weak_witness_persistence.cpp

/*    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):       Siargey Kachanovich
 *
 *    Copyright (C) 2016 Inria
 *
 *    Modification(s):
 *      - YYYY/MM Author: Description of the modification
 */
 
#include <gudhi/Simplex_tree.h>
#include <gudhi/Euclidean_witness_complex.h>
#include <gudhi/Persistent_cohomology.h>
#include <gudhi/Points_off_io.h>
#include <gudhi/pick_n_random_points.h>
#include <gudhi/choose_n_farthest_points.h>
 
#include <boost/program_options.hpp>
 
#include <CGAL/Epick_d.h>
 
#include <string>
#include <vector>
#include <limits>  // infinity
 
using K = CGAL::Epick_d<CGAL::Dynamic_dimension_tag>;
using Point_d = K::Point_d;
 
using Point_vector = std::vector<Point_d>;
using Witness_complex = Gudhi::witness_complex::Euclidean_witness_complex<K>;
using SimplexTree = Gudhi::Simplex_tree<>;
 
using Filtration_value = SimplexTree::Filtration_value;
 
using Field_Zp = Gudhi::persistent_cohomology::Field_Zp;
using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<SimplexTree, Field_Zp>;
 
void program_options(int argc, char* argv[], int& nbL, std::string& file_name, std::string& filediag,
                     Filtration_value& max_squared_alpha, int& p, int& dim_max, Filtration_value& min_persistence);
 
int main(int argc, char* argv[]) {
  std::string file_name;
  std::string filediag;
  Filtration_value max_squared_alpha;
  int p, nbL, lim_d;
  Filtration_value min_persistence;
  SimplexTree simplex_tree;
 
  program_options(argc, argv, nbL, file_name, filediag, max_squared_alpha, p, lim_d, min_persistence);
 
  // Extract the points from the file file_name
  Point_vector witnesses, landmarks;
  Gudhi::Points_off_reader<Point_d> off_reader(file_name);
  if (!off_reader.is_valid()) {
    std::cerr << "Witness complex - Unable to read file " << file_name << "\n";
    exit(-1);  // ----- >>
  }
  witnesses = Point_vector(off_reader.get_point_cloud());
  std::clog << "Successfully read " << witnesses.size() << " points.\n";
  std::clog << "Ambient dimension is " << witnesses[0].dimension() << ".\n";
 
  // Choose landmarks (decomment one of the following two lines)
  // Gudhi::subsampling::pick_n_random_points(point_vector, nbL, std::back_inserter(landmarks));
  Gudhi::subsampling::choose_n_farthest_points(K().squared_distance_d_object(), witnesses, nbL,
                                               Gudhi::subsampling::random_starting_point,
                                               std::back_inserter(landmarks));
 
  // Compute witness complex
  Witness_complex witness_complex(landmarks, witnesses);
 
  witness_complex.create_complex(simplex_tree, max_squared_alpha, lim_d);
 
  std::clog << "The complex contains " << simplex_tree.num_simplices() << " simplices \n";
  std::clog << "   and has dimension " << simplex_tree.dimension() << " \n";
 
  // Sort the simplices in the order of the filtration
  simplex_tree.initialize_filtration();
 
  // Compute the persistence diagram of the complex
  Persistent_cohomology pcoh(simplex_tree);
  // initializes the coefficient field for homology
  pcoh.init_coefficients(p);
 
  pcoh.compute_persistent_cohomology(min_persistence);
 
  // Output the diagram in filediag
  if (filediag.empty()) {
    pcoh.output_diagram();
  } else {
    std::ofstream out(filediag);
    pcoh.output_diagram(out);
    out.close();
  }
 
  return 0;
}
 
void program_options(int argc, char* argv[], int& nbL, std::string& file_name, std::string& filediag,
                     Filtration_value& max_squared_alpha, int& p, int& dim_max, Filtration_value& min_persistence) {
  namespace po = boost::program_options;
 
  po::options_description hidden("Hidden options");
  hidden.add_options()("input-file", po::value<std::string>(&file_name),
                       "Name of file containing a point set in off format.");
 
  Filtration_value default_alpha = std::numeric_limits<Filtration_value>::infinity();
  po::options_description visible("Allowed options", 100);
  visible.add_options()("help,h", "produce help message")("landmarks,l", po::value<int>(&nbL),
                                                          "Number of landmarks to choose from the point cloud.")(
      "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 standard output")(
      "max-sq-alpha,a", po::value<Filtration_value>(&max_squared_alpha)->default_value(default_alpha),
      "Maximal squared relaxation parameter.")(
      "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)->default_value(0),
      "Minimal lifetime of homology feature to be recorded. Default is 0. Enter a negative value to see zero length "
      "intervals")("cpx-dimension,d", po::value<int>(&dim_max)->default_value(std::numeric_limits<int>::max()),
                   "Maximal dimension of the weak witness complex we want to compute.");
 
  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::clog << std::endl;
    std::clog << "Compute the persistent homology with coefficient field Z/pZ \n";
    std::clog << "of a Weak witness 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;
    exit(-1);
  }
}