diff --git a/candlegp/models/gpmc.py b/candlegp/models/gpmc.py new file mode 100644 index 0000000..6e6c1b3 --- /dev/null +++ b/candlegp/models/gpmc.py @@ -0,0 +1,86 @@ +# Copyright 2016 James Hensman, alexggmatthews +# Copyright 2017 Thomas Viehmann +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + + +import torch +from torch.autograd import Variable + +from .. import likelihoods +from .. import densities +from .. import parameter +from .. import priors +from .. import conditionals + +from .model import GPModel + + +class GPMC(GPModel): + def __init__(self, X, Y, kern, likelihood, + mean_function=None, + num_latent=None, + **kwargs): + """ + X is a data matrix, size N x D + Y is a data matrix, size N x R + kern, likelihood, mean_function are appropriate GPflow objects + + This is a vanilla implementation of a GP with a non-Gaussian + likelihood. The latent function values are represented by centered + (whitened) variables, so + + v ~ N(0, I) + f = Lv + m(x) + + with + + L L^T = K + + """ + GPModel.__init__(self, X, Y, kern, likelihood, mean_function, **kwargs) + self.num_data = X.size(0) + self.num_latent = num_latent or Y.size(1) + self.V = parameter.Param(self.X.data.new(self.num_data, self.num_latent).zero_()) + self.V.prior = priors.Gaussian(0., 1.) + + def compute_log_likelihood(self): + """ + Construct a tf function to compute the likelihood of a general GP + model. + + \log p(Y, V | theta). + + """ + K = self.kern.K(self.X) + L = torch.potrf( + K + Variable(torch.eye(self.X.size(0), out=K.data.new()) * self.jitter_level), upper=False) + F = torch.matmul(L, self.V.get()) + self.mean_function(self.X) + + return self.likelihood.logp(F, self.Y).sum() + + def predict_f(self, Xnew, full_cov=False): + """ + Xnew is a data matrix, point at which we want to predict + + This method computes + + p(F* | (F=LV) ) + + where F* are points on the GP at Xnew, F=LV are points on the GP at X. + + """ + mu, var = conditionals.conditional(Xnew, self.X, self.kern, self.V, + full_cov=full_cov, + q_sqrt=None, whiten=True) + return mu + self.mean_function(Xnew), var diff --git a/notebooks/mcmc.ipynb b/notebooks/mcmc.ipynb new file mode 100644 index 0000000..28d7196 --- /dev/null +++ b/notebooks/mcmc.ipynb @@ -0,0 +1,580 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "cell_id": "60999B877FB04A348964DC63A3B89460" + }, + "source": [ + "# Fully Bayesian inference for generalized GP models with HMC\n", + "\n", + "*James Hensman, 2015-16*\n", + "\n", + "Converted to candlegp *Thomas Viehmann*\n", + "\n", + "It's possible to construct a very flexible models with Gaussian processes by combining them with different likelihoods (sometimes called 'families' in the GLM literature). This makes inference of the GP intractable since the likelihoods is not generally conjugate to the Gaussian process. The general form of the model is \n", + "$$\\theta \\sim p(\\theta)\\\\f \\sim \\mathcal {GP}(m(x; \\theta),\\, k(x, x'; \\theta))\\\\y_i \\sim p(y | g(f(x_i))\\,.$$\n", + "\n", + "\n", + "To perform inference in this model, we'll run MCMC using Hamiltonian Monte Carlo (HMC) over the function-values and the parameters $\\theta$ jointly. Key to an effective scheme is rotation of the field using the Cholesky decomposition. We write\n", + "\n", + "$$\\theta \\sim p(\\theta)\\\\v \\sim \\mathcal {N}(0,\\, I)\\\\LL^\\top = K\\\\f = m + Lv\\\\y_i \\sim p(y | g(f(x_i))\\,.$$\n", + "\n", + "Joint HMC over v and the function values is not widely adopted in the literature becate of the difficulty in differentiating $LL^\\top=K$. We've made this derivative available in tensorflow, and so application of HMC is relatively straightforward. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "cell_id": "CD79F257C3AB4A1694B310D895F75A17" + }, + "source": [ + "### Exponential Regression example\n", + "The first illustration in this notebook is 'Exponential Regression'. The model is \n", + "$$\\theta \\sim p(\\theta)\\\\f \\sim \\mathcal {GP}(0, k(x, x'; \\theta))\\\\f_i = f(x_i)\\\\y_i \\sim \\mathcal {Exp} (e^{f_i})$$\n", + "\n", + "We'll use MCMC to deal with both the kernel parameters $\\theta$ and the latent function values $f$. first, generate a data set." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "cell_id": "B0EFB17161DC4E7E84087F2B99D12E7D" + }, + "outputs": [], + "source": [ + "import sys, os\n", + "sys.path.append(os.path.join(os.getcwd(),'..'))\n", + "\n", + "import candlegp\n", + "import candlegp.training.hmc\n", + "import numpy\n", + "import torch\n", + "from torch.autograd import Variable\n", + "from matplotlib import pyplot\n", + "pyplot.style.use('ggplot')\n", + "%matplotlib inline\n", + "\n", + "\n", + "X = Variable(torch.linspace(-3,3,20,out=torch.DoubleTensor()))\n", + "Y = Variable(torch.from_numpy(numpy.random.exponential(((X.data.sin())**2).numpy())))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "cell_id": "0D7ADCE6053048AA9B0FF69D4A9C70D9" + }, + "source": [ + "GPflow's model for fully-Bayesian MCMC is called GPMC. It's constructed like any other model, but contains a parameter `V` which represents the centered values of the function. " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "cell_id": "6442FD69F2E8481D8F4DE557744228D7", + "scrolled": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "Model GPMC
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kern.kern_list.0.lengthscales[ 0.99999996]NonePositiveParam
kern.kern_list.1.variance[ 0.99999996]NonePositiveParam
" + ], + "text/plain": [ + "GPMC(\n", + " (mean_function): Zero(\n", + " )\n", + " (kern): Add(\n", + " (kern_list): ModuleList(\n", + " (0): Matern32(\n", + " )\n", + " (1): Bias(\n", + " )\n", + " )\n", + " )\n", + " (likelihood): Exponential(\n", + " )\n", + ")" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#build the model\n", + "k = candlegp.kernels.Matern32(1,ARD=False).double() + candlegp.kernels.Bias(1).double()\n", + "l = candlegp.likelihoods.Exponential()\n", + "m = candlegp.models.GPMC(X[:,None], Y[:,None], k, l)\n", + "m" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "cell_id": "13A872266B474EF49C839B8D3AFDE730" + }, + "source": [ + "The `V` parameter already has a prior applied. We'll add priors to the parameters also (these are rather arbitrary, for illustration). " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "cell_id": "8E41B7B549F045E989F0EA0FA25CC690" + }, + "outputs": [ + { + "data": { + "text/html": [ + "Model GPMC
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" + ], + "text/plain": [ + "GPMC(\n", + " (mean_function): Zero(\n", + " )\n", + " (kern): Add(\n", + " (kern_list): ModuleList(\n", + " (0): Matern32(\n", + " )\n", + " (1): Bias(\n", + " )\n", + " )\n", + " )\n", + " (likelihood): Exponential(\n", + " )\n", + ")" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m.kern.kern_list[0].lengthscales.prior = candlegp.priors.Gamma(1., 1., ttype=torch.DoubleTensor)\n", + "m.kern.kern_list[0].variance.prior = candlegp.priors.Gamma(1.,1., ttype=torch.DoubleTensor)\n", + "m.kern.kern_list[1].variance.prior = candlegp.priors.Gamma(1.,1., ttype=torch.DoubleTensor)\n", + "m.V.prior = candlegp.priors.Gaussian(0.,1., ttype=torch.DoubleTensor)\n", + "m" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "cell_id": "751FB374D852409D89C7F9C9A7103C70" + }, + "source": [ + "Running HMC is as easy as hitting m.sample(). GPflow only has HMC sampling for the moment, and it's a relatively vanilla implementation (no NUTS, for example). There are two setting to tune, the step size (epsilon) and the maximum noumber of steps Lmax. Each proposal will take a random number of steps between 1 and Lmax, each of length epsilon. \n", + "\n", + "We'll use the `verbose` setting so that we can see the acceptance rate." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "cell_id": "A656A10091E04FD08641ED16E8E64A28" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0 : 33.20290796311981\n", + "5 : 18.804564032305457\n", + "10 : 18.529321293602706\n", + "15 : 18.524561421348164\n", + "20 : 18.524500359469663\n", + "25 : 18.524499677457708\n", + "30 : 18.524499672925263\n", + "35 : 18.52449966883608\n", + "40 : 18.524499665145953\n", + "45 : 18.52449966181525\n" + ] + }, + { + "data": { + "text/html": [ + "Model GPMC
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" + ], + "text/plain": [ + "GPMC(\n", + " (mean_function): Zero(\n", + " )\n", + " (kern): Add(\n", + " (kern_list): ModuleList(\n", + " (0): Matern32(\n", + " )\n", + " (1): Bias(\n", + " )\n", + " )\n", + " )\n", + " (likelihood): Exponential(\n", + " )\n", + ")" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# start near MAP\n", + "opt = torch.optim.LBFGS(m.parameters(), lr=1e-2, max_iter=40)\n", + "def eval_model():\n", + " obj = m()\n", + " opt.zero_grad()\n", + " obj.backward()\n", + " return obj\n", + "\n", + "for i in range(50):\n", + " obj = m()\n", + " opt.zero_grad()\n", + " obj.backward()\n", + " opt.step(eval_model)\n", + " if i%5==0:\n", + " print(i,':',obj.data[0])\n", + "m\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "cell_id": "7160966566F94A1180E67A1E4BC58063", + "scrolled": true + }, + "outputs": [], + "source": [ + "res = candlegp.training.hmc.hmc_sample(m,500,0.2,burn=50, thin=10)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "cell_id": "B85E4F657D7D4CECB75280DB195127C8" + }, + "outputs": [], + "source": [ + "xtest = torch.linspace(-4,4,100).double().unsqueeze(1)\n", + "\n", + "f_samples = []\n", + "for i in range(len(res[0])):\n", + " for j,mp in enumerate(m.parameters()):\n", + " mp.set(res[j+1][i])\n", + " f_samples.append(m.predict_f_samples(Variable(xtest), 5).squeeze(0).t())\n", + "f_samples = torch.cat(f_samples, dim=0)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "cell_id": "F3F0B3A5BBAA4EBB8C11DB0DC9B0CD3D" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(-0.1, 3.3576400854995505)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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SOeERAgXGcdSsB7ObEq76wsDyZCPPx223wnsNpS2/+ATWTleKiJxONz/x4zIZ\n0IxxtCozwcZtOU06P+2SLj8CU5o1DpPfaAzXJoNCAWZK636aNOYXL8nloF6LehTSb9roFU+6KY2M\n32rqxuQsFBjHkHMO6gv9K701jMrTUEhhOsAZOOegFrQaX48gDzCdy20um9WHQ8pZpwOmUm2x1G6v\n+/1JVs/M4MgaG04NCQXGcVXQrHGoaoNLo4gNF7QaX5f5Sjrzi49rawNemlm7ldb7uhQwzeZHwEqT\n4HeVd38WQxYpJEcw47cQtGuUdbFWE7rD9wbscvlgpnw9UpxfDKgyRdo16kHKjMRPLo+pA95ABQ2n\nSn1tOJUGKf7ES4FCHptRXeP1svIM5IZ02ajVCmbN1sB8P/0zOp2OlnPTrNlQqbaYclnVEh8kM4Px\nwTScSjoFxjHmXEZvHGFYmA92QQ+jQh6bnlrTP7V6dQjyM03pFGnWaWvJOM7UGnpgbPLoELyfh2NI\no4UEabU0o7UO1m6lf9bzLJzLwMJ8MFuwWtNTQV3tNMtmsYYqU6RWZ3iv/UTotNf23iSr4tcWoDKr\nFIoeKTCOOzNMs8ZrZuUZGPZajb6Pzc+t7p80GtAcgtddNgcKjNNrmEo0JtEwpGtFzHwfjh5WCsUq\nKDCOu0Ie5tdZWWCYVYc4jWKRKxSgssqaxqVjQT3tlHPOKZUipazTAV+zkbGWzWA13Zj2k02Og7KJ\nVmW4I4YECPKMVWt1LazdVhH54+oNrMcKDNZpL5a3G5J3Uy23p5K6Gsafy+WhrtbQ/eI36jBfDjY6\nSs8UGCdBq6k84zWw8nS6a/CuRj6HzfZWus2mjg3XeWt3lOeYRo0G5BQQxJ424PVPZVaphGugwDgR\nDBuGfM+wLVRxGX0wAsF5mK+sGABatzt86SdmykVNo2YDl9Vmo9hTjnH/NOrprkPfJzpjSZDPw1wl\n6lEkirXb0NJS6skMO3rw7I+YKQ1f3VcH1lK6Uuoo4EoG3+85zUt6Z6bOgmulwDgBVM949YJqFJot\nOpHL5qBewz9Dq3HzfajMDF8+Wi4P2gCUPl0FW4mQcaq81AfWqIPfjXoYiaTAOCmUZ7w6C/NKo1iG\ny+WhMou/TL6xVWZhWDbcncBlMtqkmUZtpcckQi4Pag0dvuq88ovXSIFxYijPuFfWaYOWxs/I5fNQ\nmsCvnlLbeLY0vAXgteSYKtZpB7njEnvOOW3A64fGwnDtFQmRzlpS5POwyiYNw8oqs8EshJyRKxRg\n/BB+PUiNqQoLAAAgAElEQVQh8OfnoDvEM2zafJcqphudZNHvK1RmBk2tgq2VAuOEcC4DdeVB9qQ6\nN3x5smvgRkbg8D78VgumJ9Pf/vlsut2gIoekQ70Gw7r6kUSdjq6/MLVaQVdBWRMFxknSbinPeAXW\naetOeTXyBTjwnCp4ODRrlSbNhm6Ok8Q5rKn0t7DYwpxuDNdBgXGSmK83jxUEaRR6Q+iVcw7y+WD2\neJhls5hWZNJDqTHJkstpA16Yagu6MVwHBcZJksvDvOoZn5XSKFZtaFo/n4XL5qChwDg1VBc3UVwm\no5W+MGkCbV0UGCeIy2T04X0W1unozVXWTsFUKpgZKF81eVQyMRTWbun1v04KjJOm1Vqxre+wsrlZ\nyGm2WNZIy+/p0O1o41EStduYGlKsmy3MD1/30pApME4av6suQWcyPxcsiYusRaetza0pYK3WUDaq\nSTwHphW/9VuoDm89+pAoME6afAFObcwgi2kUumGQdTCUTpEGjZpmzJIol4NaNepRJN+wVxgKgQLj\nhHGZDNQXoh5G7NhcWdUoZH0yDmto00riqVRbIrlMFrQaui7WaUNbN/frpcA4iZpN5RmfqlpRGoWs\nTy6nm8400Kx/cmkD3rrYQhUySiNaLwXGSWS+8oxPYN2uytPIujmX0WxLGmgTZXK1lee/LgtVXL4Q\n9SgST4FxEinP+CQ2X4GMXsoSgo663yWZmSkwTjJDHSjXo6UJszAomkggl8nAvALjJdU5XC4f9Sgk\nDbQMn2ydDijNLLlyWaymdKa1sG5XK14hWTEps1gs/jlwMzDped51y3z/JuBLwL7FL93red7vhTlI\nWUanjd9okNmwIeqRRK9Rh7wCYwmBb1inrRuthLJ2C5RimVgumwtas2/fGfVQEse0PyI0vexWugv4\nNHD3WR7zT57n3RzKiKQ3hQLMTMGuS6IeSaSs3QLrAgpkJATOYa2WAuOkatRUnSbpVG5sbeYrQZql\nrNuKqRSe530TmBnAWGQVnHNQqw79RgWbK0NWQYyEJJdVZYokazaCsl8ruOue+yjNzC79vTQzy133\n3NfPkUmvOm1VXVqLZjOIC2Tdwrq1fl2xWHwSGAd+2/O8p0N6XjkbFwSGbnRH1COJTq2qmqUSGpfJ\nqvtWkvWQI37XPffxO39wJ3ffez/ep+4EoPjxO9i9bz8At73/ff0coazE94MNeIWRqEeSGOb7Qak7\nnbNQhBEYPwZc5nletVgsvgu4H7h6uQcWi8XbgdsBPM9jbGwshMOvjrXb+JUSo6OjAz92Pxg+hT6f\nx1wuF8nvaiVmRntqHFeI1/JRNptNzetrEOJ2vgzX92tqPeJ6PcZBa2bitBvlU19fH37vu/n8/V/m\nx3v28taP/jIQzBi/8Kor+fB73x2r12IUor4erdMmu2GE7I5kvMbjcD12q/N0t27DJWDPUabTZmzn\nGC7G+4JcL0sWxWLxcuCB5TbfLfPY/cArPc8rrfBQGx8f72WMobJOm23TE1RS0uHKmk3cFVf3tXbh\n2NgYpdJKv87B8xt1OLgXNxKvu+TR0VHK5XLUw0iMuJ0v63TIXPXCqIdxRnG9HqNmZthzz552o7zc\n66s0M8tbbr2N6cWv7xwd5aHP38XYju0DG29cxeF6tMIImQuTsX8mDtejf3Av+J2gFnvMbduwgcrO\n8yPZx7Fr1y7oYXvuus9isVi8oFgsusU/v3rxOafX+7zSo0Iem56KehTRmK+oGoWEr9sNWqtKsnTa\nwHDvuUgNbcDrmT89Ce1mIoLipOilXNsXgJuAsWKxeBj4XRZLAHie90fAB4B/WSwWO0Ad+KDnecqc\nHxDnMtjCPGY2fIn3tYWgprNImBxYo47bopuuJLFWk15qtZVmZil+/A6my2V2LqYMTJfLFD9+B96n\n7tSscRyoyUdP/HoNZqZwyi0O1YqBsed5H1rh+58mKOcmUfF9bH4Ot3Vb1CMZGPP9YFYhZvnFkgL5\nPCxUYcvWqEciq1GrQQ/Lsw98/Rvs3refa664/LTNdw98/RvafBcHvmHtdqzzUKNmfhfGDyoo7gMV\nfEwBVyhglRIMU2Bcr6nDlfSFc5nF2UdJlHazpxWk44HvzW+6aWl22PvUnQqK4yTjsHoNlx+ez7TV\nsqOHITNkq8QDosA4LeqN4erYNV/RbLH0j3KMk2cVy++nBsBjO7YrKI6TXB5q1aGa7FkNf3YG6jXN\nqPeJEjTTIp/DZoZop3q9Nnw51TI4nXawVCnJ0elEPQIJiXNOG/DOwG82oHRUQXEfKTBOCZfJwnxl\nKDoGWbcLHW3OkD4ysGY6SjoOA/O7oBuZdNEGvNOY78ORg2r93GcKjNPE72K1atSj6DtbqIJmi6Wf\n8jmoqTV0YrTb2nOQNiqbeBqbOgoMYQWqAVNgnCKuMALDkE5RnetrQxMRl8lCox71MKRH1qiDWsOn\nS8YFv1cBggY2zM+d1tlRwqfAOG2ajfSnUzRqUY9AhoGWcpOjUYOs9pKnSi4HC/NRjyI2rDqvVZEB\nUWCcNuYHpcxSyjptVQyQwWi303+TmRbttpaXU8a5DLR0c7qkPH1au3PpDwXGaZMvQGU26lH0jVXn\nNDMkg2GmWeOk0GbcdNL1ByxuOE/xhFfcKDBOGedculMN5udxOQXGMgDZLKYNeMmgUm3p1OkEQeGQ\ns8oM5JRbPCgKjNOo3Urvbt6mNmPIYLhcDuoKjOPOOm3wlfKSSs5hDV2DzFdwWikdGAXGaZTLYXOV\nqEcROms1VatUBks5jrFnrRYovTid8nmYnYl6FJGydgtUU32gFBinkMvmYGEu6mGEzirloFWoyKAo\nxzH+GrWggoGkjnMO6rWh7kJpM1Nq6DFgCozTqtlM3476hXnVcJTB8v30piWlRbMR1J2WdMq4VK6A\n9qw6j8soVBskne20SlnZNmu3oaXlJBkwNRmIv3byblys1cTMj3oYieByeZhLb6Wls/FrC+DrdTJo\nWn9Kq3wBKjOwaXPUIwmFzZa0nCSDd7zJwJatUY9EzqTTjn3XO+t04NBebO9PYM+PYfIojO6E170J\nrn9VEPzJmdUbWKc9fOdpthTkWctAKTBOKedSNtNVncdltcAhg+VcJtjcJbFkvh+UaothYGz1BXjq\nMey5Z+HAnlMaEzkoT2N/90X45lfg1T8HN74et2FjZOONtUIOm53GnXtB1CMZGPN9qNdwCowHToFx\nmi2WbUv6XbbfaCzOCo1EPRQZRtqAF18xzP+2mSnse9+EJ79/8mvnvAvhqhfirrwWLr4cfvoM9vBD\ncOwI9vW/gYcfwm58Pe6G18HoDnXyO4HLZIPmTsMUGM8PcV51xBQYp1kuh82VcTvOjXok61OehkKy\ng3tJsG7QZEAbP+PHGg3IRB9Amhkc3Is98o+w+2lgcePzldfirnsFXHEt7pxT0nFe/HJ40fWwbzf2\n8Ndg/0/h4a8Ff96yFbvkCtzFl8MlV8D5F+n1127jNxpkNmyIeiSDMTej2eKIKDBOMZfNYQvzkPTA\neEHd7iRCBtZq4DamI18/VWJQqs327g5mfI8eCr6QzcJ1N+Je80bceRee9d8654Lg+cprsSMHgsB6\n326ozsGzT2LPPhk8MJfHXvAi3Nvei9s62uefKKYKeZidggsviXokfWedDtQbMKJV0igo2ki7xbJt\nSV2W82sL0O1G/uEnQyyfg2oVFBjHT7uFc9HsPbDqHPbgl+Dpx4MvbNoMN74Bd+MbcFvOWfXzuYsu\nw93y0aBaxfQUHNqHHd4Ph/bBzBT8+IfY/p/Cu34R9+KXr23MZrBQXdP4ouZcBluoJvrzrFc2O63P\nvAjpzKed+VhtAbd5S9QjWZvyDBRUjUKi4zJZTKUC46ndHnjXOzMfHvsu9rUHgo5kuRzuZ94Gr/k5\nXAiVc5zLwNj5MHY+7obXBseszGJ/+1ew58fYvXdju5/GveOWnjbrWbcDB/Zgu5+CnzwN82XslW/A\nvf19kd1UrJkZtjCPS3GVGDOD+bJSZyKkwDjt8oWgBmQCA2Mzg1pVeVYSvXYz6hHIcjrtgZazsonx\noJLE4f3BF656Ie4d78dt39nX47pt2+GDvwqPPYw9+GV46lHs4F54z4dwl73g5DG2WzBXholx7CdP\nwXPPnN5S+AffDurcv/vDywZgd91zHze/6SbGdmwHoDQzywNf/wa3vf99ffsZe+EKhWA2Nc2B8Vw5\nqF2swDgyCoxTzjmH1ZNZts1q85C27n2STO0O5vvqQBUj1ukMtPmBPfpt7O/vA/Nhyzm4t70PXnT9\nwJb1nXNw4xvg8quxL/0FjB/CPveH2IuvD0rWzc0GAXFt4fR/fO4FcM11uGtfCs0G9ld/Dk8/jjUb\n8P6PnTTT/cf//S/5nT+4k7vvvR/vU3cCUPz4Hezetx8g8uCYei21m2HNDKYnNRkUMQXGw6DTxtrt\n5F1sszM4pVFIHJgfLNtrM0xs2ADL6Nnh/c8Hxa98A+6md0VWc9jtPA8+9q+wbz0I33oQnnni5Adk\ns3DOKGzfibvqhXDNS06vTHTrr2Nf+Aw89yz23/8YfulXln6e97395/njv/gCu/ft5y233gbAdLnM\nNVdczs1vuqnvP9+KslmsMovbMRb1SEJncxXwu5otjpgC42GQy2LzySrbZr4Pjbq6/kg85HJYrYpT\nYBwfjTrk+h9AWKOO3ff5ICh+zRvJ/Px7+n7MlbhsFvfGd2DXvhQO7Q1SC7Zth62jsHnLirnDbtcl\n8LHfxP7ij4NNfp/7L/ChX8NtOYfzdu7E+9SdvOXW25gulwHYOTqK96k7l1IrouRyOWy+DCkMjIPZ\nYk0GRU3rgkPAZRfb2iaIiptLnLhsLigNJvHRqAW/lz4yM+xvPKjMwIUX4970C3093mq5Cy7Cvepn\ncS+6HrfrUtyWrT1vqHNj5+Nu+3hQznNiHPvsp7CZUp9HHJJmE2vHr7nLevjzc+B3oh6GoMB4eDQa\nQU5eUszNJi/1Q9KtpQ14sTKIrnePfxeefRIKI7j3fSR19dTdtu24j/0mXHAxzJawP/l9Dv3dlyj+\n5v/MdLnMztFRdo6OMl0uU/z4HZRmZqMeciCfx2anoh5FuErHNFscEwqMh0Uui80k443Eul1I6IZB\nSbFWK3htSjz0+Ubfpo5h/3A/AO6dH0hUKtpquM3n4D7y60EnvnaLL/7Zn7B7/wGuufQSHvr8XTz0\n+bu45orL2b1vPw98/RtRDxcg2AQ7Vwk2q6WAX52LZXvzYZWu2185I5fJYnNlbOz82O+st8qsNh9I\n/OSy2NQx3AUXRT2SoWdmQWDcp8251m5h994dBCsvexXupTf25Thx4UY2BM1FXnQ9t33lPgB+4dLz\n2bnnKXjlG/A+dWcsyrWdzLDq/OmttpOodAxX0P6FuIh3hCThcotBZ0z5jQb+4f1QmkjdkqUkn8tk\ng+YIKcttTKROG+hfqTZ78MswdQx2nIt7xy19O07cuBddz7Z//R/42LvezljGsK/ch33uv7KTbsyC\nYoK0g9mE5ESfhb8wD+0EpTkOAQXGQ8Tl8rF8I/EX5vAP7IFDz0GnrZ3/El/5PDZxOOpRDL2gE2F/\n6gfbj38Ijz0M2Szulo8O3UxeZvM5ZG75CO4Dt8Hmc+DgXuxPfh979OH4pS7U61jSUxCmjqksacwo\nMB423U6w+zUG/MoM/t7dMH4Yh+EKGwZWLF9kLZzLQK2G31AOfKRqdciFvznXul1sMZXAvfXdQ502\n4174Mtyv/a/wkhug3cL+7ovYX/5JvCoGFXLJqaSxDL9Whdbg6nFLbxQYDxlXGIGIN+FZt4t/eF9w\np5zN6G5ZkqVQgIkjUY9iuLWb/dkr8dOnYb4CO8+DV/5M+M+fMG7TZjLv+wjulo/Cxk2w58fYH/+/\n2NOPr+t577rnvpMqXJRmZrnrnvtWP75MFuYTvAlv6phWSGNIgfEwatXxG41IDu3Xqti+3dBuqzSN\nJJJzDlqtYCe5RKNPXe/s0YcBcK94nVavTuBe/HLc7f8arnohNOrYfZ/Dv/dzWH2Z9tMruOue+/id\nP7hzqfxbaWaW4sfv4Hf+4M41Bcf4XayWrDr9sFi3WLPFsaTAeBjlR6B0bKCHNDP8qQk4fACXz8e+\nMobI2bhCASaPJnemKun6UKrNZqZg3+4gReNlrwr9+ZPOnbMN98Ffxb3rFyFfgGcex/70E6suA3rz\nm25aKv/2lltv4y233sbuffvX3HI6WAVNVjqF+T5MjWu1NKYUnQwh5xzUFga2acE6bezgnqBph5aN\nJC18HyvPRD2KoWN+F/zw60nbY98J/vCSG3AbN4X+/GngnAtm03/1t2HXJVCZxT77aWxivOfnGNux\nHe9Tdy41DjneSGRdLafr9UQ1sLLpKdA9dWwpMB5W+TxWmuz7YfxWE9v3UzBfJdgkVVw+D9OTweyP\nDIz1ofmPddrw5PeBII1Czs7tGMPd+utw+dWwMI997r9gh/dHN6B8DothxaXlWKcD5ZI+D2Nsxd9M\nsVj8c+BmYNLzvOuW+b4DPgm8C6gBt3me91jYA5VwuUwGm69g510QbGDoA+t04OBeyOeVryfplHHY\n9CTu3AuiHsnwmCkFS/lhevZJqC8ErZF3XRruc6eUK4zAB38Fu/dzsPsp7C/+CH7xn+GuvOas/+54\nTvHxmWJgqeX0WmeNXSYbVMtIwHVoE0cgH35FFQlPLzPGdwHvOMv33wlcvfjf7cAfrn9YMhDZDDY7\n3ZenNt/HDu2DXFZBsaSWy+agPKNW0QMStItfCP09ZWnT3Y2v1/vVKrhcHveBj8FLXxmUdPsff4L9\n5Kmz/psHvv6NpZziUFtOdztBs4wY82sLUJsPyj5KbK342/E875vA2RLp3gPc7XmeeZ73XWC0WCxe\nGNYApX+WPtRDXgo2M+zIgSB9Qm8AknYZF6/arilm5WkIeQnaJsbh8H4Y2RDU7A1BWOXIksBlsrh3\nfzAob9ftYl+8C/vhD874+Nve/z7+4289Pzt8POf4P/7WHevqrpeITXiTR3CFDVGPQlYQRtRyEXDo\nhL8fXvyaJEHGYQf3BhtaQmKTR6DVxGX7k6IhEicul4f5ctTDGA5z5dDfV+yxYLaYl74ylC53oZcj\nSwDnMri3vw9+5ufBfOyvv4AdO3OHyNve/76TUibGdmwPp+V0oxbbTXj+7ExfqqlI+MK49V5u3WnZ\n/ZbFYvF2gnQLPM9jbGwshMOvjrXb+JUSo4u5TbJYOqY8Tf7Ka5bdEJDL5Xr+XXUnj9HNZnAR/G7j\nIpvN6vW1Cmk4X9Zqkt++fSA3g6u5HtOku1Cls3kTmZHVzbid7fVljTqzTz0KwNab3k4uhNfhh9/7\nbj5//5f58Z69vPWjvwwEM8YvvOpKPvzed8f+tb6u6/G9H2LBfJrffojsV7/MOb/xvw80NcW6HTLO\nJzfA66OX69G6XVpT42TOPW9Ao4qvTKfN2M6xYPNyTIURGB8GLjnh7xcDy9Zu8TzvM8BnFv9qpdLg\nlz2s02Zbp0uluvrC5Glm5sOjj+AuuzKYATvB2NgYvfyu/EoZJo/XZqz1aaTxNzo6SrmsGcRepeF8\nWbsF+/eS2bbGclOr0Ov1mDb+4f3QaePqq2tOdLbXlz36MDSbcMmVVDdshhBeh4Vslr/85Cd4y623\nLaVT7Bwd5S8/+QkK2WzsX+vrvR7tdW+GJ75HZ/9zlP/pq7gB14S20jQ0W2Q2bRnI8Xq5Hv2JI7BQ\n1SoqsG3DBmamS6fFGYOwa9eunh4XRirFl4GPFotFVywWXwtUPM87GsLzygA5lwk24+37KX6redbH\nWqeNNWr45Rn8iSP4Rw7gH3juhKBYZLi4fAHm4h3wJFk/Nt2Z2VIahbvx9aE977BzGzbi3nIzAPbQ\nA1gj/PJ6Zz3+yAgcObji59ig+I06VMJPAZL+6aVc2xeAm4CxYrF4GPhdIA/ged4fAX9LUKrtOYJp\nwl/u12Clv5xzWD4PB57Dv+RKMhs2Yr5Pt7aAP3UMGrWgheXxHfjZLGRPqDqhoFiGWaOO+b66OvaB\nVWaC95swHTkAE+OwaQu88GWhPW0/ypElzktfCY99Fw7vw775Fdzb3jvY4+fzcGgfdvnVkQak5nfh\nyEE1tkqYFQNjz/M+tML3DfiN0EYkkXLOQWEEO7QPv1CAVovutq2wUAs+8HO50HeFy3Czdgs7dgRK\nx4KmM6Vj0GrhrrkOXnw9bkBLouvmHFadx23dFvVI0qcyG1TRCdHxEm28/NWhNls4sRyZ96k7ASh+\n/I6lcmShbDKLOeccvOMW7M8+Ad//Fvby1+DOG1yxKucclslgh/fBpVdFVoLPjh5WG7UEUoQjy1pK\niSgUcCMbVp3XJ3ImZgbjB7HHvwv7n2O2MgN2+n5d2/sT+If7sBe8CHfdjXDNSyLJS+uVy+exyiwo\nMA6VX1uAThtCqBhxnNVr8MwTgMPdEG6nu+OB781vumlpdtj71J1DExQf5y64CLvx9fCDb2N/fy98\n5NcHGqC6TAbrdrCjB3G7LhvYcY/zyzNQW1B6YQIpMBaRgbBmA556FHvsO8ES9nGZLOzYCWPnw9j5\nuLHzwQx7+jHYuxt2P43tfhpGNmAvuh73xnfiztna17Hedc99JwU2pZnZ3gKbptIpQjfbh053zzwO\n3Q5ccQ1u+85wnxtOe52EVo4sYdwb34k98wQc3BPciIRUJ7rn42dzWL2GP3WMzAC74vmtJkweVQpF\nQikwFpG+solx7Pv/BE8/Du1W8MVNm+Flr8JddyOjL7iWSrV62r9zL3slVp2Hpx/DnnoUjh6GJx7B\n9jwbtJ7tU+ve43Vo7773/tOWwuH0oOckZlititvS38B9WJjfhVo1lPrCJz3vk98DwF0/2IoJw8Zt\n3ARv+gXsbzzsq1+CF7wIt8pye+seQy6PVabx83ncth19n7U234fDB7TnJsEUGItIX5jvw7e/in3z\nH8AWuytedhXuFa+Ha1+6lNd5tvxOt+UceM0bca95IzZ1DPvbL8Khvdjdn4abfylIsQjZzW+6ibvv\nvZ/d+/bzlltvA4LNU9dccTk3v+mms/5bVyhg5RlQYBwKK88EKwphPufUMRg/FHS6u/aloT63LOPl\nr4bHvxukT33rQdxb/qeBD8HlR7CpCaw0ieULsGEDbNmG27gp9NUdmxwHfJxTeJVUWu8TkdBZZRb7\n3H/F/vHvg6D4xtfj/uX/RuYjv4F7yQ1r2uzkzr0Ad+u/gBteC50Odv9f4H/tgdBbmh9vUbtzdJTp\ncnmpukDPFQUa9SCPWtavPBvqxjh4fraYl9wQlNmTvnIug3vHLYCDR/4Rm52OZhyFAi6fx2FQX4Aj\nB7DnnsXf/xx+M5w9NP5cBaqV0DeKymApMBaRUNkzT2B/8vtwaC9s2Yr78L8g884P4Hauv+uTy+Zw\n7/rF4IPWZeDhr2Henwf5y3FhPlZTA6H1Wtp0FyLrduFHPwDAXf/qUJ9bzsztuhSuewX4frDpNurx\nuAxuZCT4zwEH9gQNqtbB2m2YOILLK6846RQYi0gorNXE/+u/xO69m8/++ACli6/E3f7buCuvoTQz\ny1333BfKcZxzuFf+DO7DvwYbN8Fzz2D/7ZPY9GQoz39qHdrjM8fFj9+x1MnsrPIFqMyEMpZhZe02\njB8MP09zz7OwUA02evYpR30Q7rrnvpNei2FeX/2y1ETlh98LcsdjxI2MwNQR/InxNa32WLeLHdwb\n1E+WxFNgLCLrZhPj2J9+Ap78Hp89VOL/eOYQH/yH7zPdaC8Fmr/zB3eG+uHtrrga98t3wLkXQGkC\n+9NPYD/8/rqf98Q6tA99/i4e+vxdXHPF5Ut1aFccl3NQrymdYo2s08EO7oFcLvSNUiduuouqtu16\nHd8cevxGrV/XV+guvhx2ngfVeXju2ahHcxqXH4HqHHZwb7Cy0CPz/SAozrjEvqbkZEqEEYmAmUGz\nAdW54L/aAmzfCeftSlzrUPvRD7C/+atg2fu8C7n5l36Nz/27/2tNm9dWy+0Yg9v+VXD8Zx7HvvwF\nbO9u3Dvfv+bd76HUofW7WL2G27R5TWMYVuYvzrxlM+EHxQvz8NNnghScl74y1OcepPVsDo2Scw5e\n/hrsob/GHn8kaOATMy6XC16D+3ZjF19OZsPGsz7ezOgc2AvmJ+59W87MRTirYePj4ys/KuyDdtps\nm56g0ohRTmLMjY6OUi6vL/9qmJzpfNmeZ7HvfCNYZp+fWz5/MpeHXZfAxZfjLrocLr4Mt/mcvo95\nLazTwR68H453EHvZq4KANF+gNDPLW269jenF87BzdJSHPn/XspvXwnh9mRk8+T3sK/cFJeG2j+Fu\n+QjuwkvW9bzrGs/IBjJ9OP7Y2BilUin0542a+T52aC/4XVyIlSiOv77skX/EHvwSXP1iMr/0K6E9\nfxRWc32tVj/f721hHvvkvwcz3L/6t7hz4tsMx1ot2LYdN3beGV+P/vghRgt5Kgunl5uU5W3bsIHK\nzvMjada0a9cugBXvuDVjLNJn1mpiX/0yPPadk7+RLwRlvbZsDXJlp44FzQwO7oWDezl+y2pXXot7\nxy24HecOfOxnYpVZ7J7PBnmg2Szu7bfADa+NbCnx+GwUF1+O3Xs3TB7F/tt/hjf/Arzm53BusFlj\nzjlMH5Y9MzPsyAHodvsy82ZmJ6RRaNNdVNzmc7BrroMf/xB++H14w1ujHtIZuUIBq85hc7PY9jHc\n9rGTSrv5U8egNo/bvP5NxRIvCoxPYWbBTF6zsfhfM6h5OLpT3axk1ezQPuxL/x3K00EA+XPvgBe+\nNAiGCyOnBZK2UA3KCB3eD0f2w5GDsPcn2Gf+P/iZt8Hrboq8FJDt3Y3d/7kg/WPbdtz7b8Pten5m\n9NTNa8DS5rWeS56tkRs7H/7ZHdhX/xp+8K3ghmT/c/CeD+E2DjitwffxawtklE6xIjt6GFrN0Euz\nLTl2GCaPBo1lrn5xf44xIFFeX2FwN7wG+/EPsScegde/eeA3ravhslnIZrHyDDY7je08Dze6AyvP\nQiorsDwAACAASURBVHlG7Z5TaqgCYztyAPvh96mXJvCr89CoQb32/P+PB8PL1UXN5bFzz4dzL8Sd\ndyGceyHsunjwH7aSCNbpYN/8e/jO18EMzt+Fe8+HceftOuu/c5u3wDUvwV3zkuB5FqpBcPejH2Df\n+Ft4+jF41y/iLrliED/GaezRh7G/vyf4ma68FvfeW0/Loz1x89qpneNWlae7Ri6Xx73jFuyKa7C/\n/kJQteJP/xO8/2MnBfD95kZGsNIEXHrlwI6ZRP7UMahX+7q0ulS7+LpXRH5juV5RX1/rdsW1sHUU\nZqfhwB64/OqoR7Si4zdsNj2JzZaClQ0Fxak1VDnG/sMPYf/tkys/MJsLuiKNbICRkaC8z3xl+cfd\n8Frc69+M2zoa/oBjQjnGvbPqHJumjrLw4JeDGSrn4HVvxv3c29c1G2Z7d2N/91fBhwkOXvE63Jt/\nAbfC5pCwmBn2za/AP/1D8IWf+fngZzrDKspd99x30ua10szsGT+0+5rTWJ4JUj6OHgpm7N/2vuDc\nDSjlw5pNuOwqMiG2wU1TjrFfKcNUf2u/btu8mdl/fwc06rhf/S3c+Rf17ViDsprra7UG8X7v/+Pf\nB+8lL3kFmffd2tdj9Zs+H1dnaz7P3Hm7Yp1jPFSBsR3cg//wQ2zA0cwXYMPGILdz46bgzxs2QmHD\nsgGM1WtBDujkUWzqKEyMw+H9wTezWbj+NUGAPLpjoD/TIAz7hW9mQfc254CTS/LYQhUOPIcd2AMH\nnoPSxPP/cPtO3Ls/HNrsrrVb2Le+Ct/5WrCqseUc3FvfE3Tw6mOgZ74fzBI/9h1wLmiwccNrQ3v+\nfr++TtskeN2NuHd9AFfofyF+M4NcnszFl4f2nGkJjP1mAw7sCWrI9tGmAz+l+rk/hAsuIvMrv9XX\nY6XBIN7vrTyDffr/DG5W7/h3uI2b+nq8fhr2z8deWXUO+8G3cY9/B/71/03mossGPgZtvluGu/Qq\nMrsuZeP0BK1VVqVwGzcFS6KXXrl0Vm1yPAhUnnkSHnsYe+K72MtehXvDW3Hbd4b/A8hAWbMRVDr4\nwbdhZur5r+OCINk5OLVQfb5A7oqr6V5yBdz4hlCDL5cv4N70LuwlN2B/+1dweD92/+fhiUfgne8P\npbPcqazTDo7x4x8FdWVv+WgsyyydjcvlcO/8AHbxFcF5e+pRbOIIfOC2vpyzk47tHLawgLXbOBX/\nX2LdLhze3/egGKD5/W8B2nQXJ250B3blNbD3J/DUo/Cqn416SNInNnkUe+Qfg99zt4sB7rHvQASB\nca+GasYY+lOuzUoT2LcehKcfD3IvszncB38Fd8U1oR0jSsN2R2wzU9j3vwVPfg9azcWvLt0Onfzg\nXA4uvgJ3+QvgshfArkvYvnOs/zMu5sMT38O+9kCQH5/NBikbb3gLLh9O7ps16pj353BwD2zYiCv+\nc1wf8mUH+fqyqWPYF++C6UnYfA7uV/6XvpeMMvNhZGNopduSPmNsZtihfdDt9H1Ds81XsP/8e+Ay\nuDt+F7dpS1+PlwaDuh7tmSeCCjLnXYj71d9ObHOMYft87IWZD3t/ij3yjeDmBwAH176Ec372bVRf\n8XoyIX1OrYZmjAfIjZ2Pe++t2M++DfvG38GzTwYfvh/7zRU3W0l82IE92He/Dj99lqUA+LKrcK/+\nObj6JbhMZrGbmQU3QGbBB24E1Uqcy8ANr4Vrr8MeeiAI4r/1IPbUY/DOW3BXvWhdz2/zc9hffiZI\nGTpnK+5Dt6fitezOvSCoWvE//gwO7sHuuRs+8ut9Lc7vXCY4n+d2+ld1IUFs8ii0W4M5Fz/8QXCd\n/v/tvXeUFFeW5/95kZllKG/xFIUphAwyCFq+EQhZBDJNIC+Q1NKoW5rW9Mz+9sxM727vzunfmd5e\n9dAjaWdaLakR8oEAGeSFkffIC1TCU7jyUAXlMuPuHy+rKEqYMpkZad7nnDxkJpkRl0dExjfuu+97\nJ5xgRHG8UXEiZGbptRi7qrR/uyFhkGAQqjbr8tKmvbCvEfbthaZGvSars3tgIA1OnoKaeh6qsAR/\nRkbc3wSZX+kIoopK4aobkWVocfzUX2DBr5J6YV4yIG4IWf2ydpAAvajyxNNQU8/90UIdFa4zPvY9\nZ2xQg7JRl1+DnDwVeeVZqNmNPPUX5PhTUDOvQOXk9nmbUleNPPmgbkRSVKpFcRLVzqv0DLjqJuTh\ne6FqM7LyRdSFV0R3pwE/Ul+dFDcXA8HdWw/7GmOyot94F8c3yu9HJp0OH72FfPFhTB1jDH1HxNU3\nMZsqkc2V2m//cE2qOsktQE0+Uy92TjD3LiOMI4xSFsy5DmneB9s3I0//BW6+u9/taQ3RRZr26em8\n7Zt0q9izpus726yjZ5eiuSq8P9tXo8bAbX8PH7+FvP06fPcFsnG9bnBx2pm99gqVHVuRZx7SHsXD\nRumSoCTMtKnsHLjqZuSxB+Djt5ERo1HHnxK9/Vk+ZF8jUjw4ol3dEgm3tQWqd8Vk0SMAO7ZCfY0u\nlRk7ITb7NPQJdcpPwvWna5ELZsfu2DD0mq4a4Q3faYeu7pQO1aWEefmQkw+5edqKLycvYiV9XmCE\ncRRQ/gDYtyCL7tPTDM8ugmtuS3j/zGRDtvyALH8c9jdBdq5eWNaLGtpFS5fzm3sXsnjZcz/yEQW4\n59YFA4rrWNs/ojgO1xkz8RTk1WXav/eVpXo6+bK5x8xWysZ1yLOP6pbKY49DXX1zUl+o1MhymDkH\neW058uLTutaxeHD0dmhZSENd1Bf8xSPihmDH1pgeT53Z4vTJZ9Keojcj8Y4qGYKMGK0dnr79XJeH\nGTxHRHT31Q9Wa0HcSU4ulE/Q66fKK3SCIQkxSi1KqMwsuObnyKI/weZK5KUlcPk1cV9bkwqIuPDe\nKuStV3T9Ydk41JU39vokn3X+NBYve47KzVuYccN8QHeeqigfzazzpw04voFuX+UXwrxbYf1XyGvL\ndSe9v/wRmXI26riTdSa4R32nfPUpsuJpbQM3aQrqMjuqdbdxw+nndF2UZclf4ZZ7oja7o3x+3T2r\nR2vZVEB2bIMY/pulo10LLSB9yjm0x2zPhr6iJp+FVG3RWclTpsZ1J7xkR8SF77/RgnjHVv2mP6D/\nX047C0qGpISGMcI4iqiCIpj3cz1d+9UnSF4B6qcXex1WSiNtrTpL3HkXfPYFqJ9e3CehUlxYgHPf\nQmbcMJ+68Grkovz8iLVjjcT2lVIw8WQor9ALQj99Dz5+B/n4HfD5keFl2nqwbCzs2o6sekl/8azp\nqPMvS4kfPwiP02U2smcn1O5BVjwDV90UXV/ovQ0pZefo1lVDW0tsp1bXf60dZYaPwjd4GBjXgPjl\n+FNh1UvaA37jehiX2C27ExXZvhl5yTnoxZ85CE4/B3X6OccsLUw2jDCOMmrYSL0gz3kE3nkdNxRC\nTbsk5TJG8YDsb9ZOC7uqtP3YFdejkvxHWGVk6vbIk6YgX32sF0xU79IWbNs2apvBzs/OnIP6yU89\njNYbVFo6zF2APPxvsO5L+PhtiNI4qEAAaahF8gtT4ubDbTkAdTUx8SvuTteiu0lm0V28o3w+mHou\nsnIF8uFbSf+bHG9IKIi89ZpuHCUCeQWoM6bByVOTupTuaBh1FgPU+BNQl87VDSHeX4k8+WfdMc0Q\nM2RvA7L4fi2K84tQt/xdv3+Aa+sbsO++h7rGRory8ynKz6eusRH77nuorW8YcKzR2L4aNhLr4qux\nbv8vqL//F9TcW7T4GzoCMrNQV9yQkqK4E1VUirr8GgB9gT5cC/hI4YaQuurobT9OkFC4rjjWorix\nHrZs0B7jJ5wa030b+smpZ0JaOmz5AdlV5XU0KYNU70IeWQjvr9RvnDUddec/oqacm7KiGIwwjhnq\n1DNQ198JWdn65H/oj0hnDY8hqkjtHr0Qsq5aL7C6+W5UYXG/t7di9RoqN2+honw0Kx9fxMrHF1FR\nPprKzVtYsXrNgOON9vZVZhZqwolYM+dg3fprrL//F9SJpw14u4mOmngyTDhJC9e1H0RvP4E0aKzD\n3boBt6uBjLe4zU24NbtxWw4QqaZPsmOrbjwTa776BBCYcBIqIzP2+zf0GZWR2bXwTj5c420wKYC4\nLvLBauThP2qv+vwi1E13YU2fZbzWMaUUMUWNHge3/lrbg1VtQR69Hy68AiaflRLTql4gO7dpP+mW\n/dpW5prbBnyx7HSF6G6n5ty3MGJ2bdHevuHIqKnnIt9/rVu8n31B1C4SKpCmBejWDbj5xajiUk9+\nA8QNIbt3wIEm8AWgsQ5BIWlpkJ6pm7tkZvW59Mut2QMdbdqhJ4aIuMhXnwCmjCLRUFPP02sgvvsC\nmX4ZKm/g6zUMP0b2N+nGRts26jdOPQN1wWxjKdsNkzGOMSo3H3XjL3RveDeEvLoUef5JvYraEFFk\ncyXy+H9oUTxuIur6OyKWQZp/9ZWHLIQrLiyIqGiN9vYTnUVLlx9SVlJb38CipcsHvuFRY7U35/5m\n+O6LgW/vKCil9HTlvgZkyw/a57cbIoIEO5C2Vtz9TUh7G+K6Edu/27wP2VQZXhiXjrIsVFo6Ki1N\n969pPQA7tyObv8fd39T77R5ohobamItiQNfQN9ZrT9Xy8bHfv6HfqLwCOP5kEBf5+G2vw0lKpK0V\neepBLYqzclDzbsW6zDaiuAcmY+wByudHXXQlMrxMrwL95jNd03jNbQltih0viAh88RHy6lLdlvLE\n01CXX5sa9mMpQH99nnuDUgqmnIu85CCfvAMnTY56JrczKy3bNuFmZkBIIBTU1nmdLciVorPCob2x\nBrepGQIBSM9A5RX0SYR2zxKrwJHrCJVSEO5QJzu34ebmoUqGHTF7LG4IqauFxtqY1xV3xfClzhYz\n6XSzwDkBUWdMQ779HD7/EDn3QlMKE0Ek2IE88zDs3gEFRaib7u5XZ9RUwPxyeIg68TTUgl9Bdi5s\n3YA4jyBHa7FoOCbS1oo894S+4QiFYMq5qDnXGVGcRMw6f1pXzfWMG+Yz44b5XTXZkfCR5sTTtFXR\nru0HvTxjgEpPR7mCUlosq7Q0/V56hs7kpocfPh8KQXW062zzpkrcbRtx9zYcMaMsIkhbG259zSFZ\n4l7HlpYO+5sPn9l2Q7g1u5FN30NTg2eLdqS9TbuKAOrkKZ7EYBgYauhIKBunrfY+/9DrcJIGcUPI\n8sd0pjg7F3Xd3xhRfBSMMPYYVToUdUN4Ud7mSuTZRUgw6HVYCYns3qEtt75dC4E01JzrsC660hjG\nJxmdPs+dbh2d7h2R8pFWgbSDC4E+eWfA24smyvJpsSwCYXHq7tiKe2A/bvM+3N07cLduRDasQ7Zt\ngMZ6VCDQr7bUyufXN5jbNuHW7EFC3QXxXlQgzdvunt99qbs2jixHFZZ4F4dhQKgzpwEgH7+NhMy1\ncKCIiG4w9v032qb0uttTyke9PxjFEAeo4sHasSIzCzasQ5Y9an4Q+oCIIJ++h/z1T1Bfo50nbvs1\n6qTTvQ7NkKCoyWeDsmDdl9G1bosgKhBABQJaHO7YAruroPWAzi6npemscwRmTlR6uC560/pugtj7\nGZku7+KTzaK7hGbscVA8GJr2Rr3OPxWQVSvgy4/BH0DNuw1VOszrkOIeI4zjBFU6FHX930BGJlR+\niyx/XPuAGo6KtLYgyxaH64mDcNqZqAW/QhWVeh2aIUpE20cawguBJpwIrot89n5EthkrOhf1qUBa\n1OqjdalHZIR2JJD6Gti+CQJpuuOjIWFRyuryVJcP10TMPjAVkQ9WwQerwbJQP5uPGlnudUgJgRHG\ncYQaMlyL4/QMWP+VdqtwjTg+EvL918h//l7XFaalo668EevSuWYBY5ITbZ/nTtSUc/WTtR+Y8qY4\nRz58Sz85/hSzwj4ZOGkyZOVoj93NP3gdTUIin3+IrFwBgJp9LWrcRI8jShyMK0WcoYaOhOvuQJ74\nT/jucwSB2dcZ0+1uSHMT8vryg9NsI0brE9/UFaYEMfN5HjUGBg/TF+fvPodJZkFXPCJN+/RUMQp1\n5vleh2OIAMof0O4wa17WpQCj7zEuI31Avv1c1xUD6qIrUSdO9jiixMIcaXGIGl6GuvZ23SLzuy+Q\npx5EeqwET0VEBPn6U+TPv9eiOJCGuvAK1E13GVGcYsTC51kp1ZU1lk/eMVO6cYp8/JYuo5pwIqp4\nsNfhGCLF1HMhN1/XyhuHil4jP3yLPP8EIKifXnJw5svQa4wwjlPUyHLUTXdBdo62clt8f8IsAooG\nsq8ReeYh5PknoeUAlFegbv8vqKnnmUyCIXqccKpeFLurCqq2eB2NoQfScgDCNeDq7BkeR2OIJCot\nHTVzDgCy+iXkQLPHEcU/suUH5NlHtQf6mefDORd4HVJCYhRFHKOGDEfN/xUUlUL1LmTRvyO1e7wO\nK+bIt58jD/4BNqzTdjOzrkFdd4exnDFEnUSybktJPn1Xe96WV6CGjfI6GkOkOW4SlFdAawuy+mWv\no4lrpGqLbuARCsLks1DTZ3nSZj4Z6FXhqm3bFwN/AnzAQ47j/GuPv58P/AHYEX7rfsdxHopgnCmL\nyi+Em+/SB/yOrcij98G821AjRnsdWtSRtlbk1WXw9af6jXHHoy6ze2VMvmjp8kNqUGvrGyJfg2pI\nCdTks5APVusFsXXVxvEkTpD2NuRjfbNissXJiVIKLroSefD/wOcfIaeeYW6ADoPs2YE8/Rdt1XjS\n6aiLrzKieAAcM2Ns27YPeAC4BDgeuNa27eMP89FnHMc5JfwwojiCqEHZugnI+OOh5QDy+P9Fvv/G\n67CiimzbpH8Mv/5U+y9e8jPUvFt7LYp/c+/CLvuuTnuv39y7kEVLl8cgekMyofIKYNLp2rrt+SeM\njWK88PmH0LIfhpfpbmmGpEQVD4afnAcI8upSRA7f3TFVkdo9yBN/htYWmHAS6vJ5pqnVAOnN6E0F\nNjiOs8lxnHbgaWBOdMMy9EQF0lBzF8ApP4FgEFny16T0eJRQCHf1y8hjD8DeehgyQjfrmHxWr++A\no94y2JByqJlzIK8Adm5H3n7N63BSHgkGkQ/XADpbbLJjyY06Zybk5MLO7fD5R16HEzfId18gjyyE\nA80wZgLqyhv71dXScCi9EcbDge3dXleF3+vJ1bZtf2Xb9rO2bY+MSHSGQ1CWT5cSTLsEEOTNF5CX\nnKTpkid7dujude+9CQKcNQO14G/7vNI82i2DDamHyshEzbkelIL3ViLbNnkdUmrz9ae6M1rJED2T\nZkhqVHoG6oLOhXgvIy37PY7IWyQYxH11GbJssa6xn3gyau4CY+saIXozioe7Fe+ZpnwReMpxnDbb\ntv8GeBSY3vNLtm3fDtwO4DgOxcXFfQx34EhHB+7eWvLz82O+74gxay7tI0fT/NRD8MVH+Jr2kn3z\nL7AGZUdldz6fL6rjJR0dtLz5Iq2rXwE3hFVQRNY1txEYO6Hf22wPhVDWwUNXWYrcvNyY/L9He7yS\njYQZr/zTODD9UlpXvoR68Slyf/0/sTIHxTyMhBmvKCGuy96P3kKArJmXk15QeNTPp/p49ZV4HS85\naxpNX31CcON60t5fSdbVN3kdEhD78QrV1dD8+H8QqtoCPh+DLr+G9LOnJ8ysiRXsoLioWLevj1N6\nI4yrgO4Z4BHAzu4fcBynrtvLvwC/P9yGHMd5EHgw/FJqa2t7H2mEkGAHecEQe5sT/I6zbDzqpl8i\nzsMEN66nceG/6BrcKCwMys/Pp7GxMeLbBZDtm5EVz0BdNaDg9HOQ8y9lf3oG9HOfnTXFtfUNFIV/\nsGrrG7j4pltikjWO5nglI4k0XjJ1Gnz3Fe6u7TQ+8wjWFTfEPIZEGq9oIN99od158gs5MLqClmOM\nRaqPV1+J5/GSC2bD5kraPniL9uNP1Q2xPCaW4yXff4288BS0tUJeIerqm2gdNorWvYlj5ZqXkUF9\nXa1u4hJjhg0b1qvP9aaU4hNgvG3b5bZtpwHXAC90/4Bt20O7vZwNrOtlnIYBoIaNQi24BwYPh/oa\n5K9/QhKkfaa0t+G+thx59H4tiotKUTf9Euviqwbc0jVWLYMNqYfy+VBXXA+BNPhmLfLNWq9DSilE\nBHnvTQDUmdNNPWWKoUqGwJRzAUFefBrpaPc6pJggbgj3zReQJX/VorjiRL32xjh0RIVjZowdxwna\ntn0X8Braru0Rx3G+tW37fwGfOo7zAvC3tm3PBoJAPTA/ijEbuqHyCrSd23OPQ+W3yJN/hgsuh6nn\nxeXUirS2wNr3tc1S8z5QFpw5HXXehRG7g4xZy2BDSqKKSmHmHOTlJcgrz+qW5PlHn843RIjvv9Yt\nurNz4GTTojsVUeddhFR+q73933gedelcr0OKKtKyH1n2GGyuBMtCTZ8FP/lpXF7fkwXloauB7Ny5\n89ifivROgx3k1e1hb2trzPcdTcR1kTUvw/ur9BvHn4KaNQ+Vlj7gbUdiqkj2NSIfvw1rP9CLBUA7\nTlxmo4aOGHCM8UQ8T0XGI4k4XiKiszeV38CoMagbfhGzDoyJOF6RQPY2IA/dCy0HdCv4qef16nup\nOl79JRHGS3ZX6YXaoZB2YjjhVM9iiWqpYfVOxPkrNNbBoGzU1TejysZGZV+xIi8jg71Fg70spTjm\nHYVZwpgkqPCdpAwdibz4NHz3BVKzG+YuQBWWeBaX1OxG3l8F367VbSoBRo9HnTkNxhxn7noNCYlS\nCi6zkZ1bYdsm5O3Xwm4xhmggoRCy/DHdDn7scTDlHK9DMniIGjICZl6hfY1fcmDoCE+vc9FA1n2p\n64k72nUSae4CPUNsiDrGBTrJUBNPRt1yj24jXbMbefjf9LRTjBHXRd5942CTDhGdxb7177BuuBM1\ndqIRxYaERmVlo2aHLdzefQP5IfbnWaogq1+Cqi2Qk4+ac51pYGCAyWfBxJOhvQ1Z9hgSTBLbUnFx\n17yCLH1Ui+ITT0PdfJcRxTHE/LokIap4sBbHE06CtlbEeRh31UtIZwlDlJGmvcgT/4mseQXEhdPO\nRP3in7CuuikuVhEbDJFCjanoyhTLc08g9TUeR5R8SOU38OEaUBbqqhtRUbKlNCQWSinUZTbkF8Lu\nKmTlC8f+Upwj1buQJx+Ed98ApVAXzEbNuR4VSPM6tJTCCOMkRaVnoH42HzX9Mp3Ren8l8sD/j3z8\nNhLsiNp+5YdvdZZ46wbIykZdezvWpXNRBUVR26fB4ClnzYAJJ+qb0GcXpcxK+VggjfV6OhlQ0y9D\njSz3OCJDPKEyMlFX3QSWDz55F1n/ldch9QtpqMN97gl97dxcCRmZqGtvR50xzcyseoCpMU5ilFL6\noj18tL6b3rkdef05+GANnDsTTp6K8kXG7kiCQWTVi/DxO/qNMRNQs69DZedEZPsGQ7yilILLr0Vq\nFuqV8i85MOd6c0EbIBIKIssehdYWGH8CnDHN65AMcYgaNgpmzELeeF6vrxk8PGESMdK8D3n3DVj7\nIbghLfAnn4k6e6a5dnqIEcYpgCobCwvu0XZub72iL94vL9EOFuddCCec1m+BLCKw+Qdk5YuwZ4e2\nkzn/UjhjmqkDNKQMKiMT5i5AHlkI36yF4WVhv1VDf5E3X4Sd2yGvADX7GnOjEWMkFIJgB1gWnQv5\n47Zb2dTzYOtGqPwGeepBvei8ZIjXUR0RCXYg774JH72l64hRcNLpqPMuShhRn8wYYZwiKKX0dG/F\n8fDdl8jbr0FdtZ6mXP0KTDkbTj0T1csWt1oQV+rtVG3Rb+YX6RpAYzpuSEFUyRCYNQ9Z/hjyxvN6\nJbmZ+u8zIgKfvQ+fvAOWD3XVTajMLK/DSnrEDUFHUDuA+AKQk4fKyoU0Xd8qext0Db0biruaVz1r\nMw9ZXKsXnT+yEC65GjUp/ryuD+32im7WMe0SVOnQo3/REDN8v/3tb73a92+bmppiv1fXJaNlP21J\nsoK1ryil9Ak4+UxUfjHU12iPxM0/wKfvIs17obDkkAtRRkYGrWHfZxGBTd9rQf3eStjXCJlZqHMv\n1Fmd/N7d7S5aupwRQ4YwKDMT0C2bnZdf5ZTjJ0b+Hx1juo+X4dgk03ip0qFIW6u+Wdy4Xs/GpA/c\nS7w7yTRePZGW/cjzT+rFdoCaOQc18eQBbdOr8RI3BO3tIBKxkrXD7kdkQNl0CQUhGNSOH8NGkVs2\nhhZ/GiozC+X362uGUrqet6AYCaTDgf3Q0YbyxU9uTQXSYNLpsG8v7NoO33+D7GuE8oqojn9vjy/p\naNczqy8/Cy37oXgw6mcLsM6ajspKnbKJDL+ftkHZnnStzMnJAfifx/pc/BzVhpiiLJ/uHDVpsha6\nH76li/4/fQ/59H1kTAVkZoG4NPv9uO1t4Arsa4DdO/RGMrO0H/Hks/vUxnnR0uX85t6FLF72HM59\nCwGw776Hys1bAEx3OkNCo6bPQnZt1/7Gz/wFbvzlgNucpwKy5Qctipv2Qlo66uKr4aTJ3sTST7Ep\nwSCEQpCeDtn5qPwC3dyooQYViOwNknSEF1FnZSMCdLRpgRsK6QXXfv9Rm85IMKhtNPMKUUXFvRYq\nVk4u5OTiHtiP1O6BtpaINJKKBCotHWZfC2VjkVeXwhcfITu3wdU3646VHiFbN+gscUOd7vZ61gzU\nuTM9aXJhODam852hC6nepbvTff0ZhI6SUR+UhTrjfDj97H79INbWN3QJ4aL8fADqGhupKB+Nc9/C\nrjbOiUoidI6KJ5JxvGR/M/LofXpGpmwc6tqfR+wimGzjJaEg8tar8P5qQHSL7TnXR6zWsi/jJa4L\nHR2QlQOW0k2JQiG9MKrzOYRLbpUWoKD/DAQgOw+Vk4fyH5pzchvqoXbXgAWkiAvtHZCWDgVFel89\nxK8Eg9qac38zBNsPimU3pP8U0XXDBUWoguIffb+4uJja2tpex+Qe2A+1u6G1NeKzIwNB9uxAli7W\n52BaurZVHDMBikoiuv7laMeXtOxH1rwKn72n3ygdirr8mpS2LU2EzndGGBt+hOxv0qUVIqAUQFpK\n6gAAGq5JREFUg7KzOdDS0pWFYNTYAf/A19Y3MOOG+dSFf1CK8vNZ+fiihBfFkHzCJdok63hJQx3y\n6L9DcxMcN0nXykagbXQyjZfUVSPPPQ67qrRv67kXwjkXRHSatTfj1VlfS26+9oH3R34y1d1bD3t2\n9Us8SjCohXl2DhSWYPVzBkJEtDi2rCMei30Vxp24B/ZDzW5ob42bDLK0tWqXmO++OPhmRiYML0ON\nGA3DR8PwUQOa0Tnc8SXBDm0f996b2lXFslDnzISzZ8RV+YkXJIIwTu3/IcNhUVk5cOJpXa/T8/Np\nSZILscEQK1RBEVx7B7L4flj/FfLqMr0gyLgraCH60Vs6UxwM6un8K66P+WJFcUMH62tHRkcQd2Ll\nFeIqH7K7qtfiWNrbwefT2d38wgHfMKjO5EYUsAZlQdlYXWJRsxvaWiEQiMjNYH9R6Rlw5Y0w/gTd\nKKZqMzTtg43rkY3rwx9SSOlQGD5ai+URo/V496eURlz4Zi2y+hVddggweryulR88LGL/LkN0McLY\nEHM6SynqGhsPKaWw774nKUopDIZO1OBhYN+KPPlnWPs+kpWN+unFXoflKVK9C1nxtLZiA5g0BXXh\nFdryLpZxhIKQloEaNS6qi7O6Y+Xm4VoWsmvbEbOqXeUcmYNg2CisrMTq9NcpkKWjA6mvRpr2AeKZ\nk4VSCk6ajDppss6Y72uEqi1I1RbYsUWvmdmzE/bsRNa+r7+UlY0ML0MNGQFDR2qHmZzcw25fRJDW\nFr3N1S9r21LQZRMzLtee/uZmOKEwwtgQc1asXkPl5i1dNcVwcPHditVrzOK7JETa2yCQlpIXCFU2\nFq66EXl2EbzzOpKdg5p8ttdhxRwJheD9Vcg7r+t619x81GVzUWNj70Qjrgs+P2p4WcyPSSs7B3d4\nGbJnl65jVpYuU1OWfu0P6NrfePUM7iUqEEANHo6UDkMONCH1ddB6QGeRPfK4V0pBXoH2xj7hVEC7\nRbCrCqo2I1VbtaPM/mbt+1/5bdd3JTsHhoyEohJoOaAFdtNeGpr3QlvbwZ3k5Ot65pMme5otN/Qf\nI4wNMadT+M46f1pXdti5b6ERxUmIdC5WGjoSGuqQ1v2otNRzaFATToJL5yIvOcgry/T0/ZRzPLEs\n8gLZXYW8+MzBbNppZ6JmXO6JW4eIgOuiRo317EbNGpQN5eM92XesUUp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[0.5921438188336057] \n", + "6 [1.3404237928157525] [0.4241448934651531] \n", + "7 [0.9825708450923527] [0.9594493236660923] \n", + "8 [0.3555684618930405] [0.7719114194548434] \n", + "9 [0.23275385813306335] [1.464791372243463] \n", + "\n", + " kern.kern_list.1.variance \n", + "0 [1.2720246353326516] \n", + "1 [1.2395359477008205] \n", + "2 [0.8621121645070724] \n", + "3 [1.2438263168137242] \n", + "4 [2.68133348675961] \n", + "5 [1.6638535187996304] \n", + "6 [1.024398703348455] \n", + "7 [0.619018694545985] \n", + "8 [0.7551095943341086] \n", + "9 [1.1758487570645073] " + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas\n", + "df = pandas.DataFrame(res[1:],index=[n for n,p in m.named_parameters()]).transpose()\n", + "df[:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "cell_id": "4E57DE6B13CF4EEFAF6FC03F222C89BD" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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