{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Object reconstruction from a cloud of points in 2D using $\\alpha$-shapes and Vietoris-Rips complexes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will generate a cloud of points in 2D space, in our example a circle. Then Vietoris-Rips, Chech and $\\alpha$-complexes for the given radius will be constructed. \n", "\n", "The number of simplices for each construction will be determined and the resulting complex drawn using matplotlib.\n", "\n", "Let us start with Vietoris-Rips and $\\alpha$ complexes, since we can calculate them from Python. First some basic imports and helper functions." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false }, "tags": [] }, "outputs": [], "source": [ "import dionysus\n", "import math\n", "from random import random\n", "from matplotlib import pyplot\n", "import numpy as np\n", "import time\n", "import diode" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we define methods for generating a cloud of points and drawing." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [] }, "outputs": [], "source": [ "def generate_circle(n, radius, max_noise):\n", " \"\"\"\n", " Generate n points on a sphere with the center in the point (0,0) \n", " with the given radius. \n", " \n", " Noise is added so that the distance from\n", " the generated point to some point on the sphere does not\n", " exceed max_noise parameter.\n", " \n", " Returns the list of generated points. \n", " \"\"\"\n", " points = []\n", " for i in range(n):\n", " angle = 2 * math.pi * random()\n", " noise = max_noise * random()\n", " r = radius * (1 + noise)\n", " point = [r * math.cos(angle), r * math.sin(angle)]\n", " points.append(point)\n", " return points" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "tags": [] }, "outputs": [], "source": [ "def plot_points(points, figure=None, radius=0, color='r'):\n", " \"\"\"\n", " Plot the given list of points on the given figure using matplotlib. \n", " If figure is not specified plot on the current figure.\n", " \n", " If radius is bigger than zero, then around each\n", " point the ball centered in the point with the \n", " given radius and color will be drawn. If color is not given \n", " circles are drawn using red color.\n", " \"\"\"\n", " xs, ys = map(list, zip(*points))\n", " pyplot.axis([min(xs)-1, max(xs)+1,min(ys)-1,max(ys)+1])\n", " pyplot.plot(xs, ys, 'ro')\n", " if radius > 0:\n", " if figure is None:\n", " figure = pyplot.gcf()\n", " axes = figure.gca()\n", " for circle in [pyplot.Circle(point, radius, color=color)\n", " for point in points]:\n", " axes.add_artist(circle)" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "tags": [] }, "outputs": [], "source": [ "def get_points(points, indices):\n", " '''\n", " Get data from point array on the given indices.\n", " Useful since simplex spanned by a list of points\n", " is given as a list of positions of the points\n", " in a points array.\n", " '''\n", " return [points[index] for index in indices]\n", "\n", "def draw_triangle(triangle):\n", " '''\n", " Draw a triangle on the current figure. \n", " Triangle must be given as a list of three 2D points, \n", " each point as a list of two numbers.\n", " '''\n", " p1, p2, p3 = triangle\n", " pyplot.plot([p1[0], p2[0]],[p1[1],p2[1]])\n", " pyplot.plot([p1[0], p3[0]],[p1[1],p3[1]])\n", " pyplot.plot([p2[0], p3[0]],[p2[1],p3[1]])\n", " \n", "def draw_line(line):\n", " '''\n", " Draw a line on the current figure.\n", " Line must be given as a list of two 2D points, \n", " each point as a list of two numbers. \n", " '''\n", " p1, p2 = line\n", " pyplot.plot([p1[0], p2[0]],[p1[1],p2[1]])\n", " \n", "def draw_point(point):\n", " '''\n", " Draw a point on the current figure.\n", " Point must be given as a list of two numbers. \n", " '''\n", " pyplot.plot(point)\n", "\n", "def draw_simplicial_complex(simplices, points):\n", " '''\n", " Draw 2D simplicial complex on the current figure. \n", " Input must be a list of simplices, each simplex a\n", " list of indices in the points array. \n", " '''\n", " handlers = [draw_point, draw_line, draw_triangle]\n", " for simplex in simplices:\n", " handlers[len(simplex)-1](get_points(points, simplex))" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "circle = generate_circle(70, 3, 0.1)\n", "plot_points(circle, color=\"r\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now construct $\\alpha$-shapes and Vietoris-Rips complex from this cloud of points." ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false }, "tags": [] }, "outputs": [], "source": [ "def rips(points, skeleton, max):\n", " \"\"\"\n", " Generate the Vietoris-Rips complex on the given set of points in 2D.\n", " Only simplexes up to dimension skeleton are computed.\n", " The max parameter denotes the distance cut-off value.\n", " \"\"\"\n", " print(time.asctime(), \"Starting Rips complex generation.\")\n", " rips = dionysus.fill_rips(np.array(points), skeleton, max)\n", " print(time.asctime(), \"Generated complex: %d simplices\" % len(rips))\n", " return rips" ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sat Nov 25 16:01:49 2023 Starting Rips complex generation.\n", "Sat Nov 25 16:01:49 2023 Generated complex: 2899 simplices\n" ] }, { "data": { "image/png": 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UDjf9sJWBixCNYvruuxF78MG6+V+x/fuRGRsz5cmEKIo4efIkRkdHwRno9WuaI7Jv3z5s2bIFXq8X/f39uO666/Dxxx9r+ZSakLvfTkxMUBBSRzPb9Fra0tdkTgkhRHut7rKxzsxg8K/+qnH+17naJKuYJKdE7mNjpBl5TWdE3njjDezatQtbtmxBqVTCN7/5TXz2s5/Fhx9+CLfbreVTt00ymcTU1JTew9CfiuWNZj6IWv3QamfhJrJ2DMPAZrPB6XQq08WCIIDnefA8T/lTJtJoprJStTYLjCTVTXKt1ExNISN+FuTzeRw5cgRerxd+vx9er7enZ0g6miMyOzuL/v5+vPHGG/j93//9hrfXM0dEzlZOJBIdfd5upPpN3o4ckWZR/kdHsSwLp9MJr9cLr9cLm81Wd1uhKIrgeR6CICgXURQhiiJKpRJEUUS5XEYXp6qRJtQqMd9ulW0YKKdkidfrRTAYhNfr7Yqtvl2brHr06FGcd955eO+993DhhReu+rl8FiXLZDIYHBzseCBSLpcxMTFh7v4v5zT7Jm9l1wzpLhzHwWazwW63w+PxwOPxwGLRZhK1XC4vC1B4nsfi4iJKpRKKxaIStJDut5ZdNCupbkypRZ+qHsdxHAKBAMLhsK5JrV0ZiJTLZXzhC19AKpXCf/7nf1a9zX333Yf7779/1fWdDEQkScLk5CQymUxHnk939WYU1vgm9x06hIH77oMlnV52+2IggLP33ktBSBfhOA5WqxV2ux1OpxNOpxN2ux0cx3XFWVUlSZJQLBaVpZ/KJaBSqUSzKt2k8nMlFAIYBpZEApZEQtXOGgkAGKZh476md9CZTDgcRiQS0ewEop6u3DWza9cuvP/++zWDEADYu3cvdp+b1gN+NyPSSbOzs6YJQhotuay1GZ3S60JlZVWydnKwwDCMcuE4DhzHwWKxwGq1LvtqsViUn7Nsb9UzlPNRbDYbPB7Pqp9Xzqo0ukiSpAQulf9e+fsEoPy+6l3kD3qe55HP55HL5ZDL5cw7i1Nrl40oIvzEEw13vE3fdRdiDz7YMP9rrX2qzCKRSGB+fh59fX3o6+vr2jySjgQit912G/793/8db775JjZs2FDzdna7HXa7vRNDqmpxcREzMzO6PX9HnDtT8b72GsJPPrnqx3LVw8mHH4arWmZ6FVXf5ByH3JVXInflla2O2PRYllVahTudTr2H07VYlgXLsrr25pBnlcLhsDKDk8/nkc/nsbCwAKGFZoyGcG7H2+Du3ZBqzHjIwUbm2mvbliBv5kaWkiRhdnYWiUQCkUgE4XC4605CNF2akSQJt99+O5577jm8/vrrOO+885q6f6eSVcvlMhKJBOItrGn2ArVrtxLDQPT7waVSNZNOK5l12lNLLMvC7/fD5/PB4/F03TIJWRtRFFEoFMDzPBYWFpDP51EqlfQeVsepraLckLx83GCGxUw5Io3YbDYMDw9rftLfNTkiX//61/HUU0/hhRdewPnnn69c7/f7VZ3ZaR2IlMtlJJNJzMzMGH4KtVbSaT21EsaUn9ObvK0sFouyFc/tdlPwYRKiKCqfQ6ba7tymHW+1duqYbddMMxiGwdDQELxer2bP0TWBSK0P0gMHDuDGG29seH8tA5F0Oo2zZ8+a42xExbbatZBAO2BaxTAMQqEQ+vv7u3b9lnSGJElIJBKYnZ01/IlRu7VthsVkotEo+vr6NDnp6Zpk1W7MYpckCfF4HHNzc3oPpWPUlF5fi8QNN9CbfI0cDgdCoRACgUDXrdcSfTAMg76+PoRCISSTSWqo2QQlQZ5qCjUlHo8rf3d6MlWvmVKphMnJSdPVB2k2Y7zRkowsOza2pvGYlcViQSAQQDAY1DUpm3Q3lmURDocRDAaVGRIKSFSgnlJrMj09DZvNpmtjWdMEIsViEcePHzdlr5hmMsblddWizwdLJqOuqRypyWq1KkmnTqeT8j6IaizLIhKJIBQKKdswTbGU3E1MUrl5amoKbrdbt+VhUwQicsdCMwYhQHM9IOS9+gAabrEz4huyVRaLBW63Gy6XC263G3a7nYIP0hKO49Df349IJIJcLod4PI7FxUW9h2V4ZupfI4oiZmdnEYvFdHn+jpZ4b1a7klUnJiaQzWbbOLLeU7NU+7mviRtuQHZsbFnETwlgjdntdiXwcLlcupZUJuZRKpUwPT2NVCql91AMyYz9a1iWxSc/+cm2nTh1za6ZVrUjEFlYWMDJkyfbO7Bu0sTUYfThh9H3xBNgKtabJZbF3I4diFdUtF3r4xtZZd8Vu90Oh8MBl8tFO12IruQz2UQi0ZWbA3qSifvXbNq0CS6Xqy2P1TW7ZrrB9PS03kPQTDNTh75Dh9B38CCw8sOqXEbfwYNYvOii6hG+iRLAKoONyq82m40CDtKVOI5DLBZDX18fZmdnkUwmKbG1RWttbWEEhUKhbYFIMwwdiAiCgEKhoPcwNFE5dVipskS7EliIImIPPFC1mBmDpS3Nsf37kRkbM1yE34jFYsHw8DAcDgflcpCeZbFYsG7dOkSjUWQyGSSTSdPtDmwXM/evmZ+fh81m63hBRcMWMFhcXMTU1JTew9BGvcDiXGAS278fOFcUSY7wa/1ZMYAS4ZuJy+XC5s2baTcLMQyWZREIBLBx40acf/75iMVi1J+oSWbuX1MoFHDy5EmcOHGio4GsoWZEJElCKpXC3NwceJ7XeziaaXbq0KKymJna2xlBOBxGLBajAIQYltVqVbquFotFZDIZZLNZ5PN5Wr6po9EuQzOUL8jn8zhx4gQ8Hg+i0ajmwawhAhFJkpDJZBCPx03R3bLZqUNLMqnu9ipv18usVitisRj8fr/eQyGkY6xWK8LhsNIVmOf5ZV2BqT5JBZUdgs2wjL2wsICFhQX4fD5Eo1HNCjH2dCAiSRJyuRymp6cNmwtSjdopQfuxY3CPj6Ok8qBbCgZbGVZX4zgO0WgUwWCQZkGIqTEMA4fDobQZAJYKPsqBSS6XA8/zpt6Fk9m2DZMPP7xqM4BcZ8loW3cbyWQyyGQymvWm6dntu/l8HtPT08jn8zqNTkeNWl9jeYn2UjCoarbjxI9+ZLgscACIxWIIhULU04UQlSRJQqlUgiAI4Hle+crzPIrFonmCFCpfsIrf78f69esbfp4aevuuJEmYn5/H2bNn9R6KfupNHVa7eSqlXF91XzyAYixmyDXPkZEReDwevYdBSE9hGAZWqxVWqxVut3vZz+QgRQ5Q5ufnjTsjbaLyBWql02kUCgUMDw+3rYBjT50ilstlTE1NmTsIOUeeOiz296/6Wa2dNMDqQEUCAIYx5JqnXG6dENI+cpDi8XgQCoWwadMmep+ZDM/zOHHiRNtyi3pmRqRUKmFiYsLcPRZWTBNmxsaU1tfut95C//e/X3eLLgAUg0FYK5ZpigYu2b5u3TrKByFEYyzLYmRkBPF4HHNzc3oPh3RIsVjEyZMnsWnTppaXvXsiECmXyzh16pSpg5BqVVSLwSDSf/zHyI6Ngd+4UdXjTN99N0rRqOHXPN1ut65trQkxE4ZhEIvF4HA4MDU1ZZ4cklpMkltSKBQwMzPTcrO8nghEzp49C/FccS4zqllFNZlE35NPou/JJ1XveClFo4Zf87TZbBgaGqLZEEI6LBAIwG634+zZs+bcSABzde0FgLm5OYRCoZbyRXoiRySdTus9BO2IItzj4/C/+CLc4+NKNdTKn9eqolqJSyYhoXqyKrC0/10waEJqJavVipGREeoNQ4hOnE4nNm7ciJGRETgcDr2H01HySaN1RXFIufWG79AhnUamrfn5+Zbu3xMzIkalJnJuVEVVxuB3QcjK7btmKcLjdrsxNDREQQghOmMYBh6PB6Ojo+YpNtmg9YbEMIbt6ZXNZltanumJGREjqhk5x+MY/MY3EPne9wBRbKqxEnPusnKZphiNLm+CZ0B9fX00E0JIl2EYBn6/H+eddx7Wr1/ftu2e3ahhT6+K1htGw/N8S20DaEZEDw264QJA9LHH0HfwIDLXXtv0w5slIRVY2qI7MDBAiamEdDGGYRAMBhEIBHD8+HFDbjwwc9deAC0lKFMgogO1yy1cLofg//2/dYuRVWOGhFQA6O/vRyQSoaRUQnoEwzCw2+2GDETM3LWXYZiWtvDS0owO1hIRqznUmiUhFQCGh4fR399PQQghPcaolY7lrr1Sjc8kI38+u93ulj6LKRDRQbMRsdogBDB+QirHcRgdHYXX69V7KISQNTBqICK33gCwKhgx+udzq0vjFIjooFHkrMbK1TgzJKQ6nU6cd955cDqdeg+FELJGFosFfX19eg9DE7Vabxj589lisSAQCLT2GO0ZCmlKZdM6qM/9qCTfZ+Z//2/krrzS0AmpABAKhRCLxaiDLiEG0NfXh/n5+ZZ2WnSrzLZtSusNM2wYKJVKmJubaylfjwIRnciRc2zfPthmZtb8OPzoqKETU10uF9avXw+73a73UAghLZIkCQsLC5ienjZkEKIwWdfemZkZLC4uYsOGDWsqodATp5etTvt0q8y2bfjtyy8jvYYtujIjZmDLYrEYNm3aREEIIQYgiiImJiYwMTEBnuf1Hg5ps2w2i2PHjq2pcF1PBCLr1q2Dy+XSexja4DjMX39903czcgY2y7LYvHmzYdeRCTEbnudx7NgxLCws6D2UzmnUvsOABEHAyZMnm+4Np3kg8thjjyk9B7Zu3Ypf/epXTT+G3NnRqJTk1Ro/X3m90TOwR0dHTdejghCjymazOHr0qPFLvFfwHTqET2zfjo0334zBPXuw8eab8Ynt2w3ba6aSIAiYmJhoqsCZpoHIM888g927d+Pee+/F4cOHcfHFF2P79u2YWUNOxFru0yt8r70GplComrRa7b/SyBnYsViMlmIIMYhsNtv0QanXNWp8F/ne9ww/S5LP55FMJlXfnpE0/AvZunUrtmzZgn/+538GAJTLZQwODuL222/HPef2W9eTyWTg9/sxPz+PqakprYapK/mPtlZ33VIggDPf+hbEYNDwGdhutxsjIyNUpIwQAygUCjh27JipghCIIj6xfTusNXrOrNwlubLJqZEsLi7iiiuuQDqdblhnRLNdM4Ig4O2338bevXuV61iWxbZt2/CLX/yiqcfK5XLtHl53qNNzBlj6oy3b7Uv9ZgwYeFSy2+0YGhqiIIQQA5AkCZOTk8YOQkRx1RbdRu07Vn66ybMkRpzhbiZPRLNAZG5uDqIoIhqNLrs+Go3io48+qnofnueXZVNnMhkAS/uUjUjNH60tHof78GFDbwVzOp0YGhqizrmEGEQymTT0zhjfoUOIPfDAss9vIRpF5rOfbepxGEmCxDCI7d+PzNiY4U84a+mqXTP79u2D3+9XLoODg3oPSVNm79YILG3N3rhxI6xWq95DIYS0ydzcnN5D0Ey9HJDwk082/XiMJME2PQ334cPtGmLP0SwQ6evrA8dxiK/4z4rH4zV3wOzduxfpdFq5TE5OAoBhkxfN3K0RACKRCNavX0/VUgkxEEEQjLtDps5yOnNuGUpi2TW17zDyCWcjmh0BbDYbLrvsMrz66qvKdeVyGa+++iquuuqqqvex2+3w+XzLLsBSdU0jHqzM3K3RYrEgGo1STgghBlMoFPQegmbk5fRan1oMAKZcBs4tuTTDqCecamh6dN+9ezd+8IMf4IknnsCRI0dw6623IpfL4aabbmrqcRiGQTAY1GiUOjJxt8ZwOKz3EAghGjBy6Xa1sxaJG25Y1fiuZp0oA59wqqVpIPLVr34VDz30EP7mb/4Gl1xyCd5991289NJLqxJY1YhEIoacFTFjt0ar1UqBCCEGZbEYt4WZ2lmL7NgYpu++G6WKE2gG5ipO2cxst6Z1RFol1xGR9yFX5o0YTpWtYEb7w5SNjIzA4/HoPQxCiAbK5TKOHDlizK27cp2QmRklJ6SSxDAoRqOYvusuDP6f/7Mql2RVHZFYDNN79hjyhNPlcmF0dFTfOiJa8Pv94HnemFVWTdKtcf369RSEEGJgLMvC4/Egm83qPZT2O7ecPrh7NySGWRaMKLMbd92F2IMPVk9oxVIwIvr9mPyHf0Du8ssNecJpt9sRCoVU377n1joikQgiJk7q6WXr1q0zZq4PIWSZtSy/94pGy+miz9cwodWSTgMsa8ggxGKxYGRkpKlUip6aEQGW1p2i0SgcDgdOnz5tzOk/g2EYBv39/fD7/XoPhRDSAQ6HA8FgsKl+I70ks20bMmNjq5bTfa+9hsG/+itVj2HU7bojIyOwWq1YXFxUfZ+eC0Rkfr8fdrsdExMTKBaLeg+H1CFJEuLxOOLxOKxWK9xuN1wuF1wuF+x2O23hJcQgJElCPp9HOp1WKmMb1orl9Mq+YWoYcbuuy+VaU+f0ng1EgKWoe/PmzUgkEpidnaXZkR5QLBaRSqWQSqUALK0ny4GJ2+2Gw+Ew5O4oQoxMEASkUikkk0lznhg26BtWSU5oNeJ23UZJqbX0dCACABzHob+/H6FQCHNzc0gkEhSQ9JByuYxsNrsssc3j8cDv98Pn81H/GUK6mCAIiMfjSKfTeg9FV436hsnkI5NRt+uudfm95wMRmcViQSwWQzgcxszMjGHXJs1gYWEBCwsLmJqagtvtRiAQoKCEkC5SLBYxOzuL+fl5vYfSFdTme4h+P87cd58ht+tGIpE19wwzTCAis1qtWL9+Pfr6+pBIJJBKpQxd6c/ocrkccrkczpw5A7/fj2AwCJfLRXklhOigVCrRzPNKoghLIqHqppP/8A/Ibd2q8YA6z+FwoK+vb833N1wgIrPb7RgYGEAsFkM2m0UymcTCwoLewyJrJEmSkltit9sRi8Xg8XgoICGkAyRJwvz8PKanpykAqeA7dAixBx5ouCyj5IVcfnmHRtY5FosFw8PDLeX2GTYQkbEsC7/fD7/fj1KphGw2i3Q6TUFJD+N5HhMTE3A6nYjFYnC73XoPiRDDKpfLOHPmjJJgTpbU2iWzsnqqkcu4A8DGjRvXvCQjM3wgUslisSAYDCIYDEIURWSzWeTzeeRyOfA8r/fwSJMWFxdx4sQJuN1uxGIxOJ1OvYdEiKEUi0VMTEwYuqPumtTZJbPy+2I0atgy7hs2bIDdbm/5cUwViFTiOA6BQACBQAAAIIoi8vm8EpgsLi7SFGSPyOVyOHbsGPx+PwYGBiiplZA2EAQBx48fR6lU0nsoXUftLpmzd9+NxJ/9mSFnQpxOZ9uKVJo2EFmJ4zh4vV643W6wLNtUVTjSHdLpNAqFAoaHh2Gz2fQeDiE9SxRFTExMUBBSg9pdMqVw2JBBiNVqxfDwcNty9CgQOUeSJCSTScTjcYiiqPdwyBrxPI+jR49iaGiImusRskZTU1O0XF2H2qqoRqyeCiyVcbdY2hc+UAlLLCVjnT59GmfOnKEgxADK5TJOnjxp/BLThGggl8sZ/70jinCPj8P/4otwj48DTX7u5y69FEI0qiSiriQxDIRYzJDVU6PRaFvyQiqZfkZEEARMTExQ9G9Ak5OT2LhxI1wul95DIaRnxFXkPvSyaltuhWgU0/fcoz6hlOMwfc89GNy9GxLDgKnIJzTyLhmO4xAOh9v+uKaeEVlcXMSxY8coCDEoSZJw6tQpmuUiRCU5ad+o5C231hXBlnVmBoO7d8N36JDqx8ps24bJhx9Gsb9/2fXFaBSTDz9syF0yAwMDmvQCY6Qu3hqSyWTg9/uRTqfX3EynFkEQcOzYMfMepERxVQtro0Xvskgkgmg0qvcwCOl62WwWExMTeg9DG6KIT2zfDms8XrUxnVx07LcvvdTcZ6FJPkuDwSAGBgZUJ6g2c/w25dKMJEmYmJgwbRDSlqnJHjI3N4dIJEJdfQlpwMifiY223DKSBNv0NNyHDyO3ZYv6B+a45m7fgzweT1NBSLNM+cmcSCSMvRxTJxGrnVOTvUKSJORyOb2HQUjXM3KwrnbLrdrbmUUgEMDQ0JCm7TRMNyMiiiJmZmb0HoZm6s52jI3VrgYoSZAYBrH9+5EZGzPc1GIul4PX69V7GIR0LUmSDN27yexbbtdi3bp1CIVCmv9dmC4QyeVyhu3GW6v3gTzbMfP1r2szNdkDBEFAuVw29BkfIc2QJAmFQgHZbBa5XA75fN7Q1aTlLbfWmZllu1xkSmM6A265bZbFYsHg4GDH+niZLhAxbLO7er0Pzs12hP/1X1U9lBGnJjOZDD788ENYrVbYbDbY7XbY7Xbl31ar1dBng4QAS8HH4uIiMpkMUqmUuSqnmnTLbTNYlkV/fz9CoVBHT9pMF4gUi0W9h6AJNYlYlnRa1WMZeWqyWCyiWCyuyhlhWRZutxtutxsulwsOh4NmT4hhCIKAVCqFZDJp2M9ANeQttyuXr43cmE4NhmEQiUQQDod16dVlukDEqGe9qnsf+P3gMhmamlyhXC4jm80im80CWPo7cTqdSmDicrmomR7pKZIkIZvNYnZ2lnpnVchs24bM2Jgpttw2wjAMwuEw+vr62lqyvVmmC0TaXZq2W6idxUh87Wvo/5d/oanJBiRJUroxyxwOB/x+P/x+PzXVI11FFEUIggBBEMDzPLLZLAqFgqFzPlpigi239dhsNoRCIQQCAV0DEJn+I+gwr9eLWQPmQKhNxJrduRP85s00NbkGhUIBhUIB8XgcdrsdgUAAgUAAVqtV76ERkyiXy1hcXEQ+nwfP88rFqAn4pH04joPf70cwGITD4eiq1QHTVVaVJAlHjx41ZB0RZdcMUHW2Y1nZYZNUA+wElmWV5FeLxQKO48BxHCwWC2w2G2w2G+WbkDUplUrI5/PI5XLI5XIoFAp6D4n0EIvFAr/fD5/PB5fL1dHgo5njt+kCEWBp58zJkyfb9njdpGodkViMZjt0ZrFYlu3UqdytQ0EKkQmCoAQduVzO1ImlpHkWiwUej0fJbbPZbLrNfFCJ9wY8Hg+CwSCSyaTeQ2k7SsTqTqVSCaVSqWqFV6vVuiwxttumTYm2eJ5HJpNBOp2mGQ/SNIvFgnA4jGAw2BX5HmuhyahPnjyJv/3bv8V//Md/YHp6GgMDA/ja176Gv/7rv+6aJL+BgQEUi0Vj1hUxeSJWr5G3FGcyGQBLmewul0sJTJxOJ+3Y6RGSJEEURYiiCEmSlGTRlV/L5TIWFhaQzWYhCIJu4yW9y+FwIBaLwePx6D2UlmkSiHz00Ucol8t4/PHHsXnzZrz//vvYuXMncrkcHnroIS2esmkMw2BwcBCTk5PGDEZIz5J741TOnjgcDrjdbvj9fjidTpox0Vi5XIYoiiiVSigWi0pSqHxduVxWblMZcBCiNbvdjmg0Cq/Xa5jPgY7liPz93/89vvvd7+L48eOq76NVjkglSZIwMzNjyJ00xJg4jkMgENAlAc0o5JkLnuchCIKyI4rneXNVGyU9w+fzIRgMwuPx9MR7vitzRNLpNEKhUN3byGcdMnmqWksMwyAajcLhcOD06dN0ZkO6niiKSCQSSCQSYFkWHo8HgUAAbreblnCqkHeeLC4uKkGHIAj0Xu9GtJtvGafTiUAgAL/f37P5H2p05JUdPXoUjz76aMNlmX379uH+++/vxJBWkae8Z2ZmkEqldBkDIc0ql8vIZDJK0F65lVjemeNyubq+1om8vCGKopIzI+daVF4ql0Mq71fte1oy6S11O4ebaMefy+VSttx2+/u2XZpamrnnnnuwf//+urc5cuQILrjgAuX7qakpXH311bjmmmvwwx/+sO59q82IDA4Oaro0U2sc8Xi8IzMyhHSC1WpdVq7ebrd3ZHpXkiSUSiUIgoBisahU/1wZbBBzq+wcXvlXWbUGksHIO+bcbjecTqdhZj40qyMyOzuLRCJR9zabNm1SdsacOXMG11xzDa688kocPHiw6XoJncgRqWdxcRHxeJySWYnhyE3+5MDE6XSuuZ6JPJMhlxfneV7JuaB8C9KQKOIT27fDGo+v6hwO/K4q9G9fesmQyzSf/OQnDbmkqlmOSCQSQURlT5OpqSmMjY3hsssuw4EDB3qyaJPT6cTIyAhyuRwSiQTNkLRC7dovrRF3xMomfyzLwufzwefzwePx1H2/yt2L5V48PM/TEghZMzWdw23T03AfPmzIsgSCIMDpdOo9DF1pMgc0NTWFa665BsPDw3jooYeW7UiJxWJaPKWm5GkzURSRTqeRTCapm2UT1K790hqxfsrlMlKpFFKpFBiGUTL0XS6XUu1TLjVOsxykndR2Dld7O9J7NAlEXnnlFRw9ehRHjx7Fhg0blv2sl8+cOI5DKBRCKBSCIAhKNUQKSmqrXPutZJ2ZweDu3crar9rbEe1JkoR0Oo10Oq33UIgJqO0crvZ2vcYsCan1mLLXTLsVi0Vks1nljJH6Q5yjdu33//0/fOJznzPtGjEhXavaUinQ3uVT+XOiQedwI77/nU4nRkdH9R6GJrqyjoiRWa1WZaYEoI6ZMrVrv+FnnjH1GjEh3ajaUmnJ74cEwFoxW9by8inHYfqeezC4ezckhqnaOXx6zx7DBSEAEAgE9B5CV+i9DNIeYLFY4PP5sG7dOmzevBmf+tSnMDIygv7+fvj9fjgcjp5M3m2W2jVd2+RkWx+PENIaeanUuuIEgUunYVmxZCcvn/oOHVrz82W2bcPkww+j2N+/7PpiNGrYZVmr1YpgMKj3MLoCzYh0gFz9cmVzIrm+wtmzZw2ZZ6J2TVcYHGzr47WEdu0QsxNFxB54YFVNDwBVl04ZSYLEMIjt34/M2Nia3y9m6xy+fv16U5yQqkGBiI4sFgssFguCwaAhA5HcpZdCiEYbrv0mvvpVhJ94ouHt5PVprdCuHUIaL6lW07blU5N0Dh8YGDBE19x2oXCsC3i9Xr2HoI1za7/A79Z6ZcvWfm02dbfT8Myo1lR0O6adCeklrSyB0vJpY9FotGHfNbOhQKQLyMmuRqR27VfXNeJ6U9HnZmhi+/cDcilyUYR7fBz+F1+Ee3z8d9cTYgCtLIEadYttOzAMg6GhIdVFQc2Elma6RH9/P1KpFMrlst5DaTu1a796rRE3U9mRS6dp+YbUVyvPqEfyjxotqVbTqeXTXmW1WjE8PAyHw6H3ULoSBSJdwmKxYGRkBMePH9d7KNpQu/arwxqx2ulk72uvIfyv/7r2oms9ciAia1crzyj9uc/B/+KLvRHA1ttOe+5rtcZ0Rt1i2wqGYRAOhxGJRAzZT6ZdqKBZl0mn05hUuZ2VtId7fBwbb7654e1KwSC4ZHJNRdcoEdb4anaQrfh3L3WWrVpHJBCAJEnL64jEYpjes6crX4OegsEg+vv7TVs5VbPuu51mxkAEABYWFnDq1ClDLtN0JRWVHUuBAKzJZMOHOvGjH62a0TFzi/OOaGamSatZqUZVhFF962vXVw3tRGVVg/H7/ejv74fdbtd7KLqiyqo9zuPxYPPmzZiYmADP83oPx/hUVHZM//Efo+/JJxs+1KplngaJsO2ov2AKNQKIZmaatJyVaphnVOv6bq8aXGOptCvHqjOfz4f+/n7KA1kDCkS6lM1mw+joKM6ePYukijNx0hp5187KA1UxGsX0nj0Q/X5VgYjt1Kll35u9xXk71Mu76Dt4UFXOjtZNFVvdtkrbXnuT0+lEMBiE3++nHJAWUCDSxViWxfr169HX14d4PI5MJqP3kAyt7q4dUVzaSVBj6h1Ymn4PPvssZnfuVGY3qMV5a+oFEH0HDgBYPduwaqYJ0HxWqtVtq7TttXc4HA74/X74fD7TL7+0CwUiPcBut2NoaAiLi4uIx+NYWFjQe0jGVWvXDsch+aUvIfrYYzXvygCwxePLZjfM3uK8JSrqu9RSOdMEQPNZqYZVhFE/R4S2vXYvlmXhdrvhdrvh8/lgs9n0HpLhUCDSQ5xOJ0ZGRpDL5TA9PW3IsvDdTBgaUnW7ytkNtWXu6UC02lpKja/UzExTS7NSKra8rgxGaNtrd7JarXC73XC5XHC73bDZbGCYWvOgpB2osmoPcrvdGB0dxebNmxEOh2ltskPWNLuhtsw9/R+u0o7lqlIk0rFZqZrVgWMxzN10E4rR6PLrDdxZtlcwDAOHw4FwOIzBwUGcf/75OP/887FhwwaEQiHY7XYKQjqAZkR6mMPhwLp16xCLxZDNZpFOp5HJZNDFO7J72lpnNxolwtKBqLpWAoOV/xedmpWql2cUv+MO2vbaBRiGQSAQQCQSoWWWLkF1RAymXC4jl8shnU4jm81CpD4obaUkTwJVt/nWPcOlyqrNaVTfpeLfjeqztPT/RgyB4zgEg0H09fXBYqFzcK1RQTMCAJAkCYIgIJ/PI5/PI5fLQRAEvYfV86puJ6XqkppoFEDM3Xjj6tLpNf4v6P/NnHw+H4LBIDweDy2zdBAFIqSmUqm0LDChhNc1otmNjmkYQHRDZVXSVbxeL/x+P7xeL+XQ6YQCEaJauVxGsVgEz/MQBAGCIIDnefA8j1KppPfwCFlCAQSpw2azwePxwO12w+PxUPDRBajEO1GNZVnY7faqhXnK5fKy4KRYLEIURYiiiFKppPybeuIQzenQlZl0L3lrrcvlgsvlosCjx1EgQmpiWRYOh6Nh7wRJklAul5cFKeVyGZIkKTt4CoUC5ufnaUcPIaQpNpsNDodDCTocDgdYlipPGAkFIqRlDMOA47iGZyXhcJga+RFCVuE4Dna7HQ6HA06nEzabDTabDRaLhRJMTYACEdIxNpsNmzdvRjqdRjweR7FY1HtIhBANMAwDlmWVC8dxsFgssNlssNvtsFqtynUUbBAKREhHycWE/H4/kskkZmZmKCmWkC7jdDrh8XjgdDqVIKHaVznI4DiOlkvImlEgQnTBMAxCoRACgQDm5+cxMzNDSa+E6Mjj8ShbXqngF+kk+msjumJZFn19fQgGg0in00gmk1TbhJAOcDgcys4T2vJK9ESBCOkKHMchFAohFAqB53mkUimkUinKIyGkTeRW9i6XC06nkwIP0jUoECFdx263IxqNor+/HzzPI51OI51OU3n6Nqlsc86yLBYWFpBOp2lrtUHItYEcDgfsdjvcbjccDgclhJKupXkgwvM8tm7dit/85jd45513cMkll2j9lMQg5BbdDocD0Wh0Vd8c2gasjjwFLwcfK9f/A4EABgYGsLCwgEwmg0wmQ/k6XY5hGFitVtjtdjidTqUooc1mo6RR0nM0D0TuvvtuDAwM4De/+Y3WT0UMTq4tEAgEAACiKK7qm2PWs3q5DkPlAUm+qDkwsSwLn88Hn8+ndHCWL5Szoz2GYZbtQmFZFhaLBVarddWWV9qhQoxG00DkZz/7GV5++WX85Cc/wc9+9jMtn4qYEMdx8Hq98Hq9AJZK0hcKBaVvjtwzRxCEng5Q5FoMch2GlQeodp8Fsyy76ve6uLioBHz5fJ5mTJpksVjgdDqV2Sm73U71Mwg5R7NAJB6PY+fOnXj++efhcrlU3Uc+cMgymYxWwyMGxLKsUga6kiRJKJVKSnBS+VXulaPHgVU+A5YDC3mqXZ5u5ziuKw5ULMsqSzuRSASSJIHneWU2qvJ3aWaVfZsqg0SbzUaJoYTUoUkgIkkSbrzxRtxyyy24/PLLcfLkSVX327dvH+6///5V11NAQtpFruRYLViRe+VUXip76Mi3k7/K/65X6Kmy4FPlpd4MhiRJyOfzbX/t7WaxWJZ11RRFcVmDRPnEolgs9vQMSmULA/ki/x1VzkxVCzaKxSLt/CKmJB+3Vc1GS03Ys2ePBKDu5ciRI9I//dM/SZ/5zGekUqkkSZIknThxQgIgvfPOO3Ufv1AoSOl0Wrl8+OGHDZ+PLnShC13oQhe6dOdlcnKyYWzBSE0sns/OziKRSNS9zaZNm/CVr3wFP/3pT5dNK4uiCI7jcP311+OJJ55Q9XzlchlnzpyB1+tteoo6k8lgcHAQk5OTy87ajIZep7HQ6zQes7xWep3G0urrlCQJ2WwWAwMDDXPYmlqaiUQiiEQiDW/3ne98B9/+9reV78+cOYPt27fjmWeewdatW1U/H8uy2LBhQzNDXEXeCWB09DqNhV6n8ZjltdLrNJZWXqff71d1O01yRIaGhpZ97/F4AACjo6MtBxaEEEIIMQ7ajE4IIYQQ3XSkxPvIyEjH6zjY7Xbce++9sNvtHX3eTqPXaSz0Oo3HLK+VXqexdPJ1NpWsSgghhBDSTrQ0QwghhBDdUCBCCCGEEN1QIEIIIYQQ3VAgQgghhBDdmCoQ4Xkel1xyCRiGwbvvvqv3cNruC1/4AoaGhuBwOLBu3TrccMMNOHPmjN7DaquTJ0/iL/7iL7Bx40Y4nU6Mjo7i3nvvhSAIeg+t7f7u7/4On/70p+FyuRAIBPQeTls99thjGBkZgcPhwNatW/GrX/1K7yG13Ztvvok/+ZM/wcDAABiGwfPPP6/3kNpu37592LJlC7xeL/r7+3Hdddfh448/1ntYmvjud7+Liy66SCnwddVVVxm+q/wDDzwAhmFw5513avo8pgpE7r77bgwMDOg9DM2MjY3h3/7t3/Dxxx/jJz/5CY4dO4YvfelLeg+rrT766COUy2U8/vjj+OCDD/DII4/ge9/7Hr75zW/qPbS2EwQBX/7yl3HrrbfqPZS2euaZZ7B7927ce++9OHz4MC6++GJs374dMzMzeg+trXK5HC6++GI89thjeg9FM2+88QZ27dqFt956C6+88gqKxSI++9nPIpfL6T20ttuwYQMeeOABvP322/j1r3+NP/iDP8Cf/umf4oMPPtB7aJoYHx/H448/josuukj7J2um6V0ve/HFF6ULLrhA+uCDDySgcQM+I3jhhRckhmEkQRD0HoqmHnzwQWnjxo16D0MzBw4ckPx+v97DaJsrrrhC2rVrl/K9KIrSwMCAtG/fPh1HpS0A0nPPPaf3MDQ3MzMjAZDeeOMNvYfSEcFgUPrhD3+o9zDaLpvNSuedd570yiuvSFdffbV0xx13aPp8ppgRicfj2LlzJ5588slV7d+Nan5+Hj/+8Y/x6U9/GlarVe/haCqdTiMUCuk9DKKCIAh4++23sW3bNuU6lmWxbds2/OIXv9BxZKQd0uk0ABj+/SiKIp5++mnkcjlcddVVeg+n7Xbt2oXPf/7zy96nWjJ8ICJJEm688UbccsstuPzyy/Uejub27NkDt9uNcDiMU6dO4YUXXtB7SJo6evQoHn30UfzlX/6l3kMhKszNzUEURUSj0WXXR6NRTE9P6zQq0g7lchl33nknPvOZz+DCCy/UeziaeO+99+DxeGC323HLLbfgueeew6c+9Sm9h9VWTz/9NA4fPox9+/Z17Dl7NhC55557wDBM3ctHH32ERx99FNlsFnv37tV7yGui9nXK7rrrLrzzzjt4+eWXwXEc/vzP/7zj5fXXotnXCQBTU1P4wz/8Q3z5y1/Gzp07dRp5c9byOgnpBbt27cL777+Pp59+Wu+haOb888/Hu+++i1/+8pe49dZbsWPHDnz44Yd6D6ttJicncccdd+DHP/4xHA5Hx563Z0u8z87OIpFI1L3Npk2b8JWvfAU//elPwTCMcr0oiuA4Dtdffz2eeOIJrYfaErWv02azrbr+9OnTGBwcxH/91391/fRhs6/zzJkzuOaaa3DllVfi4MGDYNneiKnX8v958OBB3HnnnUilUhqPTnuCIMDlcuHZZ5/Fddddp1y/Y8cOpFIpw87gMQyD5557btlrNpLbbrsNL7zwAt58801s3LhR7+F0zLZt2zA6OorHH39c76G0xfPPP48vfvGL4DhOuU4URTAMA5ZlwfP8sp+1S0ea3mkhEokgEok0vN13vvMdfPvb31a+P3PmDLZv345nnnkGW7du1XKIbaH2dVZTLpcBLG1b7nbNvM6pqSmMjY3hsssuw4EDB3omCAFa+/80ApvNhssuuwyvvvqqclAul8t49dVXcdttt+k7ONI0SZJw++2347nnnsPrr79uqiAEWPrb7YXPV7WuvfZavPfee8uuu+mmm3DBBRdgz549mgQhQA8HImoNDQ0t+97j8QAARkdHsWHDBj2GpIlf/vKXGB8fx+/93u8hGAzi2LFj+Na3voXR0dGunw1pxtTUFK655hoMDw/joYcewuzsrPKzWCym48ja79SpU5ifn8epU6cgiqJS+2bz5s3K33Ev2r17N3bs2IHLL78cV1xxBf7xH/8RuVwON910k95Da6uFhQUcPXpU+f7EiRN49913EQqFVn0u9apdu3bhqaeewgsvvACv16vk+fj9fjidTp1H11579+7FH/3RH2FoaAjZbBZPPfUUXn/9dfz85z/Xe2ht4/V6V+X3yDmHmub9aLonpwudOHHCkNt3//u//1saGxuTQqGQZLfbpZGREemWW26RTp8+rffQ2urAgQMSgKoXo9mxY0fV1/naa6/pPbSWPfroo9LQ0JBks9mkK664Qnrrrbf0HlLbvfbaa1X//3bs2KH30Nqm1nvxwIEDeg+t7W6++WZpeHhYstlsUiQSka699lrp5Zdf1ntYmuvE9t2ezREhhBBCSO/rncV1QgghhBgOBSKEEEII0Q0FIoQQQgjRDQUihBBCCNENBSKEEEII0Q0FIoQQQgjRDQUihBBCCNENBSKEEEII0Q0FIoQQQgjRDQUihBBCCNENBSKEEEII0Q0FIoQQQgjRzf8HlmThZfWQANEAAAAASUVORK5CYII=", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "radius = 1\n", "rips_complex = rips(points=circle, skeleton=2, max=2*radius)\n", "pyplot.subplot(211)\n", "plot_points(circle, radius=radius, color=\"lightgray\")\n", "pyplot.figure(100)\n", "draw_simplicial_complex(rips_complex, circle)\n" ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sat Nov 25 16:01:53 2023 Starting Rips complex generation.\n", "Sat Nov 25 16:01:53 2023 Generated complex: 9534 simplices\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rips_complex = rips(points=circle, skeleton=3, max=2*radius)\n", "persistence = dionysus.homology_persistence(rips_complex)\n", "diagrams = dionysus.init_diagrams(persistence, rips_complex)\n", "dionysus.plot.plot_bars(diagrams[1], show = True)" ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Generators in dimension 0:\n", "(0,inf)\n", "Generators in dimension 1:\n", "(1.43748,inf)\n", "Generators in dimension 2:\n" ] } ], "source": [ "# Output generators by dimension. \n", "# Note: the computed Rips must have skeleton argument at least dimension + 1,\n", "# where dimension is the last dimension of homology we are interested in.\n", "inf = float(\"inf\")\n", "for i in range(3):\n", " print(f\"Generators in dimension {i}:\")\n", " dgm = diagrams[i]\n", " for p in dgm:\n", " if p.death == inf:\n", " print(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now just compute the entire Vietoris-Rips complex without restriction on the top dimension. Print also the dimension of such complex. As you can see the complex becomes big pretty fast." ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sat Nov 25 15:25:35 2023 Starting Rips complex generation.\n", "Sat Nov 25 15:25:35 2023 Generated complex: 1413 simplices\n", "Dimension 9\n" ] } ], "source": [ "radius = 0.5\n", "max_dimension = 10000\n", "rips_complex = rips(points=circle, skeleton=max_dimension, max=2*radius)\n", "print('Dimension', max((len(s) for s in rips_complex)))" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sat Nov 25 15:27:37 2023 Starting Rips complex generation.\n", "Sat Nov 25 15:27:37 2023 Generated complex: 6124 simplices\n", "Dimension 11\n" ] } ], "source": [ "radius = 0.75\n", "max_dimension = 10000\n", "rips_complex = rips(points=circle, skeleton=max_dimension, max=2*radius)\n", "print('Dimension', max((len(s) for s in rips_complex)))" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sat Nov 25 15:28:01 2023 Starting Rips complex generation.\n", "Sat Nov 25 15:28:31 2023 Generated complex: 17430528 simplices\n", "Dimension 22\n" ] } ], "source": [ "radius = 2\n", "max_dimension = 10000\n", "rips_complex = rips(points=circle, skeleton=max_dimension, max=2*radius)\n", "print('Dimension', max((len(s) for s in rips_complex)))" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [], "source": [ "def alpha_shapes(points):\n", " \"\"\"\n", " Generate the Alpha shapes complex on the given set of points in 2D.\n", "\n", " It requires no argument: only 2D and 3D shapes are supported and the\n", " dimension is infered from the points.\n", " \"\"\"\n", " print(time.asctime(), \"Starting Alpha shapes complex generation.\")\n", " alpha = diode.fill_alpha_shapes(np.array(points))\n", " print(time.asctime(), \"Generated complex: %d simplices\" % len(alpha))\n", " return alpha" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sat Nov 25 16:03:00 2023 Starting Alpha shapes complex generation.\n", "Sat Nov 25 16:03:00 2023 Generated complex: 365 simplices\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "radius = 1\n", "alpha_complex = alpha_shapes(points=circle)\n", "pyplot.figure(100)\n", "# Just filter simplices that have radious less than 1.\n", "radious = 1\n", "simplices = [entry[0] for entry in alpha_complex if entry[1] <= radious]\n", "draw_simplicial_complex(simplices, circle)" ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sat Nov 25 16:10:00 2023 Starting Alpha shapes complex generation.\n", "Sat Nov 25 16:10:00 2023 Generated complex: 365 simplices\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "radious = 1\n", "alpha_complex = alpha_shapes(points=circle)\n", "filtered_alpha_complex = [entry for entry in alpha_complex if entry[1] <= radious]\n", "filtration = dionysus.Filtration(filtered_alpha_complex)\n", "persistence = dionysus.homology_persistence(filtration)\n", "diagrams = dionysus.init_diagrams(persistence, filtration)\n", "dionysus.plot.plot_bars(diagrams[1], show = True)" ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Generators in dimension 0:\n", "(0,inf)\n", "Generators in dimension 1:\n", "(0.516585,inf)\n", "Generators in dimension 2:\n" ] } ], "source": [ "# Output generators by dimension. \n", "# Note: the computed Rips must have skeleton argument at least dimension + 1,\n", "# where dimension is the last dimension of homology we are interested in.\n", "inf = float(\"inf\")\n", "for i in range(3):\n", " print(f\"Generators in dimension {i}:\")\n", " dgm = diagrams[i]\n", " for p in dgm:\n", " if p.death == inf:\n", " print(p)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.6" } }, "nbformat": 4, "nbformat_minor": 4 }