polymake-common 3.2r2-3 / usr / share / polymake / demo / persistent_homology.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Persistent Homology Tutorial \n",
    "\n",
    "Persistent homology is a construct from algebraic topology that formalizes the effect that changing a topological space in a certain way has on its homology. It attempts to overcome the lack of robustness homology shows: changing the space of interest just a little can result in a drastic change in homology. The approach to this is to consider the homology of the space at different \"resolutions\", so to say -- for example by approximating it by a sequence of chain complexes that grow more and more complicated and accurate. One can then try to distinguish prominent topological features in arbitrary dimensions from the irrelevant ones by discarding the features that are only present at a few resolutions.\n",
    "\n",
    "[This paper](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.5064) introduces the concept and presents the algorithms. See e.g. [this article](http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01249-X/) for a deeper survey of the topic.\n",
    "\n",
    "To use the function, one has to switch to the `topaz` application. See this [tutorial](topaz_tutorial) for a general introduction to `topaz`.\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "application 'topaz';"
   ]
  },
  {
   "attachments": {
    "small_filtration.png": {
     "image/png": [
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"
     ]
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Filtrations\n",
    "\n",
    "The objects of study are filtrations of chain complexes with finitely many frames. The data structure is templated by the type of matrix used for the description of the boundary maps.\n",
    "\n",
    "### From Hasse diagrams\n",
    "\n",
    "A filtration can be initialized by passing the Hasse diagram of the last frame of the filtration and an array containing the degree of each cell, indexed in the same order as the node indexing in the Hasse diagram (without the empty set and the dummy node with index 0, thus shifted by one). Consider this small three-frame example filtration:\n",
    "\n",
    "![{{ :tutorial:small_filtration.png?800 |}}](attachment:small_filtration.png)\n",
    "\n",
    "You can construct it in `polymake` like this:\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "$S = new SimplicialComplex(FACETS=>[[0,1],[0,2],[1,2],[3]]);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0:-1\n",
       "1:0 1\n",
       "2:0 2\n",
       "3:1 2\n",
       "4:3\n",
       "5:0\n",
       "6:1\n",
       "7:2\n",
       "8:\n"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "$HD = $S->HASSE_DIAGRAM;              # Hasse diagram of the last frame\n",
    "print rows_numbered($HD->FACES);      # check indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "$a = new Array<Int>(1,2,1,2,0,0,1);   # assign degrees to the simplices ([0,1] gets degree 1, [0,2] degree 2 etc)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "$F = new Filtration<SparseMatrix<Rational>>($HD,$a);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "You can print the boundary matrix for each frame and dimension:\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1 -1 0\n",
       "0 1 -1\n",
       "\n"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print $F->boundary_matrix(1,1);     # print dimension 1 matrix of frame 1"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find out which rows correspond to which cells, you can print the cells of the filtration. They will be output as an array of 3-tuples, each representing one cell with degree, dimension and boundary matrix index.\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0,0,1) (0,0,2) (1,0,3) (1,1,0) (1,1,2) (2,0,0) (2,1,1)\n",
       "\n"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print $F->cells;"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### From boundary matrices\n",
    "\n",
    "It is also possible to construct a filtration by passing such an array of cells, together with an array of matrices to be used as boundary matrices. To construct the same filtration as above:\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "        $C->[1] = new Cell(0,0,2);\n",
       "        $C->[2] = new Cell(1,0,3);\n",
       "        $C->[3] = new Cell(1,1,0);\n",
       "        $C->[4] = new Cell(1,1,2);\n",
       "        $C->[5] = new Cell(2,0,0);\n",
       "        $C->[6] = new Cell(2,1,1);\n",
       "        \n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "$C = new Array<Cell>(7);\n",
    "$C->[0] = new Cell(0,0,1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "        $bd->[1] = new SparseMatrix<Rational>([0,1,-1,0],[0,1,0,-1],[0,0,1,-1]);\n",
       "        $bd->[2] = new SparseMatrix<Rational>();\n",
       "    \n"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "$bd = new Array<SparseMatrix<Rational>>(3);\n",
    "$bd->[0] = new SparseMatrix<Rational>([1],[1],[1],[1]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "$F = new Filtration<SparseMatrix<Rational>>($C,$bd);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "### Vietoris-Rips filtration\n",
    "\n",
    "It is also possible to compute the Vietoris-Rips-filtration of a point set given a metric. The input consists of the distance matrix of the point set (that is, the matrix whose i,j-entry is the distance between points i and j), an array containing the filtration degrees of the points, the increase in ball size per frame, and an upper bound to the dimension (so one can compute lower-dimensional skeletons and save space). The following computes the four-skeleton of the VR-filtration of six random points in 5-space using the euclidean metric:\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "$S = polytope::rand_sphere(5,6)->VERTICES;\n",
    "$P = $S->minor(All,sequence(1,5));     # dehomogenize"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sub dist($){                          # define euclidean metric\n",
    "my $v = $_[0] - $_[1];\n",
    "return sqrt(new Float($v*$v));};"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "$D = distance_matrix($P,\\&dist);       # conmpute distance matrix of the point set"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "$a = new Array<Int>(6);               #zero array -- all points get degree 0"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "$F = vietoris_rips_filtration<Rational>($D,$a,0.1,4);"
   ]
  },
  {
   "attachments": {
    "barcode.png": {
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"
     ]
    },
    "rp2_filtration.png": {
     "image/png": [
      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"
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    "\n",
    "\n",
    "![{{ :tutorial:rp2_filtration.png?600|}}](attachment:rp2_filtration.png)\n",
    "## Computing Persistence\n",
    "\n",
    "There are two different functions, one to compute persistent homology for coefficients from arbitrary euclidean domains, and another for computing persistence barcodes for field coefficients. Both are templated by the boundary matrix type. The following examples compute both for this filtration of the 5-simplex, whose 3rd frame is the real projective plane:\n",
    "\n",
    "### Coefficients from arbitrary euclidean domains\n",
    "\n",
    "The function for coefficients from arbitrary euclidean domains takes as parameters a filtration object matching the matrix type and indices `i,p,k`. It outputs a sparse matrix containing (as rows) the generators of the torsion-free part of the `p`-persistent `k`-th homology group of the `i`-th frame, and a list of paired torsion coefficients and corresponding generator matrices.\n",
    "\n",
    "The following code loads a filtration object with Integer coefficients containing the example that was previously saved to disk, which you can download {{ :tutorial:filtrationexample.top |here}}. It then computes the 3-persistent first homology group of frame 0, with the result that the torsion-free part is empty, and the part with torsion coefficient 2 has one generator, namely `-v_0+v_1-v_5`:\n",
    "\n",
    "    \n",
    "     topaz > $F = load_data(\"FiltrationExample.top\");\n",
    "     topaz > print persistent_homology<SparseMatrix<Integer>>($F,0,3,1);\n",
    "    <>\n",
    "    <(2, <(15) (0 -1) (1 1) (5 -1)>)>\n",
    "\n",
    "\n",
    "### Field coefficients and barcodes\n",
    "\n",
    "![{{ :tutorial:barcode.png?200|}}](attachment:barcode.png)The function for field coefficients requires only a filtration object of matching type as parameter. The output is an array with an entry for each dimension, containing a list of persistence intervals encoded as tuples of integers (where -1 encodes infinite lifetime). The following computes the intervals of the same filtration as above but with rational coefficients, downloadable {{ :tutorial:filtrationexamplerational.top |here}}.\n",
    "\n",
    "    \n",
    "     topaz > $F2 = load_data(\"FiltrationExampleRational.top\");\n",
    "     topaz > print persistent_homology<SparseMatrix<Rational>>($F2);\n",
    "    {(0 2) (0 -1)}\n",
    "    {(2 3) (2 3) (2 3) (1 3) (2 3) (0 3)}\n",
    "    {}\n",
    "    {}\n",
    "    {}\n",
    "    {}\n",
    "    {}\n",
    "\n",
    "\n",
    "The output corresponds to the barcode on the right.\n"
   ]
  }
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