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Diffstat (limited to 'example/Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp')
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diff --git a/example/Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp b/example/Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp new file mode 100644 index 00000000..fd164b22 --- /dev/null +++ b/example/Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp @@ -0,0 +1,190 @@ +/* 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/distance_functions.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 Simplex_tree = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>; +using Filtration_value = Simplex_tree::Filtration_value; +using Rips_complex = Gudhi::rips_complex::Rips_complex<Filtration_value>; +using Field_Zp = Gudhi::persistent_cohomology::Field_Zp; +using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<Simplex_tree, Field_Zp >; +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(); + } +} |