/* This file is part of the Gudhi Library. The Gudhi library
* (Geometric Understanding in Higher Dimensions) is a generic C++
* library for computational topology.
* Author(s): Clément Maria
* Copyright (C) 2014 INRIA Sophia Antipolis-Méditerranée (France)
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* GNU General Public License for more details.
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <>.
#include <gudhi/graph_simplicial_complex.h>
#include <gudhi/Simplex_tree.h>
#include <gudhi/Persistent_cohomology.h>
#include <gudhi/Points_off_io.h>
#include <boost/program_options.hpp>
#include <string>
#include <vector>
#include <limits> // infinity
#include <utility> // for pair
#include <map>
// ----------------------------------------------------------------------------
// rips_persistence_step_by_step is an example of each step that is required to
// build a Rips over a Simplex_tree. Please refer to rips_persistence to see
// how to do the same thing with the Rips_complex wrapper for less detailed
// steps.
// ----------------------------------------------------------------------------
// Types definition
using Vertex_handle = Simplex_tree::Vertex_handle;
using Filtration_value = Simplex_tree::Filtration_value;
using Graph_t = boost::adjacency_list < boost::vecS, boost::vecS, boost::undirectedS
, boost::property < vertex_filtration_t, Filtration_value >
, boost::property < edge_filtration_t, Filtration_value >
using Edge_t = std::pair< Vertex_handle, Vertex_handle >;
template< typename InputPointRange, typename Distance >
Graph_t compute_proximity_graph(InputPointRange &points, Filtration_value threshold, Distance distance);
using Point = std::vector<double>;
using Points_off_reader = Gudhi::Points_off_reader<Point>;
void program_options(int argc, char * argv[]
, std::string & off_file_points
, std::string & filediag
, Filtration_value & threshold
, int & dim_max
, int & p
, Filtration_value & min_persistence);
int main(int argc, char * argv[]) {
std::string off_file_points;
std::string filediag;
Filtration_value threshold;
int dim_max;
int p;
Filtration_value min_persistence;
program_options(argc, argv, off_file_points, filediag, threshold, dim_max, p, min_persistence);
// Extract the points from the file filepoints
Points_off_reader off_reader(off_file_points);
// Compute the proximity graph of the points
Graph_t prox_graph = compute_proximity_graph(off_reader.get_point_cloud(), threshold
// Construct the Rips complex in a Simplex Tree
Simplex_tree st;
// insert the proximity graph in the simplex tree
// expand the graph until dimension dim_max
std::cout << "The complex contains " << st.num_simplices() << " simplices \n";
std::cout << " and has dimension " << st.dimension() << " \n";
// Sort the simplices in the order of the filtration
// Compute the persistence diagram of the complex
Persistent_cohomology pcoh(st);
// initializes the coefficient field for homology
// Output the diagram in filediag
if (filediag.empty()) {
} else {
std::ofstream out(filediag);
return 0;
void program_options(int argc, char * argv[]
, std::string & off_file_points
, std::string & filediag
, Filtration_value & threshold
, int & dim_max
, int & p
, Filtration_value & min_persistence) {
namespace po = boost::program_options;
po::options_description hidden("Hidden options");
("input-file", po::value<std::string>(&off_file_points),
"Name of an OFF file containing a point set.\n");
po::options_description visible("Allowed options", 100);
("help,h", "produce help message")
("output-file,o", po::value<std::string>(&filediag)->default_value(std::string()),
"Name of file in which the persistence diagram is written. Default print in std::cout")
"Maximal length of an edge for the Rips complex construction.")
("cpx-dimension,d", po::value<int>(&dim_max)->default_value(1),
"Maximal dimension of the Rips complex we want to compute.")
("field-charac,p", po::value<int>(&p)->default_value(11),
"Characteristic p of the coefficient field Z/pZ for computing homology.")
("min-persistence,m", po::value<Filtration_value>(&min_persistence),
"Minimal lifetime of homology feature to be recorded. Default is 0. Enter a negative value to see zero length intervals");
po::positional_options_description pos;
pos.add("input-file", 1);
po::options_description all;
po::variables_map vm;
po::store(po::command_line_parser(argc, argv).
options(all).positional(pos).run(), vm);
if (vm.count("help") || !vm.count("input-file")) {
std::cout << std::endl;
std::cout << "Compute the persistent homology with coefficient field Z/pZ \n";
std::cout << "of a Rips complex defined on a set of input points.\n \n";
std::cout << "The output diagram contains one bar per line, written with the convention: \n";
std::cout << " p dim b d \n";
std::cout << "where dim is the dimension of the homological feature,\n";
std::cout << "b and d are respectively the birth and death of the feature and \n";
std::cout << "p is the characteristic of the field Z/pZ used for homology coefficients." << std::endl << std::endl;
std::cout << "Usage: " << argv[0] << " [options] input-file" << std::endl << std::endl;
std::cout << visible << std::endl;
template< typename InputPointRange, typename Distance >
Graph_t compute_proximity_graph(InputPointRange &points, Filtration_value threshold, Distance distance) {
std::vector< Edge_t > edges;
std::vector< Filtration_value > edges_fil;
Vertex_handle idx_u, idx_v;
Filtration_value fil;
idx_u = 0;
for (auto it_u = points.begin(); it_u != points.end(); ++it_u) {
idx_v = idx_u + 1;
for (auto it_v = it_u + 1; it_v != points.end(); ++it_v, ++idx_v) {
fil = distance(*it_u, *it_v);
if (fil <= threshold) {
edges.emplace_back(idx_u, idx_v);
Graph_t skel_graph(edges.begin()
, edges.end()
, edges_fil.begin()
, idx_u); // number of points labeled from 0 to idx_u-1
auto vertex_prop = boost::get(vertex_filtration_t(), skel_graph);
boost::graph_traits<Graph_t>::vertex_iterator vi, vi_end;
for (std::tie(vi, vi_end) = boost::vertices(skel_graph);
vi != vi_end; ++vi) {
boost::put(vertex_prop, *vi, 0.);
return skel_graph;
GUDHI  Version 2.0.0  - C++ library for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding. Generated on Wed Apr 19 2017 22:26:16 for GUDHI by doxygen 1.8.11