diff --git a/bayes_opt/bayesian_optimization.py b/bayes_opt/bayesian_optimization.py index 09881926..48e83ec6 100644 --- a/bayes_opt/bayesian_optimization.py +++ b/bayes_opt/bayesian_optimization.py @@ -242,6 +242,7 @@ def maximize(self, n_iter=25, acq='ucb', kappa=2.576, + xi=0.0, **gp_params): """ Main optimization method. @@ -272,7 +273,7 @@ def maximize(self, self.plog.reset_timer() # Set acquisition function - self.util = UtilityFunction(kind=acq, kappa=kappa) + self.util = UtilityFunction(kind=acq, kappa=kappa, xi=xi) # Initialize x, y and find current y_max if not self.initialized: diff --git a/bayes_opt/helpers.py b/bayes_opt/helpers.py index 03ec53fd..dfdee5a1 100644 --- a/bayes_opt/helpers.py +++ b/bayes_opt/helpers.py @@ -10,11 +10,13 @@ class UtilityFunction(object): An object to compute the acquisition functions. """ - def __init__(self, kind='ucb', kappa=1.96): + def __init__(self, kind, kappa, xi): """ If UCB is to be used, a constant kappa is needed. """ self.kappa = kappa + + self.xi = xi if kind not in ['ucb', 'ei', 'poi']: err = "The utility function " \ @@ -28,9 +30,9 @@ def utility(self, x, gp, y_max): if self.kind == 'ucb': return self._ucb(x, gp, self.kappa) if self.kind == 'ei': - return self._ei(x, gp, y_max) + return self._ei(x, gp, y_max, self.xi) if self.kind == 'poi': - return self._ucb(x, gp, y_max) + return self._poi(x, gp, y_max, self.xi) @staticmethod def _ucb(x, gp, kappa): @@ -38,23 +40,23 @@ def _ucb(x, gp, kappa): return mean + kappa * np.sqrt(var) @staticmethod - def _ei(x, gp, y_max): + def _ei(x, gp, y_max, xi): mean, var = gp.predict(x, eval_MSE=True) # Avoid points with zero variance var = np.maximum(var, 1e-9 + 0 * var) - z = (mean - y_max)/np.sqrt(var) - return (mean - y_max) * norm.cdf(z) + np.sqrt(var) * norm.pdf(z) + z = (mean - y_max - xi)/np.sqrt(var) + return (mean - y_max - xi) * norm.cdf(z) + np.sqrt(var) * norm.pdf(z) @staticmethod - def _poi(x, gp, y_max): + def _poi(x, gp, y_max, xi): mean, var = gp.predict(x, eval_MSE=True) # Avoid points with zero variance var = np.maximum(var, 1e-9 + 0 * var) - z = (mean - y_max)/np.sqrt(var) + z = (mean - y_max - xi)/np.sqrt(var) return norm.cdf(z) diff --git a/examples/exploitation vs exploration.ipynb b/examples/exploitation vs exploration.ipynb new file mode 100644 index 00000000..05634051 --- /dev/null +++ b/examples/exploitation vs exploration.ipynb @@ -0,0 +1,285 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exploitation vs Exploration" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from bayes_opt import BayesianOptimization\n", + "\n", + "# use sklearn's default parameters for theta and random_start\n", + "gp_params = {\"corr\": \"cubic\", \"theta0\": 0.1, \"thetaL\": None, \"thetaU\": None, \"random_start\": 1}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Target function" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(42)\n", + "xs = np.linspace(-2, 10, 10000)\n", + "f = np.exp(-(xs - 2)**2) + np.exp(-(xs - 6)**2/10) + 1/ (xs**2 + 1)\n", + "\n", + "plt.plot(f)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Utility function for plotting" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def plot_bo(f, bo):\n", + " xs = [x[\"x\"] for x in bo.res[\"all\"][\"params\"]]\n", + " ys = bo.res[\"all\"][\"values\"]\n", + "\n", + " mean, var = bo.gp.predict(np.arange(len(f)).reshape(-1, 1), eval_MSE=True)\n", + " \n", + " plt.figure(figsize=(16, 9))\n", + " plt.plot(f)\n", + " plt.plot(np.arange(len(f)), mean)\n", + " plt.fill_between(np.arange(len(f)), mean+var, mean-var, alpha=0.1)\n", + " plt.scatter(bo.X.flatten(), bo.Y, c=\"red\", s=50, zorder=10)\n", + " plt.xlim(0, len(f))\n", + " plt.ylim(f.min()-0.1*(f.max()-f.min()), f.max()+0.1*(f.max()-f.min()))\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Acquisition Function \"Expected Improvement\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Prefer exploitation (xi=0.0)\n", + "\n", + "Note that most points are around the peak(s)." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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kzw+bN2c9LpSvEI1LNSL65xhrg4mIiIhcB5VXcRsZGdDv6QM8FR9Ky3sK8eOH\niziUJw8/AIFAHHDxBiBLgfU+3hyevpEu5foStaol9fs/QcWgIGKffhq/oUOJffppKgYFERcX5/Tv\nydVN/XkaXr8256GeGtLk7tq2hXnz/n3c+87ezEmcRXp6unWhRERERK6Dpg2LW0hPh/b99rOs9L08\neXc/nq43gJIlS1522vA9wIZspg3P/mEt3ZuFMi/dfsH9sUuBHgEBJB4+jL+/hhIBmKbJ7Z/Uxjb7\nXQ7+0AJPT33W5c5WrYKnnoItW7Ien804S/EPS7Ay8gfurFDD2nAickNsNhvR0dEkJiRQISRE28OJ\niEvIyWnD2rBRXF5mJnTofYgV5ZryUuNHePSuhwgMDAQgNDSUA0ePZu3zunAh9TMyKBQYyKnixYmo\nUoUpkZEXlNETCb/Q0jsPzdLPXPAezYDQ84OdoqKinPntuawNhzdw+K9TPNG4gYprLtCwIfz+Oxw4\nAKVLQx6vPEQEt+Xb7TNUXkXcUFxcHB3Dwwm126mTkkKsnx8vDRqk7eFEJFdTeRWX98TzJ1lRujmP\nN4i8oLj+zd/fn4EDBzJw4MCrvlZiQgJ3nTmT7bnaKSkk7t3rkMy5wfA1o8hYN4CHx/pYHUUcwMsL\nWrXKGtz06KNZx/rW7svjC59gyNmXyZNH9zSLuAvb+W3gpths/64iSklhKdAxPFyriEQk11J5FZc2\n+stMJqZ0o33ju3n6rscvKa7Xq0JICLF+fpCScsm5zX5+tA4OvqnXzy2SUpOI2TmHJgW3Ur58Pqvj\niINERMCECf+W17AKYZxMO0lcwlqaVm9iZTSRW1pKChw7Bgf/SGP/0WOcSk3m1NlkbGeTSU5LwfAw\n8fIy8PH2wNvLgz3rllM/PSPb7eG0ikhEcjOVV3FZW7bAoEWDqXJfCu/dO4SSJUve9GtGRkby0qBB\nLIVL7nldZcCkyMibfo/cYFL8N3gmtmRg39usjiIO1KIFPPhg1i/Kfn7gYXgQWaUrM3bP4v5qYdrH\nVySHmCYcPgzrN6eydvdeth/eQ+KpBI6k7ybZ8yCm3x8YAX9g+tjwTi+MV2Z+vE0/vPHDm3xg98CO\nHdM0ybTbSdm4k1fOpmb7XrVTUnhv0iQO+hWlZa1q3BVSFk8P3fohIrmDBjaJS0pOhpBOU8gIfZUV\nPeZRpVwVPBz0j+9/7xOqnZLCZj8/lpxLhy6l2D9qPUXzF3HI+7gr0zQpO7QKHrFfsG95mO53zWWa\nNoXHH4dyebJgAAAgAElEQVT27bMex/8RT8vJrdjz6G4C/DXoReRKrnVA0vHjELvyBAs2bmbLkS38\nnr6ZjMDNkP8AAZllKe5dkXL5y3NHsXJULRlE6YKBFMtXjEJ5C5LH1wdPT89//vPw8LjggyXTNBk/\nfjzLXnyR2dncBhPu7cO2sEakVPLiVJ4dmL5J5D9TnUr56tOs8j30atKQO0qVuOHvTUTkanJyYJPK\nq7ikro/uYV6Re1jQdRqNb2+Mj49j77tMTk7O+kd6714qBAcTEdGVqs+/iHepeHa/sgT/PLfuvUI/\n/PoDrUc9yisF1zB4cEGr44iDDR8O27bBuHH/HqvyWVVeq/cGD9TvbF0wERd38YCkTX5+xHl4EBMb\nS7Vq9zA19jdmbVzF5hOrOF1gNUb+I5SgBlULVaNB+SrcU74aFQtUxD9fXvLmzYuvry9eXl43tOLB\nZrNRMSjownteuXByvo+PD6mpZ9m2509it2xnVeIWdiZvIMl/Pd4ZhQjxuJ+ONcJ5vM19JGyPv+z3\npuFPInK9VF4l1/vvJ75n0svxRcpoXop4gGcbDSR//vxOyXDkTzsVn+9B+dtPsvnFufh43ZqDiiIm\nPsD34xvy+8yHKFIkr9VxxMESE6FBA/jjD/h7McM7K95h2+EdTH1gEp6entYGFHFBVyqL7by9SX0k\nEJ+ATIK9G9C4bD3a1ryLaoGV8ffzw8/PDx8fH4cvy89uFdHVCmdGRgZ/JZ1m5qqfmbV1NZtOruCU\n73ryfnaWuemZ2kJORBxC5VVytYs/zV7l6UWcl8nkaTPo0KGDU7Ns2ZZGvWFtaVkviHkDvr7l7gE8\nknyEch/dQacDPzNlXCmr40gOqVo168pr/fpZjw+cOkD1kTXYM2A3RQsVtTaciAsaO3YssU8/TUw2\nw/7CfXyo/MIzPPvIEwQEBODv7++w21yu5uJVRJEXbQ93NRkZGbz7waesf/NVFp5Lu+R8Rz8/Wg8f\nruFPInJdcrK8XvVvV8MwxhmG8adhGNuu8JzPDMNIMAxjq2EYdzo2ouRm/x33H5OSwsvAkswM5qRl\nMqBPH5KTk52ap1YNX0bfF82SXT/x8rx3nPreruDztaMxtkfy9CPOudot1mjbFubP//dx6dtKU61I\nNWZum2tdKBEXZDftfLdzLe9M/pI62RRXgIbnzpE3wyAoKIj8+fM7rbhC1lZxUVFRvPPee0RFRV33\nFVIvLy/Onj5Ow2yKK2QNf/pq5gKSU885Iq6IyE27lr9hxwMtLnfSMIxWQEXTNEOAAcBoB2WTW0B0\ndDShdvsVx/07W1TPgnQ35vHx+i+YtuFbp7+/Vc5mnOXztaOpefYR7rpLQzpys4vLK0Dvmr2Ysy+G\n9PR0a0KJuAjTNNl0eDOR45/G/9UytBr5IGfMQNb6Zr8X8mY/Pyq48TZrFUJC2OTnl+25H318iE//\nhfxDSnHn4KdYskF7oYuIta5aXk3TjAOSrvCUdsCk889dD9xmGEYxx8ST3C4xIeGyn2bXTkkhca81\n/1B+NbQilbbOIGrBE6zfv96SDM42Zds0Mg7eyfP9ytxyy6VvNfXrZ93z+ttv/x7rWr0ra/9cw69/\n/m5dMBELHUk+wvurPqbUO9Vp8GlnlswLoDcxbH14OdtnTuQnH2+WXvRnlgJxHh5EuvE2a5GRkcR5\neGT7vW309eXIrA1Mb7EQT9OTVrMaEPhkG96L/g67XbeBiYjzOWJtSxBw4D+PD50/JnJVV/rE18pP\ns7294btxoXgv/5S207pyKOmQJTmcxTRN3lr6KUUTHyciQkuGcztPT2jdGubN+/dYgbwFuK/MfUzf\nPsu6YCJOZpomS/ctpeXECMp9dAdvjNxOsc2fMrHOOg5PeYnRb9ejevViBAYGEhMbS4+AADr6+fE2\nWfeD9ggIICY21q0HGgWc/x4u973ddtttdL6vLps++IRfn/qFsJJNGbL+afI9W50+n44l+YxWa4iI\n81zTwCbDMMoC803TrJHNufnAe6Zp/nj+8ffAC6Zpbs7muRrYJBew2WyUL1mCackpLjnlMDYWIr96\ngarN1rLq4WW5dgLxiv0raD3yMT4os4YnnihkdRxxgrlzs7bNWb7832OzfpnF+z98SFzUD/j6+loX\nTiSH2dJsTIqfxCdrPuevY56krX6C8NIdeP6pfNSr53/Z1Sc3OyDJlV3P93b2bBpvTpnPqG0jsXkn\n0iHwOcYOfIjb/PX3hoi4wLThq5TX0cAK0zSjzz/eBdxrmuaf2TzXfP311/95HBYWRlhY2I2nF7eX\nac+k/BM1OD5mHy18PKlz5sw1jft3pqcHZTLZbEnnRsGM7jjK6jg5ovGoCLbNasmB2f0JCMj+vi7J\nXVJToXhx2LcPihTJOnYu8xzFPyzO4g7fUe/2u6wNKJIDjqYc5ZO1nzB6wxjyn2hM0uKn6B1Wh8Ev\n5qF06dz54WROyszMZNispby3ZhhJPr8QUWgQ4594lAL++ndE5FaycuVKVq5c+c/jN954w/LyWo6s\n8lo9m3PhwEDTNFsbhlEfGGaaZv3LvI6uvMoF3lv9Pu9GL+HN4PHkD1jmkp9mp6VBvXtPcKBVHd65\nbzCPNnrE6kgOtev4LmoOa8wzRjzvv1XC6jjiRJ06QZs20K/fv8eiYh7kNo/CfBTxnlOnporkpAOn\nDjD0x6FM2jKZ4sc788fM/9GnXXFeeSUPxYrp5/xm2e12vpi9gjd/GMZfPtvoUfI1xj7RFx9v7Rst\nciuy9MqrYRhTgTCgMPAn8DrgA5imaY45/5wRQEsgBeiX3ZLh889TeZV/xB+Jp9HY+wmMWc/un8rj\n5eW6v0Ds2QN3R2zF7NWU2Afm0bBiQ6sjOUyHif1Y8m059n39LCVKuMYHBuIcU6ZAdPSF977++PuP\n9JjZk58f3uYyHyCJ3Kg/k//kjR/eYOq2aZRL6s3+KS/Qu2NhXnnFl2LFNJjO0ex2O5/OXMKQNW9x\nzuM0L9R6hzd6RuDhof+vRW4lli8bdtibqbzKeWkZadw15i5OL3mKtzr1pHdv119iNGkSDJ4yBa/m\nL7M+ai0lCrj/VcrfT/1OyEe1GJC2mc+GlrU6jjjZyZNQpgwcPgx/91TTNAkeFsLQez6mU7121gYU\nuUGn007z0Y8fMWL9CCqndWP32Ndo2bgg77/vTenSKlI5LT09g2fHfMvove+Q1x7IyIhP6XF/Hatj\niYiT5GR5dd1LXZKrDVk5BN8zpfHd1ZuePV2/uAL06gX3BfYg4GB7us3sTnqG+09YfGXRRxhb+/Hs\nwNusjiIWKFAAGjSARYv+PWYYBr1r9mJGwgwyMzOtCydyAzLtmYzeOJqQz0L4fuNu/Keux2fFML6f\nV5QpU3xUXJ3E29uLzwb25MTbm2kS2IFe34Vzx7OPkHj4L6ujiYibU3kVp9t0eBPjNo+DBaN57VVv\n3OW2OsOAkSPh7IKPOHIsk2fmD7I60k05mnKU6B2T6R0ygDJlVF5vVR07wuzZFx7rV7sfS35fyNGk\nY9aEErkB6w+up+5XdRkVN4Gyq+dx9MspjHy3IitWeFOrlkqrFQL88jLnlWeIf2gjdjOT4OFV6PnJ\naDIy7VZHExE35Sa1QXKLc5nn6De3H31KvM6f+0oRGelev1Dkzw/fTvXi+KhZxOyZy5g1X1kd6YYN\nWTwMtkcy+PEil90WQnK/du2yrrympf17rEyBMtQIrMmM+NmX/4MiLuLEmRM8OO9B2k6NoNj+R/jt\njTVE1LuLX37xok0bD/TXm/WqB5dm9ydfMbJhNLN/m8Btz9YnesUWq2OJiBtSeRWnej/ufQJ9A9k7\nuy9PPeWBt7fVia5f3bow+MlAiiybw/9WD2Zt4lqrI123oylHGRf/JT3KPU758gWsjiMWKl4cqlS5\ncL9XgL61+jBz3wzOnTtnTTCRaxCzM4aqI6vy+z7IO+4XPLdHsXWLJ6+84om2KnY9j7S7l78+XE3L\noj3otqQ5DV56idMpaVf/gyIi52lgkzjN9qPbCRsfxvj639GnQy327ze4zU1Xq9rtEB4O3rUmEV/k\nVdZHrXOrAU69Jg9i5uxz7Pz4TcqVK2R1HLHYxx/D7t0wZsy/x1LOpVDy4yDiusVRvVw168KJZOPE\nmRMMjB3I2l9/ovy2MSSubMKIER5EROgyq7uI27aXjmOf4ZTXXj67fwwDWjeyOpKIOIgGNonby7Bn\n0G9OP56r8zzfx1SnXz/3La4AHh4wcSJsmtibO30i6DK9K+cy3OMK1cHTB/l21wQer/EkZcsWtDqO\nuIAOHWDuXPjvfCY/Hz/aVmzD5G3R6ENHcSUL9yyk2shqnPitAGnD46mcrwm//OKp4upmQmsE88en\nc+ld+gUe+6ErNV98nL9OpwJgs9kYO3YsL734ImPHjsVms1mcVkRcha68ilN89ONHzN4+m68aTadR\naBBbtmRt0eHuvvsO+kVlUPalplQrejtjOn1pdaSravvlAH74Lj8JI1+iWDGVV8lSsyaMGAGN/nPx\nY8W+FQyY/yhbH95Mvnz5rAsnQtbMhMHfD2Za/HQqxn/NwTX3M368B02aqLS6u/g9Bwn/YhDHPbbz\nQtmn+fK15wi126mTksImPz/iPDyIiY0lNDTU6qgicg105VXcWsKJBN5b/R4fhH7IiuUluO++3FFc\nAZo3hx7dvPBfPIvvfvuOkXEjrY50RTuP7mHR7zN5OWyAiqtcILupw2EVwkjLPMvyXassySTyt8Sk\nRO4Zdw8rtu4kY8Rmahe+j19+8VRxzSVqVirFwWHRdC7yKB+9+AhTbDZiUlJ4GYhJSWGKzUbH8HCS\nk5OtjioiFlN5lRxlN+1EzYviiZpPUqNUdUaN8uDRR61O5Vhvvw0n/yhMp4xZvBr3Kqv2uu4v+l3H\nDaJk4rM82qeY1VHExXTokFVe/7s4xjAMelTvTvTu6drzVSwzd9dc6o25GzO+K8e/mMesyYF89pkX\nfn5WJxNHMgyDJsXy0twzD80uOtcMCLXbiY6OtiKaiLgQlVfJUWM3jyU5NZn+VfsTHx9ARgY0aWJ1\nKsfy8YFp02DSh7V5Ovgzus/pzm8nfrM61iWmb17CjqO7GNW3F/nzB1gdR1xM9epZ93Jv3Xrh8f61\n+7Pwt7kknT5pTTC5ZdlNO2/+8CYPzn6MPDFzqXDsKbb/7E3jxrramlslJiRQLzU123O1U1JI3LvX\nyYlExNWovEqO+TP5T15e9jLv3zOUkiVKMGoUPPIIuXLPvYoVYeRI+Pr5HrQv25220yI4nXra6lj/\nSM9MZ0DMMzRJf5v77w20Oo64IMOATp1g1qwLjwcXCeb2grczI36ONcHklpR8LplO0Z0Zs3whmaPW\n885jdZk+3cetB/3J1VUICWHTZS6pb/Lzo0JwsJMTiYirUXmVHDNoySA6BXehbpk6/PWXF7Gx0KeP\n1alyTpcu0LUr7PzyA24vUJlO0zqTkZlhdSwAnvn2c84cKcnwRxuTJ08eq+OIi+raFaZPv3DpMJzf\n83XvdO35Kk5x4NQB6o5uwI/LbqPk0qVs+qEkffq44abgct0iIyOJ8/Bg6UXHlwKLz6VSskodK2KJ\niAtReZUcsXTfUlb/uppn7hxEwYIF+frrrIEwBXP5jKB33wVPD4NSW7/hbOZZHpz1EHa73dJM2w8l\nMmr7uwyp+y6VK+teV7m8OnUgIwPi4y883q1GNzYcXce+I/utCSa3jG1/bqP2yIYcXNibbv7DWbs6\nP+XL61eVW0VAQAAxsbH0CAigo58fbwMd/fzoERBAtR5RtJ7TnBfH675XkVuZtsoRh0tNT6XayGq8\nUud1uteNxMvLl+DgrCs6detanS7nnTiR9X3+b0gSn5y8h04hnXm71ZuWZDFNk7KvNOe2E/ey+v3H\nKVCggCU5xH0MHpx17+u77154vOu0rlQKqMZbrV/FyI1r/8WpbDYb0dHRJCYkUCEkhMjISH46tpGI\nSZF4LR3GuGfa0LlzfqtjikWSk5Ozfj727qVCcDCRkZH4+/szbOZynlvXj9pekax5+328vfTBhogr\nysmtclRexeFeWf4KWw5sZVyLcRQvXoylS+GFF2DLFquTOU98PDRrBp9P3M9zO+7lydpP8nyT55ye\n45lvxjJi/Sg2DphDzeqlnf7+4n42b85aPpyQcOH96Uv2LOGZRc+y8aGftOer3JS4uDg6hodfsI/n\nCjMTW6c8BB+NZs6wBlSurKFykr2tCQdoPKI7PmYAm16aQtniuXxJl4gb0j6v4jZ2HtvJ6A2jeb3e\nmxQrVhSA8eOhf3+LgzlZzZoweTI82bc8I+sv5tONnzAi7gunZlixfSfDf/kfQ+sPp+odJZz63uK+\natXK+t+LP2xqFtKMU+knWbEzzvmhJNewnd+v8+J9PKefOUveb8+xbNydKq5yRXeGlObwe98T6F2a\nkKF3M+/HbVZHEhEnUnkVhzFNkwELBvBEjWeoUroShmFw8iTExkL37lanc77mzWHoUHiyZxUmNo3l\nrR/fYszar5zy3rbUs7SZ8AAtvF6lf9vqeHl5OeV9xf0Zxr+Dm/7Lw/Cgb40+TNs9jYwM1xhEJu4n\nOjqaULs92308m/oYLF4834pY4mb88/my8+MvaV/0SdrPbcrg8TOtjiQiTqLyKg4zYesETp05TZ8q\nvfH39wfg22+zls8WLmxxOIv06QMPPwxP9biTCffP57XVr/HJD5/k6Hva7SZ1Xn+EgLOV+PLhTtym\nvSXkOl1u6vBDdR9i4W9zOHbyuDXBxO0lJiRQJyUl23N1tI+nXKfpgx9n2N3RfLjjaZq8+gZ2u25N\nE8ntVF7FIU6cOcGL37/I23d/QKmgf5eojh8P/fpZGMwF/O9/8MAD8GyvukxrsZThGz/jf4teIqfu\n/275zvscOLeNxY+9T+nSJXPkPSR3q1kTPD1h06YLj5crWI6aRWvx7dZZ2f9BkauoEBLCxnzZ7+O5\nWft4yg14smMTfuj1A+uSZ1PxmX4kn9GWXiK5mQY2iUMMmD+AsynpfNz0Q4oUybrMumNH1lXX334D\nrVqFN9+EadNgzLRfeXhVOHcG3snXnceR1zvvDb/mxRM7lx1NZ0bSeyxoP4+md1fTcmG5YS+/DOnp\nWUvf/2vK1il8vnYkP/Rfjq+vrzXhxG2tXm2jRZNA5mamXbB0eCnQIyCAxMOH/1m5I3I9Dh07yZ1v\nd+ec/SybB8+gYtAtuuRLxAVo2rC4tE2HN9FqciuWtvuBGpUq/7ONxvPPZ129ef99iwO6kM8+gw8+\ngInfJvHpvl4cSjnEnG6zKVeo3HW/1sUTO9f4+LKCc7z4wQgGP9KfPHnyOP4bkFtGfDy0awf79184\ndfhs+lmCPi7Fgg6xNLi9nnUBxe18+y08NOIbjDsG4T3tDPdiUDslhc1+fsR5eBATG0toaKjVMcWN\nnU1Lp87LT5GQuYJFPedwf53brY4kcktSeRWXZTftNBjbgA5lInmy0SP/bKGRkQGlS8PKlXC7/u24\nwLx5EBUF772XSWKJ1xmzfTTvhL3Dw/Uevub9M202GxWDgphis1169cLfn8Q//tDVC7kppgmVK8M3\n30C9izrqY3MHYqZ78kXHYXh46O4TuTLThLfegs+/j8He6jFmtY2meolqzJkz55J9PEVulmmatH37\nIxbZPuXz0Gk8FnGv1ZFEbjnaKkdc1sStEzl3Lp0HKne9YO/HxYuhfHkV1+xERGSV+uHDPUn85m3G\nhcXw2U+fc+/Ye9lwcMM1vcaVJnaGmibR0dGOji23mL+nDmf3ozSg3sPEJM7gdPJp5wcTt5KWljW4\nbvK6JZjhjzA1fBL1g++mcOHCREVF8c577xEVFaXiKg5jGAYLXn2eQSHDeXxNZwaNnmF1JBFxIJVX\nuWFJqUkM/n4wr9d9h1JBxS84N2UK9O5tUTA3ULUq/PQTlCgBD7VtTP+MDTQJakGbqW1pNbEVC/cs\nJNOeedk/v2nbpstO7KytiZ3iIN26ZS31zLzoR7FmiZoE+Zdk1tZ51gQTt3DiRNaWYQcyN3Li3h6M\nbfYVjUJCdUuDOMWHD3VhZOgMhic+SZd3R1kdR0QcRMuG5YY9EfsEJ06eZHizYQQG/jsYwWbLWjK8\ndy8UKWJhQDexfTs89xz8/DP0jkoirfJYliVN4bfTv9GwVAOqFatG8YDipGems/OPX1m2cwOH1u2i\n2dI0lmSz32ZHPz9aDx9OVFSU878ZyXVq14YPP4T777/w+Mh1I5m9fT4Le8/Fx8fHmnDishISoHVr\nuLd9IguK3sPbDd6la43OBAQEWB1NbjEL1sXTfmZ7Gvj0ZeVbr+Lpqes2IjlN97yKy4k/Ek/TSU1Z\n1GYFtStXueC+t8mTs5Yaztde89dl2zYYPRrmzAFvb5Ny1X4ls9RqUnwTOZVxgpMnfDjzZynql61C\nv2YVeO7R2kxNTtbETslRn3yS9QHL119fePz02dOU/rQMa7qtpVq5O6wJJy5p1aqsJecvDDnB6PQG\n9K7Ul8fqPkKhQoWsjia3qJ927qfxmLZUMMLY+sEwfLw1iV8kJ6m8iksxTZNGXzeiRYm2PNN44CUl\nKTwcevXKWnIo189uz7pq/fPPcPw4nDsHRYrYCQ62U7OmBz4+WR8U/HfasCZ2Sk45fBiqVYNDhyDv\nRbs69Zjek1K+5Xk/4s1rHjYmudu338KTT8LXk1J599D93FmwNq81fJXixYtZHU1ucXsPHqXWhx3I\nb5Zmx7vjuc3/xrepE5ErU3kVl/JN/DcMXfUhs8MXElyx9AXnjh6FSpWyftH1y34fenGg5OTkrH1e\nNbFTclDTpjBgAHTpcuHxVftX0Wd2P35+OF4/d8KwYfDRR7AgNpM3d3bBPAfDwz6jTOlSVkcTAeBY\nko2qr3cj3TzHL6/NpGRgfqsjieRKKq/iMmxpNm7//HY+bfAl7e9qjq+v7wXnv/gCfvwxa2CTiOQO\nEyZkLWefM+fC46ZpUmn47bxd/wMi63ewJJtYz26HwYOzbhVZvBhG7H6eNfvXMKnFFCqWLaer8uJS\nUlLTqPpSP45nHCT+hdlULF346n9IRK6LtsoRl/Hu6ne5u2hDGpW/+5LiCjB1KvToYUEwEckxHTvC\nihXw118XHjcMgwdrRTF112TS09OtCSeWSk+Hvn1h9WqIi4MVSROY+cssRt/3FeVLl1FxFZfjl9eX\nPUMnUso3hGofhrN93xGrI4nIdVB5lWu2P2k/YzaNYVCN/1G06KWDN/bvhz17oNnFm4+KiFvLnx9a\ntoQZ2WyX+GDdB1l5eBmJR351ei6xVnIytG0LSUmwbBnsSlnD8989z1dNxlO5bAienp5WRxTJlo+3\nN9vfH8PteetS57OWbNx5wOpIInKNVF7lmj3/3fP0DI6iapmKeHldOqlv2rSse+K8vS0IJyI5qkeP\n7G8HKJyvMK0qtGL8lm/QbSG3jqNHoUkTCAqC2bPh2Lnf6Dy9Mx80+JQGIXdp+yRxeV5enmx6dzi1\n/ZvTcEwL4uITrY4kItdA5VWuyerfVrPuwDoeqjqAAgUuHXBgmlm/2GrJsEju1LIl7NgBv/566bnH\n6w9kWsI3JKckOz2XON/+/RAamvUzMXYsnLUnEzEtgqjKA2hXJRw/TesTN+Hp6cmat94nNKALTSa2\n4PsNu62OJCJXofIqV2U37Ty56EmervYy5UoVv2BP179t2wYpKdCggQUBRSTH+fhk7d05efKl5+4p\new/+3n7Mjl/o/GDiVDt2QOPG8NRT8NZbYGKnZ0xPbs9fhYdrPEThwtrLVdyLh4cHy94YQouCD9Iy\nugUL4nZYHUlErkDlVa5qwtYJGJmedAiJwM8vX7bPmTEj6xfbbHqtiOQS/fvD+PFZ02X/yzAMBtz1\nMJN3TdLgplxs0ya4/3547z0YODDr2GsrXuNw0h+8Vf9dSpcuaW1AkRtkGAbzX3mBdkWeoN3s1sxf\nvdPqSCJyGaoackW2NBuvLHuFF2q8QVBQ4ctOjoyJgU6dnBxORJyqTp2s/ZtXrbr0XN/affnp6Fp2\nHNCyu9xo9Wpo1QpGjYKePbOOzds9j/GbJzCi8VdULFtak4XFrRmGwcwXB9Gh6EDazwnXFVgRF6Xy\nKlf0zqp3qFukIY0q1CVPnjzZPmfnTjh9GurWdXI4EXEqw4B+/eDrry89lz9PfjpW6si4rROwX3xp\nVtza4sVZH05OnQrt22cd2/fXPqLmRjHsnlFUrxCS7RA/EXdjGAYzXniWdoEDaT+7DbE/6gqsiKtR\neZXL+vXkr3y5aQxPVRtMYGCByz4vJiZrH0gtGRbJ/Xr2hHnzsj6wutjj9Qcyfe8UTidnc1Lc0syZ\n0KcPzJkDTZtmHUtNT6VjdEceqfIUTSs3Im/evNaGFHEgwzCY9eKztC78CBGzWrN47S6rI4nIf6hu\nyGU9t/g5uleMonrZClfc9mDWrKzyKiK5X2Bg1n2P0dGXnqsdVJtS/qX4dnOM84OJw40fD08+CUuW\nQMOG/x5/bOFjlM5bnodrRlGw4OU/2BRxV4ZhMOd/z9Oy4ADazGjN9z/tsTqSiJyn8irZWv3ban48\nsJYH73iEggUv3Rrnb/v3w8GD0KiRE8OJiKX69/8/e3ceZmP9/3H8eZ9Zzuz7WGbsa9lCSFFJSJSK\nIiqVNlGiVKJFhXZUIrtk3ylKEpVSKLLvu7Fkn33Ocv/+OP2+lZQxzj1nZs7rcV2ubzP3mfv9uvRt\nZt7n87nfn/NvHQbo1uBxJm2bSHZ2dv6GEq96/33o3x+WLYPatf/8/OhfRrNi7w8MavgOycnFfZZP\nxGqGYfBZv+doEfMwLae14uvVamBFCgI1r/IPpmny9JdP80S15ymXnPCfzzLNmQO33QYBAfkYUER8\n6qabYN8+z/Pu5+p4RUc2n9rAmt3r8j+YeMWAATBsmGcwV9Wqf37+18O/0ufrF/ig0Rguq1D2vMem\niRQlhmGw8KU+NI1+gJun3MqPv+31dSQRv6efPPIPMzfNJCM7i3aV2xIdHfmfr9WUYRH/ExgInTt7\ntugzODgAACAASURBVJWeKzQolPtrdmbMb2NwuVz5H07yzDTh5Zdh6lTPdOGyZf+8dirzFO2mtaNf\n7QE0vqzufz5KIlKUGIbBly/15erItjQZ14Z12w75OpKIXzNM08y/YoZh5mc9uXg5rhwu+/ByXqgx\niA4NWhEV9e/Na0oK1KgBR46Afo8R8S/bt3seF9i/H+z2v1/bc3IPdUfWZf1DGyhdrJRvAspFMU3o\n2xcWLoSvv4Zixf685jbd3DL5FuJtSbx745sUL57gu6AiPuJyuajfrydbMn5m/TMLqVw20deRRAos\nwzAwTdOS89O08ip/89HPH5EcWpam5a8jMjLiP187bx60bq3GVcQfVaniefNqznlmM5WPK0/jUtcy\nZs0n6A3Lgs804dlnPUfifPPN3xtXgIHfDuTImd/pV/9FEhPjfBNSxMcCAgJYNWAoZYJrUOfdOzlw\n5JSvI4n4JTWv8j9nss4waMUbPFWtLyVKRF3wwHlNGRbxb926wYgR57/W65qeTNw6jvSM9PwNJRfF\nNKFXL1i+HJYuhYRzFlWX7FrCh6uGMfSaj6lQNknPuYpfCwwM4LeBHxMfWIJaAzpy/FSaryOJ+B39\nFJL/GfjtQBoXa0q90jUJCwv7z9cePw5r1ngGt4iIf2rTBnbtgo0b/3nthgo3EB4Uxqy18/I/mOSK\n2w1PPAE//eTZKhx3zqLqwbMHuXfOvbxR70PqVr5Mz7mKACH2YDYP+oTggCCqvXwfZ9MyfR1JxK+o\neRUADpw5wOi1Y+h2eW+KF7/wquuCBdC8OVygxxWRIiwoCB5+GD7++J/XDMPgyaueYNzmceTk5OR/\nOPlPbjd07Qrr1sFXX0HMOce15rhyaDetHR3Ld6FNzWZERIT7JqhIARQeGsLW16fhtKVRve9DZOc4\nfB1JxG+oeRUA+i7pS7uy93JZUhlCQ0Mv+PrZszVlWETgkUdgyhRIO8/uuc51OrP51AZ+3rUm/4PJ\nv3K5PG86bN3qec416jxHeff6ohdhRPNk3SeIj4/55wtE/FxsVDibX57FaWMftZ57CqdT09VF8oOa\nV2Hd4XV8setLHr68O4mJ5/kt5hxnzniOUWjdOh/CiUiBVqoUNGkCkyf/81poUCgP1nqAkWtH69ic\nAsLlggcfhL174YsvIPI8A+Un/zaZz7Yt5M2GQyldKlHPuYr8ixLx0ax9dg77jO9p3Pc13G63ryOJ\nFHn6iSQ8u/hZHq7SkzLF4gkJCbng6xcuhOuuO/+79SLifx5/3DO46XyDhZ+65ik+3zePg8cP5n8w\n+RunE+6913O82eefQ/h5dgJvPraZHl/04L0Go6hWvoyecxW5gEqlivN91wX84p5I2wEfacK6iMXU\nvPq5xdsXs/3ETjpWvo/4+H8/0/Wv5szRlGER+dONN0JmJqxY8c9rpaJL0bRMU0auGqdf6nzI4YCO\nHeH0ac/MgvPNK0jNTuX2qbfTo1o/rqty5QWPSxMRj/pVy7Og/QI+SxtE9w+n+jqOSJGm5tWPuU03\nzy55lh7VXqR4Qjh2u/2CX5ORAUuWwG235UNAESkUbDbo2RMGDz7/9eeufZYJW8dwJvVM/gYTAHJy\noEMHyMrynM99vg02pmnywNwHqRFdj841O5GYGJv/QUUKsZsb1GR005l8nPIUAz5d5Os4IkWWmlc/\nNnndZHAH0KpcK+Licrfqungx1K8P8fEWhxORQqVzZ8/K686d/7zWsExDykWVZ9yqT/M/mJ/LzoY7\n7/Rs6Z49G/7tPcohPw5hy9FtvHTl6yQlxeo5V5E86NKyMa9fMZ6XNz7AuEUrfR1HpEjSTyc/5XA5\neGV5f3pUf5n4eHuun2uaPVtbhkXkn8LD4dFH4f33z3+9z7XPMWrTCDIzdSZifsnKgjvu8DSsM2bA\nv32bX7FvBYNWvMF7V42mYtliudqFIyLn16/jLXQt8y6PLLuTL37a5Os4IkWOmlc/NXLVSIqHJHNt\n8tXExuZu1TUnxzOs6Y47LA4nIoVS9+6eqcOnTv3z2q2X34qJycy1c/M/mB/KyIA2bSA6GqZO9ZzJ\nez5H047SfmYHXqk9mNplKxEVlbufByLy74Z370yb2N60mXkba7bu83UckSJFzasfysjJYOCKQTxV\n8yXi4+0E/dtvNedYuhSqVYOSJS0OKCKFUlIS3HorjBr1z2uGYdD76qcZsX44Docj/8P5kfR0z7+H\n4sXh008hMPD8r3O5Xdw1vT23lLqL1pWbU6yYnnMV8Za5fXtxZfBdXDuiLfuPnOcdPRHJEzWvfmjw\niiHUiK1L3WI1iYnJ/bvsc+ZAu3YWBhORQq9XL/jwQ89OjXN1rtuZvam7Wbp5Wf4H8xNpadCqFZQp\nAxMm/HvjCtDnqz44ckx61HyWpKQYAgIC8i2niD/4YcBASgZUp87Ae0jLyPZ1HJEiQc2rnzmZfpIh\nq4bwVM0XiY8PIfC/frP5C6cT5s/XlmER+W+1a8Nll8GUKf+8Zg+006P+kwxb+xFOpzP/wxVxZ89C\ny5ZQpQqMHQv/1YvO3TSXyRum8Gb9EZRKjszVGd8icnECAmxsGDga0+agTr9uOJ0uX0cSKfTUvPqZ\nN759k+tKtqBqXLmLWnVdsQJKl4by5S0MJyJFQr9+8MYb4DrP72ndG3bnxyPfs27f+vwPVoSdOQM3\n3QS1asHIkZ7ji/7NzhM7eeTzR3m7wVgqlSxGdLSecxWxSnionXV9Z3DAXMONr7yu865FLpGaVz+S\nciaFMb+N4YkafYiPD7moLWKaMiwiudWkCSQkwKxZ/7wWFRLF/TUfYMjPQ3G73fmerSg6dQqaN/cc\nY/bRR//duGbkZHDH1LY8etnTXF2qNiVKxGEYRv6FFfFDZYrH8t1jC/ghezwPDh7r6zgihZqaVz/y\nytJXubVcB8pEXdw77W43zJ2r511FJHcMA158EQYM8Hz/ONfz1z3Hwn2fsfnglvwPV8ScPAnNmkGj\nRp5jiv6rDzVNk0fmP0rpsErcV+VBkpKi9ZyrSD5pcHlZJreex8RjfRk45XNfxxEptHLVvBqG0dIw\njK2GYWw3DOP581yPMgxjgWEY6wzD2GAYxgNeTyqXZMfvO5i5bSZdqz1DQkLoRf3CsmoVREV5nmMT\nEcmNli0954p+9tk/r5WILMG91e/h3R+HaPX1Ehw/Dk2bwo03wuDB/924Agz/aTg/H1zDa/WGUKJE\nKKGhofkTVEQA6HBDHV6/4hNe+q0LM5av9nUckULpgs2rYRg2YBhwE1Ad6GgYxrltTHdgk2matYEb\ngPcMw8jdJCDJFy9+/TL3VH6ExLAIoqIiLuprNWVYRC7WX1dfz/eIV98mfZm3ZzbbD+/I/3BFwLFj\nnsa1VSt4660LN64r963k5W9f4cNGkygZH0ZMTFT+BBWRv+nX6WY6F3+DTgvvZNWW3b6OI1Lo5Gbl\ntQGwwzTNfaZpOoBpwG3nvMYE/n8faiRwwjRNjZIsINYeXMvX+76my2VPXPSqq2nqeVcRyZvbboOs\nLFi06J/XkqKS6HBZe975YbAGmFykI0fghhs8098HDrxw43os7Rh3zWzPq/Xfp0p8KYoXj9VzriI+\nNOHph2gY9ADXj2rLoeM6A1bkYuSmeU0GDvzl44N/fO6vhgHVDMNIAX4DnvJOPPGGfl+/xCPVehId\nEnTRq67r13sa2Nq1LQonIkWWzQavvw59+57/2dcXb3iR2btmsPPwrvwPV0ilpHgGYnXoAK++euHG\n1ely0n56B1qWbkuz5OYkJUXn+og0EbHOdwP6U9Jdl9oD7iYz+zwHY4vIeXnrJ9hNwFrTNJsahlER\nWGIYRi3TNNPOfWH//v3/989NmjShSZMmXoog5/PD7h/45dgvvNlg7EVPGIY/V131Jr2I5MVtt8Gb\nb8K0adCp09+vlY4pTdsqd/Dej0MZ0e5DrQZewMGDnq3CDz4IL7yQu6954au+ZOY46FmzH8WL2/Wc\nq0gBYbMZrH/jY0r1uZkGL/ZkwzvDfR1JJM+WL1/O8uXL86WWcaHtWoZhNAT6m6bZ8o+P+wCmaZpv\n/eU1nwNvmKb5wx8fLwWeN01zzTn3MrU9LP+YpkmzcS24tmQr7q3SkfLlEy+6ea1RA0aPhquvtiik\niBR5y5fDQw/Bli2eIU5/tffUXmp/XIc196+hUlJFn+QrDPbs8QxmevxxePbZ3H3N7A2zeeKLHsy+\n6TvKJkSRlJSgNwhECphdh05y+buNaJ3Yhbl9c/kft0gBZxgGpmla8gMnN9uGVwOVDMMoaxhGMHA3\nsOCc1+wDmgEYhlEcqALoKXQfW7ZjOVtObqFd+XuIj7+4Z10Btm3znB941VUWBRQRv9CkCVSqBGPG\n/PNaudhytKvaljdXvK1nX//Fli1w3XXQu3fuG9ctR7fw2KKufHDdJIpHhOs5V5ECqmJyHAs6zmP+\n6cG8PHG2r+OIFHgXbF5N03QBTwBfAZuAaaZpbjEM4zHDMB7942UDgGsMw1gPLAGeM03zpFWh5cLc\nbjf9v32N7rX6EBrkvuhnXcEzZfiOO/77wHsRkdwYNMgzeTjtHw+TwGs3vsbsXTPYeGBT/gcr4Nat\n82wVHjAAunXL3deczTxLu+l30b3mC9SMqUZycoyecxUpwFo2qMo79acyYNPjzPx2la/jiBRoF9w2\n7NVi2jacbxZv+YqHFj7Cl61/IblEELGx0Rd9j3r14O23Pb84iYhcqvvug9KlPY3suXp9/jQpZ44w\nrdNkrRD+YeVKuP12+OgjuPPO3H2N2+3mtkl3EGxEMqDeUEqWDNaxOCKFROd3xjP16Gv88vhyalUs\n6+s4Inlm5bZhNa9FkMvl4trRTbijUmduL3srFSpc/LOue/dC/fpw+DDoDXsR8YaUFKhVC37+GSqe\n83jryYyTVP6gMgvvXEjDSg19E7AA+eYbz0ThiRPh5ptz/3X9vnyJhTu/YFKzL4iPNihZMsG6kCLi\ndVf2foEdrmXsfXUJcVGRF/4CkQLI18+8SiGzaPMXHEo/RKtSbS/6XNf/N3cutGmjxlVEvCcpyfPc\n5tNP//NaXFgcPer34LXvB+A+37k6fmThQrj7bpg58+Ia1+lrZzB2/VhGNJlBRIib4sXjrAspIpb4\n+c1BhDpKU/e1Lpw+fYYxY8bQ9/nnGTNmDKmpqb6OJ+JzWnktYpxOJ1ePakynyx7jltI352nVFaBx\nY8/ZjK1aWRBSRPxWdjZUrw7Dh0OLFn+/lp6TTsWhlZhw8ye0rNni/Dco4qZNg6eeggULLm5Y3tqD\na2k2qTljbpxH9ehKlCsXR/C5o51FpFA4ejKDMo/UJ+jznbQICuLK9HR+CQ9nhc3GnEWLaNy4sa8j\nivwnrbxKrs3f8Bknsk9yU9JteV51PXwYNm3yHMsgIuJNdjsMHQpPPAGZmX+/Fh4cTt/GL9D/h/44\nHA7fBPShDz7wrEwvWXJxjeuxs8e4Y0Y7+tZ7i8sjq5KUFKnGVaQQCwtyEbF4P3NzcpiTnk4/YE56\nOpNTU2nbqhVp55t8J+In1LwWIQ6Hg9d/GMjTdV4hKCAnTxOGAebN86y42u1eDigiAtxyC1xxBbz2\n2j+vdWvYjTM5pxn304R8z+UrpgkvvOBZjf7hB89zwbmV7cjmzukdaJrcmltKt6VYsSAiIsKtCysi\nlps+fTrXY9L8nM83Bxq73UyfPt0XsUQKBDWvRcisdXNJd6bTrGRr4uND8rTqCp4jctq29XI4EZG/\n+PBDGDsW1q79++cDbYEMuWkwA1cN4Ez6Gd+Ey0cOB3TpAsuWwYoVUPYiBoyapkm3+U/ichs8V+d1\nIiKceZosLyIFy+4dO7gyPf281+qmp7N75858TiRScKh5LSKys7MZ9NMgel/5KjYjK8+rridOwKpV\n0LKllwOKiPxFiRLw1lvw8MPgdP79WsuqLakWX41By970Tbh8kpHhOUv76FFYuhQSLnIw8KClb/Ld\nge/56Pop2IOyKVEiTscMiRQBFSpX5pfw8++g+DU8nAqVKuVzIpGCQ81rETF93UycbhdNit9EXJw9\nzwfSf/YZNGsG//I9U0TEax54AOLjz3/u6wet32f0xpHsOLwj33Plh2PHPHMFEhJg/vyL/5479Zdp\nvP/L+4xvvoDwAEhOjs3zbhsRKVg6dOjACpuNJed8fgmwwmajQ4cOvoglUiCoeS0CsrKzeOOnN+ld\n7zUMMomJyfu5YLNna8uwiOQPw4Dx4+Gjj2Dlyr9fq5JYhXur30ufpX0palPqN2+Ghg09zev48RAU\ndHFf//3OFXRf8gRjm88lITCK5OQoDWgSKUIiIyOZs2gR90RG0jY8nAHAHWHhtAmyUbbD7URE5G13\nnUhRoOa1CJj8yzQCbEFcm9jsklZdU1Ph2289w1RERPJDcjKMHAn33ANnznnEdUDzAfx05Efmrp3n\nm3AW+OoraNIEXn0VBgzwNPAXY/uR7dw1pz1vNBpBpdDKlCwZSlhYmCVZRcR3GjduzO6UFFq//z6Z\nffpwywfvM3fZZn6NXkafTyb6Op6Iz+ic10IuKyuLOiPr8Xz9QVwd34AKFeIJuti38f8wbRpMnAiL\nFnk5pIjIBXTtCmfPwuTJf2/opq+fTt+l/fit6zoiQgv3asOIEZ6mdeZMuPbai//6o2eOcv2EprSr\ndD+dKz1KXJybxMQ47wcVkQJryPSVPLO2DTNvXUC7Rlf7Oo7IeemcV/lXU36dgWEE0CixKbGxwXlu\nXMEzZbhdOy+GExHJpcGDYcsWeP/9v3++Q60OVI6tzMtL+vsklzc4HNCjh+cc1x9+yFvjeib9DLdO\nuZ2rSlzP/ZW7EhHhICEh1vthRaRA69XhajpEDKbjvE5sPbDf13FE8p1WXguxzMxM6o1uSK8rX+Ha\nhEZUqBCX5+Y1M9Mz/XPnTkhM9HJQEZFc2LvX8yzolCnQtOmfn993ah91R9ZlcYfF1Ctfz2f58uLI\nEWjfHiIjYdIkiM1Dv5mVk8Wtn95OaGA07zUaS3BQOqVLJ2Kz6f1nEX9kmlD9yT4cDVnBgYFLCLOH\n+jqSyN9o5VXOa8baubhMN9cXb0FMTOAlrbp+9RVceaUaVxHxnXLlPI1rp06we/efny8bW5bnr36e\nbou7k+PI8Vm+i/Xjj1Cvnmcw02ef5a1xdTgcdJ75INkuF+80GkOALY3k5Hg1riJ+zDBgzTuDcKXF\ncfXrXXG73b6OJJJv9NOvkMrIyGDwL+/Rq+5LuF0ZxMbmfcIwaMqwiBQMTZvCK694zpo+duzPz/e+\nrjcBRgCvLXndd+FyyTRh2DC4/XbPMKpXXoG89JpOp5MnF/Rk+6ldjGw6E5uZTqlScXkeyiciRUdY\nqI2fn5/E5rO/ct+wt30dRyTfqHktpOb89hmZrkyalmxNVJTtko5JyMmBzz+HO+7wYkARkTx6/HHo\n2BFuvtkzxAnAZtiYdOenjNgwnB93/ejbgP/h+HHP99Jx4zwrr61b5+0+LpeL5xb15ZsDy/ikxWfY\nXFmULh2jI3FE5H+qlo9i6m1zmHpwKEMXFJ2p7CL/Rc1rIZSRkcF7v7xHz7ov4XKmExd3aauuy5ZB\n1aqeIytERAqC/v2hQQNo08ZzjBdAxfiKvH7d6zy88GHSs9J9mu98li6F2rWhUiXPubWVKuXtPi6X\niz6L+rFg1wKmtfqaEBNKl44iJCTEu4FFpNC788bK9C43iWd+fIzvN633dRwRy6l5LYTmrV/EGcdp\nmie1ITLSwG63X9L9NGVYRAoaw/Bsva1SBVq0gNOnPZ9/vOHjlIkqw9MLn/ZtwL/IyIDevaFzZxg/\nHt59F/L6bdnlctH3i5eZvXMO01stJcwdSHJyhM5yFZF/9Xa3ZjR29qXlhI4cP3vK13FELKXmtZDJ\nzMxkyK+D/1h1zSA+/tJWXV0umDdPz7uKSMETEOB5ZvSqq+CGGyAlxTPBcNJdk1i0dxHjfxrv64gs\nWwa1asGhQ7BuHTRvnvd7uVwuXvryVWZun8H0VksJN4NITg4jIiLce4FFpEj6+o0eRJ6pz1VvdMHl\ncvk6johl1LwWMp9tWMzvWce4uVRbwsLMS95G9sMPkJQEFSp4KaCIiBcZBgwZ4jlu5qqrYPVqSAhP\nYGrbqTz77bNsOLTBJ7mOH4dHHvGstg4ZAlOnXtq0dofDQc8FvZm+fTrTWy0l0rSTlBRKZGSE90KL\nSJEVFGSw+tURHDh7iLZD+qOjKaWoUvNaiGRkZDDkl8E8VfdF3M4sEhMvbdUVNGVYRAo+w4AXXvBs\nI27dGkaNgkblGtOnYR/unnM3ZzLO5FuWnBxPs3r55RASAhs3wq23Xto9s3Oy6TL7UZYdXM7s1t8S\nSQhJSaFERV3693gR8R+lS4Yyp8NMPjs6jrfnzPB1HBFLGPn5zoxhGKbeCcq72as/o9d3PVh6x0aC\nbGmULVsMw8j7+b9uN5QtC19+CdWrezGoiIhFNm+Ge+6B0qVh1CiTp5bdzZnsM0y9fSqzZ81m944d\nVKhcmQ4dOhAZ6b3mz+WCWbPgpZc8g5jefReqVbv0+6ZlpHHPzM4czvid8c3nE+B0kJwcrhVXEcmz\nPsOX887+Diy950ua1Kzj6zjihwzDwDTNvDcp/0Err4VERkYGQ34dQo86/XA7sklMjLikxhU82+8i\nItS4ikjhUa0a/Pwz1KgBNWsa1Ds8kYObDlG2ZHEW9exJ+Ntvs6hnTyomJ7NixYpLrudwwKRJnnpD\nhsCHH8KiRd5pXFNOpdB84s2kO3P4tMVCAl0OSpWKUOMqIpfkzW5NuCb7JVp/eg/HTh/3dRwRr9LK\nayExd/Uinvj2cZa33UwAqZQvX/ySm9fnnoPgYBgwwEshRUTy0ebN0KNHKiuXJTHPncZfZyUtAe6J\njGR3SgoRERffDB44AGPGeP5UqgQvvgjNmnm2MHvD2v3raDfrLpqWaU2fOoMw3WcpVSqa0NBQ7xQQ\nEb+Wk2NSqttDRBY7wdZXZxEUFOTrSOJHtPLq5zIyMhi6dghP1n4BtyPHK6uupul53lVH5IhIYVWt\nGnToMJ1mwSbnDvltDjR2u5k+fXqu7mWasHs3DB0K117rmSB84gQsXgzffuuZIuyNxtU0Teaum0+L\nqS14pGYvXqgzCJtxljJlYtW4iojXBAcbrOr/EQdOH+XOD/rjdrt9HUnEKwJ9HUAu7JutK9hxZitj\nKt5HgJlKRETMJd9z3TrP/9aufcm3EhHxmT07d9AgK/281+qmpzNp4k6iojzPyEZEQGgoZGbC2bOe\n1dXt2z1Dl1as8MwBuPlmeP55zyrrJQ5z/4ccRw4vLe7P+E3j+PCGydSNuYqgoDSSkhIIDNSPYxHx\nrnKlQpl55wzu+OIa3p5XnT5tO/k6ksgl00/LAi4jI4P3f/2Arlf0xnQ4SSgRfsmrrvDnqqu3tsCJ\niPhChcqVWRQeDun/bGB/todjD63E1KmeRjU93dO4hodDZCQkJ0Plyp4JxoMGeY4Ms+p74oETB7hv\nzoOkOTJYePsqIs1woqMdJCYmYLNpE5SIWOO2pmV4euMk+q1qT4OKVWh6RT1fRxK5JHrmtYD7+rfv\n6Phle35ovwObK50KFYp55Redyy+HCRM85yaKiBRWqampVExOZnJq6j+eeW0XEsT+o8eIibr03Sp5\n5Xa7mbxmKr2X9+aOivfwTJ1XcTvSKFEilOjoKJ/lEhH/cs2TH/Fb6DB2PL+MpPgSvo4jRZyVz7yq\neS3AMjMz6TD9fqoXq8ODlbqTmGgSGxt9yffdvBlatoR9+7TyKiKF34oVK2jbqhWN3W7qpqfza3g4\n3xsGpbpVIrRiKDM7zCQ5Ojnfcx06eYgnF/ZizbHVDLl+AjWj6hAYmEFycix2uz3f84iI/8rONinV\n9VGik46w8eWZhNi9/FyEyF9oYJOf+mX3BlYc+Yb7LuuKYWQQFeWd4xNmzYK2bdW4ikjR0LhxY3an\npND6/ffJ7NOH1u+/z57Dh1k1cBVXl7yGK0fVY/6m+fmWJysnizeXvsMVo2oTFZzIl21+pXpENWJi\nnJQrV0yNq4jkO7vdYOXL77P/xAnu/uhVXC6XryOJ5IlWXguozMxMuszpRmJEEj2qv0BsrJP4eO9s\nfbviChg2zDNRU0SkqJv96xyeXv40Vxavy/A2wykRac2WOafTyfR1M3htxQBi7Qm83ugDyoaUJzAw\nk5IldQyOiPjezC/3cvfX1zLg6jfo0/Yer8xRETmXtg37oTXbNtBszvV8e9cWQlwmFSt6Zxrljh2e\npvXQIQgI8EJQEZFC4GTqSfoueZHp26fycO2H6Xt9X2JDY71y7/SsdKb+Np33fnoPmxFIr7qvcH3x\n5phmOomJoURHR2ook4gUGD3e/pbhp+5iyd2LuEEDnMQCal79TFZWFt3mPY0tMIg+tQcRFZVNsWJx\nXrn3m2/C/v0wfLhXbiciUmiYpslve9fzxo9vsXj/F7StegePX/U49ZLqXfTqg9PlZOW+lUz9bTrT\nt02jSkx1Hq35NI0Sb8A0M4iPtxMTE6kjcESkwHG7TRp0+5Bt0aPY2nsJyYklfR1Jihg1r35mw85t\nXDvzapa0+41IdzAVKsQSHBzslXvXr+9pYG+80Su3ExEpdNxuNxv3bWL8uonM2j0Dt+miZcWWXF26\nIVcmXUnF+IpEBkf+r6F1m24Onz3MrhO7WH1oDT8fWMW3B5cTERRF89JtuKvSA5QKTSYgIJu4uBCi\noiLUtIpIgZaa6qT0k11IKp3Jmhc+ISwszNeRpAhR8+pHsrKy6P35S5x0nuL1+h8SFpZOyZIJXrn3\nvn1Qrx4cPgz6vUpE/J3b7SY9PZ0fd65h6f5lbDyxnm2nN3EkMwWX6SY0IBSn6STblU1EUARJYaW4\nLOYKasbXpWHx6ygXWQ6bLYfw8ECio0MJDQ3V9mARKTTWbTxNvRFN6VitHWMfedZrCyUial79yPa9\ne2k4rT4LbvuRRFsMZctGEhLinXHmQ4bAxo0wdqxXbiciUmS4XC6ys7PJyMgmI8PBqfSzZORk/ZSo\ntgAAIABJREFUEWAEEhIYij3AjmGYBAYa2O2BhIUFERISjN1uV8MqIoXW8KmbeWLdDQxvMopHWtxC\ngAaiiBdY2bxq/a0Ayc7OZvS68VybfCPJIWUICjrrtcYVPEfkvPii124nIlJkBAQEEBYW9r+tc2Uo\nhtvt5q9vuNpsNk3mFJEipVvHaixbP4onv3ucOmUr0ODyGvo+JwWaVl4LkD0HDnLVlHpMafUVpYKS\nKFs23GtHK6SkQI0acOQIaFeIiIiIiAA4nW6qPPwaqSW+5Lde80kqXtzXkaSQs3LlVXudCoicnBwm\n/DaZK4rVp1LkZYSEuLx6JuDcudC6tRpXEREREflTYKCNFW/0Ie1YMe4a8yKpqWm+jiTyr9S8FhDH\njp9k3NYRPFm7L9nZaSQmRnj1/rNnw513evWWIiIiIlIEJJUMYW7nkfz0+7e8MnsiWVlZvo4kcl5q\nXgsAh8PB5PUzKR1Vntrx9QkKyvHqyPKjR+HXX6FFC6/dUkRERESKkJZNSvJs2Um8v+0V5v/8A06n\n09eRRP5BzWsBcOLkGUZtGUaPOv3IzEwjISHcqw/Lz57t2TLsxV3IIiIiIlLEDHqqHlefeo8Hv3iE\njbt24na7fR1J5G/UvPqY0+lk5ob5RNqjuaZ4EwIDs4iICPdqjenToUMHr95SRERERIoYm83GF+/c\nTfjBW7ljUg+OHD2Ohq1KQaLm1cdOnTrLqC0f8eQVL5CVlUFcnHcPuU9JgQ0b4KabvHZLERERESmi\nIiODWfrCqxw8ms3j09/l9Omzvo4k8j9qXn3I5XKxaOtSslyZNC9zK4aRQVSUdwc1zZoFt94KdrtX\nbysiIiIiRVSt6jGMaDqGzw9OZfjSz8nIyPB1JBFAzatPnT2bxpjNH/P4Fc+SnZVFbKydgIAAr9bQ\nlmERERERuVhd2lekY9B4+v/ai+XrfyMnJ8fXkUTUvPqK2+3mux2r2Hl2G7dX7IRpphMd7d1V1wMH\nYNs2aNbMq7cVERERkSLOZrMxtv91VDzQj04LHmH7noO4XC5fxxI/p+bVR1JT0xi9aSSP1OyJ6XAT\nHR1IUFCQV2vMmAG33w7BwV69rYiIiIj4Abs9mCWDuuA8UJf7Zr7A4cMnNMBJfErNqw+43W5+3bOF\nH44u457LHsXpTCMmxrurruBpXtu39/ptRURERMRPlC4dyewH3mLD4e288sV4Tpw47etI4sfUvPpA\nenoGYzaN5t7LHiXIHUxEhIHdyxOV9uzx/Gna1Ku3FRERERE/0/yG4vSrNIEJuwYze/UPpKam+TqS\n+Ck1r/nMNE22HtjL5/tn81CNp3A40oiLs2bVtW1bCAz0+q1FRERExI/YbDb6db+cG06PpMf3j7F2\nx26ysrJ8HUv8kJrXfJaRkcGEzZ9wa4X2xATGERrqJjQ01Ot1NGVYRERERLwlODiY6QNvJH7PI3Sc\n+zh79h/D6XT6Opb4GTWv+WxvylGm7ZzAYzWfITs7jfj4cK/X2LEDUlLguuu8fmsRERER8VPx8ZEs\n6vMExw/G8ORnb3H48EncbrevY4kfUfOajzIzM5m0eQoNk66nbEQFgoJyCAsL83qdGTPgzjvBy0fG\nioiIiIifq1UzjuHNP2TZwcWMWPEZv/9+yteRxI+oec1HR34/xSfbR9L9iufJzEwjISEcwzC8Xkdb\nhkVERETECjabjXvbJXN/6Ce8vaEP323bzJkzZ30dS/yEmtd8kp2dzYzNcykfXZmacXUJCMgiIsL7\nW4a3bIETJ6BRI6/fWkREREQEu93OkOdrUf3A23T5sgtb9x4hMzPT17HED6h5zScnT6YybtsIul3x\nHJmZ6cTHh2Kzef+vf/Jk6NgRLLi1iIiIiAgA0dGRzH21DbY9N/Hggmc4cPAUDofD17GkiFOLkw8c\nDgcLtn5JoC2Q65NbABlERXn/eBzThClToFMnr99aRERERORvypWLZdqDfdlx8CSvLh1NSooGOIm1\n1LzmgzNn0hi79eM/Vl0ziIuzE2DBNKWVK8Fuhzp1vH5rEREREZG/sdlsNL0+nv7VxzBt90jmbVjJ\n0aMnMU3T19GkiFLzajGn08k323/kcMZBbil/F253OtHR3l91Bc+q6z33gAUzoERERERE/sFut/Pk\nA6VomT6BZ3/syoYDBzl9WgOcxBpqXi2WmprO6C0f81jNZ3DmOImODiQoKMjrdRwOzxE52jIsIiIi\nIvkpKiqSUX2vJGnPM9z72UPsTzlDRkaGr2NJEZSr5tUwjJaGYWw1DGO7YRjP/8trmhiGsdYwjI2G\nYSzzbszCye12s2r3etYe/5m7q3bB6UwjNtaaVdclS6BSJahQwZLbi4iIiIj8q5IlY5nRqzOp+yrx\nxKL+HDx4hpycHF/HkiLmgs2rYRg2YBhwE1Ad6GgYxmXnvCYa+Ai4xTTNGsBdFmQtdNLS0hmzeTQP\nVOtOgDuQsDATu91uSa3Jkz1bhkVERERE8pvNZuOKK2IY2eodVh74mY9XzyUl5RQul8vX0aQIyc3K\nawNgh2ma+0zTdADTgNvOeU0nYLZpmocATNM87t2YhY9pmmzev5slBz/ngepPkJOTRny8Nauu6emw\ncCHcpbcMRERERMRH7HY7t7eK5bHYT/lgY39+2LuFY8dOaYCTeE1umtdk4MBfPj74x+f+qgoQZxjG\nMsMwVhuGcZ+3AhZWGRkZjN88gbaV7iEyIIrgYCehoaGW1Jo/H665BooVs+T2IiIiIiK5EhUVyUuP\nl+XKwx/xyJL72X3kpAY4idcEevE+dYGmQDiw0jCMlaZp7jz3hf379//fPzdp0oQmTZp4KULBsjfl\nKDN3f8rnt/9MVlYaSUnhGBaNAdaWYREREREpKIoVi2X8c9dx3Wt303lBNxbc9Sl2exBhYWG+jiYW\nWL58OcuXL8+XWsaFlvENw2gI9DdNs+UfH/cBTNM03/rLa54HQkzTfPWPj8cAX5imOfuce5n+sG0g\nMzOTAV8PYd2pX/n4hunk5PxO+fLFsNm8P9z599+hcmU4eBAirNmVLCIiIiJyUbKzs1n27UnazLiP\nW+vW483mPSlbNo7g4GBfRxOLGYaBaZqWrNrlpptaDVQyDKOsYRjBwN3AgnNeMx9obBhGgGEYYcBV\nwBbvRi08jh0/zafbR9O1Zm8yM9OJjw+zpHEFz/E4rVurcRURERGRgsNut3NNwwgG1h3J/N1Tmbf1\nO1JSTuF2u30dTQqxC3ZUpmm6gCeAr4BNwDTTNLcYhvGYYRiP/vGarcBiYD3wEzDKNM3N1sUuuHJy\ncpi3dSHFw5Ook9gAw8ggMjLcsnraMiwiIiIiBVFUVCSd28Vwu2MyfVc+wZZjhzh69KQGOEmeXXDb\nsFeL+cG24aNHT9BiZkt61OnLdcWaExvrICEh1pJaO3bAtdfCgQMQFGRJCRERERGRPHO73ezZ8zst\n+83lRKUPWdLhCyqUiiY2NtrX0cQivt42LLnkdDpZumMFZx2naV7mVtzudKKjrdvPO3EidOqkxlVE\nRERECiabzUbp0rF82vN2cvY0oOuiZzlyJIuMjAxfR5NCSM2rF509m8a4baN5tObTOHJyiI4OJMii\nztLt9jSvDzxgye1FRERERLwiODiY6tUjGHX7QNbu38mHqydx6NBZHA6Hr6NJIaPm1Uvcbjdr9m5k\n3fFVtK9yPw5HGrGx1q26Ll8OcXFQq5ZlJUREREREvCIyMoJm14fQK2kSoza/w4oDGzl06KQGOMlF\nUfPqJWlp6YzbPJb7Lu+KzRVARISB3W63rN6ECVp1FREREZHCIyEhhifujaPR7+N4fGln9p8+ze+/\nn/J1LClENLDJC0zTZM2WTTSbfy3f3bWVEFcgZcqEERoaakm91FQoXdozsCkx0ZISIiIiIiJe53A4\n2LbtBM1eG01QtS9ZeNcsyiSHExMT5eto4iUa2FTAZWZmMnHLJG6tcBcxQXHY7U5CQkIsqzdrFjRp\nosZVRERERAqXoKAgypWL5NNHu3JsbzzPfzOII0cyyczM9HU0KQTUvHrBwSO/M3XneB6t+TRZWWnE\nx4djGJa82QB4tgzff79ltxcRERERsUxERDh1agfyXuPhLNnzBdO3fMmhQ2c0wEkuSM3rJcrOzmbq\nlpnUKdaA8pGVCQzMJjw8zLJ6u3fD5s3QurVlJURERERELBUfH8NtNwXTKWA6A1b3ZuPv+zl8+JQG\nOMl/UvN6iU6cPMsn20bRtVZvMjPTiY8Pw2az7q914kTo2BGCgy0rISIiIiJiKcMwKFkyjhcfSabq\n3sF0XtiJY2czOX78tK+jSQGm5vUSOBwO5m/5gih7NA2KNcYwMoiMDLesns52FREREZGiIjAwkNKl\noxnXsyXsuJkHFzzJ78ednD2b6utoUkCpeb0EZ8+mM27rSB6r9QxZWZnExtoJCAiwrN7330N4ONSp\nY1kJEREREZF8ExoaSuXKwYzv+DJb953knZ9GcvhwBllZWb6OJgWQmtc8crvdLN+xkiOZh2hVrh1u\ndzrR0RGW1hwzBrp0AQtnQYmIiIiI5KuYmCiuucrghUoTmbT1Y77Zv5pDh07jdDp9HU0KGDWveZSW\nls7YLaN5uEZPnDkOoqMDCQoKsqzeqVPw2Wdw332WlRARERERyXeGYVCsWCwPtAuj2dlJ9Fz+MPvO\nnOTIkZOYpunreFKAqHnNA9M0WbtnCyuPfkvHqg/hdKYTG2vtquukSXDzzZCQYGkZEREREZF8FxAQ\nQHJyLO8+UY1i25+n0/z7OHHGxYkTGuAkf1LzmgeZmZmM3TSWTlUfJsgMJizMxG63W1bPNGH0aHj4\nYctKiIiIiIj4lN1up0yZMCY90ZnTuyrz1Fd9+f13B2lp6b6OJgWEmtc82JVykAX7ZtKlRg+ys9OI\nj7d21XX1akhPhxtusLSMiIiIiIhPRUVFUq2awbAWQ1mxZzUTNs4hJSWVnJwcX0eTAkDN60XKzs5m\nwoZPaVbmFhKCi2G3OwkNDbW05v+vulp4fKyIiIiISIEQHx9DiyY2Hoqcznu/vszaYzs5dOgULpfL\n19HEx4z8fAjaMAyzsD90fejwUa6cVJeJLRdSNrgsSUlBREZat/KamgplysDmzVCypGVlREREREQK\nDIfDwd69J+j02o9sLtOLpR2WUzYxkhIl4jF09EaBZhgGpmla8i9Ja3kXwel0MnX9bCpEV+HymJoE\nBmYTHh5mac3p06FJEzWuIiIiIuI/goKCKFUqmlFPNyZ0Zyc6zX2YE6fcnD591tfRxIfUvF6Es2fT\n+GT7GB6t2YvMzHTi4kKxWbyXV4OaRERERMQfhYaGUq6cnSmP9ObgARsvfTOYo0ezyczM9HU08RE1\nr7nkdrtZsu1b0pyp3Fi6NZBBVJS1g5rWr4eUFGjZ0tIyIiIiIiIFUkxMFDWrm7x39VgW7JnG3K3f\ncujQGRwOh6+jiQ+oec2l9PQMxm4ew8M1niIrM5O4ODsBAQGW1hw9Grp0AYvLiIiIiIgUSIZhULx4\nHLfeaOc++1Re+rk7W48fJSXlJG6329fxJJ+pec2ldXs3s+b3ldxV+X7c7nSio61ddU1LgylTtGVY\nRERERPybzWYjKSmWvg+Up8bR17lnfidOpDo5fvy0r6NJPlPzmgtZWVmM3TiOu6t2IcAVSFRUAEFB\nQZbWnDQJrr8eSpe2tIyIiIiISIEXHBxMqVJRjHviDoyUhnSe/TQnTrg4ezbV19EkH6l5zYV9Rw4z\nb+8MHqz+JA5HGrGx1q66miYMHw7dullaRkRERESk0AgLC6N8eTtT7hnItmO7eHP5RA4fziA7O9vX\n0SSfqHm9AIfDwYT1n9Kk1E0kBBUjLMwkJCTE0porVkBODtx4o6VlREREREQKlZiYKOrUDOSNOpOY\ntPcdluzYwKFDp3C5XL6OJvlAzesFnDx9hk+3j+WRmr3IyUknIcHaVVeAjz7yrLrq/GURERERkT8Z\nhkGxYrHc2SyWuwLH0WtFZ/acSOXIkZOYpunreGIxNa//we12M2PDPEqGl6JmXF2CgnIIDQ21tOaR\nI7B4MXTubGkZEREREZFCKSAggKSkWF67vy6VTnan/cz7OXHazalTZ3wdTSym5vU/pKWlM37LaB6p\n2YvMzDQSEsIxLF4OHT0a2reHmBhLy4iIiIiIFFr/P8Dp08ceIudUcbrMeomjR3NIS0v3dTSxkJrX\nf2GaJt9sW8GxzKO0KNOGgIAsIiLCLa3pdMLIkRrUJCIiIiJyIWFhYVSsEMrkdu+z7uQPvPftLA4f\nTiUnJ8fX0cQial7/RVZWFqM3juahGj1wZGcTHx+KzWbtX9eCBVCuHFxxhaVlRERERESKhJiYKK6q\nE87AGlMZt+dVvtq6kZSUU7jdbl9HEwuoef0XGw9s54cjy7m7ahdMM53ISGtXXeHPQU0iIiIiInJh\nhmGQmBjL3S2Kc1fgOHr+0JntR07w+++nfB1NLKDm9TwcDgej1o7mziqdCXIFERMTTGBgoKU116+H\nLVvgzjstLSMiIiIiUqTYbDaSk+MZ+OCVVDnRk/Zz7yPlWCanT5/1dTTxMjWv53Ho9yPM2jOVh6r3\nwOVKJybG+uNxhg6F7t0hONjyUiIiIiIiRUpgYCClSsUwuXtnOF6V+2Y+z+HDGWRlZfk6mniRmtdz\nuN1uxq+dRMMS11E8OInISBvBFneUR4/C3Lnw2GOWlhERERERKbJCQkKoUCGcqR3fYtvJLfRf/CmH\nDp3G6XT6Opp4iZrXc5xNTeWTbWN5tObTOBxpxMZa/6zriBGe43ESEiwvJSIiIiJSZEVFRVK/dgRD\nG37KzJTBTFu9hsOHT2Kapq+jiRdY+yBnIWOaJrN+W0BUcDS14xpgGKcJDQ21tGZWFnz8MSxbZmkZ\nERERERG/EB8fw+03ONlwYCIvr7uXqsUWExISSGJinK+jySXSyutfZGVlMXrTSB6r9QzZ2ekkJlr/\nrOuUKVCnDlx+ueWlRERERESKPMMwKFEijj4da9Ewqx/3L7qP3QfPkpqa5utoconUvP7F9zt/Yn/a\nHm4u25bg4BzCwsIsrWeankFNvXpZWkZERERExK8EBASQnBzH2K53EZXWgPZTn+bgobNkZ2f7Oppc\nAjWvf3A4HAz/dQQPVn8SZ3Y28fFhGIZhac1vvgGXC5o3t7SMiIiIiIjfCQoKomzZGGY/2J+j6Ud4\ncuYoDh06hcvl8nU0ySM1r3/YfngXyw4toWPVhzGMTCIirB/UNGQI9OwJFvfIIiIiIiJ+KTQ0lBqX\nxzC2xRiWnRnLsK+/58gRDXAqrNS84jkeZ/jqkdxW8W5CzRDi4kIICAiwtOamTbBmDdx7r6VlRERE\nRET8WlRUJDc1KskLFT9h6K7uLP51N6dOnfF1LMkDNa/A8dMnmLZjEg/XeAq3O52oKOtXXd9+G3r0\nAIuHGYuIiIiI+L34+Bi6316L1sGD6PrtPfy69Shpaem+jiUXSc0rMHbNRGonNiA5pAxRUYEEBQVZ\nWm//fvj8c+jWzdIyIiIiIiKCZwJx8eJxfPjQrZTPup32s7qye98JcnJyfB1NLoLfN6+ZmZmM3zyG\nR2r1wuFIIzbW+uNxBg+GLl0gJsbyUiIiIiIiAthsNkqVimf2471wZ4bT8dPXOXTopAY4FSJ+37wu\n3PwlJgYN4hsTEWFgt9strXfiBEycqONxRERERETyW2BgIJUrJTCz4wdsz/yJXtMmc+zYKQ1wKiT8\nunl1Op18vHYkD9fogcORTlyc9c+6DhsG7dpBUpLlpURERERE5Bx2u51G9UowvPFEFpx6l/c//47T\np8/6Opbkgl83rxsPbuKX46tpU+5ugoOdhFo8PSk9HT76CJ591tIyIiIiIiLyH8LCwmjfoiK9y4zn\n7Z1dmfv9ZjIyMnwdSy7Ab5tX0zT5cNUIOlR5EJvLJCEhHMPiA1fHjIHrroMqVSwtIyIiIiIiFxAd\nHcVzd19F6+DX6PptZ35ev18DnAo4Iz/3dxuGYRaU/eRHTx2l6seXs+i21RS3h1O+fDFsNut6+Zwc\nqFwZZs2C+vUtKyMiIiIiIrlkmiZHjpzgxrcGkmL+xsruE6laKcnSvqCoMwwD0zQtWRX0238rY1Z/\nQsMS15EQmEhcXKjl/wedMAEuv1yNq4iIiIhIQfH/R+gsePI5AtyhtBnxGocPn9AApwLKL5vXrKws\nxm0aw0M1ngIyiIqy9nicnBwYNAheecXSMiIiIiIicpFsNhvlyiay4P732c+PdPl4ogY4FVB+2bwu\n2LSQYJud2jH1iYuzExAQYGm9iRM9z7lefbWlZUREREREJA8CAwOpX6sM45qPZ0nOO7wycakGOBVA\nfte8ulwuRvz6MQ/V6IHbnU5UlLXH4zgcMHCgVl1FRERERAqy4OBg2jWtycuXjWFYSlc+WfSbBjgV\nMH7XvP52YD2/nVjLzaXaERkZQHBwsKX1Jk6EihWhUSNLy4iIiIiIyCUKCQmh91030D62P0+uvJdl\nP+/C5XL5Opb8wa+aV9M0+fDn4XSs8hABpou4OGufddWqq4iIiIhI4RIREc7Ix++lTuCdtJ31IFt2\nHNIApwLCr5rXY2eOMXf3bO6p+ihhYSYhISGW1ps0CcqVg2uvtbSMiIiIiIh4UXR0FAufeZ4YsyzN\nPnqao8dO+jqS4GfN6+hV42hU8gbiA2OJj9ezriIiIiIicn6JibEs6zmYdNthWrz1Bqmpab6O5Pf8\npnnNzslmzMYxdKn+JEFBOYSFhVlab9w4z6rr9ddbWkZERERERCxgGAaVyyexqPM4thjz6PjOeLKz\ns30dy6/5TfM6f+MCwgMjqRFVm4SEcAzDsKxWZia8/rrnbFcRERERESmcDMOgUZ3KfHLTJBZlD+C5\njxfidDp9Hctv5ap5NQyjpWEYWw3D2G4YxvP/8br6hmE4DMNo672Il87tdjNszXC6VH+SgIAsIiKs\n3TI8bBg0aOD5IyIiIiIihZfNZqN903q8XnM0H6Z05ePZq3C73b6O5Zcu2LwahmEDhgE3AdWBjoZh\nXPYvr3sTWOztkJdq7YG1bD65iZuS2xAXF4LNZt2C85kz8M47MGCAZSVERERERCQfBQYG8lyHm3mg\n5Os8taoTX67YrgnEPpCbLq4BsMM0zX2maTqAacBt53ndk8As4JgX83nFBz95jscJMlxERVl7PM67\n70Lr1lCtmqVlREREREQkHwUFBTHi8Qe4Lqojd8y4j03bj/o6kt/JTfOaDBz4y8cH//jc/xiGkQTc\nbprmCMC6h0nz4NiZY8zfPYe7Kz9EbGwwgYGBltU6ehSGD4f+/S0rISIiIiIiPmK321n47EuUCatE\n48FdOXrsrK8j+RVv7Z8dCvz1WdgC08B+vGo015ZsRkJwFNHR1j7rOnAg3HsvlC1raRkREREREfGR\nsLAwfuzzEQERp2jw8vNkZGT5OpLfyM0y5CGgzF8+LvXH5/6qHjDN8IzwTQBuNgzDYZrmgnNv1v8v\ny5JNmjShSZMmFxk593IcOYxZP5rBjT4hPNzAbrdbVmvXLpg8GbZssayEiIiIiIgUAIlxcfzUcxK1\nhraiSb93+PGdFyzd4VmQLV++nOXLl+dLLeNCDxobhhEAbANuBA4Dq4COpmmet00zDGM88JlpmnPO\nc83Mzwebp62dzqAVbzOj+WLKlg0nNDTUslp33gl160LfvpaVEBERERGRAuTHjVu57pObaBPRj1kv\nPWzpYNjCwjAMTNO0ZCfuBf92TdN0AU8AXwGbgGmmaW4xDOMxwzAePd+XeDljnpimybBVw7n/su6E\nhLgICQmxrNaKFbB6NfTqZVkJEREREREpYK6pcRlTb5nOvIyX6PXhAk0gttgFV169WiwfV15/OfAL\nN09pxdJbf6Nc6QgiI62ZMux2Q8OG0LMndOpkSQkRERERESmgTNPkg/lf0GvlA7xdaw6972ns60g+\n5dOV18Jq6I8f0rHyw4TZITw8zLI6U6eCYcDdd1tWQkRERERECijDMOhx2808U/VdnlvXgemLN/k6\nUpFVJFdej509RuVhVVjYahU1ypUgJibKkjoZGXDZZZ4GtlEjS0qIiIiIiEgh4Ha76TT0XWbtH8uy\n+77m2itL+zqST2jl9SJ9vGokTZJbUjw8ishI647HGTLEs2VYjauIiIiIiH+z2WxM6dmba+JuptnY\n9mzbfcrXkYqcIrfymuPMocLQigy9ZiJNqtQmISHWkjopKVCrFqxaBRUqWFJCREREREQKGafTSc2X\n7+Pg8TR2DZpJsQTrBscWRFp5vQizN84mMaQkNeOrER1tzZAmgN69oWtXNa4iIiIiIvKnwMBA1rw8\nlsiYLP6vvXuPt3rO9zj++m67orV3JZeumFK559I5CeUgXdQIoSTRhdMcRufMYFzGjHGO6zkubaoZ\n1LhfdshgiimaDBOVZISGkkZEM5jpslG7+p4/1mK2RFuty29tr+fj4fHY67d+6/v7rMfjY9e73+/7\n/e57yb+zuqq60CXVGXUuvN40awyndfgBjRptQ7169XJyjRkzYOZM93SVJEmS9FWpbRsy/9IHWVv+\nJvudfx7V1RsKXVKdUKfC64tLX2TxisX0bN2b7bfPzV3X6mo45xy44QZomLtFjCVJkiQVsR0aNeFP\nFz7K8oa/5+DzL2fDBveA3Vp1KrzeOLOCgW2H07islG23zc2z5TffDK1bwwkn5GR4SZIkSXXEbjs3\nY9YPH+fV+vfQ45KKQpdT9OrMgk3LVy2nw8178ESfWezfvjWpVPZXGX7/fdhvv/Qjwx06ZH14SZIk\nSXXQs6++zpF39eSE1P/w4GXDCl1OTrlgUy38ctavOKpVH5o3akzDHD3Pe8EFcNZZBldJkiRJtddt\n37155KRHmPTJRYy8blKhyylapYUuIBuq11dz67xbqTjkLnbcMUUI2Q/6Tz0Fzz4Lr7+e9aElSZIk\n1XHHdv5Xfr36foZNHciOtzTmypHdC11S0akTd14fnP8gLRruwoHN96GsLPuPC3/yCYwkphu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iRJkqTEM7xKkiRJkhLP8CpJkiRJSjzDqyRJkiQp8QyvkiRJkqTEM7xKkiRJkhLP8CpJkiRJSjzD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\nRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "bo = BayesianOptimization(f=lambda x: f[int(x)],\n", + " pbounds={\"x\": (0, len(f)-1)},\n", + " verbose=0)\n", + "\n", + "bo.maximize(init_points=2, n_iter=25, acq=\"ei\", xi=0.0, **gp_params)\n", + "\n", + "plot_bo(f, bo)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Prefer exploration (xi=0.1)\n", + "\n", + "Note that the points are more spread out across the whole range." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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6dtcPpqMAAAD4DcorAGOmpM9VE+tqlS9f1nQUv5JQ8xyV/eNSPZO22nQUAAAAv0F5BWBE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\nSPVuKGU7jhVWn3nFP3vxRSm01ROKv6a7KkdGU1wBAAAAP7Zw8GOKLdZ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "bo = BayesianOptimization(f=lambda x: f[int(x)], pbounds={\"x\": (0, len(f)-1)}, verbose=0)\n", + "\n", + "bo.maximize(init_points=2, n_iter=25, acq=\"ei\", xi=0.1, **gp_params)\n", + "\n", + "plot_bo(f, bo)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Acquisition Function \"Probability of Improvement\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Prefer exploitation (xi=0.0)\n", + "\n", + "Note that most points are around the peak(s)." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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TyhX8O+FWMoL3kbL1J6ujiIiIiLiUyquIj8nJzaF30u1UK3ITQ6oOo3DhXI9s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\ngLPOCnRbb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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "bo = BayesianOptimization(f=lambda x: f[int(x)],\n", + " pbounds={\"x\": (0, len(f)-1)},\n", + " verbose=0)\n", + "\n", + "bo.maximize(init_points=2, n_iter=25, acq=\"poi\", xi=0.0, **gp_params)\n", + "\n", + "plot_bo(f, bo)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Prefer exploration (xi=0.1)\n", + "\n", + "Note that the points are more spread out across the whole range." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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stO7nder7Zl891maa+jXorQoVTr1oRkdHa0FKigYkJyvJ51NTr1db/pw2fGmn\nxfr06znqOOsSrb7+QwqspPwCn1L2PasHW05nwnAJckffvnp51936OeOAzo3jUXDAn9xut5J8vmM+\nMJWOfoDaNPuIqve7WLkXOJRb5hcpLFMh2VUVVlBO4Xb0X79CHA45HJZsnyXblvKVo1wrU7k6+isv\n7IB8kb9J2bGKyK2uaMWpeliiEmLrqXXC+erStJ4uiq8uh4NmC6BkoLwiIGVmSldeKU2fLiUmSht3\nb1TfN/vq8bbT1f/CXoqJiTntcyYlJSk9I+Po2qNt29QzIUGzXS6VLRulQYM7aOMPN6nb7O764NqV\niilz+ucvSR57Z4VCCqJ0VYeLuENXgtSrUV1ROQl65t2P9e+R/UzHAUqs73f9plcWLlOy11vo8aS8\nfP0RUlvDLx2lhudWUc0KsYqICFNoaKhCQ0MVEhIih8Mhh8Px189g27b/+uXz+VRQUKD8/Hxl5+Ro\n2559+mrHPv2QkaGt+3fqmwOf6oN1c3TX5h8lORSb1Vz1Y5rp0gYtdU2ni1WnBh9eAQhO7POKgHTD\nDUcnDL/6qrTtwDa1fbmtprSeqisu6n9GxfVksrOlTpf4dKjj1aoc/4uWX7tckWGld51ntTG9lFSx\nu+aMu0ERERGm46AIdZ/ygNL3/qYfp//HdBSgxNj12yH95701SvlhpX7MX6XciD0qu7Ga2n+8XUvz\n8v7n9QOcTvWcPt1vU+4LCgqUl5cnrzdL67/doeXffKsNu75SWtbnOhT1mSKyaqtuWCf1b9xZNye3\nV7XYY/9dZcgUgLPhz31eKa8IOB9+KF13nfTtt1J+6B9qPbO1rqk7VDe3uPG0HhU+Xb/9JrW6OF9R\n1/dRw/jymuN6Qw5H6Ztp9vE329XhjVb64tpP1ej8OqbjoIi9/9mX6jO3vw4+8LWiowsfYgbg5FZt\n3qmnVyzUmt8W6lDZzxWb2VJNy7dXnwvbqlezegoNsdW8YcNj17zq6KyFIdHRxb6/uG3bysvL0779\nf+jNtZu15Ov1+uJwqg5HbVast5UuqdFX4/v1V86+HX8tsWnm9Wrzn0tsFqSkKCkpqdjyAghelFeU\nGtnZUqNG0rRpUnLPAnWf013nRtbSQ0kPqXr1an5//2+/lTp08ajc6DYa1LCfHuox2e/vGWha3zdO\nXm+eUu97UOXKlTMdB0XMtm2Fjz9PTzV/Q7cMbGc6DhBUVn+1XQ8vnqvU/QuUE7Fb8bk91Tuhm67v\n1EpxVctu9wYLAAAgAElEQVQpJibmmH2UU1NTC521EChFMC8vT1t37NGMZR9q6Y7l2mUtU+SMw1qc\n5wuIwg0gOBktr5ZlvSypl6S9tm03Os5rnpbUQ5JX0nW2bX9xnNdRXnFCEydKP/wgvf22NHnNZC39\nYanmdJ+n2rXOLbYMbrd0x+SflXN1K03t+KiubXVNsb23afsPZ6nylHM1t1OKruzW0nQc+EmTe0aq\nTH5VrZt6v+koQMD7ae8h3f3GW1qya7a8kVtVN/cyDW7cQ9d0bKKKFcorKirqhLMBMjMz/5q1EJ+Q\nIJfLFZAF0LZtTXtiulbfc5fey835n+P+ftQZQMnhz/J6KgObXpH0jKTZhR20LKuHpDq2bSdaltVK\n0vOSWhddRJQWO3ZIzz4rff21tPantXrm02f0fp9lqnVOzWLN4XJJGzacow2b5museuuiGo3U+JzG\nxZrBlNGz5qpiVitd0uQ801HgR1e36qsJH0xSbu7dCg8PNx0HCDg+n61ZyzfqkQ9nKD10iaod6ajh\n59+omy5NUo2qFU9aWP8uKioqKAqfZVk68NseXVxIcZWkpl6vVq75NCj+LgBKrpMu6LNtO1XSHyd4\nSV/9WWxt2/5UUjnLstgYEqft7rul22+XIsrv1+D5gzW17TQ1rHW+kXWnU6dKoXsvVjPPRA1eNFiH\nsg4Ve4bill/gk/unJ3VTk6GqWJFJlCXZTd07Kjv6e635bLvpKIARHo9HM2fO1D3jx2vmzJnyeDyS\npIOZ2bp++muKGt1SN38wWPFl6uuj/uv07X2zNG3EYNVLOE/R0dEldgp7fGKiNjsLXwufGhYm9755\nqjCqs+6fu1D5BQXFnA4ATnHNq2VZtSQtKeyxYcuylkh6xLbtdX/++QNJd9q2vaWQ1/LYMAq1YYN0\n+eXS1q3STcuvVmhBuB7r8KiqVKlsLNOePVKTprbqjh+oqlUsua+cV6IHON3/Roqmbr5HaWPfV82a\ncabjwM9qjb1CTcu118L7bjUdBShWf1+H+t+BRGtl6ZyBV+jLyu+rQnYTDW90rUZ2bacqlSspMrL0\nTJ73eDyqExd33CFTn3z5jSa5l2nB7pnyhR+Sq+Y4/efGaxVdlic4APw/4wObKK/wJ9uWkpKk4cOl\nKm3f18j3RmpFv1WqF59gOppSUqQR/8pU5K3NdWOj4bqj8zjTkfym/KhO6nfuIL34r+t4lLQUGPvK\nXM3a/Lp+n/6eQkJCTMcBisWJylm/sFA9MXep+rdvpEqVKpXoDytP5FSGTOXk5OrhOUs148sZOhT+\nvXpVvE0vjxypSjGBt5YXQPEzveb1ZHZLOudvf67559cKNWnSpL9+37FjR3Xs2LEIIiCYpaRIhw9L\nfQceUqMXbtTUNtNUu2bxDWg6keRkaWC/KH25Yb4eyWmnTnU6qvl5zU3HKnKzP/hMmWHbNaF/N4pr\nKXFn/156Iu0mffnDz2p6wXmm4wDFwu12K8l37CRdSeoiqWtYuEIO7lSVKpeaiBYwkpKSlJ6R8deQ\nqZ4JCZr9jyFTERHhevD6vprk663/LFijh1bPUNWHp6ln+XGafeutKh9Veu5WA5BWr16t1atXF8t7\nneqd1/N09M7rhYUcS5Z0i23bPS3Lai3pKdu2Cx3YxJ1X/JNtS61aSXfcIX1Y9mYdOuzRU52fNPq4\n8D/l5Eht2kjxV8zQ987ntWH4BkWVKVmfLp875krVj75QC+8cJedx1juh5Kkyuoe6V79Ms+8cbjoK\nUCyGj7hNtV96RvcWcuwhSUfuuksPP/JIcccKerZt68VF6zTxo0e1P+ILuardpVm3jlBkeJjpaAAM\n8Oed15M+E2NZ1lxJ6yTVtSxrl2VZQy3LutGyrBGSZNt2iqQdlmVtk/SCpJH+CIqSaelSKStLim/z\nud759h3d3eIeVa5cyXSsY0RESG++KX007RaV17kakzLWdKQi9cFnO/RL+Ad6dOBAimsp0zthgFb8\nvFQ+n890FMCvdv/uUbuJD+jln2fp47DCHzrb4nQqPsH8cpVgZFmWbuzfVnunL9bjLV/W+zsXKOae\nBhr/mls+HzctABSdU7rzWmRvxp1X/I1tS61bS2PG2HrG2069zumj29r+S2XLljUdrVCzZ0sPPfG7\nPEMa6YmOT2hQiytNRyoSdcfcpIplnVp+5/2KiYkxHQfFaFvGPiU+k6htN21VnVoMiUfJk51ToGEz\nXtG8vRNVM6+DHulyg2539dPczMxCBxKlZ2QE5B6swaagwKe7X3xX07fep0g7Vs/2eUJDOpe8JTcA\nCmf0zivgL8uXS5mZUv7583Qo65AG1RsUsMVVkq6+WmrZsJKa7JytUR+N0k+//2Q60llb++UubQt/\nW09cMZTiWgol1KisctmN9MSiVaajAEXusXmpKn9nS733yyw93Xq2PrvnGQ3qcYkWLl2qIdHRGuB0\n6iFJA5xODYmO1oKUFIprEQkJcWjqzf31+8MbdUmVfrp6RU/VG3e9tv6y13Q0AEGOO68wplMn6arr\nvbp/Xz093f4/6tO4p0JDi2KGmP8cPiw1bSrVGzlO2eU+14rrVgT1pNb6425WTHhZrbhzosqXL286\nDgy44vEntXHXFu2cPrvE7l2J0uWTb37WwBfHa2/kx7rhvIm6p3dP1ahR7Zif1ZmZmX8NJIpPSJDr\nHwOJULS+Tc/Q5c9M0dYIt1yVJ+r1Uf9SaAj3T4CSyvhWOUX2ZpRX/GnLFqlfP+mG2VO0cdcGvdT1\nJVWrFhyPLW7aJCX3zlPl8S016ILLNLHrBNORzsgn3/ysdm801seuNWrbpKHpODDks7RdavlyU2WM\nSVO1KrGm4wBnzHskX1c8/rSWeaeodej1euHqEap73jmKiIgwHQ1/ennJet2+cqxk+fRyv+fk6tTE\ndCQAfkB5RYkzZIhUr/EBPW3X1cKei5TUoG1Q3fV5/HFpztI07erSWu8NfE8Xx19sOtJpqzdmpGIi\nIrVy/H3cdS3lnKOb67bz79UjI/qbjgKckWcXbdaYD0fIGRKjZ5OnqHvLBipXrpzpWChETm6eBj0+\nQ4sOT1ELx7Vafs9klY8qI+noPrxut1vpaWmKT0yUy+VSdHS04cQAThflFSXKrl1S48bSNbPH6/fM\n3Xq669OqUKGC6Vinxec7uges1eQlpVebps9GbFJ0mcD/B/a/FwYrV2/SW/vnaOXEVbq0TSvTsWBY\nt4cma+f+3dr65POmowCn5ee9merx2H36PnyOhsbdr0n9+6pGjepyOHgkNdCt/zpd/V+8UwcivtBT\nHV9So/JhGpCcrCSfT828Xm12OpXqcGhBSoqSkpJMxwVwGiivKFHGjZMOa7fertRQK/p/oBb1mpmO\ndEb27pUaN7FV+44BqlczVq9cMct0pBNKTU095sIgNSxMmyMitGDpUi4MSrmVn/+g7nMv1f4J36t8\nucD/EAaQpMlzPtADW25QLetizR5yj5rWr6MyZcqYjoXT4PPZuvnpOXpp51iVee4PLcrNYwo0UAIw\nbRglxuHD0iuvSN5mD+rKuoNUt1rw7qlXtar02quWdj4zSyt2rtScTXNNRzouj8ejAcnJmuPxaIHX\nq3slLc3L05zMTA1ITlZmZqb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7pOr3dNATA6/WbV2Gm44DPxv2wgy9+uO/9WSzebqhf2OV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\nDvyVqWm7HtMj1zyhiuVYYRgAAADID55q1153XfS4ui9poy/X73Ydxy9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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "bo = BayesianOptimization(f=lambda x: f[int(x)], pbounds={\"x\": (0, len(f)-1)}, verbose=0)\n", + "\n", + "bo.maximize(init_points=2, n_iter=25, acq=\"poi\", xi=0.1, **gp_params)\n", + "\n", + "plot_bo(f, bo)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}