{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial: ECT for CW complexes\n", "\n", "This tutorial walks you through how to build a CW complex with the `EmbeddedCW` class, and then use the `ECT` class to compute the Euler characteristic transform" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from ect import ECT, EmbeddedCW, create_example_cw\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The CW complex is the same as the `EmbeddedGraph` class with that additional ability to add faces. Faces are added by passing in a list of vertices. Note that we are generally assuming that these vertices follow around an empty region (as in, no other vertex is in the interior) in the graph bounded by the vertices, and further that all edges are already included in the graph. However the class does not yet check for this so you need to be careful!" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "K = EmbeddedCW()\n", "\n", "K.add_node('A', 0,0)\n", "K.add_node('B', 1,0)\n", "K.add_node('C', 1,1)\n", "K.add_node('D', 0,1)\n", "\n", "K.add_edges_from((('A', 'B'), ('B', 'C'), ('C', 'D'), ('D', 'A')))\n", "\n", "K.add_face(['A', 'B', 'C', 'D'])\n", "\n", "K.set_centered_coordinates()\n", "K.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just to have something a bit more interesting, let's make a more complicated example that's built into the class." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PSpvVQt+05JAPIm9IGBnJ7t3Qu7da4mfVKmjZUu8S+d2M4V2I8HcYWS2M7BVeG5YJ/zszhH5Zu4rnnnuOvXv2MP+BwUTUsgW5VzSNCIv6XRCnSRgZxe7dcPnlEBUFq1dD5856lyggUhJjmD60k1/POfzSFiTF2/16ThE+qguhP/3pT0RHR/v/mrVYePzb10jZWftIvXAiYWQUrVrBnXfC999Damh/yx/VI5W/DGjvl3MdX/kOm+c9hcslEweFd2oLoTNVumbr2M3+0BWp3NzQEVL9wf4go+n0tmQJNGkCPXvCU0/pXZqgGZ/ejuQ4O9OWbKPity2ZPWWzWoiwWnh8aCccHQfzhz/8AYA/Tn8aqz+bU0RIyjmwj4Wv/JPvliykUePGPPfcc9x7773nBNDZxqe341jWXuZuKcEWGYWG52Fy5jV7c49UGPSFuqO8HNasgSuuqMtLCgkSRnpauBBGjVJziHqG3yZbo3qkcnnbZKYs2sqqjFxsVkuNoeS+v3ebJGYM76J2yexxO4AEkqiVryHkVlRUxNtT/0jq+RfTauQkvs/I8+2aPdMbb6hRs++8Y7hdmYNNwkgvH34It9wCI0eqyaxhKiUxhnfv7snuI0XMX5fJ8l1HycwrrTSvw4KaHJjevjG3XZZ6zgik22+XQBLVq2sIuT388MPk5uayfPbztG7duk7X7Cn33gs//gijR0NFhfpiGqZknpEePvpI1YhuuQXmzoUI+U5wphJHBfvzSiircBEVYaVVUqxHs9Tfeecd/vCHP3D1jb+XQBLnhNDkSZN8CiGAb7/9lv79+/Pvf/+bcePGnXN/iaOCpT9s5Jbbbue9ee8w8PJunq+s4HLBH/+oaklvvKH6jkOIp5/j8imoh7Q0VTV//nlTbP8QbLH2CJ+W1JcakgD/1YTcioqKuPvuu+nXrx9jxoyp8phYewStG0RSlrOL1g0ivVvix2qFOXPUnz/9FHJh5CkJo2BatQp69FALnnbtqndpQpIEUvjydwi5nWqeW748cNeS1QqzZ58eYXf4MDStfYfjUCJhFCz/+Q+MGAFPPAEPP6x3aUKaBFJ4CVQIgWqee+WVV/j3v/9N69at/VDaGriv0Q0b1Oi6t99WfcphQsIoGH74QV1UQ4aoBU9FwEkghb5AhhB41jwXEF27wvDhanRdYiJcfXXwnltHEkaBtm2bCqGePeG99yBStsQOFgmk0BToEHILSvNcVWw2eOstyM9XobRihdpUM8RJGAXaZ5+pNeYWLzbtXkRmJoEUOoIVQhDk5rmqREaqUbdXXw1jxsC6dSG/YoOEUaC4XKoNeNIkuP9+iJXdHPUigWRuwQwh0LF57mxxcfD55+AIj6WDJIwCoaQEBg5U32huvVWCyAAkkMwn2CHkplvzXFWSk9Wfx46pL7bPPw+hNOfyDBJG/lZeDjffDJs2QXv/LAYq/EMCyRz0CiEwQPNcdY4cUcuH7d8PX3wB9tBbpV7CyJ80DcaOha++UtXrHj30LpE4iwSScekZQmCg5rmqdO6sFlUeMEBNip0/P+Sa7iSM/Om119RyHm+/rS4aYUgSSMaidwi5Gap5ripXXAHz5qlpIp07w5QpepfIrwIaRjNnzuSTTz5hx44dREdH07t3b5566ik6dOgQyKfVz7Bhqnb024edMC4JJP0ZJYTAwM1zZ7vxRvj736FRI71L4ncBDaOVK1dy33330aNHDyoqKnj00UcZMGAA27dvJzaUOvX37oWYGLV8xx//qHdphIckkPRhpBACgzfPVeWvfz3994ICSPB+HUcjCmgYLV26tNK/586dS+PGjdm4cSNXhMpmUgUFMHgwtGgBX3+td2mElySQgsdoIeRm+Oa56jz/PLz0ktqCIilJ79LUWVD7jAoKCgBITEys8n6Hw4HD4Tj178LCwqCUy2dOp9oGIidHTWoVpiSBFFhGDSEwUfNcVYYPhxkzVB/SV1+ZfnWXoIWRpmlMnDiRPn360Llz5yqPmTlzJtOnTw9WkepuyhRYulQNtZRh3KYmgeR/Rg4hMGHz3NlatYKPP4b+/WHiRHjxRb1LVCdBC6Px48ezZcsWvv/++2qPmTx5MhMnTjz178LCQlJSUoJRPO9lZKhq8jPPwLXX6l0a4QcSSP5h9BByM23z3JmuvFKF0NixarSdiVf5DkoY3X///SxZsoTvvvuOFi1aVHuc3W7HbpbJXGlpsH07tG2rd0mEH0kg+c4sIQQmb54725gxEB+vFmQ2sYCGkaZp3H///SxatIgVK1aY/00HtU7Uyy/D+PEqkETIkUDyjplCCEKgea4qt96q/ty+XS3MbMLRygENo/vuu4/33nuPxYsXEx8fz+HDhwFISEgw7IVaq4ceUlsEDxgAnTrpXRoRIBJItTNbCLmFRPNcVUpKVLPdsGHw+ut6l8ZrAQ2j2bNnA9CvX79KP587d+6pX3JTWbRItc++9JIEURiQQKqaWUMIQqx57myxsfD003DXXXDVVWqkr4kEvJkuZBw4oN7k4cNh3Di9SyOCRALpNDOHEIRo89zZ/vAH+O9/1eT7Hj2gXTu9S+QxWZvOU/PmqZnOb7wRcgsUipqFeyCZPYTcQrZ57kwWi+rTXrdOjbD75hu9S+QxCSNPTZkC//d/0LCh3iUROgjHQAqVEIIQb547W3y86lKIj9e7JF6RMKrNmjWQmQk33RSSixMKz4VLIIVSCEGYNM+dzd2nffy46mK46CJdi+MJCaOalJbCHXeo3RZHjpTmORHSgRRqIeQWFs1z1bnvPvj+e9i61fA7xEoY1eRvf4OsLPjsMwi3i1hUK9QCKVRDCMKsea4qTzwBXbqcnpJiYBJG1fnhh9PL/YTq/kvCZ6EQSKEcQhCmzXNna91afYaNG6f2QrrmGr1LVC0Jo+o89xxcdhlMmKB3SYRBmTWQQj2E3MK6ee5Mf/yjWlD13nth1y6IitK7RFWSMKrO++9DXh7YbHqXRBiYmQIpXEIIpHmuEqtVTUnJzDRsEIGE0bk2bFD7glx0ETRrpndphAkYPZDCKYRAmueq1KqVurlcqh+8ZUu9S3QOCaMzORxqwcFmzWDFCr1LI0zEl0BylDvJLXRQ4dKIsFpIrm/HHum/mni4hZCbNM/V4OGHVZPd9u0QE6N3aSqRMDrTP/4Be/fCJ5/oXRJhQp4E0uHjJ1i9M5dfDhaQV1R2zjmS4qPo2CKB3h2SadrAt9AI1xACaZ6r1dixam3NGTPUSDsDkTByy8xUb84DD8giqMJn1QVSXpGDj9Zksiu7CKsFXNUs25hXVMbqHcf4/pdjtG8ez8heqSTFe7bHVziHEEjznEfatoVHHoFZs9QcSgOtXSdh5Pboo2qpn2nT9C6JMLmzA+ni2x5h0Y8Hcf2WQNUFkZv7/oycIp76dDsjeqZwWfvkao8P9xByk+Y5D02aBO+8A3/6E3zxhWEm80sYuT3zjGqiM9l6TsKY3IH0pzlfsHtNlk/ncGngcmp8uDqTohPlXHNR5QE1EkKnSfOcF6Kj1WKqBw7oXZJKJIzKytSmVE2bqpsQfhLVsR8Nrkjyy7m+3JRDfHQkl7VPlhA6izTP+WDQoNN/1zRD1I4kjJ57Dv71L9i925Rb9QpjysovZdqSbef8vHjLN+R98cLpH9gisdaLJTIphejWXYm7cAC22AZVnvOTtZmsmfcCaxa+LSF0Bmmeq4P774ekJHjsMb1LEuZhlJUFf/+7mqEsQST8aMqirVTU0DmUdN0EIpNaoLkqcJYU4Di4nYK1Cylct4jkGx4hutXF5zymvKKCA/YOEkJnkOa5OkpIUIMZRo9Wgxt0FN5fIyZPVn1EBvhWIELH7iNFrMrIxVlDGEU2aon9vPOpl9KZ2PMvJ7H/vTS/60UsUfU49smTOEt+PecxFmsE1vM6cd2oOyWIkOY5v5gyBZo0UQup6ix8w+h//4P33oPp0w2/tLowl/nrMrFZvW+Dj0hoTMOr7kYrO0HRpqVVHmOzWpi3NrOuRQwJ7ua5N998U5rnfBUTA08+qTbjW7tW16KE7zvocsGoUXDXXXqXRISY5TuP1lgrqkl0m+5gseLI+rnK+50ujeW7jtaleCHB3Tz39NNPS/NcXd1yC1xyCaxerWsxwrfPqGtXVTMSwo+KHRVk5pf6/HhrVD2sMfVxFudXe0xmXikljgpi7eH56yvNc35mtaodrXVeRDX8akaapnY/3LBB75KIEHQgrwTf6kRnqOUEGrA/r6Suz2Ja0jwXAFFRUF6uvqC7XLoUIfzeycWL1YSv48f1LokIQWUVdftFdpWdxHWiEFtcYkCfx6ykeS6AfvpJLRS9YIEuTx9eYeR0qtEj/furmxB+FhVRt1+pE3vWg+bCntoloM9jRtI8F2A9e8LQofC3v6nFAIIsvK7od96BX36BmTP1LokIUa2SYvF1LntFwVF+Xf4mFnss8V0HVXuc5bfnCTfSPBcEM2bA/v3w2mtBf+rw6QHVNLXSwo03QvfuepdGhKhYewSpiTEcqGUQQ/mxA+ByormcuEoLOJm1jeKt32CxWGk84lFsMQnVPjY1KSbsBi/I5NYg6dQJbr9d7WBw991Qr17Qnjp8rmiLRW2YVxK+Hb8iOLo2jeJAXjFYqv/2fmpJIFsEVnsckUktSLjsd8RddG2NQWSzWkhv39jPJTY2aZ4Lsr/+Fa65BiKCGw/hEUYuFxQUqC0iEqr/RReiLjIyMnjyySd5/4sVNL3rpSqPibuwP3EX+t5f6XRp3HZZqs+PNyNZey7I2rbVZWmg8HhnP/sMUlPVWnRC+FlGRgZ33nkn559/Pku++JJb77mLtCax+LAIQ41sVgt905JJaxw+25zI6DmdlJXBTTcFdWRd6IeRpqkBC127QkqK3qURIeTsELrjkWm8tGw1g2+/h5v7tMLq5zSKsFqYMbzmUXahRJrndBQVBYWFakCDVueZcx4J/Wa6FStg3Tq1o6EQfuBujnv33XdJSErmjkem0f+mW7HXO714aVK8nRE9U/hwtf/WkXt8aCdSEmP8dj6jk+Y5nU2eDP36weefw5AhAX+60A+jmTPh4oth4EC9SyJMzpMQOtNl7ZMpOlHOl5ty6vzcDw3owM09wqevSEbPGcAVV0CvXuozdPDggG/AF9phdPKkWndp0iRD7GQozMnbEDrTNRc1Iz46kk/WZeFyaXizfqrNaiHCauHxoZ3CKoikec4gLBZVO7rxRtizB9LSAvp0oR1G9erB0qVBa/MUoaUuIXSmy9on065ZPB+tyWRXdhFWCzWGks1qwenS6N0miRnDu4RV0xxI85yhDB6sJsE2axbwpwrdMDpyRC2GOnAg2Gx6l0aYiL9C6ExJ8XbGDGjH4eMnWL0zlx0HC8ktclQ6xoKa0JrevjG3XZYaVqPm3KR5zmCsVhVEJ0+CwxHQqTGhG0avvqq20z10CBo00Ls0wgQCEUJna9ogmhE9U6AnOMqdbN78My88/ADvzXuHgZd3C7uVFc4kzXMG5XJBly7wu9+pz9QACc0rv6IC5sxRK9BKEIlaBCOEqmKPtNEoxkJZzi5aN4gM6yACaZ4zLKtVNde98YbaGdtuD8zTBOSsevvsM1UjGjdO75IIA6tpnlCgg0hUJpNbDW7sWMjNhY8/DthThOZXsZdfVkMSL75Y75IIA9KrJiSqJs1zJtChg9p25+WXVYtTAIReGGmaqlIGeBiiMB8JIWOS5jmTGDdO9RkVFUG8/wfXhF4YWSwwYYLepRAGIiFkXDJ6zkRuuAGGDw/Y6UPra0hpKfzlL6q/SIQ96RMyNmmeMxmLRbU8rVmjdkHws9AKoyVL4B//gBMn9C6J0JGEkDnIzq0mdOQIXH45LFzo91OHVjPdvHlq4IL0F4UlaY4zD2meM6mmTeGqq9Rn7V13+fXUoRNGx46ppX/++U+9SyKCTELIXKR5zuRuu00F0cGD0KKF304bOnXjDz9UbZo33aR3SUSQSHOcOUnznMmNGKEmvr7/vl9PGzo1o6uugtmzoVEjvUsiAkxqQuYlzXMhoH59NQk2Ntavpw1oGH333Xc888wzbNy4kZycHBYtWsQNN9wQmCfr2FHdRMiSEDI3aZ4LIc895/dTBrSOXFJSwkUXXcRLL70UyKeBN99UtSIRkqQ5LjRI81yIOXAAli/32+kCWjMaNGgQgwYNCuRTqHHvs2ZB796q6ihChtSEQoc0z4Wgp55S64AeOKAWU60jQ309cTgcFBYWVrrVavNm2L0bbrkl4OUTwSE1odAizXMh6tZb1Yi61av9cjpDDWCYOXMm06dP9+5BS5aoDZ/S0wNTKBE0UhMKTbL2XIjq1QsaN1a1oz596nw6Q10ZkydPpqCg4NQtKyur9gctWQKDBkFkZOALKAJCakKhS7aGCGFWKwwZoj6D/cBQNSO73Y7d242bpk+X4dwmJTWh0CbNc2Hg5pvB6VTbkterV6dTGSqMfDJkiN4lEF6SEAoP0jwXBgYMUDc/CGgYFRcXk5GRcerf+/btY/PmzSQmJpKamlr3J/j736FHDxg4sO7nEgEnIRQ+ZPRcGMnPhx9/rPPncEC/rmzYsIGuXbvStWtXACZOnEjXrl2ZOnVq3U9eXAxPPAE7d9b9XCKgpE8ovEjzXJhZuFBtaJqXV6fTBLRm1K9fPzRNC8zJly2DsjK4/vrAnF/UmdSEwpM0z4WZIUPA5YIvv1SLqPrIvH1GS5ZAp07Qpo3eJRFnkRAKX9I8F4aaNVPdJYsXh2EYaRp8/bWadCUMQ0IovEnzXBi77jr4179UDcnH2rA5w8jphMcfh27d9C6JQEJIKNI8F8YGDID169VghuRkn05hzjCKiIC779a7FGFPQki4SfNcmOvdGz7/vE6nMGcYvfUWtGwpSwDpREJInEma5wQAJ05ARgZ06eLTw81Xl9Y0mDwZvvpK75KEHRmiLaoiW0MIAJ55Bq64QnWj+MB8V86uXXD4MPTrp3dJwoaEkKiOrD0nTunXD44fhy1bfHq4+Zrpli8Hmw0uv1zvkoQ8aY4TNZHmOVFJz55qfbrly+G3hQ68Yb4wWrFCjWmPj9e7JCFLQkh4QkbPiUrsdjWQYcUKmDjR64ebL4yuvLLOq8OaWYmjgv15JZRVuIiKsNIqKZZYu3/eRgkh4SlvRs8F8poVBnPNNT7355vvigjDrcV3Hyli/rpMlu88SmZ+KWcusGQBUhNjSO/QmFt7ptKuifc1Rgkh4Q1PmucCfc0Kg5o0Sd18YK4w2r0bsrPViA2LRe/SBFxWfilTFm1lVUYuNqsFp+vcdf404EB+Ke+uO8Bba/bTNy2ZGcO7kJIYU+v5JYSEL2pqngv0NStMQNPU/kbR3n2OmKuh9+23YdQovUsRFAvWZ9L/+ZWs3qtWwq3ql/pM7vtX782j//MrWbA+s9pjZXSc8FVNo+cCec0KE+nRAx591OuHmatmtGGDWgIoxGtFLy3fzbPLdvn0WKdLw+nSmPTJVnKLHYxPb3fqPqkJibqoqXkuUNesMKG2bdVntZfME0aaBhs3wrhxepckoBaszzznl7p4yzfkffECTe94Hnuzc39Rj340nbJjB2gx7s1KP3922S4axdnp1rBMQkjUWXXNc1Vds27ua7cq9S8dTsOrKi/r5b5mb+7hh803hT66dVMbn3q5aKp5wigrC3JzQ3px1Kz8UqYt2ebXc05euJlDr40hLsIlISR8Vt3oOU+v2aTrJhCZ1KLSz2xxiVUeO3XJNnq3TZY+JLPq1k1tfrprF5x/vscPM08Y5eerFxnCYTRl0VYqamln95ZTg07/9w8eGtVTQkj4pKbmOU+v2chGLaus1VelwqUxZdFW3r27p0/lFTq75BL15+bNIRpGF1/sUzukWew+UsSqjFy/n9ditZFPfY6fhCbhOz1L1EF1zXOBumadLo1VGblkHC0irbEM+zadhg3h0CG16Z4XzDOa7tgx1QYZouavy8RmrWVghuZCcznPuUHN30ytFvhhp/8/NEToq2n0nEfXrFsV125NbFYL89bK6DrTat7c64Fm5qkZXXop3HwzzJqld0kCYvnOo7UOhT38zp+rvc9Wv3G197k02HGwEKTVQ3ihtsmtnlyzblVdu6kPL8ZitVV5vNOlsXzXUR6jk3eFFsbw8cfwyivwzTceP8QcYXTyJBw4AO1Cc8hnsaOCzPzSWo9LGjKRyKSUc37+67evUVFYc80nt8iBo9yJPbLqX34hzlbT5FZPr1m3qq7d6oLILTOvlBJHhSwdZEbl5fDtt1BQ4HENyRzv8r59amh3+/Z6lyQgDuSV1NLQpkQmpVTZCWy1xwK1N8PlFjo4L0lGKIna1bb2nKfXrFt1125NNGB/Xgmdmid49ThhAB06qD937Tr991qYo88oI0P9GaJhVFYRnL4wf4/UE6HJk7XngnXNBut5hJ+5W7F27vT4IeaoGe3fD/XrQ+Pq+0XMLCoiON8JIjztbBZhzZOtIYJ1zQbreYSfxcer0XS7PF+Vwxzv9Pjxqs8oRJcBapUUSzBeWXJ9exCeRZiZpzu3BuOatfz2PMKkXn3Vq7VEzRFGFgs0aKB3KQIm1h5BaoBnmyfH22XwgqiRNzu3BuOaTU2KkcELZjZkCFxwgceHmyOMBg2CDz/UuxQBld6hcbVzNuIu7E/LSf+ptgO48chp56xLdyarBc5vUd8v5RShy9089+abb3q0c2tN16xbbddudWxWC+ntQ7NZPmxs3w7TpqnBZx4wRxitXg3OmifJmd2tPVM9nrPhLZcGl3dIDsi5RWjwtHnuTIG8Zp0ujdsuk8VSTS0jAx5/HHJyPDrcHGEEkBraF2a7JvH0TUv2fEa7h6wWaN88niYNZF06UTVvmufOFKhr1ma10DctWZYCMjv3Z3Z2tkeHmyeMmjfXuwQBN2N4F7+PeLNaLYzsFdpBLurG2+a5MwXimo2wWpgxvItfzyl04F6b7sgRjw43Txh5ueieGaUkxjB9qH+XPxnRM4WkeBlFJ6rmS/PcmQJxzT4+tJNsHxEKGjUCmw0OH/bocHOE0ZtvQr3wWHJ6VI9U/jLAP5N7f135Nke//9gv5xKhx9fmubP585p9aEAH2VgvVFitcM89HnexmGPc5O9+p3cJgmp8ejuS4+xMW7KNit+2ZPaUzWohwmph+tBO/I+2zJr1OABD7/L9w0aEJk8mt3rKH9fs40M7SRCFmldegcJCjw41Rxh98YVXk6dCwageqVzeNpkpi7ayKiMXm9VS4y+4+/7ebZKYMbwLKYkx3Nx9BoAEkjhHbWvP+cIf16wIMceOwcGDHh1qjjD69NOwCyNQ7fHv3t2T3UeKmL8uk+W7jpKZV1ppgUoLanJgevvG3HZZaqURSBaLhRkzJJBEZf5qnqtKXa9ZEWL+9jdYs8ajQ80RRk2b6l0CXbVrEs9jQzvxGJ0ocVSwP6+EsgoXURFWWiXF1jhLXQJJnM2fzXPVOfuaXfrDRm657Xbem/cOAy/vJisrhItmzTyeZ2SOKyLMw+hMsfYIr5fUl0ASboFonqtNrD2C1g0iKcvZResGkRJE4aRZM9VU5wFzXBUhvC5dsEggiUA2zwlRpYYNPT7UHGHUtq3eJQgJEkjhLRjNc0JUUr++mpZz8mSth5ojjHr21LsEIUMCKTzp0TwnBNdeq1ZgSKi9a8EcYVRerncJQooEUniR5jlhBuYIo927ISlJ71KEFAmk8CHNc0I32dkwYIBHh5ojjGJlt8dAkEAKfdI8J3QVGQnbtnl0qDnCKF4mxQWKBFLokuY5obu4OI8PNUcYefGChPckkEKTNM8J3dWrpxZMdblqPdQcYRQVpXcJQp4EUmiR5jlhCBaLatkqKKj10KB8XXr55Zdp3bo19erVo1u3bqxatSoYTyu85A6kSZMm8fbTj7PkzVf0LpLwgTTPCUN57TWPDgt4zeiDDz5gwoQJvPzyy1x++eXMmTOHQYMGsX37dlJDfCtxM5IakvlJ85wwlGuv9eiwgF+pzz33HHfffTf33HMPHTt25IUXXiAlJYXZs2cH+qmFj6SGZF513blVCL974w2PDgtozaisrIyNGzcyadKkSj8fMGAAq1evPud4h8OBw+E49e9CDzdlEv4nNSTzkeY5YUj/+IdHhwU0jHJzc3E6nTRp0qTSz5s0acLhKvZFnzlzJtOnTw9kkYQXJJDMRZrnhCF5eC0GZTSdxWKp9G9N0875GcDkyZOZOHHiqX8XFhaSkpIS8PKJ6kkgmYOMnhOG5cGwbghwGCUnJ2Oz2c6pBR09evSc2hKA3W7HbrcHskjCBxJIxibNc8LQPAyjgNblo6Ki6NatG19//XWln3/99df07t07kE8t/EwGNRiXu3nuzTfflOY5YTz9+3t0WMCb6SZOnMjo0aPp3r07vXr14tVXXyUzM1O+wZmQ1JCMR5rnhOG99BK8+26thwU8jG6++Wby8vJ4/PHHycnJoXPnznzxxRe0bNky0E8tAkACyTikeU6YwqFDHh0WlAEM48aNY9y4cb6f4Izh3kJ/EkjGIKPnhOFpGnTu7NGh5librqQEGjXSuxTiDBJI+pLmOWEKJ08aYzSd3xQV6V0CUQUJJH1I85wwDS8+u80RRsXFepdAVEMCKfikeU6YRsiFkWwhYWgSSMEjzXPCVLyoSJgjjNq107sEohYSSIEnzXPCdC68EI4cgSoWOTibOcJIRtOZggRSYEnznDAdi0Xt9uoBc4TRxx/D2LF6l0J4QAIpMKR5TpjSN9+Ah4tfmyOMjh/XuwTCCxJI/iXNc8K09uyBH37w6FBzhFEV200IY5NA8h9pnhOmlZMDjRurfqNaSBiJgPE1kBzlTnILHVS4NCKsFpLr27FH2gJaVj04yp0cK9WIataefcfL6eCoINZe+VdSmufMocRRwb7j5TW+l2EpJweaNvUojCyapmlBKJJPCgsLSUhIoOCKK6i/cqXexRE+0jSNKVOmMGvWLO54eGqVgXT4+AlW78zll4MF5BWVnXN/UnwUHVsk0LtDMk0bRAej2AFR0+u0AKmJMaR3aMytPVNpGgNdunShdevWfPvtt6auFf30009069aNjRs3cskll+hdHL/YfaSI+esyWb7zKJn5pZz5QXr2e9muSbxexdTX9ddTWFZGwrJlFBQUUL9+/WoPNUd0f/SR3iUQdVBTDSmvyMFHazLZlV2E1QKuar4a5RWVsXrHMb7/5Rjtm8czslcqSfHm2fvKk9epAQfyS3l33QHeWrOfpPKj5JdZWC5bQxhKVn4pUxZtZVVGLjarBWcVb+bZ72XftGRmDO9CSmJM8AuspwcfVMu5LVtW66HmCCMPhwYK46oqkBr3uZFP1mXh+u2XubogcnPfn5FTxFOfbmdEzxQua58csDL7y9pduV69TveHW641kcZ3/It1uTakhc4YFqzPZNqSbVT89h5VFURnct+/em8e/Z9fyfShnRjVIzXg5TSMq66CwkKPDjVHGA0ZAkuXQkyYfasIMWcG0ssrd9DQmunTeVwauJwaH67OpOhEOddc1MyfxfSrr/+Xw5ebcnx6rMUWQQUw6ZOt5BY7GJ8uk7/19NLy3Ty7bJdPj3W6NJwuLbzeS6cT/vUv6NfPo8PNUfdftUp1hAnTs1gsXDh8LA2vvN0v5/tyUw5rd+X65Vz+tnZXrs9BdLZnl+3ig/W+hbeouwXrM30OorOFzXt57BhMnAg7d3p0uDlqRqDCqG1bvUsh6igrv5THPttW4zFlR/dRuGEJjsytOIvzAbDFJ1Gv5UXEXXQt9maVv1V+si6Lds3iDdWHlFfk4JN1WVXeV7zlG/K+eKHSz6zR9YlMTqV+zxHEpF1a5eOmLtlG77bJ4dfvoLOs/FKmLan5mnVzv7dN73j+nOv0TGHxXrorEB4sBQRmqRkBHDigdwmEH0xZtPVUe3tVijZ9Sc5bEyjL3kl896E0unEqjW6cRv3uwyjPzeTw2w9S/mvl2obLpfHRGmN90/xoTeapPqLqJF03gaajn6Xp6GdIGjgei9XKsY8fp3T3uiqPr3BpTFm0NRDFFTWo7Zr1RVi8l5m//U6ed55Hh5ujZtSoEezerXcpRB3tPlLEqozqm9ROHtxO/rLZRLftTqPhk7HYIk/f2eoi4rsNoWTH91giKq/i7tJgV3YRR46foIkBhn0fPn6CXdm1L50f2ahlpW/P9dp0I+uFUZT88h0x7Xqec7zTpbEqI5eMo0WkNQ7TocJBVts166uweC937YK4uBCrGc2aBUOH6l0KUUfz12Vis1qqvb9wzYdgsZI4cHzlIDpD7Pl9iIhPOufnVgv8sNMYfUerd+ZSw8usliUiCostAou1+gm+NquFeWuNVQsMZbVds3UR8u9l06Zw661qsVQPmCOMbrwRQmSiXDhbvvNotUNhNZeTkwe2Ym+WRkRcotfndmmw46BnQ0gD7ZeDBbUO3wZAc6G5nGjOCioKc/n1m1fRyh3EXnBltQ9xujSW7zrqv8KKGtV0zdZVyL+Xo0fDK694fLg5mun27IH//leNzPAwZYWxFDsqyMwvrfZ+14lCtAoHtvqNz7lPczkr/8BixVLFdZBb5MBR7tR16aCT5c4qV5CoyuF3/lz5B7ZIEq8ZQ3SbbjU+LjOvlBJZbibgartm/SGk38udO/Fmgpw5/gd27IC//AVuuQWaGXdOiajegbwSfP1+mfPWBMqP7jv17wbpd5HQc0SVx+YWOjgvSb8RSnmFnu+9lTRkIpFJKYAK49Jda8hfNhtNc1K/2/XVPk4D9ueV0Kl5Ql2LK2pQl2vWUyH7XhYUwPnnw/z5ap6oB8wRRmlp6s9duySMTKqswlXj/dbo+lgi7DgLz222SB76EFq5A2dxPscW/r3G8/h71JO3vHn+yKSUSgMYott0o6LgKMeXv0Vcp3Ss9eKqfWxt/5+i7oL1fxyS76V7wFmHDh4/xBx9Rq1agdWqwkiYUlREzZeaxWqjXssLceRkUPHb3KJTj01Oxd6sHVGNWtX6PBEB6mz2VF2fP6pxK7QKB+X5h2o+rpb/T1F3wfo/Dsn30v1Z3c7zlSbM8b9gt6tA8nAmrzCeVkmx1PYxXb/XSNBc5C/9N5qzwqfnSa6v78TXuj5/2RHVHGmNqb7ZxoL6/xSB5ck1W1ch+17u3KlG09WwSvfZzNFMBzByJLRpo3cphI9i7RGkJsZwoIYO4XotLiBxwBjyv55DzlsPEHfRQCKTU7FYLDhLfqV0p9ox0mqvuk8oOV7/fY/skTaS4qM8GsRQfuwA/DY4w3miiNJdqzm5fxPR7XsR2aBptY9LTYoJzQ5vg/Hkmq2rkH0vjx2Djh29eoh5/hdmzdK7BKKO0js05t11B2ocKhvf9Trszc+ncMMSitZ/SkVxPhaLBVt8EvbzOtJ41JNEt7ronMdZLXB+C8+/hQVSxxYJrN5xrNbh3WcuCWSxxxKR0ISGV91D/CWDq32MzWohvf25Iw5FYHhyzfoqpN/Ll1+GMs9GlbqZJ4ycTvjlF0hN9arqJ4zj1p6pvLVmf63HRTVpQ/LgCV6d26XB5R2MsZ1E7w7JfP/LsWrvj7uwP3EX9vfp3E6Xxm2XhdEWBDrz9Jp18+a9Ddn3UtPUFJyoqNqPPYM5+oxALbrXpYuabyRMqV2TePqmJft9RrvVAu2bxxtiKSCApg2iad883qdVGGpis1rom5YcusvHGFCgrtmQfi+/+UbNLzp82KuHmSeMzjsPGjeGjRv1LomogxnDu/h9xJvVamFkL2N9wxzZKxWrn19nhNXCjOFd/HpOUbtAXLMh/V5u2AB5eerz2gvmCSOLBbp3lzAyuZTEGKYP7eTXc47omWKo7SMAkuLt9E3x7wfY40M7hfaWAwaVkhjD1MHedcbXJqTfy40b1fJtVu/ixTxhBNCtm0pdTd+JjaJuRvVI5S8D2vvlXNdd0tyQW4/v3baFhY/cQuwe/zQrl65dQGpFzXOPRGBUVFSw+LmHKVg1zy/ne2hAB24O5a3HN25Un9VeMlcYde8OsbFw/LjeJRF1ND69HbNGdMEeYcWieTcD3WqBCJuFm3qn0v/C6odA62Xvti08ftcozm/fntWvTT31Or3td7BZLdgjrEwf3J6OrkyuvfZa1qxZE6BSi6pUVFRwyy23sGjRIt56aFSd38unRnThvvS0AJXWAPLyYP9+9VntJXOF0fXXw7590LCh3iURfjCqRyrv3dqRk5lbAGrt8Hffn9YsnkduuMCwNSJ3EH399TISEhIY1SOVbx68kt5t1NYXtX2Que/v3SaJbx68kjv6tOPzzz+na9euEkhBdGYQffzxxwwbNqzO72VI14gAGjSArVth4ECvH2qeod1wesXuEycg2hgjp0TdvPvKCxT9Zy5/WbSKTYdOsuNgIblF5y42mhxv5/wW9bm8Q7JhRs2draogcktJjOHdu3uy+0gR89dlsnzXUTLzSistxGlBTYJMb9+Y2y5LrTTSKi4ujs8//5zBgwdz7bXX8tVXX9GrV6/gvbgwU1UQudX1vQxpNht07uzTQy2aZtwOmMLCQhISEigoKKC+e27Rn/8Mq1bBjz/qWzhRZzk5ObRp04Zh99zHTeNPb6fgKHeSW+igwqURYbWQXF//lRVqU1MQVafEUcH+vBLKKlxERVhplRRb62z84uJiBg8ezKZNm0wVSD/99BPdunVj48aNXGLwvclqCqLq+PJehqRx4+Cyy+D220/9qMrP8SqY73/r/PPhhRegsFAmv5rcU089hS0yisG331Pp5/ZIm67bQHjLlyACtdyMt1sHSA0psHwJIvDtvQw5J0/Cm296tVL3mczVZwTQrx+4XKp2JEwrJyeHOXPmMOSOe4mtb95fYl+DqC7cgSR9SP7laxCJ36xdCw6H+oz2gfnCKC1NTYBdsULvkog6qK5WZCZ6BJGbBJJ/SRD5wfLlkJioVsrxgfnCyGJRySt9RqYVCrUiPYPITQLJPySI/GTFCrjySq8nu7qZr88I4F//kv4iEzN7rcgIQeQmfUh1I0HkR3//O0RG+vxw89WMQFUFI8yZo+HO7LUiIwWRm9SQfCNB5GdXXAF1+CJkzjAC+P3vYcoUvUshvGTmWpERg8hNAsk7EkR+Nn8+zJlTp1OYN4xiYmDRIr1LIbxg5lqRkYPITQLJMxJEAfDcc2oAQx2YN4yGDoUdO2DXLr1LIjxk1lqRGYLITQKpZhJEAXDwIPz0E9Tx/9K8YdS/P9SrB599pndJhAfMWisyUxC5SSBVTYIoQD77TPXh+7Ae3ZnMG0axsSqQPv9c75IID5ixVmTGIHKTQKpMgiiAlixRgxfquIB1QMPoySefpHfv3sTExNCgQQP/P8GLL8Lixf4/r/ArM9aKzBxEbhJIigRRgI0dC488UufTBDSMysrKGDlyJGPHjg3ME7RqBfFhshquiZmtVhQKQeQW7oEkQRQEQ4fCgAF1Pk1Aw2j69Ok8+OCDdPFxeQiPTJ0K95jjQy4cma1WFEpB5BaugSRBFASzZ8OXX/rlVIbqM3I4HBQWFla61SoqCj78UC3QJwzHTLWiUAwit3ALJAmiIHA6VWXAT4tWGyqMZs6cSUJCwqlbSkpK7Q8aOhSKiuDbbwNfQOEVM9WKQjmI3MIlkCSIguT77yE3V30G+4HXYfTYY49hsVhqvG3YsMGnwkyePJmCgoJTt6ysrNof1KULdOyoZgALQzFLrSgcgsgt1ANJgiiI5s9X/fY9e/rldF4v8DZ+/HhGjRpV4zGtWrXyqTB2ux273e7dgywWuO02mDlTbe5Ur55Pzy38y10rGnbPfYauFYVTELmF6uKqEkRBdPKk6h4ZP159BvuB12GUnJxMcnKyX57cb/7v/2D0aAkiAzFDrSgcg8gt1AJJgijINA1mzVJzPf0koH1GmZmZbN68mczMTJxOJ5s3b2bz5s0UFxf794mSkyElRf0HCd2Zoa8onIPILVSa7CSIdBAdDWPGqM1O/SSgYTR16lS6du3KtGnTKC4upmvXrnTt2tXnPqUarVsHbdrAkSP+P7fwitFrRRJEp5k9kCSIdHD8OIwbB5706XshoGH01ltvoWnaObd+Pu6RXqN27eDQIViwwP/nFh4zeq1IguhcZg0kCSKdfPyx2i7Cz3vKGWpod50kJsJ118moOp0ZuVYkQVQ9swWSBJGO5s2Dq6+GZs38etrQCSNQo+rWr4edO/UuSVgycq1Igqh2ZgkkCSIdZWbCypXqs9bPQiuMhgxRNaRPP9W7JGHJqLUiCSLPGT2QJIh09vrrEBcHw4f7/dShFUb16sGmTfDww3qXJOwYtVYkQeQ9owaSBJEB3HEHvP12QBaoDq0wAkhNVZOwPFnXTviNEWtFEkS+M1ogSRAZRNu2MGJEQE4demEE8Oc/qw42ERRGrBVJENWdUQJJgsggbr89oKOVQzOM0tNhwwY1mEEEnNFqRRJE/qN3IEkQGcS2bfDuu35b+qcqoRlGgwZBy5bw8st6lyTkGa1WJEHkf3oFkgSRgcyeDU2aBGTggltohpHNppaqWLAA8vL0Lk1IM1KtSIIocIIdSBJEBlJUBO+8A/feq/aPC5DQDCOAu+6Chg3h55/1LknIMlKtSIIo8HwNpBJHBfuOlxPVrD37jpdT4qio8XgJIoNZtAhKStSC1AFk0TTjri5aWFhIQkICBQUF1K9f3/sTOJ2qliQCYsKECbz+5lxmf7tO1zCSIAqu4uJiBg8ezKZNm6pd7Xv3kSLmr8tk+c6jZOaXcuaHjAVITYwhvUNjbu2ZSrsmp4cJSxAZkMsFW7bAxRf79HBPP8dDO4wAjh1Ta9b5+B8pqpaTk0ObNm0Yds993DT+z7qVQ4JIH9UFUlZ+KVMWbWVVRi42qwWnq/qPF/f9fdOSmTG8C83qR0kQGU1JCcTG1ukUEkZuI0bArl0q2a2h2yoZbEaoFUkQ6evsQDoQcR7TlmyjwqXVGEJns1ktRFgtNMv+nh/eeVqCyCg0Te3ietVVau8iH0kYuX3/PfTtC4sX+22v9nBnhFqRBJExuAPpF2tLYi672fcTaRpYLAxOcfLvcfJ7agjffAPXXANLl8K11/p8Gk8/x0O/qtCnj7rNnCmb7/mJ3iPoJIiMIy4ujjufeL1uQQSn5q98nmXjg/WZfiiZqLOZM6FrVxgwIChP598NKYxq8mQYPFitNhuIvZTCiHsE3bB77tOleU6CyFiy8kuZuSyjyvuKt3xD3hcvVPvYJr+fQb2WF57z86lLttG7bTIpiTH+Kqbw1o8/wn//Cx9+GNCJrmcKjzAaNAjuv18N9RZ1ometSILIeKYs2kpFLf1DSddNIDKpxTk/j0xOrfL4CpfGlEVbeffunn4po/DBzp3QrVvA1qGrSniEkcUC//qX3qUwPT1rRRJExrP7SBGrMnJrPS6yUUvszdp5fF6nS2NVRi4ZR4tIa+z/1aGFB0aPhltvDeqgr9DvMzrTN9/ApEl6l8K09KoVSRAZ0/x1mdisgWnCsVktzFsrfUe6+OgjtetBkEcfh1cYHTkCTz0Fq1frXRLT0Wu1BQki41q+86hnQ7g1F5rLec6tJk6XxvJdR/1UUuGxzZvhpptUIAVZeDTTuf3+9/D006p2tHJl0DrmQoEetSIJIuMqdlSQmV/q0bGH36li+L/FSstHltT4uMy8UkocFcTaw+tjSleTJ0P79moTvSALr3fZalXDFQcPhi+/hOuu07tEpqBHX5EEkbEdyCvB04kSSUMmEpmUUvmHHnwR1ID9eSV0ai7vfVCsWKHmFH30EUQEPxrCK4xAjay74go1oEHCyCPBrhVJEBlfWYXL42Mjk1K8GsDg6/OIOtA01WLUvTv87ne6FCH8wshiUZtEJSfrXRJTCHatSILIHKIigtPdHKznCXsWC8yYATExunVfhF8YAaT+Nr8hKwsaNwa7Xd/yGFgwa0USRObRKikWC3jcVOcLy2/PIwLM5VIBdNVVuhYjfL925OXB+efDq6/qXRLDCuYIOgkic4m1R5Dq4QoJ5ccO4Di045ybs7SgxselJsXI4IVgeOstuPJKcDh0LUb4vtNJSXDzzfD442pyV2Ki3iUynGDViiSIzKlb83pk5hWjWWr+TlvdkkCJg+4n/qKqF+C0WS2kt29c1yKK2hQVwd/+ptbv1LmFKHzDCODJJ+Hjj9Wb8e9/610aQwlWX5EEkfkcOHCAGTNm8O7ir2l854vVHhd3YX/iLuzv03M4XRq3XVb1ckHCj/7+d/j1VzXlRWfh20wH0KwZTJ8Or7wCmzbpXRpDCUatSILIXA4cOMAf//hH2rVrxyeffML0P4+lV+uGfl+FwWa10DctWZYCCrTt2+H552HKFGjZUu/ShHnNCGD8eNi3Dxo00LskhhGMWpEEkXm4a0Jz584lISGBJ598krFjxxIXF0dWfin9n1/p1WZ6tYmwWpgxvIvfzieqsXu32gH7L3/RuyRAuNeMACIj1Zyj1q1lv6PfBLpWJEFkDmfXhJ588kn27dvHQw89RFxcHAApiTFMH9rJr8/7+NBOsn1EMAwbpraKqFdP75IAEkanrVsHl12m2k/DWKBH0EkQGZ8nIXSmUT1S+cuA9n557ocGdODmHtJXFFDFxWrZn19/NdSSaBJGbi1aqDbUqVP1LomuAlkrkiAyNm9D6Ezj09sxa0QX7BFWr/uQbFYL9ggrT43own3paXV5CcITTzwBL7wABTUPrQ82CSO3886DadPg5ZfVyrVhKJC1Igki46pLCJ1pVI9UvnnwSnq3SQKoNZTc9/duk8Q3D14pNaJg2LEDnntO1YxatdK7NJVYNM24HSWFhYUkJCRQUFBA/fr1A/+E5eVqz/d69WDNGtWfFEYmTJjA62/OZfa36/waRhJExnT2wISHH3741MCEutp9pIj56zJZvusomXmllVZqsKAmtKa3b8xtl6XKqLlgcTrV5NbDh+Hnn4PWV+Tp57iMpjtTZCTMnQu33QYHD6pBDWEiUCPoJIiMp6bRcf7Srkk8jw3txGN0osRRwf68EsoqXERFWGmVFCsrK+jhu+/Ul+zlyw0zaOFMckWcrUcP1Xdks+ldkqAKRF+RBJGxBCOEqhJrj5BtIIwgPV0N527TRu+SVEn6jKpis8GePTBunGq6C3GB6CuSIDIOf/UJCZNyOmHBArUgqkGDCCSMqpefrxZRNcAyGYHm71qRBJExSAgJAF58Ue1ybfBVZiSMqtOjBzz8sFou6Oef9S5NwPi7ViRBpD8JIXHK7t1quZ8//Qm6ddO7NDWSMKrJtGnQrh384Q8h21znz1qRBJG+JIREJU4n3HknNG+uNs4zOAmjmtjtaq+P3btDsnbkz1qRBJF+JIRElRYuhNWr1QjhWONvUiij6WrTowfs3w8NG+pdEr/zV61Igkgfeo2OEyZx441qGHffvnqXxCNSM/JEw4ZQUqJWtz12TO/S+IW/akUSRMEnNSFRo+PH4b//BatVTXI1CakZeaqgAN5+W81B+s9/1BttYv6oFUkQBZfUhEStNA3uuUeF0f79EIyVa/zE3J+owdS8ObzzDnz5pVrbycT8USuSIAoeqQkJj82erfqKXn/dVEEEEkbeGTQIHnpILTK4bp3epfFZXWtFEkTBISEkvLJ5M0ycCPfdByNG6F0arwUsjPbv38/dd99N69atiY6Opm3btkybNo2ysrJAPWVwPPkkdO8O336rd0l8UtdakQRR4EkICZ88+ih07AjPPqt3SXwSsD6jHTt24HK5mDNnDmlpafz888/ce++9lJSU8KxJ/7MAtZiqQRca9ERdakUSRIElfUKiTt5/X22YZ9LPpqBuIfHMM88we/Zs9u7d69HxQd9Cwltz5qg3f9IkvUvikZycHNq0acOwe+7jpvF/9uqxEkSBE8itHEQYmDcPLr/csLsMePo5HtQ+o4KCAhITE6u93+FwUFhYWOlmaIcPq/6jxYv1LolHfK0VSRAFhjTHiTr76iu44w410tfkghZGe/bs4cUXX2TMmDHVHjNz5kwSEhJO3VJSUoJVPN/87W/wu9+p/Y8MvkKDr31FEkT+JyEk/GLXLhg1CgYOVJ9FJud1GD322GNYLJYabxs2bKj0mOzsbAYOHMjIkSO5557qv5VPnjyZgoKCU7esrCzvX1EwWa3qG0nbtjB0KOTl6V2iavlSK5Ig8q+qQmj//v0SQsJ7BQXqM6dJE3jvvZDYf83rAQzjx49n1KhRNR7T6oy91bOzs0lPT6dXr168+uqrNT7Obrdjt9u9LZK+YmNVM92ECWphQgPyZRdXCSL/qWpgwrhx44g1wXphwqD+9z8oLlaTW0Pkd9PrMEpOTiY5OdmjYw8dOkR6ejrdunVj7ty5WE2+akG1WraERYvU3wsLDTfZzNtakQSRf0gIiYC54grIyDDtyLmqBCwdsrOz6devHykpKTz77LMcO3aMw4cPc/jw4UA9pf5yc+GCC+CVV/QuySne9hVJENVdTc1xEkSiTt59Vw1YqKgIqSCCAM4zWrZsGRkZGWRkZNCiRYtK9wVxNHlwJSermc/33aeWDxo6VO8SeVUrkiCqG6kJiYBatgzuugtuvz0k+ojOFtR5Rt4y/DyjqjidaoTLf/4DX38NffroVhRv5hVJEPmuqnlCEkLCr9avh/R06NcPPv0UIsyzxrUh5xmFBZtNVaUvuwxGjoQTJ3Qriqe1Igki30hznAiKrCy47jro0gU+/NBUQeSN0HxVeqtXT3172b4doqN1KYKnI+gkiLwnzXEiqJo3hwcegLFjISZG79IEjNSMAiUhAXr1Uh2Njz0W9DlIntSKJIi8IzUhEVQFBfD996q15a9/haQkvUsUUBJGgZaTAy+/DIMHq91ig/KUtY+gkyDynISQCLqTJ2HYMLV1eGmp3qUJCgmjQEtJgS++UMsF3XgjOBwBf8raakUSRJ6REBK6KC+HW25Re6YtXBjSTXNnkjAKhu7dVR/S8uVqUEMA93SqrVYkQVQ7CSGhm4oKtdblf/4DH32kVuMOExJGwdK/vwqk5s0DOkegplqRBFHNJISE7o4cgQ0b4IMPYMgQvUsTVDKaLpgGDlQ3gE2boHNntVmfn9Q0gk6CqHoyOk7ozulUfUPnnadG4ZptjU4/kJqRHn79VU1eGzXKr0121dWKJIiqJjUhYQgVFWpVhYEDweUKyyACqRnpo2FDmD9f7YV0002qSu7hBVjiqGB/XgllFS6iIqy0Sool1h5Rba3IjEFU3Wv0F6kJCcMoL1d9RAsXqm3DQ3UxaQ9IGOllyBC10veIESqUPv642oUPdx8pYv66TJbvPEpmfilnrt9kAVITY7Ad3UFU49aVakVmCiJPXmN6h8bc2jOVdk3ifXoOCSFhKOXl8Pvfqy1oPvxQfRaEMVmbTm/LlqmZ1cuXQ2pqpbuy8kuZsmgrqzJysVktOF3Vv1Way4nFaqN983hG9kqlIHOnKYLIm9fovr9vWjIzhnchJdGzIa+ydpwwpM8/VwH00UeGWFQ5UDz9HJcwMoKyMoiKguPH1WS3pk1ZsD6TaUu2UeHSavyAPpvVomoShctfp7Uz29BB5OtrtFktRFgtTB/aiVE9Uqs9TkJIGFJp6em5QwcOqP3QQpgslGomUVHqzzFjoHdvXvpoLZM+2YqjwuXVhzSAS4MKl0Zsv3u4afobhg2il5bv9vk1Ol0ajgoXkz7ZykvLd59zvwxMEIa1fz907QruXa9DPIi8IWFkJE89xYJ2fXn2p7qtY2exWAB46bsDfLA+0x8l86sF6zN5dtkuv5zr2WW7Tr1GCSFhaFu2QO/eavTcVVfpXRrDkTAykKz4Rky79GaooeW0cMMSDswaQvbr4zw659Ql28jKN87aVln5pUxbsq3W44q3fMOBWUNw5Jxb8znb3xb/zOixD0oICeNauVJtFd6kCfzwA6Sl6V0iw5EwMpApi7ZS4QJ+q9lUpXjL1wCU52biyN5Z6zkrXBpTFm31VxHrTL1G/3ZTOsorWF7cVEJIGJOmwZNPQrduKpSaNtW7RIYkYWQQu48UsSojt8b+E0fObsqP7iO6bQ8Aiv+3rNbzOl0aqzJyyTha5Ley+sqT1+gLi9VGRIvODL9jjISQMA5Ng+xs9eXyo4/UgsmhPBCrjiSMDGL+ukxs1uprRADFW1T4NOh3B/bzOlLyy3e4yk/Wem6b1cK8tfr3HXnyGn1llNcoBKBGxd5+O/ToAcXFan+zMF1ZwVMSRgaxfOfRGmsMrnIHJdu/I6pZO6IatSL2wmvQyk5QuuOHWs/tdGks33XUn8X1SW2vsS6M8hqFIDsbrrxSTWR/9lmIi9O7RKYgYWQAxY4KMmsZZFC68wc0RwlxFw4AILZjXyxR0R411QFk5pVS4qioc1l95clrrCu9X6MQ/Pij2jLm0CFYtUqtsCA8ImFkAAfySqitvlD8v2VYIuzEdrwCAGtUNDEdLsdxcBvl+YdqfQ4N2J8XnJ1mq+LJa6wrvV+jEDid0KGD2gaie3e9S2MqEkYGUFbhqvH+8l+zcWRtI7ptd0DDdbIY18liYs9XG2+5R9jV9XkCKVjPredrFGGqogJeeUWtNderF/z3vzJizgeyUKoBREXU/J1AhY1G6c4fKN15bh9Ryc//pcEVo7FYa960r7bnCaRgPbeer1GEoYMHVVPcmjXQvr2azFrD1AxRPQkjA2iVFIsFqmzG0lxOSrZ+S0SDZiQNuv+c+0/sWU/hj4s4sXcjMWmXVvsclt+eRy81vUZ/0fs1ijDz2Wfwhz+odeZWrIA+ffQukanJ10gDiLVHkFrNCtQn9m7EWZxP3MXXUq/lhefc6l92I9giax3IkJoU49c9gbxV02uskRffMvV+jSKMrFunVtq+/HLYvFmCyA8kjAwivUPjKufgFP9vGdgiiLvwmiofZ4tJIKZ9L07sWY+z5Neqj7FaSG/f2K/l9UV1r7EqWoUDAIvNs3AxymsUIS7vt3UjL71UbQGxeDEkJelbphAhYWQQt/ZMrXIOTuPf/ZWWD32KLab61bcbDXuYlg8vxhbbsMr7nS6N2y6rfquFYKnuNValPO8gWKxE1PcsYIzyGkUI+/BDaNMGPv1U1divu076h/xIwsgg2jWJp29ast9XKLBZoG9aMmmNfdsd1Z88eY2OwxkUbfqC4q3fEJ12KVZ77U17NqvFMK9RhKDjx+HOO+Hmm2HgQEhP17tEIUnCyEBmDO9ChD/DSNOIKC9jxrVt/HfOOqrtNR5bNJPjK98hOu1Skq77k0fnjLBamDG8i7+KKMRp27dD587wySfwxhuwYIFa2kf4nYSRgaQkxjB9aCf/ndBi4fHUclJaNFKT8fLz/XduH9X2GluMfYOUCQtoNPQhbNGeLSr5+NBOHm9BLoRHKn5byaNtWzVQ4eef4a67pFkugCSMDGZUj1T+MqC9X8710IAO3Hz/Teof//wndOwIixb55dx14ffXWMPW40J47Ysv1Jyhn39Wi5u+/DKkpOhdqpAnYWRA49PbMWtEF+wRVq/7kGxWC/YIK0+N6MJ96Wds4HXLLWp2+IgR6u95ddtNtq4C8hqFqAt339DgwSqMGjTQu0RhxaJpNWwrqrPCwkISEhIoKCigfhjuA5KVX8qURVtZlZGLzWqpcSSa+/6+acnMGN6l6mYrTYP33oP774eICFi/Hlq2DOArqJ3fX6MQvvjhBxg5EkpK4LnnpEnOjzz9HJcwMoHdR4qYvy6T5buOkplXWmkVAwtqsmd6+8bcdlmqZyPKcnJg7lyYPFn9wu3bB61bB6r4HvH7axTCE6WlagWFQ4fg4Ydh1ixpkvMzCaMQVeKoYH9eCWUVLqIirLRKiq3bqgMrV6r1tMaOhb//HRpWPVcpmPz+GoU4W2EhPPaY2oH1559lhFwAefo5Ln1GJhNrj6BT8wS6pjakU/OEun9I9+4NzzwD77yjlr6fOxdc+q587ffXKISbpsG8eepanzMH7rsP6tXTu1QCCSMRGQkTJ8LOnTBggGornz1b71IJERhjxsDo0dC3L+zYAZMmyXbgBiHNdKKyVavgkksgNlYtf9K1K7Rrp3ephPDdvn1w4gRccAGsXQvFxdC/v96lChvSTCd807evCqKKCpg6Vf0Cjx0L2dl6l0wI7xw9Cn/6k2qSmzpV/eyyyySIDErCSFQtIkItjT9rlqohpaWp0XdOp94lE6JmxcUwbZpa1PSdd2D6dHj7bb1LJWohYSSqV68e/PnPsHev6lfaswdsNtUJfPKk3qUTojJ3j0NZGbz6Kowbp67dyZNVbV8YmoSRqF1CAjzxBHzwgfr34sXQqhU89ZQaIiuEnoqL1UTVLl3UyiKJiaqf6Omn1d+FKUgYCc+5Z6RfeKFaPHLqVEhNhUcfVe3zQgRTXp6aK9SyJTzyCPTocbrGLsO1TUfCSHivTRvVDLJ3L9xzj1qE9f331X3GHZwpQs1dd6naz223qSbkuXPhvPP0LpXwkQztFnWXn6++icbEwAMPqAUnH34YOvlxOwwhdu5UE7RvvFFtcpeRoZqQGzXSu2SiBoYY2j106FBSU1OpV68ezZo1Y/To0WTLEOHQk5ioggjg/PPh22/VhmRXXaWWWykv17d8wrwqKtQ23wMGqGvr88+hoEDdl5YmQRRCAhpG6enpfPjhh+zcuZOFCxeyZ88ebrzxxkA+pdDb2LGq+e7991UI3XST+jeoUU5CeMLdYPPGGzB8OBQVqWHa+/ap7b9FyAlqM92SJUu44YYbcDgcREZG1nq8NNOFgL17VR+Ty6Um0HburIbcpqfLEv2iMk2D779Xm9k1bQrPP69qQXv2qFVBhCkZopnuTPn5+cyfP5/evXt7FEQiRLRpo/6sqFD7KP3yC1x9tdp1duZMcDj0LZ/QX26u6gvq0gWuuAJ++kldH6D6hCSIwkLAw+iRRx4hNjaWpKQkMjMzWbx4cbXHOhwOCgsLK91EiIiKUisk//wzrFihPmDee0/9HOCTT+DXX3UtogiiggK1wgeoMHIvPfX112oB0//7P12LJ4LP6zB67LHHsFgsNd42bNhw6viHHnqITZs2sWzZMmw2G7fffjvVtQzOnDmThISEU7cU2eQq9FgscOWVKoj+9z/178OHVd9S06aqf2DhQlnhIRSVlakJ0yNHQpMm8Pvfq5+ffz4cO6aWnerfX5pvw5TXfUa5ubnk5ubWeEyrVq2oV8Wks4MHD5KSksLq1avp1avXOfc7HA4cZzTbFBYWkpKSIn1G4eDwYbXCw7x5sGGDmky7bx9YraopT5b5NydNU+Gydy90765qvxdfrOYGjRol84LCgKd9Rl7vWpacnExycrJPhXLnnqOafgK73Y5dPnTCU9Omao7SAw+o+STbt6sgKiyEFi2gTx+4/np1a9FC79KKmmRnw3/+A0uWqL7CpUvVKgl/+pOaI9S5s94lFAYUsNF0P/74Iz/++CN9+vShYcOG7N27l6lTp5KTk8O2bds8Ch0ZTScoLFQz65csUVukO51w6aWwevXpRVulWccYdu1SNZ7169UXib59VbPrAw/oXTKho4DVjDwVHR3NJ598wrRp0ygpKaFZs2YMHDiQBQsWSO1HeK5+/dM1pl9/Vd+y3auHV1So/oaLL4Z+/dTtggvUB6EIHE1ToyJXrIDly6FBA3jtNdXk1qaNqgENGgRJSXqXVJiILAckzKu4WK1NtmKF2sGzvBySk1VY1a+v+qGaNJGaU11pmtopNSYGvvtODUA4elTteXXppTBsmFr+SYgq6F4zEiLg4uLg8cfV30tLYc0aNVzYfcH37q1m7nfvDt26qdvVV5++X1Tt6FH1f7lxo7pt2AA33ABz5kDbtnD33WrScu/esk+Q8BupGYnQpGlqjbxVq05/oB45Alu2qMmVr70GBw6ogOraVY3eC7fmPZcLsrJUgG/cCEOGqJrO88+rzRQbNTod4gMHqkEkQnjJ089xCSMRHjRNjfJq2lT1N02aBG+9pQIK1NDxl15SW2Ls2KGa/dq3V7ekJHM39eXnq8EFu3ap+Vz16sGYMWqttxMn1DGNGqkN6m67TU1CPXFCjVo08+sWhiBhJERt3AG1ZYv6oL7ySjUYYs4c9WHt1rAh3HKLCqsTJ+DZZ6FZM2jeXP3ZrJk+fVMulwqO7GzIyVE3iwXuvFO9tj591DD5vLzTj9m2TQ3y+OADdXy7dmqzRAkeESAhEUYFBQU0aNCArKwsCSMRXKWlaqJmRoa6NW4Mt98Ohw6p9dPOnvh9+DBER8O996oAiI1VfVrx8aq21bu3ag5bsUJ1/Fut6paSos7pcp2+OZ3quRo2hLffVkPai4rUgI2SElV7+b//g6++UjWdM118sToeVO0vMVEFTlqaGukmfTwiyNyLFxw/fpyEhIRqjzN0GLlXbBBCCGFuWVlZtKhhwrqhw8jlcpGdnU18fDwWD5oQ3Akc6jWpcHid4fAaQV5nKAmH1wjev05N0ygqKqJ58+ZYaxgkZOih3VartcYkrU79+vVD+mJwC4fXGQ6vEeR1hpJweI3g3eusqXnOLczGsgohhDAiCSMhhBC6C6kwstvtTJs2LeTXvguH1xkOrxHkdYaScHiNELjXaegBDEIIIcJDSNWMhBBCmJOEkRBCCN1JGAkhhNCdhJEQQgjdhWwYDR06lNTUVOrVq0ezZs0YPXo02dnZehfLr/bv38/dd99N69atiY6Opm3btkybNo2ysjK9i+Z3Tz75JL179yYmJoYGDRroXRy/ePnll2ndujX16tWjW7durFq1Su8i+d13333H9ddfT/PmzbFYLHz66ad6F8nvZs6cSY8ePYiPj6dx48bccMMN7Ny5U+9i+d3s2bO58MILT0127dWrF19++aXfzh+yYZSens6HH37Izp07WbhwIXv27OHGG2/Uu1h+tWPHDlwuF3PmzGHbtm08//zzvPLKK0yZMkXvovldWVkZI0eOZOzYsXoXxS8++OADJkyYwKOPPsqmTZvo27cvgwYNIjMzU++i+VVJSQkXXXQRL730kt5FCZiVK1dy3333sXbtWr7++msqKioYMGAAJSUlehfNr1q0aMGsWbPYsGEDGzZs4KqrrmLYsGFs27bNP0+ghYnFixdrFotFKysr07soAfX0009rrVu31rsYATN37lwtISFB72LU2aWXXqqNGTOm0s/OP/98bdKkSTqVKPAAbdGiRXoXI+COHj2qAdrKlSv1LkrANWzYUHv99df9cq6QrRmdKT8/n/nz59O7d28iIyP1Lk5AFRQUkJiYqHcxRA3KysrYuHEjAwYMqPTzAQMGsHr1ap1KJfyloKAAIKR/D51OJwsWLKCkpIRevXr55ZwhHUaPPPIIsbGxJCUlkZmZyeLFi/UuUkDt2bOHF198kTFnbgwnDCc3Nxen00mTJk0q/bxJkyYcPnxYp1IJf9A0jYkTJ9KnTx86d+6sd3H8buvWrcTFxWG32xkzZgyLFi3iggsu8Mu5TRVGjz32GBaLpcbbhg0bTh3/0EMPsWnTJpYtW4bNZuP2229HM8GCE96+ToDs7GwGDhzIyJEjueeee3QquXd8eZ2h5OxtUTRN82irFGFc48ePZ8uWLbz//vt6FyUgOnTowObNm1m7di1jx47ljjvuYPv27X45t6G3kDjb+PHjGTVqVI3HtGrV6tTfk5OTSU5Opn379nTs2JGUlBTWrl3rt2ploHj7OrOzs0lPT6dXr168+uqrAS6d/3j7OkNFcnIyNpvtnFrQ0aNHz6ktCfO4//77WbJkCd99951PW9+YQVRUFGlpaQB0796d9evX889//pM5c+bU+dymCiN3uPjCXSNyOBz+LFJAePM6Dx06RHp6Ot26dWPu3Lk1bl5lNHV5P80sKiqKbt268fXXXzN8+PBTP//6668ZNmyYjiUTvtA0jfvvv59FixaxYsUKWrdurXeRgkbTNL99ppoqjDz1448/8uOPP9KnTx8aNmzI3r17mTp1Km3btjV8rcgb2dnZ9OvXj9TUVJ599lmOHTt26r6mTZvqWDL/y8zMJD8/n8zMTJxOJ5s3bwYgLS2NuLg4fQvng4kTJzJ69Gi6d+9+qkabmZkZcv19xcXFZGRknPr3vn372Lx5M4mJiaSmpupYMv+57777eO+991i8eDHx8fGnarwJCQlER0frXDr/mTJlCoMGDSIlJYWioiIWLFjAihUrWLp0qX+ewC9j8gxmy5YtWnp6upaYmKjZ7XatVatW2pgxY7SDBw/qXTS/mjt3rgZUeQs1d9xxR5Wvc/ny5XoXzWf//ve/tZYtW2pRUVHaJZdcEpJDgZcvX17l+3bHHXfoXTS/qe53cO7cuXoXza/uuuuuU9dro0aNtKuvvlpbtmyZ384vW0gIIYTQnXk6GIQQQoQsCSMhhBC6kzASQgihOwkjIYQQupMwEkIIoTsJIyGEELqTMBJCCKE7CSMhhBC6kzASQgihOwkjIYQQupMwEkIIoTsJIyGEELr7f540le0fzh0TAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "K = create_example_cw(centered = True)\n", "K.plot(bounding_circle=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also color the nodes based on a function value for a given direction." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = np.pi/7\n", "K.plot(bounding_circle=True,color_nodes_theta=theta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function value for any direction can be computed and returned for vertices, edges, or faces. The function value for an edge or face $\\sigma$ is given by $g_\\omega(\\sigma) = \\max_{v \\in \\sigma}\\{f(v)\\}$. Here we show the function values for the triangle `KDC` and its faces." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "K: 0.18\n", "D: 0.65\n", "C: 2.89\n", "('D', 'K'): 0.65\n", "('C', 'D'): 2.89\n", "('C', 'K'): 2.89\n", "('K', 'D', 'C'): 2.89\n" ] } ], "source": [ "vert_g = K.g_omega(theta)\n", "edge_g = K.g_omega_edges(theta)\n", "face_g = K.g_omega_faces(theta)\n", "\n", "for v in ['K','D','C']:\n", " print(f'{v}: {round(vert_g[v],2)}')\n", "\n", "for edge in [('D','K'),('C','D'),('C','K')]:\n", " print(f'{edge}: {round(edge_g[edge],2)}')\n", "\n", "for face in [('K','D','C')]:\n", " print(f'{face}: {round(face_g[face],2)}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As with the `EmbeddedGraph` class, we can initialize the `ECT` class by deciding how many directions and how many thresholds to use. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "myect = ECT(num_dirs = 100,num_thresh = 80)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we can compute the ECC for a single direction. In this case, the $x$-axis will be computed for the `num_thresh=80` stopping points in the interval $[-1.2r,1.2r]$ where $r$ is the minimum bounding radius for the input complex. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", " 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3,\n", " 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1,\n", " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1,\n", " -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = K.get_bounding_radius()\n", "myect.calculateECC(K,0,1.2*r)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But of course it's easier to see this in a plot. This command calculates the ECC and immediately plots it. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "myect.plotECC(K,theta,1.2*r)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, we can compute the ECT and return the matrix. We make sure to internally set the bounding radius to use to control the $y$ axis of the plot. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0., 0., 0., ..., -1., -1., -1.],\n", " [ 0., 0., 0., ..., -1., -1., -1.],\n", " [ 0., 0., 0., ..., -1., -1., -1.],\n", " ...,\n", " [ 0., 0., 0., ..., -1., -1., -1.],\n", " [ 0., 0., 0., ..., -1., -1., -1.],\n", " [ 0., 0., 0., ..., -1., -1., -1.]])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "myect.set_bounding_radius(1.2*r)\n", "myect.calculateECT(K)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once it's been computed, we can use the internal plotting function to take a look." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.841874542459709\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "myect.plotECT()\n", "print(myect.bound_radius)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly we can take a look at the SECT. This one was computed when we asked to compute the ECT. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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