577\n",
"0.6377649133277207\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pca_opt(pca, scaling=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### PCA with monomial representers"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"ncurves, npoints = x.shape\n",
"cl = (npoints-1)*np.ones((1,ncurves),dtype=int)\n",
"u = representer(x,y,ncurves,cl,npoints,10)\n",
"u1 = np.zeros((ncurves,np.shape(u)[1]*np.shape(u)[2]*2))\n",
"for i in range(ncurves):\n",
" u1[i,:] = np.matrix.flatten(u[i,:,:,:])"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"pca = PCA(u1, x, y)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Tfv7zn2M0xmG1jqDBvRK93t4n03g7U1//Fa2tpcTHnY7BMDCzy5SeGfQAItpWB60ByqSU84UQ2cDLQAywDrhCShkQQpiA54HjgDrgh1LK4oGurynDgSnDgevcHPzFHlq3N+AvdNP0eQm090IIg4Yu2ow+xowWZUCz6NHMOqQEwpJwU4BgtY9gadP+zL7x101W+4EofaqhYSW7dv0ZT+N6dDob8XFzSUg4i+joGQe1NKSUhMNeGps2423aSnX1+xTurOfJJ5/nq6+WYrcnM2/eeZx99hmMHj2GhPgzqap6j5rapYQjrdht49Hp+i4LsJQSt2c1nsb17Rl7O04BpAy+oXDHuhXYBjjav/4j8P+klC8LIZ4EFgFPtH9skFKOFEJc2n7eDwejwtAWJMyjojGPigYgEggTrGgmWO4lVNfalvq9vpVAuRfZEkLu6+MWoNmN6GPN2E/NwDo5Dn2CVe2NoPSZSCTIjp3/S1nZi5hNKYwe9VuSk3+wP8X6oYQQ6PV2YqJnEu2aTkvLXj799CkmT07G0/genkaYNNnE35+9m+uvPw0Q6HRR6HU2fL4iNm78KSNzfklKykVHXXcpIzQ2bqSlpYRo10xcruPV38YQNqgBRAiRBpwD3A/cLtp+U04FLms/5Tngd7QFkAXtnwO8DvxVCCHkEEmUoxl1mDIdmDIdHR6X4QgI0e8rhJXvNykl27b9ksqqJWSkL2LEiNt6NFtKCA2rNYsTT7iSP//pdQz6k9DpW/j6q8Xk5Y0jOnomMhIiFG4iFGxECB3BYB3bvr2LnYX3kZlxHZmZP+3VTd/bvJNtW++isWkjGemLSE66QAWPIW6wWyAPA3cB+9rTsYBbSrlvvmMpkNr+eSpQAiClDAkhPO3nHxMpbMUA7M+gKPX1X1FZtYTs7J8zIvvmXl9n3Lhx/PKXd7NgwbXYbDamTp2FxWIh2jXtoPOklERZR7Jr9/9RX/8Vu3Y/yJ69T5GVdTNJiedhMh156q2UksbGAsrK/kVF5Vvo9Q4mTny0R2tMlMEzaAFECDEfqJZSrhVCnLLv4Q5Old04duB1rwOuA8jIyOiDmirKsaOq+j30eidZmdcf9bUWLVq0f4Hfr371K9LS0g47RwiBwzGRKXnPEgw2snXbXdTWLqWw8PcUFv6eqKhROOyTsFqzMRrj0DQT4UgrgUAtzd4deDzraPWXo2lmMtKvJjPz+h5PEVYGz2C2QE4AzhNCzAPMtI2BPAy4hBD69lZIGlDefn4pkA6UCiH0gBOoP/SiUsqngacB8vPzh0T3lqIMFH9rOVbriB7lqDrUvpxVlkY3kzPS2Lt3L2+88QbffPPNEcsZDA5yJz9JWflrfPvt3STEzyMUbqK+/msqKt847HyTKQmnYwrZsbeQkHBWl1OIlaFn0AKIlPK/gP8CaG+B3CGlvFwI8RrwA9pmYl0FLGkv8nb719+0H182VMY/FGWoCIW9NDYW9Lr8gTmrHrvkIvTeRixGI4899hjR0dHdukZK8g8oKnoEITSm5P2jrV6hZkIhD5GIHyGMGI1xamHgMDDYYyAd+SXwshDiPmA9sLj98cXAC0KIQtpaHpcOUv0UZcjaFzxaW8t7lXjwwJxVN766hBOjbUx39WyvciEEOp2FiPwuYaJeH9XpLDDl2DUkRnallMullPPbP98tpZwmpRwppbxYSulvf7y1/euR7cd3D26tFWXoOT7/TQCqqt/vVfl9OasEbVlzD0293h1e73Z8vt04HHm9qoNy7BgSAURRlL7hcEzG5ZrO3r1/Ixzu+YZo+3JWnRhtO2LCw86Ew362fftf6PV2UlMGbZmWMkBUAFGUYSZnxO0EAjUUFT3aq/IpZiPTXbYeB49QqJmNG6+jsbGAceP+iMGgdtYc7lQAUZRhxuXKJyX5EvbsfYaGhpUD8pze5p2sXfdD6htWMG7sH0mIP3NAnlcZXCqAKMowNGrUr7Bas9i46Qaam/tvuFDKCCUl/2D16gX4/VXk5j7To50KlWObCiCKMgzp9XbychcjhMa69ZfR1LStz5/D76+hrPxlduy8l+joGUyf9j5xsaf0+fMoQ5cKIIoyTFksGUyd+iJC6Fi77odUVPybvlg65fXuYNOmm/jq6xnsKX6CSRMfI3fy4i7TlijDz1BcB6IoSh+xRY0iP//fbNlyG1u33UVl1TuMHHk3dtvYHl+ryfste4qfoKr6PXQ6K9lZt5CZeV2PkjUqw4sKIIoyzJlNSUyd8k9KSp+nqOhRVq06h5iYk0hJuYTYmNno9Z0vFAwE6qmtXUZ5xat4PGvR6axkZv6UzIxFGAzdW5muDF9iOGcDyc/Pl2vWrBnsaijKkBEMuiktfYGy8pfx+ysRwoDDMYmoqNGYTUnodFZC4Wb8rRU0ebfS1LQViGCxZJCaejkpyT9Q03O/B4QQa6WU+V2epwKIonz/RCIhPJ611NYto9FTgLd5R/t2t20MhhhstrE4nVOJj5uL3T5R7c3xPdLdAKK6sBTle0jT9ERHTyc6evr+xyKRIJFIK5pmQdPUrUHpmvotURQFAE0zoGmGwa6GcgxR03gVRVGUXlEBRFEURekVFUAURVGUXlEBRFEURekVFUAURVGUXlEBRFEURekVFUAURVGUXlEBRFEURekVFUAURVGUXlEr0RVF+V6QUhIOSUL+MMFAmEhYIiNtuQB1eg29UcNkNaDpVM6v7lIBRFGUYSPQGsJT3YKnpoXG2u/+TzgplYZKH5HIkZPHCgFmmwFnnAVXohV7rFklkTwCFUAURTnm+BoDNFQ201Dp++5jRTPeBv9B55ltBhxxFsw2A4nZDgwmHXqjDoNR46bbfsaHH39AfFw833yxhqA/zNU/uYLCXTsJhyJ4mxux250s//Br4tLtGEy6QXq1Q5dK564oyjGhttTLli/K2Lu1jsba1v2P640a0UlRRCdZiU6KwpVoxZlgwRlnwWjp/D3yF198gc1m48orr2Tz5s0HHQuHItx8463owmauOP8GNJ0gdbSL5Jyu90KRUvKvlXt5fW0pdc1+nBYDI+Nt5KW7mJYdy7hk+5Bv1ah07oqiDBsr39nNmveK0Rs10sbGMOmUNGKSo3AlWbFHmxFaz2/Is2fPpri4uMNjmk7wzvtvsWzZMlKTUtm1tpqSbQ3EJEdhsh45Y/E/V+7lN29tZmKqg6kZ0bh9Qb7ZXcdbG8oByIq1cs7kZM6ZlHJMBJMjUQFEUZQhrXhTLWveK2bsjCROuHgU5qj+Tzn/5ZdfkpiYyKhRo6gtaaK1OYjVbsRg7vqW+dqaEnLTnLx14wkHBYcKTwufb6/hvU0VPPn5bh77bBdP/vg4HBY9oxPtxEYZj7lgMmgBRAiRDjwPJAER4Gkp5SNCiBjgFSALKAYukVI2iLbv7CPAPMAHLJRSrhuMuiuKMnCKN9ZitOg55Yqx6HQDs/LgpZde4tJLL2XvljoqixpxxJoZmZ+A1o2WTrm7hdPHJx4WDJKdFi6dlsGl0zKo8/r5aEsVFqOO1UX1rCqqJybKyKgEO6MTbcTaTP310vrUYLZAQsAvpJTrhBB2YK0QYimwEPhUSvmAEOJu4G7gl8DZwKj2/9OBJ9o/KorSTcW1zXyzu46NpW5KG1q4cmYm5e628QS9TmAz6XGYDSQ6zGTGWokyDX4nhabT2qbbDtBwbSgU4o033uDfz31EZVEjSdkO0sfFdLubzKjTCISOXNlYm4nLpmcAkJ8ZTWGNl51VTawsqmNlUR33X3EqDocDq8mAyWhgqI7lDtpvh5SyAqho/7xJCLENSAUWAKe0n/YcsJy2ALIAeF62jfr/RwjhEkIkt19HUZROSCn5YHMlT32xm4ISNwBOi4GsuCisRj3xdhMSCIYieFtDlDW0UFDqRgjB2EQ7J4+Jx2wYvBlImRNj2bS8lG0rKpg4O/Wor9dUV4OnuhpnQkKHxz/55BNyskZhDDlJG+MiZVR0j66f4DBT7m7p9vlRJj25aS5y01w0+0MUVnv5vRBc/fu/Y3PGEGczsXJ3HaMS7cREGXtUl/42+G8vACFEFjAFWAkk7gsKUsoKIcS+n3IqUHJAsdL2x1QAUZROVDe28vNXNrBiVx0j4qP41byxnD4+iaxYa6f97REpqfMG2FbRyIYSN75gmPPzUgatfz5jQgypY6L5+rWdxKXbSMp29vpaTXU1bPl8GTIS4Zqf/JWNOwupq68nLS2Ne+65h0WLFvHyyy9z6qx52KJNJI/setbVoUbER/F1YW2v6hdl0pOb7sJq1PHjGVk0hE3srPLyze46vtldR7TVSE68jXHJdqKtxm51qfWnQU9lIoSwAf8Gfi6lbDzSqR08dlg7UQhxnRBijRBiTU1NTV9VU1GOOaUNPi54fAXr97q5/4KJLL3tZK6bnUN2XNQRg8G1ixYxISedGy6cw+zR8eypa+aGX/wXqamp5OXlkZeXx/vvvz9gr0MIwRmLJmB1Gnn74Q0Ub+rdzRnAU12NjESQUnLPz29izfJlBINBSktLWbRoEQCLn/k75532I6ITOw+yRzI60U5Vo586r7/rkzshhODCc+dx7QVzca//gEUnZjNnTAJ2s551exv4bHs10//wKb96cxPLt1fjD4V7/VxHY1ADiBDCQFvw+JeU8o32h6uEEMntx5OB6vbHS4H0A4qnAeWHXlNK+bSUMl9KmR8fH99/lVeUIazZH+LKxatoag3y2k9ncvn0THTdfLe6cOFCPvzwQwBy05xkxFjZU9fMop/dxIYNG9iwYQPz5s3rz+ofxuowcuEdx+FMsPDe4xv5+vWdhII9v2k6ExIQmoYQAqFpHXZjBQNt1zWYe9dtNyW9rdWyob27sDe+/vpr1q1bxwcffMBjjz3G+lXfkJvu4sKpaVw3ewTTsmKYlhXDkvVlLHx2Nfn3fsKdrxVQXNvc6+fsjUELIO2zqhYD26SUDx1w6G3gqvbPrwKWHPD4laLNDMCjxj8UpWN/+GAbRXXNPHVFPhNTe9blM3v2bGJiYoC2d8JnTkjCoNPYWOph+fZq3L5Af1S5S1EuExfecRwTT0plwyclvHLf6h63Ruyx8Uw4+VTSJ0xmwsmnYo89/E1mOBQB2vJj9cakNCc6TbB+b+8DSEpKCgAJCQlccMEFrFq1av8xs0FHRmwUj10+lbW/OZ1nFx7PmROTeH9TBec//jUNzQP38xnMFsgJwBXAqUKIDe3/5wEPAKcLIXYCp7d/DfA+sBsoBJ4BbhiEOivKkLe7xstLq0q4ckYmM3Nij/p6USY9E1OdfPPOv7js7NmceeGP+NcXW9hT18xAZ7IwmHScfNkYzr0lF4D3HtvIO48WUFPS1O1r2GPjSRs3ocPgARAJt72m3iZVtBr1jEu2s3ZPQ88Kespgzwqay3fS1NT2epqbm/n444+ZOHFih0XMBh1zxibw4MW5PHrZFNy+IJvLPb2qd28M5iysr+h4XAPgtA7Ol8CN/VopRRkG/rGiGJ0muPHUkX12zVtuupH//d3/4AuEuekXd/P4A7+j5vb7ibeZOHFUHJmxUX32XN2RMT6WS38Tzablpax+r5hX719NzpR4jp+fTWyq7aiuHWlvgWhHsebkhJw4/v51EV5/CFt3pkJ7yqDgJYiEqap0c8F9S0BnIBQKcdlll3HWWWd1eYltFW1BJ2sAfxZDYhaWoih9IxSO8O7GCk4fn0iC3dxn101MTATAbtFxz123MH/+fE4fn8jq4gbeXF/GzBGxTB9x9K2dntDpNfLmZjBuVjIbPi2h4NMSdm2oIWdKAlPPzCAh09Gr6wZa28ZAjL0cAwGYMzaBp77YzVc7azhrYnLXBdx7IBIGIoxIclHw3t8gc1a3n6+otpknlu/ilDHxpMdYe13vnlIBRFGGkW0VTdQ3BzhzQlLPC3vK2m5krszDDlVUVJCc3HYjfPPNN5k4cSITUpyMSbTzybZqvtldR2q0hbTogbt57WOyGph+7ghyT01nw9K9bFpeyq511aSOcTHl9EwyJsT0aDaVlBJHrBljN9KWdOa4zGgcZj0fbq7sXgBxZYK2oi0nh6br8GfQmbV76rnpxfUYdIJ7F3Tc1dVfVABRlGGkoLRt4HbfTKBuO6AL5Uf33sjyLeXU1n23PmL58uVs2LABIQSaecVwAAAgAElEQVRZWVk89dRTAOh1GnPHJVBU28zW8sZBCSD7mKMMzDg/h6lnZrLly3IKlpXw7l8LiEmJIm9uBqPyE9Abu25VfP16IaFAmLEzu3Hj74RBp3Fubgqvry3lnpYgTksX+bucqZD7o+8CuLPrBZOF1U08sXw3b64vJdlp4cWfzBjQ1geoAKIow0q5uwW9Jkh1WXpW8IAulJd+cylkn3RQF8q+NRId0es0YqKMNPlDvax13zJa9Ew5I4PJp6axc00V6z/ey7Lnt/H16zsZMz2J8SemdDpO0ljbQkWhm6lndb8F0JkfHp/Ov1bu5Z2Ccn48oxvXc6Z2GTjqmwMUVntpbA1y7XNrMBs0rj4hm9tOH929sZY+pgKIogwjdd4AMVG9WKF8FF0oAL5AiARH34259AWdXmPsjGTGTE+idHsDW78qZ/MXZWz8rJS4dBtZk+JIHxdDbJoNo0mHu9rHp89tQ2fQ+iRlyqRUJ+OSHbzwzR4un57Rq0WJUkpqvQEKq5vYWe2lvn2K7uQ0J7+aN5aLpqYNauJFFUAUZRiJSIm+N+ktetGFso/bF8DTEmRyWs/TfgwEIQTpY2NIHxtDizfA9v9UsntDDWs/KGbN+8UHnaszaJx+zXhs0UcfDIUQXHtiNr94rYDlO2qYM6bj3FuHklJS0+RnR7WXwqom3C1BBJAabWFyWgI58VHYzQZOHZt41HU8WiqAKMowotMEoS72/e5UN7pQOrKprG3dwejEo5s+OxAsNiN5czPIm5tBizdAVVEjRRtr2fplOSdeMoqRxyUQ5ey7d/Tn5qbw54+289Tnu7oMIM3+EBtL3ZS1J2IUCEbE20iLtpDisgxqQsvOqACiKMOI02rA7QsSCkfQD8DeGW5fgA0lbsYmObCb+3+jp75ksRnJmhRH1qQ45lw+tl+ew6jXuPakbO57bxtLt1Zx+viDWw1NrUE+3lLFv9eVsmJX3f7Hbzglh2tPGjHksu8eSgUQRRlGctNcBMIRfvXmJs6fksq4JAfR/XQTavaHeKegHL2mMWvkwK4BOZZcNSuLf68r4/ZXN3D32WPJjImiqK6ZFYW1LPu2Gn8oQnqMhdvmjuai41IHdSZbT4mBTkUwkPLz8+VQ3YhFUfpDOCL533e28OKqvQTbU3LYTHoSHSaSnRYSHWbibEZibUZio0xMzXThshgxGTRMeg2dduRWi5QSrz9EaUMLO6uaCEs4ISd2yA2gDzVl7hauf2ENm8u+Szie6DBxxvgkFuSlcFxm9JDazlYIsVZKmd/leSqAKMrw4/EFKSh1821lI+XuVio9rVQ2tlLV2EqdN0AgHDli+Zz4KCxGHRaDDr2m0RIM4wu0BQ5fe7baE0fG8dtzxzM60T4QL+mYJ6Vke1UTbl+QFKeF9BjLkAoaB+puAFFdWIoyDDmtBmaPjmf26MMTBu5rRdR5A9Q1+9s/Bqjz+nn262LqmgOMTXbQGgjTEgwTDEewm9taMbNy4hiVaOOkkfFkxB47XS1DgRCCsUm9S68yVKkAoijfM0II7GYDdnPbtrYHuunUUYNUK+VYNOg7EiqKoijHJhVAFEVRlF5RAURRFEXpFRVAFEVRlF5RAURRFEXpFRVAFEVRlF5RAURRFEXpFbUORFEUIjJCZXMl1b5q6lrrqGupIzc+l/rWesIyTDgSJiIjCCHQCR06TYdBM2DRW7DoLVj1VuxGO1GGqCG7ulrpeyqAKMr3TDAcZEvdFjZUb2Bz3WaKPEXsadyDP+w/6Lx7T7iXquYqdJoOndChCQ0pZVtAkWFCkcN3INRrelwmF0lRSeTG5+I0OQfqZSmDQAUQ5XtDSokMRZDBCJpBA732vXm3HAwH+bTkU5YWL+XLsi9pCbXtOZFqSyXHlcOM5BlkObNIjkom1hxLjDmGeEs82iHJFa+55hreffddEhISKNhUQGuolZZQC4//9XGefepZ0MGUk6cw94a51LXUccGoCwbj5SoDRAUQZdgLuf14vyjFt6kW51lZhBtaARAmHTqXCX2cFUO8BaEffkOCoUiIV7a/wrObn6XKV0WMOYb5I+YzK2UWeQl5xFnienS9hQsXctNNN3HllVeiEzqiDFGs+moVX3z0Bd9u+RaTycS3e75luXu5an18D3QZQIQQDiBeSrnrkMcnSyk39lvNFOUoyWCExuUlNC0vAcAyPhZjmg2ZEoUMRAg3Bgi7WwlV+WjVBPp4C4bEKPRxFkRvtoUdYhpaG7h52c0U1BRwXOJx/Hbmbzkh5QR0Wu93tps9ezbFxcUHPfbEE09w9913YzKZCEVCFLQWYNKZmJky8yhfgTLUHTGACCEuAR4GqoUQBmChlHJ1++F/AFP7t3qK0jutu9y43ywkVNuCNS8ex5lZ6DvY51pKydVXLOT9D94nzhHDf575GPQaW+t2cesf7sIfCqDX63n88ceZNm3aILyS3glHwtzwyQ3sdO/kjyf9kbOzz+637rodO3bw5Zdf8utf/xoMcMfv7uDi2Rdj0Vv65fmUoaOrNvuvgOOklHnA1cALQogL248d+2/RlGEn4g/T8FYhtc9sQkYkcYsmEnPp2A6DB7Rlpr3mukV8uPQjtCgD1rwEDPEWfvWH33LXhTfw5V/e5b+vu5M7b7+DY2nvnM9LP2dz3WZ+N+t3zBsxr1/HekKhEA0NDbyz7B1+8T+/4PZFtxNliOq6oHLM66oLSyelrACQUq4SQswB3hVCpAGD8tckhDgLeATQAX+TUj4wGPVQhp7WXW4aXt9B2O3HdmIqjjMy0Yxdd9cc2C2jj7Ogj7NgiDHTGivQOU3U76kmwRhN88pKjKk2DElRCMPQHi8p8hQBcHLayX1yvWBFBcGycgypKYcdS0tL47wF57GxdiN5+XkY9UZqa2uJjz98LxJleOkqgDQJIXL2jX9IKSuEEKcAbwET+rtyhxJC6IDHgNOBUmC1EOJtKeXWga6LMrT4Cqqpf3k7+hgz8ddPxpR1dAO4Dz/yCGeeeSZ3y/8mEomw/N8fg4DW7fW0Frqx5sajc5mG7FjJmJgxAHxQ9AGXjLnkqK4VrKjAs2QJMhxG6HQEp04lIiN8tvcz9jTuIfq4aB565SHm3zCfUFWI5tZmKqmkrr4Og2bAoBkw6owYNANmvZmIjGAz2L43M+CGs64CyM84pKtKStnU3go4ut/K3pkGFEopdwMIIV4GFgAqgHyPhb0BGl7fiTHTQdw1E7vV6ujKE088wf/7f/+Piy66iFdffZWf/fetfPLJJ4Qb/fiLG4m0hgiXBDAkWtHMQ28y46yUWUxPms4Dqx4g2hzN6Zmn9/pawbJyZDgMUnLd3/7G18VF1Hk8XHj8hVz9i6u5+fqbue/2+7jvB/cRExXDg088iFlvJhQJ0RxsJhgJEpFtW+jajXaW7V2GTuhwmpy4TC4SrAkkWhNJjEpEr/XuexmREYo9xVT5qnj525eZljyNbGc2idZEEqwJKmD1kyPuiS6EGAkkSim/PuTxk4DyQ2dm9TchxA+As6SU17Z/fQUwXUp50wHnXAdcB5CRkXHcnj17BrKKyiBoXltFw2s7SLhlCsYUW6+uUVxczPz589m8eTMATqcTt9uNEIJIJILT5WLj7gqC4QiagFSbGa2uFaETICXG1KG3L7jH7+GGT29gY03bZMnPf/g5MeaYHl/nuxZIBKkJPp8IkYQYzs46G4epbYtWKSVPbXyKi0ZdRLz14K4rKSVLlixhx84djBw5krGzx+L2u/H4PdS31uPxewBIt6ezdM9Szss5jznpc7o1W8wX9PHkxid5a+dbNPgbOj3PqreSGJW4P1hdPu5ypJSY9ea2VpLOgIa2f9V9SIa++yjDRCIRIkQwakZsRhsJ1gRMOlOPv5fHir7aE/1h2gbSD9XSfuzcXtTtaHT0FuKgCCilfBp4GiA/P//YGfVUei3SHARAH9vxQHlnPB4Pbrcbl8t12LGUlBSWfbYcV04uL775Hq6kDJZsKNt//IzxiXiDIcbqTUS21rOzJUB0nJU4mwnjEFlP4jQ5+fuZf+f4fx6PRHLum+dyR/4dnJtzbo/e6RuSk3EuWEDVrs18IwvREhM4L2f+QTdQIQQOo+Ow1ez7jk2ZMoXp06ezcuVKxseOP+h4a6iVKl8VHr+HLXVb+KzkM0a6RnLfifcxIbbznvJgOMhPlv6ETTWbmJs5l9lps0m3p+Pxe4i1xBKKhKj2VVPtq6ayuZIqXxXVvmpWVa5ietJ0Sr2lB13vhd+9wOYvNmOPsfPfr/83AOuWruO9J9+jqqiKO1+4k8wJmQBoQmNM9BhOSD0Bo87Y7e/lcNPVb1FWR2s9pJRrhBBZ/VKjIysF0g/4Og0oH4R6KEOIMLW9U420hNFM3bsxejweCgoKiEQi3HvvvWzZsoW6ujrS0tK45557ePrpp7n6+htp8QeIslh48JHHOCk/HZNeIyLBpNdwtwTxRCQ2oKHYw9LiOgCirUbi7SbibEZiokzERhlxWgxogzBeYtKZ2HjVRtZVreOhtQ/x2xW/ZfHmxVw3+TrmZc/rdiCpd2i8Z99NnCWB+YcEj31SbCn4Qj6klId1F2VmZuJ2uzu8tllvJtPRdmP+6KKPWLpnKQ+ufpCrP7yaf5z1j8MCzj4fFn/IxpqNPHDSA5wz4pxuvY59IjKCL+ijNdxKKBIiGA4Se10sjl84uO3627h49MXoNB35Ip8bz76RW2+8lfNyzmPS+El4/B6KPcVsrttMIBLgzKwze/Tcw0lXvz1Heks3GJO8VwOjhBDZQBlwKXDZINRDGUL2rSD372hAPy2pW2XcbjeRSFu//G9+8xuys7PJzMzcf3x7ZRM3/eV1ThwZR35Wx90+DosBKSVNeo3cuChSEs3ccsP1fPXpR0S5Yrnz6XcAaG5088L9t+GuLic5LZ0HHnuWrJQEEuwmXFbDgPTNT02cyvNnP8+yvct4suBJfv3Vr3my4EmuHH8l5+Wch9Vg7bRsS6iFD4o/IMoQxbwR8zrtukmzpRGSIXwhX6+n8eo1PWdnn83xScfzg7d/wF/X/5XH5z7e4blb67Zi0Vs4O/vsHj+PJjRsRhs2vuvy/OG8H1JcXIxe0+/vhpuWO23/+Sa9CYfRgcPoIN2ejl7Ts6F6A4Fw4HvbCumqrb1aCPGTQx8UQiwC1vZPlTonpQwBNwEfAduAV6WUWwa6HsrQorO3/fG2bKvrdhmXy7U/z5OmaYd1Y20u9+CyGDguM/qI15H+MIQimGLMjIi3cdfN17Psk4+Jthq44ZSRXHp8Brs++RcnzzmVp975ipzcGfzpjw/wweYKnvummGe+3M0HmyrYXeMlEunfHldNaMzNnMur577KI3MewWF0cP/K+5n7+lweWvMQFd6KDsutKF9Ba6iVs7LPOuLiwBRb2xTfRn/jUdc1zhLHlIQp7G3a2+k5Zr2ZYPi7AfqBZtKZkO3/vq+6aoH8HHhTCHE53wWMfMAIDEqWNCnl+8D7g/HcytBkGulCGNvyWnWX0+kkNzd3/xiI0/ndtN9wRFLW0MKUDNcRWwcyFCHs8aNZDRiS2t5xH7imxKjXSHKa+frTD1m+fDnJyclM+5/bOOWUU7h8+l+pbGylvKGForpmtlc1MTbJgUmvMWdsQu++Ed2kCY1TM05lTvocCmoKeGHrCzy/9Xme2/ocs1JmsSBnAXMy5mDSmfAFfXgDXk5MPbHLvFlWgxWn0bk/S2/E5yPi86FZrWhWK3q9noqKjoPUoVpCLayuWs3M5M7ToYyOHk1Ihthcu5m8hLzufwP6QERG2NGwgzhL3LAeTO/KEQOIlLIKmNW+gHBi+8PvSSmX9XvNFKWbhCYwJFkJVjT3qJzT6TwocOzT4AsQkZJ4e+c3BhmKECj3Igw6LJPijrgepKqqiuTkZACSk5Oprq4m3m4i3m5iUqqTcESyu8bL7tpmrv7Han4zfzyLTszu0WvpDSEEeQl55CXkUeGt4LUdr/HO7ne484s7sRvsnJZ5GiadiVe2v8Lb57/drWtWt1SzqmIVV8afQ9OSt/evHXEuWECt389jjz3Gz372sy6v89K3L+Hxe/jR2B91es6JqSei1/R8VPzRUQWQIy2S7MyaqjXUt9ZzRtYZvX7e4eCIXVhCCLMQ4ufARUAAeEIFD2UoMmY4CJQ0EfYGjvpaLYEwAFHGw99fSSkJlHsJ1rRARKKPNe/vQustnSYYlWhn7rgEzpqQxL3vbmX93s6npPaHZFsyt0y9hY8u+ohnzniGU9JP4dM9n/LK9lcA+NOqP/HclufYUrelw31A9ok2RROMBKkv371/7YgMR7hs4UJmzpzJ9u3bSUtLY/HixZ1ew+P38LdNf+Ok1JOYmth5uj270c4ZmWfwxs439k8F7ql9U5SbV/4Hz5IlBKurj3i+lJKVFStZU7mGsTFjyXHm9Op5h4uuurCeA4LAl8DZwDjaurUUZUiJmpaE9+syPO8XEX3x6KMamN5XNHLAGikpJeH6Vlp3eYg0+rHkJWCIt7cN4HvKwL0HXJngTD3seomJiVRUVJCcnExFRQUJCR13Uek0jQcvyeWbB+p44Zs9TMk48vhLf9CExozkGcxInkEwEuQv6/7CP7b8g0JPIV+VfwVAlCGK3PhcRkePZqRrJNnObKJN0QghaAy0jX/oExIROh0yHEHoNF78xz8wtLfCurJ482K8AS+3Tr21y3OvmXgNHxR9wJMFT/LLab/s8es9dJHkiuJi6jye/bPxYmJiuPnmm6mpqeGcc84hfUw61/zlGsbHjuektJO+94sTuwog46WUkwCEEIuBVf1fJUXpOUOCFfucdJqWlSDDEue8bPTO3vVNR1uNpEVbCIUjhH1Bwp4A4boWIv4wmlmHaUQC+lhz282jtREKXoJIGLQVkHt4l8t5553Hc889x913381zzz3HggULOn1um0nPlAwX26uaelX3vmTQDFw14Sr+te1fTEuaxi1TbmFd9TrWVq2loKaAF7e9SCBycIvv3hPuJcuRRVzaSEILbPu7hrobPCqbK3lx24ucm3Pu/nQsRzImZgwXj76YF799kfk584+4bqTD15iasj/QPX3ttTgXLDisrhdccAGtoVY+KPqAiuYKZiTPYErClO998ICuA0hw3ydSypD6hilDmeP0TIReo/HTvbRsrMGU7cSQZkfnMKKZvlvVLCMSQhFkuK17RYYktH+U4bYdCx3rK4igUdHWm4Uxw07U9GQs42IPTqRYtbkteBCBCPzoioUsX72Z2tra/e9i7777bi655BIWL15MRkYGr7322hFfh6clSFQ317P0tzhLHFeOv5LFmxczI3kG5+acu3/abCgSoqSphD2Ne2gKNBGKhDgp9SRizDEIITAkJ3c7cOzzx1V/RErJjXk3drvMLVNvYXnpcu78/E5env8yDqOj22X3LZI8UqBrDjazpHAJTYEmTs88nVHRo7p9/eGuq1QmYWDfyKSgbe2Hr/1zKaXs/k9qEOTn58s1a9YMdjWUARaqa6F5dSWtO91tA+vdmR6rEwidhtAL0GmUyTBrfa1cumAs9nFx6BydjHN4yg5ogejaWiAddGN11946H6c8+Bk3zhnJL87o+h34QAhGgvx06U9ZU7WGX0//NRePvrhf3n2XNJUw74153Dr1Vq6ddG2Pym6o3sDVH17NrNRZPDLnkV7n1DpUa6iVtwrfoinQxDkjztk/VXm4624qkyMGkGOdCiCKjEgiLSFkILw/EY4Qom0/dJ1oG8PQicNuiMu3V7Pw2dX87cp85o5PPPKTdDEG0l2RiOSqZ1exurie5XfMIcnZs9Qs/ckX9HHH53fwZdmXzM2Yy13H30WyrWetiyOp8FawpmoNr+94nb+d+TcMmqHH13h1+6vc+597OXfEudx34n1o4uhTynxc/DG7PbuZP2I+afa0o77esaKvcmEpyjFNaAJdlAGienZDmpUTh92k56MtlV0HEGfqUQUOgGA4wtriBr7cWcsDF04aUsED2tZ4PHrqozy/9XkeXf8on5d+zvkjz+fCURcyIXbCUbVISptKWV+9Hm/Qy8NzHu5V8AC4ZMwl1LfW89iGx4gQ4d5Z92LQ9e5aAIXuQgrdhUxPnj6gwUNKSWsoQlNLkEA4sj91jsWgw2bWow2hoQQVQBSlA0a9xmnjEli6rYpQOIJe1z8JEqWUFNU288WOGmxmPb+eN45Lp2X0y3MdLZ2m4+qJV3NW1lk8tfEp3t71Nq/teI2kqCRmJM8gPzEfl8nFrNRZXQYBKSWbazfz9ManWV66nNz4XP5y6l+INh/dzLPrJ1+PXtPzyLpHqG+p588n/xmnqed7wwTCAQobCpkQO4EpCVOOqk7dtaXcQzAcYd1eN40twQ7PMejaFqeOSrAxOtGO2XD0WxccDdWFpSideG9jBTe+uI7Xfzqz03xYvdXsD7Gjqomt5Y3UeP04LQbmT04m3j60Wh5H0hhoZGnxUr4u/5qVFSv3T+GFtlXiOc4cspxZuEwu7EY7oUiIxkAjRZ4iVlWuoqSpBLvBzqJJi7hqwlV9Nm4B8FbhW9yz4h4SoxL50+w/MTl+co/K3/vNvby+83VeOuelTpM59gUpJV/srOWxzwpZVVTPQ5fkotME6TFtmZ0tBh2agJZgmMaWEFWNreyt99HgC2DUaRyXGU1+Vgy6Pk7UqcZAUAFEOTpuX4Ap9y7lllNHcdvpo3t9HSklzf4Q7pYgtV4/NU1+PO3vMF1WIznxNjJjrIOSrbevhCNhttZt5aG1D5EclYzb72aXexflzYcny3aZXEyMm8ic9DnMy56Hzdi7PVy6srFmI3d9cRdVzVVcMeEKfjr5p0dMGrnPe7vf4+4v7+bK8Vdy5/F39kvdADaVevjDB9tYsauOVJeFhbOyuGpWVpfbAUgpqWnys6q4nsJqL6kuCwvyUvt0GwEVQFABRDl6Fz2xgtIGH/9cNJ1RiZ1vGhWJSGq8fkrqfZQ0+Cipb6Gk3seOai87q5rwta9uNxva3jXOHBHLmROSjnjN4SAYCdLob6Qx0IhBM2Az2HCZD99/pb80Bhr58+o/81bhWyRaE7l20rWcP/J8zPrDW3pSSl7d/ip/WPUH8hLyeOb0Z45qDKXTOrUG+b+PtvP8f/YQbTVy86kjuWx6BiZ9z7ujtlU08vGWSkYm2Dhnct/NEFMBBBVAlKO3uczDjxevxO0LMjLBRqrLgtWo44PNlQCMTbJT1xygoTlA6JDpwgl2EyMTbIxJsjMuycGYJDtjk+29ulH0RigYxtvgx9vgp9ntp9UbJOgPIzSBxWbAmWAhLt2OyTL8h0LXV6/nwTUPsrFmIy6Ti9MyTmsbHLelEZZhdjTs4K3Ct9hUu4kTUk/goZMf6lZrpac+2FTB/7y9hRqvnytnZPKLM8fgMHcdpD788ENuvfVWwuEw1157LXfffff+Y6uL6/m6sJZLj08nydk3u2yoAIIKIErfqGny89raEtbtcVPj9dPsD1FY7QXg9PGJ7RtHGUlyWkiPtpAeYyXVZRnQAU4pJU11rUgpqa/w4W1opaWprZtMABaHEYvNgMGsIxKW+BoDeBv8CA0SMx2kjo5GZxgaOyn2Fykla6rW8Nr21/i89HN8Id9Bx7McWVw98WrOH3l+n0wBPpCnJcj/LNnMWxvKmZDi4PcXTCI3vXstsXA4zOjRo1m6dClpaWkcf/zxvPTSS4wf3zY2E45IFn9VxIQUByeMPHLG5O5S03gVpY/E203ccMrIwa7GQSIRSV2Zl4pCDxW73FQUemh2+zn1qnH4PAFs0SZiU2zYok1EuUzoOugf9/uClO90U1XUSEOVj5HHJRDVy/QvxwIhBMcnHc/xSccTCAco8hRR0VyBJjQyHZlk2DP6ZYHkf3bX8YtXC6hsbOW2uaO5cU5Oj2b1rVq1ipEjRzJixAgALr30UpYsWbI/gOg0wYQUBxWeFsrdLaS4Bm6vPxVAFOUYEQ5FKN5Uy/b/VFK2vYFAa9u4ii3aRMooF8k5TrInx2Gy6g+6EV5zzTW8++67JCQksHnzZgDuvPNO3nnnHYxGI5npWdz1k/v59pswo6clYY85dmaC9ZZRZ2RMzJhu5dvqLSnbWga/f38bGTFWXv/pzF4lyCwrKyM9/budvNPS0li5cuVB50xMdVLhaeHl1SXcfhQTPnpKBZD/3969x0dZ3Ykf/3znnmQymZAbuUAI4Y4gIAgqXqqCohZra/1p3XrZvupqtXXb7d2+tnXdbmv7q9qtu2sv8lNXt2ixKlrXG1pLtQqCINeQQLhEEnKf3CZze87vj5lggECSgTAJfN+v17yYOc955jknk+Gb85zn+R6lhjkrZrH1r/tZ+6fddLWFSc9yMXFeAYUT/BROyMKXc+y/OG+55RbuuusubrrppoNlixYt4ic/+QkOh4PvfOc7vLD6CW666m4q1x5g2sIiPIO88VIdyrIM9zy/md+v2cuSM0bzfz9/ZtL5zfqaZjh8pJSV5mS0z8PPXqngqxdPwDlE9y0dTgOIUsNYZ2uIV3+3mdqqAIUTsvjUF6cwdtoobIP4D6L3Kok9Fi/+ZCGkBQsWsGLFCibPL2DL6v3s2tDA1HMLNdvscfiXl7by+zV7ueOicr61eHJyl2gnUuSU+N3s27fvYHFNTQ1FRUdecVWe76W+PcTLm2q5etbxZUYYqFN71kypEayrLcxzv1hPw74OLr11Gtf80xzGzcgdVPAYiGXLlrFkyRLc6U7GTBtFR0uIlrqu/ndUfXqrop7H3t3NlxaW8Z3LpyQfPDb+HqpXM8++jcqK7VRXVxMOh1m+fDlLly49YpfRPg8T8r08+PoOwtGTs068BhClhqm3ntxOR2uIq++exeT5o4dkRPDjH/8Yh8PBjTfeCEBuiRd3moP63W397KmO5qn39lDsT+M7l09J/k1a9xxcJsBhg4d/9FUuu+wypk6dynXXXcf06UeueyIi3HPFVHY3dfHke3uSP/Yg6CkspcDv65kAACAASURBVIahhr3t7P6okQWfGc/o8YPP5TQQjz/+OC+99BKrVq06GJxEhJwSL/srW4mGYzhcqc21NBI1dIQpyU47vjvD/aXxBcoswGbnimtu4IpbvtnvbhdNzuP8ibn8clUl18wuJjvj+JZb7o+OQJQahnZvagSB6QuTP5fd3tRAzbYttDc1HLHtlVde4f7772flypWkpx96w5wvJ34VVkdLKOljn87OGZ/D2t3NvLerKfk3ySqOry1Tdv6g1pgREX5w5TTauyM8+tfq5I8/QBpAlBqGOltDeDKceLzJXQ3V3tTAlrffZN+Wj/jc1Z9hwfz5VFRUUFJSwqOPPspdd91Fe3s7ixYtYtasWdx+++0H901PLJ4V7Og7I6w6tq98qpzSnHS+9Nh7vPTRkbnABiyrGErPHfRSAZMKvORnevhgT3Pyxx4gPYWl1DDk8ToJd0WJhGM4kziNFKivx1gWxhju/ce7GDN9JiVTPzlv/qUvfemo+zpcduwOG+EuDSCD0drdyorKFby17y26Cndiy+vku+tt3Ls+nzmF07lywsVcUXbFCc063FvMsvhrVRM3L1sDwNJZQ796ogYQpYahGReVkJWfTldriKz8wedkysrPp2abDSwLsdnIys8f1P4uj51IKDbo456OjDH8YccfeGDdA3RGOpmRO4PPTLganyuL93fX8WFtJX/dt5Z361aBEdx2D9NyplCcWTzolCmWMQTDMTpDUTrDUdq7ozR1hGnsCOGw2fj6MxsAEOGk3FCoAUSpYSjd5yIWsaj+qJHpFxQPehSSmZPH9AsvJlBfT1Z+Ppk5eYPaX2yCNZC15BW/+OAXPL71cc4tOpdvzf0WE7I/SXtz52xo6Qzz5Hu7eXLD20TDo6gJbWFnoBI7HvyOseS5y8hyjQIMhVlpOO02LGOIWebgv067jXV7WghFjwzqDpuNXK8bm8D/u2UeC8bnkHaSLn5ISTJFEfk58GkgDOwEbjXGtCa2fQ/4EhADvmaMeTVRfjnwS8AO/M4Y89P+jqPJFNVI1hkIsfWd/aT73Ew+u+CkXhG16c81eLxOJs7tZznf09zf9v+N216/jesnX8/35n/vmCMKyzK0BiNUHGhlX/teWqJ7iNkb6Grv4KkfPc3+qjrAyQ3/9BPKp8/B7bThcthxO2yMyU7jxY215Pvc5Ge6ycv0kO9zU+DzUOjznPC1ZIZ7MsXXge8ZY6Iicj/wPeA7IjINuB6YDhQBb4hIzzjsP4BFQA2wVkRWGmO2pqDtSp0QJmZhIhZWRwQrGMUKxzDhGCZiYaIWWIZJWS5CnRFa/1KD021PZMwVxC6Iy44904mjICO+7vsJEotYdHdF8Cdx6ux089a+t0h3pPOted/q93SUzSaMynBxzvh8ziEfmEt3tJvrbryOBRfPZcYvZhCLxMi2RZldGqbcX37IuiULJw5uFHkypCSAGGNe6/XyPeDaxPOrgeXGmBBQLSJVwNmJbVXGmF0AIrI8UVcDiBr2jDHE2sJEPu4gsr+D8P5OIgc6ibV0k/25ScRaug/WFaeNr/z8W7zy7hvkZeeydsVfEJedH/7y33jlndew2WzkjcrlkX/+JUXZ+UQbugjtCiBjMolle/BkODGWoWl/J7GIBQJ2hw2n237E42gZevduacZYMKoo42T+mEYky1jYxZ70xHi4K8ymNZt4YfkLBMIBKlsqqWqt4u2at1n98WqKvcWM9Y1lfNZ4vE7vsEsvMxzmQP4eeDrxvJh4QOlRkygD2HdY+fyhb5pSg2diFpH9nYR2BwhVtxHe24bVc0msgCMnDVeRF8fMPFylPqQ8C1uaA3HaEZvwZfkKX/d+m5tuuomM2fHJ7x8+fB//dOBe9le28vTKx/j+f/6c7975Y+zAaKfg3dvO7qoAeRP9ZPjdtDd3Y7fH/7OJxfo+TW2zCQ6nDbvThrEMsYhFJGIhEE/t7j91U7ufKGfmncnTFU+zuXHzoNddB9i1axd5eXnceuutbNy4kbPOOouHHnqIbns3lS2V7G7bzTsfv0N1oJpfb/w1C4sXcn7J+cwtmDskC14N1pAFEBF5Axjdx6Z7jDEvJOrcA0SBp3p266O+oe/7Vfr8VojIbcBtAGPHjh1kq5VKTrQpSHBbM90VzYT3tGHC8VxE9hwPnknZuEoycRZl4Cz0YnMfey6jr+SHfn8Wfj+UTM7m9Q0uApEMxs/Kw1gGicSQ6gDlk/w4i7w43XayctOQxHlxyzJ0d0ToagvRFQjT1ZZ4BMJ0tYUIdkRwuOy40x3klngZPzuv3wy/Ku7CMReS5khjxY4VSQWQaDTK+vXr+dWvfsX8+fO5++67uf/++7nvvvvITcvlnKJzaAu10dTdRLm/nOernmd5xXKcNidz8udwXvF5LCpdRElmyRD0rn9DFkCMMZcea7uI3AxcBVxiPpnJrwHG9KpWAvTciXO08sOP+xvgNxCfRB98y5UauO6drQRe3EWkrhMAR34a6WcV4C7Lwj3Oh9134v6Kv+eee3jiiSfIysrirbfeIjfPC4AVjNJRHcCd7sTVx1yIzSak+1zxGwRT8//MKcvn8rG0fCl/rPwjX5vzNXLTBrciYElJCSUlJcyfHz+hcu211/LTnx56fZDP7cPn9vHwJQ8TioVYd2Ad7378Lu/sf4cH1j3AA+seYN7oeXxt9teYlT/rhPVtIFJyJ3riiqrvAEuNMb3Tfq4ErhcRt4iUAROBNcBaYKKIlImIi/hE+8qT3W6lDte6cieRuk4yLx7D6G/NZfQ35pJ99QTSZ+ad0OAB8cSH+/bt48Ybb+Thhx8+WB7rjJ8es50Ga5sPRzdNu4mYibFs87JB7ReprcVX8zElBQVUVFQAsGrVqoMrDfbFbXdzbtG5fHPeN3nu6ud49XOvcvecu9kT2MPNr9zMxoaNx9WXwUpVKpOHgUzgdRHZICKPABhjtgDPEJ8cfwW40xgTM8ZEgbuAV4FtwDOJukqllO9TY8AudK49QLTXZPhQ+sIXvsCzzz578HWsuRtEsGcNbeI81bexvrEsLV/K09uf5kDngQHtE6mtJfDCC3S+/x73XXopX7juOmbOnMmGDRv4/ve/P+BjZzgzyE3LJS89D8tY1HbWJtuNpKTqKqyjLjBtjPkx8OM+yl8GXh7Kdik1WOmz8nHkpdO8fDuNj24m84ISfItKkSQysQYCAVpbW/H7/Udsq6ysZOLEiQCsXLmSKVPiqcKNMUQOdOLI8SAnaRU6daTbz7ydl3a9xG83/ZYfLPhBv/UjH+/HxGJgDGcUFbP60WWkzz1rQMdq7W7lzX1v8tqe13h///tETZSijCLunnM3i0sX9/8GJ5COeZU6Tq5iL/lfnU3gT7tof7uG7qpWcm6YgiN34BPRgUCAjRs3YlkW9913H1u2bKGpqYmSkhLuvfdeXn75ZSoqKrDZbJSWlvLII48A8dGHCcVwTtJLblOp2FvM5yZ+jmcrn+WW6bf0O6ntLC5C7HZMzELsNpzFx85bFYqFeHHni7y2+zXW1K0hZmIUe4v54vQvsrh0MdNzpqfkEt+U3Il+suid6OpkC25upPnZSgBybpyCZ0L2gPbbs2cP1dWfpN8uKyujtLS03/061x/A6ojgPa8YsQ+vewRON/Vd9Vzxxyu4bNxl/HjhESdRjhCprSXy8X6cxUU4CwuP2N4d7aY6UE1VaxXGGO555x7GZo5l8bjFLCpdxNRRU4csaAz3O9GVOiWlnZFLQWEGjU9spXHZZvyfLsd7Tv9ZUf1+PzabDcuysNlsfZ7GOlw0ECLW3I17gl+DxzCQn57PF6Z+gcc2P8YXp32RKaOOvSKhs7DwiMDRHe1m1d5VGAw17TVYxiLLncXs/Nms+PQKJmVPGlY3E+oIRKkhYHVHaV5eQff2ZjIWFOL/9Ph+5yh6z4FkZR17FUJjDJ1r6zDdMbznFiU156JOvLZwG1f+8UomZ0/mt4t/O+D/7BuDjWxt2srmxs0Hy2blz2KCfwJ5aXknPWjoCESpFLJ5HOTcNI3Aq7vpeLuGyIEucm6cgt179CulsrKy+g0cPcJ72rHawnim52rwGEZ8Lh+3n3k7P13zU1Z/vJoLSi44at2oFaWypZKtTVs50HUAu9iZmD2RoowipuZMHXSq91TQEYhSQ6zzw3panq3EnuEk54tTcZVkHtf7RRuDdG2sx5GXTtqM3GF1SkNBJBbhmpXX4BAHK5auOCJPVne0m91tu6kOVBOKhfC5fJT6ShmTOQaXfXhcij3QEcjwD3FKjXAZs/PJv+NMEKh/ZGP81FOSf7hF6rvo+qgBW4aLtGk5GjyGIafdydfnfJ2dgZ08U/HMwfL2cDu/XP9Lzl9+Pp9/8fP8adefKPYW86kxn6LcXz5sgsdg6CkspU4CV7GX/Ltm0fz77bQ8W0lwSxP+z0zAMcCEhfEEjR1E6oM4CzNwT8jWU1fD2MVjL+a8ovN4YN0DlPvLqWqt4tcbf01LqIUryq7gH878B8ZnjU91M4+bnsJS6iQylqHj3f20vbobYxkyzh6Nd34hjoL0I0YTxhiiB7ro+rCezrV1WMEoGfML8V85HnFq8BjuGoON3PCnG6jrrANg/uj5fGPuN5iWc/RUJcPFQE9haQBRKgWiLd20v7mPznUHwDLYs9w4CzOwpTvAQNeH9Z9UtoFn8ih8l5biKvamrtFq0Fq6W1i1dxXjfOM4q+CsEXPKUQMIGkDU8BdrDxPc3EhodxvRA51Y3fE1r2OtIQCyPzcRz+TsE56YUalj0ct4lRoB7JkuvOcUDehmQ6WGGz2RqpRSKikaQJRSSiVFA4hSSqmkaABRSimVFA0gSimlkqIBRCmlVFI0gCillEqKBhCllFJJ0RsJlRqmjGUwMQssQEBsAnYZMekw1KlPA4hSKWYiMUJ72wlXB4gc6CLaGMR7QTGxpu4jK9sFm8eB3efC7vfgyEvD5rKf/EYrhQYQpVLCGENoRwuda+sIbm+GqAEBR04ajtw0nLlpOPyeeMp2u4BlMDGD6Y5iBaNEG4NEajthW/z90mbl48xNS22n1GlHA4hSJ1m0uZvmZyoI727D5nXiPbsQ96Rs3KU+bGkD+0oaY7DaIwS3NmF1hAluqCeSl45ncjY2j36t1cmhv2lKnUSRxiAN/7kBY4H/mglkzC1A7AO7lqW7u5sLLriAUChENBrl2muv5d5778XELMJ72wntDhDcamGiFhnzRutciRpyGkCUOkmMMbSs2AFA/p1n4sxLH9T+brebN998E6/XSyQSYeHChSxZsoQFCxbgLsvCWZhBeG87jcs2E6psJfvzk3R+RA0pvYxXqZMk2hAkvLuNzIvHDjp4AIgIXm98QalIJEIkEjlklGHzOHBP9JO1ZBzBzY00/PojYm3hE9Z+pQ6X0gAiIt8UESMiuYnXIiL/LiJVIvKRiMzpVfdmEalMPG5OXauVSk6krhMA9/ispN8jFosxa9Ys8vPzWbRoEfPnzz9ku4iQeeEYcm6aRrS+i/r/2kC0tY+ruZQ6AVIWQERkDLAI2NureAkwMfG4DfivRN1RwA+B+cDZwA9FJPukNlip45VY/FNsyc9N2O12NmzYQE1NDWvWrGHz5s191kubmkPebTOxglEaf7uJWLuORNSJl8oRyIPAtzn4tQLgauAJE/ce4BeRQuAy4HVjTLMxpgV4Hbj8pLdYqePgGOUBINIQPO738vv9XHTRRbzyyitHreMak0nurWcQDYRpfroCY526y1er1EhJABGRpcDHxpiNh20qBvb1el2TKDtaeV/vfZuIfCAiHzQ0NJzAVit1fJyFGYjLRqiqZVD7BQIB9uzZw86dO2ltbQUgGAzyxhtvMGXKlGPu6y714V86nlBVK8GN+n1QJ9aQXYUlIm8Ao/vYdA/wfWBxX7v1UWaOUX5koTG/AX4DMHfuXP2TSw0b4rDhmZhNcFsz/qvNgE5lBQIBNm7ciGVZVFdX8+CDDwJgWRbXXXcdV111Vb/vkTF3NB2rP6ZzbR3ps/OPux9K9RiyAGKMubSvchGZAZQBGxNXkJQA60XkbOIjizG9qpcA+xPlFx1W/ucT3milhljaGbkEtzQR3teOu9TXb/3W1lYsywKgrKyMF198kdLS0kEdU2yCq9RHd8XgRj5K9eekn8IyxmwyxuQbY8YZY8YRDw5zjDF1wErgpsTVWAuAgDGmFngVWCwi2YnJ88WJMqVGFM/UUWAXgpsaB1Tf7/djs8W/pjabDb/fn9Rxo03d2L3OpPZV6miG242ELwNXAFVAF3ArgDGmWUTuA9Ym6v2LMaY5NU1UKnk2jyN+GmtzI1lXlvV7t3hWVhZnnnkmra2t+P1+srIGfwlwd1Ur4eoAvsWDG7ko1Z+UB5DEKKTnuQHuPEq9ZcCyk9QspYZM2oxcurc3E6npwDUms9/6WVlZSQUOgNCuVpqe2oYjLw3veX1ed6JU0lIeQJQ60UJdEQINQUKdUSzL4E534M12k+F3D4v8UGnTcmixC10fNQwogAyWsQzhvW10rj1A1/oDOHLSyL1lOja3pjVRJ5YGEDXiWZahZlszOz9soGZ7M22Nfd95ne5zUTw5m3M/W05Glvu4bujrEY12EgrV4Xbn43AMLBjY0hx4JvgJbmzAt6j0mPmqTMwi1hbGag9jhWKYUCx+P4dlMAYwJn49YuJfW7qDpt9vj6eHd9jwnleM79KxmqFXDQn9rVIjVixiseWvH2MscKU7KJ7kZ+LcfNIyXbjSHNgdNkQgFrWIhGIE28N0tIaJRixaDnSR7nPhTnccMiqJxWLMnTuX4uJiXnrppYPllhUlGm2nqelNOjoq6OjcQWfHDkLhAwDY7V7Onvc86ellA2q794ISGn+7icZlm/FdWoqrKANsQiwQIlzTgS3DCZbBCkY/2UlAnDbELuCwxdstiXIAEWJdEbznFuMq9uKZko3NrV9xNXT0t0uNSHu2NPH2UxW0N3dz+e1lRGQtTl89EYkRCVsQEWziQmxObOLEZnMhXie+TBcO9zw6mm0E28OkZ9mIyS6cHhsYw8MP/zfl5QW0t7fQ0LiKWKyLSLiZSDSAx1PMtm3fxmZzkZE+kexR55KRPoFgcA/7a5+hq2v3gAOIp9xP9v+ZTOvKnTT+btMR28VtxzUmE9fYTFxjfbiKvNi8zoGNmmYN9qepVHI0gKgRJRqJsXr5Dra+U0t2YQZX3jUNT+4auoL7SM+YhNORSfzqdAvLimCZMMaKJJ5HMLFOsAfwZLcRCXqJhQvZvTkN39g1NASq+dOfXuQrdy5i2aNv09W1C7stDZcrF693Mh7PGBbMf5309FJEPjnttGHDrTido8jOnn/UdvclY3Y+adNGEdoZINrcDZbB7nPhLMzAkZd+Qk6xKTWUNICoEaMzEOLl/9pE/e425lw2lnlXleFw2gmHF9K9/2PC4UZycy7Ebh9gqnR/PCA5K9Np23sBP/vPZ3noocfp6OggPX0PpWO/3O9bNDS8TlPzX5gw4bsDP24vNreDtGk5g95PqeFA1wNRI0JnIMTzD3xI8/4OlvzDDM65ZgIOZ3wU4HKNoqBgKdFoG7V1zxGLdVNRUcGsWbMOPnw+Hw899NAR7+tw2pl2XjHvbfgzLuNjUumZ2GwDu+EuGm2nouKHeL1TGFNyy4nsrlIjgo5A1LAXCkZZ+csNdLSG+PTXZlE04ci7sdPSihld8GnqDqykru45Jky4hg0bNgDxifHi4mKuueaaPt/f6bazp3kbb7/3BtNmTsKSKG1tbfzd3/0dTz755FHbtWPHfYTCDcyc+ciAg45SpxIdgahhzRjDm49vo6WuiyvvmNFn8OiRljaWgvwrCYebqKt7nlgsBMCqVasoLy/vM4dUVyzG+60dfP2++9jy4Q6ef3Q1D/zrI1x88cXHDB61tX+ktu5Zxo37Cj7fzOPvqFIjkAYQNaxte7eWXRsaOPez5ZRMGdVv/fT0MgoKriQcbqTuwPNYVojly5dzww03HFG3PRpjdzDMX1s6eKaumUiem6IJWQQagkTDsaMeo7Oziu0V/4zfP5/xZV87rv4pNZJpAFHDVigY5W/P7aRwQhZnXjKm/x0S0tPLyM9fQjhUz759z7Fy5Uo+//nPH1EvEI1hJe7DixnY1x2maKKfBXPP48EfPdrne0ciAT7adAd2expnTH/wkKuxlDrdaABRw9b2d2vp7ohw3rUTB52CJCOjnNzcS3jl1TeYOXMCBQUFR9TJctixJW7CswuM8biw2W0UlmfR3hyiq+3QZWCNsdi0+U6CwX3MOOM/cLuPfE+lTicaQNSwVfnBAfLGZlIwrv91M3q0NzVQs20L7U0NeL1T+d+Xd7BkyaSD8yG9ZTrsjEtzsTDby3WjR1HkcQGQU+JFBJr3dxysa4whEPiQlpa/MXXKv5Gdffbxd1CpEU4DiBq2mms7GT1+4Flo25sa2PL2m+zb8hFb3n6T+pq9rF69mcWLp9HRsbXPfdLtdub7vQeDB4DTZSct00Vn4JMRSEvre3QFdzOu9A4KCz+bfKeUOoVoAFHDljvNQXNtJ1bMGlD9QH09xrIwxmAsi0hHB01NzeTkjKGza+egju102w9OpLe2fkBr6xrS08Yxfvw3Bt0PpU5VGkDUsDXr0rF8XNHCf//gb/z5qe3s29ZMfMmYvmXl5yO2eJJBsdnIyo+v/52WPpZQdx3GRI+67+HC3VEcLju1tc/R3PIOGRmTyMqajYh+ZZTqoTcSqmHrzEvG4MtLY/u7texYc4Atq/cz57JSzrmmvM/6mTl5TL/wYgL19WTl55OZkweA2z0aw3pC4UY87tH9HjfYHsbhsuMrCGKw8HhKyM+7TIOHUofRAKKGtbKZuZTNzCUaifGX3+9g/at7KJmSzZipfd8TkpmTdzBw9OgJGqHu2n4DSHdnhOd+sZ7O9gCli79Bds4UZs96TIOHUn3Qb4UaERxOO+dfP4ns0em88dhWWuu7Br6vIxOnw08wuO+Y9doagzz/wDpa69spmPvvlIz9NGfNWT7ghaKUOt1oAFEjhtNl57Ivn4EVM6z46Qdse3f/gCfY09JLCXbvIxo7MvBYlmHrX/ez/F/fo6W+heKFv2LGgiVMnfITzXGl1DHIsSYlR7q5c+eaDz74INXNUCdYa30Xqx7bRt2uAL5cD5fcPI3cEi9Oj/2oNxxGIu00NL6Gx1NMtv9sRGwYy9BS18mrv9tA8/4wabmVlC58jlnzvk9OzgUnuVdKDR8iss4YM7e/ejoHokYcf346n/3mHKo3NrJh1V6e+8V6ALzZbgon+CkY5yO7MJ1RhRlk+N2ICE5nJpFIC1s2/QATPJtww0UcqCigu92D01tP8TkvMGX+ZMaP/x9crv5zbimldASiTgHtzd3s/qiR/ZWt7K9qpavXDYA2u+DJcOL02ImGYnS1hTBGQGJ4R1dReEY15bPGUFz8OTyeohT2QqnhQ0cg6rSROcrDjItKmHFRCcYYgu0RWmo7aanrpL25m+6OCJFQDIfLTka2m7ySTIom+fFkLEp105Ua0TSAqFOKiJDuc5Huc1E8OTvVzVHqlKZXYSmllEpKygKIiHxVRCpEZIuI/KxX+fdEpCqx7bJe5ZcnyqpE5LupabVSSqkeKTmFJSKfAq4GZhpjQiKSnyifBlwPTAeKgDdEZFJit/8AFgE1wFoRWWmM6TvFqlJKqSGXqjmQO4CfGmNCAMaY+kT51cDyRHm1iFQBPQsvVBljdgGIyPJEXQ0gSimVIqk6hTUJOF9E3heRt0VkXqK8GOidb6ImUXa0cqWUUikyZCMQEXkD6Ctz3T2J42YDC4B5wDMiMp746qKHM/Qd6Pq8gUVEbgNuAxg7duzgG66UUmpAhiyAGGMuPdo2EbkD+KOJ38W4RkQsIJf4yGJMr6olwP7E86OVH37c3wC/gfiNhEl3QCml1DGl6hTW88DFAIlJchfQCKwErhcRt4iUAROBNcBaYKKIlImIi/hE+8qUtFwppRSQukn0ZcAyEdkMhIGbE6ORLSLyDPHJ8ShwpzEmBiAidwGvAnZgmTFmS38HWbduXaOI7DlBbc4lHuROJ6dbn0+3/oL2+XSQTH9LB1LplM6FdSKJyAcDyQ1zKjnd+ny69Re0z6eDoeyv3omulFIqKRpAlFJKJUUDyMD9JtUNSIHTrc+nW39B+3w6GLL+6hyIUkqppOgIRCmlVFI0gBzF6ZgtWES+KSJGRHITr0VE/j3Rp49EZE6vujeLSGXicXPqWp0cEfm5iGxP9Os5EfH32nbKfsY9TqW+9CYiY0TkLRHZlvju3p0oHyUiryd+X18XkexE+VF/x0cSEbGLyIci8lLidVkiVVSliDyduH+OxD12Tyf6+76IjDuuAxtj9HHYA/gU8AbgTrzOT/w7DdgIuIEyYCfx+1Lsiefjid8UuRGYlup+DLLPY4jfZ7MHyE2UXQH8L/EUMwuA9xPlo4BdiX+zE8+zU92HQfZ3MeBIPL8fuP9U/4x79f2U6UsffSsE5iSeZwI7Ep/pz4DvJsq/2+vz7vN3fKQ9gG8A/wO8lHj9DHB94vkjwB2J518BHkk8vx54+niOqyOQvvWbLdgYUw30ZAs+m0S2YGNMGOjJFjySPAh8m0NzjF0NPGHi3gP8IlIIXAa8boxpNsa0AK8Dl5/0Fh8HY8xrxpho4uV7xNPjwKn9Gfc4lfpyCGNMrTFmfeJ5O7CNeOLVq4HHE9UeBz6TeH603/ERQ0RKgCuB3yVeC/FMHysSVQ7vb8/PYQVwSaJ+UjSA9O20yhYsIkuBj40xGw/bdEr2tw9/T/yvUDg9+nwq9eWoEqdnZgPvAwXGmFqIBxkgP1HtVPhZPET8jz8r8ToHaO31B1LvPh3sb2J7IFE/KaftmuipyhacKv309/vET+kcsVsfZeYY5cPKsfpsjHkhUece4mlznurZrY/6I+IzHoQR8fkdDxHxAs8C/2iMaTvGH9kj+mchIlcB9caYdSJyVulZWAAAAvhJREFUUU9xH1XNALYN2mkbQEyKsgWnytH6KyIziJ/r35j4kpUA60XkbI7e3xrgosPK/3zCG32cjvUZQ/xCAOAq4JLEZw0j+DMehGP1ccQTESfx4PGUMeaPieIDIlJojKlNnKLqOS090n8W5wFLReQKwAP4iI9I/CLiSIwyevepp781IuIAsoDmpI+e6smf4fgAbgf+JfF8EvEhnxBfarf3BOsu4hOSjsTzMj6ZlJye6n4k2ffdfDKJfiWHTjCuSZSPAqqJj9KyE89Hpbrtg+zn5cSTduYdVn46fManTF/66JsATwAPHVb+cw6dRP9Z4nmfv+Mj8UH8j7qeSfQ/cOgk+lcSz+/k0En0Z47rmKnu9HB8JL5UTwKbgfXAxb223UP8CpYKYEmv8iuIX/Gxk/gpkpT3I8m+9w4gQnwt+p3AJmBur3p/T3yCuQq4NdXtTqKfVYk/DDYkHo+cLp/xqdaXw/q1kPgpmY96fbZXED/PvwqoTPw7KlH/qL/jI+1xWAAZT3wpjKpEMOm5otSTeF2V2D7+eI6pd6IrpZRKil6FpZRSKikaQJRSSiVFA4hSSqmkaABRSimVFA0gSimlkqIBRKkhICIxEdkgIptF5A8ikp4oHy0iy0Vkp4hsFZGXRWRSYtsrItLak1FVqeFOA4hSQyNojJlljDkDCAO3J5LWPQf82RhTboyZRjyNTEFin58DX0xNc5UaPA0gSg291cAE4ssERIwxj/RsMMZsMMasTjxfBbSnpolKDZ4GEKWGUCLf0BLidzmfAaxLbYuUOnE0gCg1NNJEZAPwAbAXeDTF7VHqhDtts/EqNcSCxphZvQtEZAtwbYrao9QJpyMQpU6eNwG3iHy5p0BE5onIhSlsk1JJ0wCi1Eli4plLrwEWJS7j3QL8iMRaDSKymnim1EtEpEZELktZY5UaAM3Gq5RSKik6AlFKKZUUDSBKKaWSogFEKaVUUjSAKKWUSooGEKWUUknRAKKUUiopGkCUUkolRQOIUkqppPx/iHf+1wX75ZEAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pca.plot(scaling=.01)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pe = monomial_current_pca(x, y, 10)\n",
"pca = PCA(pe, x, y)\n",
"plt.figure(figsize=(8,8))\n",
"pca.plot(scaling=20)\n",
"plt.axis('equal');"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.10093538456899297\n",
"0.0635731169568216\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pca_opt(pca, scaling=20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"d(0,1), d(0,2), d(0,3)\n",
"order 1, mesh = 10, 20, 40\n",
"(2.2949783713748606, 2.4006275209345507, 2.2316118057013319)\n",
"(1.6047046605854045, 1.6207933275335604, 1.6825498540372308)\n",
"(1.2664142928892494, 1.2783837142622918, 1.3259963291001282)\n",
"\n",
"order 4, mesh = 5, 10, 20\n",
"(2.2997301392640863, 2.2460204102017722, 2.2746276352501957)\n",
"(1.7498901419675774, 1.7855146077354773, 1.7592703776709591)\n",
"\n",
"d(0,1), d(0,2), d(1,2)\n",
"order 4, mesh = 5, 10, 20\n",
"(2.7899967862469111, 2.8270892665201925, 0.8246409669811765)\n",
"(2.8852668644254802, 2.9246305575121454, 1.0339455136119406)\n",
"(2.9389698376057898, 2.9713066427066308, 1.1315582359980916)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.6.6"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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