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@AustinRochford
Created September 26, 2016 12:46
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Bayesian GP PyMC3 PPC Problem
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"import pymc3 as pm\n",
"import scipy as sp\n",
"import seaborn as sns\n",
"from theano import shared\n",
"from theano import tensor as tt"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"blue, _, red, *__ = sns.color_palette()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"SEED = 6533961 # from random.org\n",
"\n",
"np.random.seed(SEED)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def f(x):\n",
" return 5 * np.sin(x) + np.sin(5 * x)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"n = 20\n",
"sigma = 0.2\n",
"\n",
"xmax = np.pi\n",
"\n",
"x = sp.stats.uniform.rvs(scale=xmax, size=n)\n",
"y = f(x) + sp.stats.norm.rvs(scale=sigma, size=n)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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AqRCwevZQ3DY3Hvq6n+652lPBvq54/NYkZBfq8d7OLGz7/iJKq5tx/+IEaDX8cUHUH/jJ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\n0JEMYiGEEEJHMoiFEEIIHf0D1LxExXOA2bAAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff2bf249940>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"plot_x = np.linspace(0, np.pi, 100)\n",
"\n",
"ax.plot(plot_x, f(plot_x),\n",
" label='True function');\n",
"ax.scatter(x, y,\n",
" c=red, label='Observations');\n",
"\n",
"ax.set_xlim(0, xmax);\n",
"ax.legend();"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x_diffs = np.subtract.outer(x, x)\n",
"x_diffs_shared = shared(x_diffs)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied lowerbound-transform to tau and added transformed tau_lowerbound_ to model.\n",
"Applied lowerbound-transform to l and added transformed l_lowerbound_ to model.\n",
"Applied interval-transform to log_sigma and added transformed log_sigma_interval_ to model.\n"
]
}
],
"source": [
"with pm.Model() as model:\n",
" tau = pm.StudentTpos('tau', nu=4)\n",
" l = pm.StudentTpos('l', nu=4)\n",
" K = pm.Deterministic('K', tau**2 * tt.exp(-x_diffs_shared**2 / l**2))\n",
" \n",
" log_sigma = pm.Uniform('log_sigma', -2., 2.)\n",
" sigma = pm.Deterministic('sigma', tt.power(10., log_sigma))\n",
" \n",
" prec = pm.Deterministic('prec', tt.nlinalg.matrix_inverse(K + sigma**2 * tt.eye(x_diffs_shared.shape[0])))\n",
" y_obs = pm.MvNormal('y_obs', 0., prec, observed=y)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING (theano.tensor.blas): We did not found a dynamic library into the library_dir of the library we use for blas. If you use ATLAS, make sure to compile it with dynamics library.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 10000 of 10000 complete in 10.8 sec"
]
}
],
"source": [
"SAMPLES = 10000\n",
"BURN = 5000\n",
"THIN = 5\n",
"\n",
"with model:\n",
" step = pm.Metropolis()\n",
" trace_ = pm.sample(SAMPLES, step, random_seed=SEED)\n",
"\n",
"trace = trace_[BURN::THIN]"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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Ot1/8gL4aT0KGVC8NNHdXjQyKMXDui77e009WaJ/NZsO8efOwfv36biEUsivs\nzZs3D/PmzYt476677hI8dvPmzbL6HMywLIdtu+uhYBj8eG5FusVJGQzD4KdXTYKp04Wvj5mwddcp\nLJ9fGb8hQRDEAGXUqFF45513Emojpj6Ewvn6Uu9sNNrQ3OHArIkGqFWJ7fnYl/RH+XO+58PU6UJ5\nUY5kie9kpzlkGKTiNE41B3NMOqxujIiTR9Yb+tO4kRrKH2DRYXWjKDczprx2IiIyTO++N67usvle\nX6o9UuJCfneiHQAwd2r8vet6M5rkte+jm1pOgZLeXC+fn8WZNjtGFGUnXcafP35fL4rI8kgplUr4\nfL7wRBmNRihStPvxUGf/sTa0dDjxo+mlKdntfSChUirw6+uqUJyfhdo9Dfj8YEu6RSIIgkBHRwfu\nu+8+rFq1CgBw9OhRvP766ykZK74npHdKbkuHA2fagivrzd1hNLbuylvpIiK0L0XL3tHhfFaHcInv\n3gzv9vrDimg6Q/v6cy2/9zaXeAeNRjtOt1hxti02nLU/zzF066T6mva3c07ot0aWDN3TwAHwJxGa\nmerTbGq3o63TiRNNXX3SX19fdlnW0MqVK3HnnXfCYrHg6aefxsqVK7F69eq+lWQYwHEctu1uAMMA\n1RcOXW8UH22WGnfXzEB2hgqbPjiKb4/HDy0gCIJIJY888ghmzZoFqzW4V8q4cePw2muvpUWW3ipb\nDUYbmtpTG6IkhpzQvlQR8kipu5P5Q4aV1eHts9yXNl4uBSMQDtRXnp6BlX4l/5w83kDMHEhNidMd\nNPBDG7/2lmSnn+u+V5gU+AP4xowc8frSWyjUFT+kLt5t1uXwoL41/v5RAoOklEAgOIDUxtuJ0Neh\nfbJuo6VLl+K2225DdXU1XC4XnnjiiaTKoQ93DpzowFmTHXOmlKCkIDvd4vQbZYU5uOf6c6BSMfjL\n24dRV29Ot0gEQQxjjEYjVqxYAWV3iW6NRtPvURYMbxU4WcxWt0jf/aWZ90gfTipHlDKZIiUrZDip\nVd2GVICD3eXDkQYzjjZYJCRNfIxgB5E9/HCmE/vqjGBZDh5fAI1GW+pC6HrbbwLNExmq0xGb35e0\npEmcY7J5b6n0SHGiL4QJGQl9PnbovX5Y1RDKf4q+Nhwn/lk0J5q60NTO81qGfit7cS78Mfs6N052\nsOHs2bPjlnglxOE4Dtv21AMYPt4oPuNH5uI3183AU1sOYMObh3DfinNROSI33WIRBDEMUakiH31W\nqzVlRRqY3VPaAAAgAElEQVTEumX6INXb7kpzCB/v7wajDWWFObEfpIiQ0cL3SHm7K8Ta3T3z0ptZ\n5nu2ok/JbAsasb4Aix/OdMLh9kGhYDBS5l5I/UlCG/L252BJNmN6mSQV+q6nZL2BbzDIOCuxKof+\nAAun2w99AuXkhX7D+iM/TtATFvNepKdOaurbu4Ke4PLuvMGeKo3Jy5hKZBlSy5cvF1zh2rJlS9y2\nu3btwrp168BxHJYvX47bb7894vO///3vePXVV6FUKpGTk4M//OEPqKwcekUJjjZYcKrZipkTigbk\nD21/MG1sAX6xZBqeeft7rP/HAdx7wzmoLCdjiiCI/uXKK6/E7373OzgcDrz11lt47bXXsHz5ctnt\nWZbF8uXLUVJSgmeffTY5IUKP1F6tsibfNpWwCSqT8vvt6SukgKq6PVJ+lu1zT5yfF0okNdchA66v\nQo+i6e0MJrRIkEjRB8Hm4h309e3a6wIiKahbxybojQ2wLIDYwjCHT5vh8voxY1whsjNl7l8my6CJ\nJRXzEH0fxHjqEhiy52st/4qzHAdnP+3TJ8uQeuCBB8J/ezwe1NbWRmysKwbLsli7di02bdqE4uJi\n1NTUYOHChRGG0jXXXIObbroJALBjxw48/vjjeP755xM9jwHPtj0NAIDFPxqTXkHSzKxJxbjtmql4\n/r06/Okf3+GemhmYNDo/3WIRBDGM+Ld/+ze8++67sFqt2LlzJ26++WZce+21sttv3rwZlZWVsNvj\nh4jELzWRvHrZ29VmluV6lS8gPjwn+GciHD/bCbvTh5kTDbzxeIZU95+hDU/jhkglIYcvwFeKhTtg\n0BNKmez1SLWil5gd1bt7Su5Ypk4X6lt5G7P20oAbrIjtgebqziPz+Fhky9wlR7AnqXnto5UYeR6p\nHliOg0LkKgp9zxiB0L54lQIbjTa0mp0YNyIXxXlZKV10kmVIzZkzJ+L1xRdfjBUrVsRtd/DgQVRU\nVKC8vBwAUF1dje3bt0cYUjk5PSU/nU7nkKwGeLKpC3UNFkwbk4+xZfp0i5N25k4thUqhwHPvHsaf\n/3kAv1k+A9PGFqRbLIIghhFLlizBkiVLEm7X2tqKnTt34o477sDf/va3+A3EFHCeR4plOXDgYkpC\nJ4scD4TPH8DXP5hQnJeNcSP69rnUF0pLh0D+F7/fsEeKF9oneN69MFL4YVdyqkgP1BSplI3Vi7k9\n2RxZgS2pU+x16ljfT2yi10pqM+nEx47tq93qQrknB1kZsep+3/lP4+dIyc0FEzoq2mN2/GwnzFYP\nLphaItqP2RrM37M7fShOcYXspAqy2+12tLe3xz3OaDSirKws/LqkpASHDh2KOe7VV1/Fpk2b4Pf7\n8dJLLyUj0oBm2+56AOSN4jN7cjHUKgX+39bv8T9vHMCt1VMwd1rf7adAEAQRzZNPPin5+f333x+3\nj3Xr1uH++++HzWaLeywgxyMV3BaD5biE95QR84DIUeYc3ZuBtnU6ZRlSpk4XLDYPJo7K440jMr7I\n38nAcly4KECEIRUuSx4WRjTfJChH7GceXwA+PwttlnDoFL+NmNLNgb8nWJIeqQSO5TgO/gAXLrLh\ndPtx7IwF48tzocsWzqcZKJuhhqYnUQ+cP8DC1OlCnjZD0CDgY7a6kZWhkjxOwTBgOS4lBmqihVaO\nNlowbUyB6LVLbGzh98+a7JgwMi/2gz46fzkeqSMNZtHP5MoU+s6HFlkCLCu6+NRzr4W6Td13QNby\n1/Lly1FTU4Oamhpcd911WLhwoax4crk/KqtWrcK//vUv3HfffXjmmWdktRksNLTacOBkB8aPzI14\nABHAOeOLcO8N50CjVmLje0fwwd6GlCV8EwRBZGdnS/6Lx6effoqioiJMmTKl179V/ATqZEPCRMuP\ncxyMFme43HQibcU42dwFs80NjzfQ0wfvc/6qcaIloKWINI74oX3dhpSCAQMGLITnUUpl//a4Cd+f\n7giPcazRgq+P8bboiAglEu6D4zgwcY7pS441duLrH9rg8wevw1mTHR5fAKdbxMtWJxTa19scqSTn\nQOr7dKrZigajDQdOtoPluLBy3GSyRxQE8QdY/HC2EwdOxl/oB1JTiIHfo9HilFUhrrk9dl+tEKmM\n+gzPeRJjRHhrBfuWHFniE/HQvmikvFz9qUsmnCOlVCoxcuRIlJSIu9RClJaWorm5OfzaaDRK5lb9\n+Mc/xqOPPipHpEFD7Z56AMCSH43px5K0g4fJFfl4cNV5+PMbB/DGpyfRYXVjxeUT+izEhSAIIsSd\nd97Zq/bffPMNduzYgZ07d8Lj8cDhcOD++++X9HRxHKDXBUNLioq04eeAxeWHO8BBo1bA6wsqg4WF\n2oRylkx2L7zdemRRkTY8TpY2Ew0tVnTYfZh/3kjBtgqNCvrO4MquwaCLO5Ze1xUeJzNDhbNtNrRZ\nveExGaanH93ZrrAiVZCfA0NRTkx/HMfB1OmCP8AKjh8aT6FRo8PqxqSKfHj9LPQtQcU0V58NTyA4\nZ12uAHKy1cjLz4be7os4p9YuD1iFArpsTcw4oTEKi7RQKRU4cqYLWbzjdK12ZHQXksjLy45oH25b\nqIW+ywO124/8/CxZcxndR0FhDgxFwkWoDAYdGHXPtWIRvJ9ydFnI1WagzeaFHwxystRQaFQIBDgU\nd2+vEuo/Ly8bLj8XMS98OI4LX8fCIq2ohy4aVqmEyRa5EbJU+9x2J1QuFfLysuCP0t7z83NE5+50\nmwP67uMLC7XQ6+3hwh4OP4fxpcF2Pn8A+mab6HmG5WixwednkavPTuh6CWFzeuH1BVCYG5w/l8cP\nfWvwHnX5Obj8Aej0WcjkechYtme+ASA/L/a+4d9fBXp5SVKdbj8cvh7DMjRGXnf/qkw39OaevdG0\n2WoYDDrkWVxglLEFL8Tmxh9g8cWB5p7ftUJtxPkB3fNgDM6DF0zE+RYW6ZChVoaPUykZqFXKcN96\nXfAa5ugykZ2pht3Hwu5lw78xobnJL8gJF+LwB9hwmC8A6Jtt8AdYFBQE7ytWqYTeKrxpd29JKkdK\nLlVVVWhsbERTUxMMBgNqa2uxfv36iGMaGhpQUVEBAPjkk08wZsyYpMYaiDS1O/D1MRPGlOooB0iC\nkcVaPHzzLPzPGwew45smGC0u/PLaafIr1RAEQSSA3W7HM888g71794JhGMydOxe//OUvodVKV1S9\n9957ce+99wIA9u3bhxdffDFuuCDHcbDagsrLnu/OhkNsOjudsNpcUCsV8HWvqrcau8IKhRwsFies\n3WW420y28DgmNdPzt0k4BNFi88Q9hk/o2PZ2OzI0Snxb1xrxOQMm3E+XtUdZ6zCroeJiszGMFidO\nt1gxblQBinWxYU2h8fYdagIAqBkOGSpl+H0VOFhtbljMatjtbvi8PihZNuacurqcsNo9YH3+mPPk\nH6tSKgTbBlgOLMchQwGYslQxbdvb7bBYnPD6A1CBg0krP0Qr1IfZrIY6IiQsGHZWUqKHyWSD2eoO\nHxuivcMOr8sLi8UBq90Dv9eP3W1Br1QoRDTUJlMpfT/w79H2dhtcMp+95i5XrFwS7bu6nHB6/OFr\nF9GXWgGdRngBtavLBbfPH5bfanXBF2Ch12WhzWRDbkbwO+PzB2Td0zabm3e9eqdn7D0S/B6E5tzl\n8cfMSZvJFhFqGODdp0Dw3jaZIu+b0OcdHXYEPMKe5eiCC8Hfg2A7vS4r4rti0mrQ5fBGjOv3Br8T\nnV0u2JyxRobYHLZ0OCL6MbXbkKmJNaRCx3xzJHI+zjR1Ire7rHv0/PkDPXPz+ddnMHOiAZ288zLx\nfueMbTZos9Ro6XCgwWjDlNH5yNVmAAA6u5xgOQ45agVMGUqYO2Pv1b5CliE1d+5cQW9K6CLu2bNH\nsJ1SqcSaNWuwevVqcByHmpoaVFZWYsOGDaiqqsJll12GV155BXv27IFarYZer8cTTzzRuzMaQLy/\npx4cgGvIGxWXAn0mHvzJLGx89zAOnOzA2s1f4+6aGSgdRhsXEwTRPzz00EPQarV45JFHwHEctm7d\nioceeggbNmxI6bgdVjcmRL3Hj0AJ5r7I7080R0lGVEvq9s2S16/bE/T0dNo8goZUbMeRYT+h0KKe\nQg/xcqTkE9JtOC5+Po3HF4C3O8wu+tz5+V1SRB9x4EQH3D4/rimRXwREahip/BCfPwCbs0dRFztP\nqXyUiLFScVvxzi04x2IV3xLrLhXfAeF8IU7yGCn9UOyTY40WWOweXDClpPteDYbzJiJcoufvD7Bh\nI5/PdyfaMX1sYYQnUqpvu9OL3ByN4DH8t7yh7QTEQvu6v+/N7cHz7rB6woZUiL7Y+Dwesn6yV6xY\ngc7OTtx4443gOA5btmxBbm6urDypefPmYd68eRHv3XXXXeG/H3744QRFHhy0WZzYe8SIkQYtzplQ\nlG5xBgVZGSr8ZvkMbNl5Eh9+2Yi1L+3HL5ZMxYxKmj+CIPqO48eP44MPPgi/njVrFq6++uqE+pgz\nZ05S0RpeXwAatVJQ8bU5vXC4fSjKlVdlKkIPESjEIEVf54dw4ODzB2KV7TjDJCJHdPljIKiEMgwD\nlovew4eDzeWDxe5JqN+QyKHLEy4kIXIi/Jwxi92DLkdQSWyzOHGqxZpUIYGQ90VMvkSRal/XYIHT\n4xc/AMDZNjvOttsxcWReZJhZP6Wh8L8qMdeKf0/E6Ydlu/OrujtMpGCez8+GC3wI0eMdiu00epxY\nQ0q+HCFC93VLhxMjinLg8QUkjz/WaIHdFXVfJTjm96fMcPv8GF0cG/LX0GqLiLySrCfR/WGjUSh/\nTH6eYyAgXncwurBJKm9VWYkoO3fuxKOPPorJkydjypQpWLNmDXbu3Iny8vJwaXMikto9DeA4YPGP\nKmStSBFBFAoGN1w2HrdWT4HPz+KpNw7i3S9O98vu3ARBDA+Ki4thNvdUkbJYLLLyfpNBTPET2gTz\nVIsVJ5q6IhLopfsWrion5+cy2arLLMeJbjxb12CR3oiTB9+TJBf+oSHln2G6K/fFGFLAGUFFTajf\n2JV6f4AFB0CpiK0YyMcXda3qGsw43WLFqe7iD22dMsKJuifDH2BhFQix6jUSUxxtRAldj1ZzcMWf\n77kChMtnJ+vl4d83Hm8gItSMr0I53H74AsJGA7/4gCvqvNxeP7462oYfznTyCr3Ik9Xu8uHrH9pQ\n3ype0CN07wn1GK2/RI/bmw1xG9tsMecqhMXuiZ23BGtNhAx8od+n2HMU74dD0BPaYo4tsiHo0RPp\np8sR+V3h3yf9WalSlkfKbrfDbDajoCBobZrNZlkbEQ5XTJ0u7P6+FaUF2Zg9Kf7GxUQsF1WVYURR\nDv7f1kN4+7PTaGi14dbqqcjOTKpiP0EQRJj8/Hxce+21uOyyywAEq/HNnj07nO8kpwy6XKIf6G5f\nABkaZfj9xCte8fsWbiOlIHbZPTDbPMiOU0ZajEajTdTL4/T4BQxHDkcbLNDlaFDOKzohVNJciujZ\nChkwDEIeKQ4sT79jOS7CyImn2PFpNNrDYVIZ6uB6s1jYoFDlMH6Ildz9cwDgaIMFdjc/zC501rF9\nBAIc9tUZwwosXxmODilMyOsn871uAeUfyzs83kLBtyeClRPnTCmJWYiuj6pOaLa50dTuQGuHI+J6\nHzjZjpnjDcjQBPOn3N4AOHCw2D3hQgdy58XarbC3mp0YUyocbhnqSji0r+fvAMvGjNvbtfboQgty\nSdbo9Qvc09HfD6m+WVY8VDbSyd4drht1rFqphC8QiOtJBYCmdjtyMlUpLakp65f0Zz/7WcRDZ+fO\nnfjFL36RMqEGO+/trkeA5bDk4jG92jV+uDO2TI/f/fx8PPfOYXx7vB1/eOkr/HpZFUYVSyeEEwRB\nSDF+/HiMHz8+/PqGG27ot7HrGsw4d3wRT/FKSHWNPCpCQet5IZUrVNdoAQDZ4YPRxAuV43vcOHBg\nOaDT4UGnwxNhSCWjPAqdFcME/3FsrEeK30BSeY/qmG8IhZ7hYkp3tEcqmkQ2XLVHlat3uHzhMufR\nWB1eiX3EuIgJllJqQzlgPQeL9Cc0jsB7Da02TByZFzZgQrAsB5c3qPgKed1Ec4v4sXgAPALzcaZN\nuCiCp3vRIjR+tOB9qVuHjV7BvJ+e97462pZYvzKOOVxvRoFOvLKf2PVL1ivdW48UIH5e0bK2d7li\njlUoAASkf+f4tHQ4YciTV/kwGWQZUqtWrcKsWbPw1VdfgeM4rFq1CpMmTUqZUIMZo8WJ3YdaUVaY\njTmTUxMqMpzQZ2tw743nYOuu03h/bwMe27wfNy+ahIuqyuI3JgiCEKC3ZdATQuBZb3eJ7+8ESCs4\nDa025OkyYpK1vz3es/8RX8HosscmYANBBSUV9OQuBZUpMSWOn2Df3ulCUV58w06oq1COFMexMXtO\n8T05Xn8AFpsH+brYuZAKA2IYJmxsNLU7oFIyKMnvKYLkFwlzDCEWBhkpACdoFH19tA1WmwvjR+TG\nfBYTFsUzTNssLpQV9hitUkqtUqEAG4jcG4xlOZxutaK0IBs5vAp8McavQL8Otw+H6804b6Ih4v36\nVnkbWEd0HzLKk1yPFvXYht8Tnhi7ywe7y4dCfQbUqsh8Rr73h98+dOsJdRlP4Zf6vMnkQF7U91dI\nbnNUFUR5JOuREjCkot6SMt4tdk84XDRGoqhmAZYTLdbR4+2Nfx6pDPST7dsfOXIkAoEApk2blkJx\nBj/bvqgHy3G49uKx5I3qI5QKBWourURluR7Pb6vDC7V1+OFMJ1ZdMREatfxSwQRBEADgdruxbds2\nNDY2wu/vCQ/py5C+EEIPcJcnECcUSPix7/L40WJ2oMXswNyppaIGF98LUtdowexJxUmF/rAcB3+c\nJPtoQiMrwuF2YoZUz98nmrtkGlKxfSm6c6RCBkCP7LFz22kXMaQktCwG3efCcmHPB9+QiudxcoqU\nruZzipdT1Rc0GG0w8OZTKoQt1jjiYOpywdTpQkeXG3OmiC8Ii/XqjfIacRyHts44FeUEYFkOUCa1\nX2xsX9HeSsQq/yGONVrgC7DweHNQURpZWKGuwYKqcYUxfYbuPUH/cmg8Uc+Q+PWxuWK9d4l4OaVI\n1iPn9sZ6BaO/m6YuccPO7Y0fkhfZd8/fwcqBwb8DYhcwmhSr4rKLTVRXV+M3v/kNAODQoUO44447\nZA2wa9cuXHXVVVi0aBE2btwY8/mmTZtQXV2Na6+9FrfccgtaWloSEH9g0Wp2YvfhVpQbcjB7MuVG\n9TUzJxjw6M9nY3SJFp8dbMF/bv5adFWDIAhCjDvvvBMff/wxlEolsrOzw//i4fV6cf3112Pp0qW4\n5ppr8H//7/+N2+bwyY6Y91i2x1si5A0RU3BiV+aFD4xWtKQUL6liSPvqjPjmuCkhJZ9fTS/4Wvg4\nqZLPgoYkJ55XESr/HF21T3b+lZQhxTBQKBhRpVuOUtvbYklyWkcXLODnj8QzFKPHChkF4QIKIu3j\n5cGE6LDG95ZI5Rb1hdkQKat4GB7QE64pdG0dvPBL/j0R7kqgT68/AKPZKbqo0GF1x626x0duSFv4\neLHr1/1/onZGtKEMAH6Wxanmnt+JpIuORDVrMNoirkPQCxV8HXo/Oj+0qT22iEUqXVKyPFIbNmzA\nli1bcNtttwHo2Wg3HizLYu3atdi0aROKi4tRU1ODhQsXorKyMnzM1KlT8dZbbyEjIwOvv/46nnzy\nSfz5z39O8nTSy3tfnAbHAddeNJYq9aWI4vxsPHzzLPx9+wl88m0T/mPTV/jZVZPCm7kRBEHEo6Wl\nBbW1tQm302g02Lx5M7KyshAIBLBixQrMmzcPM2bMEG0jpESzHCf5YBdXXCP7EEu2jlYApRQvluPi\nJqub5FSei5IxFJAhZkREPyIbWm3QqBXIzlBBlxNbLpzlevrkE2A5gAmOE+t1kKs9SXhsgG5DSvgY\nOQojy3JQKJPXCZLRAZ1uviGVgCWFSCO3qd3RY/RHdSPVrdPjD+8r5PXF9xwILSj0GHK904L9ATYi\ntLDHQxRHpjjjRtxvCBmfscc1GINj+yUGNFlcGCkz/1vKMM/OUMd6QaVy6RIgJp8uirZOJ8aNCBbj\nSNTY40kl2G8IP8vyrl9sSGyH1S2aM5cqZPvrDYbIeFeNJv6+CAcPHkRFRQXKy8uhVqtRXV2N7du3\nRxwzZ84cZGQEXe3nnnsujEajXJEGFGfa7Nh72IhRxVqcN8kQvwGRNGqVEjcvmoRfLAmGmW589wg2\nfVCX0IoOQRDDlwkTJqCtLbGk7xBZWcGQKa/XGxEWmCjSakbPp/4Ai5NNXTBb3RH6kFlilT9RJWb/\nsWBZ6L4kpIyLKl5Rb7eYHWgw2lDXaBFP2Bd4X6lgwooMv0JeQmXVEQz7EyJYXl3ckJLjbeKHIpk6\nXWg1O/H9qVhPpRi+JJ5tEZ4Tnoi2qEIP0Z4sjou0raSUUqkz//50R7j0ezLl/PmvpbyXcvo702YX\nvE6+QEBStniXln9P9ITqijeKnsvyIi1mTgjqiw53/BBQOXJlamLTHcTOkOOAJpNdMFQv0XF7c2xE\nuzif+wORJjd/LymGEa6SKby7V98hyyOVk5OD9vb28M385ZdfQqeL3ZArGqPRiLKynqIAJSUlOHTo\nkOjxW7Zsidm8d7DwxqcnwAGoubSSvFH9xAVTSzCmVIe/vP09dh1owckmK+64dhrKDVTVjyAIce68\n807ccMMNmDx5cnghDwCeeuqpuG1ZlsV1112HxsZGrFq1StIbxSdUxQ6I75HiK75ddm8wZ6XLhRnd\nuRmAdFltf1Qcmhyjwmxzo67ejFElOmiz1EmHo/GLTQRfixwn2Yd0G/7KeK42Ay0dwRVrvieOk+gn\nmk67V9JgUCjEQ/jkpGmE5uRkkzWpogBnTPG3m4m+xvyNgvmfHa43S0ZwuL1+ce9b9B5hcSa42eRA\ncV4WjBYZHk0OOBgVBhsSQ6NSQCBYK36X3e29UYYo/94+1WzFxFF5gu3brS4U2YWrvXU5vPDwcn2S\n8cAwADLUSqgUCnjlFCUJjSUx70oBty0ncT3l3FtAd6isnKIOHBfejiAZ4jULBNiI+y66FLtYbYLe\nejWlkGVI/fu//ztuu+02nD17FjfffDPq6+vxl7/8JW67RAR/5513cPjwYbz88suy2wwUjtSb8f0p\nM6ZU5GM6b2dnIvWUFGTj4Z/Owj93nMT2b87iDy/tx00LxuPSmeVJr2IRBDG0uf/++7FgwQJMnToV\nSmViBWsUCgXefvtt2O12/OpXv8KJEyciSqmLEapiBwT/l1JKIquB8f/uOUbKIxUNywU3hvXEWXnu\ncnrRdbojWMgiydCcUKuwRyqJkDihj1iOA8MxPX3zDgr91Ptl7hsFAGd5CqTLLe5ZZBgGSoYRvV6y\nQvs4Dk63P7wfUSqIViD5JcYlRYwOsTSKG5Qx+wfFOXV/gMXh02ZZRQE4IFwePfweJx4uJwdWIIcm\n2F/PG/xNhu0uX4wBcLKpC6W8Cogh6hrMEa97yp/Lly903yoVjOTCSMg46Xkt3qdSIIRUrsdJaFx/\ngINKycg+L3+Ag1ol//hE8fGKTYRe8xFyZHh8gfA9lKFSYkyZ8F5gySLLkDrnnHOwefNmfPPNNwCA\nmTNnQq+PL0hpaSmam5vDr41GI4qLY4sw7N69Gxs3bsQrr7wCtVod8/lAhuU4vPHJSQDA9ZdVkvKe\nBtQqJVZdORFTx+Tjxffr8PLHP+DQKTNu+fFk6LLjh6ASBDG88Pl8+N3vfterPrRaLebMmYPPPvss\nriGl12VFGFK5uVngOMDHCT8vCgu14ZLlzgAHvc4bfl/fHvS+cN395uky0GmT3ttJnalGe3c7vS5+\ndTyDQQevLwC9LvFcg4ICLfQmJ3Q5GqgcXuhzM+Hv1tYNhp5IFjcLWJx+QZn8DBPzXkGBFkoFA32n\nGyqVIlx23GDQwez0IcBEZirk5mVDa3ZFGHL5+dlhGY6c6QqPkZeXDa+I4pefn4VAgAPHM7gNBh30\nui7Zc6LUqHHqTCeyc2IrBsZDzvUCEMwrE1kUyNAooeEp061dHkwdWwClUoFckwMaCUOSj5cFcnSZ\nyO4uiW73sbB64ivpcs4hLzcb3ih7K78gBzmZanC8a5VI3/kFOTAUZKOlyw1WIZzJomAYGAw6sCyH\nI981CfaZn5eNLlfPHAld//yCHBTmZoFVKqG3Sn8fQxQU5MBg0KGg3QmvLxDx/eD3X1iki/A0qW2e\n8O9ANEWFWjh9nOB5JIomKwN1x00oyM3E5IoC6HXxi87k5WcjO1MNXYcTjEr+IlXo3DV28XMDAL0+\nCzp7j/F7tsMFrTYTLMchPz8HedoMGAXmv8vlh16XhWnjCmVVCE2EuIZUIBBATU0Ntm7divnz5yfU\neagoRVNTEwwGA2pra7F+/fqIY44cOYJHH30UL7zwAvLz8xOTfgCwr86IBqMNc6YUi+54TfQPMyca\n8IcyPf763mF8d6Ida17Yh59fPRnnji9Kt2gEQQwgzj33XBw7dizh/RDNZjPUajV0Oh3cbjf27NmD\n22+/PW47qy0ytEmF4N4oVpG8HFO7HV6XF/4Ai4PH2njv2yL6UikUyFQyMf1H821dYntGtRq7cLLJ\nCmsSYWghGblAADanF0wgEPaOmEw9hlmH2QGrzQW9LitG/gPHgq8zNapwqeR9h5owbkQurDYX1EpF\neCXaZLLB5fTG9PHFt2dikuOzVAxMmUG1h3+8hom9RvzP9DnqiM93f3smobk5fYZLai6F5kYMv9cv\nWmpdrVTCx9srympzgQkEUFKQDWuXK8YTJMXpMxYUdyui5u5rmAj8a8pH6Bq0t9tx2OwU/Z7Em5/v\nfzBCUVmETotTcBPgEM0tQaNFrK92jSLiM5PJJihrwONDR5db9px0dqqQpWRgt7nhcPsivh/8Ptra\nrPD6WDjcPhjystBl94iO0ZWpFP1eJUpjkwVWmwtWmwsacLL62/Pd2XBhGLFiONEoGAZ7D5yFxepB\nRfZBj6YAACAASURBVKlOcpw2k0L08xy1AgGPT7K92ewA5/NHGK29Ja4hFSoP6/F4ImLJ5aBUKrFm\nzRqsXr0aHMehpqYGlZWV2LBhA6qqqnDZZZfhv/7rv+ByuXD33XeD4ziMGDECzzzzTNIn1J94fQG8\ntfMUlAoG182vjN+ASDn5ugzcd9NMfPRVI7buOoUNWw7ikhlluGnhBGRlyN42jSCIIczBgwexfPly\njB07NuK5tmXLFsl2JpMJv/3tb8GyLFiWxY9//OOEFxgBGeFg3Z/zw46C70e+jN6os69oNNqT3OAz\nuIEo0FPJqktMgZUR+xOd79Eerh4Y+X5OpvBve3SYVlKhdUxQ+ecjp5w3n1TmZ4SQCp/jG1EhQnOT\naAhn6Fy8vkBsqJ8MivSZONsem5cjtg2AR0bFPzGcHj8sNo9ktTwguJn1KImKedH5cULX84ezwWIt\nFSXyFfRQBJNCwfRUoONiwzRZlsPBU+0Agt95qdNRJrFfnBj8zaRD5xcPKeMpU6OC1xcQzJ8KVQY9\n2Szt6Q2F72pUSsEy7P3wVYtBlmY5duxYrFq1CosWLYrYa2PVqlVx286bNy+mgMRdd90V/vtvf/ub\nXFkHHO/vbUB7lxtXnj8qvEJDpB+FgsHVF1Sgamwh/rrtCD472ILD9Wb8dNEkzKgk7xRBDHcefvjh\npNpNmjQJW7du7fX4YoqQNkvdnacRfO3yCOeMhBDKh0iEkvxsGC2xYTRC78mlyxH0HgiFubd0OJCh\nVsLlDchKco8uMhBS3KO7zs3RoLQgG3anDxq1UtQIdHn98PkDMcUP4m1YK2eeK0p0ovlFfbR/qiSh\nHJtCfSbc3kDcKnAc110wQUAZlaLT5oHd5UuoJD4f8WIAse/ZXT5ZGxpLcbKpK6b4SojsDBWcHj9Y\njpPMDYv+PkhdTofMMEkgMkcKAA6caIfHF0BuVAgov0+W4yQNc/78nlNZBI1aga+OJlehNDr/qDfM\nGFeIDI1SUJZEClOEjLvsDBVKCrJjisT0x6JFNLIMqUAggAkTJuDUqVOplmfQ0GZx4v29jcjTanDt\nxWPTLQ4hwMhiLdb8bDbe+6Ie7+9twP+8cRBzp5VgxcIJlDtFEMOYOXPmpHX8QICN2a6hJD8bmRol\n7C5fz6p/lJIbrSKolArBVVm5CFX4SgRdtiamnHYIIYVZSlkVQqOOzLEIKdXRPTMMEw6tN5qdkt60\nr38wxbwndTwDRtY8lRZkw2zzCM5HbzfklUPIWAhtIBz3+ACLtiQMZotImJ1cxOZS6Bo08TxXIw3a\niAIhchEzogAgNydDdvgZH7kbEccjNBOhPdxCvwmhxYgQx85Ywn8bzU40d4jXMFTx5lepYKAUyQ2T\ng1+ikmCRPgvtVvnGdFaGqk9qCISMO4YB1AILHPzZn1JRIFoUpC+RNKT++Mc/4re//S0ef/xxfPHF\nF7jooov6XIDBCMdxePVfx+EPsBQyNsBRKRVYNm8cZk8uxqYP6rD3sBGHTnZg+fxKzDtnhKwHDkEQ\nQwubzYa//vWvqKurg8fTo7Rs3ry5X8a3i3gLohWN6I1Mo3UAlZKBzZm8IdXb3z8pFU2uzqRWifei\nEflMKlSrt8ZhNAwDWcoowzCi8yFWfjoVMACUvMmvHJErGC7V3OGAqhdKdrIke89JbRgdj9xsjWCI\nabJ6vZQuLmZIlRZko9UcabiGvu9i97kQUkYUEDm/vTVcfBKGVKJdh2ThbwORDCFPK8PEGokcerx1\n40fkIjdHE+N1T8WihuTV+/LLL8N//+lPf+rzwQcr3/zQjkOnOjB1TD7OnxxbhZAYeIwq1uLhm2fj\npoUTEGA5bP7oGP5z8/648bgEQQw9HnroISgUCtTX1+OGG26AUqmUvR9UqlAwTFg5ae5w4GRTV8z+\nN9F5MEqlolf7Fvba5JAYW64SlyuR56VWC1f9kjKW+Iqkvo8iD2SHUIqcc394pHpEYKDiKeZScyXl\nrUkVyd6uql6EsepzhO+DZA0NsT3FAKDTIeyxE/qeht7SqPvOoI00pMSPU8vY9kFswSd6nESoKI3M\nIZP7+1U5IjfiNcPE3hMR2/OJdJuKNQ3Jq8d3gaUj7nAg4vL48fftP0CpYLDqiolU7nwQoVAwuPL8\nUVh3+1zMnVqC+lYbHtv8NZ5953teEjNBEEOdhoYG3HPPPcjMzMTixYvx3HPPYf/+/WmViWF6nv12\nlw+mLleMIhO92q1SML1Y2+1BSpmRUriknn5iyms0Uop+dBGJfG0Gxo3IRVGu8CapQGSyfWV5j/IV\nXTBCiAJdbL8MI1/ZEzuVZMLHkoVhgpu8hujL4gNiTBmdH5PXI0ayhn8iIWq6LA0MuT1567naDIyP\nUsSB5I06e3QRGBkIGR6huYgOYe0N/NC+0JjRc65WKjF9XOyep1PHyN8HNWmDOGoe5N4PapUiopAH\nAyZchp9PyFQR6zfZ/fGkkLwzvV4vTp48iRMnTkT8Hfo3HHl9+3F0WD24em4FygQ2aSMGPnnaDNy+\nZBoeWDkTFaU67Ktrw0N/3Yt/7DguGu9PEMTQQaMJKvlqtRqdnZ1Qq9Uwm81xWqUWpYKJuzB3qiVy\nHxeVStGrMlUF+kzk5mRgfHmkkpmvzcAogxYl+dnQZokbIAwTPDaakvzsCGVeCrGVbV2WBjlRitKk\n0fkozsuSnCd+d3wZzh1fFNdDJdQt020u5skwFAbKwmqGWp5HSoyRRVpJBXfGuEJMGd2zXU2uNgMl\n+T2GS3mRcAW8nEw1MjTJGQ2JeEA0agV02T33joKB4N5BiVyvkUVa5HbfP8ebIivYFenjFxuTug59\nGY4a4ZHq/j/6J6KyXI8MtRKTR0duOaTNkr+PK8NbRhELERW6h6INe7neXoZhoOa1VasUUKsUmDu1\nNGwAxivEAaTGkJJconG73bjtttvCr/l/MwyD7du3xx1g165dWLduHTiOw/Lly2P23Ni/fz/WrVuH\nY8eO4c9//jOuvPLKRM+h3/j2BxM+P9iC0SVaLLloTLrFIXrJpNH5WPOz2fjyiBFv7jyJj/adwc7v\nmnHl+aNw5fmjkS1SUpcgiMHNmDFj0NnZiWuuuQY33ngjdDodpk2bFrdda2sr7r//frS3t0OpVOL6\n66/HT3/60z6RSalUJLzKq1IoJD1SYiWCQ2RlqDClInb/Ro1aiXJDUBk+LlH2mGU5TK7Ix5d1xoj3\nx5bpYYmzSXAIMQV5ypigXKOKdTGVuUIwAj4xKeVYKs9GrVSiUJ8ZLm0equiW2a34S+VyRZOdocL0\nsYVgOQ7fnzZH7JukUiiSDqkr0GUKFmXg76ulYBioeRuhRivpY0v1KMrLxDc/tIuWTNdrNcjJUkcU\nOQgxc7wBGRpljMLKn/c8rQY2pya8dxMDBlMq8qHP0YTLVydKorYGX4kXuycS6TMrQxVTICaEnHtD\nyjDty1xtvucudN75ugzB+yZPm4HJo/NxtDF4nflShHKZFAyDPG1sezkyKxUKjC/TRRhy0YZTUN74\neZ7B6pk958YPX83ovt9NnS5kqlXdxwvLp0rgeywXSU1xx44dveqcZVmsXbsWmzZtQnFxMWpqarBw\n4UJUVvbsuTRixAj88Y9/xIsvvtirsVJNl8OLTR8ehUqpwG3XTOtV4iMxcFAwDC6cVorZkwz49Ntm\n1O6px7tf1ON/95/F5bNH4vLZoxJapSEIYuATyvm95ZZbUFVVBZvNFrNNhxBKpRIPPvggpkyZAofD\ngeuuuw4XXXRRxDMtWVQKJuHCRSolI+mQElIlElXkpQyTAMvFfK7pVmrkLkQJrcZnZ6jDimdJfpao\nISVESKkVCknUZatFK/RNGJkbYRxMH1sIX4ANe7XydRkwdbnC8hXoMgT3QwqhUDBQgEGGWhlhSGVn\nqiQ3h5WiKFfYkCrKzUKL2YHsDBUMeZkROTzRuoouWw2lQiEZlqlgGARETPSQR4lhGEwald8TPhZV\n5CA0lbnZGkwa3XOcSqlATqYaLMsltBGwmOI+uliHxpgS2JH3bV8YKoW5maLXjZ/jdMGUEvgDbEx1\nSEZAhnhhaEDwXkukBLzQ92lUsRZ5ugyc6s4JjzCYxAwOJQNfgINSoUBJflbMfRfy+JUWZKO9U/g7\npVAEvd581NEeKZnXRsEwAO8rHVGgg9eF2+fvPj74OidLDXSvBwRDPsXDgpMlpdbAwYMHUVFRgfLy\ncqjValRXV8d4sUaMGIGJEwd2rhHHcXjpg6OwOX2oubQS5UUU0jfUUKuUuOL8UXjijh9h+fxxUCgY\nvPtFPf7PX3bjnztOwJzgBowEQQx8rFYrOjs7UVZWBqWM5GuDwYApU6YAAHJyclBZWYm2tuT2aImG\nYRjkZKpRUaKDWqkI55yUFmRjlCEyVErBMCgtyIZGHekZKC3IjjiuMEppKNRnSm482iNL5FhiCFXP\nCx2eoVZi5gSDjLEEwn+iSjgnQoZaiakVBZhRGZvvIZQDFUKhiCwbrlAwEaGBfIWwKDcTI2XMI4AY\nfaGyPFdSDikUCgZTKgowY1zkfoi6bDVmTTRgRmURsjPVEcaTWqXANF7uC99bBQSVy7KCSBnl5q3k\n6zKQ250Lx2/CMLwNdgXKsVeNK8SYUvkb104fWyjofQSC3q9oRhVrBe/hbN5ChSFXOkQ03H9OBkYV\n6yL6iYa/2Mp0ewTPqSyKyDkSuo1Dc8SfnzGl+vBiRKZGhcmj8yTli84dExIxK0MVsdcpPycr8rrx\nv3fBfpVKRtAI1KgUmDOlJCivSBiv0HxFh3bKN6SATLUyfB/w8ycF++gem284leTLu+aJktLYJaPR\niLKysvDrkpISHDp0KJVDpoQPvmzEdyfaMaUiH5fPHplucYgUkqFRovrCMbh81ijs/K4JH+xrxIf7\nGvHxV2dw/pRiXDF7FMaW6Qa04U8QhDD3/X/2zjxMqurM/99be1VXVXd1d/XGTgMK2ICBqAmKCgpG\nUEAgGLckGM3yE4y4JUSTTEx0ookZiTNjnIk6mkSjCPoYHHVk1aioyCb73tBL9VLVtW+37vn9UV23\na7m1dlVXdfN+ngetrjr3nPeee+695z3ve973vvvwve99D+effz56enqwcOFC6PV62Gw23HPPPVi2\nbFnGdZ09exaHDh3KW7S/iEJUX1WG+qoyMMbgC4SgUcnh9ccmsG1sKBeVpIgqY9KrMbrOCH8gBJvL\nj7H1Rhh0qphwyRy4jCLIRU9aUz3qpCYw0d+plXJMG1eN3ce6krclUb8syeQuU5IFulCmiI4ml6W2\n7kWTjYVDEzdxVCvlGFNvSJm7CpDed8IBouISL0+0gpRohVJhxnk1CASFBDc0nUaBUXUG1Ji02HO8\nq7e+lKJJEuNKB4gDM1lPZbNVRa9Vxlj1oonfczOsWp/ghhc5n/NGmrDraNhS1DisHG1pQokDwPlR\nrq/JhmJZryJl0PZdG61ageidU1JKhSBhkVIpZJg8phIOdwCVRrVkkA25TIYKvQrdDh+UChlCgbCF\neYRZn9H9Ej0mkymHCjkHBMPuu9JlOPH7uiqdaO2KKSFxXHxdmd5LHMdBpZTjKxPMvRH7otz85DJM\nGF6Bk22OmDxTCTIUaNpWUIvUUIj0t/toF17fehwmgxp3XjepX6FmicGDWiXH3ItG4vEffA3fvfZ8\n1FfrsOOABb9+8XP8y/OfYcsXZ+HJIoM5QRDF58CBAzj//PMBAG+++SYaGxuxceNGrF+/Hn/5y18y\nrsftdmPVqlVYs2YNysr656Gg7w2ooIqbcHMcJyax1GkUmD6hL9VGbETdvvIAMG54OSaNrkSNSZcQ\nHpgPCVnHpoi882Qch4beAEtKuRwmvRojJawy8RNbjUqBqY3VGFFjwJh6Y0L0PKk3avzkqtakSxrA\nIBtkHIcqY3JrULpJaMRKGFkNj/RNdDQxIHZzv9T+mXTtTBpVidH1mVts4uclUqHCFXJZjLtlpI8j\ninV0HTKOg1adXVCI+D1JEWU2mVKb7fwwWZ8ls2hwcecDIOMAKEBY+WyICyiWrC0Zx2HGeTWS+w3F\nMjIOY+uNscFZIn0viy2nVsphrtCKStR5I0ziPqBIexW99cQE+TCnvkfG1BsxqjZ2ITjZUIxYmQJ8\nKO0esJoKbYyVVNt7j0sp/QAwYXiflS2VC/CY3iTb0XIqFTLJrTWVRg3MUVa36NOaMLwCBq0KJkNm\nkSWzpaAWqbq6OrS2top/WywW1NQMnrxLLZ0u/Omt/VAqZFi5pCllvgtiaKJUyHHZlAZc2lSPA6ds\n2PzFWew51o2X3juCVzYfQ9PYKnz1/BpMHVeVUXhdgiCKh1rd9wzfuXMnrrrqKgDhd1Wmlg+e57Fq\n1SosXLhQPD4VE0aacLZDAY1aAas90Qrx9SkNcHkDMGXg7nW0LbwXRGfQwGwOT7SNnW4ofAqYTFrx\nuwghgcHYFrZkVZVrUF9dBpc3iB5veBEouvzwOi8c7vAeEHO1XvzNGRDgDgqQyThMm1SPynYH6qrK\nYvZzGQ19q9HVFYlyAMDI3v97DrRDFbUIxXEcjIbYqGdVJl1MHfH1MbkcTn8IVeUaybaiubhJDnCA\n2aQT69pzpBM9rr5gGNUVWowYVgFfIARjh1uyTQCorCyD28eLysGcci1cnqAYEa7DGQCPsOIbffxX\n5XIcPm0T6+VDAoytsft6Jo+twv4T3QCAxtFV4fq+OBvTN1XVenGcmKtc8AfCVpeaGgMMcREJG91B\nlGmUSfunstMNj4+HwRC+Xv5gCEaLq7c+I5QKGaqrDdhztFNsJ1m/AIDHF4SxM9x31dV6DG+owFi3\nHxV6teS9xRRyGO3ha1Bp1CS4z9dW6WDp9ohtBvkQjO1h+UY3GNHa6UZdlQ71deViXyoVMlwwoQYq\npRwqrR8tVq94PhEiY9VsNsAnADZPeCx+fUoD2rpcONkajox5QWMVqspjx6VPAOy+xMAIqcZgpL3q\nKj1MvUp8W5cbx1t6MH5Mteiea2wJn4O52oCKuAm/2WyA3qjB0eZw4BeFQoZJ42sweoQJOo0STr8A\nQWB9z4Soc0wnp9YbhLGzr5/nXByWUaNSYPfRTpgrtBhea0CFKWwl77B60NrpxvBhFQmK5ane6z95\nbDjQSlW5VlL5NJsN0OjUcHmDGDeiAg6JPgWAYfXl6HYH+45JM8fyCYCr1zpnNvfdE2azAef1fxtr\nUgo682tqakJzczNaWlpgNpuxceNGPPnkk0nLl5IFy+4OYO3re+EPhPCDhZMxOkozJs49OI7D5DGV\nmDymEj0uP/65rw0ffdmOL4504osjnVDIZRg/vBwTR5kwcbQJI2sMWUV5IghiYLBYLCgvL8enn36K\nVatWid/7/ZlFmVuzZg3GjRuHb3/72xmVr68ug4IJONXugMOZmK+uxxaefHSmSH4ZwaRT4LTFCRbU\nobMzPPHqsXvhC/BQcRC/iybS5qQR5RACPKzdbvG76PJ15WoowODyBKHimPibzRYuL+M4WLtd0Ctl\ncDm8cEm0AQBaBScpRwR7j1fcEA4AgmAUj1cr5PDzIWjkqesAY6iv0MCgU6Yuh76V6ehySo7FyDxp\nRDm6egNHaBUcystUKevt9MSOlUhZu90Dh9OHoF8Rc7wcQGOtXiwrCCxhLLAgL3ldoss57V7wveNk\nZJVWDGhgs7rhi0sEa+7dO5TsPGSCAIfTi3JtWFaB9clk7XaJFiveH4QjSulMVp8/GBKP7+52iZPe\nriTjWhAEMD6E+iodKgwq+L0BtFnD98LYhnLolTIcjeoPPiSI9evk5RhXF1b2Ozud4veXTKqDvSes\nFLh9wZT92dnphNXady/02Nyw2719fWB1Q4hzJ3Q7fQnXbWpjdcqx4nL5IDCG7m4X+N6gEQoA5zUY\nRVmj5bLZ3Aj6EoNa2GwesUx9ZZnYptvpw7j6vrEVqcto0Ka9N4BwblSpfnIDGFGpTfjeqJbDONwI\na3dioBUhyMPlC8Lj8kGrVkiWiaBTcNAZVLDb3Al9WlepQ7vVA6/bHzMm4/f3xeNweGPGoM+dPFBY\nugWYbCioIiWXy/Hwww9jxYoVYIxh6dKlaGxsxNq1a9HU1IQrr7wS+/btw1133QWHw4EtW7bg6aef\nxltvvVVIsdJid/nx+Mu70Nnjw3VfH42LJtYWVR6itKjQqzH/a6Nx7SWj0NLlxueHOrDraBcOnrbh\n4GkbsD3sAjCsugwjaw2or9KhxqRFrUmHqnJN1pG5CILID3feeScWLVoEpVKJ6dOnY9y4cQCA3bt3\no6GhIe3xO3fuxFtvvYUJEyZg0aJF4DgO99xzT0YR/6Q2y09trJYomZz6qjLUmnQxrm/iAmQSg1pd\npU7cvA5Iu3IBYdevukodEBejId4FLBWVhsyCWUTar9CrY5Jq1lTqcLbDJRlAIBqO4/rlpmOu0EKn\nUWBfrwUomjH1hVk0jdlkn+RaVRk1Kd3Pove2RE8qc4lKN6JGD2OZSnS/knEcxg0rh8fHJ0Tgy4Ro\nETJJniuXhfcCRYgsPHLgUFOhTRhvqc5x8ujKBMuHVq0Ah0QXxaaxVWJUw/gRHV2D1DYOTVxdE0dV\npn2fT2msgtXhz9ijKdn1j47EGJ0jS0pWc4UWtRkqCqE85lWaNLoSIUFIq/BEEz++hpv1GG7WS7gg\nph+H2gz2fhWCgs/oZs2alfCSiV4FbGpqwrZt2wotRsb0uPx44uVdaOv2YO5XR2DRZWOKLRJRonAc\nJ970iy4bC4cngEOnbTh8pgfN7U40d7jQ3JG4IqNVK1BlVKPSqIHJoEalQR12h+n9Z9QpKZgFQRSA\nb3zjG5gxYwa6urrEvVIAUF9fj0ceeSTt8dOnT8fBgwdzaruhWgePn0d5mUoM15zLokrChLIvOJok\n8d4U8Xuq0qHKwrI+YUTqCGPRVBo1GDesPGZ/yLDqMtRX6QZkEqRTK1Bl1OQcQS8V6aam8WcXkWH8\n8Nj+iyhfY+rCrnbJ8yFl319c1D6bCNXlWiA2NzNG9UbXSxccI1o2qT1a6agxaeH0BNDQG+UwISgB\nx6HWpIuJ1hYh3q0xUn7G+eaEPYExSZ7jf4yLPBiPVqWAWilHkBdw/ihT2gTPQNhFrqE68/s8mSdL\nkM88ZUFjQ7lorUuHGN4/D1tXwpEvs0+4PKrWgNOWsKzDe/d5xY/1TMa4QafCpFGV8Ab4AV2wpqXx\nKLrsXvzh1T2iErV89jia0BIZY9SpcNHEWtGCGRIEtFu96LB6YLF50WHzoNvhh9XpQ5fdh7Od0hGD\ntGoFGqp1aKgqC6/M1BkwslZPe7AIIg+YzWaYzbFhuWtrC+91oFTIMXGUCYyF8+dUpwh6kA1Skb9S\nYdAp0WYNh/DOhEyeOxOGV2T8royEfE5WeqBWkjmOS1BcBorovpo+oSap4jH9/BqcaVFJKgrRZBsi\nPhvUSjkmjKjAJwfaU5bLxYoVjUIuw3kjY4M1TBxpiglekq21MJ1lLMEilSb3lEzGYdq46oSy+WDi\nSFPKEJnR/RCvAPcHpUKGGefVFHQMpSOTez7T7jaWqZIGOCkUNDPrZf8pK/705n64vEFcc9FILLuy\nkZQool/IZTIMqy5LmnfM6+dhdfjQ7fCj2+5FZ48PHT1etHW7carNieMtDrEsh/Bei7ENRowbVo7G\nBiPqq8soiiRBDDI4jkNjQ3n6ghkyYUQ5Trc7xZX8dFQaNWgaW5Xxiq2xTIURZn1K16T4pJupMOhU\n8Nu9YrSuoZTc3lgWDkldmYXbYaq9tEqFPK0SBeQn4Ww6zhthgjyFpakQ76JCB/iK5JWKWGOizyBZ\n3qpCzQvTnWt9VThYSq1Jm/frXex7MHIPqCRcAk16NXpcgZKej5/zihRjDP+7oxmvbzsOGcfh1nnn\n4YppDSV90YihgVatwDCzXjJkKR8SYLF6cKbDhVPtTpxud+JUuxOtXW58uLdNPL5xmBHjGsoxtsGI\nMQ3GWLcFgiCGPAadCheMrcrqmGyfE+nCKmfD6DoDKvQqUfkq16sxwqwvWGjigaSmQosyjTJlSOd8\nMnl0JQLBzF2++kMm16fWpEvIm1XKVBo1OH+kSUyoGx3wLH4/VLGRcVzSRdnBjsmgxqhag+QYO2+k\nqaQC0UlxTitSzRYn/vp/R3D0rB0mgxo/WnQBGoflb6WQIHJFIZeJStYlk+sAhBPjtXS5cbzFjuMt\ndhxtsePLE1Z8ecIqHldr0mJEjR4javQYXqNHjUmHmgpNVps/CYIgCoVCLgvvxYkin4paMeE4TpyU\nDwSZWKsGkkIF6igk0W5ygah9SOTtMXBwHIf6quRKYqkbNs5JRSoQDGHd1uPY9MVZMAZMn2DGLfPO\nS5o8jCBKAZmME5WkKy4cBgBwuAM43mrHiVYHTrY5cKrNic8Pd+Lzw53icRyACoMaFXoVysvUMJYp\nw1nXVQpoVHIoFTLI5TIo5TLIZBzkMg4cx0EuD3+Wyzgo5DIoFeF/GqUcGrUCWrU8o+hMBEEQRCzh\nSHP0/CwlItN1PXl2EFlQcEVq+/btePTRR8EYw5IlS3DnnXfG/B4IBPDggw9i//79MJlM+MMf/pBR\nGNr+sOOABe/vPItakxY3Xz0ha7cIgigVjGUqXDjejAvHhzfPM8Zgc/rR3OFCS6cLnT1edNjC+6/O\ndLhxMpQ+ik82qFVyGLRKGHRKGHThULrlvQpbhV6NCoMKFWVqlOtVRffDJoh8sGbNGmzduhVVVVVF\nT9VBDF5KzZpEhNMLCCycMoAgMqWgipQgCHjkkUfwwgsvoKamBkuXLsWcOXPQ2NiXYnjdunUoLy/H\ne++9h7fffhtPPPEE/vCHPxRSLFw0qRYGnQqTx1RS0lRiSMFxHCqNGlQaNWJ0oQiMMXj9POzuAHyB\nELx+Hl5/CHxIEP8JAoPAgFBICP9fEBASGPiQgEBQQJAX4A9GjuXh8fFweoM40+EGn0ZJ02uVKNer\nYNSpRMVLr1WiTKNAmUYJjVoOTa+VTK2UQ6WUQaUIW8wUchkUcq7kTfzE0OeGG27ArbfeigceGd0f\nXQAAIABJREFUeKDYohAEkUciXh8EkQ0FVaT27t2LUaNGYdiwsBvS/PnzsWnTphhFatOmTWJeqXnz\n5uFXv/pVIUUCEA7nOW18dokQCWKww3EcdBplTALMfMEYgy8Qgt0dgN3lR4+r7/89Lj96XH7Y3QFY\nHX60JAn7ngkKOQe5XAZFr7thRMESPys4UflSKWRQKcNKmVoph1olh0b8F3ZNjChuWrUCWnX4M1nO\niFTMmDEDLS0txRaDIAiCKAEKqkhZLBbU19eLf9fW1mLfvn0xZTo6OlBXF95ML5fLYTQa0dPTg4qK\n4uR3IAgieziOE5WRdG4RfEiA0xOEwx2AxxeE28fD5QvC5w/BF+DhC4QQ4AUEgiH4gyHwfNhaFgwx\nhEICgiEBfO9nPhRW4PhQEHyIIcgLEPoZ4Uch5xIsY2qlHEqFHCqFDEqlDAqZTFTq5DIuZm+ZjAv3\nR7TtjKEvIpTAwp8ZAwTGwlZAgfV9Zgyh3u9CvRZCsXxv0iDGGFRKOZZe0QhzhTbxJAiCIAiCKDgF\nVaQyCVkYX4YxltZ9x2w29EsugiCKS336IgQxZKB3Vmqof5JDfZMa6p/kUN8MDAX1Yamrq0Nra6v4\nt8ViQU1NTUKZ9vZwxuxQKASXy4XycgpBThAEQRAEQRBE6VJQRaqpqQnNzc1oaWlBIBDAxo0bMWfO\nnJgyV155JTZs2AAAeOedd3DJJZcUUiSCIAiC6BelniCSIAiCGBg4VuA3wvbt2/Gb3/wGjDEsXboU\nd955J9auXYumpiZceeWVCAQCuP/++3Hw4EFUVFTgySefxPDhwwspEkEQBEHkxL333osdO3agp6cH\n1dXVWLlyJZYsWVJssQiCIIgiUHBFiiAIgiAIgiAIYqhBcX4JgiAIgiAIgiCyhBQpgiAIgiAIgiCI\nLCFFiiAIgiAIgiAIIksGlSK1Zs0afP3rX8d1111XbFH6TXt7O2677TZce+21uO666/Diiy8WW6Sc\nCQQCWLZsGRYtWoTrrrsOTz/9dLFF6jeCIGDx4sX4wQ9+UGxR+sXs2bNx/fXXY9GiRVi6dGmxxekX\nTqcTq1atwje+8Q3Mnz8fe/bsKbZIOXHy5EksWrQIixcvxqJFizB9+vRBff+/8MILWLBgAa677jrc\ne++9CAQCxRapZNi+fTuuueYazJs3D88++2yxxRlwkr3n7HY7VqxYgXnz5uH222+H0+kUj/n1r3+N\nuXPnYuHChTh48GCxRB8w4t81Z8+exTe/+U3MmzcPq1evBs/zAMLv2XvuuQdz587F8uXLY1LLDFWk\nnvk0dvqQevaeq+NHSj/IZaxs2LAB8+bNw7x58/DGG29k1jgbRHz22WfswIEDbMGCBcUWpd90dHSw\nAwcOMMYYc7lcbO7cuezYsWNFlip3PB4PY4wxnufZsmXL2J49e4osUf94/vnn2b333su+//3vF1uU\nfjF79mzW09NTbDHywoMPPsjWrVvHGGMsGAwyp9NZZIn6TygUYjNnzmStra3FFiUn2tvb2ezZs5nf\n72eMMXb33XezDRs2FFmq0iAUCrGrrrqKnT17lgUCAXb99dcP6md8LiR7zz3++OPs2WefZYwx9qc/\n/Yk98cQTjDHGtm7dyu644w7GGGO7d+9my5YtK47gA0j8u+buu+9mb7/9NmOMsZ///Ofs5ZdfZowx\n9te//pX94he/YIwxtnHjRvbjH/+4KPIOJPHPfIfDQWOnF6ln7/r168/Z8SOlH2Q7Vnp6eticOXOY\nw+Fgdrtd/JyOQWWRmjFjBoxGY7HFyAtmsxkTJ04EAJSVlaGxsREdHR1Flip3tFotgPCqR2QFZLDS\n3t6Obdu2YdmyZcUWpd8wxiAIQrHF6Dculwuff/65GGZaoVBAr9cXWar+89FHH2HkyJGor68vtig5\nIwgCvF4veJ6Hz+dLSLp+rrJ3716MGjUKw4YNg1KpxPz587Fp06ZiizWgSL3nLBYLNm3ahMWLFwMA\nFi9eLPbLpk2bsGjRIgDA1KlT4XQ60dXVVRzhBwCpd80nn3yCefPmAQj3zfvvvw8AMX02b948fPzx\nxwMv8AAi9cw3GAw0dqKQevbu2LHjnBw/UvpBtmPlww8/xMyZM2EwGGA0GjFz5kx88MEHadseVIrU\nUOXs2bM4dOgQpkyZUmxRckYQBCxatAgzZ87EzJkzB/W5PProo3jggQfAcVyxRek3HMfh9ttvx5Il\nS/Dqq68WW5ycOXv2LEwmE376059i8eLFePjhh+Hz+YotVr95++23MX/+/GKLkTO1tbX47ne/iyuu\nuAKzZs2CwWDA17/+9WKLVRJYLJYYBbm2tnZQL5b1l8h7burUqeju7kZ1dTWAsLJltVoBAB0dHair\nqxOPqa2thcViKYq8A0H8u8Zms6G8vBwyWXhqVldXJ55/dN/I5XIYjUb09PQUR/ABQOqZ7/V6aez0\nIvXsnTRpEoxGI42fXqxWa0ZjJdJPUs/sTMYQKVJFxu12Y9WqVVizZg3KysqKLU7OyGQyvPHGG9i+\nfTv27NmDY8eOFVuknNi6dSuqq6sxceJEsCGQYu2VV17B+vXr8V//9V/461//is8//7zYIuUEz/M4\ncOAAbrrpJmzYsAEajWbQ7zkJBoPYvHkzvvGNbxRblJxxOBzYtGkTtmzZgg8++AAejwdvvfVWscUq\nCYbC8yNfxL/nki1SSfXZUFjQkkLqXcMYS+iDyPnHf88YG7J9AyQ+87VaLZ599lkaO73EP3u9Xi+2\nb9+eUO5cHT+pSNYXuY4hUqSKCM/zWLVqFRYuXIirrrqq2OLkBb1ej4suuigjc2gp8sUXX2Dz5s2Y\nM2cO7r33XuzYsQMPPPBAscXKGbPZDACorKzE1VdfjX379hVZotyoq6tDXV0dmpqaAIRdEw4cOFBk\nqfrH9u3bMXnyZFRWVhZblJz56KOPMGLECFRUVEAul+Pqq6/Grl27ii1WSVBXVxezodtisZyTbo9S\n77mqqirR7aqzs1O8B2pra9He3i4e297ePmT7TOpd8+ijj8LpdIru2NHnH903oVAILpcL5eXlRZO/\n0MQ/8+fOnYsDBw7Q2Okl/tl71VVXYdeuXXA4HDR+esl2rMQ/szMdQ4NOkRpKq3xr1qzBuHHj8O1v\nf7vYovQLq9UqRkPx+Xz4+OOPMXbs2CJLlRurV6/G1q1bsWnTJjz55JO4+OKL8fjjjxdbrJzwer1w\nu90AAI/Hgw8//BDjx48vslS5UV1djfr6epw8eRJAeB9BY2NjkaXqHxs3bsSCBQuKLUa/aGhowJ49\ne+D3+8EYGxLXJV80NTWhubkZLS0tCAQC2LhxI+bMmVNssQYcqffc7NmzsX79egDhKFmRfpkzZ44Y\nKWv37t0wGo2ia85QQ+pd87vf/Q4XX3wx3nnnHQCxfTN79mxs2LABAPDOO+/gkksuKZrsA4HUM3/c\nuHE0dnqRevaOHz/+nB4/8fpBtmPl0ksvxUcffQSn0wm73Y6PPvoIl156adp2OTaINJPIqk1PTw+q\nq6uxcuVKcSPiYGPnzp245ZZbMGHCBHAcB47jcM8992DWrFnFFi1rDh8+jJ/85CcQBAGCIODaa6/F\nD3/4w2KL1W8+/fRTPPfcc3jmmWeKLUpOnDlzBnfddRc4jkMoFMJ1112HO++8s9hi5cyhQ4fws5/9\nDDzPY8SIEXjsscdgMBiKLVZO+Hw+XHHFFXj//fcHfdCMp59+Ghs3boRCocCkSZPw61//Gkqlsthi\nlQTbt2/Hb37zGzDGsHTp0kF9/+VCsvfclClT8OMf/xhtbW1oaGjAU089JW4U/9WvfoUPPvgAWq0W\njz32GCZPnlzksyg80e+aM2fOYPXq1XA4HJg4cSKeeOIJKJVKBAIB3H///Th48CAqKirw5JNPYvjw\n4cUWvaBIPfNDoRCNnV6knr3t7e3n5PiR0g+uuuoq3H333VmNlfXr1+OZZ54Bx3H44Q9/KAalSMWg\nUqQIgiAIgiAIgiBKgUHn2kcQBEEQBEEQBFFsSJEiCIIgCIIgCILIElKkCIIgCIIgCIIgsoQUKYIg\nCIIgCIIgiCwhRYogCIIgCIIgCCJLSJEiCIIgCIIgCILIElKkCIIgCIIgCIIgsoQUKYIgCIIgCIIg\niCwhRYogCIIgCIIgCCJLSJEiCIIgCIIgCILIElKkCIIgCIIgCIIgsoQUKYIgCIIgCIIgiCwhRYog\nisTs2bPx8ccfF1sMgiAIgkgJva8IQhpSpAiCIAiCIAiCILKEFCmCIAiCIAiCIIgsIUWKIAiCIAiC\nIAgiS0iRIgiCIAiCIAiCyBJSpAiCIAiCIAiCILKEFCmCIAiCIAiCIIgsIUWKIAiCIAiCIAgiS0iR\nIgiCIAiCIAiCyBJSpAiiSHAcV2wRCIIgCCIt9L4iCGk4xhgrthBAOGu2Xq+HTCaDQqHAunXrii0S\nQRAEcY6wZs0abN26FVVVVXjrrbcSfj9x4gTWrFmD/fv3Y/Xq1fjud79bBCkJgiCIUkJRbAEicByH\nl156CeXl5cUWhSAIgjjHuOGGG3DrrbfigQcekPy9oqICDz30EN5///0BlowgCIIoVUrGtY8xBkEQ\nii0GQRAEcQ4yY8YMGI3GpL9XVlbiggsugEJRMuuPBEEQRJEpGUWK4zjcfvvtWLJkCV599dVii0MQ\nBEEQBEEQBJGUkllae+WVV2A2m2G1WvHd734XY8eOxYwZMyTLdnY6B1g6giAIIhVms6HYIpQkjDHa\nqE8QBDFEKRlFymw2Awi7T1x99dXYt29fUkWKIAiCIAYDHMfR4l8KzGYD9U8SqG9SQ/2THOqb1ORz\n4a8kXPu8Xi/cbjcAwOPx4MMPP8T48eOLLBVBEARxLpFpENsSCXZLZAgfov3XBEEUhpKwSHV1deGu\nu+4Cx3EIhUK47rrrcOmllxZbLIIgCOIc4d5778WOHTvQ09ODK664AitXrkQwGATHcVi+fDm6urqw\nZMkSuN1uyGQyvPjii9i4cSPKysqKLTqRgtPtTrRZ3WgaW4UyjbLY4hAEMcQomTxS2UDmSoIgiNKC\n9kglh95ZySm0C9InB9oBAKNqDaivGlxKL7lnpYb6JznUN6kZcq59BEEQBEEQBEEQgwlSpAiCIAiC\nIAiCILKkJPZIEcRgwO0L4tDpHhxvseNYix1Wpw9KuQxKhRwGnRITRlRg0mgTxtQboZDTGgVBEARB\nEMRQhhQpgkiD3R3AuzuasXnXWQSC4ehPMo6DyaCCLxCC0xNES6cLB0/b8OaHJ6FVK3D51AZcNWM4\nKo2aIktPEARBEARBFAJSpAgiCUFewBsfnMD7O88iyAuo0Ktw7cXDMGFEBcbUG6FWycWyLm8Qh5tt\nOHDahp2HO/HOp834v8/P4JJJtVh02VhUlZNCRRAEQRAEMZQgRYogJGi3evDMm1+i2eJClVGNay8Z\nhUun1EOpkEuW12uVmH5eDaafV4MbZ4/Dx/stePfTZvzzy3Z8drgD188cg7lfHUEufwRRoqxZswZb\nt25FVVUV3nrrLckyv/71r7F9+3ZotVr867/+KyZOnDjAUhIEQRClBM3qCCKOT/a3419e+AzNFhdm\nTW3Ar++4BFd+ZXhSJSoepUKOWVMb8Mj3Lsbt8ydCrZRj3dbj+MVzn+J4q73A0hMEkQs33HAD/vzn\nPyf9fdu2bWhubsZ7772HX/3qV/jFL34xgNIRBEEQpQgpUgQRxdufnMazbx0AB+AHCyfjO984H2pl\nZgpUPDKOw8ymejx65yW48sJhaO/24LGXvsA/PjoFQRh06dsIYkgzY8YMGI3GpL9v2rQJixYtAgBM\nnToVTqcTXV1dAyUeQRAE0U98AR52lz+vdZIiRRAAGGN4fdtxrNt6HJVGNR7+9gxcNLE2L3WXaZS4\ndd55uO/GaTCWKbF++wn87pVdsDnzezMTBAF8/PHH+Mtf/gIA6OrqwsmTJ/NSb0dHB+rq6sS/a2tr\nYbFY8lL3YIIxhpZOF7x+vtiiEARBZMXuY1042GzLa520R4o452GM4W/vH8WmnWdRY9Li/hsvLEhw\niImjK/EvKy7C828fwu5jXfjVC5/h/93QhHHDyvPeFkGcizz77LPYtm0bOjs7ccstt4DneaxZswYv\nv/xyv+tmLNGKzHFcRseazYZ+t18qdNu9sPtCcAY8uGzasLzUWcj+MRrC7tQmU9mgvA6DUeaBhPon\nOdQ3iUSeB/mkZBQpQRCwZMkS1NbW4plnnim2OMQ5xGtbj2PTzrMYbi7DvcunoVyvLlhbBp0KK5c0\n4b3PzuDVLcfw+N++wK1zz8NlUxsK1iZBnCv84x//wOuvv45ly5YBAOrq6uByufJSd21tLdrb28W/\n29vbUVNTk9GxnZ3OvMhQCnT2eOFwesOf83BeZrOhoP0TkdVmU0AzyHxwCt03gx3qn+Sk6xuXNwiF\nnINGVTJqwIAQeR7kk5J5rLz44otobGwsthjEOcY7O5rxzo5m1FXqcP+3LiyoEhWB4zjMu2gkVi+f\nBrVSjuf/9xD+9v4R2jdFEP1Eo9FAqVTGfJep1QiQtjpFmDNnDt544w0AwO7du2E0GlFdXZ2VfHxI\ngNMTyOoYgiBiSXWfEpnx5clu7D5GezzzQUkoUu3t7di2bZu4ikgQA8E/97Xh1S3HYDKosXr5VBh0\nqgFtf/LoSjz8na9iWHUZ3v/8LP7jjS8RCIYGVAaCGErU1dXh888/B8dxEAQB//Ef/4Hx48dndOy9\n996LG2+8ESdPnsQVV1yB119/Ha+88gr+/ve/AwAuv/xyDB8+HFdffTV+/vOf5xS173BzD/afssLl\nDWZ9bKlAU9jiEuTPXWWcMYaDp6zYcdCCLnv+LQsEkQslYdN79NFH8cADD8DpJBMtMTDsP2nF828f\ngk6twD3fnIrqcm1R5Kip0OKnt3wFT6/fhy+OdOKJl3dh5dIpMA6wUkcQQ4GHH34YDz74II4ePYqp\nU6dixowZ+N3vfpfRsb///e/Tlvn5z3/eL/mc3vAE2Ofnodcq05QmiES+PNENPx/CtHHV55xbVofN\nC3uvEtlt9xVZGmn4kIDdR7tQX12GYdVlxRZHErLo5ZeiW6S2bt2K6upqTJw4kS4uMSC0dLnxH2/s\ng0wGrFo6BcPN+qLKo9MosXr5NFwyuRbHWx147KWdJfuSIIhSxmw247nnnsNnn32GTz75BM8//zyq\nqqqKLVYimXsbEkQMfj7stRDghSJL0ocvwONYix1BvrAeFd5AX6TIbFx2BxK3jwcvCDjTUbqGAZpp\n55eiL2d88cUX2Lx5M7Zt2wa/3w+3240HHngAjz/+eLFFI4YgDk8AT722B15/CHdcNwkTRlQUWyQA\ngEIuwx0LJsFkUON/P2nGo3/ZiftunIb6qtJc0SKIUmTbtm2S319++eUDLElqONKkCkZbtxtBXsDI\nWopYNlCcanOix+0HGDBueOGi0EbfN7ISVaRKVKxYBkiTOnTaBrVKjjH1yfPzScGHBJxodaChumxQ\nWO6LrkitXr0aq1evBgB8+umneO6550iJIgpCkBfw7+v3ocvuw/UzR+Nrk+vSHzSAcByHZVeMg16j\nxGtbj+Oxv3yBe745NeuHEEGcq/z3f/+3+DkQCODgwYOYNGlSySlSg5oS9xw5bQlbAkiRGjgiI8Jf\n4D2+0UqKN8CjtcsFOWMlpVSVjiTJEQbgHm7rdoeVazeynsO0Wz2wOn1wuAOYcX5mkVGLSdEVKYIY\nCBhjePHdQzh61o6LJtZg4aVjii1SUr5xySiUaZX4n3cO4YmXd+Geb07F+OGlYTkjiFLmpZdeivn7\n2LFj+POf/1wkaZJTQvO+ghDkBRxutsGgU2FUHSk0Qx2lPLxLJFhgd8NohcntC+Jocw/qKzQwGQof\nbTdTStXlcCBhjIkLGrkdH/5/aJBEMs7rHqnbb78dW7ZsyXmv00UXXUQ5pIiC8O6nZ/DPfe0YU2/A\nimsnlvzDbtbUBnz/+skIBAU8+fc9OHQ6v5m4CeJcYNy4cdi/f3+xxTjn8PiCcPmCaLO6C95WSCid\nvUIDSgnNMRWK8PuUD2V/LewuP9q6MxsnUq/tUksbIivtqQWAkjcqDzryqkgtX74c//M//4OrrroK\nzz77LGw2mvwRxWfv8S68tuUYKvQq3HXDFKiU8mKLlBEXTazFjxZfAD4k4N9e24P9J63FFokgSppt\n27aJ/7Zs2YK1a9dCocjc8WL79u245pprMG/ePDz77LMJv7e2tuI73/kOrr/+etx2222wWCw5yVnq\nCzmpyGQOVsiVZEFgYpqIIC/gs0MdOHbWXtD2vH4+fcFzGLksPJXkc1BqDzbbcNrizGwBXuK+YaWk\nUZYQjDF4fMEk/VrYPstX7fm+toUKaJdX1765c+di7ty5OHHiBP72t79hwYIFmDlzJm677TZccMEF\n+WyKIDKipcuNZ97cD4VChpVLppSUC0AmfGWCGSuXNOHp9V/iqXV7sXJJE5rGlmAUMoIoAaL3SCkU\nCowYMQJPPfVURscKgoBHHnkEL7zwAmpqarB06VLMmTMnJlH8b3/7WyxevBgLFy7Ejh078Pvf/572\n9EqQi2UiU/ad6IY3wGPGeTXw9Co4XQ4vxqEwQQ4ON9tg9wQwaXQlpaVIQj7WBRhLX4+ktYf0qARC\ngoDtu1rgcHpRV6nD6LrYPUolZsRLoFDLTIWyxBV0j5RSqYRarcaDDz6Iyy67DD/5yU8K2RxBxBCJ\n0OcLhPD96ycP2qANUxqrcffSKVj7+l788fV9pEwRRBLi90hlw969ezFq1CgMGzYMADB//nxs2rQp\nRpE6fvw41qxZAwC4+OKL8aMf/SintlJNGAWBQTYY/INSUEiLVCQEdkhgA+LWFclbRMnSC0vY+pB6\n3EtZckvNsbOYOoo/GEKQF+Dx9SX87nFJJG8utJBJ6rc6fFAp5UWLxFeoIBt5VaTee+89/OUvf0F3\ndzduuukmbNy4EWVlZeB5HnPnziVFihgw4iP0XTypttgi9YvJYyqxagkpUwQhRbKw5xEyidpnsVhQ\nX18v/l1bW4t9+/bFlDn//PPx3nvv4dZbb8V7770Hj8cDu92O8vL8WEMOnrLC7gngovNrB7Uy5fQE\n0xfKAwOaezLPTfmDIVgdPlSXa6BUDA5380KSkWdfrgeeI+w+2gUGhlFRESulHiPFcoc8crYHAHDJ\npOJETB4Urn3r1q3DHXfcgcsuuyy2EYUCDz30UD6bIoikMMbwP+8Mjgh92RCvTK1a0oQLSJkiiBiX\nvng4jstIkcrkJfvAAw/gkUcewYYNGzBjxgzU1tZCLk8/Cbb7QjAZ1TAatACAqio9Ko0a8fd9x7oQ\n4ENgcjmMBi0qKsugLtG9nEGOQ7crrCiZzdIR+Q6csYvnWlmlhzyNUpisHimMBrt4jNLph9Huj6kj\n+vfov02msqzaiW/PVFkGcx7z+u0/0Q2bh4e2jGF8fXK54mWOyFNVpUdFElf1TpsXOo0CZQO08u/m\nGRy+sMUu2z6OnE91tT6tQhkAh253rJJuqiyDuVqf8jhBYOi2+1BZrkk7FrPF4wsiyAso14evhcYT\ngLHTAyD7vugvht6+NBi1sHmcMBq00OuUCXJ4fEEYLe6CyRgKCTAaHAAAtUoOs9kAxpj4TEjXpodn\ncPhzG0+p8Pp5GA2uvNUXIa+K1J/+9Kekm2hnz56dz6YIIikbPz6Nj75sx5h646CI0JcNk8dUYtXS\nKVi7bi/Wvr4Pdy+dgsljKostFkEUlf649EWoq6tDa2ur+LfFYkFNTWwOk5qaGvzxj38EAHg8Hrz3\n3nvQ61NP4rx+HgdPdMZ819XlQsjfNyE81RIbmKm7y1lwK4XAGA6dtqHWpENVuSb9Ab1YrR44nF4A\nQGendIjjyO8A0NHhgEKePK6V2WxIWk+qujs7nehx+RNkSfa3zaaAJsvwWiFBEI9vaZNBCATzdl3a\nOxzw+HkowFChkZ6KSfVNRJ7ubheCvkS3LT4k4PPDHQCASkNYcWgcVrgkuQBgtbrTjolkRI7r6HAm\nDQQVEgR4/SE43IGYsWU0aGHtdkOZZhGkpcuNMx1O1FToMLYhvy7+nxxoB9BnZXF5gzn3RX+JtNva\n6ybpcHoh8HyCHB4fn1RGpyeAMo0ypUXcHwxhz7EujKk3wlyhTfidD/XdNyqFHJ2d4WAimfaL1Zb7\neJKS9ejZHoyqNUAu42LGT77Ia9S+m266CXZ7X/Scnp4e3HzzzflsgiBS8vH+dqzffgKVRjVWLmka\nNBH6smHy6EqsXNIEAFj7+l4cOEXR/AgigtPpxN69e/HZZ5+J/zKhqakJzc3NaGlpQSAQwMaNGzFn\nzpyYMjabTbRc/elPf8KSJUvS1pubO0nhF3+c7gAcngCOtvTkve7ofD8Fc79jsXmLCpHDiA/1yd7a\n7cbOI50pSpcG0f1tdfrQac//xDFVm6lweYPYfawLHl9iFMRUNRw5Y8eXJ7vR3JE4qc6kZbc32Nu+\nxH6hIYjV6RM/Sy8kS/ea1eHD/lNWnGx3pK7f4YPAGI63po+WGRkauT4FTrY5wIcEtHS58elBS9aB\nbFq73HB5gzhyxl6wvZt5VaQ8Hk+Mr3hFRQVcrvyb0QhCioOnbXhu40Fo1Qrcs2wqKvSDK0JfNlww\npgorlzSBMYa160iZIggAePvtt7FgwQJ8+9vfxkMPPYTbbrsNjz76aEbHyuVyPPzww1ixYgUWLFiA\n+fPno7GxEWvXrsWWLVsAAJ9++imuueYaXHPNNbBarfjBD36Qtl6pOWb6iWfh9zDkw1Lv8fGSCkz0\n6RUqHoTAGFq7+vIPpUsAmos+V8jog/1VlktpZ1CmfXuqzQFfgMcZKYWIMQR5Ad12X8JvvhTh5wd0\nn1wG5EMePiTgZJsDVkdiX6RCIUuc0mcT6NDRG1jF5vCnbEeWy7Mjx26x2Dxo7bUoCoyJSnHGzUY/\niwr0MMqra58gCPB4PNDpdAAAt9uNUIgi3RCFp6XThafXhzeG37X4Agwzp3a3GQo0ja1CGES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bM5fWLZ8nItfHGTuna7P6GuCOXlWgSExPr5kACjIaxYunkGg04JY5k6aT0AoNKq0OX0o6vHi5lT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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff2afedf048>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace, varnames=['tau', 'l', 'sigma']);"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"plot_x_diffs = np.subtract.outer(plot_x, plot_x)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"ename": "ValueError",
"evalue": "total size of new array must be unchanged",
"output_type": "error",
"traceback": [
"\u001b[1;31m\u001b[0m",
"\u001b[1;31mValueError\u001b[0mTraceback (most recent call last)",
"\u001b[1;32m<ipython-input-19-cc3564653fc1>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;32mwith\u001b[0m \u001b[0mmodel\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m \u001b[0mppc_trace\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msample_ppc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtrace\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mPPC_SAMPLES\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[1;32m/opt/conda/lib/python3.5/site-packages/pymc3/sampling.py\u001b[0m in \u001b[0;36msample_ppc\u001b[1;34m(trace, samples, model, vars, size)\u001b[0m\n\u001b[0;32m 353\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mvar\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mvars\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 354\u001b[0m ppc[var.name].append(var.distribution.random(point=param,\n\u001b[1;32m--> 355\u001b[1;33m size=size))\n\u001b[0m\u001b[0;32m 356\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 357\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[1;33m{\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0masarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mv\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mppc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m/opt/conda/lib/python3.5/site-packages/pymc3/distributions/multivariate.py\u001b[0m in \u001b[0;36mrandom\u001b[1;34m(self, point, size)\u001b[0m\n\u001b[0;32m 63\u001b[0m \u001b[0mdist_shape\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 64\u001b[0m \u001b[0mbroadcast_shape\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmu\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 65\u001b[1;33m size=size)\n\u001b[0m\u001b[0;32m 66\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0msamples\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 67\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m/opt/conda/lib/python3.5/site-packages/pymc3/distributions/distribution.py\u001b[0m in \u001b[0;36mgenerate_samples\u001b[1;34m(generator, *args, **kwargs)\u001b[0m\n\u001b[0;32m 329\u001b[0m \u001b[0msamples\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgenerator\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msize\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msize\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 330\u001b[0m \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 331\u001b[1;33m \u001b[0msamples\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgenerator\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msize\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 332\u001b[0m \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 333\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0msize\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m/opt/conda/lib/python3.5/site-packages/pymc3/distributions/multivariate.py\u001b[0m in \u001b[0;36m_random\u001b[1;34m(mean, cov, size)\u001b[0m\n\u001b[0;32m 57\u001b[0m \u001b[1;31m# FIXME: cov here is actually precision?\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 58\u001b[0m return stats.multivariate_normal.rvs(\n\u001b[1;32m---> 59\u001b[1;33m mean, cov, None if size == mean.shape else size)\n\u001b[0m\u001b[0;32m 60\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 61\u001b[0m samples = generate_samples(_random,\n",
"\u001b[1;32m/opt/conda/lib/python3.5/site-packages/scipy/stats/_multivariate.py\u001b[0m in \u001b[0;36mrvs\u001b[1;34m(self, mean, cov, size, random_state)\u001b[0m\n\u001b[0;32m 523\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 524\u001b[0m \"\"\"\n\u001b[1;32m--> 525\u001b[1;33m \u001b[0mdim\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmean\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcov\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_process_parameters\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmean\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcov\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 526\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 527\u001b[0m \u001b[0mrandom_state\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_random_state\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrandom_state\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m/opt/conda/lib/python3.5/site-packages/scipy/stats/_multivariate.py\u001b[0m in \u001b[0;36m_process_parameters\u001b[1;34m(self, dim, mean, cov)\u001b[0m\n\u001b[0;32m 380\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mdim\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 381\u001b[0m \u001b[0mmean\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 382\u001b[1;33m \u001b[0mcov\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 383\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 384\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mmean\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[1;36m1\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mmean\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0mdim\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;31mValueError\u001b[0m: total size of new array must be unchanged"
]
}
],
"source": [
"x_diffs_shared.set_value(plot_x_diffs)\n",
"\n",
"PPC_SAMPLES = 5000\n",
"\n",
"with model:\n",
" ppc_trace = pm.sample_ppc(trace, PPC_SAMPLES)"
]
}
],
"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": "3.5.1"
},
"widgets": {
"state": {},
"version": "1.1.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
@twiecki
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twiecki commented Sep 28, 2016

I was able to get the PPC to start sampling with this (hacky) change:

with pm.Model() as model:
    tau = pm.StudentTpos('tau', nu=4)
    l = pm.StudentTpos('l', nu=4)
    K = pm.Deterministic('K', tau**2 * tt.exp(-x_diffs_shared**2 / l**2))

    log_sigma = pm.Uniform('log_sigma', -2., 2.)
    sigma = pm.Deterministic('sigma', tt.power(10., log_sigma))

    cov = pm.Deterministic('cov', K + sigma**2 * tt.eye(x_diffs_shared.shape[0]))
    y_obs = pm.MvNormal('y_obs', tt.zeros_like(cov)[0, :], cov, observed=y)

However, the output does not seem correct:
image

@twiecki
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twiecki commented Sep 28, 2016

Actually seems to work somewhat:
image

@AustinRochford
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Author

Interesting! I'll see if I can take this any further.

@avidaa
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avidaa commented May 8, 2017

I am looking for an example of Gaussian Process classification in PyMC3 with PPC sampling. The only example of Gaussian Process for classification that is provided in the documentation[1] does not provide an example of PPC sampling. When I use that example with PPC I receive the following error: TypeError: object of type 'NoneType' has no len(). Here is the code that I use at the moment:

# ******************** Modelling *******************************
print("Modelling ...")
model_input = theano.shared(np.array(X_train))
model_output = theano.shared(y_train.values)
n, p = X_train.shape
with pm.Model() as gp_model:
    # prior over alpha
    alpha = pm.Normal('alpha', mu=0.5, sd=5 ** -5, shape=(1))
    # prior over betas, notice that each beta has its own distribution
    betas = pm.Normal('betas', mu=0, sd=10 ** -5, shape=(1, p))
    # Logistic Regression model, you have alpha and beta * x^i
    f_transform = pm.invlogit(alpha + tt.sum(betas * model_input, 1))

    # Binomial likelihood
    y = pm.Binomial('y', observed=model_output, n=np.ones(n), p=f_transform, 
    shape=n)
    # Interpolate function values using noiseless covariance matrix
    L = tt.slinalg.cholesky(K_stable)
    f_pred = pm.Deterministic('f_pred', tt.dot(K_s.T, tt.slinalg.solve(L.T, 
    tt.slinalg.solve(L, f_transform))))

with gp_model:
    if sampler == "1":
        print("Mini_batch does not work ATM!")

    if sampler == "2":
        step = pm.NUTS()
        trace = pm.sample(advi_iter, step)

    # save the trace plot
    pm.traceplot(trace[n_burn_in:])
    plt.savefig(output_dir + "trace_" + str(trace_draws) + "_draw.png")
    print("Test the model ...")
    # Replace shared variables with testing set
    model_input.set_value(X_test)
    model_output.set_value(y_test)
    n = X_test.shape[0]
    print("OK ....")
    # Create posterior predictive samples from ADVI
    ppc = pm.sample_ppc(trace, model=gp_model, samples=ppc_samples)
    # Use probability of > 0.5 to assume prediction of class 1
    pred = ppc['f_pred'].mean(axis=0) > 0.5

[1]https://pymc-devs.github.io/pymc3/notebooks/GP-slice-sampling.html#Gaussian-Process-Classification

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