{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib.patches import Ellipse\n", "import matplotlib.transforms as transforms" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def confidence_ellipse(x, y, ax, n_std=3, **kwargs):\n", " \"\"\"\n", " Create a plot of the covariation confidence ellipse op x and y\n", "\n", " Parameters\n", " ----------\n", " x, y : array_like, shape (n, )\n", " Input data\n", "\n", " Returns\n", " -------\n", " float: the Pearson Correlation Coefficient for x and y.\n", "\n", " Other parameters\n", " ----------------\n", " kwargs : ~matplotlib.patches.Patch properties\n", "\n", " author : Carsten Schelp\n", " license: GNU General Public License v3.0 (https://github.com/CarstenSchelp/CarstenSchelp.github.io/blob/master/LICENSE)\n", " \"\"\"\n", " if x.size != y.size:\n", " raise ValueError(\"x and y must be the same size\")\n", " \n", " cov = np.cov(x, y)\n", " pearson = cov[0, 1]/np.sqrt(cov[0, 0] * cov[1,1])\n", " ell_radius_x = np.sqrt(1 + pearson)\n", " ell_radius_y = np.sqrt(1 - pearson)\n", " ellipse = Ellipse((0,0), width=ell_radius_x * 2, height=ell_radius_y * 2, **kwargs)\n", "\n", " # calculating the stdandarddeviation of x from the squareroot of the variance\n", " # np.sqrt(cov[0, 0])\n", " scale_x = np.sqrt(cov[0, 0]) * n_std\n", " mean_x = np.mean(x)\n", " \n", " # calculating the stdandarddeviation of y from the squareroot of the variance\n", " # np.sqrt(cov[1, 1])\n", " scale_y = np.sqrt(cov[1, 1]) * n_std\n", " mean_y = np.mean(y)\n", " \n", " transf = transforms.Affine2D() \\\n", " .rotate_deg(45) \\\n", " .scale(scale_x, scale_y) \\\n", " .translate(mean_x, mean_y)\n", " \n", " ellipse.set_transform(transf + ax.transData)\n", " ax.add_patch(ellipse)\n", " \n", " return pearson \n", " # render plot with \"plt.show()\".\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create the plots for the blog-post" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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2uOceOPts6NDBb0uyQvSwyot4X7JtBGlImU4VRSAnJmOyyowZ0K5dxruxApkN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\n9SwCbEBpvSAAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(5, 5))\n", "np.random.seed(567)\n", "latent = np.random.randn(500, 2)\n", "dependency = np.array([\n", " [0.9, 0.4],\n", " [0.1, -0.6]\n", "])\n", "mu = np.array([2, 4]).transpose()\n", "scale = np.array([2, 4]).transpose()\n", "dependent = latent.dot(dependency)\n", "scaled = dependent * scale\n", "scaled_with_offset = scaled + mu\n", "\n", "data = np.array([[-3,2,5],[-4,-3,5]]).transpose()\n", "pearson = confidence_ellipse(scaled_with_offset[:,0],scaled_with_offset[:,1], ax, facecolor='none', edgecolor='red')\n", "\n", "ax.scatter(scaled_with_offset[:,0], scaled_with_offset[:,1], s=0.5)\n", "ax.axvline(c='grey', lw=1)\n", "ax.axhline(c='grey', lw=1)\n", "ax.scatter([mu[0]], [mu[1]],c='red')\n", "\n", "ax.set_xlim(-5,8)\n", "ax.set_ylim(-6,14)\n", "ax.set_title(f'Pearson Coefficient = {pearson:.3f}')\n", "plt.savefig('./img/001_vanilla_ellipse.png', bbox_inches='tight')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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RI2HTptDJJDDn3IPOucXOuTn5PlfNOfeKc+7rxJ9qwCICMH++rQ774QeYMQP2\n3z90ouy2eLF9T5o1S8rdqdAgJdemDTz7rJ3dGTs2dBoRkWiZMQP23deW2c+YYQWHbbYJnUqSoWpV\nGDYMXnvNlv0ecICdDZJsNgZoVeBzvYHXvPd7AK8lPhbJbm+9ZWfOTz0VnnlGDZCj4I037D116dJJ\nubvMKzSoOVMYhxxi88f79IGBA/V9EEkznUWLoNxcuP12aN3ajotPPaUZ4Jlqn33sBdq118Lpp0Pv\n3rBhQ+hUEoD3/i3g9wKfPhnIOxMzFmiT1lAiUXP//XDaaTBunDVB1uq+aHjtNTj66KTdXeYUGurW\ntb4B334bOkn2atDAGpw98QR0764lpCLpNQadRYuOX36xLWXPPAMffWQvqCSzOQcdOtjKldmzbTnw\n99+HTiXRUMN7/3Pi778ANQq7kXOum3NuhnNuxhJN9ZJMtHEjXH65FeHffhuOPTZ0IslPhYbNcE7b\nJ6KgVi1480345hto185m4YpIyuksWoS89JLtM23e3I6Hu+0WOpGkU/XqMHmyFR0OOsiK7yIJ3nsP\nFLrs03s/ynvfzHvfrHr16mlOJpJiS5faCr8vv4T334c99wydSPKbNw9WrYK9907aXWZOoQGs0PDm\nm6FTSJUq8MILtgf5mGPUjVsknCKdRQOdSUuK9euhVy/o2hUmTICbb07aPkeJGedsqsiUKbad4oIL\nVHjPboucc7UAEn8uDpxHJL3mzrV+DHvvbe8R1I8hel5/Hf7976RuY8msQkOrVvDii7YsR8IqW9b2\nXR1xBBx6qFXJRCSYLZ1FS1yvM2kl8fXX1qvmm29g1iw48sjQiSQKmjWDjz+2s0TNm8Nnn4VOJGFM\nAs5J/P0c4LmAWUTSa+pU20p21VUwZIgK8FGV5G0TkGmFhjp1YJdd1PE5KkqVgltugYsvtmLD//4X\nOpFIttFZtFTz3oqqhxwC555rPRm23z50KomSKlVg/Hhb7XLkkTBqlBomZzDn3ETgPWAv59wC59z5\nwC3Asc65r4FjEh+LZDbv4a674Jxz4MknbSSwRJP3tqIhyYWGzCspnXKKdfbW2aTouPRS2GknaNnS\nxn8ddVToRCLZIu8s2i3oLFrybdwIl1xivYFee81GWIoUxjkbAX3wwda74dVXreCw3Xahk0mSee87\nbuaq5L6CF4my9evtROP778N779nJYImuzz+HChWSPhkrs1Y0gDUgfOYZGysm0dGunTXE6tDBtreI\nSFLpLFpkN1H9AAAgAElEQVSarV5tx7XvvoMPPlCRQYqmQQP7ealeHQ48UJOyRCTzLFli0yQWL7Zp\ndCoyRN9LL6VkAkhSCg2Rmt/eoAFsuy18+GFaHk6K4cgjYdIkO6vz9NOh04hkFO99R+99Le99Ge/9\nzt770d7737z3R3vv9/DeH+O9LziVQrbGb79Zo9sqVWy6QOXKoRNJnJQvDyNGwJVX2r7ljz8OnUhE\nJDlmz7Z+NIceaid+9fwYDxMnpmQMd7JWNIwhSvPb87ZPSPQcfDC8/LItpxo/PnQaEZHimTfPXkAd\nfjiMHWuNb0W2xkUXwfDhcNxxtpVCRCTOJk2yqQUDBsDAgdarTaLv669hwYKUbG1Pyk9A5Oa3t2tn\nZ8zVbCmamja1/cy9e9seVRGROPjkEzjsMOjeHQYP1osoKbm8EyNnnGEjUUVE4mj4cCuevvCCHc8k\nPiZOhPbtIScn6XedymaQRZ7fnnRNmtifn3xib2oleho1gjfftOXHf/xh88ZFRKLq9dfh9NPtxVT7\n9qHTSCY54ggrvrduDb/8YlsqRETiIDcXrr0WnnsO3n1X/RjixnsrNDz4YEruPi1TJ7z33jlX6PIC\n51w3oBvArrvumpwHdO7PswQqNERXvXp/LTZcf71970REouTRR+Gyy2xqjiYaSSrss4+9SG/VCn7+\nWStmRCT61q+3sc7z5tnxS6Od4+eTT2DtWtvangKpfBYr0vx27/0o730z732z6tWrJ+/R87ZPSLTt\nuquNhnvsMbjuOm13EZFoGTIErrrK9tCryCCptOuu8M479oL97LPtRbyISBQtXw7HH28TmF59VUWG\nuJo40VZrpuhEbyoLDXnz2yHE/Pbmze2X4Msv0/qwshVq1oRp02DqVLj8co0mFZFouOkmuP9+e+On\n8ZWSDtWq2Yv2lSvhxBPtTxGRKFm40LZ8NWwITz4JFSqETiRbIzfXVmx27Jiyh0jWeMvozW8vVcq2\nTzz+eFofVrbS9tvbHuiZM6FrV9i0KXQiEclmgwfbC6g337QzzSLpUrGibf3cbTfr4L5sWehEIiLm\ns8/gkEOs4ePdd6ekgaCkyXvvwTbb2Na9FEnW1Ilozm/v3BkeekhnyONi221t9OW8edCpE2zYEDqR\niGSjkSNtIs4rr0Ayt/SJFFXp0nDffdCiBZxwgvUxEhEJ6a23/hxfec016qsWdxMnWsEohd/HzO40\ntP/+ULWqnSmXeNhmG5g82ZaLnnYarFsXOpGIZJPx42HQICsy1K4dOo1kM+dg6FDYYw9boannQxEJ\n5Ykn4NRT4ZFH7GSgxNvGjfY9Pf30lD5MZhcaALp0sT22Eh8VKlgjzzJloE0b64YqIpJqzz5rjR9f\nfhl23z10GhHbBnr//VC5su2j3bgxdCIRyTZDh9oY+qlTbVKcxN/rr9so0nr1UvowmV9oOOMMe9H4\n66+hk0hxlC1rS3oqV7YKqs7kiEgqvfMOdOsGL7wAjRqFTiPyp9Kl7Szi6tVw/vnaDioi6ZGbC716\n2VbCd9+Fpk1DJ5JkeeABm26UYplfaNhuOzjpJHj44dBJpLjyXlyVLQsdOqhng4ikxpdfWkFz/Hjb\ncicSNeXK2Uq/776zvdEiIqm0bh2ceSZ8+KEV4nfbLXQiSZaFC226kQoNSdK1q1VuvA+dRIqrTBkb\nvZKba8tGVWwQkWT65RebBT54MLRsGTqNyOZVrAjPPWd9jIYNC51GRDLV8uXQqpVt1Zo61cbuSua4\n7z4rIlWunPKHyo5Cw2GH2S/Le++FTiJbo2xZa1iyZg2cdZb2qIpIcqxcCf/5jy1HP+ec0GlE/lm1\navDii3DrrTYCU0QkmZYsgaOOgsaN7URf+fKhE0kyrV9vfX+6d0/Lw2VHocE5awr5wAOhk8jWKlfO\nXlQtXWpjSzdtCp1IROIsN9e6LR9wAFx/feg0IkVXpw48/zxcdJHtmxYRSYaFC+Ff/4LWrW3VVE5O\n6ESSbE89BXvvDQ0bpuXhsqPQALYP5ZlnYMWK0Elka5Uvb13hf/7ZCkdqiCUiW2vQIFvRMHKkZoFL\n/Oy3n/UUadcOvvoqdBoRibvvv4cjjrDVff3763kxUw0fDpdckraHy55CQ40acPTRtgxI4qtCBZg0\nyRpiXXCBig0iUnxvvQV3322TbUqXDp1GZOu0bAl9+lgj0zVrQqcRkbj64gsrMvTsqWazmezjj2HB\nAjjhhLQ9ZPYUGsDOgt9/f+gUUlKVKtkIui++sKqcmnyKSFEtWWJNkMaMgdq1Q6cRKZkLLrC91Jdf\nHjqJiMTR//4H//43DByYtn37EsiIEbblLo0nWLKr0HDssbBoEcyaFTqJlNQ228CUKXaAvPxyFRtE\n5J/l5to2ujPPtI7aInHnnHUQnzbNxkGLiBTV9On2XDhihDVbl8z12282Ivn889P6sNlVaMjJsVUN\n99wTOokkQ5Uq8NJLNk2kVy8VG0Rky267zfr03Hxz6CQiyVO5sk1m6tED5s4NnUZE4uDVV+Hkk2Hc\nODjllNBpJNUefNC+39Wrp/Vhs6vQAHDhhfD44/Drr6GTSDJsu63N+H3jDejdW8UGESncu+/CkCHW\np6dMmdBpRJKrSRMYMABOO039GkRky557Ds44w85wH3dc6DSSaps2WePrNDaBzJN9hYYdd7TK3X33\nhU4iyVK1Krzyiq1uuPFGFRtE5K9++w06drQRx7vsEjqNSGp07ap+DSKyZRMmWG+XKVPg8MNDp5F0\nmDLFhiI0a5b2h86+QgPAFVfYfqR160InkWTZfntbBvbMMzB4cOg0IhIVubk2rqt9+7R2WhZJO/Vr\nEJEtGTUKrrrKXi8HeNMpgQwbBhdfHOShs7PQ0LixXR57LHQSSabq1W0bxX33abqIiJg777StcoMG\nhU4iknrq1yAihbnjDnsefPNNew8k2WHmTPjyS+jQIcjDZ2ehAWxVw5AhWmafaWrXtmLDf/8LTz0V\nOo2IhDRzpjWAfOwx9WWQ7KF+DSKSx3t7TTxqFLz1FtSvHzqRpNOgQdYwv2zZIA+fvYWG446DtWut\nsieZZY894IUXbFbsq6+GTiMiIWzaZM1/b70VdtstdBqR9Mrr19CjR+gkIhKK97ZV4tlnrcigHkXZ\n5Ysv4O23beJiINlbaChVCq680s52SebZbz948knrqvvhh6HTiEi63X8/lC8PZ58dOolI+uX1a3jx\nRevZICLZxXvo2dOmsr3xhjUDlOwyeDBcdhlUqhQsQvYWGgDOOgs+/hhmzw6dRFLhiCNg9Gg46SSr\n6olIdliyBG66ycY5ORc6jUgYlSvD0KHQvTusXx86jYikS95KhmnTbCpbtWqhE0m6zZsHzz8frAlk\nnuwuNJQvb5We228PnURS5cQTben0ccfBDz+ETiMi6XDNNdCpE+yzT+gkImG1bQt161pTVBHJfN7b\nc+Brr9n2YRUZstPtt9sWuu22CxqjdNBHj4ILL4R69eDHH7V3KVOdfTb8/ju0bGl7lapXD51IRFLl\n3XetIeznn4dOIhKec3D33dC8OZx+OtSpEzqRiKSK99C7t61iUJEhe/38M0yYEInXQdm9ogGgalU4\n91xbXiiZq0cP68B9/PGwYkXoNCKSChs32jLx22+HKlVCpxGJht13t+fAyy8PnUREUsV7uO46ePll\nKzJsv33oRBLKrbfaSdaaNUMnUaEBsCfghx6CpUtDJ5FU6tcPDjwQ2rSxiSMiklmGD4cddgg2L1ok\nsq66ymapT5oUOomIJJv3cP31MGWKigzZ7pdfYOxYuPrq0EkAFRrMLrvYXv6RI0MnkVRyzt6IVK8O\nHTva2U8RyQw//QT9+8OIEWoAKVJQuXL2Gueyy+CPP0KnEZFk8R5uvBEmT7a+DDvsEDqRhHTbbTbs\nYKedQicBVGj4U+/ecNddWlaf6XJy4OGHYfVquOACO0CLSPz16gXdukGDBqGTiETT0UfDIYdYQU5E\n4s97+O9/4bnnVGQQWLTIVuhfc03oJP9PhYY8DRtas8Bhw0InkVQrWxaeftqapETol1FEttLrr8P0\n6bZ0VEQ274474IEHItEkTERKqG9fez372mtqdC7Wn+rMMyOzmgFUaPirm26yVQ3Ll4dOIqlWqRK8\n8ILtZ7v11tBpRGRreQ89e9obqEqVQqcRibZatey1TvfuWtEnEmd9+8ITT1ihfccdQ6eR0BYvhgcf\njNwJVBUa8ttzT2jd2ooNkvmqVbPuvMOHw8SJodOIyNZ44QV7w3TKKaGTiMRD9+6wcqWe90Ti6uab\n4bHHVGSQPw0aZP3ndt45dJK/UKGhoBtvtO0Ty5aFTiLpULu2NdC5/HJ4663QaUSkOLy3/ebXX68G\nkCJFlZMDgwfbJKZNm0KnEZHi6N8fJkywIkONGqHTSBR8/z2MG2fvYSNGhYaC6teHk06CIUNCJ5F0\n2XdfeOQROO00G/8lIvHw2mu21U2rGUSK5+ijoWpVW3otIvEwcCCMH29Fhpo1Q6eRqLj+ejthGsHC\nkwoNhbnhBltO//vvoZNIuhx7LNxyi22dWbw4dBoRKYoBA+C66+wMrYgUnXPWq6F/f8jNDZ1GRP7J\nnXfC2LHwxhvWa0UEYOZMmDYNrrwydJJCqdBQmN13tzNkd94ZOomk07nnQqdOcOKJNv5SRKLrnXdg\n/nzbkygixdeqFVSoAM88EzqJiGzJ6NG2rfvVV1VkkD95D1dfbUXjbbYJnaZQKjRszvXXwz33wK+/\nhk4i6dS3rzUFPfNM7V0VibIBA6B3byhdOnQSkXjKW9XQr59WNaSJc26ec262c26Wc25G6DwSA088\nYXvvp06FXXYJnUai5OWXYeFCOP/80Ek2S4WGzalTx/bs33FH6CSSTs5Z5XjZMhuZJyLRM3MmzJkD\n55wTOolIvJ1wApQqBc8/HzpJNjnKe9/Ue98sdBCJuJdegksugRdftJNgInk2bbJRloMGQZkyodNs\nlgoNW3LddTBqFCxZEjqJpFPZsvD001Y91qhTkegZMACuugrKlQudRCTenLOzpf362TJcEYmGd96B\ns86yrU1NmoROI1Ezfrxtl2jTJnSSLVKhYUt23RVOPx1uuy10Ekm3qlVhyhS49VZ49tnQaUQkz5w5\nMH06dOkSOolIZmjTBtavt7OmkmoeeNU5N9M51y10GImojz+2XnETJsAhh4ROI1GzZo0ViG+7LfKj\nvVVo+CfXXgsPPACLFoVOIulWpw489xx06wYffhg6jchWy6h9wQMHwhVXQMWKoZOIZIZSpbSqIX0O\n8943BY4HLnbOHZH/SudcN+fcDOfcjCVaTZudvvwS/vMfuPdem4gmUtDdd8MBB8SiCKVCwz/ZeWeb\nRDB4cOgkEkKzZvDgg3bG57vvQqcRKYn47wueN8+2NF10UegkIpmlXTtYsQJeeSV0kozmvV+Y+HMx\n8AzQvMD1o7z3zbz3zapXrx4iooQ0fz60bGn77k85JXQaiaLff7eVDIMGhU5SJCo0FMV119ns2u+/\nD51EQjjhBLjhBmjd2n7BRSSMsWNtnGWVKqGTiGSWnBybtnXzzaGTZCznXCXnXOW8vwMtgTlhU0lk\nLFpkKxh69oTOnUOnkagaONAKww0ahE5SJCo0FEXNmnD55VZwkOzUvbsVHNq0gbVrQ6cRKa5/3Bcc\n+SW7ublWaNALMJHU6NDBzqh+8knoJJmqBvCOc+4T4EPgBe/9S4EzSRQsXWorGTp1svcbIoWZNw8e\negj69AmdpMhUaCiqnj3hrbfggw9CJ5FQbr0VatSAc8/VPlaJmy3uC4YYLNl95x2oVAn23z90EpHM\nVLq0FfIeeih0kozkvf/Oe98kcdnbez8gdCaJgFWrrCfD0UdbrxSRzbnxRht3WrNm6CRFpkJDUVWq\nZEsKe/XSm8xsVaoUjBtnFUUtL5UY+ad9wbEwZgycc07kOyyLxFrnzvDII7BuXegkIplv3Tpo2xYa\nNoQ77tDzm2zeRx/Bq6/a+9AYUaGhOM45B5Yv17jDbFahgs00Hj0anngidBqRf5QR+4L/+MN+7848\nM3QSkcy2++7QuDE8/3zoJCKZbeNG6zm03XYwapSKDLJ5ublw8cVwyy1QuXLoNMWS8kJDRo1Vy8mB\n22+Hq6+2mdOSnWrWtGJT9+4261gk2uK/L/jpp+HQQ6FWrdBJRDLfeefZtCURSY3cXOjSxYro48fb\n+wuRzRk9GsqUgbPOCp2k2NK1oiH+Y9XytGwJ9erBffeFTiIh7befzThu0wZ+/jl0GpHNyoh9wWPG\nqAmkSLq0awfvvw8LFoROIpJ5vLe+b19/bUX0cuVCJ5Io+/13m3w3YoRt4Y6Z+CWOgttvh/79Ydmy\n0EkkpHbtoGtXKzasWRM6jUhmyuuCf+KJoZOIZIeKFeG006wnkYgk1x13wCuvwOTJ1v9NZEuuv96O\nx02bhk6yVdJRaNjiWLXIj1QrTOPGcNJJMGhQ6CQS2g03QN26VnBQk1CR5Hv4YRu7p7M+IumTt31C\nz2siyfPIIzBsGLz4IlStGjqNRN3MmdafKsYN6NNRaNjiWLXIj1TbnH794IEHbAKBZC/nbBTY3LnW\npEVEksd7GDtW2yZE0q15cyvuvf126CQimeHVV+HKK2HKFNhll9BpJOryGkAOHBjrolTKCw0ZMVat\nMLVqwWWX2ZIWyW4VKlhzyBEjYNKk0GlEMsf06VC2LDSLf3sfkVhxTk0hRZJl1iw44wybVta4ceg0\nEgdjxtifMT/RktJCQ0aMVduSXr1g2jSbbSrZrXZteOop6yL8+eeh04hkhokToVMnjf0SCaFTJyui\nr1gROolIfH3/PfznPzByJBxxxD/fXmTpUrjuutg2gMwv1enjP1ZtSypVsi0UvXppH6PAQQdZo9CT\nT7YusSJSMlOnQuvWoVOIZKcaNeCoo+wsrIgU36+/QqtW0Ls3nHpq6DQSFzfeCG3bwgEHhE5SYikt\nNGTEWLV/0rmzvanUknkBOPts645/+umwcWPoNCLx9f33diZ1n31CJxHJXqedptc3Iltj9Wp7Pdi2\nLVx6aeg0EhezZllxd0BmvGWO93qMKMjJsbPYvXrBunWh00gU3Hqr/XnNNWFziMTZK6/AMcfEftmg\nSKy1bGlbRNevD51EJD42bYIzz4T69TWhToourwFk//5QrVroNEmhV3DJcNxxsPfeVnAQKV0aHn0U\nnntOc8hFttbUqfYmR0TC2WEHaNAA3nkndBKRePAerrgCli+H0aPVY0iK7uGHYcMGOP/80EmSRoWG\nZBk6FIYMgfnzQyeRKKhWzQoNPXvChx+GTiMSL5s2weuvw7HHhk4iIq1awUuZ015LJKWGDrXnr6ef\ntqlJIkWxbJn18siABpD5Zc5XElqdOtCjh1UxRcBWuTzwAJxyCvz8c+g0IvExYwbsvLONERaRsI4/\nXoUGkaJ48km4806YMgW22y50GomTm26ynh4HHhg6SVKp0JBMvXrB7Nnw4ouhk0hUnHwydO0K7dvb\ncigR+WdTp2o1g0hUHHggLFwICxaETiISXe++C927w/PPw667hk4jcfL++9YAcuDA0EmSToWGZCpf\nHoYNg8sug7VrQ6eRqLjxRqhc2ZZEicg/U38GkejIybHC38svh04iEk1ffQXt2tke+6ZNQ6eROFm3\nznoyDB1qPXEyjAoNyXb88dC4sRpDyp9KlYLx422/nuaRi2zZihU23unww0MnEZE82j4hUrjFi+33\nY+BAaw4vUhyDBtl0kvbtQydJCRUaUmHIEKtMzZsXOolERbVqtneve3f48svQaUSia9o0OPhgqFgx\ndBIRydOyJbz6KmzcGDqJSHSsWQMnnWSjLM87L3QaiZs5c6z548iRGTudRIWGVKhTx5pC9ugROolE\nyQEHWOXylFNg1arQaUSiSf0ZRKKnVi17bfP++6GTiESD97bkvW5d6Ns3dBqJm02b7OdnwACoXTt0\nmpRRoSFVevWCzz6DF14InUSipEsXaNHCGkR6HzqNSPS8/jocc0zoFCJSkLZPiPxpwAD45ht48MGM\nPRstKTRsGFSoYO8LMpgKDalSrhzcfbcaQ8rfDR8Oc+faz4eI/Gn1attyts8+oZOISEGtWmmqlgjA\nU0/BqFHw3HP2ZlGkOL77zgpV999vfdwyWGZ/daG1agVNmsBtt4VOIlFSoYL1axgwAKZPD51GJDo+\n/xz22APKlAmdREQKatECvvhCW/8ku338MVx4ITz7rG0pEikO76FbN7jmGnu9k+FUaEi1vMaQ338f\nOolEye67w+jR0KEDLFoUOo1INMyeDfvuGzqFiBSmTBlo1Mh+T0Wy0U8/wcknw733wv77h04jcfTQ\nQ7BsmfXyywIqNKTabrtBz55qDCl/d8IJ0LkzdOyoTt4iAJ9+qm0TIlHWtKmNnxXJNmvWQJs2tpqh\nXbvQaSSOfv4Zeve2E42lS4dOkxYqNKRDz5623HDy5NBJJGr69LGDzQ03hE4iEt7s2So0iESZCg2S\njbyHc8+1pe7XXRc6jcTVJZfYtokmTUInSRsVGtKhXDlrAHjppdrbKH+VkwMTJsDEibbfTySbaeuE\nSLSp0CDZ6OabrVHxAw9owoRsnaeesmmEWXZiUYWGdGnZEg4/HG68MXQSiZoddoAnnrAq59dfh04j\nEsaiRbBhA+y0U+gkIrI5++4Lc+Zou59kj8cft6Xuzz6rCROydZYutZPNo0dD+fKh06SVCg3pNGQI\nPPoovP9+6CQSNc2bQ9++tu9v9erQaUTSL281g84WiURXlSrWaV9FcckGH30EF19sYyxr1gydRuKq\nZ0845RQ49NDQSdJOhYZ02n57KzZ06QLr14dOI1Fz4YW2LPXCC20/oEg2UX8GkXjQ9gnJBgsXQtu2\nMGqU/cyLbI2pU+G112DQoNBJglChId06dIC6dbP2B062wDkbmfTxxzB2bOg0IumliRMi8aBCg2S6\n1attjOXFF1uxQWRrLF0K559vvT0qVw6dJggVGtLNObjnHmsO+dlnodNI1FSsCI89BlddBXPnhk4j\nkj5qBCkSDyo0SCbLzYVzzoGGDW0UocjWuvhi2zJx7LGhkwSjQkMIO+8M/frZFopNm0KnkajZe2/o\n399Wv6xdGzqNSOpt2gSff24/+yISbU2bwv/+py1+kpn69rVtE/ffr55BsvUmTrTj5C23hE4SlAoN\noVxwAZQpAyNGhE4iUdStm81rvvrq0ElEUu+nn6Bq1axdWigSK7Vr21nfX34JnUQkuZ580rauPvNM\n1k0HkCRasAAuvxwefjjrJ5Wo0BBKqVK2Z6dfP5g/P3QaiRrnrJr+/PMwaVLoNCKptXgx1KgROoWI\nFIVz0KQJfPJJ6CQiyfP553DRRfD003o+kq2XmwudO8Nll0GzZqHTBKdCQ0h77mkjTy64QEsQ5e+2\n2w4mTLDVDQsWhE4jkjqLF8OOO4ZOISJFVaeOnpckcyxfbk0fb78d9t8/dBqJs+HD4Y8/1N8jQYWG\n0Hr1gkWLYPz40Ekkilq0sKromWeqn4dkLhUaROKlZk34+efQKURKLq/549FH258iW+vzz22l+sMP\nQ+nSodNEggoNoZUpY1soevWyF9siBV1zjR2w+vcPnUQkNRYvhurVQ6cQkaKqVUs9GiQz3HKLnfAb\nOjR0Eomz9evhrLNg4ECoXz90mshQoSEKDjjAqqiXXRY6iURRTo5VR++9F956K3QakeTTigaReNGK\nBskEL79sTdmffBLKlg2dRuLs5putANu1a+gkkaJCQ1T06QMzZljzP5GCdtoJRo+GTp3gt99CpxFJ\nriVLVGgQiZNatVRokHj7/ns4+2x49FGbpCKytd57zxq4P/CARqIWoEJDVFSsaD+k3btbUxqRglq3\nhtNOg/POU/NQySxa0SASL9o6IXG2ejWccgpcdx0cfnjoNBJnq1bZlomRI22ll/yFCg1RctRRcPzx\n1q9BpDCDBsHChbbUTyRTqNAgEi81a1qhQUVviRvv4cILoVEjbVmWkuvZ04pVp5wSOkkkqSVm1Nx+\nu82nnjwZTjghdBqJmrJlbZlfixZ2YGvSJHQikZJToUEkXipWtOej5cttFLNIXIwcCZ98AtOna5m7\nlMzkyTB1qv08SaG0oiFqqlSBMWOgWzf49dfQaSSK6teHIUOgQweb1SsSZ95r6oRIHKlPg8TN9Ok2\nfvDpp6FSpdBpJM6WLLH3amPH2ns3KZQKDVH0r3/BGWfY0i4tS5TCdOoEBx0El14aOolIyaxaZWN+\nK1YMnUREikOTJ4rNOdfKOTfXOfeNc6536DxZ5eefoX17eOghqFcvdBqJM++tyHDWWXDEEaHTRJoK\nDVHVvz988QVMmBA6iUTViBHwzjs2lkkkrrSaQSSe1BCyWJxzOcAI4HigEdDROdcobKossWGDFRm6\ndbPG2iIlcc89MH++rY6RLVKhIarKl4eHH4YrroAFC0KnkSjaZhsYNw4uuUQv9iS+Vq2CypVDpxCR\n4tKKhuJqDnzjvf/Oe78eeBQ4OXCm7NCrl/USueGG0Ekk7mbNgv/+Fx57DMqVC50m8lRoiLL997eO\nuOeeC7m5odNIFB18MHTpAl27apuNxNOmTVBKT0UisVOjBixaFDpFnNQGfsz38YLE5/6fc66bc26G\nc27GkiVL0houY40fD1Om2Mk7PddISaxcaStjhg2DPfYInSYW9BsXdb172w/2yJGhk0hU3XSTrXp5\n8MHQSUSKLzdXL/5E4qh8eVi3LnSKjOK9H+W9b+a9b1ZdW8pKbvZsWxn89NOajiIl4z1cdJH10evY\nMXSa2NCru6grXdqWx/fpA3Pnhk4jUVS2rFXqe/eG774LnUYiKNINyHJzIScndAoRKa4yZWzvuxTV\nQmCXfB/vnPicpMKqVXb2+c47YZ99QqeRuBszxrZN3HVX6CSxokJDHOy5J/TtC2efDRs3hk4jUdS4\nsRUaOne2pegiCZFvQKatEyLxVLYsrF8fOkWcfATs4Zyr65wrC5wOTAqcKXNdcoltLz3rrNBJJO4+\n/ySkZD4AACAASURBVByuvtr6MmhCVrHo1V1cXHQRbLst3HJL6CQSVT16gHMwZEjoJBIt0W5AphUN\nIvGkFQ3F4r3fCFwCvAx8ATzuvf8sbKoMNW4cfPABDB8eOonE3erVtjJm8GDYe+/QaWKndOgAUkSl\nStke/P33t9E8++8fOpFETU6OLe1q3hxatbJVDiKFNyA7KFCWv8vNtQKZiMSLCg3F5r2fAkwJnSOj\nffkl9OwJr78OlSqFTiNxd/nl0LSpNeaXYtOKhjjZeWc7W33WWbB2beg0EkV169qql7PO0pJWKZZg\n3c7LlNGWMJE4UqFBombNGujQAQYOVF8GKbmJE+HNN+Gee3RCZCup0BA3Z5wBjRrB9deHTiJRdd55\nVpTq1y90EomGIjUgC9btvEwZFcVE4qhUKY3elmi58kpo2NDGfouUxNdfw2WXweOPQ+XKodPEVsoL\nDZHudh5Hzlll7dFHYdq00GkkipyD+++HBx6A994LnUbCi3YDsrJldVZUJI7UX0Wi5PHH4ZVXYNQo\nnX2Wklm3Dk4/3Sb+NW0aOk2spbTQEPlu53G1ww52IO3cGZYtC51GoqhmTRgxwiaV/PFH6DQSUOQb\nkGn5tUg8aWKMRMV339mUiccegypVQqeRuLv6aqhTB7p3D50k9lL9DBHtbudx9p//wIknQrdu4H3o\nNBJF7dpBixZ2wJSs5r2f4r3f03tfz3s/IHSev1ChQSSetKJBomD9euvLcMMNcMABodNI3D37LEya\nBKNHa2VMEqS60FBYt/Pa+W8QrAFZJrjtNvjqK1siL1KYYcPg+efh5ZdDJxEpXNmy6tEgEkda0SBR\n0Ls31K4Nl14aOonE3fz5dgL30Udhu+1Cp8kIwZ8hgjUgywTly9svw3XXwWfRWQktEbLddjYWtUsX\nWLo0dBqRv6tSRVvAROJIKxoktEmT4Kmn7HWOzj5LSWzYYH0Zrr4aDorOBPC4S3WhoUjdzqUEGjSA\nwYNt2diaNaHTSBQdcwy0batqv0RTlSp2ZnTVqtBJRKQ4NmyA0qVDp5Bs9eOP0LWrjSCsVi10Gom7\nq66C7be3ySWSNKkuNES723mmOPdcmxesXw7ZnEGD4N134cUXQycR+SvnoFYt+OWX0ElEpDh+/dWa\nU4uk28aN0LEjXHEFHHJI6DQSd488ApMnw8MPaztYkqX0fzPy3c4zhXNw770wdaotIRMpqFIluO8+\nuPBCWLkydBqRv6pZE37+OXQKESmOJUtgxx1Dp5Bs9N//2usaNbuWkvrkE+jRA55+GqpWDZ0m46S8\nbBPpbueZZNttbfnYRRdZMxORglq2hKOOsp4eIlGiFQ0i8bN4sQoNkn6vvAJjxujss5Tc0qU2oe2u\nu2DffUOnyUj6Dc0kzZvbHqMzzrBlZSIF3XmnrXqZPj10EpE/aUWDSPyo0CDp9ttvtl147Fj97EnJ\n5OZCp05w4on2vklSQoWGTNOzJ1SuDH36hE4iUVStmlVuu3SBdetCpxExtWqp0CASN4sXg6aFSbp4\nb6t2TzvNmlyLlES/ftaE+tZbQyfJaCo0ZJpSpazS++CD8PrrodNIFJ16Kuy5JwzQTiaJCG2dEIkf\nrWiQdJowwUa5DxwYOonE3eTJMHo0PPYYlCkTOk1GU6EhE9WoYcWGs8+2Zk0i+TkHI0bAPffA7Nmh\n04ho64RI3HhvUye0okHS4ccfbcLE+PFQoULoNBJn33wD550Hjz9urz0kpVRoyFTHHmt7j845x/Yh\nieRXu7ataOjSBTZtCp1Gsp1WNIjEy7Jl1vW/bNnQSSTT5eZC585WaNhvv9BpJM7++APatoW+faFF\ni9BpsoIKDZns5pvh999h6NDQSSSKunSBihVh2LDQSSTbaUWDSLxo24Sky7BhsHatRllKyXhvr3ub\nNbNR75IWpUMHkBQqU8ZGXjZvDv/6FxxwQOhEEiWlSsH998PBB8PJJ8Puu4dOJNlqxx2tKLpxI5TW\n05JI5KkRpKTDZ5/Z6sv334ecnNBpJM6GDoWvvoJ33rEtxJIWWtGQ6erWheHD4fTTYfny0GkkaurX\nt7MEF1xg1V6REHJyYIcdtH1CJC60okFSbf162wI8aBDUqxc6jcTZm2/C4ME23l09PtJKhYZs0KGD\njQI67zy9mZS/u/JKO5s8ZkzoJJLNGjSAL74InUJEikKFBkm1Pn1gl13g/PNDJ5E4W7AAOnaEhx+G\nOnVCp8k6KjRki6FDrWvvHXeETiJRU7q0jfm55hqdUZZwmjaFWbNCpxCRoliwwJq4iqTCu+/CQw/Z\n9k4tc5ettW6djXS/9FJrki9pp0JDtihXDp58Em6/3ZYQieTXtKk1ybn00tBJJFup0CASH3PmQOPG\noVNIJlq50saz33uvjWsX2Vo9esBOO0Hv3qGTZC0VGrLJrrvCuHG2hOinn0Knkai56Sb49FOYNCl0\nEslGKjSIxMenn8I++4ROIZnoyivhqKOsSbXI1ho1Ct54w7YFa1VMMCo0ZJuWLeGii6B9e9iwIXQa\niZLy5WHECLj8cli9OnQayTYNG8L338OaNaGTiMiWrFhhPRrUoE+SbdIkeO01GDIkdBKJs9dft5Nn\nkydDlSqh02Q1FRqy0fXXw7bb2p58kfyOOcbGod5yS+gkkm3KloW99rIl2SISXXPmQKNGGjcoybV4\nsU3AGjcOKlcOnUbi6uuvbeX2xIk2WU2CUqEhG5UqZd1Xn30WHn88dBqJmjvugJEj4ZtvQieRbKPt\nEyLRN3u2tk1IcnkP3bpB585w2GGh00hcLVsGJ54I/frZ9hsJToWGbFWtmjWHvPhijZSTv9p5Z7j6\narjsMo1DlfRSoUEk+mbPhn33DZ1CMsmECfDdd9C3b+gkElcbN9q28FatbGWMRIIKDdls//1tiXy7\ndrBq1f+1d+fxVk/7H8dfq1ESpTJFVLdQqVBUqBANhhQRiXAlUkKuMpVEJFMpIRElJUqExquuDKmu\nexWlSahQRGjurN8fn9NPl1Nn2vus/f3u9/Px2I8z1Tnv7zl7r/3dn+9anxU6jaSS7t1tvbwaQ0pB\nUqFBJPWpEaQk0rp11gDyuedsCZ1IXtx8sy3nGjgwdBLZjQoN6e6aa6BhQ9vaUFevZZdixeDJJ9UY\nUgpW7dr2IiYjI3QSEcmK95rRIIl10022nWW9eqGTSFQNHWpNRF95BYoUCZ1GdqNCg8DgwfDllzBo\nUOgkkkrOPBPq14f+/UMnkXRRujSUKwfLl4dOIiJZ+fZbKF4cypcPnUTi4K23YO5cLZmQvJs+3Xoy\nvPmmNbqXlKJCg0CJEvDaa/DAAzBnTug0kkoeeQSeesq6+IoUBC2fEEldagQpibJxI9xwAzz7LOy7\nb+g0EkVffgnt28PYsdpuN0Wp0CCmUiUYMQLatYPvvw+dRlJFhQrQs6caQ0rBOfFE+Pjj0ClEJCta\nNiGJcvvt1rhPuwNIXmzYAOeeaxdJGzcOnUb2QIUG+cM558BVV1mxYceO0GkkVdx0E6xaBW+8ETqJ\npIOzzoIpU0KnEJGsqBGkJMKsWTbVfcCA0EkkirZvh7ZtbSvLa64JnUb2QoUG+V+9e1sjwDvuCJ1E\nUkXRotYYsnt3NYaU5KtbF9auhW++CZ1ERHbnPcyebQ2kRfJq82a49loYMsT68ojk1k03Wa8YFapS\nngoN8r8KF4bRo2H8eBgzJnQaSRVnnAENGtgUNZFkKlwYzj5bsxpEUs3ixfb4rFo1dBKJsnvvheOP\nh1atQieRKBoyxAqeY8bYeCQpTYUG+aty5WDiRFuXv2BB6DSSKgYOhGHDrPmOSDI1bw7vvBM6hYjs\nbupUKwI6FzqJRNWCBfD889rlTPJm6lTo1w8mTYL99w+dRnJAhQbJWq1a9qKydWs1hxRToQL06gVd\nu6oxpCRXs2a2J/b27aGTiMguuwoNInmxfbutp3/4YTj44NBpJGoWL4YOHWDcOKhcOXQaySEVGmTP\nLrwQOnaEiy6CbdtCp5FU0K2b7aM+aVLoJBJnBx9sW1V99FHoJCICsHUr/OtftoxOJC8GDrSxvUOH\n0Ekkan74wXaYePBBOO200GkkF1RokL3r3RvKltVVbDFFi9rJwu2362qzJJeWT4ikjg8/hGOPhQMP\nDJ1EomjJEnjkEXj6aS29kdzZtAnOPx8uvdR2xpNIUaFB9q5QIXjpJZgzx5ZSiDRvDkccAc8+GzqJ\nxFnz5vDuu6FTiAho2YTkXUYG/P3vduHqyCNDp5Eo2bkTLrsMqlWDvn1Dp5E8UKFBsleqFLzxBvTp\nY3sfS3pzzmY19O0Lv/wSOo3EVYMGsHIlfPdd6CQiokKD5NXTT1ux4YYbQieRKPHetlX/9VcYPlwz\nYSJKhQbJmSpVbNvLSy6xk39Jb7VrQ8uWtl5OJBmKFIEzz9Q2lyKhrVsHS5dC/fqhk0jUfP893HMP\nPPOMtiKU3Hn0UXjvPXj9dShWLHQaySMVGiTnmjaFO++E886DjRtDp5HQ7rvPTh6+/jp0EokrLZ8Q\nCW/GDGjSxHr0iORGz55w5ZVQo0boJBIlr74Kjz8Ob78NBxwQOo3kgwoNkjs33ginnALt29vaKUlf\nFSpAly5WfBJJhubNbcq2dr0RCUfLJiQvPvzQ7ju9e4dOIlHy/vt2bvnWW9YPTCJNhQbJHefgySfh\nt9/gjjtCp5HQbrsNpk+H+fNDJ5E4OvxwOO44O+EQkYLnPUybBmedFTpJpDnn+jjnVjvnPs28tQyd\nKal27rQXiw8/bH2+RHJi8WK48EIYNcqW6ErkqdAguVe0KIwfb7eRI0OnkZBKlYJ774UePbT9qSTH\n1VfDiBGhU4ikp48/hhIloGrV0Eni4DHvfZ3M29uhwyTV00/D/vvbloQiObF2LbRoAQ89pBlUMaJC\ng+RN2bIwaZK9wPzgg9BpJKSrr4YfftBVZ0mOCy+0MWbNmtBJRNLPyJG2xl4d3yWn1q2zXcqefFL3\nG8mZjRutyHDttdCxY+g0kkAqNEje1ahhJyEXXQSrVoVOI6EUKWLTI2+7DbZvD51G4qZkSRtjXnwx\ndBKR9LJlC4wbBx06hE4SF12dc/91zo1wzpXJ6h845zo55+Y55+atW7euoPMlRq9e1serZs3QSSQK\ntm2DNm2s/1uvXqHTSIKp0CD507Il3HornH++7XUr6alFC1tPP3x46CQSR7uWT2h5jkjBeeMNOOEE\nqFgxdJJIcM5Nd84tzOLWCngKqAzUAdYCj2T1Pbz3z3jv63rv65YvX74A0yfIxx/bTgF9+oROIlGQ\nkQFXXWXLbAYN0gyYGCoSOoDEwC23wJIlcPHF8OabdoVb0otzMHCg7RLQvr09aYgkyskn2x7sc+bA\nqaeGTiOSHkaO1DTmXPDeN83Jv3POPQvEb63hrgaQDz2kLQklZ26/3WZET5tmz/ESO5rRIPnnHAwZ\nYlcbu3TRVcd0VafOH418RBLJOZvV8PzzoZOIpIc1a2x7wtatQyeJBefcobt92BpYGCpL0gwfbo1D\nL788dBKJgscfh8mTrd9biRKh00iSqNAgiVG0KLz6qk2b0wvN9HXffTBsGHzzTegkQsy2VOvQAV5/\n3bbWFZHkGj3aGrHuu2/oJHExwDn3mXPuv8DpwM2hAyXUjz/C3XerAaTkzNix8Mgj8O67cOCBodNI\nEqnQIIlTqpRVJ4cOhTFjQqeREA4/HDp1gn79QieRP8RjS7VDDoFGjaygKSLJ4z288IKWTSSQ976D\n9/44730t7/353vu1oTMl1B13wCWXQO3aoZNIqpsyBbp2tdcL6v8Seyo0SGJVqGDbHN50E/zrX6HT\nSAg9esD48fDVV6GTSNzsagopIskzbx5s3Wpd4EWyM2+eNQ69777QSSTVzZljS2smTIBatUKnkQKQ\ntEJDrKbsSu7UqmXTLi+6yJpESnopWxauv16zGlJHtluqQUS2VWvZEpYuhS+/DJ1EJL5GjoQrr9QU\neMleRob15urfH0qXDp1GUtmnn1rPl1GjVMRMI8me0RCPKbuSe2edZU88LVvCDz+ETiMF7ZZbYOJE\nWLEidJLYS8SWahCRbdWKFoUrrrDlWSKSeFu3wiuv2ONMJDsjR0KhQlaYEtmTL7+01wNDh0KzZqHT\nSAHSPoSSPFdfDStXwnnnwT//qaZS6eTAA+0qR79+muqeZGm3pVr37lCzJvTqBQcfHDqNSLxMmmTr\n7I88MnQSSXWbNsE998C4cVZsEMnK11/bxcd+/Wyms6SVZI8MOZqyKzHWty9Uqwbt29sey5I+br7Z\nTlqXLQudJG3Fcku1ww6Dyy6zjtUikjjew4ABViQWyc6gQXDSSdCgQegkkqq+/96KDN2728VHSTv5\nKjQkYspuJNYFS945B889Bz//bE0CJX2ULg3duqlBVFjx3FLt9tttXFm/PnQSkfiYNs2uUl9wQegk\nkurWr4eBA22JrEhWfv7Zlkm0a2cXniQt5WvpRCKm7HrvnwGeAahbt67PTx5JUcWKweuvW/OXQYPs\nxaekh5tugr/9zZqCHn106DRpx3vfIXSGpDjiCGjbFh57DO6/P3QakXjo1w/uvFPT4CV7998PF19s\nM1ZF/uz33+Gcc6BxY+jTJ3QaCSiZu07Eb8qu5F2ZMvD22/DQQ9YkUNLDAQfYlDnNapBE69kThg2D\nn34KnUQk+mbPhjVr7MWjyN6sXAkvvgi9e4dOIqlo61Zo0waqVrWLAdq9Jq0ls2wdzym7kndHHWV7\nLXfqBHPnhk4jBaVbN5g6Fb74InQSiZOjjrIp3k88ETqJSPT162cNVouoR7hk48477XldzXjlz3bs\nsJ5sJUvC8OGaHSXJKzR47zt474/z3tfy3p/vvV+brJ8lEVK3rq2tbtUKli8PnUYKQqlStt1l376h\nk0jc3HEHDBkCv/wSOolIdM2dC4sXQ4d4rrSSBJo/H957D269NXQSSTUZGXDttbBxI4wZo6KlAMnf\ndULkr847z6bcNWsG330XOo0UhBtvtC1OFy0KnUTipEoVWwc6eHDoJCLRdf/91mC1WLHQSSSVeQ//\n+IdtabnffqHTSCrx3i4oLVkCEyZA8eKhE0mKUKFBwujcGa680ooNP/8cOo0k23772RWQe+8NnUTi\n5o47bPnEr7+GTiISPf/5D3zyibaek+xNmQKrV8M114ROIqmmb1+7mDR5si2bEMmkQoOEc9dd0KSJ\nzXDYtCl0Gkm2G26whmOffRY6icTJ0UfD2WfbEgoRyZ0HHrArkSVKhE4iqWznTpv10r8/FC0aOo2k\nkscfh9GjrRdXmTKh00iKUaFBwnHOOtIedZR1ut6+PXQiSaaSJaFHD+27LYl35502lqhXg0jOLV5s\nVyE7dw6dRFLdqFE2M/GCC0InkVTy7LPw6KMwbZqag0qWVGiQsAoVghEj7P2rrrJmMhJfnTpZ1Xvl\nytBJJE6qV7eZUXffHTqJSHT072+7B2i9vezNli02tg4YoK0K5Q/Dh9vW5TNnwpFHhk4jKUqFBgmv\naFEYNw5WrYLu3a2pjMTT/vtbV+LHHgudROLmoYdg7FhYsCB0EpHUN2+erbm/8cbQSSTVDR4MJ54I\np5wSOomkihEjrOfWjBnwt7+FTiMpTIUGSQ377gtvvmlr+Pv1C51GkqlbN5uGuX596CQSJ2XL2hXa\n66+39cQikrWdO61nzoMPQunSodNIKvv5Z5vJoCWPssvzz9vOIzNmQNWqodNIilOhQVJH6dLw7rsw\nciQMHRo6jSTLoYdCmzb6G0videxoe3cPHx46iUjqGj7ctrK84orQSSTVPfGEbSF8zDGhk0gqGDnS\nltHMmAHVqoVOIxFQJHQAkf9xyCHWVOa006x77aWXhk4kydCjBzRubG/33Td0GomLQoXgqaegaVNo\n3RoOOih0IpHUsm6dvVCYPt0eLyJ78ssvtmziww9DJ5FU8OKLtp30jBm225NIDuhZRlJPpUrwzjvW\nr+Hdd0OnkWQ45hho0MCm4IkkUq1adqX2tttCJxFJPT17Qvv29jgR2ZtBg2w2g6bHy6hR0KuXFRk0\nu0VyQYUGSU3HHQcTJ9oLhg8+CJ1GkqFHD2sKqfX0kmh9+lgn7FmzQicRSR1z5ljx/t57QyeRVLdx\noxUa7rordBIJbfRo+Mc/bBaUigySSyo0SOpq0MCmarVuDZ99FjqNJNopp8CBB8Jbb4VOInGz337w\n+OPW8G7bttBpRMLbscMeDwMH2u4/InszeDA0b67ZDOnu5ZdtduD06XDssaHTSASp0CCprXlze8HQ\nogWsWBE6jSSSc3DzzdrqUpKjTRvb2/vxx0MnEQlvyBAoVw7atQudRFLdxo02bmo2Q3obM8Zmnk6b\nBtWrh04jEaVCg6S+Sy+1BjRnnQXffhs6jSTSRRfB8uWwYEHoJBI3zsGTT9rWbKtWhU4jEs7atbZt\n9JAh9rgQ2ZuhQ+18Sw3/0tfYsXDLLTB1KtSoETqNRJgKDRINN9wAnTvDGWfAmjWh00iiFC0KN96o\nWQ2SHJUr26yZa6+FjIzQaUTC6NED/v53ra+W7G3aZLMZ7rgjdBIJZdw4a8Y+dSrUrBk6jUScCg0S\nHbfdBh07wplnwvffh04jidKpk/VpUAFJkuH222HLFnjwwdBJRAre1Knw/vuaBi85M2IE1K+vF5jp\n6tVX4aabYMoUa8oukk8qNEi03HGHrTE94wzbD1yir0wZ225t6NDQSSSOihSxtaaDB8Ps2aHTiBSc\ntWutOD9iBJQsGTqNpLpt2+Dhh20bQ0k/48dD1662M422v5UEUaFBoueee2wniqZN4ccfQ6eRROjc\nGZ5/3jqjiyRahQrwwgtw2WXwww+h04gk386dVsDt1MlmAYpk5+WXbZeJk08OnUQK2osv/lFkqF07\ndBqJERUaJHqcg/vusx0pzjoLNmwInUjyq2ZNqFgR3nkndBKJq2bN4IoroEMH9WuQ+OvXz97efXfY\nHBINO3fa8jL1Zkg/Q4fCnXfCzJlQp07oNBIzKjRINDlnT4pNmtgLiF9+CZ1I8uvaa2H48NApJM76\n9rVmZ+rXIHE2cyY8/TSMHg2FC4dOI1EwYQKULg2nnx46iRSkhx6CRx6xZYXHHhs6jcSQCg0SXc7Z\nAFm/vs1u2LgxdCLJj4svtic7NYWUZNnVr2HQIPVrkHj6/nubtTNyJBx6aOg0EhWPPmqNc7X9aXrw\n3mYxjBxpz4WVKoVOJDGlQoNEm3PwxBNw/PHQsiX89lvoRJJX++0HbdvaWnqRZDn8cPVrkHjauRMu\nvxyuusqWFYrkxPz5VuA///zQSaQgZGTY9pXvvAOzZlkPI5EkUaFBos85ePJJm/Z17rnw+++hE0le\n/f3v8NxzWkMvydW8ufo1SPz07w9bt0KfPqGTSJQMGQLXX69lNulg5047z5o/35ZYlS8fOpHEnAoN\nEg+FCtma1EqVrCq/eXPoRJIX9erZzIb33gudROJO/RokTmbNsoL7mDG2REgkJ3780fozXHNN6CSS\nbNu2waWXwjffwJQp1pNDJMlUaJD4KFTImgkedhhccAFs2RI6keSWc1ZtV1NISbYiReCVV2DwYHj7\n7dBpRPJu3TrbyvKFFzQNWnLnuefsfKlcudBJJJk2b7a/87Zt8OabULJk6ESSJlRokHgpXBiefx4O\nPBAuvNCmkUq0tG9vL/x+/DF0Eom7ChXg9dfhyith3rzQaURyb/t26zdy+eW2JEgkp3butK0Nu3QJ\nnUSS6ddfoUULOy9+9VXYZ5/QiSSNqNAg8VOkCLz0Euy7r1VwtYwiWg48EM45B0aNCp1E0kGDBjaD\n5vzzYcWK0GlEcs572xZ4n32gX7/QaSRqJk+GQw6BunVDJ5Fk+eknaNoUjjkGXnwRihYNnUjSjAoN\nEk+7trErV852o/j119CJJDd2LZ/wPnQSSQetWtlWXy1awPr1odOI5Ezv3vD557YESH0ZJLeefBJu\nvDF0CkmW776DJk2gUSN46ilbXixSwHSvk/gqUsT2CK5WDc4+GzZsCJ1IcqpJE+uxMXdu6CSSLrp0\ngdatbWbDpk2h04js3fDh8PLL8NZbWm8tubdkCfznP7altMTP119bgeHii2HAAOt/JRKACg0Sb4UK\nwbBhUL8+nHGGNc2S1Oec7QU/cmToJJJOHngAqlSxk+9t20KnEcna22/D3XfDO+/AQQeFTiNRNHSo\nLbspXjx0Ekm0xYutyHDDDXDXXSoySFAqNEj8OQePPgrnnguNG8OaNaETSU5cdJFtu5WRETqJpItC\nhWDECFvHevnl1ixNJJW8/741L50wAapWDZ1GoujXX60H0nXXhU4iiTZnjs0I7dMHuncPnUZEhQZJ\nE87BfffBFVdYpXfVqtCJJDvVqlmPjQ8/DJ1E0knRorbm/aefoFMnFbokdSxYAG3awOjRNktPJC9G\njYLTT4cjjgidRBJpwgRb/jdyJHTsGDqNCKBCg6Sbnj2hWzcrNixdGjqNZOfCC+G110KnkHSzzz4w\ncSJ88QXcequakkp4n39ujY2fftp6DonkhfcwZIiaQMbNrsae774LzZqFTiPy/1RokPTTrRvcc49N\nL1u4MHQa2Zs2beD11/VCTwrefvvZ9m///Cf06qX7oISzYoW9eHj4YbtiKSnJOdfWObfIOZfhnKv7\np6/1cs4tc84tcc6FeyX473/blt+NGweLIAmUkWEX0AYPtmVVJ5wQOpHI/1ChQdLTNdfAwIG2v/D8\n+aHTyJ4cd5xNZV+wIHQSSUdlysD06VZsuOYa2L49dCJJNytW2PNUr17QoUPoNLJ3C4E2wOzdP+mc\nqw60A2oAzYGhzrnCBR8P2/a7XTs1CIyDbdtsOfDs2daboVKl0IlE/kKFBklfl15q01BbtLBBWlKP\nc1o+IWGVKwczZ9qe5BdcAL//HjqRpIsFC+C006BHD+sgLynNe/+F935JFl9qBbzivd/qvV8JLANO\nKth02NXvV16xcx+Jtl9+saVUv/8OM2bY85RIClKhQdJbq1bw0ks2HXXGjNBpJCtt2lihQVPX3Tjb\n6QAAHS5JREFUJZSSJeGNN6B8eTjzTFi/PnQiibtp06B5c5sSrSJD1FUAvtnt428zP1ew5syB0qWh\nZs0C/9GSQGvWWJ+xo4+G8eOhRInQiUT2SIUGkWbNbLC+9FJ4663QaeTP6tWzNaWffx46iaSzokXh\n+efhjDPglFPgq69CJ5K4Gj3atld97TUrtErKcM5Nd84tzOLWKkHfv5Nzbp5zbt66desS8S3/MGYM\nXHZZYr+nFKzPP4eGDe189cknoXCYFTgiOVUkdACRlNCoEbz5ps1w6N8frroqdCLZxbk/ZjXUqBE6\njaQz5+CBB+DQQ+HUU61ZZO3aoVNJXHgPjzxisxhmztR4l4K8903z8N9WA7vvJXl45uey+v7PAM8A\n1K1bN3HT+LZvtwsqH3+csG8pBexf/4KLLrL+YurXIhGhGQ0iu5x8MsyaBffdB/36aap+KtlVaBBJ\nBV27wqOPwllnWaNIkfzKyIBbboGRI22Ku4oMcTIJaOecK+6cqwRUBeYWaIIZM6BKFTUMjKrx461f\n1ahRKjJIpKjQILK7o4+GDz6wLRU7d4YdO0InErCp6t9/D8uWhU4iYi6+GMaOhUsugXHjQqeRKNu6\n1aa0z59vHeQPPzx0IskD51xr59y3QANgsnNuCoD3fhEwDvgceBfo4r3fWaDhxoxRE8ioeuIJ6N4d\npk614rZIhKjQIPJnhxxiMxu++squpG/aFDqRFC5sjdGmTQudROQPp59u98lbbrEZDpoFJbn1yy+2\n89GOHfZCokyZ0Ikkj7z3E7z3h3vvi3vvD/beN9vta/d776t474/23r9ToME2b4ZJk6w4KtGxYwfc\nfDMMG2aznOrUCZ1IJNdUaBDJSqlS1rOhdGl1mU8VjRvb1T75C+dcW+fcIudchnOu7p++1ss5t8w5\nt8Q512xP30PyqHZteP99ePll273mxx9DJ5KoWLHC+gNVr26zY/bZJ3QiiaO334YTT7SLKBINP/8M\n554LCxdakeHII0MnEskTFRpE9qRYMVsve/rpNnV/5crQidJbo0ZWaNBV46wsBNoA/1OJcc5VB9oB\nNYDmwFDnnNpUJ9pRR9mSqypV4PjjrWmXyN6MGWN9ga6+2po/qnu8JIuWTUTL0qVQvz5UqwbvvAMH\nHhg6kUie5avQoKtoEnu7usx362Zd5hcsCJ0ofVWubG9XrAibIwV577/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pTGfsIumsbFno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\nRERERBLm/wBflEATHy8vJwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=1, ncols=3, figsize=(18, 6))\n", "np.random.seed(456)\n", "\n", "data_neg = np.array([[-3,2,5],[4,3,-5]]).transpose()\n", "pearson_neg = confidence_ellipse(data_neg[:,0],data_neg[:,1], ax[0], facecolor='none', edgecolor='red')\n", "ax[0].set_xlim(-12,16)\n", "ax[0].set_ylim(-15,16)\n", "ax[0].set_title(f'Pearson Coefficient = {pearson_neg:.3f}')\n", "\n", "data_low = np.random.randn(20000, 2) * 4\n", "pearson_low = confidence_ellipse(data_low[:,0],data_low[:,1], ax[1], facecolor='none', edgecolor='red')\n", "ax[1].set_xlim(-15,15)\n", "ax[1].set_ylim(-15,15)\n", "ax[1].set_title(f'Pearson Coefficient = {pearson_low:.3f}')\n", "\n", "data_pos = np.array([[-3,2,5],[-4,-3,5]]).transpose()\n", "pearson_pos = confidence_ellipse(data_pos[:,0],data_pos[:,1], ax[2], facecolor='none', edgecolor='red')\n", "ax[2].set_xlim(-12,14)\n", "ax[2].set_ylim(-16,15)\n", "ax[2].set_title(f'Pearson Coefficient = {pearson_pos:.3f}')\n", "plt.savefig('./img/001_neg_low_pos.png', bbox_inches='tight')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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TtMml0t+K5ymE8FgKXk8jBiwC7ieOQv1opXXLbO+lFDSdSnyOeem0HzdmlrlV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N1Zi3kJ43Cw6QKaOi/jxQXx6DdbsCAxDAWHW2FhFiSOHwkwYMXsSMyYNApgwLenj0fd2Ut49+hp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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(16, 8))\n", "np.random.seed(123)\n", "latent = np.random.randn(1000, 2)\n", "dependency = np.array([\n", " [0.9, -0.3],\n", " [0.1, 0.7]\n", "])\n", "\n", "scale = np.array([1.5, 3]).transpose()\n", "\n", "dependent = latent.dot(dependency)\n", "normalized = dependent / np.std(dependent, axis=0)\n", "scaled = normalized * scale\n", "\n", "tickmarks = list(range(-9,10,1))\n", "plt.suptitle('Confidence Ellipses of 3 Standard Deviations\\nsame dataset, once scaled, once normalized', fontsize=16)\n", "\n", "ax[0].scatter(scaled[:,0], scaled[:,1], s=0.5)\n", "confidence_ellipse(scaled[:,0], scaled[:,1],ax[0], facecolor='none', edgecolor='red')\n", "ax[0].set_title(f'dataset at scale (stddev x = 1.5, stddev y = 3)')\n", "ax[0].set_xlim(-10,10)\n", "ax[0].set_ylim(-10,10)\n", "ax[0].xaxis.set_ticks(tickmarks)\n", "ax[0].yaxis.set_ticks(tickmarks)\n", "\n", "ax[0].axhline(y=-9, c='grey', lw=1, ls='dashed')\n", "ax[0].axhline(y=9, c='grey', lw=1, ls='dashed')\n", "ax[0].axvline(x=-4.5, c='grey', lw=1, ls='dashed')\n", "ax[0].axvline(x=4.5, c='grey', lw=1, ls='dashed')\n", "\n", "ax[1].scatter(normalized[:,0], normalized[:,1], s=0.5)\n", "confidence_ellipse(normalized[:,0], normalized[:,1], ax[1], facecolor='none', edgecolor='red')\n", "ax[1].set_title(f'normalized dataset (both stddevs = 1)')\n", "ax[1].set_xlim(-10,10)\n", "ax[1].set_ylim(-10,10)\n", "ax[1].xaxis.set_ticks(tickmarks)\n", "ax[1].yaxis.set_ticks(tickmarks)\n", "\n", "ax[1].axhline(y=-3, c='grey', lw=1, ls='dashed')\n", "ax[1].axhline(y=3, c='grey', lw=1, ls='dashed')\n", "ax[1].axvline(x=-3, c='grey', lw=1, ls='dashed')\n", "ax[1].axvline(x=3, c='grey', lw=1, ls='dashed')\n", "\n", "plt.savefig('./img/001_scaled_norm.png', bbox_inches='tight')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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bWQCSPBb4NM0VDbdLsgvwyqr6m+m2raoTgBPGzTus5/HVwJ/NNLQkSWu5LyX5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\nXruPewHf71n+1fb+rJ58kqTVY222No9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(16, 4))\n", "points_x = np.array([-1, 0, 1])\n", "ax[0].scatter(points_x, [0, 1, np.sqrt(2)], c='red')\n", "ax[1].scatter(-1 * points_x, [0, 1, np.sqrt(2)], c='red')\n", "\n", "x = np.linspace(0, 2.5, num=200)\n", "ax[0].axhline(y=0, color='black')\n", "ax[0].axvline(x=0, color='black')\n", "ax[0].grid(which='major')\n", "ax[0].set_xlabel('Pearson Correlation Coefficient')\n", "ax[0].set_ylabel('R ascending ellipse-axis')\n", "ax[0].set_title('Points for R of ascending axis')\n", "\n", "ax[1].axhline(color='black')\n", "ax[1].axvline(color='black')\n", "ax[1].grid(which='major')\n", "ax[1].set_xlabel('Pearson Correlation Coefficient')\n", "ax[1].set_ylabel('R descending ellipse-axis')\n", "ax[1].set_title('Points for R of descending axis')\n", "\n", "plt.savefig('./img/001_guess_func.png', bbox_inches='tight')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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4B5gKqDIrIqssLw8mT47uZaNGwQ8/dKRWrbiY2X//qMjWqZN2SpHyxd0/AU4u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\nS44bs2ZmZmZmZpYcN2bNzMzMzMwsOf8PsKQo+nRqutkAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(16, 4))\n", "points_x = np.array([-1, 0, 1])\n", "ax[0].scatter(points_x, [0, 1, np.sqrt(2)], c='red')\n", "ax[1].scatter(points_x, [np.sqrt(2), 1, 0], c='red')\n", "\n", "p = np.linspace(-1, 1, num=500)\n", "r_asc = np.sqrt( 1 + p )\n", "r_desc = np.sqrt( 1 - p )\n", "ax[0].axhline(y=0, color='black')\n", "ax[0].axvline(x=0, color='black')\n", "ax[0].plot(p, r_asc, c='blue')\n", "ax[0].grid(which='major')\n", "ax[0].set_xlabel('Pearson Correlation Coefficient')\n", "ax[0].set_ylabel('R ascending ellipse-axis')\n", "ax[0].set_title('Points for R of ascending axis')\n", "\n", "ax[1].plot(p, r_desc, c='blue')\n", "ax[1].axhline(color='black')\n", "ax[1].axvline(color='black')\n", "ax[1].grid(which='major')\n", "ax[1].set_xlabel('Pearson Correlation Coefficient')\n", "ax[1].set_ylabel('R descending ellipse-axis')\n", "ax[1].set_title('Points for R of descending axis')\n", "\n", "plt.savefig('./img/001_guess_func_2.png', bbox_inches='tight')\n", "plt.show()" ] } ], "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }