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pymc nonparametric bayes sample
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# PyMCによるディリクレ過程混合モデル"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"original code http://austinrochford.com/posts/2016-02-25-density-estimation-dpm.html"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ディリクレ過程\n",
"集合$\\Omega$の任意の分割$S_1, \\ldots, S_n$に対してディリクレ分布Dirとパラメータ$\\alpha$を用いて$\\Omega$上のディリクレ過程Pは\n",
"$$(P(S_1), \\ldots, P(S_n)) \\sim \\textrm{Dir}(\\alpha P_0(S_1), \\ldots, \\alpha P_0(S_n)).$$\n",
"と書かれる。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"観測$ \\omega_1, \\ldots \\omega_n$に対して新たな観測$\\omega$の事後分布は\n",
"$$\\omega\\ |\\ \\omega_1, \\ldots, \\omega_n \\sim \\frac{\\alpha}{\\alpha + n} P_0 + \\frac{1}{\\alpha + n} \\sum_{i = 1}^n \\delta_{\\omega_i}.$$\n",
"\n",
"と書け、\n",
"$$P\\ |\\ \\omega_1, \\ldots, \\omega_n \\sim \\textrm{DP}\\left(\\alpha + n, \\frac{\\alpha}{\\alpha + n} P_0 + \\frac{1}{\\alpha + n} \\sum_{i = 1}^n \\delta_{\\omega_i}\\right),$$\n",
"\n",
"ディリクレ過程$DP(\\alpha,P_0)$からサンプルされる経験分布Pは\n",
"観測$ \\omega_1, \\ldots \\omega_n$、重み$w_i$を用いて\n",
"\n",
"$$P = \\sum_{i = 1}^\\infty w_i \\delta_{\\omega_i}.$$\n",
"\n",
"と書かれる。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### STB([stick-breaking process](https://en.wikipedia.org/wiki/Dirichlet_process#The_stick-breaking_process))\n",
"経験分布\n",
"$$ \\sum_{i=1}^{\\infty} w_i \\delta_{w_i}$$\n",
"の重み$w_i, \\sum_{i=1}^{\\inf} w_i=1$は\n",
"ベータ分布$Beta(1,\\alpha)$に従う$\\beta_1, \\beta_2, \\ldots $を用いて\n",
"$w_i = \\beta_i \\prod_{j = 1}^{i - 1} (1 - \\beta_j)$\n",
"と書かれる。"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from __future__ import division"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Using gpu device 0: GeForce GTX 970 (CNMeM is disabled, CuDNN not available)\n"
]
}
],
"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 statsmodels.datasets import get_rdataset\n",
"from theano import tensor as T"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"blue = sns.color_palette()[0]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"np.random.seed(462233) # from random.org"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"N = 20\n",
"K = 30\n",
"\n",
"alpha = 2.\n",
"P0 = sp.stats.norm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We draw and plot samples from the stick-breaking process."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def gen_sample_cdfs(K,alpha):\n",
" beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
" w = np.empty_like(beta)\n",
" w[:, 0] = beta[:, 0]\n",
" w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
"\n",
" omega = P0.rvs(size=(N, K))\n",
"\n",
" x_plot = np.linspace(-3, 3, 200)\n",
"\n",
" return x_plot, (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def cdfplot(K,alpha):\n",
" x_plot,sample_cdfs = gen_sample_cdfs(K,alpha)\n",
"\n",
" fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
" ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75, label='DP sample CDFs');\n",
" ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
" ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
"\n",
" ax.set_title(r'$\\alpha = {}, K={}$'.format(alpha,K));\n",
" ax.legend(loc=2);"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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UeJ7HccedgBtu+Ml3usYPP3wfjY0NuOWWn+c0/qOP/ou33/4nDAYDBEHAD35wNRYsWISt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D2ZxZBFUcQ///P1iESGsXTpMpx66icM9qvGkOvrG2zvVWshq32s7VvIkiTh/fffweHDB02PkUVW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\nH7f6NLpcJodpAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fcc4742a710>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cdfplot(K=30,alpha=2.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As stated above, as $\\alpha \\to \\infty$, samples from the Dirichlet process converge to the base distribution."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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Vjel8HD9+zBQJyogFgJFiO6SCp5NMJtE0neeeewpZltA0PevvV9M0IpEwFouF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\ny12rck+PHXudQkFl1642fvrTlzBNCARCyLKLZFIBFCYnJzh69DCSJLF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aWlr49//+t6iq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\n7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Nnfra0rRR/gOdCHwxEWFlKk0ylSqXmOHn2BSqVMS0urt7Eci8XZunU7fX39BINhnnji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3rRnS9QwMXKG/v49EIlG0iw/xyCPvYXCwn6mpCfbs2c/ly5fsVuI7pbRJsJbYFG26AoFAILgX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"text/plain": [
"<matplotlib.figure.Figure at 0x7fcc45625390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (l_ax, r_ax) = plt.subplots(ncols=2, sharex=True, sharey=True, figsize=(16, 6))\n",
"\n",
"K = 50\n",
"alpha = 10.\n",
"\n",
"x_plot, sample_cdfs = gen_sample_cdfs(K,alpha)\n",
"\n",
"l_ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n",
" label='DP sample CDFs');\n",
"l_ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
"l_ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
"\n",
"l_ax.set_title(r'$\\alpha = {}$'.format(alpha));\n",
"l_ax.legend(loc=2);\n",
"\n",
"K = 200\n",
"alpha = 50.\n",
"\n",
"x_plot, sample_cdfs = gen_sample_cdfs(K,alpha)\n",
"\n",
"r_ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n",
" label='DP sample CDFs');\n",
"r_ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
"r_ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
"\n",
"r_ax.set_title(r'$\\alpha = {}$'.format(alpha));\n",
"r_ax.legend(loc=2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ディリクレ過程混合モデル\n",
"ディリクレ過程からサンプルされた分布Pからサンプルされたパラメータ$\\theta_i$に基づく分布\n",
"$$ x_i\\ |\\ \\theta_i \\sim f_{\\theta_i} $$\n",
"$$ \\theta_1, \\ldots, \\theta_n \\sim P $$\n",
"$$ P \\sim \\textrm{DP}(\\alpha, P_0) $$\n",
"\n",
"ここでは正規分布Nに対して\n",
"$$\\alpha = 2, $$\n",
"$$\\theta \\sim N(0, 1)$$\n",
"$$x\\ |\\ \\theta \\sim N(\\theta, (0.3)^2)$$\n",
"となるような場合を図示する。"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"N = 5\n",
"K = 30\n",
"\n",
"alpha = 2\n",
"P0 = sp.stats.norm\n",
"f = lambda x, theta: sp.stats.norm.pdf(x, theta, 0.3)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
"w = np.empty_like(beta)\n",
"w[:, 0] = beta[:, 0]\n",
"w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
"\n",
"theta = P0.rvs(size=(N, K))\n",
"\n",
"dpm_pdf_components = f(x_plot[np.newaxis, np.newaxis, :], theta[..., np.newaxis])\n",
"dpm_pdfs = (w[..., np.newaxis] * dpm_pdf_components).sum(axis=1)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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U/f4gBEEgS/UaQKJKGI58Xm78oPfA6kFwudyoVitU4N8HTFR5Xm7sYYQkpUKh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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fcc69c9a750>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"ax.plot(x_plot, dpm_pdfs.T, c='gray');\n",
"ax.set_yticklabels([]);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now focus on a single mixture and decompose it into its individual (weighted) mixture components."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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pVq5chu7dg5CSkixYPcbGxli6dBF+/nkTAMVc1TLk5eUJVhPpJ4YqEWlVdXU1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\nBAKBkRBBVSAQCAQCI/F/v7ksDXR+CGkAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fcc45616a50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"ix = 1\n",
"\n",
"ax.plot(x_plot, dpm_pdfs[ix], c='k', label='Density');\n",
"ax.plot(x_plot, (w[..., np.newaxis] * dpm_pdf_components)[ix, 0],\n",
" '--', c='k', label='Mixture components (weighted)');\n",
"ax.plot(x_plot, (w[..., np.newaxis] * dpm_pdf_components)[ix].T,\n",
" '--', c='k');\n",
"\n",
"ax.set_yticklabels([]);\n",
"ax.legend(loc=1);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 実例:間欠泉のデータ\n",
" Yellow Stone国立公園の間欠泉[Old Faithful](https://en.wikipedia.org/wiki/Old_Faithful)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>waiting</th>\n",
" <th>std_waiting</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>79</td>\n",
" <td>0.596025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>54</td>\n",
" <td>-1.242890</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>74</td>\n",
" <td>0.228242</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>62</td>\n",
" <td>-0.654437</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>85</td>\n",
" <td>1.037364</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" waiting std_waiting\n",
"0 79 0.596025\n",
"1 54 -1.242890\n",
"2 74 0.228242\n",
"3 62 -0.654437\n",
"4 85 1.037364"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"old_faithful_df = get_rdataset('faithful', cache=True).data[['waiting']]\n",
"old_faithful_df['std_waiting'] = (old_faithful_df.waiting - old_faithful_df.waiting.mean()) / old_faithful_df.waiting.std()\n",
"old_faithful_df.head()"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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OM2DAAGOMMb///rtp27ZtlvsLMxal7vD7U089pTFjxkiSqlatqvj4+GyPMWXg\nA/vO+hEdHa377rtPdrtd3t7eCgoK0p49e0qi1FzVrFlT8+bNk91uz/UxZWEsnPWjLIzFjXMmPPTQ\nQznWV5rHIq85H06dOiVfX1/5+/vLZrOpTZs22rFjR0mWmyNn81YYY0r1GGTy9vbWwoULVb169Wz3\nlZWxkPLuh1Q2xqNp06aaM2eOJKly5cpKTk521FzYsSh1oV6uXDl5e1+/zOqSJUv0xBNPZHtMSkqK\nRowYoV69eumjjz5yc4X546wff7wGftWqVRUbG+vWGp3x8vJy+piyMBbO+lEWxuLGGm02mzw8PHTt\n2rUsjynNY5HXnA85bf+YmBi31+hMfuatmDhxonr16qVZs2a5u7x88/DwyPVvoqyMhZR3PzKV9vHw\n8PDQLbfcIklatWqV2rRp4zhlVtixKNFz6qtWrdJnn30mm83mOA/4yiuvqFWrVlqxYoV++uknLViw\nINvzRo8eraeeekqSFBISoqZNm6pRo0buLt+hsP24UUm/o8yrD3kpS2ORX6VpLDLr+fHHH7M8JiMj\nI9vzSttY5CWvbVzS2z+//ljn0KFD1bp1a/n6+mrgwIH65ptv1KFDhxKqrniUlbHISVkaj40bN2r1\n6tVatGhRro/J71iUaKg/88wzeuaZZ7ItX7VqlTZv3qz33ntPnp6e2e7v0aOH43bLli31888/l+g/\nr8L0o0aNGln2Bs+fP6/GjRu7vNbc5NYHZ8rKWOSlLIzFmDFjFBcXp4YNGzr20MuVy/rnW9rG4kZ5\nzfmQ0/YvjR9ocjZvxd/+9jfH7b/85S/6+eefS22I5KasjEV+lJXx2Lp1q8LDw7Vo0SJVqlTJsbyw\nY1HqDr+fOnVKn3zyiebNm6fy5ctnu//YsWMaOHCgMjIylJ6err179+qOO+4ogUrz5qwf999/v/bv\n36+EhAQlJiZq7969atKkSQlUmj85vUssK2Nxo5z6URbGolWrVlq/fr0kadOmTWrevHmW+0v7WOQ1\n50Pt2rWVmJioM2fO6Nq1a9q8ebMefvjhkiw3R3n1ISEhQaGhoUpJSZEk7d69W3feeWeJ1VpYZWUs\nnCkr45GQkKDp06drwYIF8vHJOnFZYcei1F0mdvbs2Vq3bp1q1arlOHy6ePFiLV68WM2bN9f999+v\nmTNn6t///re8vLzUrl07vfjiiyVddjb56cc333yjDz74QB4eHurdu7f++te/lnTZWWzYsEH/+Mc/\nFBMTI7tuZ8HQAAAOgklEQVTdrltvvVUREREKDw8vU2ORn36U9rHIyMjQ2LFjdeLECXl7e2vKlCny\n9/cvU2Mxa9YsRUVFOeZ8+Omnn+Tj46NHH31Uu3fv1owZMyRJjz32mPr27VuyxeYirz4sW7ZMERER\nstvtuuuuuzRu3LiSLjdH0dHRGjdunC5evChPT09VqVJFXbt2VZ06dcrUWDjrR1kYj08//VTz5s3T\n7bff7siJFi1aqEGDBoUei1IX6gAAoHBK3eF3AABQOIQ6AAAWQagDAGARhDoAABZBqAMAYBGEOgAA\nFkGow222bNmi0NBQPffcc3rmmWc0fPhwJSQkSJL27t2r06dPF8t62rRpozNnzhT5+Vu3btXChQuL\nXM/IkSP1+eefF7mdTH369JExRlevXtWGDRskqdhqjYmJcUwasWbNGkVERBS5zRuNGTNGn332WYGe\n88UXXxRrDaXF0aNHdfDgQUlSeHi4tmzZUsIVwQoIdbhFWlqaRo0apTlz5mjJkiVatWqVatWqpVWr\nVkmSVq9erVOnThXLuoo6h3jm81u3bl3qLuAiSUuXLpXNZtOBAwf0zTffSCq+Wnfu3OkI9c6dO6tr\n165FbrMozp8/r5UrV5ZoDa6yYcMG7d+/X5L0wgsvqE2bNiVcEaygRK/9jptHSkqKrl69qsTERFWr\nVk3S9T1Y6fpkBuvXr9e+ffs0ZswYlStXTtOnT1eFChV09epVTZw4UXfddZfGjBmjGjVq6PDhwzpx\n4oS6du2q//mf/9GFCxc0bNgwZWRk6O6773ZcCjY5OVmvv/66Ll26pOTkZHXo0EEDBgxQVFSU3nvv\nPVWoUEGPPPKIgoODc3z+mjVrtH37dg0fPlyjRo1yTBKzd+9effzxx7rvvvs0e/Zs7dmzRykpKWra\ntKlGjhwpY4zCwsL0yy+/KCAgQElJSdm2R+/evTV+/Hg1aNBAU6dO1cGDB/XRRx8pPT1dwcHB+te/\n/qV58+Zp+/bt8vT0lL+/v6ZPny5PT08FBgZqz549GjdunK5cuaIZM2aofv362r59u6ZPn67g4GD1\n6dNHW7du1enTp/XGG2+oRYsW2rt3r9544w1VrlxZjzzyiJYsWaJNmzY5ajp9+rRmz54tSfL19VVC\nQoLS09M1dOhQNW7cWAMHDtSmTZuUlpamF198UatWrdLx48c1adIkPfTQQzp79qzeeOMNXb16VUlJ\nSXr11VfVsmXLbH3/z3/+o6+//loxMTHq0qWL+vXrp7S0NL355ps6efKkEhMT9cQTT6hv374aMWKE\nfvnlF73++uvavXu3/u///k+VKlXSsGHDVLFiRU2ePFlxcXHq16+f1q5dq+XLl2v9+vW6du2a6tWr\np0mTJsnLy0tff/21li9fLun6bFd///vfVaVKFT344IN6+eWX9d133ykuLk7vvvtutsuJHj58WFOn\nTtW1a9d07do1TZgwQYGBgerdu7fuuusu/fTTT1q6dKnuvvtu/fTTT/Lw8NCaNWv0/fffa9q0aQoO\nDtaTTz6p6OhoXbp0SWFhYfLy8tLy5cvl4+OjihUratu2bWrSpIm6deumzz77TJ988oluueUWVa9e\nXW+99Zbsdnuutc6YMUNRUVHy8vKSv7+/pkyZkuOlqXGTKMS87kChhIeHmwceeMD069fPvP/+++bX\nX3913BcaGmq+//57Y4wxGzduNAcPHjTGGPPll1+aIUOGGGOMGT16tBk+fLgxxpjffvvNNGnSxBhj\nzKxZs8yMGTOMMcYcOHDABAYGmt9++82cOnXKrFmzxhhjTEpKimnSpIlJSEgwO3fuNA8++KC5fPly\nns9fvXq1GTlyZJY+LF++3LHs66+/NqNHj3bcN2jQIPOvf/3LbNu2zfTo0cMYY0xycrJp1aqVo45M\n77//vlm+fLmj7/369TOpqalm79695pVXXjHp6ekmPDzcpKenG2OMef75583mzZuNMcYEBgaa9PT0\nLPXdeLtdu3Zm5cqVxhhj1qxZYwYOHGiMMaZHjx5my5Ytjj4HBwdnG6O5c+ead999N9vthg0bOsYn\nNDTUhIWFOdY7aNAgY4wxL7zwgtm5c6cxxpjY2FjTrl07R/2ZRo8ebV588UVjjDGXL182zZo1M/Hx\n8eaDDz4wc+fONcYYk56ebrp27WoOHz5sdu7caXr16mWMMWbcuHGObRAaGmpCQ0ONMddfI1OmTDHR\n0dGmT58+jnVNnjzZLF++3Jw9e9Y89dRTJjU11RhjzJIlS8yUKVMc/dq6daujv2+//Xa2bfLEE0+Y\nkydPGmOMOXjwoOncubOjhsztc+O45DQeH374oTHGmO3btzueP3r0aLNq1aost8+cOWPatGljkpKS\njDHGTJkyxcybNy/XWuPj403jxo1NRkaGMcaYr776ypw9ezZbH3DzYE8dbjNgwAB1795d//73v7Vj\nxw716NFDw4cPV8+ePSX9d7KV6tWra/r06UpJSdGVK1dUpUoVRxvNmjWTJAUEBCgxMVHGGB0+fNjR\nxt133+2Y6ahatWras2ePVq5cqfLlyys1NVXx8fGSpLp16zomUPjj8/84sUKmvXv3as2aNVqxYoWk\n64eq9+7d6zjHnZiYqNOnTystLc0xy1uFChV0//33Z2vroYce0ocffqinnnpKFSpUUGBgoKKjo/XD\nDz/o4YcfloeHhzw8PBQSEqJy5crp2LFj+v333/O9rW/cTpl9Pnz4sGOimvbt2+vLL7/Md3uSFBQU\nJEmqWbOmo381a9bUlStXHNvjxqMSXl5eunDhQpaZzDL7Lkk+Pj66/fbbdfz4ce3cuVPnz5/Xzp07\nJUmpqak6efKkKleu7Hhey5YtFRUVpZo1a6pu3bpKSEjQuXPntHPnTnXs2FFRUVE6depUls8clC9f\nXnv37lVsbKz69+8vY4zS0tJ02223ZdtWtWvXznYK6OLFizp27JjGjh3reH0mJSU5bud3Nr/MiTia\nNGmio0eP5vq4AwcO6J577nHMsd28efMspx/+WGvlypXVunVrhYSEqH379urUqZP8/f3zVROsiVCH\n21y9elVVqlRRp06d1KlTJz322GOaOnWqI1AzjRo1Sm+99ZaaNWumzZs3a/HixY77/jiFbeY/1xvP\no6enp0uSlixZorS0NMc/xRYtWjge88fDkzc+P3Nq0xvFxcVpwoQJev/99+Xt7S3pemj16NFD/fr1\ny/LYxYsXy8Pjvx9XyaznRvfee69+/vlnRUVFqWnTpmrYsKF27dql3bt366233tKePXu0evVqrV69\nWt7e3hoyZEi2NvJy47SsmdvIGJOlroK6sc2c2vfy8tK8efOyvAnLyY01ZGRkyGazycvLS4MGDco2\nNWZUVJTj9kMPPaRly5apZs2aat68uS5duqSoqCjHxB5Hjx5VcHBwtok7vv32W913331asGBBtlps\nNluOfcnk5eUlb29vLV26NMe+3Pg6uvG5aWlpWR6XkZHheExen/nIPMVzY5s3Pj6nWufMmaNjx45p\n8+bNCg0N1dy5cxUYGJjrOmBtfFAObrFt2zZ1797d8Wl36fr0tH/+858lXf9HnxmmFy5c0B133KH0\n9HR9/fXXSk1NzbHNzH9q9evX1969eyVdn7kpOTlZ0vUgrl+/vqTr/9hTUlJybCu352dKT0/X8OHD\nNWLECNWpU8exvEmTJvrmm28coT1//nydPHlS9evXV3R0tKTrUyv++OOP2dZps9lUv359rVq1Ss2a\nNVNQUJCioqL0+++/KyAgQBcuXFDt2rXl7e2t3377Tf/5z38ctd/4RianNyC5qVevnvbt2+fYHjkp\naJs3atKkib766itJ1/dwJ0+enOPjMj+IFx8fr9OnT6tu3bpq0qSJ1q1bJ+l6AE6ZMkWXL1+Wh4eH\nIyB9fX1ljNGWLVvUrFkzPfjgg1q3bp38/Pzk5eWloKAgfffdd46jBR9//LGio6N17733at++fY65\n0NevX+/4LMEfQ/yPKlWqpNq1azs+mX7s2DHNnz8/x8f6+Pjo7NmzkuQ44vDHPu/evVsNGzaUlPO2\nvueee/TTTz85+rB9+/Y8jwacPn1aH330kerWrat+/fqpffv2OnToUJ59grWxpw63ePjhh3XixAn1\n7dtXFStWlDFG1atX14QJEyRdn6t64sSJCgsL04ABA9SnTx/5+/trwIABGj16dI57Spl7MH369NGw\nYcPUt29f3XHHHY5Dq926ddPw4cP13XffOT6sNGLECL3++utZ2snt+ZkiIyN14MABLVq0SB988IFs\nNpueffZZPf7444qOjlbPnj3l6empRo0a6bbbblOdOnX05Zdfqnv37goICMj1n3KrVq00depUzZ8/\nX56enrp8+bLj8HirVq20ePFiPfvss6pfv76GDBmi9957T82aNXP0+7777tPMmTM1duxYNW3aNNt2\n+aMRI0bojTfeUM2aNRUUFJRlry/Tgw8+qOHDh6t8+fJZ9qhvbDO39seOHasJEyboq6++Ulpaml5+\n+eUcH1ejRg0NGjRIJ0+e1ODBg1WpUiWFhIToyJEj6tmzpzIyMtS2bVtVrlxZd9xxh+Li4tS/f38t\nWrRIzZo104YNG+Tn5yc/Pz9FR0c7PvV/zz33qFevXurdu7cqVKigGjVqqGvXrvL29tbYsWP14osv\nqmLFiqpQoYKmTp2aZ19uNG3aNL311lv63//9X127dk1jxozJ8bkDBgzQ888/r9tvv12BgYGOgJeu\nf1XwpZde0rlz5zRp0iRJ148cTZs2LcsbC39/fw0dOlR9+/aVt7e3/P399dprr+Vaa82aNXXw4EF1\n795dFStWVJUqVfTKK6847ROsi6lXgZvEjh07VL16dd1xxx36+uuv9fnnnxfLd9uRt+DgYC1ZsiTb\nm0XAFdhTB24Snp6eGjVqlCpWrKiMjAy98cYbJV3STaGo100ACoI9dQAALIIPygEAYBGEOgAAFkGo\nAwBgEYQ6AAAWQagDAGARhDoAABbx/2BFFcwgjeMiAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fcc47355bd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"n_bins = 20\n",
"ax.hist(old_faithful_df.std_waiting, bins=n_bins, color=blue, lw=0, alpha=0.5);\n",
"\n",
"ax.set_xlabel('Standardized waiting time between eruptions');\n",
"ax.set_ylabel('Number of eruptions');"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"N = old_faithful_df.shape[0]\n",
"K = 30"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### モデル\n",
"$$\n",
"\\begin{align*}\n",
" x_i\\ |\\ \\mu_i, \\lambda_i, \\tau_i\n",
" & \\sim N\\left(\\mu, (\\lambda_i \\tau_i)^{-1}\\right) \\\\\n",
" \\mu_i\\ |\\ \\lambda_i, \\tau_i\n",
" & \\sim N\\left(0, (\\lambda_i \\tau_i)^{-1}\\right) \\\\\n",
" (\\lambda_1, \\tau_1), (\\lambda_2, \\tau_2), \\ldots\n",
" & \\sim P \\\\\n",
" P\n",
" & \\sim \\textrm{DP}(\\alpha, U(0, 5) \\times \\textrm{Gamma}(1, 1)) \\\\\n",
" \\alpha\n",
" & \\sim \\textrm{Gamma}(1, 1).\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied log-transform to alpha and added transformed alpha_log to model.\n",
"Applied logodds-transform to beta and added transformed beta_logodds to model.\n",
"Applied log-transform to tau and added transformed tau_log to model.\n",
"Applied interval-transform to lambda and added transformed lambda_interval to model.\n"
]
}
],
"source": [
"with pm.Model() as model:\n",
" alpha = pm.Gamma('alpha', 1., 1.)\n",
" beta = pm.Beta('beta', 1., alpha, shape=K)\n",
" w = pm.Deterministic('w', beta * T.concatenate([[1], T.extra_ops.cumprod(1 - beta)[:-1]]))\n",
" component = pm.Categorical('component', w, shape=N)\n",
"\n",
" tau = pm.Gamma('tau', 1., 1., shape=K)\n",
" lambda_ = pm.Uniform('lambda', 0, 5, shape=K)\n",
" mu = pm.Normal('mu', 0, lambda_ * tau, shape=K)\n",
" obs = pm.Normal('obs', mu[component], lambda_[component] * tau[component],\n",
" observed=old_faithful_df.std_waiting.values)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"MCMCの実行"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 20000 of 20000 complete in 155.3 sec"
]
}
],
"source": [
"with model:\n",
" step1 = pm.Metropolis(vars=[alpha, beta, w, lambda_, tau, mu, obs])\n",
" step2 = pm.ElemwiseCategoricalStep([component], np.arange(K))\n",
" \n",
" trace_ = pm.sample(20000, [step1, step2])\n",
"\n",
"trace = trace_[10000::10]"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7fcc293fce90>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7fcc25bc5090>]], dtype=object)"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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v44EDB0IgiG4V1khOuPS3Ca/zMbI7XBAKLu7eH5Gi9xE3dJzCi8UxUjQbYLG5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\nEEIIIYQQQsbp/wG49XdUmDiMrQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fcc293fc050>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace, varnames=['alpha'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"要素数の推定"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"n_components_used = np.apply_along_axis(lambda x: np.unique(x).size, 1, trace['component'])"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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+kZHhCg11XtVj+5LLFRHoCNYItrEKC/P6JxAQwZorGAXbWAXbe/yCYM0VbGwaJ6/v/GbN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\n6RZL0o7GJQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fcc25adf050>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"bins = np.arange(n_components_used.min(), n_components_used.max() + 1)\n",
"ax.hist(n_components_used + 1, bins=bins, normed=True, lw=0, alpha=0.75);\n",
"\n",
"ax.set_xticks(bins + 0.5);\n",
"ax.set_xticklabels(bins);\n",
"ax.set_xlim(bins.min(), bins.max() + 1);\n",
"ax.set_xlabel('Number of mixture components used');\n",
"\n",
"ax.set_ylabel('Posterior probability');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"5個位ある"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 事後分布の計算と表示"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"post_pdf_contribs = sp.stats.norm.pdf(np.atleast_3d(x_plot),\n",
" trace['mu'][:, np.newaxis, :],\n",
" 1. / np.sqrt(trace['lambda'] * trace['tau'])[:, np.newaxis, :])\n",
"post_pdfs = (trace['w'][:, np.newaxis, :] * post_pdf_contribs).sum(axis=-1)\n",
"\n",
"post_pdf_low, post_pdf_high = np.percentile(post_pdfs, [2.5, 97.5], axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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a81ejspNkE2NQe/zvJcRCkZGyEGLRFfonK6XAioPud+td5/cf79z2GAAbN24E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k5CIOCnrq623+3BYJB3310NwNVXX43NZmPSpCkcOdLVP+FOrW6yYlfXo9WUNwcnKdssOYeYTCb8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\nkUiGCP8fzJbAKt2hKBYAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fcc25a7d050>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"n_bins = 20\n",
"ax.hist(old_faithful_df.std_waiting.values, bins=n_bins, normed=True,\n",
" color=blue, lw=0, alpha=0.5);\n",
"\n",
"ax.fill_between(x_plot, post_pdf_low, post_pdf_high,\n",
" color='gray', alpha=0.45);\n",
"ax.plot(x_plot, post_pdfs[0],\n",
" c='gray', label='Posterior sample densities');\n",
"ax.plot(x_plot, post_pdfs[::100].T, c='gray');\n",
"ax.plot(x_plot, post_pdfs.mean(axis=0),\n",
" c='k', label='Posterior expected density');\n",
"\n",
"ax.set_xlabel('Standardized waiting time between eruptions');\n",
"\n",
"ax.set_yticklabels([]);\n",
"ax.set_ylabel('Density');\n",
"\n",
"ax.legend(loc=2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 要素ごとのplot"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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ZpONHUKnVpfdsLVnpfeVEGewllCNFWQhhElptIcmJR3Fv5YudvYPScW6ptCif\nkPvKQjlSlIUQJnEm5QSFBXkWObVmRTy926FWW8ljUUJRUpSFECZRcj+5jV+wwkkMY2trT8tWPqSe\nPE5RkVbpOKKekqIshDCJlMSjQPEAqtqitW97CgvyOHsqUekoop6SoiyEMInkxKPY2tnTvGVrpaMY\nrLWP3FcWypKiLIQwuvy8XNJOJ9HKOwC1lZXScQwm020KpUlRFkIYXerJY+h1ulrxKFRZLTx9sLax\nlceihGKkKAshjC7lelHz8glUOEnVaDTWeHr7cyYlgYL8PKXjiHpIirIQwuhKBnnVtqIMxfeVdboi\nkhPjlI4i6iEpykIIo0tOOIq9gxOuzT2VjlJlJfeVk67P2y2EOUlRFkIYVW7ONdLPJuPlE4haXfv+\niWnte70oH5cR2ML8at/fGCGERUtNKr7sWxsvXQO4NvfE3sFJzpSFIqQoCyGMquRxotpalNXXF9BI\nO5NMTvYVpeOIekaKshDCqEpn8qplj0OVVbo4RcJRhZOI+kaKshDCqJITj+Lo3Iimri2VjlJtJfeV\nS75gCGEuUpSFEEaTffUymemnae0TiEqlUjpOtbXybgfAqZPHFE4i6hspykIIo0lJqr3PJ5fVxLUF\nTs4NSwetCWEuUpSFEEZTmycNKUulUuHlE0DGuVPkZF9VOo6oR6QoCyGMpmTktTkGeRUU5LHq56+J\njdxjkv239i3+YnE6Od4k+xeiIlKUhRBGk5x4lAaNXGjUpJnJj3U+7RR/rVzEzA+f481nbyPuyD6j\n7r/19bP91JNyCVuYjxRlIYRRXLmUxcXMc2Yb5OXg1IDgsD5Y29hx4Xwa099/lt8Wf2m0/ZecKacm\nyWAvYT5SlIUQRlF6P9nXuPeTYw7vZuPqxeV+3ripGy+8PYuZS3Yx8I6HAdi0dgnrfp9vlOM2d/fC\n1s6BVBmBLcxIo3QAIUTdYIpBXpcuZPDNpy9SpNXSsdsA3Fp4lWuj0Wh4cOxEWnr6sOqnmfTod6dR\njq1Wq/Fo3Zak+CPk5+dia2tvlP0KcTNypiyEMIrkkqLcxjhFWafT8fGbj1Kk1eLlE1hhQS6r75B7\n+fL77TR1bWGU4wN4tQlAr9NxJiXBaPsU4makKAshakyv15OcEEvjpm40bOxilH3O/+oNLmalY2fv\nyGsfLDRoG2OvSiWTiAhzk6IshKixSxcyuHIp02iXrlOS4ji8dxOoVLz6wQJs7ZS5dOzZprgoyyQi\nwlykKAs/O7eXAAAgAElEQVQhaszYi1BEH94JQPc+t+PVJqDa+9HpdORcq/5KTy082qDRWMtgL2E2\nMtBLCFFjxh7kNeK+pwntNgi35p7V3kdCXAQzPnyO5u6teefzX6q1D43GGncvP86knECrLax2FiEM\nJWfKQogaSzbByGt3Tx801jbV3r6llx/awgJSk+I4EXe42vtp5d0OrbaQtNNJ1d6HEIZS7EzZ1dVZ\nqUPXOtJXhpF+Moyx+0mv15OadBTX5h64NXcz6r5rwtHRlgHD72PL+mUsnvUuM37YXK19+AYEs3Pz\nStLPJMpnrBLSL8ajWFE+f14meTeEq6uz9JUBpJ8MY4p+Sk1N4erli7QN7Ex2dr5R911T9z7+Ojs2\nreZ8+hnC9/5DQIfuBm/r6GhLdnY+bi19AUg4Fi2fsQrI3z3DGfLlRS5fCyFqJCoqAqj5TF4Xs9LR\n6XTGiFRKo9HQe8g9ACyv5hScHl5+qNVWpMgIbGEGUpSFEDUSGVlclFv7BNVoPx+9/hATHulJZsYZ\nY8Qqdc+YCdjZO9HS06da29vY2tHcw5vTyceN/qVBiP+S0ddCiBopKcqtrj/TW619HNzO1csXsLN3\nxKWZu7GiAWBrZ8/XP+2q0T5aebfjbGoCSUmJ+Pr6GSmZEOXJmbIQotr0ej1RURG4tfTCwbH6g33+\n+GUOAH2H3mesaEZV8oUjOjpK4SSirpOiLISotpMnk7hy5XKNHoW6euUip1PiUanU3Hn/s0ZMZzyt\nvIsnMDlyRIqyMC0pykKIaouMLH7+tyZFecWSGQD4+IcoNp3mrXh6+wNSlIXpGVSUv/jiC1JSUkyd\nRQhRy/w7yKv602va2thhpdFwzyMTjBXrprRaLdeuXqrSNvYOTjRr7kl0dCR6vd5EyYQwsCg3aNCA\nF198kUcffZTVq1eTn29ZzyIKIZQRFRWBWq3G07v6g7we+t9bfPPLAXwDQo2YrGIH92zk+Ye6Mfez\nV6u8rad3Oy5dusTp06dMkEyIYgYV5aeffprVq1czZcoUUlNTeeCBB5gyZQqJiYmmzieEsFBFRUUc\nORJF27b+2Nk71Ghfxl5ysTJtA8LQ6YpIPBaJtrCgStv+O9jriCmiCQFU8Z5yRkYGqamp5OXl4ejo\nyBtvvMHSpUtNlU0IYcESExPIzr5GSIjpz3CNpWFjF9xaeqHTFfH3mh+rtG3J1QAZgS1MyaCiPGvW\nLAYPHsz333/P8OHD+fPPP3n99ddZunQpv/76q6kzCiEsUMkgr44da09RBhgy8jEAdm1dVaXtWl0v\nyjExcqYsTMegopyVlcUPP/zA/PnzGTx4MFZWVpw6dQobGxtee+01U2cUQligkqJcm86UAXoPuhu1\n2orM9DNVGvDVoFFT3Nyay+VrYVK3LMo6nY7ExERatmyJTqdDp9NRUFDAc889B0Dfvn1NHlIIYXki\nIyOwsrKiffvgKm975dIFxj/YlflfTTRBsptTq9V4+QRia+fAqeT4Km0bHNyBs2fPkJWVZaJ0or67\n6TSb69atY9asWaSkpBAQEFD6c7VaTe/evU0eTghhmbRaLTExR2jXLhB7+6o/W7x2+VwKCwu4dCHT\nBOlu7fWPvkejqfosw8HBHdi8+W+io6Po33+gCZKJ+u6mn8oRI0YwYsQIZs2axQsvvGCuTEIIC3f8\n+DHy8vIIDe1Ure0P79sCwPC7nzRmLINVpyADBAWFAMUjsKUoC1O46Sfzn3/+oV+/fjRv3pzff/+9\n3Ov33WeZ89QKIUyrZLnG6txPzjqfxtXLF7C2tqFDWB9jRzOp4OAOAMTEyAhsYRo3LcrHjx+nX79+\nHD58uMLXpSgLUT/VZOT1hlWLAGjj39GomczBy6s1DRo0lMFewmRuWpSffvppAD7++GP0ej0qlYqC\nggKysrJo0aKFWQIKISxPZORhbGxsaNeu6nNen4yPBmDQiIeNHcvkVCoVQUHB7N27m2vXruHk5KR0\nJFHHGHRj5dtvv8XW1pYHH3yQe+65B0dHR3r37s2LL75o6nyijlq9M6la243q08bISURV5efnExsb\nQ/v2Qdja2lZ5+3e++JX42EO0bR9mgnRVExd9gN8Wf0HnHkO5/b6nDNomOLgDe/bs4ujRWLp27Wbi\nhKK+Meg55W3btvH444/z119/MWDAAH777TcOHTpk6mxCCAt07NhRCgsLCQmp3iAvwCIKMsDli5mc\nTo5n55aVBm8TFFR8X1lm9hKmYFBR1mg0qFQqduzYweDBg4Hi55eFEPVPycpQ1R15bUm69h6OWm1F\nVsZZ8nJzDNomOLh4BLbM7CVMwaCi7OzszNNPP01iYiKhoaFs27YNlUpl6mxCCAtUk5HXlkatVtOy\nlQ8A2/4ybMpgP7+22NraymAvYRIGFeUvv/yS+++/n8WLFwNgY2PDp59+aspcQggLFRkZgZ2dHf7+\n1V+u0ZL07D8SgP07/jSovbW1NQEBgaWX8YUwJoOKspWVFVB8b/n3338nLS2NPXv2mDSYEMLy5Obm\nEhcXS1BQhypPwPHHsrns3roarVZronTV03fYfaBSkXb6pMG35YKDQygoKOD48WMmTifqG4P+Vo0b\nNw61Wo27u/sNP5fnlIWoX2JjoykqKqry88k6nY71vy9ApysirMfQas+oZQo2Nnbc99gr+AWGGryu\nc8lgr5iYIwQFVX3ubyEqY9DfDK1WK0s0CiGqfT856uB2dLoiGjd1w87ewRTRamToyEer1L5kZq/o\n6CgefHCMKSKJesqgr4W+vr5cvHjR1FmEEBYuIqJkJq+qjbz+Z+NvAASH1Y1V5QIDg1Cr1TLYSxid\nQWfK586dY+jQofj4+JTeXwb4+eefTRZMWL7qTgAiaq/IyMM4Ojrh6+tXpe0Sjxc/0ztk5COmiGV2\nDg4O+Pr6ERMTjU6nM/iytxC3YlBRLpluUwhRf127dpUTJ+Lp0aPXDV/ObyXtVBL5eTnY2Tvh1sLL\nhAnNKyioA/Hxx0lOPkmbNj5KxxF1hEFf77p27UpOTg7x8fF07dqV5s2b06VLF1NnE0JYkKioSPR6\nfZUvXas1VgR16k2vgSNNlMx4CgryiDm826C2MomIMAWDzpQ///xzUlJSOHv2LI888ghr167lwoUL\nvPvuu6bOJ4SwECX3kzt1qtoUmW4tvJgwabYpIhndK0/0pyA/j1k/78XR8ebzev872OsII0febY54\noh4w6Ez54MGDzJ49G0dHRwDGjx9PbGysSYMJISxLRETxfPdVPVOuTVzcPADYtWXVLduWHYEthLEY\nVJT/uxJMUVERRUVFJgkkhLBMkZGHadq0KZ6erZSOYjIduwwA4NCeTbds27hxEzw8PGUEtjAqg4py\np06dePPNNzl//jzff/89Y8aMoWvXrqbOJoSwEJmZmZw6lUrHjp3q9Lz3/YePBiD1pGEzdQUFdeD8\n+QzS08+ZMpaoRwwqyiNHjqRv375YWVlx+PBhxo0bx+uvv27qbEIICxEZWXzpOjTUMpZcNJVGTZph\n7+BEQX4u6WdTbtleLmELY7tpUc7Ly2P8+PE8/fTTbNy4ETc3N8LDw9m4cSMFBQXmyiiEUFjJIK+q\nLNd4MSud/7u/M19PHW+qWCbhF9gJR6eGpJ9NvWXbkhHYcglbGMtNR1/PmTOHFi1aMHPmzNK5anNz\nc5k6dSrTp0/njTfeMEtIIYSy/h3kZfiZ8vYNyygq0pKXY9g6xZbi+be+BsDR0Zbs7Pybti07AlsI\nY7jpmXJ4eDgTJ068YfJ4e3t7Jk+ezK5du0weTgihPL1eT2TkYTw8PHF1dTV4u8gD2wHo2vc2EyVT\nXsuW7jRp0kQuXwujuWlRtrKywsbGptzPra2tadCggclCCSEsx+nTp8jMzKzS/WSdTld6T7bnAMuf\nNKS6VCoVQUEhpKQkc+XKZaXjiDrgpkX5ZqMsqzLNnhCi9oqMrPoiFMeO7EenK6JhY1dsbOxMFc0i\nlFzCjomJVjiJqAtuek85IiKC/v37l/u5Xq+XVaOEqCcOHy4ZeW14UY48uA2AgOC6/+hk2RHYPXv2\nVjiNqO1uWpQ3bNhgrhxCCAsVGXkYlUpFSEhHg7d5+H9vM2D4g9g5OJowmWmtXb6AHZtW8+bHS266\nBrSMwBbGdNOi7O7ubq4cop66mJXO/p3rOZ0cT9rpk2g01jRu6oantz/d+t6OSzP5DCpJp9MRFRWJ\nn19bnJ2rNo6khWcbE6Uyjz3b/+TsqUR2bV7J4DsrX3KyTRsfHBwcpCgLozBoQQohjC0jLZW1y+dx\ncPff6Iq0AFjb2KLTFXHyRDSH921mzS/fEBjSg/uffI2WnrI0nhISEk5w7drVOj3fdWXCegwkNekY\n4Xv+vmlRtrKyIjAwiIiIQ+Tl5WFnV7fvoQvTkqIszEqv17Nn2xp+Xfgp+Xm5tPT0YdCIMbQL6krT\nZi0BuHr5AjERu9i9dQ1Ho/by0WsPcvu9TzH8nrEKp69/Dh8OB6p2P7muGHzHg6z6eQ6nU+Jv2TY4\nuAPh4Qc4duxovfwCI4xHirIwm6IiLT/OmcLe7euwc3Bi3EvT6Nr7ttJR/kfCd7Dm1zl4evvTLqgr\nr0yeT0zkbpbOn8ofy+aSGH+E4V1+w8nJSeF3Un9UZ+R1XdGoiSv2Ds7k5lwl7VTSTS/Hl72vXB/7\nShiPYkXZ1dVZqUPXOpbaV7dab7YsrbaQbz6ZxIFdG/Hx78ALb32Fa/Mb7xc3a+7GuTMnOXXyGHu2\nrmHNL7O5476xfDrvD+Z8PpGogzt54IG7+PPPPyucxMJS+8nSVKWfYmKi0Gg09O/f86aXZUs+C5kZ\naRzc9Tf9ht2Lg2Pt//Lk264D0Yd3s3vrCh5/7p1K+65v3x4AJCTE1cvPYX18z6aiWFE+f/6qUoeu\nVVxdnS22r241BWEJXVER3345kYj9W/Bo7Y/G2ha1xr7c9s09/Pn6p92knT7J7i2r2Ll5JT/Oncql\nCxd45rWvWDL3A/ZuX8ugQUNYs2Y9Tk7//kNgyf1kSarSTwUFBURGRtK+fTBXrxZy9WphpW1Lfpdr\nly9i87qfOLR/Oy+/N88omZXi6GjL4JGP49LMgz5D7yc7O7/SvnNz80Kj0XDgQHi9+xzK3z3DGfLl\nxaBVooSoiVVLZxGxfwstPH04dzqJ+NhwYiP3VtjWykqDh5cfD4ydyMdz19N/+P0MvOMhNBprnnj+\nAx555HGio6N46qnH0Wq1Zn4n9UtsbDQFBQVVuhwbG7kHgC49h5kqllkFBHflof+9hVsLr5u2s7W1\npW3bdsTFxcpa86JGpCgLk9q/cz0bVy+mQcMmnDt9EiuNhgnvfENYj8G33Na5YRMe/t/bODgWP4qj\nUqn47LPpDBo0hK1bN/Pmm6+ZOn69Fh5+AIDOnbsYvE16WvHKSnV5vuvKBAd3ICcnh8TEBKWjiFpM\nirIwmdMpJ/hxzvtY29hy5fIFHJwa8Or739G+Y89q71Oj0fDddz8QFNSBH39cxO+/LzNiYlHWwYP7\nAejSpZtB7U/EHUZXpKVBo6Z1fmrNisjaysIYpCgLk9AWFrLo60kUFuTjF9AJWzsHXpnyLa19g2q8\nb3t7e7788mscHZ14/fWXSUpKNEJi8V/h4Qdp2rQp3t6GTQKya/MqAHzbhZoylsWSmb2EMcgjUcIk\n/vz9O04nx9N70N08+n/vkZGWilvLm9+XM0ReXh5PPjmGrKxMPv74cyZM+D+eeWZs6VmdMI60tLOc\nPn2KYcNuu+nCNGW5tfCiQaOm9Bx4l4nTKSMvNwetVnvDUrZlBQUFA1KURc3ImbIwuuSEWP5auZAm\nLi0Y/cSrqFQqoxRkKB5Q4+rajMjICPbu3c2DD44hKiqCzz//3Cj7F8VK7icbeuka4Pb7nuKLhVvo\nENbHVLEU880nLzHhkZ6sWbOi0jbOzg1o3dqb6OhI9Hq9GdOJukSKsjAqXVERP337ETpdEU88/z72\nDsZ9VrVksFdISCi//PITffr0w82tOR988AGJiSeMeqz67ODBkkFedX+VJ0M0alL8XPyKFb/ftF3H\njqFcunSJlJRkM6QSdZEUZWFUu7asIjUpjm5976CdiZbts7Oz45tv5mNra8vkyW/z1lvvkZ+fz6uv\nvohOpzPJMeub8PADWFlZERJSP+8P/1efIfcCcOjQwZu2CwkpfnwsKirC5JlE3SRFWRhN9tXLrPx5\nFmorDb0Gmfa+Ytu2/rz11ntkZmZy8mQio0aNYs+eXSxbttSkx60P8vPzOXIkkqCgDjg61t6lF42p\nlXc7NBprLl68wJUrVyptVzJHeETEYXNFE3WMFGVhNGt+nUPOtcvoirTs3rLG5Md75pnnmDHjG954\nYxKzZs3CwcGBqVPf59o1mV2oJo4ciaSgoKBKzyfXB809vAH49defK20THNwBlUolZ8qi2qQoC6PI\nSEvln79/R6VSYWfvyH2PvWzyY1pZWfHww4+i0Wjw8PDg+edfIiMjnZkzvzL5seuy8PDiS7SG3k9e\nvnwpbz93Bzs3rzRlLMV1COsHQHz8sUrbODs3wNfXj6ioSLmVIqpFirIwij9+nYNeV4Rer2fUwy/Q\nsLGL2TM899wE3N09mDdvtgy0qYGqThqydOlPZKafIeP6bF511W33jCU5+RxffDHzpu1CQkK5du2q\nPD8vqkWKsqixUyePcWDXBgA8vNrSf9hoRXI4ODjw3nsfkJ+fz9SpUxTJUNvp9XrCww/QrJkbnp6t\nDNqm5LncvkOV+b2bi62dPQ4ODrdsV3JfuWTZSyGqQoqyqLFVS2cDYGNrx72PvYTaykqxLCNG3EVo\naCdWr14p0x1Ww5kzpzl3Lo0uXboZNGlIeno6V69ewcbWHlc391u2rw9KRmBLURbVIUVZ1MjJE9HE\nHN5F2/ZhfDr/bwJDeiiWZd26P+jSpQOPPvokANOmfaBYltqq5NK1ofeTf/xxEQDuXn4my1TbBAUF\no1ariYyUwV6i6qQoixpZv2IhACNGP4ujUwODp2Q0BVtbG86ePcPff2+gd+++bNmyiX379iiWpzb6\nd2Uow4ryxo1/ARDadYDJMtU2Dg4O+PsHEBNzRJYXFVUmc1+LajudHE/Uwe34+IfgH9RZ6TgMHjyM\nbt16sGHDn3zxxUx27drB1Knv88cfGxT9slCbhIcfwNrampCQjga1//77Jfz442K8Qu80cTLLsHpn\nEmdSTrBtw3IGjRhDC/fWFbZr0sKPuLhYvl22FfdWvozqY9iiHkLImbKotvUri8+Sb7/3KYsoeiqV\ninfeeR+ANWtWMXTocPbv38vevbsVTlY75ObmEh19hA4dQrCzM2zpRU9PLyZNmoyTcyMTp7Mcvy+Z\nwY6/f2P7+l8qbePlEwhASkKsuWKJOkKKsqiWxMQThO/eiEdrf4I69VY6Tqlu3brTr98Adu7czrBh\ntwMwfbosVmGIqKgItFqtzHd9C117Dwfg6JF9lbZp7VtclJMTpSiLqpGiLKplzpziEdf5eTloCwsU\nTnOjV199g7CwzgQEBNKnTz/++WcbERGHlI5l8UoWoajKylD1UZdewwA4f+50pW3cvdpipdGQnHjU\nXLFEHSFFWVRZZmYmv/76EwCerdtibWOrcKIbde/ek/Xrt9C5c1defvl1AKZP/0LhVJbv4MHiMz85\nU745jbUNDRu7otMVcTwmvMI21tY2eHi15XRyPNrCQjMnFLWZFGVRZd9//x2F1/+huf3e/ymcpmIl\n97h79epD585d2bDhT44elUuJldHpdOzbt4dWrVrTsuWtnzc+f/48WVmZZkhmmfwCi1fP2r1lVaVt\nvHwC0RYWcPaUzOwlDCdFWVRJbm4u8+fPAcA/qAut2rRTONHNqVQqXn75NQBmzpSz5cocOxbHpUuX\n6NGjp0Htp0yZREBAGyZPfsfEySxTnyH30dLTB7/2YZW2KR3sJfeVRRVIURZVsmLFci5fvgwUzwVc\nGwwePIygoA6sWbOKpKQEpeNYpJIR6j169DKo/Z49uwDo1ctyBvmZU0BwV6bMWEGfwfdU2qb19aKc\nLCOwRRVIURYG0+v1LFjwLWq1mgEDBhHQobvSkQxy9eoVnn12PDqdjq+/nq50HItUMslK9+63PlPW\narWcPXsGtVrN4MFDTR2t1mrh6YO1ja0M9hJVIpOHCIPt37+Po0djGDnybhYs+IHVO5OUjnRLe/fu\nZsyY+3n++Rdp7u7Nr8t+IbjvwzR1bWHwPur6xA96vZ69e3fTsLErUafhyJmb/14P7dmEXq+nabOW\n/LE72TwhayGNxhrP1v4kJx4lLy/P4Ge/Rf0mZ8rCYIsXfwfAk08+pXASwwUFBaNSqVi06DuGjHwU\nXZGWrX8uVTqWRTl5MpGMjHT8AjsZNAnMvn/WARAQLI9O3YqXTyC6Ii1Hj8YoHUXUElKUhUEyMjJY\nu3YN7doF0LNn7bmP6OzcgEceeZyMjHRUqGjY2JWdm1eSm3NN6WgWY+/e4kvXbQM7GdS+UFsIKhV9\nhtxrylh1Qmvf9gAcPlzxo1NC/JcUZWGQn35aTGFhIU88YRlTalbFU089g5WVFVvX/8KA2x4gLzeb\nXTd5lKW+KRnk1Taw8pHEZb307hzm/HqwtODUZ+tXLOClx/ryz8bfKny9TdsOAISHHzRnLFGLSVEW\nt6TVavn++wU4ODgyevQDSsepMk/PVtx5512cTomnhUcbbGzt2PrnUoqKZAWfkvvJjRs3prmH4ffO\nNRoZjgKQl5tNTvYVDuzaUOHrzVq0wtG5kRRlYTApyuKWNm78i/T0c6hUkJubp3Scann22ecJ7TYQ\nVzcPeg64i6zzaUTs26J0LMWlpCRz6lQqPXv2Qa2Wfw6qqu/Q+wA4dfJYha+rVCratA0mNTWZjIwM\nc0YTtZT8LRS3NGfO10DxGaerq6vCaaqnU6fO/N/Er/Bo3ZZBdzyMSqXi77VL0Ov1SkdT1M6d/wDQ\np08/hZPUTi7N3LGxtScvN5vLFyue4ezfS9gHzBlN1FJSlMVNnTgRz8GD+wF47rkJte5+ckXcWnrR\noXM/kk/EkHQ8Suk4itq1S4pyTXl4+QGw4+/fK3zdxz8EkKIsDCNFWdzUggXzAHBycmbUqLoz2nbI\nnY8CsGntTwonUY5er2fnzh24uTXH19fvlu0P7PyLRTMncUbmcr5BaLeBAMREVLxud2vfINRqtRRl\nYRAZrVFH1GQij8omx8jJyeGXX34G4IknxtWpyQ/8Ajvh5RNIxIGtnD93GtfmHkpHMrtjx+LIzDzP\nffc9YNAVkE1rl5CSeBR3Lz/cPX3MkLB26DP4HpwbNqZr79sqfN3O3oGAgPZERUVQWFiItbW1mROK\n2kTOlEWl1q5dTV5eLi1bujN2rGWuBlVdVy9fYNCIMeh1Oraur5+TiVT10vXZ1OIz5F6DRpksU23k\n4NSAngPuQmNtU2mbsLAu5ObmEhsbbcZkojaSoiwq9fPPPwKwevV6PDw8FU5jPJv+WMLE/w2liUtz\nGjVpxq4tq8nJvqJ0LLMrGeTVu3ffW7ZNO5VEYWE+Do4NcHJuZOpodU7nzl0Aua8sbk2KsqhQYuIJ\n9u3bQ58+/Wnd2lvpOEbl0botOl0RuzavYuAdD5Gfl8OuzfVrMhGtVsvu3bto3dobT89Wt2y/Y1Px\nICaZMKR6unTpCkhRFrcmRVlU6OeflwAwZsyjCicxvnbBXXFr2Zrw3RsJ7TYIWzt7tvy5FK22UOlo\nZhMZeZirV68YfOk6NrJ4Ks4uvYeZMlad1aaNL02aNJFJRMQtSVEW5RQWFrJs2VIaNWrE7bffqXQc\no1OpVPQbdh9abSGR+7fSa+AoLmalc3jvZqWjmc3WrcXvdcCAwQa17zfsfrz9gunW53ZTxqr1EuIi\nyMw4U+7nKpWKsLAupKamkJ6erkAyUVtIURblbN78N+fPZ3DffQ/UqRHXZfXoPxJrGzv++ft3Btz2\nECqVik31aDKRbdu2YGVlRd++hp0pD7rjYd76ZMlNBzPVd4u/mcxn7zzJ2mXzKny9c2e5hC1uTYqy\nKGfevNlA8QpLdZWjUwP6DrmH9h170LBxUzp2HUhK4lES4iKUjmZyFy9eICLiEJ07d6VBg4ZKx6kz\nOnUbBMDxmIovUUtRFoaQ55TFDdLSzpauGtShQ0eF05jWA2Mnlv55yMhHiNi/hU1rl+Bn4BKGtdWO\nHdvR6XQMGDBI6Sh1SlCn3qhUai5mpaPVasst2hEaGiaTiIhbkqIsblDyGJSTkzNDhw5XOI35+Ph3\npLVve6IObicjLZVmLf4dkWyKiVmUVHI/eeBAw+4nC8Oo1WqauLYgK+MMUQe2EdZzyA2vOzk5lU4i\nUlBQgI2N3AoQ5cnla1FKp9OxaNF3AIwZ81i9mnlIpVIx+M5H0ev1bF3/i9JxTEav17Nt2xaaNm1q\n0JUQnU5nhlR1R7ug4ueR9+34s8LXO3fuSl5enkwiIiolRVmU2rt3N5mZ5wF48smnFE5jfp26D6Kx\nS3N2b11N9rW6OZlITEwM586l0a/fQIOWavz83bG8MKYncdFyydUQfYbci8baBnsHpwpfl0lExK0o\ndvna1dVZqUPXOob0laOjbY33v2xZ8bPJnTt3plu3W59F1eSY1XWzvrhVP90qb2GBittGPcrSBZ+z\nf8ca7hxd8y8mlvY5X7iw+Axu1Kg7y2WrqH9Sk+IoLMinbUB7RX7fSqvqew4O7cwPa8uvPFbS18OG\nFS9eER0dYXGfjZqoS+9FaYoV5fPnryp16FrF1dXZoL7Kzs6v9jHOn7/KpUsXWb16NW3a+LBmzUaT\nH7O6KstlSD9Vljc/L5dZ057H1s6BcS9OZcVPs9mwagl9hz6IRlOzS/iW9jn/448/UKvVdO3ap1y2\n//bPmZQTFBbk4+jUACuNoyK/byU5Otoa7T2X9HXDhm40bdqUXbt2W9xno7oM/TdKGPblRS5fCwBW\nrPiNvLw8Hn64ft1LBrC1s6ewoICYw7vIzcmm18BRXLqQwaG9m5SOZlQZGRns27ePbt160KRJ01u2\n33K29fwAACAASURBVPrXrwC0ub4esKg5lUpFt249OX36FKdOpSodR1ggKcoCgKVLl2BlZcUDDzys\ndBRF9B16L3q9nl2bVzHojjHFk4n8UbcmE9m8eSN6vZ5hwwybleto1F4Aeg64y5Sx6p3u3XsAsG/f\nHoWTCEskRVlw5Egk0dFRDBkyHDc3N6XjKKJzz2HYOTixe+sqmrg2p2PXgaQmxXHi6GGloxnNhg3r\nARg+vOJ1f//ryqUsVCo1od0GmjJWvdOjRy9AirKomBRlUfps8pgxjymcRDm2dvZ073sHly6c50j4\nDoaMfASAv9f8oHAy48jJyeGff7YSEBBAmza+Bm0z6+e9vP3ZzwaN0hY3OhF3mM/fHce2v5aVe619\n+2CcnJxLJ+kRoiyZPKSeK8jPY8lPP2JtbcvpbOcaTZRR2/Udeh8R+7eSn5dLx64D8PEP4cihHZxJ\nTcC9lWGFzBJU9DuMOvgPubm5+Ab3Mvh3rFar8WoTYOx49cLpk/GcOHqI7GuXGHDbAze8ptFo6Nq1\nG1u3biYjI4NmzZoplFJYIvkKXM+F79mEtrAAnV6Ho1P9Xrzew8uPT779i+797kClUjH87rEAbFy9\nWNlgRhB5YBsAod0GKJykfug1eBQA504nVzgBS8kl7P3795o1l7B8UpTruU1/FF+6Du02EDt7B4XT\nKM/K6t+LR8FhfWjp6cOBnX+RlXFWwVQ1oy0sJOLAVho1ccUvoG7PZ24pbGzsaNzUDZ2uiJjDu8q9\n3r17yX1luYQtbiRFuR7LSEvlTOoJAIaOrL/3kyujVqsZNupJdLoiNq1donScaouL3k/OtSuE9Rgi\n94fNKDCkeJT1jk2/l3utY8dQ7Ozs2LtXBnuJG8nf0Hps6/qlADRxaY6XT6DCaSxTl97DaOLSgp2b\nV3H18gWl41RL+O6NAHTuOdSg9utXLOBopFxWramBdxQ/XpgQF1nuNVtbW8LCuhAbG82lSxfNHU1Y\nMCnK9VRRkZZ9O4ofkRk04hFUKpXCiSyTRmPN0Lseo7Agj63rf1U6TpUVFhYQeWAbjV2a4922wy3b\na7Va1vzyDTM/eg6tVmuGhHWXZ+u29Bo4iide+KDC13v27I1er5ezZXEDKcr1VMzh3eRcu0LvQaPo\nO+RepeNYnMP7tvD+y6PJTD9Dr0GjcGrQmG0bfiUvN1vpaFUSF7WP3JxrdDbw0vX+HevQ6/W4uHmU\nWw9YVN3j46fQsUv/Cl/r06cfALt2/WPGRMLSSVGup3ZtWQVAv+EPYGtnr3Aay5Ofl8OZ1BPs3LwS\nW1t7Bt7+EDnXrrBz00qlo1XJweuXrsMMvHS9e8saAJkwxAw6deqMvb09u3btUDqKsCBSlOuhSxfP\nE31oJ57e7eQ51EqE9RiCg1MDdm9dg1ZbyIDrX142rf2RwsICpeMZJC83h8gDW2narCXefkEGbZOS\neBSAIXc+aspoArCxsaFbtx7ExR0lIyND6TjCQsj1qXpo3/Z16HRF9B40SukoFsvG1o4e/Uaw5c+l\nRB38h7Aeg+k7dDSb/viR3VtW0X/4A7feicIO791Efl4uQ0Y+ZtCYgYS4CAoL83FybkTDxi5mSFh/\nVDZhSxOPYGArMxetoEuvYRW2GdWnjQmTCUsjZ8r1jF6vZ9eWVVjb2NK1j2ELE9RXfa7fay95pGXY\nXY9jbWPH+hULKSyw/GUM92z/A4Ce/Uca1N7a1g4f/xB69L/TlLHqJZ1OR2bGmXI/bxfcBYD/b+++\nw6K4ugAO/3YXWDoIUu1iwV5QLGjsPRqNBStqorF9GjX2XmI3dmPXGEvsvWvsDazYe0VUpPe2O98f\nxI1kQVGBXeC+z+MTnb0z9+xA5ky5c8+9mz6ZHZKgp0RSzmEe3L5CwOsXFCxSCjNzS12Ho9ec87lQ\npEQFQoMCiIuLwdLaljqN2xEaHKB5Jq+v3r3x48HtKxQrVYncDnnStE6BwiUYPnUtbbv9ksHR5SzR\nkeH09azM5F+0767kK+SKiak590VSFv4hknIOc3DnKgDxClQa9R0+lwnztqNUJg2Ga9iyG0ZKYw7u\n0O+r5fMnkq6SPeqKsou6ZmpuiaGRkpjoSK2rZYXCgGKlKhHw5iVB717rKEJBn4iknINERoRy19cb\ngKate+g4mqzB3MI62QmMpZUNtRt7Ehr8jpOHt+gwstSp1WounNyL0tiUilXr6zocAShYJGmg3fH9\nf2l95lr6/S1s70yNSdBPIinnIKePbEOS1JhZWONapoquw8myGrfqjrGpOQe2ryI6KkLX4Wi5de0s\nwYGvqezRSLzupieq10l6Tu976aTWZyXKVQXgtphFTUAk5RxDkiTNWXrtxu3EHMhfwdzCmkbfdSUq\nIlRT0EOfvP85/7dkoKA7lWs0QSaT8y7gFfHxsck+c8pbmFy2Dtz1vYhapdJRhIK+EEfmHOLR3WuE\nhwUhk8mo06S9rsPJ8up/2xlL69wc3buOsJBAXYej8eDBfe74XqBoSTfyFXJN0zqnj26nb3t3dqyf\nn8HR5VwGBgY45S2EkZExr148SvaZTCajVPnqREWG8fzJHR1FKOgLkZRziNNHtwPg+cMwLK1sdBxN\n1hMbE8WeTb9raisrjU1o3q4X8XGx7Nm8RLfBfWDVqmUA1G3aIc3rnDu+m8SEeGRyRUaF9VVCgt5q\nJbL3Xvs95cLJfXp1YpSaMbP+YtHGCxQqoj2RS8nySRWlxC1sQSTlHCAqIowrF47i4FxAXCV/IYWB\nIScObeHw7rWaGb086rXEKW9hzh7bwcun93QcIYSHh7F581/kyu1IeffaaV7v5ZO7ANT/tlMGRfb5\nYmOiOX7gL6aO6MzwnxpxcPvKFNvdu+nNmoVjGNqjPlOGdeTM0e3ExcVkcrRpY2BolOpnJcpWRSaX\nc/u6KE6R04mknANcPLWPxIR4ajZoLV6F+kKGhkZ41P2OyPAQLp87AiRVkPL8YSiSJLFp9SwkSdJp\njGvWrCQ6OorajdqhUKRtsr4bV86QmJiApbUtFpa5MjjCT4uLjWHPpt8Z0bsxm1bN4MXju7iWqUIZ\nt5opti9VwYM2XQfjWqYKL589YN3SyYz4qTFXLhzL5Mi/jpm5JYWKlObpg5t6OXhQyDwiKWdzkiRx\n+uh2DAwMxUxNX6l243bI5HKOH9ioScAly1WjXOXaPLxzhSsXjuostsjISJYsWYiVlTW1GrVN83rH\n9q0HoFwqlYwyW1xsNMf2b0QuV9DcszczVx5l8IRlVPmmWYrt7R3z0bCFF4MnLGPakv00a9MTuUKB\nU56CmRt4OihZripqtUrM7pXDiaSczT2+f53Xfk+oUKWeXlwJZWW57fNQ1u0bnj++w9OHNzXL23Yd\njIGBIVvWzCYmOlInsa1evYLg4GB69eqLqZlFmtd74/cUgCbf/5BRoX0WS2tbBoxeyLQlB2jervdn\njX/IZevAdx36MX3ZIZzzF8nAKDNGqfLVAbh97ZyOIxF0SSTlbO7AtqQZvFK70hA+z/sBVHdv/DvR\ng71Tfhp//wOhwQHs3LAw02OKjIzk99/nY2lpRc+evT9r3ZkrjjBi2jpy26dtKs7MUMS1wle9X234\nkWe3+uDKhWNMHtKeh3evJlteqGgZzCysuXn1jM4fhQi6I5JyNhYeFszt60ln3SamZjqOJntwLePO\nhHnbadamZ7LlTb7/Eae8hTl1eAuP713P1JhWrVqmuUq2srL+7PULFyuTAVF92r2bPpmWfCRJYvPq\nmXoxkMrX5wQvn97TjOR/T65QUKZiDUKD3/Hin8F3Qs4jknI2dmT3WiRJwiqXHUVKVNB1ONmCTCbD\nOZ+L1nJDQyM69x6LJEn8uWQS8XGxKayd/t68ec28eb9hY2PDTz/1yZQ+v5ZarWbb2jnMmfBTpk2+\n8trvCacOb2XBlP9p5gXXlSb/nNDdv3VZ67Oylb4B4MaV05kak6A/RFLOphITEzh1eCuQ9LxQjLrO\neEVLVKB2Y09e+z1h+7p5mdLnpEnjiIqKZNSo8V90lZzZVKpE1i4ez5E9f+LgXJDy7nUypV/nfC78\nMnEFJqbm/LFoHH/v35gp/abEKU9BTM0siYuN5smDm8k+K1muGnKFATcui6ScU4mknE1duXCUuNho\nDAyN8KjXUtfh5BitvQbilLcwJw5uyvADq7f3RbZt20zZsuXp1MkrQ/tKD4kJCSybPZQLJ/dSsEgp\nhk1Zg71T/kzr38W1PEMnr8bSOjebV8/k0M41mdb3f5WqkDSo6/B/YjA1s6BYSTeeP75DaHCALkIT\ndCxtLzMKWc7+bUmTLVT9ppmm7GB2sOvMkxSXm5kpiYrSfSlFpdKEnoNnMHV4J/5YPJ4eng1wdk7/\nQVSxsbEMGzYQgKlTZ6FQfN5sXL/PGES12s2pUKVuuseWmu3r5nLd5wSuZdzpO3wuxiaZP84hT/4i\nDJuyht/G9+Ti6f3UbdoBI6VxpsfR9PsfuXT2EHdTqAxVrtI33Lvpzc0rZ6jZoHWmxybolrhSzob8\nnj3gjd8T8hcuQXPPzxuNK6RdwJuXbFg+heePk89XnLdAUdp2HUxkeAheXh2IiopK974nTx7H3bt3\n8PL6AXf3z6v4dePyaa77nGD9sinpHtfHNGrVnZoNWtNv5HydJOT37B3z8cvEFfwycYVOEjJAngJF\nqdesI4MmLNP6rMw/z5V9xS3sHEkk5WzoxMFNADRv15tctg46jib7evfmJacOb+Xo3nVan9Vu7EmN\n+q24ceM6/fv3Rq1Wp1u/R48eYsWKpRQrVpxJk6Z+9vqH/hn1W6la5tZats5lR5feY/Xizo29Yz6d\nv7fv+cOwFOfBtnfMh3M+F+74XiA2Jv1P6AT9JpJyNhMVEcbF0wfIbZ+HMhVr6DqcbK1kuWrkyV+U\ny+eOEBTgn+wzmUxGxx6jqF69Bvv27Wbs2BHp8vrPkyePGTCgD0ZGRixduhpTU9PPWl+tVvP0wQ0A\nmrXt9dXxCBmjYtV6JCbEc/PqWV2HImQykZSzmXPHd5EQH0vtJp7IP/M5o/B5ZDIZjVp2Q61Waaar\n/JCBoSGrV6/D1bUEK1YsZfToYV+VmN+8eU27di0JCgpi6tRZlC79+e8Xnz22G5UqERs7JyytRbWw\nD0mSRFRkuK7DAKBi1aS7GFez2BzewtcTSTkbUatUnDi0GUMjYzzqihHXmaGSR0Ny5XbkzLEdREaE\nan1uY2PL9u37KFGiFCtXLmPQoP8RG/v57zAHBATg6dmKFy+eM2zYKLy8un9RvAd3rgWgWq2MnQf9\n8vkjbFkzO11v22cktUrFmoVjmTX2B70oCJGnQFHsHfNx69pZoqOjdR2OkIlEUs5GLl84SlCAPxWr\n1MXM3FLX4eQIBgaGNGjemcTERB7euZpiGzs7O3bs2EfZsuXZuHEdzZs34sWL52nu4/JlH+rXr8nd\nu3fo0aMXv/wy/Ivj9eo7mpLlqtG41Zcl9bS4f+sSq+eP5uzfOwl865dh/aQnmVyOiak5/i8esey3\noSQmJmRa34kJ8Zw8vCXZCYxMJqNitQbExcZw4sTfmRaLoHsiKWcTkiSxc8MCAAyNlDqOJmepUe97\npv6+76OvF9na2rJ372E6dOiMr+81atWqxqxZ04iMTP2qLCwslBkzpvDdd00ICHjL2LGTmDJl5ldN\nBFOiTGUGjlvyVXNLf8xb/+csmfULEhJ9hs3J1PeQv4ZMJsOz+1DKun3DXd+L7Fg3P9P6nvSLJxuX\nT8X79P5kyytWrQfAvn27My0WQfdEUs4m7t30ISjAH5lMRov2WWO6xezC2MQUm9yOn2xnYmLC/Pm/\ns2DBEkxMTJg1axqVKpVhwIA+7N69g0uXvLl505edO7cxYsQvuLmV4bffZmBlZc2mTTvo33+gXs/M\nFh0VzqJpPxMdGU6XXmMpUfbzXtXSNblCwY8Dp+KYpxDH9q3n3Il9mdLv++fHR/ckH8VfwKUktnZO\nHDlyiLg43b+DL2QOkZSzia1r5wBJdXGtbex1HI3wMe3bd8LHx5dhw0YhlyvYtGkDPXt2o1mzBtSr\nV5NevX5g9eoVGBgoGDt2Epcu3aB27cyb5ONLbV83n7f+z2jQwovqdb/TdThfxMTUXDOxydG9GzPl\nmfj7aXD9nj8k+oPSnzKZDLdqDYiICOfYsSMZHoegH8SMXtnAzZs38Ht2H4A2XoN0HI2QFubm5gwZ\nMoLBg4fh63uNM2dOExYWSmxsDM7OeXF3r0LZsuVRKrPOo4hWnfpjaWVL83ZZ+1UrxzwFGTR+KUVd\nS5GoyvjrFqWxCfkLl+D54zvs37qctl0Haz6r8k1Tjuz5k+3bt9CsWcYOzhP0g0jK2cCvv44HoEiJ\nClnmGZ6QRC6XU6GCGxUquGVYH2q1mvPHd2f41au5hTXfdeiboX1klkJFy6A0VpKYSVO3Nm3dgyUz\nB3Px1L5kSTlvweIUL+7K0aOHCAsLzRJFR4SvI25fZ3EvXjzn9OmT2Dvmx6vPeF2Hk+O9efWMRVMH\ncPPKGV2HonHq8Fb+XDKRqcM66joUIRUVqtTFwbkApf8z4Y9MJqNNG0/i4uLYt0+3JSeFzCGScha3\nZMlCVCoV37brhWOegroOJ8dLTEzg5tUz7Nm8JF1m8EoPR/6pWez+TTMdRyJ8zOSFu+n+v0lay7//\nvi0A27dvyeyQBB0QSTkLCwwMZOPGdeTNm49KHg11HY5AUjEKt+oNef74Dtd9Tug6HN6+fk5QwCsU\nCgPqf9sp3bYbGxPN/m0rMvV9Xl2KjYniz98nEvj2Vab3nS9ffqpUqca5c2fw98/8/oXMpbNnynZ2\nFrrqOstJbV8tWjSbmJgYhgz5BSsr80yOSv+YmenHoCjPbgO4cuEo+7YsZdG0n5HLM/fc98P9sGt9\n0vu2ZSvVwMLCROvzL6FWq1k2eyxXLvyNpZUljVvqfy3nL/V+X924/Ddn/96J3/P7jJ+zEaNMnAvA\nzs6C7t274u19gQMHdjJy5MhM6zutxPE8/cgkHd1je/dO91PZZQV2dhYp7quwsFDc3MpgYKDgypXb\nHL36VgfR6Q99qaf83qr5o/E+vZ+VK9fSokWrTO37fc3pxMRE+nesikqVyMQFu3DKUzBd9tPODQs5\nuGMVrmXcGTBmMQYGhukRtt75775au3gC547vomb97+nSZ1ymxdGyZmHCw8MoW7Y49vYOXLx4LdNP\n9D4mtWOUoC0tJy/685MVPsvUqZMJDw+jU6eumJnprjatkLLm7Xpham5JcHCwzmJQJSZQzr0OLq7l\ncUqn8QbeZw5wcMcq7B3z0euXWdk2IaekQ48R5CtUnDPHdnD+eMbOshUdGU5ocIDm35aWVrRo0Ypn\nz55y7pz+DCIU0p94JSoLCgkJZt26PwAoUaKkboMRUmTvlJ+Zy49gpDTWXLl+jpY1C391DEpjE3oP\nmfXV23nv+eM7rF08ARNTc/qNXICZhVW6bTsrMFIa03vIb0wZ1oENK6ZSsEgpnPMXSfd+zhzbwbql\nkyleqjK/TFyuWd6pU1c2bdrAhg1rqVmzVrr3K+gHkZSzoClTJpKYmICDg6NmZKagf4yUxroOIV3Z\nOeajZLlq1G7cDqe8hXQdjk7YOeale/9fuXH5FHaO+TKkjzIVa4Ak8eD2ZeJiYzTL3d2rUKxYcfbt\n20NwcBA2NrYZ0r+gW+L2dRbz7t07NmxImiP3119n6NWzJSF7MzWzoN+IeZSu4KHrUHSqXOVadOkz\nLsMKv1jb2JOvYHEkSc32dXM1y2UyGZ06dSU+Pp6tWzdlSN+C7okjehYzatRQVKpE8uTJS4sWomay\nkLn0uSBGdtKu+1AAzh3fk2z+7XbtOqBUKlm9ekWWqVUtfB6RlLOQZ8+esnfvLgDmzFkgDpBZiCRJ\nvHn1LFP6unT2ULLbnkLWU7x0Jaxt7EmIj2X16n+fK9va2tK6dTuePn3CsWOHdRihkFFEUs5Cpk//\nFbVazfTpv1GnTn1dhyN8hmWzhzJlWAdCQ95laD/+/q9YMXcEv/xQ96uvpO74XiQ+LjadIsveoqMi\nCA8NStdtNmvTEzNzKywtLZMt79kzqTTr8uVL07U/QT+IpJxF+PpeY8eOrZQtW55u3X7UdTjCZypZ\nripxsTHs3rg4Q/sZPLg/AC6u5b5qvMEd34ss+LUfy+cMT6/Qsq2IsGCmDu/E0tlD0nWGs1qN2jJ3\n7SnatUs+Z3mpUqXx8KjJ6dMnuHfvbrr1J+gHkZSzAEmSGD066eA4YcKvYnBXFuRRryV58hfl/Ind\nPHlwM0P6CAkJ5sSJvwHo0nvsF2/H/8Ujls0eglwup1HLbukUXfZlbpmLfAWL8+juNXZuWJgpffbo\n0RuAFSuWZEp/QuYRR3c9Epeg4m1wdLI//u8iWbv+L3x8LlK/QTOKlqyk1eZtcDQqtX4UPxBSplAY\n0KHHCCRJ4q+V01CrVOnex8CB/ZAkiULFypLbPs8XbSPo3WvmTe5LTHQkXftNoGiJCukcZfYjk8nw\n6jseB+eCHN3zJ1cuHMvwPhs3bkqBAgXZsuUv3r59k+H9CZlHTLOpRwJCojl/K/n/YAYKNQO7NSA6\nKoKJ83Zg55g3xXVj4hIxUebc1871bZrN1KyaPwrv0wf4YcAUqtZKv6pNYSGBDOvZAEmSNFNqpuRj\n+ykyIpQZo7rx1v8ZbboOpmGL7DundVp87u+U/4tHTB3RGblcweiZG3FwLpCB0cHpI9tYv+xXGrTw\nSlaD+b30mIAmLcQ0m2knptnMBtYvn054aBB5CxRNNSELWUdrr0G06z4k3at6WVjZ0KCFF1VqNv3i\nKTWVxqbkKVCERi275fiE/CWc8xehS++xxMZEcc37eLpv/+WzB7x6/lDz72p1WmBtY8/pI1uJCA9J\n9/4E3ci5l1ZZgP/Lxxw/uBWA+t921nE0QnqwzmWXIT9LuVxOG69BX7UNQ0Mjfho0A5kYs/DFqnzT\nDHun/BQqWiZdt3v+xG7+WDQee6f8/LpoD5D082r0XVc2r5nF8f0b+a5Dv3TtU9AN8X+fnpIkid9n\nDgZJomCR0lSu0VjXIQk5gFyhEO+/f6X0TsgA7jWaYGBgSMDrF1y/dFKzvEaD77GwzMXxA38RFRGW\n7v0KmU8kZT11/MBGAvyfI5cr6DVkljhQCkIOZmBoRMPvugGwfulkzXKl0oRGrboTEx3JwZ2rdRSd\nkJ5EUtZDIUFv2f7nPAC+69ALWzsnHUckZKSY6MhM71OlSmTvlqU66TsnSo/xtC3a98HYxIzw0CBO\nHd6qWV6nsSe5cjty/MBfBAeKkdhZnUjKekaSJP5cMonExAQqVKlHq459dB2SkIHu3bzEmH7Nv+g1\nmsO7/uC38T0/e5CPSpXIqnmj2Lt5Kbv/ytjJTAR4+ew+00d6ERL09qu2I5fL+b7LzwBsXzdPs9zQ\nSMl37fuSmBDPns3iveWsTiRlPXP2753cvnaOkuWq0XvobBQKMRYvO7PKlZvY2BjWL52crKj9p0RH\nR7Lrr8Xcv3WJe7d80rxeYmICK+eO5PL5IxQtUZGWHft/SdjCZ7h/6xJPH95k0bQBxMZEf9W2ajdq\nRxm3mvT6T53sqt80wzl/ES6c3Ivfswdf1YegWyIp65Hnz56wZc1sjE3N8eo7XjxHzgGc8haijddA\noiLDWDV/dJonFVk0dQCqxATyFChK5eqN0rRObEw0v03ox5ULRyla0o3+oxdhbGL6NeELaVCvWSdq\n1v+el0/vs+y3oSQmfN1UnP1HLaRU+erJlskVCtp4DUJSq9m4clq63C4XdEMkZT0RFxfH0MG9iYuN\nptNPo7DJ7ajrkIRMUruxJ+Uq1+b+rUvs3bLsk+2vXDjGo7tXkcnl/Dwm7befTxzcxI3LZyhdwYP+\noxaKhJxJZDIZHXqOpHQFD25fO8fqBWk/+focpSt4UKFKXR7dvcaFk3vTfftC5hBJWU8MHTqQO7dv\n4FG3JVVqNtV1OEImkslkdPvfJGztnTm0azVB716n2jY+PpY/FiXNa92sTU+sbezT3E/D77zo2ncM\n/UbOFwk5kxkYGNJr6GyKlKjA5fNHPuuRw+do130oRkpjtv85l9BQMaFIViSSsh7YvHkjmzZtwNDQ\nkO87/6zrcAQdMDO3pPeQ2Qwev/yjo+2jIsIwUppgY+dEC8/PGwSoUBjQsEUnMU5BR5RKE/43cgG9\nh/5GyXLV0m27arWa+PikEpu2dk40a/MTEeEhTJz45UVJBN0Rc1/r2K1bN6lf/xvUahWtWnegScfk\npfLSOv+umPs6a8x9nR7UajXRUeGYW1h/9ro5aT99raywr96+fs7M0T9gbWPH2NmbAEhMSGDayM68\nfHqfDRu20KBBxk48JOa+Tjsx97WeCwkJpmXLpqjVKkqVKs34SbM+vZKQ48nl8o8m5NiYaP5amTRn\nupC9mZlbER0Zxsun9zi4I2nyEANDQ7r3/xUjIyMGDvwfQUHi9yArEUlZR2JjY2natD7h4WFYWVmz\nY8c+DAxy7pWukD5e+z1l2ojOnDi4iUM71+g6HCGNAt+++qIR0+YW1nj1HQ/Aro0LefH0HgB5CxRl\n+PAxvHsXwC+/DBCjsbMQkZR1QK1W06/fTzx+/AgDA0N27z5Irlw2ug5L0EPXL51kVxom+JAkiTNH\ntzN1eCde+z2hXrOOYnxCFvHqxSN+HdaBdUsmfdGo7Gq1m1PevQ6SJDFn/E8kJsQD0Ldvf6pV8+DA\ngb0sWbIovcMWMohIyplMkiRGjhzC3r27qFbNg7NnfShZspSuwxL0UGJiAmsXjefAthVsWD4l1XZq\ntZqFU/7HuqWTkcnl9Bw8A88fhmFgaJiJ0QpfytLaFjuHvJz9eycr5o74oveYew/9DUtrW6Kjwvlj\ncdKVs0KhYPnyP3BwcGTy5HGcP382vUMXMoBIyplIkiTGjRvJmjUrKVGiFGvXbqRwYRddhyXoqVOH\ntxIVGab5+8Edq1JsJ5fLyVfIldIVazBx3nYqe6RtMhFBP1hY5mLwhOUULenGlQtHWTClH1GRrs+B\nAgAAIABJREFU4Z+1Dblczohpf1KsVCW69B6nWe7g4MCKFWuRyWT06NGV58+fpXP0QnoTo68ziSRJ\nTJo0jsWL51OsWHF27jyAnZ1dsjYBIdGcv5V8Qnkx+jptssJI2c9x5fxRlv02FICG33Xl8rkjBAe+\n5tt2vWjerrfWbG8qVSJy+afLLma3/ZSRMntfxcXFsHLuSHwvncQ5fxHGzPoLA4P0udtx8tBmNq6Y\nhoNzAYZPXfvJkfstaxZO87bF6Ou0E6Ov9YRKpaJbt04sXjwfF5cibN++VyshC8J717yPs3zOMCCp\nAlAbr0EMmbSS3A55ObJ7LYFvX2mto1AYiGlZszil0oQ+w+bQqGU36jXrmG4JGZJmjWvUshtv/Z+z\naNoA4uJi0m3bQvoSSTmDxcTE0LJlUw4e3IdSqWTbtr04OIgpNIXUHd71B5Ik4V6zCR16jgTA1NyC\ncpVro1KpeeP/TLcBChlGLpfTustAatb/Pt233arTAKp805Qn92+wcEr/ry6OIWQMkZQz0OvX/lSv\nXglv7wvIZDLmzl1Injx5dB2WoOeGTF5Nhx4j6TFwGmEhgWxfN48RvZrw9771mFtYoUr8uoIGQs4R\nGPCKgV7fcO74LuRyOV37TaRi1fo8uH2ZBVP6ERsTpesQhf8QSTmDnDlziipVKvDq1UuUSiVbtuyi\nTZv2ug5LyAIMDAyo08STh3euMrJPUw7v+gMjpQnfd/mZXxftobx7HV2HKOiAz9lDnD6y7bPeOT57\nbBfRUeGsXTyBQzvXYGBgSI9B06jk0YhHd68xa+wPX13nWUhfigkTJkzQRcfR0fG66DbDqVQq5syZ\nycCB/UhMTMDR0Yljx05TrlyFT64bFZvAy4DIZMuMjAxISPj0u4uJKjWGBjn3HCut+ykrsbSy4d5N\nH5q07kH3/02keKlKKT5nPH7gL87+vYvipSp/8jWo7LifMoo+7auEhHgWTxuAz5mDPLxzFZfi5dI0\nzaprGXfi42N5fO86d2948/b1cypVb0h59zqEhwZx88oZLp87TLFSlbC2+Xeci2uBXGmOzcxMmW2P\n5+nNzEz5yTYiKaejhw8f0LVrR7Zu3USePHnp1u1HVq36Ezu7tFXyEUn5y+nTATSt7t64yNRhnbCw\ntiG3vTOGRsn/h1UoDPCo25KCLiVTLSKhVqnYtGYmNy6dwufsQZzzuWDnmDfVPrPiftIVfdpXCoWC\nStUbEvD6JXeun+fUkW1ERYRSqEhpjJTGH123ZLmqmJhZcNv3Aq+eP+Ty+SNJ5UIr1cLYxIxr3sc5\nf3IvZuZWFHApiUwmE0k5g4iknEliY2NZsGAOffr8yIsXz/nuu+9Zv34zjRo1xcjIKM3bEUn5y+nT\nAfRTEuLj+G18Tw5sW0lCfBy+PiexdypA/sKun70tmVxO1W+aIUlqbl09x4WTe3nr/4xCxcpgYmqu\n1T4r7Sdd07d9ZWJqTuUajclboBjPHt3m1rVzvHrxiCrffLrUa+FiZXEt486ls4cws7CmThNPZDIZ\nLsXLUdClFDevnuXqhaO8ev6I4qUqUa542se+iKScdmlJyuI95a8gSRJbtvzFpEnjePcuAHt7B2bM\nmEOzZs2/aHviPeUvl1Xev12zaBwXTuzR/FthYEil6g2p3bgdLsXLfdW2nz+5y/qlk3n++A7lKtem\n34h5Wm2yyn7SB/q8rxIS4jl5cDNFSpSnUNEyaV4vIjwEmUymdes7JOgtK+eN4uGdK5iaWTDl12l0\n6NAZufzTJ/riPeW0S8t7yiIpfwFJkti7dxdjxozgzZukgvSdOnVl4sRfsbS0+uLtiqT85fTtABob\nE42xiWmyZa9ePmbiwNYAKI1NaN1lEB71WmJomPa7KZ+iVqu5cHIPhYqWwTmf9mxx+raf9FlW3ldx\ncTEolSZpbq9Wq1GrVJw+up2dGxYQFxtN2bLlGT9+MjVr1vrouiIpp11aknLOPYp/gZiYGP74YxUL\nFswhKCgQAENDQ3788SdGjRqPsfHHn+0I2Y8kSYQEvcXv2QNePrvPy6f3efboNla5cjNy+rpkbfPk\nc6GSRyOKl65MrYZtMiQeuVyOR92WqX7+xv85Flbp8568Wq0mJjqSqMgwEuPjcMxbOMUrqzu+F5DU\nEjK5DJlMnvRHLqOIa/kUn5Wr1eo0XaEJKQsNecf4Aa0o41aTKt80o2S5qqmOSXjvyO61HNi2gmZt\nf2L83G1cPrqGHTu20rp1czw8atK//yDq1KknJqjJBCIpf4Jareb69ats2fIX27dvJSwsFABDQyM6\nd+7KqFFjsbL6/GLzQtYiSVKKB6SgAH9G9W2WbJmpuSW2Bk4prvPT4BkZGufHvI81b8FiVK/dAvea\nTbCwskGSJGJjooiKDCMqIozIiFCiIsNxq1Y/xYP5xEFtCQ15R3RUOJJarVk+f93ZFJ9jL501JMX3\nYVNrP6jrN8THx2JkZIzS2BRTMwtMzCwYMHpRiu1vXD6Niak55pa5sLSywcTMIkcn9eB3r7GwssHn\nzEF8zhzEwsoG9xqNqV73O/IVLJ7iOr6XTxEbG832dfPYs3kpHTt0ZOfOfSxYMJcTJ/7m3LkzuLqW\noEuXbrRt2x5r67QPBBM+j7h9nYKEhATOnTvDwYP7OHToAK9f+wPg4OBIo0ZNyJevAD169MLMzCxd\n+xW3r79cet1qlCQJ30snCQ58S0jQGwJevyTg9QtCgwP4bc0JrYO9JEmsXjAaU3MrXvs94eXT+0RF\nhGJuYc2cP05+dTxfIijAn6jI8KQkGxlGVGQ40ZFhlCzvweGdK7jqfQq1KhG5woDipSvx9MHNFJPm\n7NXHsbTSLik6aXA7VKpEzCysMDO3wszcEkMjJW28BqM01r5lenTvOhIT4lGr1UiShCSpkdRqmrTu\nkeKt+/mT+xITHUl8XCyxsdHEREcSExXBoo0XU3zlq297d025QgC5XIG5ZS6mLN6bYjw3Lp/GzNwS\nC2tbLK1sUBqbpnjClZVvX0uSxNOHN7l4aj+Xzh0mKiKUes064vnDsFTXOX9iN7s2LiY0OAAAmUzG\nokXLcHUtweLF89m7dzcJCQkYGhri4VGTpk2b06RJM0qXLqrXx3N9Ip4pp1FcXByXL19i795dnDt3\nmsePH5GYmAhArly5aNiwCc2bf0fdug0wMMi4xCeS8pf72H4KCwkkPCyIiLBgIsKCCQ8LJiIshOae\nvVNMCgO61CA2+t9R8EpjU+yd8jN4/DLMLJKPGXjy4Cazx/5A4gezbBkYGlGqXDX6DJ/7ySs2SZKI\nj4slLi4GM3PLFK9Mfc4cJDQ4gOioCKKjIjRJqmu/CVikkDSH9WyoObB+aOqS/RQoVJg3/q/xOXOQ\ni6f38/zxHRycCmDvnB9zCytMza0wt7DGzNySqrW+xdgkfU88v1RqdyrUajXHD2wkIiyEyPAQwsOC\niQwPIToqggnztmutk5iYQF/PysmWGRoZY2ltw5RFe5ErFJrlZmZKIiNjuXvDG0srGyytbTGzsPrk\nrWB9k5iQwK3r58ht50zegsW0Pr987jBRUREULloa5/xFeHT3Oid2L+HWrZvcvPlAU+v93bt3bNq0\ngd27d3DjxnUgKXFXrVqVKlU8qFzZHTe3ytjY2Gbq98tKxDPl/5AkiYCAt9y7d5d79+5w9+4d7t69\nzfXr17RmybGysuL331dSp069DE3Ewud7+vAm4aHBREeF/5OowkmIi6JRyx5aSRNgyrCOKSapGvVb\nYe+YT2t5W6/BKAwNsbSyQaEw5K3/M548uIGBkfbrDHkLFiUxMQEjIyW5cjtS0KUUVjZ2JCbEExke\ngqW19gFq9rgevPZ7QnxcDHGx/xYGmLxwNw7OBbTa792ylLf+z7WWR4SHpJiUq9X+lrjYmH+uZK0x\ns7DE3NwaC8ukthZWNtT7thP1vu1EaHAAkiSRy9ZBazv7ti7n0d1r5C1YDKe8hXDKWxjHPIUwNfv0\ngSW9pfYsUy6XU//bzmnejqRW07brL/+cnAX9c4IWTGJCQrKE/F5cbDTzJvVOFoeZhTW5bB0YO3uT\nVvvExATu37yEqbkFpmaWmlvv6Vlc4nMZGBpSvnLtVD8/cXAzD+9e/aetEY7OBXF3K8vcuYs1CRnA\nzs6O/v0HUq9eQ+rXr4G5edJjggsXLnDhwgVNuyJFilK+fEWKF3elaNHiFCtWnIIFC4njaBpli70k\nSRJhYaEEBQXy7l0gDx/e5+XLF/j7v+LVKz/8/V8RFBRIXFwccXHJr6YMDQ0xMDDA3NycMmXK0bBh\nYxo0aEzBgoXEoIYv9Nb/OTHRkSQkxJMQH0diQjwJCXGUKFs1xQP6jvULePv6ObExUcTFxBAbG0Vc\nbDT9Ry1McQTx0llDUpwasGyluhQpoT1zmq29M8YmZsgVCuSypCtXlSox1Xl//1o5LdmV73ulylfX\neifUyMgYp7yFee33hLf+z5Mlzxr1v08xKSsMDDA1sySXrQNKpQlGxiYolSapHrjbdvsFSS0lHeBN\nzTH557+pXcW26jQgxeUpsbZJfWKbN35PuON7gTu+F5It7zNsDhWq1NVq/+rFIyS1GnOrXJibW39y\ndjFdMDRS0qBFl89ap4VnH8L/SeIRYSFEhAWjUiWm2DYqIoz5v/bVWm5r58S0pQe1lsdER7J381KM\nTUxRGv/7x9zCijJuNbXaq9Vq4mKjMTRSpltlsE69RvPk/g2ePLzBy6f3ee33hB07HvDzz0NSbD9m\nzDASExMJDQ1JtlypNKZq1WpcuXKZbds2J/tMoVDg5ORM3rz5cHbOQ548eXFwcCBXLhtsbGzIlctG\n83dLS6scfezVSVJu0KABb98GolarUKkSUanUSJIKD49a5MmTh4SEBM2f+Pg49uzZRVRUJGq1GpVK\npfmT9MODyMhIze3mj3FycqZixUoUK1aMEiVK4epaksKFXRg0qL/mF+zkyROcPPk3AIMGDaNy5Spa\n2+nV6weCgt798y+J9xfZQ4aMpFo1D6323bp10ozWVquTnqkBjBo1nho1tP/HmzuhF+HhIUhIyAC1\nKulZXNuuAynj9o1W+1+Hdkh6/xCQ4J/ndhKePw6hUtWGWu1H9m1GTGTYP3FLqJNWokPP4VSv/Z1W\n+4FeNYmOigLUyZZ7/jiCek215/Me//P3qNXaky5832UwjVt6aS0/tHO11jKAy+eP0cJTOymHhgSm\n2P7hg5spJuXH966n2P7qxRPkL6Q9Ycd/E7JcYYixUgmKlA8UrmWrUsClJAoDAxQKA+QKAwwUBsgV\nKb/q5FatITFR2o9v1KS8/ZDgd8REaBe9r1ijEfb2zlrLTx7dRkxE0vYl/r0DVLlGE8wKFdRuf2Qr\nUZrt/9v+u44D6NBjJP5+T3jj9+Sf/z7l2eM7+Ps91bR7fwC9dvFvnj++rVlubGqOubkVlWo0xNTU\nUqvf+IREUCdgZJx0QqJQJO2/mJjoZHHI/tkvTnkLYWJmjlyuAGTI5TJAxrPHd0iIj/2gfZKCRcpg\nZmGFXC5PilEmQy6Tc+eGN/Hx2qULi7q6YfXBlWF8rJLYmDhy2Tpiam6FY55CyTp4+ewhllbJBzzF\nREdSvko9YqMj/nksEUtCXCwGRkpePn+E1X/aB717zbF967ViMTUz55fJa7H6z4Cq4MA3TB3W8d/v\nKlegUBhiaWVN/9FLsLRKfqcoPCyYlXNHgizpWbtcJkeuUGBsZo5n9xFYWllhaW1L+Sp1KF+lDtFR\nEez4cz7WZjBr1nQMDQ2Qy+WYmprQp88AbGxsePjwgVa8AEqlES4uRSlSpCixsbGUK1eet28D+P33\nBcTEROPn9xI/v5cprqtNhkIhRy6Xo1KpUCgMMDc3w8bGFiMjI4yMlBQu7IK5uTlPnjwmJCQEhUKB\nXC4nODgYhUJB7ty5yZ07N3K5HENDJWXLlsXaOhcPHtzj3bt3//zeSrx48QJJksidOze2trkBMDAw\npHz5ClhaWvL48SPevXuHXC5HkuDJkweo1ZA7tx02NrbI5XIMDGRUrFgZS0srnj17RnBwIPxzRL53\n7x6JiYmUKVOWSZPGfvqb6+KZcnqdBclkMlxdS2BmZq7Zoblz2zF//m8pts+bNz9Xr97SWm5vr33A\nAMifvwCXL9/MtPbB4bHceBxEu0YlUmxv55iXxWuPai1Prb2tvTPTlhzQWv5T6/Lp0j63fV6mLtmX\n5vb2TgX4ddHuNLd3zl+ECXO3pbl93oLFGPfbljS3dylenuFT/0hz+wpV69FnqPbvVlZqP2TCIq1n\n7+m1/bwFi1HEtQKR4SFERoQSERZCVGQoocHvUmxvYmpOTHRkip+l2N7MIsWTmVTbZ/T2c1h7a2tr\nQkNDM6y9gYFhineospO0pFudDfQSBEEQBCG5nPsynyAIgiDoGZGUBUEQBEFPiKQsCIIgCHpCJGVB\nEARB0BMiKQuCIAiCnhBJWRAEQRD0hE6ScnBwMD179sTLy4uOHTty48YNXYSh91QqFSNGjKBjx460\nb9+eq1ev6jokvebt7U316tU5deqUrkPRS9OmTaN9+/Z06NCBmze136cX/nXv3j0aNGjAhg0bdB2K\nXps5cybt27enbdu2HD2qPYeCALGxsQwcOJAuXbrg6enJyZMnP9peJzN67dmzh5YtW9KsWTMuXbrE\n/PnzWbVqlS5C0Wu7d+/G2NiYjRs38ujRI0aOHMnWrVt1HZZeevHiBevWraNSpUq6DkUvXbp0iefP\nn7Np0yYeP37M6NGj2bRJe+5mIalu+owZM/Dw0J6dT/iXt7c3jx49YtOmTYSGhtKqVSsaNGig67D0\nzvHjxylTpgw//vgj/v7+dO/endq1a6faXidJuVu3bpq/+/v74+iYPkXXs5sWLVrQrFlSrV4bGxvC\nwsJ0HJH+cnR0ZNGiRYwcOVLXoeilCxcuUL9+fQBcXFwIDw8nKioq3cuPZgdKpZJly5axfPlyXYei\n1ypXrkzZsmUBsLS0JCYmJtVqXjlZ06b/zpfv7++Pk5PTR9vrrCBFYGAgvXv3Jjo6mrVr1+oqDL1m\nYGCgqayydu1avv32Wx1HpL+MjFKeZ1pIEhgYSOnSpTX/zpUrF4GBgSIpp0Aul4vfpzSQy+WYmCTV\nq966dSu1atUSCfkj2rdvT0BAAEuXLv1ouwxPylu3bmXbtm3IZDLNWVT//v3x8PBg27ZtnD59mhEj\nRuT429cf208bNmzgzp07n/xh5hQf21dC2ojZdYX0cuzYMXbs2JHjj+GfsmnTJu7du8eQIUPYs2dP\nqu0yPCm3bduWtm3bJlvm4+NDWFgYVlZWfPPNNwwbNiyjw9B7Ke0nSEpAJ0+e5Pfff0eRQr3XnCi1\nfSWkzt7ensDAf6trBQQEYGdnp8OIhOzgzJkzLF++nFWrVmFubq7rcPTSrVu3sLW1xcnJCVdXV1Qq\nFcHBwdjYaNdCBx2Nvj569Ci7du0C4P79+zg7a5efE+Dly5ds3ryZRYsWYaiHtWn1lbgK1Obh4cHh\nw4cBuH37Ng4ODpiamuo4KiEri4yMZNasWSxduhQLC+066UKSy5cvs2bNGiDpMVJMTEyqCRl0VCUq\nJCSEESNGEB0dTXx8PKNHj9YMGBD+NXfuXA4cOICTk5PmNu3q1as1z5mFfx09epQFCxYQEBCAmZkZ\nuXLlYvv27boOS6/MmTMHHx8fFAoF48aNo3jx4roOSS/5+voyZswYTV1eKysr1q9fj9V/ahXndFu2\nbGHRokUULFhQc3yaOXOmGLj7H3FxcYwaNYo3b94QFxdH//79qVWrVqrtRelGQRAEQdATYkYvQRAE\nQdATIikLgiAIgp4QSVkQBEEQ9IRIyoIgCIKgJ0RSFgRBEAQ9IZKyIAiCIOgJkZSFL3bq1Ck6d+5M\n165dadu2LYMHDyYyMhKAa9eu4efnly791KpVC39//69e/8yZMyxbtuyr4xk6dKhm8pv04OXlhSRJ\nxMbGasrfpVesAQEBXLx4EYCdO3em+7vbI0eOZNu2bZ+1zsemGMzKHj9+zN27dwFYvny5KCEqfBGR\nlIUvkpCQwLBhw5g/fz5r165l69atODk5aUpL7tixg5cvX6ZLX187yf379WvWrEmvXr3SI6R09eef\nfyKTybh9+zZHjhwB0i9Wb29vTVJu1aoVrVu3/uptfo23b99m25KRR48e5datWwD89NNPH50gQhBS\nI6aGEr5IXFwcsbGxREVFYWtrCyRdQULSBPWHDh3i5s2bjBw5EgMDA2bNmoWxsTGxsbGMHz+eEiVK\nMHLkSOzt7bl//z7Pnz+ndevW9OjRg6CgIAYOHIharaZkyZKaaTNjYmIYPnw4oaGhxMTE0LBhQ3r2\n7ImPjw+///47xsbG1KtXj7p166a4/s6dOzl//jyDBw9m2LBhmoIW165dY+PGjZQtW5a5c+dy9epV\n4uLiqFy5MkOHDkWSJEaNGsXDhw9xdnYmOjpaa3906dKFsWPHUqxYMWbMmMHdu3f5448/UKlU1K1b\nlxMnTrBo0SLOnz+PQqHAwcGBWbNmoVAocHV15erVq4wZM4aIiAhmz56Ni4sL58+fZ9asWdStWxcv\nLy/OnDmDn58fEydOpGrVqly7do2JEydiaWlJvXr1WLt2LcePH9fE5Ofnx9y5cwGwtrYmMjISlUrF\nzz//TIUKFejbty/Hjx8nISGBXr16sXXrVp49e8aECROoXr06r1+/ZuLEicTGxhIdHc2gQYOoVq2a\n1ne/fv06Bw8eJCAggO+//57u3buTkJDApEmTePHiBVFRUXz77bd069aNIUOG8PDhQ4YPH87ly5fZ\nvXs35ubmDBw4EFNTU6ZOnUpgYCDdu3dn7969rF+/nkOHDpGYmEjhwoWZMGECRkZGHDx4kPXr1wNJ\nZU1//fVXrKysqFSpEn369OH06dMEBgYyb948ihYtmize+/fvM2PGDBITE0lMTGTcuHG4urrSpUsX\nSpQowZ07d/jzzz8pWbIkd+7cQS6Xs3PnTi5cuMDMmTOpW7cuzZs3x9fXl9DQUEaNGoWRkRHr16/H\nwsICU1NTzp49i5ubG23atGHbtm1s3rwZExMTcufOzeTJkzEzM0s11tmzZ+Pj44ORkREODg5Mnz5d\nTLObk0iC8IWWL18ulS9fXurevbu0ZMkS6cmTJ5rPOnfuLF24cEGSJEk6duyYdPfuXUmSJGnfvn3S\ngAEDJEmSpBEjRkiDBw+WJEmSXr16Jbm5uUmSJElz5syRZs+eLUmSJN2+fVtydXWVXr16Jb18+VLa\nuXOnJEmSFBcXJ7m5uUmRkZGSt7e3VKlSJSk8PPyj6+/YsUMaOnRosu+wfv16zbKDBw9KI0aM0HzW\nr18/6cSJE9LZs2clT09PSZIkKSYmRvLw8NDE8d6SJUuk9evXa7579+7dpfj4eOnatWtS//79JZVK\nJS1fvlxSqVSSJEnSDz/8IJ08eVKSJElydXWVVCpVsvg+/HudOnWkTZs2SZIkSTt37pT69u0rSZIk\neXp6SqdOndJ857p162r9jBYuXCjNmzdP6+/FixfX/Hw6d+4sjRo1StNvv379JEmSpJ9++kny9vaW\nJEmS3r17J9WpU0cT/3sjRoyQevXqJUmSJIWHh0vu7u5SWFiYtHLlSmnhwoWSJEmSSqWSWrduLd2/\nf1/y9vaWOnbsKEmSJI0ZM0azDzp37ix17txZkqSk35Hp06dLvr6+kpeXl6avqVOnSuvXr5dev34t\ntWjRQoqPj5ckSZLWrl0rTZ8+XfO9zpw5o/m+U6ZM0don3377rfTixQtJkiTp7t27UqtWrTQxvN8/\nH/5cUvp5rFmzRpIkSTp//rxm/REjRkhbt25N9nd/f3+pVq1aUnR0tCRJkjR9+nRp0aJFqcYaFhYm\nVahQQVKr1ZIkSdL+/ful169fa30HIfsSV8rCF+vZsyft2rXj3LlzXLx4EU9PTwYPHkz79u2BfwtD\n5M6dm1mzZhEXF0dERESyOYTd3d0BcHZ2JioqCkmSuH//vmYbJUuW1FSfsbW15erVq2zatAlDQ0Pi\n4+MJCwsDoFChQppJ8f+7fmqT5V+7do2dO3eyYcMGIOlW77Vr1zTPeKOiovDz8yMhIYEKFSoAYGxs\nTLly5bS2Vb16ddasWUOLFi0wNjbG1dUVX19frly5Qo0aNZDL5cjlcjp16oSBgQFPnz4lJCQkzfv6\nw/30/jvfv38fNzc3ABo0aMC+ffvSvD2AihUrAuDo6Kj5fo6OjkRERGj2x4d3BYyMjAgKCtKqLlW9\nenUALCwsKFiwIM+ePcPb25u3b9/i7e0NQHx8PC9evMDS0lKzXrVq1fDx8cHR0ZFChQoRGRnJmzdv\n8Pb2plGjRvj4+PDy5ctkz9wNDQ25du0a796948cff0SSJBISEsiXL5/WvsqTJ4/WI5Tg4GCePn3K\n6NGjNb+f0dHRmr+/3w+fUqNGDQDc3Nx4/Phxqu1u375N6dKlNXWHq1Spkuz2/X9jtbS0pGbNmnTq\n1IkGDRrQtGlTHBwc0hSTkD2IpCx8sdjYWKysrGjatClNmzalcePGzJgxQ5MQ3xs2bBiTJ0/G3d2d\nkydPsnr1as1n/y1H+f7g+OFzZJVKBcDatWtJSEjQHNSqVq2qafPf23sfrp+YmKgVe2BgIOPGjWPJ\nkiUolUogKel4enrSvXv3ZG1Xr16NXP7v8Iv38XyoTJkyPHjwAB8fHypXrkzx4sW5dOkSly9fZvLk\nyVy9epUdO3awY8cOlEolAwYM0NrGx3xYhOT9PpIkKVlcn+vDbaa0fSMjIxYtWvTJQgwfxqBWq5HJ\nZBgZGdGvXz8aNmyYrK2Pj4/m79WrV2fdunU4OjpSpUoVQkND8fHx0RSEePz4MXXr1mXMmDHJtvH3\n339TtmzZFOuLy2SyFL/Le0ZGRiiVSv78888Uv8uHv0cfrpuQkJCsnVqt1rT52JiH949IPtzmh+1T\ninX+/Pk8ffqUkydP0rlzZxYuXIirq2uqfQjZixjoJXyRs2fP0q5dO81oa0gqNVmgQAF95+0NAAAE\nCklEQVQg6UD9PhkGBQVRpEgRVCoVBw8eJD4+PsVtvj8oubi4cO3aNSCpYk9MTAyQlEhdXFyApANz\nXFxcittKbf33VCoVgwcPZsiQIeTNm1ez3M3NjSNHjmiS7uLFi3nx4gUuLi74+voCSeXqbty4odWn\nTCbDxcWFrVu34u7uTsWKFfHx8SEkJARnZ2eCgoLIkycPSqWSV69ecf36dU3sH56IpHQCkZrChQtz\n8+ZNzf5Iyedu80Nubm7s378fSLrCnDp1aort3g8kCwsLw8/Pj0KFCuHm5saBAweApAQ2ffp0wsPD\nkcvlmgRnbW2NJEmcOnUKd3d3KlWqxIEDB7Czs8PIyIiKFSty+vRpzdX6xo0b8fX1pUyZMty8eVNT\nH/rQoUOaZ+n/TcL/ZW5uTp48eTQjo58+fcrixYtTbGthYcHr168BNFf8//3Oly9f1lTbSmlfly5d\nmjt37mi+w/nz5z96Ne7n58cff/xBoUKF6N69Ow0aNODevXsf/U5C9iKulIUvUqNGDZ4/f063bt0w\nNTVFkiRy587NuHHjgKT6vePHj2fUqFH07NkTLy8vHBwc6NmzJyNGjEjxSuX9FYSXlxcDBw6kW7du\nFClSRHNrsk2bNgwePJjTp09rBtsMGTKE4cOHJ9tOauu/d/jwYW7fvs2qVatYuXIlMpmMDh060KRJ\nE3x9fWnfvj0KhYJSpUqRL18+8ubNy759+2jXrh3Ozs6pHlQ9PDyYMWMGixcvRqFQEB4errm97OHh\nwerVq+nQoQMuLi4MGDCA33//HXd3d833Llu2LL/99hujR4+mcuXKWvvlv4YMGcLEiRNxdHSkYsWK\nKZb0rFSpEoMHD8bQ0DDZFe2H20xt+6NHj2bcuHHs37+fhIQE+vTpk2I7e3t7+vXrx4sXL/jf//6H\nubk5nTp14tGjR7Rv3x61Wk3t2rWxtLSkSJEiBAYG8uOPP7Jq1Src3d05evQodnZ22NnZ4evrqxl1\nXrp0aTp27EiXLl0wNjbG3t6e1q1bo1QqGT16NL169cLU1BRjY2NmzJjx0e/yoZkzZzJ58mRWrFhB\nYmIiI0eOTHHdnj178sMPP1CwYEFcXV01CRqSXjXr3bs3b968YcKECUDSnZuZM2cmOzFwcHDg559/\nplu3biiVShwcHPjll19SjdXR0ZG7d+/Srl07TE1NsbKyon///p/8TkL2IUo3CkIWdfHiRXLnzk2R\nIkU4ePAgu3btSpd3m4WPq1u3LmvXrtU62ROE9CCulAUhi1IoFAwbNgxTU1PUajUTJ07UdUg5wte+\nNy8IHyOulAVBEARBT4iBXoIgCIKgJ0RSFgRBEAQ9IZKyIAiCIOgJkZQFQRAEQU+IpCwIgiAIekIk\nZUEQBEHQE/8H6idwQm5qm0sAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fcc25a65ed0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"n_bins = 20\n",
"ax.hist(old_faithful_df.std_waiting.values, bins=n_bins, normed=True,\n",
" color=blue, lw=0, alpha=0.5);\n",
"\n",
"ax.plot(x_plot, post_pdfs.mean(axis=0),\n",
" c='k', label='Posterior expected density');\n",
"ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pdf_contribs).mean(axis=0)[:, 0],\n",
" '--', c='k', label='Posterior expected mixture\\ncomponents\\n(weighted)');\n",
"ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pdf_contribs).mean(axis=0),\n",
" '--', c='k');\n",
"\n",
"ax.set_xlabel('Standardized waiting time between eruptions');\n",
"\n",
"ax.set_yticklabels([]);\n",
"ax.set_ylabel('Density');\n",
"\n",
"ax.legend(loc=2);"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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