{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial : ECT for embedded graphs \n",
    "\n",
    "This jupyter notebook will walk you through using the `ect` package to compute the Euler characteristic transform of a 2D embedded graph. This tutorial assumes you already know what an ECT is; see [this paper](https://arxiv.org/abs/2310.10395) for a more thorough treatment of details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ect import ECT, EmbeddedGraph, create_example_graph\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constructing the embedded graph\n",
    "\n",
    "We assume our input is an undirected graph $G$ with an embedding in 2D given by a map on the vertices $f: V(G) \\to \\mathbb{R}^2$. A graph can be constructed as follows. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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y+NtGpEJs0ZXFESeRynAWXXkMTiIVYYueHGzViVSELXpycMRJpBJs0ZOHwUmkAmzRk4utOpEKsEVPLo44iTIcW/TkY3ASZTC26KnBVp0og7FFTw2OOIkyFFv01GFwEmUgtuipxVadKAOxRU8tjjiJMgxb9NRjcBJlELbo6YGtOlEGYYueHjjiJMoQbNHTB4OTKAMEW/ScnBy26GmArTpRBmCLnl444iRKc2zR0w+DkyiNsUVPT2zVidIYW/T0xBEnUZpii56+GJxEaYgtenpjq06UhtiipzeOOInSDFv09MfgJEojbNEzA1t1ojTCFj0zcMRJlCbYomcOBidRGmCLnlnYqhOlAbbomYUjTqIUY4ueeRicRCnEFj0zsVUnSiGpLbrH68N5pwcDvgCyDTpMsphhNvJ/42Tj3zhRisTaord1uvHqCQcaz3TB0dMPccgyAYC9wITqaVY8WGlHybhcxesmBidRSsTSonf09GNTfTOOtndDrxPgD4gj1hEBXOjpx54TF/DKn85jXnEhapaXw1ZgUvgbaBvPcRKlQLBFf/nll0O26HVNDix84TCOnXUCQMjQHCq4/NhZJxa+cBh1TQ7Za6brOOIkSrJoLfr2xjZs298a1779ARH+gIhnftOM7j4v1laXJFouhcARJ1ESRWvR65occYfmjbbtb8UvOfJUBEecREkUaRa9o6cfmxtaQm7Xd/ognH/4cchleV9YjpsWPBJy2Q8aWlA1tZDnPGXG4CRKkmgt+qb6ZviinMu0LHkSWZYJw36mzykIu74vIGJTfTP2PFIZX9EUEoOTKAmitehtnW4cbe+Oup+ssRNhHB/7eUt/QMTR9m60d7lRbOWlSnKRdI5zy5YtEARh2Ofmm29WqjYi1Yg2i/7qCQf0OkGRY+t1AvYe57lOOUmeHCorK8PFixcHP83NzUrURaQasVzo3nimK+olRwAAMQAx4B/2icYfENHY2iW1bIpAcqtuMBg4yiSKUSwXuvd5fXD09Me0v0u7vzfiZ/b/9ToEnT7idg5nPzxeH2/PlInkv8W2tjYUFRXBaDSisrISNTU1mDJlStj1vV4vvF7v4J9dLld8lRJloJ///OdR70W/4PQghrEmAMCydAOyLLZhP4sWmsC1O4zOOz0oK8qP8UgUiaRWvbKyErt37x48V3Pp0iVUVVXB6XSG3aa2thb5+fmDH5vNFnZdIjXp6OjAhg0bot6LPuALxLzPLIsNxvElwz6xknIcikxScC5evBhf//rXUV5ejoULF+L3v/89AOAXv/hF2G02btyI3t7ewU9HR0diFRNlACmPi8s2JOc+lGQdRwsSOuFhNptRXl6Otra2sOsYjUYYjcZEDkOUcWJp0YMmWcwQgJjb9XgInx2H5JHQP0FerxcffPABxo8fL1c9RBkv1hY9yGw0wK7wnT12i4kTQzKSFJxPPfUUDh8+jHPnzuHEiRP4xje+AZfLhdWrVytVH1FGifeJ7tXTrIpex1ldalVk31ol6Z+gv/71r/jWt76F7u5ujB07FrNnz8bx48cxceJEpeojyihSWvShHqy045U/nQ+7PKdiIXIqFsZVkz8gYtVse1zbUmiSgrOurk6pOogyntQWfaiScbmYV1yIY2edsV0IHyO9TkDVFAtvt5QZp9mIZCDHS9dqlpfDIHO7btAJqFleLus+icFJJItgix7uXvRY2ApMeHZZmax1PbesjI+UUwCDkyhBibToN1o5y46nFpXKUtf3F03Dilk8t6kEXp9AlAAl3ou+troEhTlGbG5oge+zV2HESq8TYNAJeG5ZGUNTQQxOogTEO4sezcpZdsydWhj1LZdBweVVUyx8y2USMDiJ4iRnix6KrcCEPY9UXn+vemsXHM4Q71W3mFBdasWq2XbOnicJg5MoDkq06OGUjMvFlmVl2IIyeLw+7PvjKfzdqr/Ha3t346tz7+AdQSnAv3GiOCjVokdjNhoweUwWBi62YvKYLIZminBWnUgipVt0Sn8MTiIJktmiU/riOJ9IglS16JReOOIkihFbdApicBLFgC06DcVWnSgGbNFpKI44iaJgi043YnASRcAWnUJhq04UAVt0CoUjTqIw2KJTOAxOohDYolMkbNWJQmCLTpFwxEl0A7boFA2Dk2gItugUC7bqREOwRadYcMRJ9Bm26BQrBicR2KKTNGzVicAWnaThiJM0jy06ScXgJE1ji07xYKtOmsYWneLBESdpFlt0iheDkzSJLTolgq06aRJbdEoER5ykOWzRKVEMTtIUtugkB7bqpCls0UkOHHGSZrBFJ7kwOEkT2KKTnNiqkyawRSc5ccRJqscWneTG4CRVY4tOSmCrTqrGFp2UwBEnZSSP14dzn15F9vhSnPv0Kjxe34h12KKTUjjipIzR1unGqyccaDzTBUdPP0QA41f/G753oBtPHXgT9gITqqdZ8WClHcXWHLbopBgGJ6W9jp5+bKpvxtH2buh1AvwBccQ6IoALPf3Yc+ICXvnTeUwZ7cXR4+/i9dd+zhadZMfgpLRW1+TA5oYW+D4Ly1ChOVRw+YceA2yP74Rr7AzFayTtYXBS2tre2IZt+1vj2lbQ6REA8MxvmtHd58Xa6hJ5iyNN4+QQpaW6JkfcoXmjbftb8csmhyz7IgI44qQ01NHTj80NLSGX9Z0+COcffjzsZ7rRecgqtCOv8n6Yir8QcrsfNLSgamohbAUmucslDeKIk9LOpvrmwXOa4ViWPImbv70NN3/7X2H56loIOh3+9p/Pob/tRMj1fQERm+qblSiXNIjBSWmlrdONo+3dUSeBssZOhPGWW2G85TaYplVh7Dc2A/oseD44EnJ9f0DE0fZutHe5lSibNCah4KytrYUgCHjyySdlKoe07tUTDuh1guTtBEM2BL0Bgk4fdh29TsDe4zzXSYmLOzibmpqwc+dOVFRUyFkPaVzjma6oo00AgBiAGPBD9Pvgc3Xjk4M7IV71wjx9fthN/AERja1dMlZLWhXX5FBfXx8efPBBvPzyy3j++eflrok0qs/rg6OnP6Z1L+3+3vAf6LNQcPfjGD3ljojbOZz98Hh9MBs5L0rxi+u3Z82aNbjnnnuwcOHCqMHp9Xrh9XoH/+xyueI5JGnABacHMYw1AQCWpRuQZbEBAAKXXehv/RN69u+AKPqRd8e9YbcTAZx3elBWlJ94waRZkoOzrq4O77zzDpqammJav7a2Fs8++6zkwkh7BnyBmNfNsthgHH/9ovbRU+6Ar7cLnza+gpyyauhG5chyHKJQJJ3j7OjowBNPPIG9e/di1KhRMW2zceNG9Pb2Dn46OjriKpTUL9uQ2EUe2dZJEH1eXO35SNHjEEkacZ46dQpdXV24447r55H8fj+OHDmC7du3w+v1Qq8fPqtpNBphNBrlqZZUbZLFDAGIuV2/0UDnOQCAzhS+DRc+Ow5RIiQF51133YXm5uEXEX/nO9/BrbfeiqeffnpEaBJJYTYaYC8w4UIME0RX/3YBCPgBAP7LbvS3HsOV8/+N0aVzkDXm5rDb2S0mTgxRwiT9BuXm5mLGjOFPmzGbzbBYLCN+ThSP6mlW7DlxIeolSUNvuxSMZhjyx+GmBY8i9/P3hN1GrxNQXWqVq1TSMP7TS2nlwUo7XvnT+bDLcyoWIqdiYVz79gdErJptj7MyousSDs5Dhw7JUAbRNSXjcjGvuBDHzjpjuxA+RnqdgKopFhRbc2XbJ2kXpxcp7dQsL4chjtsuIzHoBNQsL5d1n6RdDE5KO7YCE9bMHivrPr+/YCIfKUeyYXBS2mlvb8e/Pr4c+pY/yLK/qyd/jX9/YiW6u7tl2R8Rg5PSSnt7O6qrq2EymfD2S/+CrfeXw2jQSX5ikl4nwGjQ4Uf3l+PAi0+hs7MTCxYsYHiSLBiclDaGhuahQ4cwfvx4rJxlx8H181E1xQIAUQM0uLxqigUH18/Hill2TJ8+HY2NjQxPkg0vR6K0ECo0g2wFJux5pPL6e9Vbu+Bw9g+7w0jAtYvbq0utWDXbPmL2PBie1dXVWLBgAd566y0UFhYm58uR6jA4KeUiheZQJeNysWVZGbagDB6vD+edHgz4Asg26DDJYo56RxDDk+TCVp1SKtbQvJHZaEBZUT5m2m9CWVF+zLdRsm0nOTA4KWXiDc1EMTwpUQxOSolUhWYQw5MSweCkpEt1aAYxPCleDE5KqnQJzSCGJ8WDwUlJk26hGcTwJKkYnJQU6RqaQQxPkoLBSYpL99AMYnhSrBicpKhMCc0ghifFgsFJism00AxieFI0DE5SRKaGZhDDkyJhcJLsMj00gxieFA6Dk2SlltAMYnhSKAxOko3aQjOI4Uk3YnCSLNQamkEMTxqKwUkJU3toBjE8KYjBSQnRSmgGMTwJYHBSArQWmkEMT2JwUly0GppBDE9tY3CSZFoPzSCGp3YxOEkShuZwDE9tYnBSzBiaoTE8tYfBSTFhaEbG8NQWBidFxdCMDcNTOxicFBFDUxqGpzYwOCkshmZ8GJ7qx+CkkBiaiWF4qhuDk0ZgaMqD4aleDE4ahqEpL4anOjE4aRBDUxkMT/VhcBIAhqbSGJ7qwuAkhmaSMDzVg8GpcQzN5GJ4qgODU8MYmqnB8Mx8DE6NYmimVrzh6fH6cO7Tq8geX4pzn16Fx+tTuFIKRRBFUUzmAV0uF/Lz89Hb24u8vLxkHpo+w9BMH++//z6qq6sxbtw4vPXWWygsLByxTlunG6+ecKDxTBccPf0Y+j+sAMBeYEL1NCserLSjZFxu0mpXGynZxODUGIZm+gkXnh09/dhU34yj7d3Q6wT4A+H/Vw0un1dciJrl5bAVmJJVvmpIySa26hrC0ExPodr2uiYHFr5wGMfOOgEgYmgOXX7srBMLXziMuiaH4nVrGUecGsHQTH/BkeeYuSvgnfaVhPf31KJSrK0ukaEybeCIk4ZhaGaG6dOn4+mdDbKEJgBs29+KX3LkqQhDqgsgZTE0M0dHTz9eOtkTclnf6YNw/uHHYbcd960ajJpYMeLnP2hoQdXUQp7zlBmDU8UYmpllU30zfFHOZVqWPIksy4QRP88qtIdc3xcQsam+GXseqZSlRrqGwalSDM3M0tbpxtH26NdyZo2dCOP42M9b+gMijrZ3o73LjWIrL1WSi6RznDt27EBFRQXy8vKQl5eHOXPm4I033lCqNooTQzPzvHrCAb1OUGTfep2Avcd5rlNOkoJzwoQJ2Lp1K06ePImTJ09iwYIF+NrXvoaWlhal6iOJGJqZqfFMV9RLjgAAYgBiwD/iE4k/IKKxtUumSgmQ2Krfe++9w/78wx/+EDt27MDx48dRVlYma2EkHUMzM/V5fXD09Me07qXd3xv5Q0GHiU83RNzO4eyHx+uD2cizc3KI+2/R7/fjV7/6FTweD+bMmRN2Pa/XC6/XO/hnl8sV7yEpAoZm5rrg9CDWi6ktSzcgy2Ib/kMheosvAjjv9KCsKF9yfTSS5OBsbm7GnDlzcOXKFeTk5KC+vh7Tp08Pu35tbS2effbZhIqkyBiamW3AF4h53SyLTdLkULzHocgkXwA/bdo0vPvuuzh+/Dj+6Z/+CatXr8b7778fdv2NGzeit7d38NPR0ZFQwTQcQzPzZRuScx9Kso6jBZJHnNnZ2SguLgYA3HnnnWhqasKLL76Il156KeT6RqMRRqMxsSopJIamOkyymCEAMbfr8RA+Ow7JI+EzxaIoDjuHScnB0FQPs9EAe4EJF2KYILr6twtAiFl0w03joTeFP39pt5g4MSQjSX+TmzZtwuLFi2Gz2eB2u1FXV4dDhw5h3759StVHITA01ad6mhV7TlyIeklSuNsuCxavQ+7toe9x1+sEVJdaEy2RhpAUnJ2dnfj2t7+NixcvIj8/HxUVFdi3bx/uvvtupeqjGzA01enBSjte+dP5sMtzKhYip2JhXPv2B0Ssmh36lkyKj6Tg/NnPfqZUHRQDhqZ6lYzLxbziQhw764ztQvgY6XUCqqZYeLulzDjNliEYmupXs7wcBplvuzToBNQsL5d1n8TgzAgMTW2wFZjw7DJ578B7blkZHymnAAZnmmNoasvKWXY8tahUln19f9E0rJjFc5tK4PUJaYyhqU1rq0tQmGPE5oYW+AKipHOeep0Ag07Ac8vKGJoK4ogzTTE0tW3lLDsOrp+PqikWAIj6yLng8qopFhxcP5+hqTCOONMQQ5OAa+c89zxSef296q1dcDhDvFfdYkJ1qRWrZts5e54kfMtlmmFoUiQerw/nnR4M+ALINugwyWLmHUEykZJN/BtPIwxNisZsNPDRcGmA5zjTBEOTKHMwONMAQ5MoszA4U4yhSZR5GJwpxNAkykwMzhRhaBJlLgZnCjA0iTIbgzPJGJpEmY/BmUQMTSJ1YHAmCUOTSD0YnEnA0CRSFwanwhiaROrD4FQQQ5NInRicCmFoEqkXg1MBDE0idWNwyoyhSaR+DE4ZMTSJtIHBKROGJpF2MDhlwNAk0hYGZ4IYmkTaw+BMAEOTSJsYnHFiaBJpF4MzDgxNIm1jcErE0CQiBqcEDE0iAhicMWNoElEQgzMGDE0iGorBGQVDk4huxOCMgKFJRKEwOMNgaBJROAzOEBiaRBQJg/MGDE0iiobBOQRDk4hiweD8DEOTiGJlSHUBcvN4fTjv9GDAF0C2QYdJFjPMxshfk6FJRFKoIjjbOt149YQDjWe64OjphzhkmQDAXmBC9TQrHqy0o2Rc7rBtGZpEJJUgiqIYfTX5uFwu5Ofno7e3F3l5eQntq6OnH5vqm3G0vRt6nQB/IPxXCS6fV1yImuXlsBWYGJpENEhKNmXsiLOuyYHNDS3wfRaWkUJz6PJjZ51Y+MJhrJk9Fv/6+HKGJhFJlpGTQ9sb2/DMb5rh9QWiBuaN/AERXl8A//Z2J7JnLmNoEpFkGRecdU0ObNvfKsu+/GVLcOSvV2XZFxFpR0YFZ0dPPzY3tERdz3WyARe2LsXHP/3nqOv+oKEFHT39cpRHRBqRUcG5qb558JxmJH2nDwAArnY74P34TMR1fQERm+qbZamPiLQhY4KzrdONo+3dUc9pei+24WrXOYyeOgsA0PeX/RHX9wdEHG3vRnuXW7ZaiUjdJAVnbW0tZs2ahdzcXFitVtx33304cybyiE4ur55wQK8Toq7Xd/paUI758moYb7kNng+OIHD1SsRt9DoBe487ZKmTiNRPUnAePnwYa9aswfHjx3HgwAH4fD4sWrQIHo9HqfoGNZ7pijraDFz1wvP+EWSPL0H22EkwV9wNceAy+v/njxG38wdENLZ2yVkuEamYpOs49+3bN+zPu3btgtVqxalTp/ClL31J1sKG6vP64IhhAqf/zB8hej3IqVgEADDfNg+f/NfL6PvLfuSU3xVxW4ezHx6vL+rtmURECZ3j7O3tBQAUFBSEXcfr9cLlcg37SHXB6UEsV2v2/WU/BIMR5tuuhbguezRM0+bC+9cWXO35KOK2IoDzTuVHzkSU+eIOTlEUsWHDBnzxi1/EjBkzwq5XW1uL/Pz8wY/NZpN8rAFfIOo6Vz/5GN6OFoyeeicAEYErfQhc6YP51rkArs+0J3ocIqK4+9K1a9fi9OnTePvttyOut3HjRmzYsGHwzy6XS3J4Zhui5/u1YBTRf+aP6D8z8pym5723MOZL34ag0yd0HCKiuIJz3bp1aGhowJEjRzBhwoSI6xqNRhiNxriKC5pkMUMAwrbrYsAPT/N/wTBmPCyL141YfvnDJrj+XI/LZ0/BVPyFkPsQPjsOEVE0koJTFEWsW7cO9fX1OHToECZPnqxUXcOYjQbYC0y4EGaC6PLZU/D39WDMlx/CqIkVI5ZnjZ0I16nfoe8v+8MGp91i4sQQEcVEUm+6Zs0a7N27F6+99hpyc3Nx6dIlXLp0CZcvX1aqvkHV06xhr+Ps+8t+QG9ATsXdIZfrTfkwlc7B5Q+b4Pd8MnK5TkB1qVXWeolIvSQ9j1MQQgfXrl278NBDD8W0j3ifx9nW6cbdPz4S8/pSHVz/JRRbc6OvSESqpNjzOJP8zONhSsblYl5xIY6ddUp+lFwkep2AqikWhiYRxSyjppFrlpfDEMNtl1IYdAJqlpfLuk8iUreMCk5bgQnPLiuTdZ/PLSuDrcAk6z6JSN0yKjgBYOUsO55aVCrLvr6/aBpWzLLLsi8i0o6MvP5mbXUJCnOMg+8cknLOU68TYNAJeG5ZGUOTiOKScSPOoJWz7Di4fj6qplgAIOoj54LLq6ZYcHD9fIYmEcUtI0ecQbYCE/Y8Unn9veqtXXA4Q7xX3WJCdakVq2bbOXtORAnL6Peqh+Lx+nDe6cGAL4Bsgw6TLGbeEUREUWniverhmI0GlBXlp7oMIlKxjD3HSUSUKgxOIiKJGJxERBIxOImIJGJwEhFJxOAkIpKIwUlEJBGDk4hIIgYnEZFEDE4iIokYnEREEjE4iYgkYnASEUnE4CQikojBSUQkEYOTiEiipD/IOPjAeZfLlexDExGFFcykWF6KkfTgdLvdAACbzZbsQxMRReV2u5GfH/ktEkl/51AgEMDHH3+M3NxcCELkN1PGy+VywWazoaOjQ5H3GqUjfmdtfGdAm987Gd9ZFEW43W4UFRVBp4t8FjPpI06dTocJEyYk5Vh5eXma+cUK4nfWDi1+b6W/c7SRZhAnh4iIJGJwEhFJpMrgNBqN2Lx5M4xGY6pLSRp+Z+3Q4vdOt++c9MkhIqJMp8oRJxGRkhicREQSMTiJiCRicBIRSaSq4Dxy5AjuvfdeFBUVQRAE/Pa3v011SYqrra3FrFmzkJubC6vVivvuuw9nzpxJdVmK2rFjByoqKgYvhp4zZw7eeOONVJeVVLW1tRAEAU8++WSqS1HMli1bIAjCsM/NN9+c6rIAqCw4PR4Pbr/9dmzfvj3VpSTN4cOHsWbNGhw/fhwHDhyAz+fDokWL4PF4Ul2aYiZMmICtW7fi5MmTOHnyJBYsWICvfe1raGlpSXVpSdHU1ISdO3eioqIi1aUorqysDBcvXhz8NDc3p7qka0SVAiDW19enuoyk6+rqEgGIhw8fTnUpSXXTTTeJP/3pT1NdhuLcbrdYUlIiHjhwQJw/f774xBNPpLokxWzevFm8/fbbU11GSKoacRLQ29sLACgoKEhxJcnh9/tRV1cHj8eDOXPmpLocxa1Zswb33HMPFi5cmOpSkqKtrQ1FRUWYPHkyVq5cibNnz6a6JAApeMgHKUcURWzYsAFf/OIXMWPGjFSXo6jm5mbMmTMHV65cQU5ODurr6zF9+vRUl6Wouro6vPPOO2hqakp1KUlRWVmJ3bt3o7S0FJ2dnXj++edRVVWFlpYWWCyWlNbG4FSRtWvX4vTp03j77bdTXYripk2bhnfffReffvopfv3rX2P16tU4fPiwasOzo6MDTzzxBPbv349Ro0alupykWLx48eB/l5eXY86cOZg6dSp+8YtfYMOGDSmsjMGpGuvWrUNDQwOOHDmStMf2pVJ2djaKi4sBAHfeeSeamprw4osv4qWXXkpxZco4deoUurq6cMcddwz+zO/348iRI9i+fTu8Xi/0en0KK1Se2WxGeXk52traUl0KgzPTiaKIdevWob6+HocOHcLkyZNTXVJKiKIIr9eb6jIUc9ddd42YUf7Od76DW2+9FU8//bTqQxMAvF4vPvjgA8ybNy/VpagrOPv6+tDe3j7453PnzuHdd99FQUEB7HZ7CitTzpo1a/Daa6/h9ddfR25uLi5dugTg2gNZR48eneLqlLFp0yYsXrwYNpsNbrcbdXV1OHToEPbt25fq0hSTm5s74ry12WyGxWJR7fnsp556Cvfeey/sdju6urrw/PPPw+VyYfXq1akuTV2XIzU2NooARnxWr16d6tIUE+r7AhB37dqV6tIU8/DDD4sTJ04Us7OzxbFjx4p33XWXuH///lSXlXRqvxxpxYoV4vjx48WsrCyxqKhIvP/++8WWlpZUlyWKoijysXJERBLxOk4iIokYnEREEjE4iYgkYnASEUnE4CQikojBSUQkEYOTiEgiBicRkUQMTiIiiRicREQSMTiJiCRicBIRSfT/AcYZ1ZVVEwWaAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Construct an example graph \n",
    "# Note that this is the same graph that is returned by:\n",
    "# G = create_example_graph()\n",
    "\n",
    "G = EmbeddedGraph()\n",
    "\n",
    "G.add_node('A', 1, 2)\n",
    "G.add_node('B', 3, 4)\n",
    "G.add_node('C', 5, 7)\n",
    "G.add_node('D', 3, 6)\n",
    "G.add_node('E', 4, 3)\n",
    "G.add_node('F', 4, 5)\n",
    "\n",
    "G.add_edge('A', 'B')\n",
    "G.add_edge('B', 'C')\n",
    "G.add_edge('B', 'D')\n",
    "G.add_edge('B', 'E')\n",
    "G.add_edge('C', 'D')\n",
    "G.add_edge('E', 'F')\n",
    "\n",
    "G.plot()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coordinates of all vertices, given as a dictionary, can be accessed using the `coordinates` attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': (1, 2), 'B': (3, 4), 'C': (5, 7), 'D': (3, 6), 'E': (4, 3), 'F': (4, 5)}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.coordinates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the rotational aspect of the ECT, we often want our graph to be centered, so you can use the `set_mean_centered_coordinates` method shift the graph to have the average of the vertex coordinates be 0. Note that this does overwrite the coordinates of the points. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'A': (-2.0, -2.5), 'B': (0.0, -0.5), 'C': (2.0, 2.5), 'D': (0.0, 1.5), 'E': (1.0, -1.5), 'F': (1.0, 0.5)}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G.set_centered_coordinates(type = 'min_max')\n",
    "print(G.coordinates)\n",
    "G.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get a bounding radius we can use the `get_bounding_radius` method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The radius of bounding circle centered at the origin is 3.2015621187164243\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This is actually getting the radius \n",
    "r = G.get_bounding_radius()\n",
    "print(f'The radius of bounding circle centered at the origin is {r}')\n",
    "\n",
    "# plotting the graph with it's bounding circle of radius r.\n",
    "G.plot(bounding_circle=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also rescale our graph to have unit radius using `rescale_to_unit_disk`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The radius of bounding circle centered at the origin is 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G.rescale_to_unit_disk(preserve_center=False)\n",
    "G.plot(bounding_circle=True)\n",
    "\n",
    "r = G.get_bounding_radius()\n",
    "print(f'The radius of bounding circle centered at the origin is {r}')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Directions are given in the code by specifying $\\theta \\in [0,2\\pi]$. We often convert this to $\\omega \\in \\mathbb{S}^1$ by defining the unit vector $\\omega = (\\cos(\\theta), \\sin(\\theta))$. Then the function $g_\\omega$ is defined on the vertices of $G$ by taking the dot product of the embedding coordinates with the unit vector, specifically\n",
    "$$\n",
    "g_\\omega(v) = \\langle f(v), \\omega\\rangle.\n",
    "$$\n",
    "This is done in the code using the `g_omega` method as shown. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.11043152607484681,\n",
       " 'B': 0.11043152607484658,\n",
       " 'C': -0.11043152607484681,\n",
       " 'D': -0.3312945782245397,\n",
       " 'E': 0.5521576303742327,\n",
       " 'F': 0.11043152607484646}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This gives the function value of the nodes as a dictionary\n",
    "G.g_omega(theta = 7*np.pi/4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This input to the plotting function will color the nodes by function value.\n",
    "G.plot(color_nodes_theta=7*np.pi/4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here's an example in another direction.\n",
    "G.plot(color_nodes_theta=np.pi/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the ECT of $G$\n",
    "\n",
    "Now we can set up the ECT for the embedded graph. The ECT is defined as \n",
    "$$\n",
    "\\begin{matrix}\n",
    "\\text{ECT}(G): & \\mathbb{S}^1 & \\to & \\text{Func}(\\mathbb{R}, \\mathbb{Z})\\\\\n",
    "& \\omega & \\mapsto & \\{ a \\mapsto \\chi(g_\\omega^{-1}(-\\infty,a]) \\}\n",
    "\\end{matrix}\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "When we initialize the `ECT` object, we specify the number of directions in $\\mathbb{S}^1$ to use with `num_dir`, and the number of thresholds at which to compute the Euler characteristic by `num_thresh`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directions chosen are: [0.         0.39269908 0.78539816 1.17809725 1.57079633 1.96349541\n",
      " 2.35619449 2.74889357 3.14159265 3.53429174 3.92699082 4.3196899\n",
      " 4.71238898 5.10508806 5.49778714 5.89048623]\n",
      "Thresholds chosen are: None\n"
     ]
    }
   ],
   "source": [
    "myect = ECT(num_dirs = 16, num_thresh=20)\n",
    "\n",
    "# The ECT object will automatically choose the directions. \n",
    "print(f'Directions chosen are: {myect.thetas}')\n",
    "\n",
    "# However, because a bounding radius hasn't been chosen yet, the thresholds are not yet set.\n",
    "print(f'Thresholds chosen are: {myect.threshes}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can set the bounding radius as follows. Note that some methods will automatically set `bound_radius` to be the bounding radius of the input `G` if not already set. I'm choosing the radius to be a bit bigger than the bounding radius of `G` to make some better pictures. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Internally set radius is: 1.2\n",
      "Thresholds chosen are: [-1.2        -1.07368421 -0.94736842 -0.82105263 -0.69473684 -0.56842105\n",
      " -0.44210526 -0.31578947 -0.18947368 -0.06315789  0.06315789  0.18947368\n",
      "  0.31578947  0.44210526  0.56842105  0.69473684  0.82105263  0.94736842\n",
      "  1.07368421  1.2       ]\n"
     ]
    }
   ],
   "source": [
    "myect.set_bounding_radius(1.2 * G.get_bounding_radius())\n",
    "\n",
    "print(f'Internally set radius is: {myect.bound_radius}')\n",
    "\n",
    "# Now the thresholds are set.\n",
    "print(f'Thresholds chosen are: {myect.threshes}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want the Euler characteristic curve for a fixed direction, we use the `calculateECC` function. This outputs a list of integers where each corresponds to $\\chi(f_\\omega^{-1}(-\\infty,a])$ for the $a$ values in `myect.threshes`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myect.calculateECC(G, np.pi/2,bound_radius=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This can also be calculated on the fly and plotted using the `plotECC` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myect.plotECC(G, -np.pi/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To calculate the full ECT, we call the `calculateECT` method. This matrix is size `myect.num_dirs x myect.num_thresh`. Once computed, it is stored in the `ECT` class as `ECT.matrix`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(16, 20)\n",
      "16 20\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myect.calculateECT(G)\n",
    "\n",
    "# The matrix is passed as an output above but is also saved internally. Get the saved matrix\n",
    "M = myect.get_ECT()\n",
    "\n",
    "print(M.shape)\n",
    "print(myect.num_dirs, myect.num_thresh)\n",
    "\n",
    "# We can use the built in command to plot the matrix. Unlike the plotECC function, this command does not calculate the ECT when called so it must have been run earlier. An equivalent command is myect.plotECT()\n",
    "myect.plot('ECT')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SECT \n",
    "\n",
    "The Smooth Euler Characteristic Transform (SECT) can be calculated from the ECT. Fix a radius $R$ bounding the graph. The average ECT in a direction $\\omega$ defined on function values $[-R,R]$ is given by\n",
    "$$\\overline{\\text{ECT}_\\omega} = \\frac{1}{2R} \\int_{t = -R}^{R} \\chi(g_\\omega^{-1}(-\\infty,t]) \\; dt. $$\n",
    "Then the SECT is defined by \n",
    "$$\n",
    "\\begin{matrix}\n",
    "\\text{SECT}(G): & \\mathbb{S}^1 & \\to & \\text{Func}(\\mathbb{R}, \\mathbb{Z})\\\\\n",
    "& \\omega & \\mapsto & \\{ t \\mapsto \\int_{-R}^t \\left( \\chi(g_\\omega^{-1}(-\\infty,a]) -\\overline{\\text{ECT}_\\omega}\\right)\\:da \\}\n",
    "\\end{matrix}\n",
    "$$\n",
    "\n",
    " defined from the \n",
    "TODO: Write intro "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can calculate the SECT directly using the `calculateSECT` method. Note that this both returns the function and sets the SECT internally to the `SECT_matrix` attribute. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(16, 20)\n"
     ]
    }
   ],
   "source": [
    "M_SECT = myect.calculateSECT()\n",
    "print(M_SECT.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However this is not technically necessary since, as a default, the SECT was also set internally when the ECT matrix was computed. If you don't want to calculate the SECT at the same time as calculating the ECT, you can use the following command instead.\n",
    "```python\n",
    "myect.calculateECT(G, compute_SECT=False)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also use the internally set plotting functions to easily visualize it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myect.plot('SECT')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}