{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# MVA 2021-22 - TP 1 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To download this notebook:\n", "\n", "http://geometrica.saclay.inria.fr/team/Fred.Chazal/MVA2024.html" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can install gudhi using pip or conda:\n", "\n", "https://gudhi.inria.fr/\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.9.0\n" ] } ], "source": [ "import gudhi as gd\n", "print(gd.__version__)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The goal of this first TP is to get you familiar with the basic data structures in GUDHI to build and manipulate simplicial complexes and filtrations. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simplicial complexes and simplex trees" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In Gudhi, (filtered) simplicial complexes are encoded through a data structure called simplex tree. Here is a very simple example illustrating the use of simplex tree to represent simplicial complexes. See the Gudhi documentation for a complete list of functionalities. Try the following code and a few other functionalities from the documentation to get used to the Simplex Tree data structure." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import gudhi as gd\n", "import random as rd\n", "import matplotlib.pyplot as plt\n", "\n", "from mpl_toolkits.mplot3d import Axes3D\n", "import matplotlib.cm\n", "\n", "%matplotlib inline\n", "#%matplotlib notebook" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "First simplex inserted!\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "st = gd.SimplexTree() # Create an empty simplicial complex\n", "\n", "# Simplicies can be inserted 1 by 1\n", "# Vertices are indexed by integers\n", "if st.insert([0,1]):\n", " print(\"First simplex inserted!\")\n", "st.insert([1,2])\n", "st.insert([2,3])\n", "st.insert([3,0])\n", "st.insert([0,2])\n", "st.insert([3,1])" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "([0], 0.0)\n", "([1], 0.0)\n", "([0, 1], 0.0)\n", "([2], 0.0)\n", "([0, 2], 0.0)\n", "([1, 2], 0.0)\n", "([3], 0.0)\n", "([0, 3], 0.0)\n", "([1, 3], 0.0)\n", "([2, 3], 0.0)\n" ] } ], "source": [ "L = st.get_filtration() # Get a list with all simplices\n", "# Notice that inserting an edge automatically inserts its vertices, if they were not already in the complex\n", "for simplex in L:\n", " print(simplex)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "([0], 0.0)\n", "([1], 0.0)\n", "([0, 1], 0.0)\n", "([2], 0.0)\n", "([0, 2], 0.0)\n", "([1, 2], 0.0)\n", "([3], 0.0)\n", "([0, 3], 0.0)\n", "([1, 3], 0.0)\n", "([2, 3], 0.0)\n", "([0, 1, 2], 0.1)\n", "([1, 2, 3], 0.2)\n", "([0, 2, 3], 0.3)\n", "([0, 1, 3], 0.4)\n", "([0, 1, 2, 3], 0.5)\n", "([4], 0.7)\n", "([2, 4], 0.7)\n", "([3, 4], 0.7)\n", "([2, 3, 4], 0.7)\n" ] } ], "source": [ "# Insert the 2-skeleton, giving some filtration values to the faces\n", "st.insert([0,1,2],filtration=0.1)\n", "st.insert([1,2,3],filtration=0.2)\n", "st.insert([0,2,3],filtration=0.3)\n", "st.insert([0,1,3],filtration=0.4)\n", "\n", "st.insert([0,1,2,3],filtration=0.5)\n", "\n", "# If you add a new simplex with a given filtration value, all its faces that \n", "# were not in the complex are inserted with the same filtration value\n", "st.insert([2,3,4],filtration=0.7)\n", "L = st.get_filtration()\n", "for simplex in L:\n", " print(simplex)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The filtration value of a simplex can be changed in the following way" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "([0], 0.0)\n", "([1], 0.0)\n", "([0, 1], 0.0)\n", "([2], 0.0)\n", "([0, 2], 0.0)\n", "([1, 2], 0.0)\n", "([3], 0.0)\n", "([0, 3], 0.0)\n", "([1, 3], 0.0)\n", "([2, 3], 0.0)\n", "([0, 1, 2], 0.1)\n", "([1, 2, 3], 0.2)\n", "([0, 2, 3], 0.3)\n", "([0, 1, 3], 0.4)\n", "([0, 1, 2, 3], 0.5)\n", "([4], 0.7)\n", "([2, 4], 0.7)\n", "([3, 4], 0.7)\n", "([2, 3, 4], 1.0)\n" ] } ], "source": [ "st.assign_filtration((2,3,4),1.0)\n", "\n", "L = st.get_filtration()\n", "for simplex in L:\n", " print(simplex)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "** Warning! ** Take care that after changing the filtration value of a simplex, the result could no longer be a filtration, as illustrated below :" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Giving the edge [3,4] the value 1.5:\n", "([0], 0.0)\n", "([1], 0.0)\n", "([0, 1], 0.0)\n", "([2], 0.0)\n", "([0, 2], 0.0)\n", "([1, 2], 0.0)\n", "([3], 0.0)\n", "([0, 3], 0.0)\n", "([1, 3], 0.0)\n", "([2, 3], 0.0)\n", "([0, 1, 2], 0.1)\n", "([1, 2, 3], 0.2)\n", "([0, 2, 3], 0.3)\n", "([0, 1, 3], 0.4)\n", "([0, 1, 2, 3], 0.5)\n", "([4], 0.7)\n", "([2, 4], 0.7)\n", "([2, 3, 4], 1.0)\n", "([3, 4], 1.5)\n", "The result is no longer a filtration : [3,4] has a higher value than its coface [2,3,4]\n", "To fix the problem, use make_filtration_non_decreasing()\n", "([0], 0.0)\n", "([1], 0.0)\n", "([0, 1], 0.0)\n", "([2], 0.0)\n", "([0, 2], 0.0)\n", "([1, 2], 0.0)\n", "([3], 0.0)\n", "([0, 3], 0.0)\n", "([1, 3], 0.0)\n", "([2, 3], 0.0)\n", "([0, 1, 2], 0.1)\n", "([1, 2, 3], 0.2)\n", "([0, 2, 3], 0.3)\n", "([0, 1, 3], 0.4)\n", "([0, 1, 2, 3], 0.5)\n", "([4], 0.7)\n", "([2, 4], 0.7)\n", "([3, 4], 1.5)\n", "([2, 3, 4], 1.5)\n" ] } ], "source": [ "print(\"Giving the edge [3,4] the value 1.5:\")\n", "st.assign_filtration((3,4),1.5)\n", "L = st.get_filtration()\n", "for simplex in L:\n", " print(simplex)\n", "print(\"The result is no longer a filtration : [3,4] has a higher value than its coface [2,3,4]\")\n", "print(\"To fix the problem, use make_filtration_non_decreasing()\")\n", "st.make_filtration_non_decreasing()\n", "L = st.get_filtration()\n", "for simplex in L:\n", " print(simplex)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dimension= 3\n", "filtration value of [1,2]= 0.0\n", "filtration value of [4,2]= 0.7\n", "num_simplices= 19\n", "num_vertices= 5\n", "skeleton[2]= <_cython_3_0_7.generator object at 0x000001B5B61EBAC0>\n", "skeleton[1]= <_cython_3_0_7.generator object at 0x000001B5B61EBAC0>\n", "skeleton[0]= <_cython_3_0_7.generator object at 0x000001B5B61EBAC0>\n", "([0, 1], 0.0)\n", "([0, 2], 0.0)\n", "([0, 3], 0.0)\n", "([0], 0.0)\n", "([1, 2], 0.0)\n", "([1, 3], 0.0)\n", "([1], 0.0)\n", "([2, 3], 0.0)\n", "([2, 4], 0.7)\n", "([2], 0.0)\n", "([3, 4], 1.5)\n", "([3], 0.0)\n", "([4], 0.7)\n" ] } ], "source": [ "# Many operations can be done on simplicial complexes, see also the Gudhi documentation and examples\n", "print(\"dimension=\",st.dimension())\n", "print(\"filtration value of [1,2]=\",st.filtration([1,2]))\n", "print(\"filtration value of [4,2]=\",st.filtration([4,2]))\n", "print(\"num_simplices=\", st.num_simplices())\n", "print(\"num_vertices=\", st.num_vertices())\n", "print(\"skeleton[2]=\", st.get_skeleton(2))\n", "print(\"skeleton[1]=\", st.get_skeleton(1))\n", "print(\"skeleton[0]=\", st.get_skeleton(0))\n", "L = st.get_skeleton(1)\n", "for simplex in L:\n", " print(simplex)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1. \n", "Make a few experiments with the simplex tree functions ( https://gudhi.inria.fr/python/latest/simplex_tree_ref.html ), e.g. changing the filtrations values, trying to assign values to simplices that do not lead to a filtration,... And observe the effects on the filtration. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Filtrations, persistence and Betti numbers computation" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "([0], 0.0)\n", "([1], 0.0)\n", "([2], 0.0)\n", "([3], 0.0)\n", "([4], 0.0)\n", "([0, 1], 1.0)\n", "([0, 2], 1.0)\n", "([1, 2], 1.0)\n", "([0, 3], 1.0)\n", "([1, 3], 1.0)\n", "([2, 3], 1.0)\n", "([2, 4], 1.0)\n", "([3, 4], 1.0)\n", "([0, 1, 2], 2.0)\n", "([0, 1, 3], 2.0)\n", "([0, 2, 3], 2.0)\n", "([1, 2, 3], 2.0)\n", "([2, 3, 4], 2.0)\n", "([0, 1, 2, 3], 3.0)\n" ] } ], "source": [ "# As an example, we assign to each simplex its dimension as filtration value\n", "for splx in st.get_filtration():\n", " st.assign_filtration(splx[0],len(splx[0])-1)\n", "L = st.get_filtration()\n", "for simplex in L:\n", " print(simplex)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before computing Betti numbers, we first need to compute persistence of the filtration. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(2, (2.0, 3.0)), (1, (1.0, 2.0)), (1, (1.0, 2.0)), (1, (1.0, 2.0)), (1, (1.0, 2.0)), (0, (0.0, inf)), (0, (0.0, 1.0)), (0, (0.0, 1.0)), (0, (0.0, 1.0)), (0, (0.0, 1.0))]\n" ] } ], "source": [ "# To compute the persistence diagram of the filtered complex\n", "# By default it stops at dimension-1, use persistence_dim_max=True\n", "# to compute homology in all dimensions\n", "## Here, for the moment, we use it as a preprocessing step to compute Betti numbers. \n", "diag = st.persistence(persistence_dim_max=True)\n", "# Display each interval as (dimension, (birth, death))\n", "print(diag)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 0, 0, 0]\n" ] } ], "source": [ "print(st.betti_numbers())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2. \n", "Define another filtration of the simplicial complex and check that the choice of the filtration does not change the betti numbers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 3. Persistence for functions defined over a grid\n", "When a function is defined over a grid on $[0,1]$, $[0,1]^2$, ... the grid can be directly used to build the filtration using a cubical complex as illustrated in the following examples. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Persistence of 1D function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let consider $f: t \\mapsto sin(2t)+sin(3t)$ defined over $[0, 2\\pi]$. \n", "\n", "Build a table with 200 values of f between 0 and $2\\pi$. Plot the function, compute the persistence diagram of its sublevelsets, and draw its persistence diagram." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Remark:\n", "The name top_dimensional_cells is because gudhi gives the grid values to top-dimensional cells and deduces values for other cells, instead of giving values to vertices and deducing values for other cells. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Persistence of 2D function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $p_0=(0.25, 0.25), p_1=(0.75, 0.75), p_2 = (0.0, 1.0)$ and $p_3 = (1.0, 0.0)$ be 4 points in the plane $\\mathbb{R}^2$ and $\\sigma=0.05$.\n", "1. Build on such a complex the sublevelset filtration of the function \n", "$$f(p)=\\exp(-\\frac{\\|p-p_0\\|^2}{\\sigma})+3\\exp(-\\frac{\\|p-p_1\\|^2}{\\sigma}) - 4*\\exp(-\\frac{\\|p-p_2\\|^2}{\\sigma}) \n", "- 2 \\exp(-\\frac{\\|p-p_3\\|^2}{\\sigma})$$ \n", "defined over $[-0.5,1.5]^2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the persistence diagram of the sublevel set filtration of $f$ and compute the persistence diagram of the upperlevel set filtration of $f$ and compare the obtained diagram to the previous one. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Persistence over a filtered simplicial complex and Betti number. \n", "1. Recall the torus is homeomorphic to the surface obtained by identifying the opposite sides of a square as illustrated below. ![Figure 1](TorusTriangle.PNG) Using Gudhi, construct a triangulation (2-dimensional simplicial complex) of the Torus. Define a filtration on it, compute its persistence and use it to deduce the Betti numbers of the torus.\n", "2. Use Gudhi to compute the Betti numbers of a sphere of dimension 2 and of a sphere of dimension 3 (hint: the k -dimensional sphere is homeomorphic to the boundary of a (k+1)-dimensional simplex." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Vietoris-Rips and alpha-complex filtrations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the definition of Vietoris-Rips and $\\alpha$-complexes, see the slides of the course: https://geometrica.saclay.inria.fr/team/Fred.Chazal/slides/Persistence2022.pdf\n", "\n", "See also the following book, p.137\n", "https://hal.inria.fr/hal-01615863v2/document\n", "\n", "Take care that in GUDHI the α-complex filtration is indexed by the square of the radius of the smallest empty circumscribing ball. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These are basic instructions to build Vietoris-Rips and α-complex filtrations (and compute their persistent homology)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Random point cloud" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "#Create a random point cloud in 3D\n", "nb_pts=100\n", "pt_cloud = np.random.rand(nb_pts,3)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of simplices in the V-R complex: 40830\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Build Rips-Vietoris filtration and compute its persistence diagram\n", "rips_complex1 = gd.RipsComplex(points=pt_cloud,max_edge_length=0.5)\n", "simplex_tree = rips_complex1.create_simplex_tree(max_dimension=3)\n", "print(\"Number of simplices in the V-R complex: \",simplex_tree.num_simplices())\n", "dgm = simplex_tree.persistence(homology_coeff_field=2, min_persistence=0)\n", "gd.plot_persistence_diagram(dgm)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Compute Rips-Vietoris filtration and compute its persistence diagram from\n", "#a pairwise distance matrix\n", "dist_mat = []\n", "for i in range(nb_pts):\n", " ld = []\n", " for j in range(i):\n", " ld.append(np.linalg.norm(pt_cloud[i,:]-pt_cloud[j,:]))\n", " dist_mat.append(ld)\n", "rips_complex2 = gd.RipsComplex(distance_matrix=dist_mat,max_edge_length=0.5)\n", "simplex_tree2 = rips_complex2.create_simplex_tree(max_dimension=3)\n", "diag2 = simplex_tree2.persistence(homology_coeff_field=2, min_persistence=0)\n", "gd.plot_persistence_diagram(diag2)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of simplices in the alpha-complex: 2363\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Compute the alpha-complex filtration and compute its persistence\n", "alpha_complex = gd.AlphaComplex(points=pt_cloud)\n", "simplex_tree3 = alpha_complex.create_simplex_tree()\n", "print(\"Number of simplices in the alpha-complex: \",simplex_tree3.num_simplices())\n", "diag3 = simplex_tree3.persistence(homology_coeff_field=2, min_persistence=0)\n", "gd.plot_persistence_diagram(diag3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 4. Sampled torus in $\\mathbb{R}^4$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "+ Randomly sample $n$ points (try different values of $n$) on the paramatrized torus in $\\mathbb{R}^4$:\n", "\n", "$$(s,t) \\to (\\cos(s),\\sin(s),\\cos(t),\\sin(t)), \\ \\ \\ (s,t) \\in [0,2\\pi] \\times [0,2\\pi]$$\n", "\n", "and compute the persistence diagrams of the resulting $\\alpha$-complex filtration. \n", "\n", "+ Do the same with the Vietoris-Rips complex. \n", "\n", "+ What do you observe?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "+ Now, sample the points along a 1D line embedded in the torus according to the following parametrization:\n", "\n", "$$t \\to (\\cos(t),\\sin(t),\\cos(5t),\\sin(5t)), \\ \\ \\ t \\in [0,2\\pi] $$\n", "\n", "and do the same experiment as previously. What do you observe? Explain it. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 5. \n", "+ Randomly sample n = 100 points on the unit circle in the Euclidean plane.\n", "+ For R in np.arange(0.0,0.5,0.01), compute the Betti numbers of the subcomplex of the Rips-Vietoris filtration (up to dimension 2) made of the simplices with index value at most R and plot the curve giving the Betti numbers as functions of R. These curves are called the Betti curves of the filtration. \n", "+ Can we get the same curves directly from the persistence diagram of the Rips-Vietoris filtration (you will have to guess what the persistence diagrams represent)? If so, compute them using the persistence diagram. \n", "+ Same questions using the α-complex filtrations (find a right range of values for α), and try to increase the number of points in the initial point cloud. \n", "+ Do the same for the point cloud sampled on the 2D torus in $\\mathbb{R}^4$ from the above exercise. " ] }, { "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": "3.11.5" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": false, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }