Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp
/* 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): Vincent Rouvreau
*
* Copyright (C) 2017 INRIA
*
* 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
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* 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 <http://www.gnu.org/licenses/>.
*/
#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 Filtration_value = Simplex_tree::Filtration_value;
using Kernel = CGAL::Epick_d< CGAL::Dynamic_dimension_tag >;
using Point_d = Kernel::Point_d;
using Points_off_reader = Gudhi::Points_off_reader<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::cout << "The Rips complex contains " << rips_stree.num_simplices() << " simplices and has dimension "
<< rips_stree.dimension() << " \n";
// Sort the simplices in the order of the filtration
rips_stree.initialize_filtration();
// Compute the persistence diagram of the complex
Persistent_cohomology rips_pcoh(rips_stree);
// initializes the coefficient field for homology
rips_pcoh.init_coefficients(p);
rips_pcoh.compute_persistent_cohomology(min_persistence);
// 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::cout << "The Alpha complex contains " << alpha_stree.num_simplices() << " simplices and has dimension "
<< alpha_stree.dimension() << " \n";
// Sort the simplices in the order of the filtration
alpha_stree.initialize_filtration();
// Compute the persistence diagram of the complex
Persistent_cohomology alpha_pcoh(alpha_stree);
// initializes the coefficient field for homology
alpha_pcoh.init_coefficients(p);
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::cout << "In dimension " << dim << ", bottleneck distance = " << bottleneck_distance << std::endl;
if (bottleneck_distance > max_b_distance)
max_b_distance = bottleneck_distance;
}
std::cout << "================================================================================" << std::endl;
std::cout << "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");
hidden.add_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);
visible.add_options()
("help,h", "produce help message")
("max-edge-length,r",
po::value<Filtration_value>(&threshold)->default_value(std::numeric_limits<Filtration_value>::infinity()),
"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;
all.add(visible).add(hidden);
po::variables_map vm;
po::store(po::command_line_parser(argc, argv).
options(all).positional(pos).run(), vm);
po::notify(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;
std::abort();
}
}
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