{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Kernel Density Estimation\n", "\n", "This notebook presents and compares several ways to compute the Kernel Density Estimation (KDE) of the probability density function (PDF) of a random variable. KDE plots are available in usual python data analysis and visualization packages such as [pandas](https://pandas.pydata.org/) or [seaborn](https://seaborn.pydata.org/). These packages relies on statisics pacakges to compute the KDE and this notebook will present you how to compute the KDE either by hand or using [scipy](https://docs.scipy.org).\n", "\n", "For a more complete reading about KDE, you should read [this article](https://jakevdp.github.io/PythonDataScienceHandbook/05.13-kernel-density-estimation.html)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "from scipy.stats import gaussian_kde\n", "from scipy.stats import norm\n", "import pandas as pd\n", "import seaborn as sns\n", "\n", "import matplotlib.pyplot as plt\n", "import matplotlib.patches as mpatches\n", "plt.rcParams[\"figure.figsize\"] = (9, 6)\n", "plt.rcParams[\"font.size\"] = 18\n", "\n", "# just for fun\n", "# plt.xkcd(scale=.5, length=50);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The results strongly depend on the version of the used packages. For example, `seaborn` will compute the kde using eihter `scipy` or `statsmodels` and depending on the `scipy` version, the meaning of the kde width is not the same. Hereafter are the package versions used in this notebook." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Numpy: 1.16.2\n", "Scipy: 1.2.1\n", "Pandas: 0.24.2\n", "Seaborn: 0.9.0\n" ] } ], "source": [ "print(f\"Numpy: {np.__version__}\")\n", "print(f\"Scipy: {sp.__version__}\")\n", "print(f\"Pandas: {pd.__version__}\")\n", "print(f\"Seaborn: {sns.__version__}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sample\n", "\n", "This is a data sample that will we used in this notebook." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "data = [-20.31275116, -18.3594738, -18.3553103, -14.18406452, -11.67305,\n", " -11.38179997, -11.3761126, -10.6904519, -10.68305023, -10.34148,\n", " -8.75222277, -8.7498553, -6.00130727, 1.45761078, 1.77479,\n", " 1.78314794, 2.6612791]\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`seaborn` is a good option to get a quick view of the data. You can plot the data as a *rugplot* and the KDE. In `seaborn` the default kernel is a gaussian kernel." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sns.distplot(data, hist=False, rug=True,\n", " axlabel=\"Something ?\",\n", " kde_kws=dict(label=\"kde\"),\n", " rug_kws=dict(height=.2, linewidth=2, color=\"C1\", label=\"data\"))\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compute the gaussian KDE by hands\n", "\n", "A gaussian KDE is computed from a sum of normal functions of a defined width. It could be computed as follow:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def my_kde(data, width=1, gridsize=100, normalized=True, bounds=None):\n", " \"\"\"\n", " Compute the gaussian KDE from the given sample.\n", " \n", " Args:\n", " data (array or list): sample of values\n", " width (float): width of the normal functions\n", " gridsize (int): number of grid points on which the kde is computed\n", " normalized (bool): if True the KDE is normalized (default)\n", " bounds (tuple): min and max value of the kde\n", " \n", " Returns:\n", " The grid and the KDE\n", " \"\"\"\n", " # boundaries\n", " if bounds: \n", " xmin, xmax = bounds\n", " else:\n", " xmin = min(data) - 3 * width\n", " xmax = max(data) + 3 * width\n", " \n", " # grid points\n", " x = np.linspace(xmin, xmax, gridsize)\n", " \n", " # compute kde\n", " kde = np.zeros(gridsize)\n", " for val in data:\n", " kde += norm.pdf(x, loc=val, scale=width)\n", " \n", " # normalized the KDE\n", " if normalized:\n", " kde /= sp.integrate.simps(kde, x)\n", " \n", " return x, kde" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using our function, the KDE is computed as:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "x, kde = my_kde(data, gridsize=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can compare with the KDE otained from `seaborn`. The gaussian kernel being the default, we have to give to `seaborn` the same band width, that is `1.` here, using the `bw` keyword." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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uvT1KqWHkXtU7va3J+iR6kn5hYBWE3fu6VtwOtdupTxxD6ll3aBVipVTQDW4ep1LKnga7qrcvhcU4blzPqSNf4Oa8ZzWoUUoNCw1slFL7BCHpd2puKusr9g76eKWUGggNbJRS+/SW3DuEpN+puamU72mitqlt0OdQKlI8+eSTiAhlZWWUlJQwfvx4kpKSOPLII/nwww8BWLlyJccddxzJycmMHTuWO+7Yt1rQIYccwn777YfL1TN9tbS0FBHh6aefHnI7X3/9dUaOHMnxxx/Pnj17Ore/+OKLHHbYYSQmJpKfn8/ChQtpa/P92W1paeGuu+5i2rRpJCYmkp6ezjnnnMOnn3465PYNhQY2Sql9ihbSHpPYddsQk36n5aYBsEF7bVQwOEutytaL0sOqwvUtt9zCCy+8wA033MBtt93Gpk2bmDVrFi+88ALnn38+xx9/PPfddx+TJ09m4cKFPPPMMwDMnj2bbdu28eabb/Y45xNPPEFaWhoXXnjhkNr21FNPcfbZZ3Paaafx5ptvkpGRAcDy5cs577zzqK2tZeHChVx//fU8//zz/OxnP+txjra2Ns444wxuv/12jj76aB544AFuueUWNmzYwLHHHsvq1QEvcec/Y4wtv2bMmGGUUgP3+v8uMdt+OdG4bksz5v5pxvznuSGdr6qu2Yz/2cvmsXe/DlALVSTZsGFD8E7+n+eMuXOMMbel7vu6c8yQ37NDsXTpUgOYww47zLS0tHRuf/HFFw1gYmJizKpVqzq3t7S0mJycHHPUUUcZY4ypqakxI0aMMBdddFGX827dutU4HA5z7bXXDqg9mzdvNoC57bbbjDHG3H333QYw1157reno6Ojcr7293eTn55vRo0ebqqqqzu01NTVmv/32M4BZunRp5/b777/fAOa1117rcr3a2lqTn59vTjzxxAG105/3CbDa+PH7X3tslFJdrIg5ge/H/xFZVAPz1w056Tdz04t8kDiXq8q+E1ZP1MoGApnsHmDXXnst8fHxnd8ff/zxABx11FEcfvjhndvj4+M54ogj2LhxIwBpaWlcdNFFvPjii1RXV3fut3TpUlwuF1dd5V0hxX8ul4vrrruOBQsWcMcdd/C73/0Oh2NfCPDJJ5+wbds2rrzySjIzMzu3p6Wlcc011/Q43zPPPMPkyZOZMWMG1dXVnV+tra2cdtppvPfeezQ1NfU4bjj4Nd1bKRU9Nlc3MHGQK3r34J4+Phb3DW6w08eV8iWMK1xPnDixy/ee4Z7999+/x74ZGRns2rWr8/s5c+bw1FNP8cwzzzBv3jyMMSxdupRDDz2UGTNmDKo9Dz74IHV1dfzqV7/i1ltv7fH6pk2bAJg8uefiAVOnTu2x7bPPPqOpqYm+Fpyurq4mPz9/UO0dCg1slFJdbK5u4JTJ2YE5WV9P1BrYqKEK4wrXMTExA9ru7ZhjjuHggw/m8ccfZ968eZSVlbFlyxZ++9vfDro9p512Gu+++y5//OMfufjii3sEXtZID4j0LCXnea37tunTp3P//ff3es2+gp5g0sBGKdVpb3Mb1fWt7J+ZEpgThvETtbKBooVWD6B38GyTCtezZ8/mhhtuYNWqVTz++OMkJiZy6aWXDvp806dPp6SkhKKiIk488UTeeustDjzwwM7XCwoKAKsnpjtf2w488ECqqqo45ZRTugxphYPwao1SKqS2VFvLsO2fOSIwJwzC9HGlOhUWwzlLIC0fEOvPc5bYojfw8ssvJzExkd/85jcsX76cCy64gPT09CGdc9q0abzzzjt0dHRw4okn8vnnn3e+NmPGDPLy8li6dGmX3J69e/fyhz/8oce5rrjiCiorK3vtsdm5c+eQ2joU2mOjlOq0uTOwCVCPjY2fqFWYKCy2RSDTXUZGBhdeeGHnNPCrr746IOedPHkyK1eu5JRTTuGkk06irKyMadOmERMTwwMPPEBxcTFHHHEEs2fPJjY2lieeeILRo0ezdevWLue54YYbePPNN7n55pt56623OOWUU0hNTWXr1q2UlZWRmJjI22+/HZA2D5T22CilOn2zqxGA8aMD1GPj9UTtQtgVm22bJ2qlgm3OnDkAHHDAAZx44okBO++BBx7IypUrSUxM5OSTT8bpdAJw4YUX8re//Y3U1FQWLVrEkiVLuPDCC7nnnnt6nCMuLo5XXnmFhx56iKqqKm677Tbmz5/Pc889x8SJE1mwYEHA2jtQ4ispyA5mzpxpQlogSKkIdPPz/2Hll1Ws+vmpAT/3NU9/wpff1vHWTScF/NwqfH322WdMmTIl1M2ISKtWreLII4/krrvuCmmgMBz8eZ+IyCfGmJn9nUt7bJRSnbbubiR/VIB6a7o5KGckW6obaG7rCMr5lbKb3/72t8TFxXHllVeGuikRRXNslFJWvZmyEv5aW05NbDY47wz4cNHknJG4DHz1bT0Hj0sL6LmVsouGhgZeeukl1q9fzzPPPMOcOXPIycnpsV9lZWW/50pLSyMpKSkYzQxrGtgoFe3cRfRoa8IBjGrfGZQiepNyRgLwRWWdBjZK9aKqqopLLrmElJQULrzwQu69916f+40dO7bfcy1dupQf/ehHAW5h+NPARqloN0xF9MaPGkF8rIMvdtYF7JxK2c2ECRN8FsTrztcimd1NmzYtEE2KOBrYKBXthqmIXmyMgwOzU/i8UgMbpYbq1FMDn+BvF5o8rFS0G8Yiepckfsg9Wy+BRem6IKZSKig0sFEq2hUttIrmeQtGET1nKT+ovI+xVANm34KYGtwopQJIAxulop27iN6u2DG4glmWvqyEOFdz122eXB5la3atl6YCI9DvD82xUUpBYTH//c9xjEyI5ZmrjwzONXRBzKgUHx9PU1MTI0YEpz6SinxNTU3ExcUF7HzaY6OUAqB8dyP5o4JY80IXxIxKmZmZlJeXs3v3btra2rT3RnUyxtDY2Mj27dvJzs4O2Hm1x0YpRUNLO7saWoNWdRjQBTGjVFpaGgkJCVRVVbFr1y7a29tD3SQVRuLi4hgzZgypqakBO6cGNkoptu2xFr/MzwhiYOPO2dnz0i9Ia/sWSctDihbqgphRIDExkfz8/FA3Q0UJHYpSSrF9j9WLkpcR5PLrhcW8UvQmE5ufpeLKjzWoUUoFnAY2Sim211iBzbhgBzbsW1rhS61ArJQKAg1slFJsr2kiPsZBZnJC0K91ULY7sNEKxEqpINDARinF9j1N5KYn4nBI0K+VNiKOnNREXTNKKRUUGtgopdhe00RuevCHoTwOyhmpQ1FKqaDQwEYpRUVNE+OGMbCZNCaFjTvr6XBpTROlVGBpYKNUlGttd/FtXcvw9tiMGUlLu4tvdjUM2zWVUtHB78BGRBwiMl9EPheRZhHZJiKLRSTZz+MXiMjzIrJJRIyIbOln/yNFZIWI1InIXhF5TUQO9be9Sin/VNY2Y8zwzIjyOLK+jPfi57L/I3m6yrdSKqAGUqDvAWAusBxYDExxf3+YiJxqjHH1c/xdwG7g30B6XzuKyFHAO8B2wFOW9DrgnyJyjDFm7QDarZTqjbOU7NdvY1NCBa1v50L87cGvLeMsJf+9WxCHuwKxZ5Vv0Lo2Sqkh8yuwEZFpwPXAMmPMBV7bNwNLgIuBv/RzmgJjzCb3ceuAlD72XQK0AicYY7a7jykFPsMKqk73p91KqT44S+GluSS2NYFAYkPF8AQYZSVIe1PXbZ5VvjWwUUoNkb9DUZcAAjzYbftjQCNwWX8n8AQ1/RGRA4DDgec9QY37+O3A88CpIpLjZ7uVUr0pK+m6bhPsCzCCSVf5VkoFkb+BzeGAC1jlvdEY0wyscb8eKJ5zfeDjtQ+xAqwZAbyeUtEpVAGGrvKtlAoifwObXKDaGNPi47XtQKaIxAeoTble5/V1LYBxAbqWUtErVAFG0UJrVW9vusq3UipA/A1sRgC+ghqAZq99AsFzHl/X6/NaIjJHRFaLyOqqqqoANUcpmwpVgFFYDOcsoS1lHC4jNCaNhXOWaH6NUiog/A1sGoHeFpFJ9NonEDzn8XW9Pq9ljHnUGDPTGDMzKysrQM1RyqYKizHnLGG7ycQgkJY/fAFGYTFm3jomtf+F3x7yggY1SqmA8Xe6dwUwVUQSfAxHjcMapmoNUJsqvM7bnWebr2EqpdQA7Zp4Lse2JHPbOVO58tj9h/Xa8bEOJmam6NIKSqmA8rfH5mP3vkd4bxSRROBQYHUA2/Sx+8+jfbx2FGCATwJ4PaWiVmWtNbo7Nm34ivN5OyhnpC6GqZQKKH8Dm+ewAop53bbPxsp3edazQUQKRGTyYBtkjPkKK1C6SEQ8icS4/34R8JYxpnKw51dK7bOjM7BJ7GfP4Jg0JoVtu5toaGkPyfWVUvbj11CUMWatiDwCXCciy4BX2Vd5eCVdi/OVAeOxpmV3EpHL3dsBsoB4EfmF+/tvjDFPe+1+A/A2VqXhh93brscKxG7y82dTSvVjR61Vx2ZsemgCm4PGjARg47f1HJrfZ0FypZTyy0CWVJgHbAHmAGcB1cDDwEI/llMAuAo4sdu2O9x/rgQ6AxtjzL9E5CTgTveXAf4FXGSM+c8A2qyU6sOO2mZiHUJmcm9zA4JrUo4V2HxRuVcDG6VUQPgd2BhjOrCWM1jcz34Tetl+0kAaZoz5ACgayDFKqYHZUdPEmNREHA7pf+cgyC9/hfcTFpD7yi54L8+aaq4zpJRSQzCQHhullM3sqG0mN0TDUDhLcbw8l3Gii2EqpQLH3+RhpZQNVe5tJidEM6JCtlaVUsrWNLBRKkoZY6wemxDNiNLFMJVSwaCBjVJRandDK63tLnJCFdjoYphKqSDQwEapKBXqGja6GKZSKhg0sFEqSu0IcdVhz2KYpOXjQtgdO0YXw1RKDZnOilIqSlV6ivOFqscGrCCmsJg5T61my64GVhR2L3WllFIDoz02SkWpCk9xvpTQFOfzNnXsSDZV1dPc1hHqpiilIpwGNkpFI2cps1d/jy/jf4jjoengLA1pc6aMTcVl0JW+lVJDpoGNUtHGWQovzWVU+04cmH2F8UIY3EwZmwrAZzv2hqwNSil70MBGqWgThoXx9hs1guT4GD7boT02Sqmh0cBGqWgThoXxHA5hUs5INmiPjVJqiDSwUSrahGlhvIsTPuTBHZdhFqXDAweHPO9HKRWZNLBRKtoULcQVG2aF8ZylnL/9XnKpRsIk70cpFZk0sFEq2hQWs37GHZS7MjEIpOWHvjBeWQmxruau23RBTKXUIGiBPqWi0Jr00/hlay6rbi0iOzWEBfo8wjDvRykVmbTHRqkotMNdnG90GBTnA8I270cpFXk0sFEqCu2obWZMaiIxDgl1Uyy6IKZSKkA0sFEqCu2obQrtGlHduRfE3JuQg8sIrtS80Of9KKUikgY2SkWhHbXN5IRTYANQWMxH577LxJZn+fSCf2pQo5QaFA1slIoyxhh21DaTm57U/87D7OBx1tIK67ZroT6l1OBoYKNUlNnd0Epru4uccJgN1U1OaiKZKQn8p7wm1E1RSkUoDWyUijI7aq16Mbnp4RfYiAiH5KWxtrw21E1RauicpVYVba2mPaw0sFEqylS6A5uctPAbigKYnpfGV1X11Le0h7opSg2es9Sqnl27DbSa9rDSwEapKLOj1lrZOzfckofdTmt/l3/GzSX57kx9ylWRyVkKy6+xqmd7a2uytut7Oqi08rBSUSbsivN5c5YydfUvEIf7F4LnKRd0lpSKDJ6eGtPh+3XToe/pINMeG6WiTNgV5/NWVoK0+3jK1TWjVKQoK+nZU9OdvqeDSgMbpaJM2BXn86ZrRqlI5+97Vd/TQaOBjVJRpjIci/N56JpRKsK5Usf5t6O+p4NGAxuloohxlvJs/dU8/OUp4ZmYq2tGqUjlntote8txmb53NQCtDeH3+bMJDWyUihbOUvi/uYyTaiRcp5+614xypebhMsLehBxdM0qFP6+p3QI4BAzuHLa0fJh5FSSNwhPvCEDT7vD7/NmEBjZKRYtIScwtLMZx43pOSVnOT/P+okGNCn8+EoYFYwU189fB2fdDfDI90vXD8fNnA34HNiLiEJH5IvK5iDSLyDYRWSwiyYE+Xiw/FJF/iUi1iNSJyHoRWSgiqQP5AZVSbhGWmDs9Lx0SaGojAAAgAElEQVSnLq2gIoE/n60I+/xFsoH02DwA3A9sAK4HngfmAi+JiD/nGcjxdwLPAk3A7cDNwFr3398QkTCcp6pUmIuwxNxD8tKoqG2mqq4l1E1Rqm/+fLYi7PMXyfwKbERkGlYwsswYc74x5jFjzI3AjcDJwMWBOl5EYoF5wL+B04wxDxtj/mCMuRgr2DkSOGSgP6hSUa9oIW2ObrOhwjgxd/q4NADWbtdeGxXmihbiiu0n6d1HYrwJ489fJPO3x+YSrHynB7ttfwxoBC4L4PFxQBJQaYxxddu/wv1ng3/NVkp1KizmuZz/RyVZgFjj/2GcmHtIzZu8lzCXk/93UnjO4FLKo7CYFQf8nHJXppU07Ouz5U6MJy0fg1DuyqTyhHvD9vMXyfxdUuFwwAWs8t5ojGkWkTXu1wNyvDGmSUTeBc4QkZ8BfwfagZOAnwDPGGM2+tlupZSXlzmO5WOO5e/XHhPqpvTNWUriP+aRJ7q0gooMf6qZSWPWk7x8/fG971RYDIXFVNU1c/xdZdzUdhDXDV8To4a/PTa5QLUxxtdg93YgU0TiA3j8pcDbwK+BjcBm4AmsPJ0r/GyzUqqbytrm8K067M1XWXqdQaLCkbMU1/3T+N8dZ/Bs3dV+9Sxmj0zkmoxP+MH734VF6dojGWD+9tiMAHrL4Gv22qc1QMe3AJuwgp7XsOoZXQD8wr3/r3ydSETmAHMA9ttvv14up1R0Msawo7aZ06aOCXVT+qczSFQkcNevcbQ1WaO7rZX+9Sw6S5nf9Ajxxv3rT3skA8rfHptGoLelgBO99hny8SIyAvgXkGqM+S9jzF+NMf9rjLkIeA4oEZFJvk5kjHnUGDPTGDMzKyurj+YoFX32NLbR0u5ibFpS/zuHms4gUZFgsD2LZSX7gpqBHKf84m9gU4E1XOQrOBmHNczUW2/NQI+/EDgQazp4d8+723ycn+1WSrntqLVuwBExFKVLK6hIMNieRe2RDCp/A5uP3fse4b1RRBKBQ4HVATzes4JYjI/zxHb7Uynlpx011hNi2C6A6a3bDJKdkhXWM7hUlBpsz6L2SAaVv4HNc1h5LvO6bZ+NlRvzrGeDiBSIyOTBHo9VwA/gv3y0w7PtYz/brZRy27HXCmxy0yNgKAqsIGb+Oh4+/mOOan6I2gPPC3WLlOqqaCEdMYPoWdQeyaDyq+fDGLNWRB4BrhORZcCrwBSsysErgb947V4GjId9y2IM8PiXsaaFf9c97fvv7nOdDxwPPG+M+fcgflalolpFTROxDiEzpbd0t/A0c3wGxsCnW/dw0qTsUDdHqX0Ki3lzfSUHf/YQ4xy7kLQ8Kzjpr2fR/XrTa7eR0LCDtpSxJMy6XXskA2QgQzrzgC1Ys47OAqqBh4GFPgrpDfp4Y0yHiJwKLMAKZu7F6u3ZCPwMa1kGpdQA7ahpIictkRhHZK1Ickh+OjEO4ZNvNLBR4ee55qNYnH4Ib9544sAOLCymceK5TLlzBbcWTWZOYUFwGhiF/A5sjDEdwGL3V1/7TRjK8e5964Bb3V9KqQCoqG0mNxJmRHWT/MUyPki8lcx/VcN6P5+IlRoGLpfh0201zJqaM6jjR6ckkJeRxH+21Qa4ZdFtIItgKqUiWEVNE2PTIyBx2Ju7Tki2qwoHZl+9Dy1mpsLApuoGahrbmDE+Y9DnOCQ/nTXbdD20QNLARqko0OEy7NzbHDmJwx5agViFsf+4A5LD9ksf9DnOj32f5xpnY7QCccBoYKNUFKiub6Gtw5AbCVO9vWm9DxWunKUUvV7EpoRLOeAvRw8uIHGWctIXvyLPUY1oj2TAaGCjlN05S8n443fYlPBDLvznmZF109R6HyocuYdI01srcYhBBhuQlJUQ06E9koGmgY1Sdua+Acc3bMchkNRYEVlPhFrvQ4WjQA2Rao9kUGhgo5SdRXqOSrcKxOWuTPYU3aezolRoBSog0R7JoNDARik7s8MTobsCsfOqLRzXuoT3kk4JdYtUtAtUQKI9kkGhgY1SdmajJ8KpuakkxcWwesvuUDdFRbuihbQ5uiXiDyYgcfdItiSPw2WEphG5uiZaAGhgo5Sd2eiJMC7GwXWZ/+Yna74POjVWhVJhMU+Omm8tzopAWv7gA5LCYtrmOpnY8iyPzfg/DWoCQFfJVsrO3DfJHcsWkMMA1rIJR85S5tQ+RJyxFvPsnBoLkfnzqIi2tO5w1h40iyWXHDbkc6UkxDJ+9Ag+27E3AC1T2mOjlM21TL2Ao5uX8NBxq2D+usgNAspKiHM1d90WSYnQyjb2NLRSUdvM1NzUgJ1zSk6qBjYBooGNUja3s7YFIPKqDndnh0RoZQtf7KwDYFLOyICdc8rYVL7Z3UhDS3vAzhmtNLBRyuYqaq3p3pG4AGYXNkqEVpFt47f1ABw0JpCBzUiMgc8r6wJ2zmilgY1SNldRYwU2EbcAZnc2SoRWkW3jzjpSEmIDukTJlLHWsJYORw2dBjZK2dyOWisvJeJ7bNxTY5uTc3VqrAqpL3fWcUB2CiISsHPmlb/MvxLnculrh+iMvyHSwEYpm6uoaSJjRBxJ8TGhbsrQFRbDvHVMbv8rDx68TIMaNbycpfDAwfyl4kyW1lwZuODDWYq8NJdcdDHMQNDARimbq6hpivzEYS+JcTEckp/Gh5u1UJ8aRu5116jdhgNDRtvOwAUfkb70SZjRwEYpm9tR28zYSB+G6ubI/Uezbnst9TqDRA2XYAYfOuMvoDSwUcrmrB6bCE8c7uZseY+VsdeTfHem5iOo4RHM4ENn/AWUBjZK2Vh9Szt7m9ttNRSFs5RJq35OnkPzEdQwCmbwoTP+AkoDG6VsbIdnqncAp6WGXFkJ0q75CGqYBTP4cM/4M2n5uBD2xI3RGX9DoGtFKWVjFZ6p3nbqsdF8BBUK7iCjYtkCxgZj3bXCYqSwmOI//AtBKC08OjDnjUIa2ChlY57ifLYKbNLyrOEnX9uVCqLaA8/jmOZkbv3uZOacUBCUaxyQPZJ/rNuBMSagdXKiiQ5FKWVXzlLOKjuNTQk/JHfpTPvkoGg+ggqRLdUNAEwYnRy0axyQnUJNYxu7GlqDdg2708BGKTty19xIbanEISC15fZJsHXnI+DOR6hyZGs+ghoWm92BzcSs4AU2B2anALBxZ33QrmF3GtgoZUd2L/hVWAzz13HXzH9xbOsSmqdcEOoWqSiwqboBh0D+qBFBu8aBY6zA5qtvdTHMwdLARik7ipIE2yMnjqa13cV/ttWEuikqCmypbmBcRhIJscFbniQnNZGUhFi++lZ7bAZLAxul7ChKCn4d2/gW7yXM5Yg/F2ihPhV0m6sb2D8zJajXEBEOyE5howY2g6aBjVJ2VLQQE2vzBFtnKSNen0+eaKE+FXzGGLZUN7D/6OANQ3lcFP8Bi7dfCovSNWAfBA1slLKjwmK2HHs35a5MDAJp+fZLsLV7HpEKK9X1rdS1tLN/ZvAShwFwllK84zeMpRo0YB8UrWOjlE2tHTWLua3ZvDH/BA4aMzLUzQm8KMkjUmHAWUrq64vYlLCd1vdzYeTtwXtIKCshztXcdZsnYLfTg0kQ+d1jIyIOEZkvIp+LSLOIbBORxSLiV/g60ONFJFZE5orIv0WkQURq3X//sb9tViqale9pBGCcnYrzeYuSPCIVYu7SCQkN23EIJDZWBLcHRQP2IRvIUNQDwP3ABuB64HlgLvCSiPhzHr+PF5F44GXgN8AaYD6wAFgJjB9Am5WKWuV7mhiVHE9ygk07ZrVQnxoOwz3kqQH7kPl1xxORaVjByDJjzAVe2zcDS4CLgb8E8PhfAqcCpxlj3vb7p1FKdSrf00R+hk17a2Bft3xZCaa2nAozmpyz7iJGu+tVIA13D0rRQqtHyDuY0oB9QPztsbkEEODBbtsfAxqBywJ1vHto6gbgRWPM22KxYYKAUsFVvqeRvIzgz+AIKXehvpfP28CxLUtYN3pWqFuk7Ga4e1DclbV3x47BZdfE/yDzN7A5HHABq7w3GmOasYaKDg/g8ccDI4FPROQhYC+wV0SqROQuEbFpv7pSgWOMYfueJvLs3GPj5ciJowD4aPOuELdE2U7RQsxwD3kWFvPXY19lYvOz1P9kjQY1A+RvYJMLVBtjWny8th3IdOfFBOL4Se4/5wEXAD8FfgD8CyvP5nE/26xU1Kqqa6Gl3RU1gU32yESuTlvN+SvP0NofKrAKi9lTdN+wl044wL1m1NdaqG/A/O39GAH4CkoAmr326W050oEc7xl2GgUcbIz53P19qYi8DVwhIvcYYzZ0P5GIzAHmAOy33369XE4p+9u2xxqft/1QlIezlJ+2PkK859nJU/sD9GlXDdmG0WdwWWsGf519FEcXjB6Wa3YuhvltPYfkpw/LNe3C3x6bRiChl9cSvfYJxPGejKkPvYIajz+7/zzR14mMMY8aY2YaY2ZmZWX10Ryl7M0z1TtaemwoK9kX1HhosT4VIJurrV6ToBfn87LfqBHExQhfV2mPzUD5G9hUYA0X+QpOxmENM/XWWzPQ4z2p5pU+9t3h/jPDjzYrFbXKo63HRmt/qCDaXN1IUlwMY1J7ez4PvNgYB+NHJ+tQ1CD4G9h87N73CO+NIpIIHAqsDuDxngRjXynnnm3f+tVqpaJU+Z4mMlPiSYoP3irEYUVrf6gg2lxdz/6ZyYjIsF53YmYym6obhvWaduBvYPMcYLASer3NxsqNedazQUQKRGTyYI83xmwG3geOEJHveJ03xr1/O/CGn+1WKiqV72m0b8VhX7RYnwqiLbsah3UYyqMgO4VvdjXQ3uEa9mtHMr8CG2PMWuAR4HwRWSYiV4vIYqxKwivpWlyvDPhsCMeDVcyvEVghIotE5Hr3fkcAdxljtg70B1UqajhL+U35pbxQfXb0zA5y1/6oTxyLywjtI/O09ocKiLYOF1t3hyawOanlHd6OuZ6YO0ZFz2c5AAZSE2YesAVr1tFZQDXwMLDQGONPOOn38caYT0XkGOBO93GJWMHSlcaYJwfQZqWii7MU89Jccow7Bz+aZgcVFrM9+0xmPfguvzmxkIsK80PdImUD23Y30uEyTBjuwMZZykznImIcUfhZHiK/14oyxnQYYxYbYyYZYxKMMeOMMTcaY+q77TfBGNNjINLf4732dxpjvmeMSTfGJBpjDtOgRql+lJUgw7muTZg5MDuF9BFxfLxld6ibomxiyy4rx2XYe2zKSojpiN7P8lAMZBFMpVS4i/LZQQ6HMHP8KD7esifUTVE2sanKCmwmDndgE+Wf5aHQwEYpO9HZQVyS9AFP770KoxWI1VA5S7ng3TPYlHgpGY9+Z3jfS/pZHjQNbJSyk6KFtDoSu26LptlBzlJO/uJX5DmqEcy+vAQNbtRAOUvhpblktO3EEYr3ks70GzQNbJSyk8Ji/jx6PjslC6JxZeCyEhyal6ACoazEeu94G873knumX517pl9Hqs7085eulK2Uzfyt7Rg+nFDEn/7r8FA3ZfhpXoIKlHB4LxUW83H8ifz3k6v5+wVHM2P8qOG7dgTTHhulbMQYw9bdjew3avhrboQFzUtQgRIm76WCLPcq31VagdhfGtgoZSNV9S00tnYwfnSUrBHVneYlqEApWkh7TOjz1fIyRhAf49DFMAdAAxulbOSbXdaq3vtFa2DjzktwpebhMkJtfI7mJajBKSzmrYN+QbkrExPCfLUYhzAhc0TntHPVP82xUcpGPIHN+FFRGtgAFBbjKCzm/N+9j4jw98JjQt0iFaHedJzALxKmsOrnp4a0HRMzU/jy27qQtiGSaI+NUjaydVcDDrG6r6Pd4fuPwlleQ3NbR6iboiLUll0Nw7+Ugg8F2cls3dVImy6G6RftsVGB5Sy1pkPWlkNShrWtaY+VcFe0UIcEgmxTdQPjMpKIj9VnlnPkPS6P+TUJv9ql7z81KJurGzh1yphQN4OJmSm0u6yJAZ5kYtU7vfupwHEXtKJ2G2Cgabf15SlutWw23LO/FksLok1VDXrjA3CWMm31L7VQnxq0vc1tVNe3hkmPjXtm1LeaQOwPDWxUYDhLYfk1PQtadde0W3/BBInLZdhUXc/ETA1sKCtB2rVQnxq8LdUhWvzSh4lZVhs2VWsCsT80sFFD5+mpMX7mMugvmMBzluJ64GA2OC7mxvXna+AYDsXVVETbXB2ixS99SP1yOR8kzuXHb8/Q9c/8oIGNGjpfpcf7U7tNP5yB4g4sY+vKcQikNO/QXrEwKa6mItfm6gZEID/UMwzdn++x6LCqvzSwUUPjLHXn1AyCfjgDI9Rr2oQjLdSnhmhzdQPj0pNIjIsJbUP08z1gGtiowfMMQfVKIK6Pblz9cAaGDrv05C7UR1o+LoTq2Gwt1KcGZHN1Q1jk1+jne+A0sFGD19cQVFwSnP8o/LwCzn+s93Poh3PodNjFt8JimL+On01byWmuR3AdfFGoW6QigbMU88DBvFB9Ng9XXh76XmX9fA+YBjZq8PoKSryfjguLrXLkvuiHc+h02KVPh+8/ij2NbbrWjuqfuxdaarfhwJDetjP0Q+b6+R4wDWzUwDlL4YGDMRjfr6fl9+zy9/HhNACtDaF/Iop0hcU0n/lgyNe0CVdHTBgFwEebd4e4JSrshWM+i3tY1aTl6/pnftLKw2pgPHk1bU2Ir9d7e5LwfAj/8TNM024ErOM9dW2891ED9tWYMzm7dSS/v/Q7nDl9bKibE1bGV7zCB4kLyHltF3ygFYhVH8I1n6WwGCks5owH3iV/VBJ/Kjw8tO0Jc9pjowamr7ya/noKCoshPrlnQBTqJyIb8AyzTNSqw105SxGdKqv8Feb5LAXZyXytq3z3SwMbNTC9PrkIzF/X/5NwuD4RRbjPK+uIdUh4zOIIJ+E4tKDCV5jns0zMTGHr7kZa23UxzL5oYKP85ywF6eUt4+8TTZg/EUWqLyrrKMhK0cUvu9NAWg2EO59lp2SFZb5aQXYyHS7D1t3aa9MXvQsq//S1bMJAnmh8PBG5YsPniShSfVFZx+SxI0PdjPCjgbQaINfBF3Fi+8P8aua//OuFHkaedeB0OKpvGtgo//SWWyMxA3ui8SqcZhB2mRSaiYdlc3QNlEHa29zG9pomJuVoYNNDmA8tqPBTubeZ5jYX+2eF37CuZzFMLV3QNw1slH9667o3roE/0bgLp8n5j5LiaGNEey1oYuegfVFZB8BkDWx66hZIl7sy2VN0X1g9havwsjmMVvXubmRiHNkjE9ikPTZ90sBG+ScYXfplJSSYlq7bNLFzYJylTPnfY9iU8ENOeOUUDQp9cQfS62d/w3GtS3g38eRQt0iFsXAObAAKslK0x6YfGtio/jlLMa0NPcvxDbVLXxM7h8ad95TSvAOHQGxdufZ49WHK2FRGJsRqoT7Vp83VDSTFxTBmZGKom9KTs5TfVV3B3789C6ND973SwEb1zVNi3F1Ur1PSqKHPFtDEzqHRqcwDEuMQZk7I4KNNu0LdFBXGtlQ3MCEzGYfDZwnS0HHfizPaduLAIDp03ysNbFTfeksajk8eep6CJnYOjfZ4DdgPR3zEU7VXYRala7K68sla1XtEqJvRkz7I+E0DG9W3YP7ydCd2to/Mw2WEuoSxYVUzIuxpj9fAOEs55ctfkefQKsTKt/YOF1t3N4Znfo0+yPjNr8BGRBwiMl9EPheRZhHZJiKLRcSv//2hHC8ipSJiRGSdP9dSARbsX56FxcTetJ6zR73EVaOWalAzEEULaY/plgegPV69KyshpkOfeFXvyvc00e4yTBgdhoGNPsj4zd8emweA+4ENwPXA88Bc4CWR3krRDv14ETkbuADoZXEiFVTOUtqa6jDds4aD8Mvz2lGf8EDFZTpEMBCFxbwyYQHbja7q7Rd94lV9cZYy5omZbEr4Id97e1b43YN06N5v/a7uLSLTsIKRZcaYC7y2bwaWABcDfwn08SKSAvwOeAT4np8/jwoUd6JaXFsTXbKGk0bBmfcE9pens5Tvbvk1MeKOXz1DBKC/pPvxXPNR/ClzJi9df1yomxL+0vKs95av7Sq6ue93Se77XULD9vC7B3naUVaCqS1np2SSc85d4dO+MOJPb8slWL/aHuy2/TGgEbgsSMf/Civw+oUfbVSBFsykYR/X0iGCgXO5DGvLaynMSwt1UyKDPvGq3kRKYq67JtMDx3zEMc0P0TL1gv6PiUL+BDaHAy5glfdGY0wzsMb9ekCPF5EjgOuAecaYvX60UQXacHbb6xDBoGze1UBdSzuH5KWHuimRwZ2s7kq1ktVr4nN06E5ZIuweVJCdgsvAN7saQ92UsORPYJMLVBvTvUQsANuBTBGJD9TxIhKL1ZvzhjEmzAY5o4CzFB44GNOzHJ8lGN32mhQ3KM7yGgAK87XHxm+FxThuXM/l+a9x8YjHNKhRlgi7B3kWw9ykFYh98iewGQH4CkoAmr32CdTxNwMHAv/jR9u6EJE5IrJaRFZXVVUN9HDlWcG7dhs+S1MFq9tehwgGzlnKya+ewqaES5n016PDL9ExzB1TkMnnlXVU1/d2a1JRpWghJjZy7kH7FsPUNaN88SewaQQSenkt0WufIR8vIgcAC4FfGWM2+dG2LowxjxpjZhpjZmZlZQ30cNVbXg0Ed8aN10KFLoTqmGwdIuiLOwBNb9uJQwxSq0spDNRZ/JP34ucy+r4xOgtPQWEx5cf/mnJXZMwwTE6IZWxaIl99qz02vvQ7KwqoAKaKSIKP4aRxWMNMrQE6fjGwG1juDnK82xnv3tZgjNnhR7vVQPU6niwwP8hlhAqLobCYW//u5JW1O1hz8OnEBPeKkauvRMcwvRGHFWcp4/+1AHHoLDy1z7/TTuOG1izemH8CB40ZGerm9OvAMSP5cmddqJsRlvzpsfnYvd8R3htFJBE4FFgdwOPHY+XkrAc2en2Nwxqe2oiVf6OCIQzGmY8uGE1dczuf7dCc8V5FWKJj2CkrQSJhBowaVl9/W49DYPzoMFxOwYdJY1L46tt6Oly95ENGMX8Cm+cAA8zrtn02Vm7Ms54NIlIgIpMHezzw/4CLfHxVAdvcf7/bjzargQrWCt4DdFLLO7wXP5dpj43XIYLehEEAGtE0MFQ+fF3VwPjRySTERkZf8SltKylzXIejJEPvld30OxRljFkrIo8A14nIMuBVYApW5eCVdC2uV4bV6yKDOd4Ys8JXG0TkPqDeGPO3gf14yi+eFby7P8UGoxhfP+1IW3ETaTpE0LeihTQvu45E75z8ME50DDtaqE/58NW39RRkheFSCr44Szly7e049F7pk79LKszD6k2ZhlUJ+GLgYeBsY4xrGI5XwTScxfgG2g4dIuihecoF3No+26rDEgGJjmFHZ+Gpbjpchs3VDRRkpYS6Kf4pK8GhRU175U/yMMaYDqzE3sX97DdhKMcP9LwqQMKlaz5c2hHm/r11D8vaj+Hs8+dyyuQxoW5O5OlWmn6HGU32WXcRq4Fh1Crf00hrh4uC7AgJbPRe2Sd/e2yUXTlLMb2tQzrcXfOaO+KXDzftxiEwc8KoUDclcrlL079+4Wcc07KEf6edFuoWqRDyTJuOmB4bvVf2SQObaObJrTEdPV8LRde8DhH0zV0Vet77R/Bh0g2kfrk81C2KeCe0vMP7CXM5/KmJmoAZxb6u8gQ2EZJjo/fKPmlgE816y62RmNDkbHgV6jMI200m7Wc9pLkj0KUqtANDtqtKi/INlbOUEa/NZ5xUI5h9CZj6bxpdnKVc9M8z2ZR4Kel//E5k/P+775WNSWNxGaEtZZzm2XnRwCaa9TYea1yh+4C4hwj+ccFnHNuyBOeo00PTjnCjidWBp/+myv3AkNG2E0ekBbeFxWy+/CMmtjzL66ev0KDGiwY20SgUC10O0FETRwPwwde7QtySMKHJgoGn/6YqwoPbgqwUHAJfVmoFYm8a2ESbUC10OUCjkuO5JuMTfvDembAoXfMfNFkw8PTfVEV4cJsYF8OEzGS+3KlrRnnTwCbahGqhy4FylnJj82/J7PgWIq2LOBiKFtIek9h1W5gEoRHLRwKmidV/06hig+D2oGxdM6o7DWyiTX8LXYZDUANQVkJ89zVTI6iLOKCcpVBWQkxHM+1WJkB4BaGRqluyerkrk08PvV3/TaNJ0ULaHZH9wHBQzki27Gqguc3H7NYopYFNtImUJ5QI7yIOmG5Dh7G4EM+NV38BD507Wd21cA+/i/khE9Ys1qHPaFJYzP+Nv4XtJhMToVW8DxqTgsvsm7Ku/Kw8rGzCWQruhS675NeE4xOKrudj6Su5MYJuvuEuZt3zLOKPxLe7ewl17Z2o8WLHsTw+eiavzD0+1E0ZlBm1K3gv/nbGPbrLuj/qQ4/22EQNz5N/0+6uQU3SqPB8QtECVBbtuRoeOvQZtb6uqo+cisPdOUvJefen5Dm0FpM3DWyiRbgsdOmvbgWoWqO1AFWkDB1GOg0go1JTawfba5oiN7ApK0EieLp6sGhgEy0i8cZdWMzea9YwseVZ/nzky9EX1DhLMa31PasNRWPPVbBpABmVNlXXYwwUZEfIUgrdReJ9fRhoYBMNnKUQLgtdDlBOWiLjR49g1ebdoW7K8PKs49W0JzKGDiOdDn1Gpa+rGgA4IFJW9e5OA3KfNLCxO09uTbgsdDkIR+4/ilVbduNy9VIp2Y4ibegw0rmHPk1aPi6gAwfG06Uf5fkKdvbVzjocAhNGR2iPjQbkPmlgY3fhttDlIFwQ9wEvt1+LlGRExzRcZ6nvGWEQ9V3MQVVYjBQtxOVIJAaX1VOmyZi29nllHRMyk0mMiwl1UwbHHZC3j8zDZYT6xLERc18PJg1s7C4cF7ocCGcph69dFD1Z/54ett5EeRdz0JWVEOtq7rpNkzHtyVlKyeaLKav7fmQ/MBUWE3PjOg6V57hr0vORcV8PMg1s7C7Sx2DLSnC0R0HWv3thUpbN7n3JC+1iDj5NxowOzlLM/y5OMtMAACAASURBVM0lx1TZ4oFJRJiam8r6ir2hbkpY0MDGrjwreNduo0dqSiT9grT7LxpnKdyzvxXQ9Db85KFdzMEX6Q8Cyj9lJYjNHpim5abx+Y69tHe4Qt2UkNPAxo66leF3CFa5cIi8kuF2/kXjVTSxX2n5kfN/Fsl8LYwJ0NoQsU/zygcbPjBNHZtKS7uLzdUNoW5KyGlgY0c+EoYFY/1yDKeFLv1h16x/Zyksv6b3YSdvdvh5I4VnYcykUZ31gwSs4DOChypUNzZ8YJo2LhWADTt0OEoDGzuy09NIl2m4wu7YMZHV4+TNk0ezKA2WzfE9Bb+7SOths4PCYohP7lo/CCJ+qEJ5KVpIiyR03RbhDxAFWSnExzo0zwYNbOzJbk8jhcXI/HVcf+BbnB3ze8z0i0LdooHzGh609FOTJy4Jzn8s8nrY7KLXh4NtkT2DRlkKiynhx+yJGwMRuqp3d3Hr/8Z78dezYNXRUf8e1dW97SaSVvAeoCMnjuKVtTso39NE/qgRoW6O/zzDTv700IBVXfjMeyL6JhvxeltdHvxf+dtZavXw1JZDUoa1rWmPrsAcBqrrW3i26Sgmnv3fXHXc/qFuztC5H5yyXe6h7ShfnV57bOzExwreBmxThr+ofSXvxc8lb0lu5DyR9FX5uTuJsXppfrY54v+vIp6v3C5vbU1WsOr9HvQealyU7jXTzVg5Ok27rb/XbrNeu2f/yHgP29DnO+oAmJwzMsQtCRBfhVijeOhUe2zsxGfSMPYow+8sJffdnyGOCHsi6a3yc3dxSbYIPm3D8/9QVtJ7z43psAKU5T+2Cl4i7Bti9GP5D09Csvf11LBYX1ELWDOJbMFOeZUBoD02dmLnN3dZCRJpTyR9LY0AEKlT8KNFYbGV45SW3/d+xlM3ZBBrmfnq+VFBt75iL+PSk8hIjg91UwLDbnmVQ6SBjZ3Y+c0daUFbf0sjSAyc/ygsqtUE4XDX37DUUJkOnUo+zNZV1DI11ya9NWDfshiDpIGNXXglDXdhlzd3pAVtfQ1BxSXBeX/QYCZSeGrbSBAXSmxrsoa1IiV3LFI5S3HdP40Ve89l8fZL7fNv7XmPpuVjECpMJq6zo7cXWAMbO/CRNAzYJmkYiKwnkv6GoOzyfxJNCoutYHSwPTdxydZXfyJ8zaKw5r5POvaW4xBIbam017+1e+j0+bPXckzLEjaNPTPULQoZDWzsoLfeATskDXt0eyKpJAsTjgFCv6tz69IIEcurKnHv3I8Wnt6dtHxrptvPK6yv8x/rv+cn3HPHIlWUzBw6JC8dgP9sqw1xS0LHr8BGRBwiMl9EPheRZhHZJiKLRcSPRxD/jxeRDBG5QUTecO/TJCJfiMijItJPBl8Ui7T8k8FyP5E8PWsNRzU/xNZxZ4W6RT31NwQVjj1Myn+FxdZ0/PMf25dU3CWIcedN3bbbd/6Uvz0/tdvs05MQLqLkPnlAdgoj4mNwlteEuikh4+907weAucByYDEwxf39YSJyqjGmv+VE/T3+SPfrZcBvgWrgYODHQLGIHGOM2eDvDxc1eismFq75J0N0TEEmAO9/tYvxo/2KrYdPXzfJcOxhUoNTWDz4/0t/ppKDTgUPtCi5T8Y4hB9nfMIl/7kOPq2OyoKQ/fbYiMg04HpgmTHmfGPMY8aYG4EbgZOBiwN4/OfAJGPMLGPMPcaYx40x84HvAWmAvfoMA6VoIc3Ya92TvhRkJXN58kfMevNUqxBaOCRcuouzmd6m/OoQlPLmmUp+/mO9997YcJgkpIoWYiIlT28onKX8pG4J2a4qOgtC2imXyA/+DEVdgjVw/GC37Y8BjcBlgTreGLPFGPN19xMYY1YAu7F6b5Q3Zymtbywi3rTg8vx32rwuiqx9nl+6/sDo9p2ExQfXax2oHgsngj1vniowPHk7vbHZMElIFRbzzTF3U+7KxNhkfSifykqIczV33RZlQbI/gc3hgAtY5b3RGNMMrHG/HszjEZE0YCSw04/2Rg/3L9T4+u04BBy49v0StduH1VtZCfGmpeu2UH5w+8qrsevNUwVOYXHvRQDFEVVP2sH2dvxJHNe6hJ3zK+1bPypKcon64k9gkwtUG9P9NwkA24FMEemrfONQjwf4BRAHPOVHe6NHlGT59xBuH9xeryv2vXmqwOqtCKAW7wuoNdtqyElNJCctMdRNCZ5Iq/kVBP4ENiMAX0EJQLPXPkE5XkQuBG4CXgeW9nEdRGSOiKwWkdVVVVV97WoP4fYLfriE0wfXWWo9VfsSRTcSNUR9FQGMhoeVYbJmWw2H5qeHuhnBFUk1v4LEn8CmEbpnpnZK9Non4MeLyHeBZ4FPgGJjTJ+LsRhjHjXGzDTGzMzKyuprV1swaeN8v2D3X6jh8sHta+XuKLuRqAAoLPZad6obuz+sDINd9S18s6uRQ/ezeWDjDpIbksbiMkJbyrioGw73J7CpwBou8hWcjMMaZmoN9PEicgawDFgPnG6M2etHW6ODewYOteW4uod60fAL1f3BbUkeh8sIjUm5ofng9pZbIzFRdyNRAdLbQ4nm2gyNs5QRvzuUTQk/5MpVZ9v/37KwmB1XrmZiy7MsO/G1qLsX+RPYfOze7wjvjSKSCBwKrA708SIyC6vmzefAqcaYPX60Mzp0m4HjEKwMf4iuRNXCYmJuXMch8hy3FzwXmp+5t6do44qO/wMVeJprE3jue2ZSYwUOgYSGiqj4tyzISmZUcjwfbd4d6qYMO38Cm+cAA8zrtn02Vm7Ms54NIlIgIpMHe7z7HKcDLwBfAkXGmOj7X+mLj14CwVhBTZQlqsbGOJg/Zg3z1p2HGe56Nppbo4JBc20CL0onWYgIR00cxYdf76KfLA7b6bfysDFmrYg8AlwnIsuAV9lXOXgl8Bev3cuA8bCvnMdAjheRmcCL7uOX8v/bu/touaryjuPf380bMZZgCK5KAEHECNiIFbGCrSjWLmAJFjRdYFdLLaS1FYT6kqW2MaJWAgUqqG3Bl0CLlqsrsb5hLREkljehpRcRtFiCQFBCeA0kJOQ+/WOfIZO5M3PPzJ2XM3N+n7XuGrLnnLn7Hs6c85y9n703HC3tPDNIRPxL63/mEClrwnA9Y6P80cMXML2Sg16Zzwa6G+A5t8a6adFiWLWk/ntl/J5PVYmvmSftciMf3nwBfGxjqWYgzrukwpnAOmAJcCxpqYOLgWU5llNoZf9XsCOh+MIGn1XuwKYk04LnsuZspm9vMBFVN7+8zq2xbvP3vHPKeizHRjnizo8zMpJdq3r14FcAuRbBjIjtEXF+RCyMiFkRsSAi/ioiNtVst29ETJh8tYX9V0aEmv1M7c8dAkctY9tIzRwMZW0l6NeTmHNrrNvq5NoEpJtTEZYQGSRlvWauOZuRZ8vXBQc5AxsriLFRYs3HmDa+he0lWT6hqT7NZxNFmkfHhlMl12bu3gRp6vbnnur6vYTIoFm0mJXzzuKX2gOGeSmFWiXugnNgMyiyvA49fj8jwLSyLJ/QTK/ns3lumP195Rxmb72VLZSpuXtPvFCX5Mm7E8bHg89s/E0uPHgVLH+sPIMsSvwA5sBmUJQ0s7+pqqfaccRDI3t070nMw+ytX0r85N0Jd/3ySR7fvI3XvmRev6vSW0WZyLQPHNgMCl/c6sueaq896BNsfTaIVUu6k4PgYfbWLyV+8p6ysVH2ufww/m/WyRx3ze+Vq/uu5sFvw7QXluYBzIHNoPDFrbGxUd74s0+w18jDKdjoRg6CA0vrl0aJxFufKteNulVZK+vztzzIiGD6k/eXLzcpe/A757AbOHzLp9m08IR+16gnHNgMgrFRxp/ZxIQ5lkrSrDipNWejbmb/ezI+66fKk/fseVQuAQLY/Ej5btStcPf9c94+43qumXY6cz41vxSj6hzYFF321DGy5VF2mqtw9rzSNCtOqputKZ6Mz4pg0WKYOYcJ812U9Eadi1tZk7FRDrj5I91t0S4YBzZF12gyuJlzHNRUdLObzpPxWVH4Rt0ad98na85GJWu5cmBTdL6YTa5eDsL0DrWmeDI+Kwqv/N2ao5axhVk7l5WxlbWE9xAHNgXnyeByqJnM7NkYgWezJ5KpXPCdW2NF4pW/W/KrfY/jg1v/lCdnvYhSTcxXq4T3EAc2ReXJ4FqzaDEctQzNmM10jadchKn0JTu3xorGK3+35NqfPsQ3xl/PfX98c7km5qtVr0V7yK9hDmyKyJPBtaeToyCcW2NFtGhx6gatZ4i7FlqSPRQu/vYibpz9Xg58+Lv9rlF/7dSiLe4fn8+9h58z1NcwBzZF5Mng2tPJvmTn1lhRlbBrIbedHgqDX48NyN10z81n88TSDZw//gfsdsOnYPluQzv024FNEZUw2asjGl7YI/8XOHvaC2r7/yb7HWY94pW/G/PcNU3N/d/VnDPj8+y29ZcwxEO/HdgUjRNW29couRLyfYFrugAnGPJ+aRsQXvm7MT8UNrfmbGbFMzuXDWHg58CmSJywOjVVF/y6JvsCN8qrAec2WbF45e/63E3XXEkCPwc2ReKE1anLLvjUb3NJT7T1nmbHRtN7dcm5TVZMJblR5XbUMp4d2WXnMj8U7lCSwM+BTZE4YbVzmn1Rq5vqx0ZhxX6w6rT2Psusnzxp3w5jo7DmbEbGt7CdkZR35JbWnTXqrh+yBVUd2BSFc2s6q1m+zbbNsGoJfHLPFNBsfqTx5/hpz4rMk/YlVflxI8A0xlHlu+ugZoc6C6oCQ7egqgObInBuTedVvsANBWx7avLP8dOeFZkn7Us8Giq/Eiyo6sCmCJxb0x2LFjdOJM5j7t4+9lZ8TSfta5BTNmyca9SaIT9eDmyKwLk13dOsS6oZt5TZIMmbUzasSpIU2zFDfrwc2PTb2Cjh3JruadZU38jseW4ps8EyWU7ZkHQx1DU2yvgzmyZOqemHk8YaTfI4JEnE0/tdgVLLcmvk3JruqgQo3zyj8Tw1kAKao1c4oLHBUzlnG43uG5Iuhgmya+hI7ffa3+XmKsflqqXE5kcQ2QQZlSTi6m0GkFts+sm5Nb2z0+R9She+2fPSf8/dG064FJbe42Nug6tZTtmwDv9udA2dOcff5ckMcRKxW2z6IZtvIRpN3e/cmu5YtNjH1YbbUcvqt0xWhn/DcH0HhjwJtusaHr8s6XxAzxW32PTaZOsRgXNrzKw9kw3/XnXa8CyU6fzEqRvSpHMHNr00Ngqr/7x5nodza8xsKpoN/4bhWChzbJRwfuLUDWnSuQObXmk2CV+Fp/82s06YrMVi2+b0kDVowc3YaGpxWnUacn7i1E02kenj9w1kC58Dm17I01Izd28vtGhmnZFn/qZBW3ahqhu/Iecntm6yiUwHsIXPgU235WmpcdOpmXXSTqMAmxiUlps8D4fg3Jp2TRYID8p5knFg0y1VTaZNv4xuOjWzbli0OLUCn3Bp85tW0Vtu8jwcgh8QpyJPIFz086RK7sBG0oiksyTdJWmLpPsknS9pTjf2l3SMpOslPSXpEUlflbRf3vr2zdgorNgvBTTNmkwhfRF//x8d1JhZ9+SZfbuoI6Zyt9Q4P3HKKoFws+BmQFpuFDFhIur6G0qfBs4AVgNXAQcCpwNrgTdHNEvDb21/SScAXwP+B7gUmAucCWwHDo2I9ZPV99BDD41bbrkl19/WEWOjcNXSNHNjHprmoMbMeqfS8jFZkABpQr8YTze5o5b19jqVzfOVHgwFExdL2GHGbAc0nZbrPMn+v2haasnp0Xki6daIOHTS7fIENpIOBm4HVkfEiVXlpwMXAe+MiC93Yn9JM4B1wLPAwRGxKSs/BLgV+EJELJmszl0JbKq/cJX/oZXXyb6A1fxlNLN+qLSATNats5Oam1gnbmbPXUvvh9kvSGWbH6Gl66gfDrunrfOErgfEnQ5sPgF8BPidiFhbVb4LsBH4QUQc04n9Jb0Z+A9gWUR8vOZz1gCHAvMjYluzOnc8sGnlaaeZfjwBmZlVdOpaVjFjDkyflQKT2uBn9ry0TfV7rQQvDX+nHw67bqrnSRf+H+UNbPLm2LwGGAduri6MiC3Abdn7ndq/8t831PmcG4FdgZflrHfnNFqTJK8Zs1MSn4d0m1k/5R0xlde2p3Z0wVee8Cuvmx+Z+N5UgxoPuOiNPLlZzfRxgr+8gc2ewMMR8Uyd9x4A5kua2aH996wqr7ctwIIcde6sqaw9Mnuev4hmVhx5R0wVjQdc9Naixel4t3uO9GnNrryLYD4PqBeUAGyp2mZrB/Z/XvbvettXbzuBpCXAEoB99tmnwa9r09y9Jh/lVGv2PDh6hb+EZlZMlWtTKwMfei7runI3fn9UjnfehO5qfZpXKG9g8zTwwgbv7VK1TSf2r7zOavV3RcQlwCWQcmya1Kd1jVbN3Ym/gGY2YCqr3tcbHNGJfJip8MNhMVTOEcg/aq2P8wrlDWzWAwdJmlWnO2kBqZupUWtNq/uvryq/s862UL+bqrtqo9ZOjhAwM+u36ptXRS+CnXrJx76eFlfteVLvHOnz/7+8gc2PgLcAh5HmnQGeG9V0CHBdB/f/Ufb6OuDqms/5LeAJ4Gc5691Z9b74ZmbDqtE1r9Fw7Tyjogpy87MOKeB9MW9gcyXwYdIkeWuryk8j5btcUSmQtD8wIyLuamd/4AfAg8Cpki6smsfmlcCRwJcmG+ptZmZdVMCbmVlFrsAmIm6X9FngPZJWAd8hzRx8BikQqZ6cbw3wYlJ7Zcv7R8Q2Se8lBUNrJV1KGuJ9FrAB+Gibf6uZmZkNubwtNpBaW9aRRh0dCzwMXEyaSK/pcgqt7h8RX5W0Gfhr4O9II6TWAEsjovf5NWZmZjYQcq8VNWh6vlaUmZmZdU2nZx42MzMzKzwHNmZmZjY0HNiYmZnZ0HBgY2ZmZkPDgY2ZmZkNDQc2ZmZmNjQc2JiZmdnQGNp5bCRtAO7tdz0GxHzShInWOh+79vnYtcfHrX0+du0rwrF7cUTsMdlGQxvYWH6Sbskz6ZFN5GPXPh+79vi4tc/Hrn2DdOzcFWVmZmZDw4GNmZmZDQ0HNgZwSb8rMMB87NrnY9ceH7f2+di1b2COnXNszMzMbGi4xcbMzMyGhgMbMzMzGxoObEpK0gJJH5L0A0kPSnpK0h2SzpO0e4N99pR0uaQNkjZLukXSO3pd9yKQ9GeSrpB0l6Ttkhr26UpaLika/Ly/l/UuglaOXbb9Qklfl/Rodp6ulfSmXtW36CSta3J+ze93/fpN0oiks7LzbYuk+ySdL2lOv+tWdE3Oq039rlsz0/tdAeubtwLLgW8D5wFPAocBZwJ/IOmwiPhlZWNJ84AfAi8ELgDuB04GRiW9KyK+1Nvq992HgN2B/wbmAHvl2OcsJk5wdWuH6zUIch87SfsD1wPPAucCjwOnAf8u6eiIuLr71R0IdwGfrFP+ZK8rUkAXAmcAq4HzgQOzf79K0psjYryflRsAa5mYOLytHxXJy8nDJSXpYGBjdfCSlZ8KXAqcHxHvryo/F/gAcFxEfDMrmwbcAOxPmhGy0FF8J0naF/hFRIxL+hZwbESowbbLgY8C+0XEul7VsahaPHajwInAqyPitqzs+cAdwBbg5VHyi5ikdcC6iDiyz1UpnOw6dzuwOiJOrCo/HbgIeGdEfLlf9Su6rDX1sog4pd91aYW7okoqIu6oDWoyV2avr6gpPxn4eSWoyT5jO3AxMA84pisVLaiIWNfOk56kXSWVuqU077HLugqOA66tBDXZ/puAzwMvA17TtYoOGEnTJe3a73oUzEmAgL+vKb8UeBr4w57XaABJmpk9UAwEBzZWq9It8KtKgaQXAQuAG+tsXynzDWZyY6SulC2Srpd0dL8rVHCLgFmkVsFaPu929lrSjfpxSY9JukzSnv2uVAG8BhgHbq4ujIgtwG34/Mnj7aRz60lJD0m6WNLcfleqmVI/OVpdH8teL6sqq1wgH6izfaVsQddqNPgeI/VRXw88Ciwk5TJ9O8tPWtnHuhWZz7t87iC1YN1FuqYfCZwKHJXlyq3vY936bU/g4Yh4ps57DwCHS5oZEVt7XK9BcTPwVeBuYFdSy/x7gDdIOryo6QcObAacpN1IN8m8LoqIRxp81vuAdwCXRMT3q956XvZa7+KwpWabgdHJY9dMRNQ2gyPpi8CPgQslfa2oF4hGenTshvK8q2cqxzMijq15718lXQdcQXpQOa0ztRxIz6P++QM7n0MObOqIiNfWFF0uaYyUqP5e6ies950Dm8G3GykxNa9/ASbcYLKk4fNIo6TeU/P209nrrDqft0vNNoOkI8euHRGxUdI/kkamHQ58rxOf20O9OHbDet7V09HjGRFflvRJoDboKZunSSM56xm2c6hXziOdq8fiwMa6IRtlU3dESV6S3kXqKvkecGJE1A7lqzRl12v2r5TV6y4otE4cuylal70O3FwjPTp2Q3ne1dOl47kOOKLDnzlo1gMHSZpVpztqAambyq01LYiIbZLWU+DrlpOHS07Sn5BGCFwNvK1eX3REPEi6gfxWnY+olN3StUoOrwOy11813aq8bid1I7yuzns+7yb3Unxu/Yh0nzusulDSLsAh+PxpWXbs9qLA55YDmxKTdAop6fAa4PhspEAjXwH2l/TWqv2nAaeTkmO/08WqDqxsCO6EEQSS9gbeDWwkJRVbjSzv6JvAkZJeWSnPhp2eCvwvNaNdyiabOLNe+V+Sbj7frPd+iVwJBBPzl04j5dZc0fMaDYhGM9ADHyf19hT23PIEfSUl6TjSTJxPAB8ENtdssikivl61/e6kWXJ3J808/ABpjogjgVMj4gs9qHZhZAFe5Wb7h6SRTn+T/fuxiPhMtt1uwD3A14E72TEq6lTg+cBJEfHVHla97/Ieu2zbl5KCl22kGWSfIN2UfoM0sd+/96reRSTpTOBPge+Sup4qo6LeBvwceF1EbOhX/YpA0sWkvMHVpAewyszD/wm8yTMP1yfpQlLL6DXAL0jXq2OANwI3AW+MiNr7RiE4sCmpqtlwG7k3Ivat2WcBcA5wNOkk/wmwIiKunLj7cJO0EvjjBm8/d+wkzQI+S5pnZC/ScXuYdFE9NyJK1+KQ99hVbX8g6bx7AzAT+C9guZdTAElHAEtJ3Sp7kPJ07gH+DTgnIh7rY/UKIWtZPhNYAuxL+v5dCSwbtNGIvSTpeOAvSJO17g5sJ7WSjgIXTNLC31cObMzMzGxoOMfGzMzMhoYDGzMzMxsaDmzMzMxsaDiwMTMzs6HhwMbMzMyGhgMbMzMzGxoObMzMzGxoOLAxs6Eh6RRJIenInNuvk3Rtd2tlZr3kwMasJCS9RNIlku6S9LSkRyX9RNJlkt7Y7/rlJekQScsl7dvvunSCpIMkfVbSnZKeknSvpM81WavHzJqY3u8KmFn3SToU+AFpzaXLgTuA2cDLgLcCT5LWhBkEh5CWA7mWtD7SVCwkLZLYT58D5gNfBh4Efpu0QOorJL0hPD28WUsc2JiVw0dJqxm/KiJuq35D0nuAX+9LrfosIp7pdx2ADwM3VAUwn5c0G3gHsD9wd99qZjaA3BVlVg4HABtrgxqAiBiPiPW15ZJOlfRfkjZLelzS9yS9vs52IWmlpDdJuiHr5rpf0tLs/RdI+oKkh7L3viVpzzqfM1fSCkl3S3pG0gZJX5H0kqptlgNfyv55Tfa7I1tYs9qIpPdL+nn2WT+TNGHhzXo5NpUySS+X9G1JT2Z//9ckTQgAJS3Kjs1TkjZmXXvzG9Rrgoi4vk6rzFPZ6+zJ9jeznbnFxqwcfg4slHRCRKyabGNJK4APAjeTWhR+jbQ68jWSjo+I79Ts8ipSl9YlpK6uxcA5kraQVvJeBywHXgqckW3z5qrfNxe4HtgH+CKpq+xFpNWFb5J0aETcC6zKypcAfwvcWfX3VftbUlDwT8AzpK6dlZLujoj/nOzvBxaQurpWAx8AXgn8GbAr8Jaqeh8ArCU9JF4EPAAcA1yV43fUlSU+nwSsjYjb2/0cs9KKCP/4xz9D/gO8DthKyif5GSl4eDdwYJ1tFwLjwA+BmVXlewKPkYKUaVXlkW3/2qqymaR8kXHgoprPvyDbZ2FV2aeBzcAra7Z9MfAEsLKq7JRs/yPr1L3y3n/X1H0BKcD5Ss3264Br65QFsLim/LNZ+curykazsiNqtr0yK19ZW8dJ/j+9BXga+DEwv9/njX/8M4g/7ooyK4GIuAF4NXAZMBf4E1LS6k8kra3u7gGOBwScGxFbqz5jPbCSFGy8quZX3BARN1Vtu5XU2iNSS0a1tdnrAQCSBLwTuA54IOvGmS9pPqlL5kaqWkly+lxN3R8gBXQH5Nx/fUSM1pR9P3t9aVbvaaTWmZtjYivQ+S3Wt9L6s5rU+nRkRDzc6meYmbuizEojUrfGKQCSXgy8ATiVNArn3yS9OgsG9st2uaPOx/w4e30JcEtV+f/V2fbR7PWeBuWV4cx7ZP/9FmBDg+qPNyhvpF59NpKCsqnsDzvXew7w0zrb1iubzEmkBO93O6gxa58DG7MSipSvcrmkfya1oBwBHEbqflIbH7m9ye9q9J5qXq8GVrTxu1upT96/reHfw8R619POEO09stf729jXzDIObMxKLCJC0k2kwGZBVlxJxD2YiUm5B2Wv9Vo02rWBlLuza0RcnWP7oszr8hCpq2xhnfde3sbnXUcKlp6YSqXMys45NmYlIOl3JU14kMnmS6nkr/wke/0GKXj4gKQZVdu+iJSbcy8pObcjImIcuAI4TNLbG9T/hVX/3JS9zutUHdqRtURdRar3ETVvv6+Nj/wh8BnSZIlm1ia32JiVw4XA7pK+AdxOGnmzN3Ayafbhy7McHCLip5LOIw33vk7SlewY7v184J1Nupfa9RFSq9GopFFSwvBWUk7MMcCtZPlBwI9IOTcfkfQCUqvJPdXJyz3018DvAd+V9BlSN9Kx7OhWaqV16VOkofH7MfUZlc1Ky4GNWTn8FWm0XgcaBwAAAQBJREFU0+uBE4HdgMeBMVJey8rqjSNiqaS7SfPInEMKMm4CTo6ItXRYRDyetXq8jzQHzvHAs6RA4YfA56u2/YWkdwFLgX8AZpBGe/U8sMmCwN8B/g54L7AF+Bbwl6Tuus29rpNZ2SmiKN3VZmbDQdKrSaPGPhQR5/S7PmZl4hwbM7MpyPKUqv8tUjcewH/0vkZm5eauKDOzqblN0vdJuUtzSEtL/DZwZUTc2teamZWQu6LMzKZA0rmkYGZv0sPiPaRRXisiYls/62ZWRg5szMzMbGg4x8bMzMyGhgMbMzMzGxoObMzMzGxoOLAxMzOzoeHAxszMzIaGAxszMzMbGv8PzbDGyJyDB3AAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = sns.distplot(data, hist=False, axlabel=\"Something ?\",\n", " kde_kws=dict(gridsize=200, bw=1, label=\"seaborn\"))\n", "ax.plot(x, kde, \"o\", label=\"my_kde\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compute the gaussian KDE with scipy\n", "\n", "Using available methods from reliable packages such as `scipy` is always a better option. In addition to save time the functions are generally more efficient and less buggy.\n", "\n", "Here we will use the [`gaussian_kde`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gaussian_kde.html) class from the `scipy.stats` module." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# KDE instance \n", "bw = 1. / np.std(data)\n", "g_kde = gaussian_kde(dataset=data, bw_method=bw)\n", "\n", "# compute KDE\n", "gridsize = 200\n", "g_x = np.linspace(-24, 6, gridsize)\n", "g_kde_values = g_kde(g_x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can compare with our previous KDE computed by hands. \n", "\n", "**Remark:** In `scipy`, the bandwidth is scaled by the covariance of the input data, that is the standard deviation here. Thus, for comparison, the bandwidth is divided by the standard deviation. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(g_x, g_kde_values, label=\"scipy\")\n", "plt.plot(x, kde, \"o\", label=\"by hands\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are several methods embeded in the `gaussian_kde` class in order to integrate or sample using the new kernel.\n", "\n", "Depending on the `bw_method` argument, the class can compute an estimator of the bandwidth which could be obtained from a class attribute." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Band width: 0.5674272856715801\n", "Band width: 0.6010325090449528\n" ] } ], "source": [ "g_kde = gaussian_kde(dataset=data, bw_method=\"scott\")\n", "print(f\"Band width: {g_kde.factor}\")\n", "g_kde = gaussian_kde(dataset=data, bw_method=\"silverman\")\n", "print(f\"Band width: {g_kde.factor}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you want to use this new value in our `my_kde()` functions, don't forget to scaled the bandwidth by the standard deviation of the input data." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# compute KDE value from gaussian_kde instance\n", "g_kde = gaussian_kde(dataset=data, bw_method=\"silverman\")\n", "g_kde_values = g_kde(g_x)\n", "# our functions with the computed bandwidth\n", "x, kde = my_kde(data, width=g_kde.factor * np.std(data), gridsize=200)\n", "# plot\n", "plt.plot(g_x, g_kde_values, label=\"scipy\")\n", "plt.plot(x, kde, label=\"by hands\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### About performances\n", "\n", "Hereafter is a comparison of the performances of our functions and scipy `gaussian_kde` class. You can see that scipy is three times faster." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.2 ms ± 190 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" ] } ], "source": [ "%timeit x, kde = my_kde(data, width=g_kde.factor, gridsize=200)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "755 µs ± 70.6 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" ] } ], "source": [ "%%timeit \n", "# KDE instance \n", "g_kde = gaussian_kde(dataset=data, bw_method=0.14)\n", "\n", "# compute KDE\n", "gridsize = 200\n", "g_x = np.linspace(-24, 6, gridsize)\n", "g_kde_values = g_kde(g_x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparisons\n", "\n", "Now, let us compare the KDE obtained from either our functions, `scipy`, `seaborn` or `pandas`." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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data
0-20.312751
1-18.359474
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\n", "
" ], "text/plain": [ " data\n", "0 -20.312751\n", "1 -18.359474\n", "2 -18.355310\n", "3 -14.184065\n", "4 -11.673050" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.DataFrame(data, columns=[\"data\"])\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note in the following cell that in `seaborn` (with gaussian kernel) the meaning of the bandwidth is the same as the one in our function (the width of the normal functions summed to obtain the KDE). As `pandas` uses `scipy` the meaning of the band width is different and for comparison, using `scipy` or `pandas`, you have to scale the bandwidth by the standard deviation.\n", "\n", "In the plot below, the KDE computed by hands or using `scipy` are shifted vertically for a better comparison." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# bandwidth\n", "bw = 1.\n", "bw_sp = bw / np.std(data)\n", "\n", "# KDE from our function\n", "ax = plt.subplot()\n", "x, kde = my_kde(data, width=bw, gridsize=200)\n", "ax.plot(x, kde + 0.05, label=\"by hands\")\n", "\n", "# scipy\n", "g_kde = gaussian_kde(dataset=data, bw_method=bw_sp)\n", "g_kde_values = g_kde(x)\n", "ax.plot(x, g_kde_values + 0.025, label=\"scipy\")\n", "\n", "# pandas\n", "df.data.plot.kde(bw_method=bw_sp, ax=ax, linewidth=3, label=\"pandas\")\n", "\n", "# seaborn\n", "sns.distplot(data, hist=False, rug=True, ax=ax,\n", " axlabel=\"Something ?\",\n", " kde_kws=dict(gridsize=200, shade=True, bw=bw, linewidth=0),\n", " rug_kws=dict(height=.2, linewidth=2, color=\"C7\", label=\"data\"))\n", "\n", "\n", "lgd = plt.legend(fontsize=16);\n", "lines = lgd.get_lines()\n", "lines.append(mpatches.Patch(color=\"C3\", label=\"seaborn\", alpha=.4))\n", "plt.legend(lines, [\"by hands\", \"scipy\", \"pandas\", \"data\", \"seaborn\"], fontsize=16);" ] } ], "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }