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/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
* See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
* Author(s): Vincent Rouvreau
* Copyright (C) 2017 Inria
* Modification(s):
* - YYYY/MM Author: Description of the modification
#include <gudhi/Alpha_complex.h>
#include <gudhi/Rips_complex.h>
#include <gudhi/Simplex_tree.h>
#include <gudhi/Persistent_cohomology.h>
#include <gudhi/Points_off_io.h>
#include <gudhi/Bottleneck.h>
#include <CGAL/Epick_d.h>
#include <boost/program_options.hpp>
#include <string>
#include <vector>
#include <limits> // infinity
#include <utility> // for pair
#include <algorithm> // for transform
// Types definition
using Kernel = CGAL::Epick_d< CGAL::Dynamic_dimension_tag >;
using Point_d = Kernel::Point_d;
void program_options(int argc, char * argv[]
, std::string & off_file_points
, Filtration_value & threshold
, int & dim_max
, int & p
, Filtration_value & min_persistence);
static inline std::pair<double, double> compute_root_square(std::pair<double, double> input) {
return std::make_pair(std::sqrt(input.first), std::sqrt(input.second));
int main(int argc, char * argv[]) {
std::string off_file_points;
Filtration_value threshold;
int dim_max;
int p;
Filtration_value min_persistence;
program_options(argc, argv, off_file_points, threshold, dim_max, p, min_persistence);
Points_off_reader off_reader(off_file_points);
// --------------------------------------------
// Rips persistence
// --------------------------------------------
Rips_complex rips_complex(off_reader.get_point_cloud(), threshold, Gudhi::Euclidean_distance());
// Construct the Rips complex in a Simplex Tree
Simplex_tree rips_stree;
rips_complex.create_complex(rips_stree, dim_max);
std::clog << "The Rips complex contains " << rips_stree.num_simplices() << " simplices and has dimension "
<< rips_stree.dimension() << " \n";
// Compute the persistence diagram of the complex
Persistent_cohomology rips_pcoh(rips_stree);
// initializes the coefficient field for homology
// rips_pcoh.output_diagram();
// --------------------------------------------
// Alpha persistence
// --------------------------------------------
Gudhi::alpha_complex::Alpha_complex<Kernel> alpha_complex(off_reader.get_point_cloud());
Simplex_tree alpha_stree;
alpha_complex.create_complex(alpha_stree, threshold * threshold);
std::clog << "The Alpha complex contains " << alpha_stree.num_simplices() << " simplices and has dimension "
<< alpha_stree.dimension() << " \n";
// Compute the persistence diagram of the complex
Persistent_cohomology alpha_pcoh(alpha_stree);
// initializes the coefficient field for homology
alpha_pcoh.compute_persistent_cohomology(min_persistence * min_persistence);
// alpha_pcoh.output_diagram();
// --------------------------------------------
// Bottleneck distance between both persistence
// --------------------------------------------
double max_b_distance {};
for (int dim = 0; dim < dim_max; dim ++) {
std::vector< std::pair< Filtration_value , Filtration_value > > rips_intervals;
std::vector< std::pair< Filtration_value , Filtration_value > > alpha_intervals;
rips_intervals = rips_pcoh.intervals_in_dimension(dim);
alpha_intervals = alpha_pcoh.intervals_in_dimension(dim);
std::transform(alpha_intervals.begin(), alpha_intervals.end(), alpha_intervals.begin(), compute_root_square);
double bottleneck_distance = Gudhi::persistence_diagram::bottleneck_distance(rips_intervals, alpha_intervals);
std::clog << "In dimension " << dim << ", bottleneck distance = " << bottleneck_distance << std::endl;
if (bottleneck_distance > max_b_distance)
max_b_distance = bottleneck_distance;
std::clog << "================================================================================" << std::endl;
std::clog << "Bottleneck distance is " << max_b_distance << std::endl;
return 0;
void program_options(int argc, char * argv[]
, std::string & off_file_points
, 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")
"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::clog << std::endl;
std::clog << "Compute the persistent homology with coefficient field Z/pZ \n";
std::clog << "of a Rips complex defined on a set of input points.\n \n";
std::clog << "The output diagram contains one bar per line, written with the convention: \n";
std::clog << " p dim b d \n";
std::clog << "where dim is the dimension of the homological feature,\n";
std::clog << "b and d are respectively the birth and death of the feature and \n";
std::clog << "p is the characteristic of the field Z/pZ used for homology coefficients." << std::endl << std::endl;
std::clog << "Usage: " << argv[0] << " [options] input-file" << std::endl << std::endl;
std::clog << visible << std::endl;
Compute the Euclidean distance between two Points given by a range of coordinates....
Definition: distance_functions.h:32
OFF file reader implementation in order to read points from an OFF file.
Definition: Points_off_io.h:122
Options::Filtration_value Filtration_value
Type for the value of the filtration function.
Definition: Simplex_tree.h:90
int dimension(Simplex_handle sh)
Returns the dimension of a simplex.
Definition: Simplex_tree.h:609
size_t num_simplices()
returns the number of simplices in the simplex_tree.
Definition: Simplex_tree.h:587
Alpha complex data structure.
Definition: Alpha_complex.h:103
Structure representing the coefficient field .
Definition: Field_Zp.h:27
Computes the persistent cohomology of a filtered complex.
Definition: Persistent_cohomology.h:53
Rips complex data structure.
Definition: Rips_complex.h:45
Global distance functions.
double bottleneck_distance(const Persistence_diagram1 &diag1, const Persistence_diagram2 &diag2, double e=(std::numeric_limits< double >::min)())
Function to compute the Bottleneck distance between two persistence diagrams.
Definition: Bottleneck.h:116
Value type for a filtration function on a cell complex.
Definition: FiltrationValue.h:20