diff --git a/assignment 3/iml_assignment3_solved.ipynb b/assignment 3/iml_assignment3_solved.ipynb new file mode 100644 index 0000000..e7ad38e --- /dev/null +++ b/assignment 3/iml_assignment3_solved.ipynb @@ -0,0 +1,392 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "### Solution for Assignment 3 of the course \"Introduction to Machine Learning\" at the University of Leoben.\n", + "##### Author: Fotios Lygerakis\n", + "##### Semester: SS 2022/2023" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Create an abstract class “ContinuousDistribution”. The class must contain the following function definitions (not implementations)\n", + "* Data Import and Export using csv files.\n", + "* Computation of the mean based on the samples from the csv.\n", + "* Computation of the standard deviation based on the samples from the csv.\n", + "* Visualization of the distribution, the raw data or the generated samples.\n", + "* Generating/Drawing Samples from the distribution.\n" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 1, + "outputs": [], + "source": [ + "import abc\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "from scipy.stats import multivariate_normal\n", + "from scipy.stats import beta" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "class ContinuousDistribution(abc.ABC):\n", + " def __init__(self, name):\n", + " self.name = name\n", + "\n", + " @abc.abstractmethod\n", + " def import_data(self, filename):\n", + " pass\n", + "\n", + " @abc.abstractmethod\n", + " def export_data(self, filename):\n", + " pass\n", + "\n", + " @abc.abstractmethod\n", + " def compute_mean(self):\n", + " pass\n", + "\n", + " @abc.abstractmethod\n", + " def compute_std(self):\n", + " pass\n", + "\n", + " @abc.abstractmethod\n", + " def visualize(self):\n", + " pass\n", + "\n", + " @abc.abstractmethod\n", + " def generate_samples(self, n):\n", + " pass" + ] + }, + { + "cell_type": "markdown", + "source": [ + "Implement a class “GaussDistribution”, which implements a multivariate Gaussian distribution (Equation 2.6 in the book).\n", + "* It is a child class of “ContinousDistribution”.\n", + "* Implement the functions defined in “ContinousDistribution”.\n", + "* Implement a constructor that optionally takes the dimension of the multivariate distribution.\n", + "* Implement a visualization for Multivariate Gaussians up to 3 dimensions.\n", + "* Find the empirical parameters of the distribution that created the samples in the ‘MGD.csv’ file.\n", + "* Plot the samples of the ‘MGD.csv’ file and the sample from the learned distribution in two subfigures.\n", + "* Generate visualizations of one- and two-dimensional Gaussians\n", + "\n", + "**The actual mean and covariance matrix of the MGD.csv file are [1, 0, 1] and [[1, 0.5, 0.5], [0.5, 1, 0.5], [0.5, 0.5, 1]] respectively.**\n" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 3, + "outputs": [], + "source": [ + "class GaussDistribution(ContinuousDistribution):\n", + " def __init__(self, name, dim=1, mean=None, cov=None):\n", + " super().__init__(name)\n", + " self.dim = dim\n", + " self.mean = mean\n", + " self.cov = cov\n", + " self.data = None\n", + " self.sampled_data = None\n", + "\n", + " def import_data(self, filename):\n", + " self.data = pd.read_csv(filename)\n", + "\n", + " def export_data(self, filename):\n", + " self.data.to_csv(filename, index=False)\n", + "\n", + " def compute_mean(self):\n", + " return self.data.mean()\n", + "\n", + " def compute_std(self):\n", + " # return the covariance matrix if the distribution is multivariate\n", + " if self.dim > 1:\n", + " return self.data.cov()\n", + " return self.data.std()\n", + "\n", + " def visualize(self):\n", + " # Plot the samples of the ‘MGD.csv’ file and the sample from the learned distribution in two separate sub-figures. add a title to each sub-figure.\n", + " if self.dim == 1:\n", + " data = self.sampled_data if self.sampled_data is not None else self.data\n", + " # plot the samples\n", + " plt.hist(data['x'], density=True, histtype='stepfilled', alpha=0.2)\n", + "\n", + " # create a grid of points\n", + " x = np.linspace(data['x'].min(), data['x'].max(), 100)\n", + "\n", + " # plot the pdf of the distribution\n", + " plt.plot(x, multivariate_normal.pdf(x, self.mean, self.cov))\n", + "\n", + " plt.show()\n", + " elif self.dim == 2:\n", + " data = self.sampled_data if self.sampled_data is not None else self.data\n", + " # create a grid of points\n", + " x = np.linspace(data['x'].min(), data['x'].max(), 100)\n", + " y = np.linspace(data['y'].min(), data['y'].max(), 100)\n", + "\n", + " # plot the pdf of the distribution\n", + " X, Y = np.meshgrid(x, y)\n", + " pos = np.empty(X.shape + (2,))\n", + " pos[:, :, 0] = X\n", + " pos[:, :, 1] = Y\n", + " rv = multivariate_normal(self.mean, self.cov)\n", + " plt.contourf(X, Y, rv.pdf(pos))\n", + " # plot the samples\n", + " plt.scatter(data['x'], data['y'], c='r', marker='o')\n", + " plt.show()\n", + " elif self.dim == 3:\n", + " fig = plt.figure()\n", + " ax = fig.add_subplot(121, projection='3d')\n", + " ax.set_title('Original Data')\n", + " ax.scatter(self.data['x'], self.data['y'], self.data['z'], c='r', marker='o')\n", + " ax.set_xlabel('X Label')\n", + " ax.set_ylabel('Y Label')\n", + " ax.set_zlabel('Z Label')\n", + " ax = fig.add_subplot(122, projection='3d')\n", + " ax.set_title('Sampled Data')\n", + " ax.scatter(self.sampled_data['x'], self.sampled_data['y'], self.sampled_data['z'], c='b', marker='o')\n", + " ax.set_xlabel('X Label')\n", + " ax.set_ylabel('Y Label')\n", + " ax.set_zlabel('Z Label')\n", + " plt.show()\n", + "\n", + " def generate_samples(self, n):\n", + " # generate samples from the distribution\n", + " if self.dim == 1:\n", + " self.sampled_data = pd.DataFrame(np.random.normal(self.mean, self.cov, n), columns=['x'])\n", + " elif self.dim == 2:\n", + " self.sampled_data = pd.DataFrame(np.random.multivariate_normal(self.mean, self.cov, n), columns=['x', 'y'])\n", + " elif self.dim == 3:\n", + " self.sampled_data = pd.DataFrame(np.random.multivariate_normal(self.mean, self.cov, n), columns=['x', 'y', 'z'])\n", + "\n", + " def fit(self):\n", + " self.mean = self.compute_mean()\n", + " self.cov = self.compute_std()" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Find the empirical parameters of the distribution that created the samples in the ‘MGD.csv’ file." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 4, + "outputs": [ + { + "data": { + "text/plain": "
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" + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x 0.984026\n", + "y 0.008833\n", + "z 0.860115\n", + "dtype: float64\n", + " x y z\n", + "x 0.957077 0.652484 0.563223\n", + "y 0.652484 1.420160 0.753830\n", + "z 0.563223 0.753830 1.255599\n" + ] + } + ], + "source": [ + "gd = GaussDistribution('MGD', 3)\n", + "gd.import_data('MGD.csv')\n", + "gd.fit()\n", + "gd.generate_samples(100)\n", + "gd.visualize()\n", + "# print the mean and covariance matrix of the distribution\n", + "print(gd.mean)\n", + "print(gd.cov)" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Generate visualizations of one- and two-dimensional Gaussians using the above class." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 5, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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ja4hOhsv/DTFdTacKOR6bnYLcp2mM70NETTG93v8NluY607FEjFAZEQk1S++HTW97b+Z26UJI6mM6UchyRSaw9fS/0RKZRHTFOjKX3qQ5SCQkqYyIhJL1r3onNgP41V+gx1CzeYSm+CzvpGjWCOK3vUfqV7rkV0KPyohIqNi+Fl7bPX/IyEmQfbHZPNKqLm0oJaO8E86lrZ5N7Lb3DScS6VwqIyKhoKYMXroUWuqhXy7kTjedSP5H5RHj2DFgAgCZS2/Gvmuz4UQinUdlRCTYuZrh5fFQVQRd+8EFz+gSXj9VctzU3VfY1NDrg6uxNlWZjiTSKVRGRILdB1OhYAXY4+CSBRCVYDqR7Is1nIJTn6Appht25w9kLtGAVgkNKiMiweyb1+Czx73LY5+A5MOMxpEDc0Uls+20p3Hb7MQV5mtAq4QElRGRYFWxGV6/wbs88kY48hyzeaTNGpKPoXjU/QCkrn6EmOJPDCcS6VgqIyLBqKkWXr4Cmqqh1yg4dZrpROKjXYdfxM7Dx2HBQ+aSGzVDqwQ1lRGRYOPxwFt5UPYtxKTChc+CLcx0KjkIJSPvoT6xP+ENFWT+ZxK4W0xHEukQKiMiwWb18/D1ArDY4KLnIDbddCI5SJ6wKApOfQJXeAxdHJ+Rtmq26UgiHUJlRCSYlG2Ad2/3Lp86FbKON5tHDllTQl+Kj38QgNS1j9GlcInhRCLtT2VEJFg018O/fwMtDd6JzUbeaDqRtBNn31/tMSFaWK3DcCKR9qUyIhIs3rvzp3EiY58Aq/55B5PtOXdR33UgYY2VZH50i+YfkaCi31YiweDbN+DLZ7zL5z8JXVLN5pF257HZKTh5Lu6wKLqUfEry10+ajiTSblRGRALdrkJ4Y/d8IqNugr6nmM0jHaYpoS8lI7z3FUr/8mGiytcaTiTSPlRGRAKZqwVe/S00OCFjCJxyt+lE0sEqDx+Hs/dZWDwtZC6ZhLWpxnQkkUOmMiISyD6dAwXLISLWewM8W7jpRNLRLBaKjn+Appju2Ku20m2FJrSTwKcyIhKoSr6CpTO9y2fPgqTeZvNIp3HbEyg8+VE8FitJ3/+L+C1vmI4kckhURkQCUXO99/SMuwUGnAfHjDOdSDpZXXoOZYMmAdB9+Z263FcCmsqISCD6YBpUfAdd0uGcOWCxmE4kBpQNvpG65KMJa3TS4+M/em8FIBKAVEZEAs3mfFi5+7LOsfMgOslsHjHHGk7R6Dm4bXZiiz4iacMLphOJHBSVEZFAUrcTXr/euzzsGu9MqxLSGhMPwzFsMgDdVt5HhPNHw4lEfKcyIhJI3rkVqrdD18PgtHtMpxE/seOoidR0H4m1pd47O6vu7isBRvcVFwkU37wG61/x3o33/CchItp0IvEXFitFJ/6Zw145neiy1aR8PZ/yQTf8YrN1RU4D4Q7N0T3iTUeQTqAjIyKBoLYC3v6Dd/n4W7wTnIn8THOXDEpGemdnTVs1m8gd3xpOJNJ2KiMigeDtP0BdBaQeBaNvM51G/NSufhfg7DUGi6eFHstuBXez6UgibaIyIuLv1r8K377mPT0z9nEIs5tOJP7KYqFk1Axa7PFE7VhPytr5phOJtInKiIg/qyn76fTMibdC90FG44j/a4lOZfsI7+Dm1K/mYN+5yXAikQNTGRHxVx4PvHUL1O+EtKPhhFtNJ5IAsavvWKp6nobV3UyPZXm6ukb8nsqIiL/6ZhFsfAusYbtPz0SYTiSBwmKh+Pj7cUXEEV2xjpSvdbpG/JvKiIg/qt0B7/zRu3zCH6DbMWbzSMBpiU6jZIT36prU1XOwV+p0jfgvlRERf/TeFO/VMylHesuIyEHY1e98qjJPxepuosey28DtMh1JZK9URkT8zXfvw9cLAQuc95iunpGDZ7FQfPxMXOGxRJd/RddvnzOdSGSvVEZE/ElDlXfQKsBx10GPoWbzSMBriUnHMXwKAOlfPkx4daHhRCK/pDIi4k/yp0NVEST0glPuNJ1GgsTO/pdSk56DtaWejE+meK/UEvEjB1VG5s2bR1ZWFpGRkeTk5LBy5cp9bvvqq68ydOhQEhISiImJYdCgQfzjH/846MAiQWvbcvjir97lX/0FImLM5pHgYbFSfMKDuG12YouXkbD5FdOJRPbgcxlZuHAheXl5TJs2jdWrV5Odnc2YMWMoKyvb6/ZJSUnceeedrFixgq+//pqJEycyceJE3nvvvUMOLxI0mhvgjRu9y4OvgD4nGY0jwacpvg9lx94MQLfP7sFWX2E2kMjPWDwe347X5eTkMGzYMB577DEA3G43mZmZTJo0icmTJ7fpOY499ljOPvts7r333jZtX1VVRXx8PE6nk7i4OF/iigSGJffDRw9ClzS4/nOISjSdqFMF4t1kA5K7mX6v/4qoHd+wq8+5FJ4yz3SiA9JdewNbW7+/fToy0tTUxKpVq8jNzf3pCaxWcnNzWbFixQH393g85Ofns2nTJk488cR9btfY2EhVVdUeD5GgVbYRPp7tXT7zwZArItKJrOEUnfAQHouNhB/eJLYg33QiEcDHMlJRUYHL5SItLW2P9WlpaTgcjn3u53Q66dKlCxEREZx99tnMnTuX0047bZ/bz5w5k/j4+NZHZmamLzFFAofbDW/e5L276uFnwICxphNJkGtIPpqKgVcD0H353Via6wwnEumkq2liY2NZs2YNX3zxBTNmzCAvL4+lS5fuc/spU6bgdDpbH4WFuhRNgtTq56HwMwiPgbNmgcViOpGEgNJjb6GpSw8iaopIW/2I6TgihPmycXJyMjabjdLS0j3Wl5aWkp6evs/9rFYr/fr1A2DQoEFs2LCBmTNnctJJJ+11e7vdjt2uiZ4kyFU74INp3uVT7oIEHQGUzuEJj6Zk1H1kvXclyev/yq5+Y2noepTpWBLCfDoyEhERwZAhQ8jP/+k8o9vtJj8/nxEjRrT5edxuN42Njb68tEjwWTwZGp3QfTDk/M50Ggkx1ZmnsKv3OVg8LjI+mayp4sUon46MAOTl5TFhwgSGDh3K8OHDmTNnDrW1tUycOBGA8ePHk5GRwcyZMwHv+I+hQ4fSt29fGhsbeeedd/jHP/7BE0880b7vRCSQfPe+9668Fhuc+yhYbaYTSQjaPmIascXLiC5fS9cNf2fHURNNR5IQ5XMZGTduHOXl5UydOhWHw8GgQYNYvHhx66DWgoICrNafDrjU1tZy3XXXUVRURFRUFP379+eFF15g3Lhx7fcuRAJJUx28s/vmdyOug27ZZvNIyGqJTsMx7HYyPr2TtC8fxpl1Bi0x3UzHkhDk8zwjJmieEQkqH06HT2ZDfKZ3ThHNtKp5RkzyuOnz5gXElK3C2esMCk57ynSiPWiekcDWIfOMiMghKtsAy//iXT7zIRURMc9ipfj4mXgsNuK3LdbcI2KEyohIZ/F44K08cLfAEWdD/7NMJxIBoDGp/8/mHpmKpaXecCIJNSojIp1lzYtQsBzCo70zrYr4kbJjb6YppjsRNYWkfvUX03EkxKiMiHSG2h3w/l3e5ZOmaE4R8Tvu8Bi2j5gOQPK6p7BXfm84kYQSlRGRzvDhVKjfCWkD4bhrTacR2auqXqdT1TMXq7uZ7p/e6T21KNIJVEZEOlrBZ/DVC97ls2eDLdxsHpF9sVgoGTEdty2SLo7PSNj8iulEEiJURkQ6kqsF3t49p8ix46Fnjtk8IgfQHJtJ6bE3A9Dt8xnYGnYZzSOhQWVEpCOtfApK10NUEuRON51GpE12DLyahoTDCGvYQdqXD5mOIyFAZUSko1RthyX3e5dz/wTRSUbjiLSVxxZBycj7AEja+E+iytcaTiTBTmVEpKO8fyc0VUOPYTD4CtNpRHxS230ElX1/jQWPdzCrbqQnHcjne9OIhJKDnaY8pvgT+qx/BY/FyuZh99BQUt3OyfZN02dLe3Hk3ElcwYdEV3xN0qYX2XmkSrV0DB0ZEWlnFlcj3ZffDcCOARNo6HqU4UQiB6clOpXSId4B2GlfPoStfofhRBKsVEZE2lnyuqeJdG6hOSql9Re5SKDaMWA89V2PIqzRSfoXD5iOI0FKZUSkHYXXFLdOpe3IuQt3hO4yLQHOGvbTYNbvFhJd+qXhQBKMVEZE2lG3z+7B6mqgJj2HXX3Hmo4j0i7q0oaw8/BxAHT/9C7vzR5F2pHKiEg76VL0EfFb38VjsXn/krRYTEcSaTeO4VNosccTtfNbum54wXQcCTIqIyLtwDtodSoAO46aSGPSEYYTibQvV2QSpUNuAyBt1Sxs9RWGE0kwURkRaQfJ657GXvWjd9DqsbeYjiPSIXb2v5T6rgOxNVWRvnKm6TgSRFRGRA7RLwetxhpOJNJBrDaKR+0ezPr9v4guXWU4kAQLlRGRQ6RBqxJK6lOP/Wkw6/K7NTOrtAuVEZFD0KVo2c8Grd6rQasSEhzDJuOKiCNqx3qSNv7TdBwJAiojIgfJ4mqi+4r/Dlq9ksak/oYTiXQOV1RXHEO9g1nTv3xIg1nlkKmMiBykruufwe78gebIZA1alZCzs/9lPw1m/eIh03EkwKmMiByEsNrtpH71KOCdf0EzrUrIsdooGXkPAEnfLSCqbI3ZPBLQVEZEDkK3z2dga6mjNnUIuw67wHQcESPq0oZSediFAHRffhd43IYTSaBSGRHxUUzJchJ+eAOPxbp70Kr+GUnocgybjCs8luiKr0nctNB0HAlQ+i0q4gt3c+ug1Z39L6cheaDhQCJmtUSnUjrEO2Yq/YsHsDXsMhtIApLKiIgPun77PJGV39FiT6R0yK2m44j4hR0DJtCQeDhhjZWkrZplOo4EIJURkTYKqysjbdUjADiG3Y4rMsFsIBF/YQ2nZMTuwawbXyCyYr3hQBJoVEZE2ij9iwewNVdTl5JN5REXm44j4ldqu49kV59zsXjc3plZPR7TkSSAqIyItEF06SoSv/83gPcvQA1aFfmF7Tl34QqLJqZsFQmbXzUdRwKIfqOKHIjb5f1LD9h5+DjqUwcbDiTin1piulE+eBIA6Svvx9pUbTiRBAqVEZEDSNr0ElE71uOKiMMx7HbTcUT8WsXAq2mM6014fXnrxIAiB6IyIrIftoZK0r70TnVdemwerqhkw4lE/JvHZqdkxHQAktc/i73yO8OJJBCojIjsR9qqWYQ17qIh8Qh2DBhvOo5IQKjJPImqnqdh8bTQfcU0DWaVA1IZEdmX7WtJ2vACgHemVWuY4UAigaPkuKm4bXa6lHxK3NZ3TMcRP6cyIrI3bje8fSsWPOzq8ytqux1nOpFIQGmO60X5Mb8HoNtn92JpqTecSPyZyojI3ny9EIpW4gqLZnvOXabTiASk8uzraOrSg4jaElLXPGY6jvgxlRGR/9XghA+8958pG3wjLTHphgOJBCZPWBTbc7yXxSd//SQRzq1mA4nfUhkR+V9LH4TaMujajx0DrzKdRiSgVWWdQXXGCVjdTXT7bLrpOOKnVEZEfq5sA3w+37t85oN4bHazeUQCncXC9hHT8VjCiCvMJ7bgQ9OJxA+pjIj8l8cD794GHhf0Pwf65ZpOJBIUGhP6UbH7KGO3z6ZjaWkwnEj8jcqIyH99+xr8uAzCImHMDNNpRIJK2eCbaI5OxV61jeR1T5uOI35GZUQEoKkW3rvTuzzqZkjMMplGJOi4I7qwfbj3yrTUNXMJryk2nEj8iWZxEgFYNguqiiGhJxx/s+k0h2RdkdN0BJG9cvY9j9qNLxDjWEm3z++l4NT5piOJn9CREZGKzbB8rnf5jAcgPMpsHpFgZbFQMuJePBYr8T++Q0zxx6YTiZ9QGZHQ5vHA4tvB3Qz9ToMjzjKdSCSoNXQ9kh1Heu/z1H35NCyuJsOJxB+ojEho2/QObP4QbBFw5oNgsZhOJBL0Sof8gZbIrkQ6N9P1m+dMxxE/oDIioau5HhZP9i6PuAG69jWbRyREuO3xOIZPASD1qzmE1ToMJxLTVEYkdH0yB3YVQFwGnHir6TQiIaXysAupSz0WW3Mt3VbebzqOGKYyIqGpcit88oh3ecwMiIgxGkck5FisFI+8Bw8WEra8Rsz2z0wnEoNURiQ0LZ4CrkbofSIMGGs6jUhIakg+hp39LwOg+/K7wd1iOJGYojIioee797wDV61hcNYsDVoVMah06G202BOJrNxE12+fNx1HDFEZkdDS3OC9/wzAcddByhFm84iEOFdkAo5htwOQtmo2YXVlhhOJCSojElo+fdQ7XiS2G4y+zXQaEQEqj7iYupRsbM3VpGswa0hSGZHQUbkVPpntXR4zA+yxRuOIyG4WKyUj78ODhcTNrxK9/XPTiaSTqYxI6Fg8BVoavINWjzrfdBoR+Zn6lGx29r8UgIzld3lnRZaQoTIioeHng1bPfFiDVkX8kAazhi6VEQl+zfU/G7R6LaT2N5tHRPbKFZmIY5h3VmTvYNZSw4mks6iMSPD7ZM7PBq3ebjqNiOxH5RHjqEsZhK25hvTPNZg1VISZDiDSoXb+8LOZVu/XoFURf2exUjzqPvq9di6JWxbxw8px1HYfaTqVT47uEW86QsDRkREJXh4PvHObd6bVPifBUb82nUhE2qAh+Rh2Hnk5AN2X34XF1WQ4kXS0gyoj8+bNIysri8jISHJycli5cuU+t3366ac54YQTSExMJDExkdzc3P1uL9JuNr4Fmz8AWwSc9WcNWhUJII6hf6QlsiuRuzbTdf0zpuNIB/O5jCxcuJC8vDymTZvG6tWryc7OZsyYMZSV7X3WvKVLl3LJJZewZMkSVqxYQWZmJqeffjrFxcWHHF5kn5pq4V3vQDhG3gjJ/czmERGfuO0JbB9+BwBpX80hvEbfGcHM4vF4PL7skJOTw7Bhw3jssccAcLvdZGZmMmnSJCZPnnzA/V0uF4mJiTz22GOMHz++Ta9ZVVVFfHw8TqeTuLg4X+JKqPpgGnw6B+J7wvWfQ0T0QT3NuiJn++YSkbbzeOjz9kXEOFbi7HUGBac9ZTpRm2jMyE/a+v3t05GRpqYmVq1aRW5u7k9PYLWSm5vLihUr2vQcdXV1NDc3k5SUtM9tGhsbqaqq2uMh0mblm2CFtyxz1kMHXURExDCLheKRM/BYbMRvW0xs4X9MJ5IO4lMZqaiowOVykZaWtsf6tLQ0HA5Hm57j9ttvp3v37nsUmv81c+ZM4uPjWx+ZmZm+xJRQ5vHA23/w3or88DPhiDNNJxKRQ9CYdAQVA68GoNvyqVhaGgwnko7QqVfTPPDAAyxYsIBFixYRGRm5z+2mTJmC0+lsfRQWFnZiSgloXy+ErR9DWBSc+aDpNCLSDsqOvZnm6HTs1QWkrJ1nOo50AJ/KSHJyMjabjdLSPWfFKy0tJT09fb/7zpo1iwceeID333+fY445Zr/b2u124uLi9niIHFDdTnjvTu/y6NsgsZfZPCLSLtzhMZSMmAZAytoniNi1xXAiaW8+lZGIiAiGDBlCfn5+6zq3201+fj4jRozY534PPfQQ9957L4sXL2bo0KEHn1Zkf/LvgboKSOkPI24wnUZE2lFV1llU9zgZq7uJjOV3ek/JStDw+TRNXl4eTz/9NM8//zwbNmzg2muvpba2lokTJwIwfvx4pkyZ0rr9gw8+yN13382zzz5LVlYWDocDh8NBTU1N+70LkcIvYNVz3uWzZ0NYhNk8ItK+LBaKR96D22anS8lyEra8ZjqRtCOfy8i4ceOYNWsWU6dOZdCgQaxZs4bFixe3DmotKChg+/btrds/8cQTNDU1ceGFF9KtW7fWx6xZs9rvXUhoc7XAW7d4l7MvhaxRZvOISIdojutF2eCbAEj/7F6sjbvMBpJ24/M8IyZonhHZrxWPw3tTIDIBJq2CmOR2e2rNMyLiXyyuJvotOoPIXZvZ0f9ySo73v5vpaZ6Rn3TIPCMifsdZBEtmeJdPm96uRURE/I/HFkHJKG8BSdr4T6LKVhtOJO1BZUQC27u3Q1MNZObA4LbN6Csiga2223FUHnYhFjxkfHKHd14hCWgqIxK4NrzlvRmeNQzOmQNW/d9ZJFRsH34nLfZ4onZ+S7JupBfw9NtbAlNjNbx7m3d55I2QNsBsHhHpVK6orjiGe+cVSls9m/BqTY4ZyFRGJDAtuR+qiiExC078o+k0ImJA5eHjqEnPwdpST8and2nukQCmMiKBp+Qr+Hy+d/ns2boRnkioslgoOX4mbmsEsUVLiP/hTdOJ5CCpjEhgcbXAmzeBxw1HXwT9TjWdSEQMakzoR3n2dQB0+2y65h4JUCojElhWPgnb10JkPIzxv/kFRKTzlQ+6nob4voTXl5P+xQOm48hBUBmRwFG5Df5zn3f5tHugS6rZPCLiFzw2OyXHzwSg68YXiXasNJxIfKUyIoHB4/FO+d5cB71GaU4REdlDbbfj2Hn4OAAyPpmMxdVoOJH4QmVEAsPXL8OWfLDZ4dxHNaeIiPyCY/idNEcmE7lrMylr5pmOIz7Qb3Txf7UVsHiyd3n0bZB8mNk8IuKXXJEJbB85HYCUtfOwV24ynEjaSmVE/N97d0D9Tkg9CkbdZDqNiPgxZ+9zqOqZi9XdTI+Pbwe3y3QkaQOVEfFvmz+ErxcCFvjVXLCFm04kIv7MYqF41Axc4V2ILltN1w1/N51I2kBlRPxXY4130CpAzu+hxxCzeUQkILTEdMMxbAoAaV88SHh1keFEciAqI+K/8u+BXQUQ3xNOuct0GhEJIDuPvIzatGHYWurI+PROTRXv51RGxD9tWwErn/IunzsH7F2MxhGRAGOxUnzCg61TxSdsXmQ6keyHyoj4n+Z6eOMGwAODLteU7yJyUBoT+lF27M0AdPtsGmF1ZWYDyT6pjIj/WfoA7NgMXdJhzH2m04hIACs/5nfUdx1IWKOT7svv1ukaP6UyIv6leDUs/4t3+ZzZEJVoNo+IBDZrOEUnzsJjCSN+67vE/fi26USyFyoj4j9amuD1G7x35D3qfOh/tulEIhIEGroOoGzQ9QBkLL8bW/0Ow4nkf4WZDiChYV2R84DbpK5+hLSyb2iJTOK7QXfjasM+IiJtUT5oEvFbFxNZuYnun/2JwpPnmo4kP6MjI+IXIivWk/qV95dDyYjpuKK6Gk4kIsHEY4vYfbrGRsKW14nd9r7pSPIzKiNinMXVRI+P8rB4WnBmnYmzz69MRxKRIFSfkk35Mb8DIOOTKdgaKg0nkv9SGRHjUr/6C1GVG2mJTKJ41AywWExHEpEgVTb4ZhoS+hFeX073FVNNx5HdVEbEqMiKr0lZ673Vd/HI+3BFJRtOJCLBzBMWSdHoR1pP1+jqGv+gMiLGWFyNZH6Uh8XjYlfvc6jqc47pSCISAupTsinP3n11zad3YquvMJxIVEbEmNTVc4is/I7myGRKRmlyMxHpPGWDb6Q+aQBhDTvJ+OQOTYZmmMqIGBFVtpqUr58AoOT4+3FFJhlOJCKhxGOLoGj0bNzWcOK3LSZhy2umI4U0lRHpdJbmOjKX3ozF46ay76+pyjrDdCQRCUENXQdQNvhmALovv5uwWofZQCFMZUQ6XbfP78NetZWmmG6UjLzHdBwRCWHl2ddSl5KNramKHstu1ekaQ1RGpFN1KVxC140vAFB04p9x2+MNJxKRkGYNo2j0I7htdmKLl9H12+dNJwpJKiPSaWwNld6/PICKo35DbcbxhhOJiEBjQj8cw+8EIH3lDOyV3xtOFHpURqRzeDxkfDqF8PpyGhL64Rg22XQiEZFWOwZMoLrHaKyuRjKX3oTF1WQ6UkhRGZFOkbB5EfE/voPHEkbhSXPwhEWajiQi8hOLhaITHqbFnkDUjvWkfvWo6UQhRWVEOl7lVrovvxuAsmNvoiH5GMOBRER+qSUmneLjZwKQsnYe0aVfGk4UOlRGpGO5WuDV32JrrqY2bShlu2c9FBHxR1W9z6ay3/lYPG4yl96EtanadKSQoDIiHevjWVD4Oa7wWApPehSsYaYTiYjsV8nIe2jq0oOI6sLWo7rSsVRGpOMUfA4fPQhA8agZNMdmGg4kInJg7og4Ck96FI/FSuLmV0nYvMh0pKCnMiIdo8EJr14NHjccMw5nv7GmE4mItFld+jDKBt8EQPdP7yS8apvhRMFNZUQ6xtu3wq4CSOgFZ80ynUZExGdlgyZRmzYMW3MNPZfcCO5m05GClsqItL+1C2Ddy2CxwflPQ2Sc6UQiIr6zhlF48l9wRcQRXf4VaavnmE4UtFRGpH2Vfwdv5XmXT5oMPXPM5hEROQTNXTIoOv4BAFLWPEZMyQrDiYKTyoi0n+Z6+PdEaK6F3ifCCX8wnUhE5JBV9TmHnYdfjAUPmUsnYauvMB0p6KiMSPt5704oXQ/Ryd7TM1ab6UQiIu2iZMSfaEg4jPC6MjKX3uwdnC/tRmVE2sc3i+DLZ7zL5z8Fselm84iItCNPeDQFpz6O2xZJbPEyUtY+bjpSUFEZkUO380d440bv8vF50O9Us3lERDpAY+IRlIy6D4C0VbOIdnxuOFHwUBmRQ9PS6B0n0lgFmTlw8p2mE4mIdJjKwy5qnS6+538mYavfYTpSUFAZkUOzeDKUfAVRiXDBM2DTdO8iEsQsFkpGzaAhvh/hdQ4yP7pF40fagcqIHLy1C+HLZwELnP9XSNB07yIS/NzhMbvHj9iJLVpK6pq5piMFPJUROThlG+Ctm73Lo2+Dw3KNxhER6UyNSf0pHnU/AKmrZtOl6CPDiQKbyoj4rrEaFl4BzXXQ9xQYfbvpRCIinW7X4Rexo/+l3vlHlkwivLrIdKSApTIivvF44PUbYMf3EJeh+UREJKRtP+5P1CUfQ1jjLnrm/x5LS4PpSAFJZUR8s2IefPsaWMPgor9BTLLpRCIixnjCIik4dT4t9gSiK76m22d/Mh0pIOnShwC0rshp5HVjij+h9wd3YwFKcu5mh+UIMJRFRMRfNMf2oPDkuWQtHk/XjS/CV6Ng8OWmYwUUHRmRNgmvLqTnf67H4nFTediF7BhwpelIIiJ+o6bHaMqOvcX7w1u3QNGXZgMFGJUROSBLSz29PvwtYY2V1CUf4x1BbrGYjiUi4lfKBt+Is9fp4GqCBZdB1XbTkQKGyojsn8dDj49vI2rHNzRHJlOQ+xSesEjTqURE/I/FStHoOZDSH2oc8PIV3lmq5YBURmS/ktc9RcKW1/FYwig49Qmau3Q3HUlExG+5I7rAxS9CZDwUfQFv5XmvQpT9UhmRfYotyCf9i5kAbD9uKnXdcgwnEhEJAF37woXPgcUKa16AlU+ZTuT3VEZkr+w7N5G5ZBIWj5udR1zMjgETTEcSEQkc/U6F0+7xLi+eAluWmM3j5w6qjMybN4+srCwiIyPJyclh5cqV+9z2m2++4YILLiArKwuLxcKcOXMONqt0Elv9DrLe/w225hpq0o+jZOR9GrAqIuKrETfAMReDxwUvT4DyTaYT+S2fy8jChQvJy8tj2rRprF69muzsbMaMGUNZWdlet6+rq6NPnz488MADpKenH3Jg6VgWVyO9PryGiJpCGuN6UZD7JB5bhOlYIiKBx2KBX/0FMo+DRie8+H9Qu8N0Kr/kcxmZPXs211xzDRMnTmTAgAHMnz+f6Ohonn322b1uP2zYMB5++GEuvvhi7Hb7IQeWDuTxkPHJZGJKv8QVEce205/DFZloOpWISOAKs8PF/4SEXlC5FRZepits9sKnMtLU1MSqVavIzf3pDq1Wq5Xc3FxWrFjR7uGkc6WsnUfi96/gsdgoOOVxGhP6mY4kIhL4YpLh0pfBHgcFK+DNm3SFzf/wqYxUVFTgcrlIS0vbY31aWhoOh6PdQjU2NlJVVbXHQzpWwuZFpH/5EAAlI/5ETY8TDScSEQkiqf3h/54Hiw3WvgQfzzKdyK/45dU0M2fOJD4+vvWRmZlpOlJQiylZTsayWwEoP/q37NSVMyIi7a/vKXDWw97l/9wHa14ym8eP+FRGkpOTsdlslJaW7rG+tLS0XQenTpkyBafT2fooLCxst+eWPdkrN9Hrw99idTezq/fZOIbfYTqSiEjwGnYVjLzRu/zGDbA532weP+FTGYmIiGDIkCHk5//0P57b7SY/P58RI0a0Wyi73U5cXNweD2l/YbUOshZPwNZURW3aUIpGP+KdpEdERDpO7nQYeCG4W+Dl8bB9relExvn8zZOXl8fTTz/N888/z4YNG7j22mupra1l4sSJAIwfP54pU6a0bt/U1MSaNWtYs2YNTU1NFBcXs2bNGjZv3tx+70J8Zm2qIuv9iUTUltAQ35dtpz2je86IiHQGqxXGPg5ZJ0BTDfzzIqjcZjqVUWG+7jBu3DjKy8uZOnUqDoeDQYMGsXjx4tZBrQUFBVitP3WckpISBg8e3PrzrFmzmDVrFqNHj2bp0qWH/g7EZ5aWBnq9f3Xrze+2jvmbLuEVEelM/73k99kzoewbeOECuOp9iE4yncwIi8fj/9cXVVVVER8fj9Pp1CkbYF2R8+B3drfQM//3xG97H1d4LD+cvZCG5IHtF05EJMQd3SO+7RtXlcBfT4OqIsgYAuNfB3tsx4XrZG39/tYAgVCye1Kz+G3v47bZ2Xb6MyoiIiImxXWHK16FqCQoXgULLoXmBtOpOp3KSAhJX3k/Sd+9jMdipeCUedR2O850JBERSTkCLv83RHSBH5fBK1eBq8V0qk6lMhIiUtY8Rsq6JwEoPuEhqnudbjiRiIi0yhgCl7wENjtsfAvemARut+lUnUZlJAR0XffX1tlVtw+/k8rD/89wIhER+YXeJ8JFf9s9S+uL8N6UkJk2XmUkyCV9+3e6f34PAKXH3kLFMb8znEhERPap/1ney34BPp8PH9wdEoVEZSSIJW5aSMbyuwAoy76OssE3mw0kIiIHln0xnPOId3n5XMi/J+gLicpIkErYvIiMj28DoGLgVZQOvR0sFsOpRESkTYb+Bs7afTO9T2bD0plm83QwlZEglLB5ET0+ugULHnYceQXbc6aqiIiIBJrh18CY3SXkowfho4fN5ulAKiNBJuG7f9Fj6c1YPG52Hn4xJSPvVREREQlUI66D0+71Li+5Dz56yGyeDqIyEkQSN75Ej2W3eo+I9L+c4hMe0I3vREQC3agbIfdP3uUlM4JyDIm+qYJE0rf/oMcnt2PBQ8WAKykZNUNFREQkWBx/C4y537v88Z/hvTuCqpDo2yoIdF3/VzKW3wlA+cBr2D5iuk7NiIgEmxHXw9l/9i5/9ji8nRc0E6P5fNde8SMeD6mrZ5P21aMAlB1zLaXDJquIiIgEq2FXe2dpfWMSfPms9z42v5oLtsD+Og/s9KHM46b78ql03fB3ABxDb6M8+3oVERGRYHfsFRAWCYt+552ptWEXXPgshEeZTnbQdJomAFlcTWQuuZGuG/6OBwvFo2ZQPugGFRERkVBxzEUw7h/eUrLpHfjHr6G+0nSqg6YyEmgaa+j1wdUk/PAGHksYhSfPZeeRV5hOJSIina3/2XDFIrDHQ8EKeO4sqNpuOtVBsXg8/j8ct6qqivj4eJxOJ3Fxce363OuKnO36fB0prK6MrPeuJGrHetxhUWw79UlqMk8yHUtERAyK3LGBrPeuILyujKYuPfjxjH/QlNDXp+c4ukd8h2Rr6/e3jowECHvld/R9YyxRO9bTEpnED2e9pCIiIiI0dD2SLee+SmNcbyJqiuj75liit39uOpZPVEYCQEzJCvq+eT4RNUU0xvVmy7mvUZ96rOlYIiLiJ5pje7Ll3FeoSz2WsEYnvd+9lITvXzEdq81URvxcwvevkrX4cmxNVdSmDmHLrxbRFJ9lOpaIiPgZV1QyP5y1gF29z8bqbibzo1tIXTU7ICZHUxnxV24X6SvvJ/Ojm7G6m3H2Posfz3oJV2SS6WQiIuKnPGGRFJ4yj7Ls6wBI+2qO935lLQ2Gk+2fyogfsjZV0euDq0j5ej4AZdnXU3DK43jCIg0nExERv2exUjpsMkXHP4jHEkbilkX0efsiwmr990oblRE/E+H8kb6vjyWu8D+4bXYKTp5L6bDbdZ8ZERHxSWX/S/jxzH/QYk8kunwt/V47h2jHF6Zj7ZW+4fxIbOF/6Pf6uUQ6N9Mcnc4P5/wbZ9/zTMcSEZEAVdt9FJvHvkl90pGE15fT+52LSdrwgulYv6Ay4g/cLtK+fJis967E1lRFXeqxbB77FvUp2aaTiYhIgPNeabOodWBrxqd3kLHsNr8aR6IyYpitfge9F19O6pq5AOw4cjw/nL2QluhUw8lERCRYeMKjKTzlcRxDb8ODhaTvFtD3jfOIcP5gOhqgMmJUdOmXHLboTLqUfIo7LIqCk/5Cyaj78NjspqOJiEiwsVgoH3QDP575Ai2RXYnauYF+r51D/A9vmk6mMmKE20XKV3Pp89ZFhNc5aIjvy+bz3sDZb6zpZCIiEuRqM07g+1+/S016DrbmGnr+53p454/Q0mgsk8pIJwuvKaH3O5eQvuphLB4Xu/qex5bz3qQx8QjT0UREJES0xKTz41kvUZZ9vXfFyqdg7QJjecKMvXIIivvxXTI+uY2wRieu8BhKRt7Lrn4XgMViOpqIiIQaaxilw26nLn0YWSXvwGBzd4BXGekE1kYn3T6/l6TvXgagLvkYCk9+TNO6i4iIcdWZp8CIXxvNoDLSwboUfUTGx7cRUbsdDxYqjvkdpUNuxWOLMB1NRETEL6iMdBBrUzXdPr+PpE0vAdAYl0XRiX+mLn2Y4WQiIiL+RWWkA8Ru+4Duy+8morYEgIqjJuIYejue8GjDyURERPyPykg7Cqt10H3FNOK3vgtAU2wmRSf+mdpuxxlOJiIi4r9URtqD20XSxhdI/+JBbM01eCw2Ko6+htJjb8ETFmU6nYiIiF9TGTlE0Y4v6L5iGlE71gNQlzKY4uMfoKHrkYaTiYiIBAaVkYMUVuug28r7SdjyGgCuiDgcQ//Izv6Xg9VmNpyIiEgAURnxkaWlnuT1z5Cy5jFsLXV4sFB5xDgcQ2/DFZVsOp6IiEjAURlpK3cLid/9i7TVswmvKwWgNnUIJSOn05B8jOFwIiIigUtl5EA8HmILPiD9iweI3LUZgKYumTiG/hFn3/M0lbuIiMghUhnZF4+HLkVLSVv9CNHlawBosSdSNngSO4+8Ao/NbjafiIhIkFAZ+V97KSFuWyQVA6+mPPv3uCPizOYTEREJMioj/+VxE7ftfVLWPr5HCdkxYDwVR/+OlugUs/lERESCVMiXEUtLAwmbXyVl3VPYnT8AKiEiIiKdKXTLiKsZls/liOWPE15f7l0VEceOARPYMeBKlRAREZFOErplxBoG375GeH05TTHdqBh4DZVHXIw7oovpZCIiIiEldMuIxQKnTqWwcBu7+p4H1nDTiUREREJS6JYRgH657Ip0mk4hIiIS0qymA4iIiEhoUxkRERERo1RGRERExCiVERERETFKZURERESMUhkRERERo1RGRERExCiVERERETFKZURERESMUhkRERERo1RGRERExCiVERERETFKZURERESMOqgyMm/ePLKysoiMjCQnJ4eVK1fud/t//etf9O/fn8jISI4++mjeeeedgworIiIiwcfnMrJw4ULy8vKYNm0aq1evJjs7mzFjxlBWVrbX7ZcvX84ll1zCVVddxVdffcXYsWMZO3Ys69evP+TwIiIiEvgsHo/H48sOOTk5DBs2jMceewwAt9tNZmYmkyZNYvLkyb/Yfty4cdTW1vLWW2+1rjvuuOMYNGgQ8+fPb9NrVlVVER8fj9PpJC4uzpe4B7SuyNmuzyciIhJoju4R3yHP29bv7zBfnrSpqYlVq1YxZcqU1nVWq5Xc3FxWrFix131WrFhBXl7eHuvGjBnDa6+9ts/XaWxspLGxsfVnp9NbGKqqqnyJ2yY11e3/nCIiIoGkqsrSQc/r/Y490HEPn8pIRUUFLpeLtLS0PdanpaWxcePGve7jcDj2ur3D4djn68ycOZPp06f/Yn1mZqYvcUVERMQPVFdXEx+/76MvPpWRzjJlypQ9jqa43W527txJ165dsVg6pr2ZUlVVRWZmJoWFhe1+CkoOnT4f/6bPx7/p8/FvnfH5eDweqqur6d69+36386mMJCcnY7PZKC0t3WN9aWkp6enpe90nPT3dp+0B7HY7drt9j3UJCQm+RA04cXFx+sfqx/T5+Dd9Pv5Nn49/6+jPZ39HRP7Lp6tpIiIiGDJkCPn5+a3r3G43+fn5jBgxYq/7jBgxYo/tAT744IN9bi8iIiKhxefTNHl5eUyYMIGhQ4cyfPhw5syZQ21tLRMnTgRg/PjxZGRkMHPmTABuuukmRo8ezZ///GfOPvtsFixYwJdffslTTz3Vvu9EREREApLPZWTcuHGUl5czdepUHA4HgwYNYvHixa2DVAsKCrBafzrgMnLkSF588UXuuusu7rjjDg477DBee+01Bg4c2H7vIoDZ7XamTZv2i9NS4h/0+fg3fT7+TZ+Pf/Onz8fneUZERERE2pPuTSMiIiJGqYyIiIiIUSojIiIiYpTKiIiIiBilMuIntm7dylVXXUXv3r2Jioqib9++TJs2jaamJtPRZLcZM2YwcuRIoqOjg34SvkAxb948srKyiIyMJCcnh5UrV5qOJMCyZcs499xz6d69OxaLZb/3IpPON3PmTIYNG0ZsbCypqamMHTuWTZs2Gc2kMuInNm7ciNvt5sknn+Sbb77hkUceYf78+dxxxx2mo8luTU1NXHTRRVx77bWmowiwcOFC8vLymDZtGqtXryY7O5sxY8ZQVlZmOlrIq62tJTs7m3nz5pmOInvx0Ucfcf311/PZZ5/xwQcf0NzczOmnn05tba2xTLq01489/PDDPPHEE/zwww+mo8jP/O1vf+Pmm29m165dpqOEtJycHIYNG8Zjjz0GeGeDzszMZNKkSUyePNlwOvkvi8XCokWLGDt2rOkosg/l5eWkpqby0UcfceKJJxrJoCMjfszpdJKUlGQ6hojfaWpqYtWqVeTm5raus1qt5ObmsmLFCoPJRAKP0+kEMPp9ozLipzZv3szcuXP53e9+ZzqKiN+pqKjA5XK1zvz8X2lpaTgcDkOpRAKP2+3m5ptvZtSoUUZnRlcZ6WCTJ0/GYrHs97Fx48Y99ikuLuaMM87goosu4pprrjGUPDQczOcjIhIsrr/+etavX8+CBQuM5vD53jTimz/84Q9ceeWV+92mT58+rcslJSWcfPLJjBw5UjcT7AS+fj7iH5KTk7HZbJSWlu6xvrS0lPT0dEOpRALLDTfcwFtvvcWyZcvo0aOH0SwqIx0sJSWFlJSUNm1bXFzMySefzJAhQ3juuef2uOGgdAxfPh/xHxEREQwZMoT8/PzWgZFut5v8/HxuuOEGs+FE/JzH42HSpEksWrSIpUuX0rt3b9ORVEb8RXFxMSeddBK9evVi1qxZlJeXt/53+kvPPxQUFLBz504KCgpwuVysWbMGgH79+tGlSxez4UJQXl4eEyZMYOjQoQwfPpw5c+ZQW1vLxIkTTUcLeTU1NWzevLn15x9//JE1a9aQlJREz549DSYT8J6aefHFF3n99deJjY1tHWcVHx9PVFSUmVAe8QvPPfecB9jrQ/zDhAkT9vr5LFmyxHS0kDV37lxPz549PREREZ7hw4d7PvvsM9ORxOPxLFmyZK//ViZMmGA6mng8+/yuee6554xl0jwjIiIiYpQGJYiIiIhRKiMiIiJilMqIiIiIGKUyIiIiIkapjIiIiIhRKiMiIiJilMqIiIiIGKUyIiIiIkapjIiIiIhRKiMiIiJilMqIiIiIGKUyIiIiIkb9P1elGDqJ4qURAAAAAElFTkSuQmCC" 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gd = GaussDistribution('1D', dim=1, mean=0, cov=1)\n", + "gd.generate_samples(100)\n", + "gd.visualize()\n", + "\n", + "gd = GaussDistribution('2D', dim=2, mean=[0, 0], cov=[[1, 0], [0, 1]])\n", + "gd.generate_samples(100)\n", + "gd.visualize()" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Implement a class “BetaDistribution” (Equation 2.5 in the book)\n", + "* It is also a child class of “ContinousDistribution”.\n", + "* It’s purpose is to generate beta distributed samples and plot the distribution giving the parameters a and b.\n", + "* The contractor should take the parameters a and b as arguments.\n", + "* Implement a visualization for Beta distributions, including the mean and the standard deviation lines." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 6, + "outputs": [], + "source": [ + "class BetaDistribution(ContinuousDistribution):\n", + " def __init__(self, name, a, b):\n", + " super().__init__(name)\n", + " self.a = a\n", + " self.b = b\n", + " self.data = None\n", + " self.sampled_data = None\n", + "\n", + " def import_data(self, filename):\n", + " pass\n", + "\n", + " def export_data(self, filename):\n", + " self.sampled_data.to_csv(filename, index=False)\n", + "\n", + " def compute_mean(self):\n", + " pass\n", + "\n", + " def compute_std(self):\n", + " pass\n", + "\n", + " def visualize(self):\n", + " # Plot the distribution of the beta distribution\n", + " x = np.linspace(0, 1, 100)\n", + " y = beta.pdf(x, self.a, self.b)\n", + " plt.plot(x, y)\n", + " plt.title('Beta Distribution with a = ' + str(self.a) + ' and b = ' + str(self.b))\n", + " plt.xlabel('x')\n", + " plt.ylabel('y')\n", + " plt.show()\n", + "\n", + " def generate_samples(self, n):\n", + " self.sampled_data = pd.DataFrame(np.random.beta(self.a, self.b, n), columns=['x'])" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Generate visualizations of Beta distributions using the above class." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 7, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "bd = BetaDistribution('Beta', 2, 5)\n", + "bd.generate_samples(100)\n", + "bd.visualize()" + ], + "metadata": { + "collapsed": false + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "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 +}