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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
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--- a/example/Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp
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-/* 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;
- exit(-1);
- }
-}