{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "# plot the probability density function for a mixture of two Gaussian distributions\n", "import scipy.stats\n", "\n", "means = [1, 2]\n", "variances = [.05, .05]\n", "proportions = [.3, .7]\n", "x = linspace(0, 3, 3000)\n", "y = proportions[0] * scipy.stats.norm.pdf(x, loc=means[0], scale=sqrt(variances[0])) +\\\n", " proportions[1] * scipy.stats.norm.pdf(x, loc=means[1], scale=sqrt(variances[1]))\n", "title('Mixture of 2 Gaussians with means = ' + str(means) + ' and variances = ' + str(variances))\n", "plot(x, y)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 15, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEHCAYAAAC0pdErAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nP1TFPaR1aaPXAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "# sample some points from the mixture\n", "np.random.seed(123)\n", "N = 150\n", "n1 = N * proportions[0]\n", "n2 = N - n1\n", "sampled_points = normal(means[0], sqrt(variances[0]), n1)\n", "sampled_points = np.append(sampled_points, normal(means[1], sqrt(variances[1]), n2))\n", "\n", "title('Histogram of ' + str(N) + ' points sampled from a mixture of 2 Gaussians')\n", "hist(sampled_points, bins=10);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAEHCAYAAACzy817AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJyJSOAY5EZHCMciJiBTu/wHkBm/FFY17lQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "# kernel density estimation (page 123 in PRML (2.250))\n", "def my_gaussian_kde(x, sampled_points, h):\n", " return 1.0/len(sampled_points) * sum([1/sqrt(2*pi*h**2) * exp((-1/(2*h**2))*(x-p_i)**2) for p_i in sampled_points])\n", "\n", "title('green = true density, blue = density estimated with a gaussian kernel and ' + str(len(sampled_points)) + ' points')\n", "plot(x, [my_gaussian_kde(x_i, sampled_points, .1) for x_i in x], color=\"blue\")\n", "plot(x, y, color=\"green\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAcwAAAEHCAYAAAAj9HbxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XdYFFcXB+DfUgQb9gYWQIyIBKV3pKg0G9iNBY0tGjVq\nYuyCUWONscRu1NhjQ7Fiw0IHjUaxIliwBaUqSNn7/TEfK2V3pSw7LHve58kTd2b2zpndZc7cMncE\njDEGQgghhEilwncAhBBCiCKghEkIIYSUAiVMQgghpBQoYRJCCCGlQAmTEEIIKQVKmIQQQkgpVLuE\neerUKSxYsEBu+/v+++8REBAg83I3b96MZcuWAQC2bduGjRs3lqscPz8/UTnFqaio4P379+WOURZi\nYmKgp6cn83JfvnwJe3t7AEBCQgL69esn830Ut3DhQpw4cQIAsGDBAuzevVsm5aalpcHV1bXM7zt8\n+DBcXFzKtc8FCxZgz549AIoel5+fH1atWlWuMqsiWX5PO3fuRM+ePWVSVlmEhITg66+/rpSyk5OT\noaIiPU38+eef6NWrV5Flffv2Rbt27WBqagpTU1NMnz4dAPDx40cMGTIERkZGMDQ0xPHjx2UWa+Fz\npjTdu3cv93lPrVzvqsKio6PlmgQEAgEEAoHMyx03bpzo39evXy/3H0RlxKYItLW1ERoaCgB4+vQp\nHjx4UOn7vHTpEjp27AgAMr2ISklJQXR0tMzKK43C8Rc+rur2e6qMi11l8f79e8yePRt79uwpcUEX\nERGB2NhYNG/evMhyf39/aGlpIS4uDs+fP4eNjQ0sLCygo6NT4XgKnzOluXDhAso7/cAXa5hLly7F\nV199BXNzc/zwww+i2oCfnx969eoFY2NjzJo1C7m5uZg6dSrMzc3RuXNnjBw5EhkZGQCApKQk+Pr6\nwsLCAp06dcKvv/4KAEhMTETbtm0xefJkWFtbo127dvj7779LxHDv3j3RlUrh/3bt2lVku8jISGze\nvBkHDx7E3LlzsWvXLjg6OsLc3Byurq7YtWtXkSvAwleEOTk5EuMvLD09HQMGDIChoSGcnZ1x//59\n0YdfnuO8f/8+7O3tYWFhAXNzc1FN0t/fH5MmTUJgYCCCgoLw+++/Y8OGDTA0NMT58+dF8YwZMwZr\n166V+h2Gh4fD1tYWHTt2xNSpU5Gfn19kffEr4/J8LsuWLSvx/ZiZmSElJaXEths3bkT79u1hZWWF\nP/74o8i6xYsXw9zcHKampvDx8cGrV68AAM7Ozpg9eza6dOkCPT09DB8+HIwx5OXl4bvvvoOJiQks\nLCwwYMAAfPjwAYmJiahbty6EQiFGjx6N+Ph4eHh4YMmSJfjmm29E+wsNDYWZmVmJGNPS0uDn5yf6\nLqdNmyb63BYsWIBOnTrB0tISHh4eeP36Nf744w/ExsZixowZCAwMLFIT09TUxOzZs2FiYgJdXV0c\nOnQIAwYMQIcOHeDm5oaPHz8C4K7UbWxsYGZmBl1dXWzatAkAMHLkSGRlZcHMzAxCoRD37t2Du7s7\nLCwsYGpqih07dojinj9/PgwMDGBtbY1jx46J/T2Ympri4sWLAIADBw6gZs2a+PTpEwDu97Rx40ZR\n/Bs2bChyXAAQFhYGe3t7GBgYoE+fPqL4C3v48CG6desGOzs76Orqok+fPqJ9FPbff/+hR48eMDIy\ngqOjI/r16ydKYpI+D2m/1+vXr8Pa2hoWFhawtLTE0aNHpS4v/D1J21/v3r3h6+uLr7/+Gubm5rh7\n967Yz7bA4cOHYWBggEePHgEAtm/fDgsLC5iZmaFbt26iC7jC59GZM2di5MiRmDx5MlxdXdGuXTv0\n7NkTHz58AACp37s4QqEQU6ZMgY2NDTp27AgjIyOEhYWJ9jtlyhSx+zl69CiMjIxgYWGBOXPmSCz/\n0KFD0NHRwcqVK4skoISEBGRkZGDcuHHo1KkTRo0aJToPBAYGYsyYMQCAVq1aoXv37mLP+c7Ozpgw\nYQKsra3Rtm1b+Pv7i9YFBgbCzMwMnTp1gqOjo+hisuCcCQC6uroICAiAk5MTdHV18fPPPwPg/pYA\nwNXVFS9evMDGjRvRuXNnWFlZwcnJCffu3ZP6mYJJcfbsWWZoaMjS0tIYY4x9++23TE9PjzHG2IgR\nI1i3bt1E2wYEBLCffvpJ9HrWrFlswoQJjDHGXFxcWFBQEGOMsaysLObi4sL+/vtvlpCQwAQCATt1\n6hRjjLEjR46wNm3aSAvpi/z9/dmkSZMYY4zt2LGDNWzYkGVkZIhe9+jRQ7Rt4dfS4i/shx9+YH5+\nfowxxpKTk1mbNm1YQEBAuY9z1KhRbOnSpYwxxl6/fs0GDx7MhEJhkePw8/Njq1atYowx9vvvv7MB\nAwYwxhhLS0tjTZs2FX0/4owYMYJZWlqyjx8/spycHObi4sI2btzIGGNMIBCwd+/eyeRzKa2bN2+y\nZs2asTdv3jDGGJs4caLoN7Vr1y42aNAglpeXxxhjbPPmzczLy4sxxliXLl3YwIEDGWOMZWRkMB0d\nHXb58mV29epV1qFDB1H5P//8MwsPD2cJCQmsTp06jDHGQkJCmLGxMWOMsbdv37J69eqxlJQUxhhj\nw4YNY1u2bCkR58iRI9m6desYY4zl5eWxoUOHsuXLl7Nnz56xevXqsZycHMYYY6tWrWLHjx9njDHm\n7OzMjhw5whgr+p0JBAJRWcuWLWNaWlrs5cuXTCgUMnNzc7Zv3z6WmZnJbG1t2fv37xljjIWHh7O6\ndesyxhhLTEwUHUtubi4zMjJiN27cYIwxlpqayoyMjFhERAQLDAxkHTt2ZJmZmSwvL4/17t2bubi4\nlDi2hQsXsh9//JExxv0+tLW1WXBwMMvPz2fa2trszZs3ReIvfFwjRoxgNjY2LCsri+Xn5zNzc3O2\ne/fuEvv46aef2N69e0Uxm5iYiMoobNCgQWzmzJmMMcZevXrFtLW1WUBAgNTPQ9zvtWfPnowxxlxd\nXdmBAwcYY4zdvn2bff/994wxxtzc3MQuLzjOL+2vfv36LCkpiTHG2KRJk9iIESNKHEtBXHv37mXG\nxsbsxYsXjDHu9+fk5MQ+fvzIGGPs3LlzzMjISPR5Fj6Pjhgxgjk4OLCcnByWm5vLzMzM2M6dO6V+\n75cvXxb9vgsLDw8XnSsYY+zXX38VfU7i9rNjxw72+vVrVr9+fXbv3j3GGGMrVqxgAoGgRNnijrtA\nZGQk8/X1Za9fv2b5+fls0qRJrE+fPowxxjQ1NUV/+4wxNnfuXDZt2rQSZTo7OzNPT0+Wm5vL0tLS\nmKGhITt58iS7d+8ea968OUtISGCMMXbp0iXWokULlp6eXuScqaurKzpvJSUlsZo1a7LExETG2Ofz\nXl5eHtPQ0GCvX79mjDG2e/dutnXrVqnHKrVJ9vTp0xgwYAC0tLQAABMnThRdmQoEAjg4OIi2PXny\nJNLS0kS1n5ycHDRr1gwfP37ElStXkJKSgnnz5gEAPnz4gFu3bsHS0hLq6urw8vICwF35imtOjYuL\nK1IrKDBlyhT4+fkVvwAocrVjYmKCOnXqSL9qkBJ/cRcvXsSaNWsAAI0aNULfvn0BoNzH6evri+HD\nhyMqKgpdu3bFmjVrRM1ehY+j4N8jRoxAQEAAkpOTcejQIfTs2VP0/YgjEAgwbNgw1KxZEwAwdOhQ\nnDp1CuPHj//iZ1KWz2Xp0qU4ePCg2M+rYcOGRV67u7ujadOmALhmlFOnTon2FR0dDQsLCwBAfn4+\nsrKyRMdRUIuoU6cODAwMkJKSAldXV6iqqsLa2hru7u7o27cvLC0tkZiYWOKzA4AmTZqgR48e+Ouv\nvzBs2DAEBweLahLFjzs6Ohrbt28HAGRlZUFFRQUtW7ZEp06dYGpqCk9PT3h6epaqf7Hgd6Kvr4+v\nv/4aLVq0AADo6ekhJSUFtWvXxsmTJxEUFITHjx/jn3/+EV3xF47/4cOHePLkCUaNGiValp2djZs3\nbyIuLg59+/ZF7dq1AQDffvstfvvttxKx+Pj4YNCgQVixYgWuX7+OadOm4fz586LPteC7EUcgEKBP\nnz7Q1NQEABgbG+Pt27cltlu2bBmCg4OxYsUKPHjwAC9fvhQdT2FnzpzBzZs3AQDNmzdHv379wBiT\n+nmIU/AZDRw4EBMnTkRQUBC6du2KxYsXAwAGDBggdnnBe7+0P3Nzc2hrawMAzMzMRDXU4qKionD2\n7FmsWbNG1Mx46tQpPH78GHZ2dqLtUlJSkJKSUuI8KhAI4OHhAXV1dQDA119/jffv30v83v/55x8Y\nGhqKjcXGxga//PILNm7ciCdPniAkJER0rpC0n4Lun4Iyx44dixkzZkj83MWxsrLCkSNHRK/9/f3R\nvHlz5ObmQigUltheVVVVbDljx46FmpoatLS00L9/f5w7dw4dOnRA165doaurCwBwcXFB06ZNERsb\nW+L9vXv3BsB1zzRt2hTv379HmzZtiuy3f//+sLW1hbe3N7p3744hQ4ZIPTapCVNdXb3IARbv/C34\nwwS46v/atWvh7u4OAMjMzER2djby8vIAcM2CBX9kycnJqFmzJv777z/UqFFDVIZAIBDbtmxkZCT6\no/qS4n2KhZNl8fJzcnK+GL+48gt/JgVfdkFzXVmP09vbG48ePcL58+dx8eJFBAQEiJpNiu8XAOrX\nr4/+/ftj9+7d2L9/PzZs2PDFz6Tw9yYUCovEIqvPZebMmZg5c2apYhH3+RXsa+bMmaK+iJycHLx7\n9060viDpF465Xr16uHXrFsLCwnDx4kUMHDgQkydPRp8+fSTGMHHiRHz33XdQU1NDv379UKtWrRLb\nCIVCHD58GO3btwcApKamin5bV65cQWxsLM6fP4+pU6fCxcUFv//+u9Tj1tDQEP274CRV2IsXL2Br\na4vx48eLmiZPnjxZYrv8/HzUr1+/yN/D69evUb9+ffz8888SP9vCjI2NkZOTg6CgIBgYGKBHjx4Y\nOHAg1NTURIldGjW1z6cNSX+zgwYNQn5+PgYOHAhvb288f/5c7HZqamolzjECgUDq5yHt9zp27Fj0\n7NkTwcHBOHv2LPz9/XH79m2JywvK+9LnX/i3B0BiH1iDBg1w8OBB9O/fH97e3mjTpg2EQiGGDRuG\npUuXit77/PlzNGjQAEDR8ygA0fmj8LEKhUKJ33tERITYWE6dOoUffvgBP/74I/r06QNDQ0PRQC5J\n+1FRUSlybIW/69K6fv063r9/LxoIJBQKoaKiAlVVVbRu3RovX74UXZS9ePFCbJcIUPT3m5+fD1VV\nVQiFwhKfvVAoRG5ubon3iztfFLd7927ExcXh/PnzWLZsGbZv3y7qehBHah+mt7c3jhw5gvT0dABc\nO3zBybf4zt3d3bFu3Trk5ORAKBRi/PjxmDNnDrS0tGBjYyPqJ0hLS4Ojo6No1J2sqampFfkDKqxp\n06a4c+cOPn36hLy8PAQFBUmNf/bs2SXK8PDwwPbt28EYQ2pqqujDrVu3brmOc8iQITh48CAGDhyI\nP/74A1paWnj+/LnUY5o4cSLWrl0LxpioNiYJYwwHDhxATk4OsrOzsWvXLnh6ehbZpkmTJhX+XEqr\nW7duCA4ORlJSEgCuf6jwvrZu3SrqI/X398eIESOKHEvxYzt16hTc3Nxga2uLBQsWYPjw4bh9+3aR\niyY1NbUif1C2trZQUVHBypUr8d1334mN093dHb/99hsYY8jJyYGPjw82bNiA27dvw9jYGIaGhpg5\ncyZ++OEH0Ym38Pck6YQqDmMMsbGxaNq0KebMmYNu3bqJvgPGGNTU1EQXZO3bt4empib27t0LAHj+\n/Dk6deqEmzdvwsPDA4cOHUJaWhqEQqHU0Z8+Pj6YMWMG3N3d0b59e6SmpmLv3r1iE6a0vylJgoOD\nMX/+fPTv3x8AN76g4OK5MG9vb1Et/t27dwgMDIRAIJD4eQiFQrG/14Lv287ODjdv3sSIESOwefNm\npKamIiUlBfb29mKXf+nzF1cjkqZdu3ZwdnbGpEmTRP3s3bt3x/79+/H69WsAwNatW9G9e3fRvktD\n2vcuyYULF9CzZ0+MGzcO5ubmOHbsmOh3JG6/AoEAjo6OuHv3rug3Xfjvs7QyMjIwefJk0ee7YsUK\n9O/fHyoqKujduze2bNkCgEuW586dQ48ePUqUwRjD3r17wRhDSkoKDh06hF69esHV1RXBwcFISEgA\nwA1Ie/HiBWxsbEq0LkqiqqqKnJwcJCcno3Xr1mjYsCGmTJmCX375RXTckkhNmC4uLhgzZgxsbW1h\naWmJ9PR00dV48ZrcvHnzoKurC1NTU3Ts2BFCoVCUPPbt24eIiAiYmJjA2toagwcPxuDBg0XlFFbR\nUXhubm44ceIEpkyZUiLG7t27o0uXLjA0NISTkxNMTExE68XFL645y9/fH+rq6jA0NETPnj1hbGws\nWlee45w/fz727t2Lzp07w8bGBr6+vujSpUuRbTw9PbF27VrRkGkTExM0bNhQ1KyampoKU1NT0R9k\n8f3o6+vDwcEBZmZm6NKlC4YPH16kfHd39wp/LqVlbGyM5cuXw83NDZaWlvjw4YNoX6NHj0aPHj1g\nY2MDY2Nj3Lp1q8jALnGfoaenJzp27AhjY2NYWloiPDwc/v7+YIyJtjc2NoaqqipsbGxE7/Xz84OO\njo5o9Gdxa9euxYcPH2BiYgITExMYGxtjxowZMDExwYABA0SDR3bu3InVq1cDAHr27Ikff/wRf/31\nV5FYi/9b3HF0794dLVu2RPv27eHo6AgNDQ20aNECjx8/hra2NszMzGBkZIQPHz7g+PHj2LZtGzp1\n6gR3d3f88ssvsLW1haenJ0aNGgULCwvY2NigTp06Ev+efHx8RANzAO5vQ1tbW+xoxcLHJel7KG7J\nkiXw8fGBnZ0dFi5ciL59+yI+Pr7EdqtXr8b9+/dhYmKCfv36oU2bNqhVq5bEzyM+Pl7s77XAihUr\nMH/+fJiZmcHV1RX+/v5o06YNli9fLnZ5aT7/4t+ZpJHxhZfPmTMHHz58wMqVK9G9e3f8/PPP6Nat\nGzp16oQ9e/aIBmRJ+j0Up66uLvF7l/Se8ePH48qVKzA1NYWXlxe6deuGxMRE0d+GuPc0btwY+/bt\nwzfffAMLCwvR8UtTvCxPT09MmjQJ9vb2MDQ0REJCAtavXw+AG5WcmZkJY2NjdOvWDStXrhR7W5lA\nIMCnT59gZWUFGxsbTJgwAS4uLujQoQM2bNggGoA1e/ZsBAUFoW7duqW+Y8HX1xeOjo548+YN5s6d\nCzc3N1hYWGDWrFnYtm2b9DdL6+CMiYlha9euFb1etWoVGzRokNROUVL5Hj9+zFq1asWysrJEy8aO\nHcsyMzN5jEpx5Obmsh49erC///6b71CU3oYNG1h4eDhjjLHs7GxmZWXFzp49y3NUhG/Ozs7s4MGD\nfIdRgtQa5ldffYVr167h66+/homJCS5fvlyh2oWsRUZGSr0xe+zYsZg1a5YcI6p88+fPh4ODA1at\nWiXqg8jLy4Ojo2OJvhBSUlxcHJo2bSrqCyb8MjIywqRJk2BmZgZzc3N4e3uL+ssJqWoEjCnmA6SX\nL1+OPXv2oE6dOmIHyWzevBm7du2Cs7MzlixZwkOEhBBCqhOFnRrPwMAAR48eFdvJGxYWhqioKIwb\nN67cMzoQQgghhSlswvT19RU75PnVq1dYuHAh1q9fT8mSEEKIzFS7uWQPHz6M5ORkeHl54fXr1/j4\n8SM6dOggGhlamIGBgdiRe4QQQiRr27YtHj9+zHcY8sfrkKMKSkhIYDY2NhLX79y5UzTtljgKfvhf\ntGDBAr5DqDTV+dgYo+NTdNX9+Kr7uVMShW2SLVBw383+/fuxdetWiesJIYSQilDoJlldXV3RCNmC\nCQIKKzxLDCGEEFIRCl/DJJI5OzvzHUKlqc7HBtDxKbrqfnzKSmHvw5QFSRPyEkIIkUxZz51UwySE\nEEJKgRImIYQQUgqUMAkhhJBSoIRJCCGElAIlTEIIIaQUKGESQgghpUAJkxBCCCkFSpiEEEJIKVDC\nJIQQQkqBEiYhhBBSCpQwCSGEkFKghEkIIYSUAiVMQgghpBQoYRJCCCGlQAmTEEIIKQVKmIQQQkgp\nUMIkhBBCSkGN7wAIIcohLTsN66LW4cKTCwAAr3ZemGg5EbVr1OY5MkJKh2qYhJBKd+ftHZhuNsWD\ndw8wx3EOZjnMQszLGJhuNkX8+3i+wyOkVASMMcZ3EHwRCARQ4sMnRC7i38fDaacTlrotxbBOw4qs\n2xSzCYuvLUbEtxHQ0dLhKUJSVsp67qSEqbyHT0ily8nPgc02G/h19sNk68lit1l0dRFOPzqNqyOv\nQk2FeokUgbKeO6lJlhBSaX658gta1WuFSVaTJG4z23E2aqrXxNrItXKMjJCyU+iEGRkZCRcXlxLL\n9+/fDxsbGzg4OOC7775TyishQviWmJqIDTEbsMFrAwQCgcTtVAQq2OS9CUuuLUFSepIcIySkbBQ2\nYS5fvhxjxozBp0+fiizPysrCvHnzEBISguvXryMtLQ0nT57kKUpClNesi7Mw2Wpyqfom2zVqh1Gm\no7Dk2hI5REZI+ShswjQwMMDRo0dL1B41NTURHh4OTU1NAEBeXh5q1qzJR4iEKK17/93DpYRL+NHu\nx1K/Z4b9DBy4ewCJqYmVFxghFaCwPey+vr5ITEwssVwgEKBJkyYAgHXr1uHDhw/o2rWrxHL8/f1F\n/3Z2doazs7OMIyVE+awKX4UJFhPKdI9l41qNMdZsLFaHr8YazzWVGB0pq5CQEISEhPAdBu8UepRs\nYmIiBg8ejPDw8CLLhUIhZsyYgcePH+PAgQOi2mZxyjrSi5DK9CrjFYw2GOHRpEdoXKtxmd77Iv0F\nOm3qhIQpCdDS0KqkCElFKeu5U2GbZKUZN24cPn36hGPHjklMloSQyrEldgsGdRxU5mQJAC21WqKb\nfjfsuLmjEiIjpGIUPmEWjL7bv38/tm7dips3b+LPP//EnTt34OrqChcXFwQGBvIcJSHKQciE2PHP\nDowxH1PuMr63+h6bYjcpZQ2GVG0K3SRbUcrarEBIZbnw5AJ+Ov8Tbo67We4yGGP4av1X2Ou7F1Y6\nVjKMjsiKsp47Fb6GSQipOrbf3I5RnUdVqAyBQIDhJsPx162/ZBQVIbJBNUzlPXxCZCrjUwZarm6J\nhCkJaFizYYXKSkxNhOVWS7yY+gIaahoyipDIirKeO6mGSQiRiaCHQXBo7VDhZAkAuvV1YdTECGcf\nn5VBZITIBiVMQohMHI47jP5G/WVWXn+j/jhy74jMyiOkoihhEkIqLDMnExcTLqJX+14yK9PH0Acn\nH55ETn6OzMokpCIoYRJCKuzkw5Owa2Unk+bYAjpaOmjfuD0uJ1yWWZmEVAQlTEJIhR2OO4x+HfrJ\nvNy+HfpSsyypMihhEkIqJCc/BxeeXEDP9j1lXrZvB18E3g+EkAllXjYhZUUJkxBSIaHPQvFVo6/Q\ntHZTmZet30AfjWs1RszLGJmXTUhZUcIkhFTI6Uen4dXOq9LK9zTwxJlHZyqtfEJKixImIaRCTj8+\nDe923pVWvmc7T5x5TAmT8I8SJiGk3BJTE5H8MRnm2uaVtg/H1o6I+y8OyR+TK20fhJQGJUxCSLmd\neXQGHgYeUBFU3qlEQ00DzrrOCI4PrrR9EFIalDAJIeV2+vFpeBp4Vvp+PA2oWZbwjxImIaRccvNz\ncfXpVbjpuVX6vjwMPBAcH6yUE36TqoMSJiGkXGJfxUK3vi6a1G5S6fvSa6CH2uq1EfdfXKXvixBJ\nKGESQsrlcsJluOq6ym1/LrouuJxI0+QR/lDCJISUy6XES3DVk1/CdNVzxaWES3LbHyHFUcIkhJTZ\np7xPiHgRAac2TnLbp4ueC0ISQ2iaPMIbSpiEkDKLeBEBoyZGqKdZT2771K6rjWZ1muHW61ty2ych\nhVHCJISU2aWES3LtvyzgoutCzbKEN5QwCSFlJu/+ywKueq408IfwhhImIaRMPuR8wM1XN2Hf2l7u\n+3bWdca1Z9eQJ8yT+74JoYRJCCmTyKRIdGreCbXUa8l9341rNUZLrZb4982/ct83IQqdMCMjI+Hi\n4lJieVBQEKysrGBnZ4dt27bxEBkh1df1Z9fh0MpBJmUxBly9CsycCQwZAowbB+zZA2RlSX6PQysH\nXH92XSb7J6QsFDZhLl++HGPGjMGnT5+KLM/NzcW0adNw/vx5XLlyBVu2bMHbt295ipKQ6if0eSgc\nWlc8Yd68CVhbc0lSUxPw9gaMjYF9+wB9feDvv8W/z761Pa4/p4RJ5E9hE6aBgQGOHj1aYm7Je/fu\nwcDAAPXq1YO6ujocHBxw9epVnqIkpHrJE+Yh4kUE7FrZVaicjRsBd3dgwgTg7l3A3x/45htg0iTg\n9GkgMBCYOxeYMQMQFrvt0qE1V8OkeWWJvKnxHUB5+fr6IjExscTy9PR01Kv3+d6wunXrIi0tTWI5\n/v7+on87OzvD2dlZhlESUr38++Zf6NTVQaNajcr1fsaAefOAQ4eAsDDAwED8dtbWQHg40LMnMH06\nsHr153V69fXAGENiaiL0GuiVKw5SNiEhIQgJCeE7DN4pbMKUpF69esjIyBC9zsjIQIMGDSRuXzhh\nEkKkq2hz7JIlXO0xNBRo3Fj6to0aAadOAY6OwJo1wJQp3HKBQCCqZVLClI/ilYmAgAD+guGRwjbJ\nSmJoaIhHjx4hJSUFOTk5uHr1KmxtbfkOi5Bq4fqz6+VOmH/+CezYAZw//+VkWaBBAy5pLl4MREV9\nXl6QMAmRJ4VPmAKBAACwf/9+bN26Ferq6vjtt9/g7u4OOzs7fPvtt2jRogXPURKi+BhjuP7sOuxb\nlf3+y8hIbiTsyZNAWf8c27Th+jwHDwYyM7llDq0daOAPkTsBU+Kec4FAQAMHCCmlp6lPYbPdBi+n\nvRRdqJbGmzeAhQXwxx9Ar17l3/+wYVyyXb6cG3zUcFlDJP6QiIY1G5a/UFIuynruVPgaJiFEPgqa\nY8uSLBkDRo7kkl1FkiUArFoF7NwJ/PsvoKaiBuuW1gh7HlaxQgkpA0qYhJBSKU9z7MaNwH//AbIY\nI9K0KbA7r0zOAAAgAElEQVRwITB5MpeIaQIDIm+UMAkhpRL6PLRMCfPePWDBAmDvXkBdXTYxjB4N\nvH4NnDsH2LS0QcSLCNkUTEgpUMIkhHxRxqcMPEl5gs7NO5dq+9xcYOhQYNEi4KuvZBeHmho3Ynbm\nTMCihRViX8XSROxEbihhEkK+KPZVLDo17wR11dJVFX/7jbuPcuxY2cfi4wNoaADngxqgpVZL3H17\nV/Y7IUQMSpiEkC+KSoqClbZVqbZ9/BhYsQLYtAkow/igUhMIuKn0liwBrHWsqVmWyA0lTELIF0Ul\nRcFK58sJkzFg/Hhg1ixuAvXK4uEBqKgAtVNsEJkUWXk7IqQQSpiEkC+KTIosVcLctQtITf08jV1l\nEQi4fszQgzTwh8gPJUxCiFQvM14iKzcL+g2kVxnfvOGeLrJ1Kzc4p7L16wdkxBsjMeUZUrNTK3+H\nROlRwiSESBWdFA0rHasvTljw44+Anx9gaiqfuNTUgOlT1VA7zRzRSdHy2SlRapQwCSFSlab/8to1\nICQEmD9fPjEVGD4cyLhvg7N3qVmWVD5KmIQQqb7Uf5mXB3z/PbByJVCnjhwDA7c/t/bWOB5DA39I\n5aOESQiRSMiEiHkZA0ttS4nbbN4MNGwIDBggx8AKmTnUBk9yIpCVpXyTgRP5ooRJCJHo4buHaFSr\nEZrUbiJ2/X//cfdErltXOfdcloZjZ21oqNTE+n3x/ARAlAYlTEKIRF/qv5w9m5sCz9hYjkGJYdbM\nBltOUbMsqVyUMAkhEkW+iJQ4w09sLPdAaH9/+cYkTh9zG7xSjUBcHN+RkOqMEiYhRKKol+JrmIxx\nt5EEBAD16vEQWDG2ra1R1ygC27fzHQmpzihhEkLEys7LRtx/cTBtUfLGylOnuIkKRo3iITAxzFqY\nIU09Drv3ZyMnh+9oSHVFCZMQItat17fQvlF71FKvVWR5Xh43o8/y5fKZ0ac0aqnXQvsmX0HH/B+c\nPMl3NKS6ooRJCBFL0v2Xf/4JNGsGeHvzEJQU1jrW6Ng9ipplSaWhhEkIEUvcCNnMTG6Qz8qV/N1G\nIom1jjVym0UiPBxISuI7GlIdUcIkhIglLmGuWwc4OQHm5jwFJYWVjhVuvImCry+wbx/f0ZDqiBIm\nIaSE91nv8TrzNTo07iBalp4OrF4NLFjAY2BSGDY2xJvMN+gx4B327uU7GlIdKWzCFAqFGD9+POzs\n7ODi4oL4+KKzfBw7dgyWlpawsrLCpk2beIqSEMUUnRQNc21zqKqoipatWwd06wZ06CDljTxSVVGF\nhbYFauhGIzkZuHuX74hIdaOwCTMwMBA5OTkICwvD0qVLMX369CLrp02bhvPnzyM0NBSrVq1CWloa\nT5ESoniikqKKTFiQlgb8/rv8n0ZSVtY61oh+GYnBg6lZlsiewibM0NBQeHh4AACsra0RExNTZL26\nujpSU1ORlZUFxtgXn+VHCPms+IQF69YBHh5A+/Y8BlUKVjpWiHoZhW++4RImo/nYiQwpbMJMT0+H\nlpaW6LWqqiqEQqHo9fTp02Fubg5jY2P07NmzyLaEEMkYY0UG/Hz4AKxZA8ydy3NgpWDd0hqRLyJh\nYsJQqxYQFsZ3RKQ6qSK3HZedlpYWMjIyRK+FQiFUVLj8/+zZM6xfvx5Pnz5FrVq1MHToUBw+fBj9\n+vUrUY5/oYkwnZ2d4ezsXNmhE1KlPU17ClWBKlpqtQQA7NwJODhU/dolAGjX1YammiYS0xLwzTf6\n2LsXsLfnOyrFFxISgpCQEL7D4J3CJkx7e3sEBQWhf//+iIiIgImJiWhddnY2VFVVoaGhARUVFTRt\n2hSpqaliy/GvCjNHE1KFFNQuBQIB8vOB334Ddu/mO6rSK6hlDh6sDysrru+1Rg2+o1JsxSsTAQEB\n/AXDI4VNmD4+Pjh//jzs/3/5uGPHDuzfvx+ZmZkYM2YMRowYATs7O2hqasLAwAB+fn78BkyIgijc\nHHvsGDerj50dz0GVgZW2FaKSojDYYzDatQMuXeL6XwmpKAFjytstLhAIoMSHT4hYTjucML/LfLjp\ndYWNDTBzJuDjw3dUpReSGILZF2cj7NswrF4N3LkDmi5PxpT13Kmwg34IIbKXJ8zDjVc3YKFtgYgI\n4N07oFcvvqMqG/MW5rj15hZy8nPQty9w/DiQm8t3VKQ6oIRJCBG5+/YuWtVrhfqa9bFpEzB+PKCq\n+uX3VSV1NepCv4E+/n3zL1q3BgwMgMuX+Y6KVAeUMAkhIgX9l+/ecTUzRe36t9K2QmRSJACgXz/g\n8GGeAyLVAiVMQohIwQw/O3cCPXsCjRvzHVH5WLe0RlRSFAAuYR47xj3Hk5CKoIRJCBGJTIqEhbYV\nNm8GvvuO72jKz0rncw1TV5f7j24jJBVFCZMQAgDIzMnE4/eP8S7OBDVrAra2fEdUfsZNjfE87TnS\nsrk5pPv3p2ZZUnGUMAkhAIAbr27ApJkJ9uzUwJgxVe8B0WWhpqIGsxZmiH4ZDYCaZYlsUMIkhADg\n+i87N7HC6dPAoEF8R1NxVjpWon5MfX2gZUvg6lWegyIKjRImIQQA13+Z/8wKLi6KO9inMGsda1E/\nJgD4+gKBgTwGRBQeJUxCCACuhnnrtBVGjOA7Etmw0rFC5ItI0Yw0ffpwCVMJJ6ghMkIJkxCCN5lv\nkJqVjicxBvDy4jsa2WhdrzUA4Hn6cwCAkRGgoQH88w+fURFFRgmTEILIpEg0ybHCoIEq1ebJHgKB\nQFTL5F4DvXtTsywpP0qYhBBEvohC6h0rDBvGdySyZa3zeQIDgGuWPX6cx4CIQqOESQjBpQeRUH1t\nDSsrviORrcITGADcvaUvXwIJCTwGRRQWJUxClJyQCXHzbTT62Vop9L2X4ljqWOLGqxvIE3I3YKqq\nclP+US2TlAclTEKU3IPkh8j/0AB+/ZvyHYrM1desj5ZaLXH37V3Rst69KWGS8qGESYiSOxIRiRr/\nWcPCgu9IKkfhidgBoFs34MYN7lmfhJQFJUxClFxgTBSsta2rXXNsgcKP+gKAmjUBNzfg1CkegyIK\niRImIUqMMeBOSiSGdKlmo30KKV7DBOj2ElI+lDAJUWLR/2Qhp14chriY8R1KpTFpZoL4lHhk5mSK\nlvXoAVy8CGRl8RgYUTiUMAlRYpuO/YMmAkPUqlGT71AqTQ3VGjBpZoLYl7GiZY0aAaamwPnzPAZG\nFA4lTEKU2Lm7kbBrbc13GJWueD8mwDXLnjjBU0BEIVHCJERJPX0KvNOMQk+z6p8wxfVj9uoFBAUB\nQiFPQRGFQwmTECV14gRQQy8SNq2q74CfAsUf9QUAbdsCTZoAkZES3kRIMQqbMIVCIcaPHw87Ozu4\nuLggPj6+yPro6Gg4OTnB0dERgwYNQk5ODk+RElI1HT6djHyNZBg2NuQ7lEqn30AfWblZeJnxsshy\napYlZaGwCTMwMBA5OTkICwvD0qVLMX36dNE6xhjGjh2LnTt34tq1a3Bzc0MCTR5JiEhaGhD9MgpW\nLS2hIlDY00CpFTy5RFyzLM36Q0pLYf9SQkND4eHhAQCwtrZGTEyMaN3Dhw/RqFEj/Pbbb3B2dkZq\nairat2/PV6iEVDlnzwItrSNh27r6N8cWKPyorwKWlkBKCvDoEU9BEYWisAkzPT0dWlpaoteqqqoQ\n/r/3Pjk5GWFhYZg0aRIuXLiAixcv4vLly3yFSkiVc+IEUEM/CtY61X/ATwFrHWtEvSxaw1RR4SZj\np2ZZUhpqfAdQXlpaWsjIyBC9FgqFUFHh8n+jRo1gYGAgqlV6eHggJiYGLi4uJcrx9/cX/dvZ2RnO\nzs6VGjchfMvNBU6fYcDXUbDS+ZPvcOTGUscSMS9jkC/Mh6qKqmh5r17AihVAoV4dUkxISAhCQkL4\nDoN3Cpsw7e3tERQUhP79+yMiIgImJiaidfr6+sjMzER8fDzatm2La9euYfTo0WLLKZwwCVEG164B\nrUweI1WjNlrUbcF3OHLTuFZjNKnVBA/ePYBREyPRcjc3YMgQbjL2Ro14DLAKK16ZCAgI4C8YHils\nwvTx8cH58+dhb28PANixYwf279+PzMxMjBkzBtu3b8eQIUPAGIO9vT08PT15jpiQquHECaCdazjU\nW9nxHYrcFfRjFk6YhSdjHz6cx+BIlSdgjDG+g+CLQCCAEh8+UUKMcfcfmi8YD0dDI0y2nsx3SHK1\nJmIN7iffx8YeG4ss37kTOHkSOHyYn7gUjbKeOxV20A8hpOzu3uWS5oOPYbBT1hpmUsmZCry9uXll\ns7N5CIooDEqYhCiREyeA7r3SkJCagE7NOvEdjtyZtjDF/eT7yMot+piSJk0AExOABtMTaShhEqJE\nTp4EdB0iYd7CHOqq6nyHI3eaapowamKEG69ulFjXqxfdXkKko4RJiJJ4+xaIiwM+NFDO5tgC1jol\nJ2IHPk+TR5OxE0koYRKiJM6cAbp2BaJeKXfClNSP+dVXQN26wI2SlU9CAFDCJAqIMYacfJpMv6yC\nggAv73xEJkXCpqUN3+HwxrplySeXFKC5ZYk0lDCJQniV8QqLri6C9TZraC7WRK3FtVBvaT10290N\nm2M2lxjEQYrKyQEuXAD0bO6iRZ0WaFyrMd8h8earRl8hJSsFbz+8LbGOnl5CpKGESaq0T3mf8MuV\nX2C80RjP055jedfleD/jPXLn5eLJ5CeYaDkRpx+fhv5afRy4c0Ap7w0rjatXgQ4dgAcflLs5FgBU\nBCqw1LEU249pYwO8egXQw42IODRxgfIefpX3Iv0F+v3dD41rNcZ6r/XQra8rcdvIF5H49sS36NS8\nE7b13Iaa6jXlF6gCmDIFaNoUeGA0HE5tnDDaTPxUkcpi7qW5UBGoYKHLwhLrRo0COncGJivXnA5l\noqznTqphkirpfvJ92GyzQe/2vXFi8AmpyRLg+qWix0RDyIRw2eWC1OxU+QSqABjj+i979gTCnlMN\nE5A88Aeg20uIZJQwSZVz7797cPvLDYtdF2OW46xSP+C4pnpN7PPdB5uWNnDf44607LRKjlQx3LsH\n5OUBTfXe4F3WOxg2NuQ7JN5Z6VghOilabC2pWzcgKgpIpWsuUgwlTFKlvMl8A699XljsuhgjOo8o\n8/sFAgFWu6+GeQtz+P7ti9z83EqIUrGcPMnVLq8/vwa7VnalvgCpzprXaY66GnXx6H3JJ0fXrg10\n6cLdhkNIYfSXQ6qM7Lxs9DnYB8NMhsGvs1+5yxEIBFjnuQ4aqhqYcnaK7AJUUCdPAj16AFcSr6BL\nmy58h1NlSJrAAOBGy9LtJaQ4Spikyph+bjp06uogwLniz9pTVVHF/r77EZIYgj9vKs9Dkot79w64\ndQtwcQGuPrtKCbMQm5Y2CH0WKnZdjx7AuXPc7TiEFKCESaqE4/eP4/Tj09jWaxsEAoFMyqynWQ9/\n9/8bM87PwIPkBzIpU9GcPcsly4/sPRJSEmDWwozvkKoMpzZOuPbsmth1zZsD7dsDV67IOShSpVHC\nJLx7mfESY0+OxV7fvaivWV+mZRs3NcZCl4UYcnSIUs4OFBTE1ZauP7sOm5Y2SjnhuiSdm3fGs7Rn\nSP6YLHY9TWJAiqOESXjz9i1w8ybw7ZGJGGs2ttJud/jO4ju0qNMCy64vq5Tyq6qcHCA4mHvWI/Vf\nlqSmoga7Vna4/uy62PUFt5co4e2GRAJKmETurl4F7O25Ji+f2ccQ/M89BE6fg/37K+fkJBAIsNF7\nI9ZGrcX95Puy30EVdfkyN7tPixbAladX0EWXEmZxTm2ccPXpVbHrjIwAdXWuD5gQgBImkSPGAH9/\nYMgQYNIk4NGzNOR1m4SLU7Zg1TJNrFjBXdW/fy/7fbeq1wrzneZjbNBYCJlyPL/p6FHAxwdI/5SO\n+8n3YaltyXdIVY60hCkQ0CQGpChKmERupk0DTp0CYmOBQYOAX67Ph6eBJ5z1nNC9OxARAejrA05O\nQFKS7Pc/wXICPuV/wq5/dsm+8ComP5+7LcLHBwh9FgpLHUtoqGnwHVaVY6ltifvJ95H+KV3serq9\nhBRGCZPIxbp1XH/a+fNAs2bc1Hf77uzDErclom1q1AB+/x0YNgxwdub6OGVJVUUV6z3XY86lOcj4\nlCHbwquYiAhu7ti2bbnmWKfWTnyHVCVpqGnAUscSYc/DxK63tweePgVevJBzYKRKooRJKl10NPDL\nL1ztsv7/B8H+GPwjZtrPRJPaTYpsKxAAP/8MDB4MeHkBGTLOa5Y6lujWthuWXFvy5Y0V2NGjgK8v\n92/qv5TOqbXkZlk1Ne53SM2yBKCESSrZx49cjXHdOkBXl1sWHB+M+8n38b3V9xLfFxDAPTFixAhA\nKOMux1/dfsWWG1uQkFI9n+HEGHDs2Of+yztv78C2pS3fYVVZ0voxAerHJJ9RwiSVavFioFMnYOBA\n7nWeMA/Tzk3Dyu4rpfapCQTAH39wzyZculS2MWnX1cZUm6n46fxPsi24irh9m/u/iQl3O4m1jjU9\n7kwKm5Y2+Of1PxIfQu7uDoSFAeniuzmJElHYhCkUCjF+/HjY2dnBxcUF8fHxYrcbO3YsZs2aJefo\nCADExwObNwO//fZ52b5/96FhzYbo3b73F9+voQEcPgysXy/7ibCn205HZFIkIl+If8STIjtyhKtd\nCgTAhScX0FW/K98hVWm1a9TG182+lvi4r7p1ub7Mc+fkHBipchQ2YQYGBiInJwdhYWFYunQppk+f\nXmKbzZs3486dOzKbao2UzbRpwI8/Ajo63Os8YR4WXV2EAOeAUn8nOjrAwYOAnx+QIMMW1JrqNTHf\naT5mX5otu0KrAMaAAwc+1+gvJFxAN/1u/AalALq06YLLCZclrqdmWQIocMIMDQ2Fh4cHAMDa2hox\nMTFF1oeFhSEqKgrjxo1TyieD8y08nGsanDr187IDdw6geZ3mcNZ1LlNZjo7AzJlAv35AdrbsYvTr\n7Ifnac9x4ckF2RXKsxs3uD5fS0sgKT0JrzNfo3PzznyHVeV11e+KiwkXJa7v2RM4fRrIpafFKTWF\nTZjp6enQ0tISvVZVVYXw/6NDXr16hYULF2L9+vWULHmydCnw009csyoA5AvzsejqIszvMr9cNf4f\nfgAMDIDvJY8TKjN1VXUsdFmI2RdnV5vfyf793D2uAgFwMeEiXPVcoaqiyndYVZ59K3vcenNL4v2Y\nLVsCenpAqPiHmxAlocZ3AOWlpaWFjEL3HAiFQqiocPn/8OHDSE5OhpeXF16/fo2PHz+iQ4cOGD58\neIly/P39Rf92dnaGs7NzZYde7cXFAZGRXNNggYN3D6JRrUZw03MrV5kCAbBtG2BlBWzfDnz7rWxi\nHdBxAJaFLsOx+8fg28FXNoXyRCjkmq/PnuVeX3hyAV31qP+yNGqq14S1jjWuPr2KHl/1ELtNwWTs\nyniKCAkJQUhICN9h8I8pqCNHjjA/Pz/GGGPh4eHMy8tL7HY7d+5kM2fOFLtOgQ+/ShsxgrFFiz6/\nzsvPYx3Wd2DnHp+rcNlxcYw1bsxYTEyFixI59fAU67C+A8vLz5NdoTy4coUxY2Pu30KhkLVY2YI9\nfveY36AUyJKrS9iUM1Mkrv/nH8b09RkTCuUYVBWlrOdOhW2S9fHxgaamJuzt7TF9+nSsXr0a+/fv\nx9atW0tsS4N+5Of5c+6RUhMmfF52OO4w6mnWk8ngkw4dgA0buP5MWc0562ngiQY1G+Dg3YOyKZAn\n+/dzEz4AQNx/cdBQ00Dbhm35DUqBdNXvKrU/28SEm3Lw7l05BkWqFAFj1aTzphwEAkG16buqKqZO\nBVRVgZUruddCJoTJRhOs7L4SHgYeMtvPtGnA/fvAyZOAigwu+87Hn8ekM5Nwd8Jdhezzy87m+tli\nYrgJIpaHLkdiaiI2eG/gOzSFkS/MR5MVTRA3MQ7N6zQXu83UqdxsVQsWyDm4KkZZz50KW8MkVc+7\nd8CuXUVHxh6JO4LaNWrDva27TPe1bBk3i9C0abJ5JFhX/a5oVKuRwtYyAwO5mZEKZlM69egUvNt5\n8xqTolFVUYWLngsuPpE8WnbgQK5vXglzBQElTCJDf/zB3TBfcN+lkAmx8OpCzHcq38hYadTVuSRx\n+TI3m1BFCQQC+Hfxx8IrC5EvzK94gXJWeCBUSlYKbr66CRc9F36DUkBd9briQoLkZllrayAr6/Ns\nSkS5UMIkMvHhA5cwfyo021zg/UBoqmnCq51Xpeyzfn1u9pWdOz83AVdEV/2uaFyrscLVMhMTgZs3\nuYsVgJur17GNI2qp1+I1LkVU0I8pqblRIOBu2zmoWD8RIiOUMIlM/PknN32YoSH3WsiEWHilcmqX\nhTVvDoSEADt2ADNmVKypTCAQwN9Z8WqZO3dyg300NbnX1BxbfgYNDaAqUMW95HsStxk0iJpllRUl\nTFJhubnAqlXcY7kKnHhwAqoqqhLvaZOlli2Ba9e4m8r79KnY6Fk3PTeFqmXm5XEXKwXNsfnCfJx5\nfIYSZjkJBAJ4tfPC6UenJW7TqRPXJRAdLcfASJVACZNU2MGD3Cwo1tbca8aYXGqXhTVsyPVn6usD\npqbcDeblqQEoWi3z+HGgVStuwA8ARL+MRrPazdCmfht+A1NgXu28cOrRKYnrC5plC0/MQZQDJUxS\nIYxxI1Znzvy8LOhhEIRMiF7te8k1lho1gNWruQEwP/8MeHgAV66UPXEW1DIP3Kn6Z8Q1a4ApUz6/\nPvHghFxq9dWZq54rYl/GIi07TeI2AwdyF4qyflYrqdooYZIKOX2aeyp99+7ca8YYAq4ElHvOWFno\n2hW4dQvo2xcYOxYwN+eajJ8/L937RbXMq1W7lnnzJvcEl4LBPowxHLl3BH079OU3MAVXS70WHFo7\nIDg+WOI2RkZA48bA9etyDIzwjhImqZBly7jaXEFuPP3oNHLzc9HHsA+vcdWowSXLe/eA5cu5/3fu\nDBgbc/dunjnDjeyVxE3PDU1rN63Stcy1a4GJE7n+NAC4+99dZOdlw0Lbgt/AqoEvNcsC3ECrPXvk\nFBCpEmimH+U9/AoLCwOGDQMePOBqmYwxWG+zxgz7Gehn1I/v8ErIzwdiY4HgYOD8ee5RWA4OXE20\nd2+gSZOi2198chETTk9A3IS4Kjf7z4sX3FRtjx4BjRpxywJCApCanYrVHqv5Da4aeJLyBLbbbfFq\n+iuoCMTXKwq+g6QkoGZNOQfIM2U9d1INk5TbsmXcA6LV/v/Mm7OPz+Jj7scq+9QPVVXuaSdz53J9\nmy9fAiNHcgm0XTtgyBAgKurz9q56rmhWuxn2/ruXv6AlWL4cGDXqc7IEgMP3DlfJCxVFpN9AHw1r\nNkTsy1iJ27RsyT139PhxOQZGeEUJk5TL3bvcI7z8/LjXBX2X85zmSbwir2rq1gUGDAD+/pu7+d/C\nAujfn3tY8P373FX0ItdF8A/xR25+1Xly8OvXXFPgjz9+Xvbw3UO8+/gOtq1s+QusmvFu542TD09K\n3WbECO4+WKIcFOPMRqqc5cuByZM/N0UFxwcj/VO6wtZw6tfn+jYfPgS6dAEcHYFFiwA7HScYNDTA\nnzf/5DtEkZUrgaFDuUkbChy6ewg+hj4Kc7GiCHwMfXD0/lGp2/Tpw7VKJCXJKSjCK/rrImX27Bn3\nlJDvvuNeF65dVrW+vrLS0OBqbjducM22jo7AZONFWHRtEbLzsvkODy9ecLMaFZ4kgjGGPf/uwVCT\nofwFVg3ZtrLFu4/v8PDdQ4nb1KrF9YHT4B/lQAmTlNnKlcDo0UCDBtzriwkXkZKdggEdB/AbmAy1\nasXNU9uzJzC+pxX0Nc2xKWYT32Fh7lxg/PjPE9wDQOyrWOTm58KmpQ1/gVVDKgIV+Bj64EjcEanb\n+flxT+lRwjEwSocSJimTN2+4q+mCR3gxxuAf4o+5jnMVvnZZnIoKMHs2N6n87TULEXBxKTJzMnmL\n59Yt4OzZorVLANh9azeGmgylB6VXgr5GfXHknvSEaWfHTQ9ZeMAYqZ4oYZIy+f137v6zgv6zC08u\n4F3WOwwyHsRvYJWod2/g7C4TZN1zwdjt63iJgTHuImXePEBL6/Py3PxcHLh7AN98/Q0vcVV3Tm2c\n8DTtKRJTEyVuIxBwI5a3bpVfXIQflDBJqaWmAlu2cE8FAbja5YKQBZjvNL/a1S6Ls7YGDo73x8Gn\nv2HLX6ly3//u3UBaGjBuXNHlwfHB0G+gj3aN2sk9JmWgpqKG3u174+g96YN/Ro0Cjhzh/kZI9UUJ\nk5Ta+vVcn16b/8/rHRwfjNTs1GrVdylNb4f28DHqjalHf8WxY/Lbb3Iyd5GyZcvne14LbI7djNGm\no+UXjBLq26EvDscdlrpNs2aAuzt3YUOqL5rpR3kPv0wyM4G2bblnT3bowNUubbfbYqrNVAw0Hsh3\neHLzMuMljNZ9DdXtMdi3QQ/u7pW/z6FDuXlLf/+96PJnac9gutkUz354hto1ald+IEoqJz8HLX9r\nicjRkdBroCdxuytXuJHjd+9+niqyulLWcyfVMEmprFkDuLlxyRIAzsWfQ0ZOhsLed1le2nW1Md3+\nB3T+aSaGDgWuXq3c/e3bB8TEAIsXl1y37cY2fPP1N5QsK1kN1RoY0HEA9tyWfu+IkxP3/8r+TRD+\nUMIkX5SSwtVuAgK41wV9lwu6LKj2fZfiTLebjodZYZi7JRT9+nEzHlWGxETu0V379wO1i+XE3Pxc\nbLuxDePMx4l9L5GtoSZDseffPVJrVQIBd8vPJv7vPiKVhBIm+aIVK7iRou3+P67k1KNT+Jj7Uelq\nlwVqqdfCEtcl2PduGrb/KUSvXtyk7rL08SN3Q/ysWdwDsYs7ePcgDBsbomPTjrLdMRHLWscajDFE\nv4yWut3w4dytP69eySkwIleUMIlUb94AmzcD8+dzr/OF+Zh5YSaWuC5R6mnYvjH5BowxJOvswubN\ngLc3d5+kLDDGTQrfsePn+12LrmdYHrocM+xnyGaH5IsEAgGGmgzF7lvSR/XUr8/ddrV+vZwCI3Kl\nsIYZthQAABPHSURBVGc8oVCI8ePHw87ODi4uLoiPjy+yfv/+/bCxsYGDgwO+++47peygloXFi4Fv\nvgFat+Ze7769Gw1qNkCPr3rwGxjPVAQq2NRjE2ZenAmH7slYtw7w8OAGfFQEY9yI2GfPuFGx4gaP\nnH18FgKBAO5t5TDiiIgMNRmKg3cPIic/R+p2U6dy3520560SBcUU1JEjR9jIkSMZY4xFRESw3r17\ni9Z9/PiRtW3blmVlZTHGGBs8eDA7ceJEiTIU+PDlIi6OscaNGXv7lnv9Mecja/VbKxb6LJTfwKqQ\nKWemML9AP8YYY3v3MtasGWPXr5evLKGQsblzGevUibF37yRv12VHF7bn1p7y7YRUiNMOJ3bo7qEv\nbte7N2Pr18shIJ4o67lTYWuYoaGh8PDwAABYW1sjJiZGtE5TUxPh4eHQ1NQEAOTl5aGmsj3hVQam\nT+f60AoerPxH9B8w1zaHXSs7fgOrQn5x+QUXnlxASGIIhgzh5hT18eEeGVYWeXncLQlBQdzzORs2\nFL/dhScX8DLjpdLc+1rVjDcfX6o5hadPB1av5h5aTqoPhU2Y6enp0Co0R5iqqiqEQiEArr+hyf/P\n8uvWrcOHDx/QtWtXXuJUVGfOAPHxwPffc69TslKwLHQZlrgu4TewKqauRl2s91yP0SdGI+NTBtzd\nuYQ3axY3K09pmuUSEwFXV64Z9to1oGlT8dsJmRAzL8zEItdFUFdVl+lxkNLx7eCL229uS32CCQA4\nOHAXPUFBcgqMyIXalzepmrS0tJCRkSF6LRQKoaKiUuT1jBkz8PjxYxw5InnyZH9/f9G/nZ2d4ezs\nXBnhKpScHO7ZkKtWATVqcMsWXV2EPu37oEOTDvwGVwX1NuyN4w+OY+q5qdjWaxs6dwZu3uRuCfnq\nK2DOHGDYMO6B1YW9ecMNDtm4EZg5k+v7UpVyl07BbDPKOjq5KtBQ08DIziOxJXYLVnZfKXE7gQD4\n6Sfg11+5EeaKPpFBSEgIQkJC+A6Df3y3CZfXkSNHmJ8f13cUHh7OvLy8iqwfPXo0+/7775lQKJRY\nhgIffqVavJgxLy+uT40xxuLexrHGyxuzN5lv+A2sCkvPTmf6a/TZsXvHiiyPjmasVy/G6tVjzNWV\nsdGjGRs5kjFbW8bq1+deJyR8ufyMTxms9erW7NKTS5VzAKTU4t/Hs8bLG7Os3Cyp2+XlMWZkxNiZ\nM3IKTI6U9dypsFPjMcYwYcIE3L59GwCwY8cOxMbGIjMzExYWFrCwsIBTwdQbAKZMmYI+ffoUKUNZ\np3eS5uFD7nFFsbHcnLGMMXjs9YCngSd+sPmB7/CqtPDn4fA56IPwb8NLTKH27h0QHQ08fco9Nqxd\nO8DKinsAcWn8FPwT3nx4g798/qqEyElZee31Qt8OffGt2bdStztwgJslKyxM8WuZhSnruVNhE6Ys\nKOuXLgljXF9a797AD//PjcfvH8esi7Nwa/wt6jcrhbWRa7H95naEjQqT2ZR10UnR8N7njTsT7qBp\nbQkdnESuLiVcwsTTE3F3wl2p9yPn5wPGxsDatUC3bnIMsJIp67lTYQf9ENnbvp2bZH3SJO51dl42\npp6bijUeayhZltIkq0kwa2GGEYEjIGTCCpeX/ikdg48MxgbvDZQsqxAXXRfUUq+FUw9PSd1OVZV7\nhmlAAHdBShQbJUwCAHj8mBvZuWPH54Env1z5BWYtzNCtbTW6NK5kAoEAG703IvljMiacmlChq3Ah\nE2LU8VFw03OjgT5VjEAgwAy7GVgetvyL2w4cyD2i7dw5OQRGKhUlTILcXO4RUvPmcc1HAHDr9S1s\nubEF6zzX8RucAtJU00TQ4CD88/ofTDk7pVw1TcYYfgr+Cf99/A9rPddWQpSkovoa9UVSehJCn4VK\n3U5VlRstO2MG3Zep6ChhEixcCDRo8LkpNk+Yh9FBo/Gr269oUbcFv8EpqLoadXHmmzO49eYWBh4e\niKzcrFK/lzGGny/8jOAnwTg28Bg01DQqMVJSXmoqapjjOAfzLs/74rZ9+gBaWvSAaUVHCVPJnT4N\n/Pkn1xRbMIpvTcQa1K1RF9+aSh8BSKRrULMBgocGQ1NNExZbLXDj1Y0vviclKwX9D/XH1adXccXv\nChrWlDDlD6kSRnQegRfpL3DxyUWp2wkE3FN/5s3jnkRDFBMlTCX2+DH3VIy//waaN+eW3Xl7B79e\n/xVbem6BoDqNg+eJhpoG/urzF2Y7zIbHHg+MPD4St9/cLtG3mfEpA39E/YGOGzpCp64OQvxCKFkq\nADUVNQQ4B2DOpTlf7K+2tQVsbLgp84hiottKlPTw09IAe3tu6rvx47ll2XnZsNpqhR/+1969B0V1\nng8c/7KAoqgoRhPrNQHzM/kFSoiKXAxutGKkSiXQYqJWbkbjjBds/mlnnJYUb5NoGZqOTGzRmkRr\nJMHgLT9HQtA4Yo0RvA4mViVqScJdBBbZ9/fH0VVGXRcCLOfwfGbOrLvnuL7PPO777Nnzvu+ZsIyE\n5xOc20ADqmqoIv1oOlknszC5mPB73A8PNw+u1lzl1PenMI8yszJ8JYFDAp3dVNEKVmUlYGMAf5z0\nR6KfibZ77MWL2vzbO/Oc9aq79p1SMLth+A0N8PLL2v0WMzLu/hSb8lkKV6qv8FHsR3J22YGUUpz7\n8RznfzyPpdnCYM/BBA4JpL9Hf2c3TbRR3n/ySNiVwNnFZ+ntbn81irfe0gpmTk4nNa4DdNe+Uwpm\nNwu/uVkb5m4ywbZtd6eQ7C7ZzaI9izj5+kkG9h7o3EYKoUO/2fkbxgwcw5/Mf7J7XGMj+PvD22/D\njBmd1Lh21h37TpCC2a2S3tSkLQJeUaHdRaHn7cGXJeUlhP0jjF1xuwgeHuzcRgqhU6XVpQRkBnAs\n6Rg+3j52jz14EJKS4PRp8GyfBaE6VXfrO++QQT/dRH09REdrI/Q+/fRusaxtrGXWv2bxlvktKZZC\n/ATDvYbzh4l/IH5XPM1W+xMuJ0+G8HBtbqbQDymY3UBpKUycCF5ekJ0Nt++rzS3rLV77+DVChoWw\n4IUFzm2kEAawNGgpAOmF6Y889i9/gd27ZQUgPZGCaXCffQZBQdp1y61bwf32krBKKd7Y8waNzY28\nG/muDPIRoh24mlzZ/KvNrD68mtPfn7Z7bP/+2hzopCSorOykBoqfRAqmQVVVwYIF2vb++9rNbO+t\nialfpHL82nF2xu6kh2sP5zVUCIN5asBTrJ+6nuh/RVPVUGX32MmTtUslCQmyOLseSME0mMZG7aee\np5/WRsKeOqXdsuteaQVpfHDqA/a+tpe+Pfs6p6FCGNjcn88lwieCeZ/Me+RawuvWwbVr2kpAomuT\nUbIGCf+HH2DjRvjb3yAwENauvbuQ+h1KKVK/SGX7me3kzcuTdWKF6ECWZgtT/jmFsT8byztT37F7\n2aO0FMaN06Z6mc2d2Mg2MlLf2RpyhqljdXXaB2zGDPD1hcuX4cAB2LPn/mJ5y3qLJfuWsPPcTvJ/\nmy/FUogO1sO1BzlxORy4eIDVh1fbPXb4cO3SSVwcnD/fSQ0UrSZnmDoLv74e9u/X1n/dtw9CQmD2\nbIiK0u6G8CC1jbXEZcfR1NzEjtgdsqKMEJ3oeu11wrLCWDR2Eb8L+Z3dYzdv1m42feQIDOnC32n1\n2He2BymYOgi/vl4rjh99pD2+8ALExkJMDDz2mP2/W/TfIuKy4wgfGU7Gyxm4u7p3TqOFEDal1aVE\nvB9B1P9EsWryKrs/z/75z9oX4oMHYdCgTmxkK+il72xvUjC7cPgnTkBmpvbhCQzUimR0NAwe/Oi/\na1VW3j32LqkFqWyI2MAc/zkd32AhxEOV3ywn8sNIRvYfyaYZmx464E4pWLlSmzN98GDXPNPs6n1n\nR5GC2cXCv3NdMjMTysogOVkbcj50qOPvUVxWzMLd2i1ItvxqC6MHju6g1gohWqPhVgNL9i3h0JVD\nbHtlGwFPBDz02LQ07T61ubnwzDOd2EgHdMW+szNIwewi4RcVaUVy+3YIC4PXX4dp0+4uju6IqzVX\nSTuUxs6zO0l7KY3EwERMLjKuS4iuZmvRVlb83wqSApNYGb4SDzePBx6XlaUtn5eVBb/8ZSc30o6u\n1Hd2JulNnaiuTvsgTJgAkZHaT61FRdpar5GRjhfLi5UXWbZ/Gf4b/fF09+TMG2dIfiFZiqUQXdTc\nn8+laGERFyou8HTG0/z9xN+5Zb1133Hx8bBrFyxaBIsXw40bTmissJEzzE4OXynt2uR772nXJkND\ntZ9dp08HNzfH36e+qZ793+znvRPv8e9r/yY+IJ6U4BSe6PNExzVeCNHujpQe4fcHf09pTSmLxy0m\nPiCeAb0GtDimqgqWLoVDh2DNGm08gzNXs5QzTJ2xWq0sXLiQkJAQzGYz3377bYv9ubm5jB8/npCQ\nEDZt2uSkVt519iykpmr3wYuJgWHDtFV4cnNh5kzHiuW12mt8eOpDZmfPZsg7Q8g4lsGv//fXXFl2\nhXW/WHdfsczPz++YYLoAI8cGEp/etSa+kOEhfP7bz/kg+gNOXD/Bk+lP8sqOV9h+ejs1jTWAtu7s\nli3aF+21a2H8eG2sg8XSQQGIB2rFOU3XkpOTg8Vi4ciRIxQWFrJixQpybt/CvKmpiZSUFI4fP07v\n3r0JDQ1l5syZDHZkeGk7KSuDggL4/HNtpNvNm1qh3LgRgoO1ZevsqaivoLismOKyYk7+9ySHrxym\nvL6c8JHhRPhEkD4tncGe9uPJz89n0qRJ7RdUF2Lk2EDi07vWxufi4sKEYROYMGwCFfUV5JzPYUvR\nFpI+TeLZQc8yadQkgoYG4R/gz9HCp9id60pGBqSkaCPnZ83Sxj54PPhSqGgnui2YX375JdOmTQMg\nKCiI48eP2/adO3cOX19fvLy8AAgLC6OgoICYmJh2+beVgoYGqK6G69e1Za2++w4uXYLiYm27eVP7\nD2w2Q2Ki4lk/C43Wem423eTcj5VU1FdQXl+uPd4s51rtNS5XX9a2qstYmi34Pe6H/2B/xv1sHEuD\nluL3uJ9clxTC4Lx7eZPwfAIJzyfQcKuBwu8K+eLyF2wp2sKp70/xQ90PjB44mpELRjLFOoL/XBzB\n638dwtXlA/Ad6k3AmAE8+6Q3z43ui++ongwa5IK3d+sGEIoH023BrKmpod89S9u4urpitVoxmUzU\n1NTYiiVA3759qa6ufuD7PLZsGgqFUlbtEStK3X5s8VzRbLXSbNUeXVwUrm5W3NwV7j2suLsr3Pso\nepibcftFA71p4MitBg421NO4uxH3fe54uHnQy60X3r28bdvA3gPx9vBmaL+hhAwPYWT/kYzqP4pB\nvQfJLbeE6OY83DwIHxVO+Khw22s1jTWUlJdwpfqKtg28gtczX/HjjUq+K6/ksxsVZFdU0lhYizrW\nBM09ockDF6sHpjsbbphwxeRiwoQrYMJFueKCCRdccVG3HzFp+wBwsT12W0qnUlJS1I4dO2zPhw0b\nZvtzcXGxmj59uu358uXLVXZ29n3v4ePjowDZZJNNNtlasfn4+HRsB99F6fYMMzQ0lNzcXGJjYzl6\n9Cj+/v62fWPGjOHChQtUVlbi6elJQUEBb7755n3v8c0333Rmk4UQQuiYbgvmrFmzOHDgAKGhoQBk\nZWWxbds2bty4QXJyMuvXryciIgKr1UpiYiJDuuL6UkIIIXSjW8/DFEIIIRxl+CGXepuv2VqPim/D\nhg0899xzmM1mzGYzJSUlTmpp2xUWFmJ+wF119Z67Ox4Wn95z19TUxNy5c3nxxRcJCgoiNze3xX69\n5+9R8ek9f83NzSQkJBAWFsbEiRM5c+ZMi/16z1+bOPsiakfLzs5W8fHxSimljh49qqKiomz7LBaL\n8vX1VVVVVcpisahx48apsrIyZzW1TezFp5RSc+bMUSdOnHBG09rF2rVrlZ+fnwoODm7xuhFyp9TD\n41NK/7nLyspSy5cvV0opVVFRoUaMGGHbZ4T82YtPKf3nLycnRyUmJiqllMrPzzdc39kWhj/DdHS+\npru7u22+pp7Yiw/gq6++YtWqVUycOJE1a9Y4o4k/ia+vLx9//PF9y3AZIXfw8PhA/7mLjY0lNTUV\n0H4JcbtnOSsj5M9efKD//EVFRZGZmQnApUuXGDDg7nJ9RshfWxi+YD5svuadfY7O1+yq7MUHMHv2\nbDIzM8nLy+Pw4cPs2bPHGc1ss+jo6Ps6IjBG7uDh8YH+c+fp6UmfPn2ora0lNjaWtLQ02z4j5M9e\nfKD//IHWn8yfP58lS5bw6quv2l43Qv7awvAFs1+/ftTW1tqe31ncAMDLy6vFvtra2hbfovTAXnwA\nS5cuxdvbG3d3dyIjI/n666+d0cx2Z4TcPYoRcldaWspLL73EvHnziIuLs71ulPw9LD4wRv4ANm/e\nTElJCcnJydTX1wPGyV9rGb5ghoaGsnfvXgC78zUtFgsFBQUEBwc7q6ltYi++6upq/Pz8qKurQylF\nXl4eY8eOdVZT25URcmePEXJXVlbG1KlTWbduHfPnz2+xzwj5sxefEfK3detWVq9eDUCvXr0wmUy2\n1ceMkL+20O08TEcZfb7mo+Jbs2YNZrOZnj17MmXKFNv1Tr2580E1Uu7u9aD49J67VatWUV1dTWpq\nqu1aX3JyMnV1dYbI36Pi03v+YmJimD9/PuHh4TQ1NZGens4nn3xiyM+fo2QephBCCOEAw/8kK4QQ\nQrQHKZhCCCGEA6RgCiGEEA6QgimEEEI4QAqmEEII4QApmEIIIYQDpGAKIYQQDpCCKYQQQjjg/wET\nzExWPMA3LQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "# small smoothing parameter (noisy estimation)\n", "title('green = true density, blue = density estimated with a gaussian kernel and ' + str(len(sampled_points)) + ' points')\n", "plot(x, [my_gaussian_kde(x_i, sampled_points, .05) for x_i in x], color=\"blue\")\n", "plot(x, y, color=\"green\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAcwAAAEHCAYAAAAj9HbxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFEIIIRrg/wD6ebWewLBuWQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "# big smoothing parameter (oversmoothing)\n", "title('green = true density, blue = density estimated with a gaussian kernel and ' + str(len(sampled_points)) + ' points')\n", "plot(x, [my_gaussian_kde(x_i, sampled_points, .2) for x_i in x], color=\"blue\")\n", "plot(x, y, color=\"green\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 19, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAcwAAAEHCAYAAAAj9HbxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n", "text": [ "" ] } ], "prompt_number": 19 } ], "metadata": {} } ] }