extended_persistance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Persistence and Extended Persistence Diagrams\n",
    "\n",
    "This code in this file is based on the Extended Persistance tutorial by Mathieu Carrière. \n",
    "\n",
    "The GUDHI TDA tutorials can be found here: https://github.com/GUDHI/TDA-tutorial/tree/master"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import gudhi as gd\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Gudhi, filtered simplicial complexes are encoded through a data structure called **simplex tree**.\n",
    "\n",
    "Use the `insert()` method to add simplices. The `insert()` method returns `FALSE` if we try to insert an existing simplex."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# empty simplicial complex \n",
    "st = gd.SimplexTree()\n",
    "\n",
    "# use insert() method to add simplices to st\n",
    "# insert automtically adds required sub-simplices\n",
    "st.insert([0,1])          # adding a 1-simplex\n",
    "st.insert([1,2]) \n",
    "st.insert([1,3]) \n",
    "st.insert([2,4]) \n",
    "st.insert([3,4]) \n",
    "st.insert([4,5]) \n",
    "st.insert([2,6]) \n",
    "st.insert([3,7]) \n",
    "st.assign_filtration([0], 0.)\n",
    "st.assign_filtration([1], 1.)\n",
    "st.assign_filtration([2], 2.)\n",
    "st.assign_filtration([3], 3.)\n",
    "st.assign_filtration([4], 4.)\n",
    "st.assign_filtration([5], 5.)\n",
    "st.assign_filtration([6], 0.5)\n",
    "st.assign_filtration([7], 4.5)\n",
    "_ = st.make_filtration_non_decreasing() # return value is a throw away variable\n",
    "# i.e. The purpose of this line is to call the function for its side effects (if any), without needing to store or use its return value. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the method `get_filtration()` followed by for loop to obtain all simplices and fitration values of an object of type `SimplexTree`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "([0], 0.0)\n",
      "([6], 0.5)\n",
      "([1], 1.0)\n",
      "([0, 1], 1.0)\n",
      "([2], 2.0)\n",
      "([1, 2], 2.0)\n",
      "([2, 6], 2.0)\n",
      "([3], 3.0)\n",
      "([1, 3], 3.0)\n",
      "([4], 4.0)\n",
      "([2, 4], 4.0)\n",
      "([3, 4], 4.0)\n",
      "([7], 4.5)\n",
      "([3, 7], 4.5)\n",
      "([5], 5.0)\n",
      "([4, 5], 5.0)\n"
     ]
    }
   ],
   "source": [
    "# st_gen is a generator object, so use for loop to obtain all simplices\n",
    "# notice that all filtration values are set to 0\n",
    "st_gen = st.get_filtration()\n",
    "\n",
    "for splx in st_gen:\n",
    "    print(splx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Different method calls can be used to retrieve different descriptors of the simplicial complex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "([0, 1], 1.0)\n",
      "([0], 0.0)\n",
      "([1, 2], 2.0)\n",
      "([1, 3], 3.0)\n",
      "([1], 1.0)\n",
      "([2, 4], 4.0)\n",
      "([2, 6], 2.0)\n",
      "([2], 2.0)\n",
      "([3, 4], 4.0)\n",
      "([3, 7], 4.5)\n",
      "([3], 3.0)\n",
      "([4, 5], 5.0)\n",
      "([4], 4.0)\n",
      "([5], 5.0)\n",
      "([6], 0.5)\n",
      "([7], 4.5)\n",
      "inf\n"
     ]
    }
   ],
   "source": [
    "# dimension of the complex\n",
    "st.dimension()\n",
    "\n",
    "# num of vertices or 0-simplices\n",
    "st.num_vertices()\n",
    "\n",
    "# num. of simplices\n",
    "st.num_simplices()\n",
    "\n",
    "# check the existance of a specific simplex\n",
    "st.find([1,2])\n",
    "\n",
    "# obtain d-skeleton i.e. union of all simplices of dim less than or equal to d\n",
    "# st1 is generator object\n",
    "st1 = st.get_skeleton(1)\n",
    "for splx in st1:\n",
    "    print(splx)\n",
    "\n",
    "\n",
    "# filtration value associated with particular simplex\n",
    "print(st.filtration([1,2,3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more information, refer Gudhi's [documentation on SimplexTree](https://gudhi.inria.fr/python/latest/simplex_tree_ref.html) data structures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let `st` be an object of type `SimplexTree`. There are two ways of associating filter values to simplices:\n",
    "1. `st.insert( , filteration =  )`: to assign a filter value while introducing a simplex into the complex.\n",
    "2. `st.assign_filtration()`: to modify the existing filtration value of a simplex already included in the complex."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "([0], 0.0)\n",
      "([6], 0.5)\n",
      "([1], 1.0)\n",
      "([0, 1], 1.0)\n",
      "([2], 2.0)\n",
      "([1, 2], 2.0)\n",
      "([2, 6], 2.0)\n",
      "([3], 3.0)\n",
      "([1, 3], 3.0)\n",
      "([4], 4.0)\n",
      "([2, 4], 4.0)\n",
      "([3, 4], 4.0)\n",
      "([7], 4.5)\n",
      "([3, 7], 4.5)\n",
      "([5], 5.0)\n",
      "([4, 5], 5.0)\n"
     ]
    }
   ],
   "source": [
    "# to obtain simplex-filter function values\n",
    "st_gen = st.get_filtration()\n",
    "\n",
    "for smplx in st_gen:\n",
    "    print(smplx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "([0], 0.0)\n",
      "([6], 0.5)\n",
      "([1], 1.0)\n",
      "([0, 1], 1.0)\n",
      "([2], 2.0)\n",
      "([1, 2], 2.0)\n",
      "([2, 6], 2.0)\n",
      "([3], 3.0)\n",
      "([1, 3], 3.0)\n",
      "([4], 4.0)\n",
      "([2, 4], 4.0)\n",
      "([3, 4], 4.0)\n",
      "([7], 4.5)\n",
      "([3, 7], 4.5)\n",
      "([5], 5.0)\n",
      "([4, 5], 5.0)\n"
     ]
    }
   ],
   "source": [
    "st.make_filtration_non_decreasing()\n",
    "st_gen = st.get_filtration()\n",
    "\n",
    "for smplx in st_gen:\n",
    "    print(smplx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizing the simplicial complex. In our example, the complex is a graph. We use tools from `NetworkX` module to visulaize the complex."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 1), (1, 2), (1, 3), (2, 4), (2, 6), (3, 4), (3, 7), (4, 5)]\n",
      "[0, 1, 2, 3, 4, 6, 7, 5]\n"
     ]
    }
   ],
   "source": [
    "# initialize an empty graph G and add nodes and edges based on 0 and 1 simplices\n",
    "G = nx.Graph()\n",
    "for (splx,_) in st.get_skeleton(1):\n",
    "    if len(splx) == 1:\n",
    "        G.add_node(splx[0])\n",
    "    if len(splx) == 2:\n",
    "        G.add_edge(splx[0], splx[1])\n",
    "\n",
    "\n",
    "print(G.edges())\n",
    "print(G.nodes())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: [0.0, 0.0],\n",
       " 1: [0.0, 1.0],\n",
       " 2: [-1.0, 2.0],\n",
       " 3: [1.0, 3.0],\n",
       " 4: [0.0, 4.0],\n",
       " 6: [-2.0, 0.5],\n",
       " 7: [2.0, 4.5],\n",
       " 5: [0.0, 5.0]}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dictionary containing position of vertices in the co-ord plane\n",
    "pos = {}\n",
    "for idxv, v in enumerate(G.nodes()):\n",
    "    y = st.filtration([v])\n",
    "    if v == 2:\n",
    "        x = -1.\n",
    "    elif v == 6:\n",
    "        x = -2.\n",
    "    elif v == 3:\n",
    "        x = 1.\n",
    "    elif v == 7:\n",
    "        x = 2.\n",
    "    else:\n",
    "        x = 0.\n",
    "    pos[v] = [x,y]\n",
    "\n",
    "# key = vertex/0-simplex \n",
    "# value = position in co-ord plane\n",
    "pos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "nx.draw(G, pos=pos, node_size=100, ax=ax)\n",
    "limits=plt.axis('on')\n",
    "ax.tick_params(left=True, bottom=False, labelleft=True, labelbottom=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/padmaraga/anaconda3/envs/tsvd_fmri/lib/python3.12/site-packages/gudhi/persistence_graphical_tools.py:107: UserWarning: usetex mode requires TeX.\n",
      "  warnings.warn(\"usetex mode requires TeX.\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (ordinary) Persistence diagram\n",
    "PD = st.persistence(persistence_dim_max = True)\n",
    "gd.plot_persistence_diagram(PD)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gd.plot_persistence_barcode(PD)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}