Persistent_cohomology/periodic_alpha_complex_3d_persistence.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) 2014  INRIA Saclay (France)
 *
 *    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/Simplex_tree.h>
#include <gudhi/Persistent_cohomology.h>
#include <gudhi/Points_3D_off_io.h>
#include <boost/variant.hpp>

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Periodic_3_Delaunay_triangulation_traits_3.h>
#include <CGAL/Periodic_3_Delaunay_triangulation_3.h>
#include <CGAL/Alpha_shape_3.h>
#include <CGAL/iterator.h>

#include <fstream>
#include <cmath>
#include <string>
#include <tuple>
#include <map>
#include <utility>
#include <list>
#include <vector>

// Traits
using K = CGAL::Exact_predicates_inexact_constructions_kernel;
using PK = CGAL::Periodic_3_Delaunay_triangulation_traits_3<K>;
// Vertex type
using DsVb = CGAL::Periodic_3_triangulation_ds_vertex_base_3<>;
using Vb = CGAL::Triangulation_vertex_base_3<PK, DsVb>;
using AsVb = CGAL::Alpha_shape_vertex_base_3<PK, Vb>;
// Cell type
using DsCb = CGAL::Periodic_3_triangulation_ds_cell_base_3<>;
using Cb = CGAL::Triangulation_cell_base_3<PK, DsCb>;
using AsCb = CGAL::Alpha_shape_cell_base_3<PK, Cb>;
using Tds = CGAL::Triangulation_data_structure_3<AsVb, AsCb>;
using P3DT3 = CGAL::Periodic_3_Delaunay_triangulation_3<PK, Tds>;
using Alpha_shape_3 = CGAL::Alpha_shape_3<P3DT3>;
using Point_3 = PK::Point_3;

// filtration with alpha values needed type definition
using Alpha_value_type = Alpha_shape_3::FT;
using Object = CGAL::Object;
using Dispatch = CGAL::Dispatch_output_iterator<
    CGAL::cpp11::tuple<Object, Alpha_value_type>,
    CGAL::cpp11::tuple<std::back_insert_iterator< std::vector<Object> >,
    std::back_insert_iterator< std::vector<Alpha_value_type> > > >;
using Cell_handle = Alpha_shape_3::Cell_handle;
using Facet = Alpha_shape_3::Facet;
using Edge_3 = Alpha_shape_3::Edge;
using Vertex_list = std::list<Alpha_shape_3::Vertex_handle>;

// gudhi type definition
using ST = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
using Simplex_tree_vertex = ST::Vertex_handle;
using Alpha_shape_simplex_tree_map = std::map<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex >;
using Alpha_shape_simplex_tree_pair = std::pair<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex>;
using Simplex_tree_vector_vertex = std::vector< Simplex_tree_vertex >;
using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<
    ST, Gudhi::persistent_cohomology::Field_Zp >;

Vertex_list from(const Cell_handle& ch) {
  Vertex_list the_list;
  for (auto i = 0; i < 4; i++) {
#ifdef DEBUG_TRACES
    std::cout << "from cell[" << i << "]=" << ch->vertex(i)->point() << std::endl;
#endif  // DEBUG_TRACES
    the_list.push_back(ch->vertex(i));
  }
  return the_list;
}

Vertex_list from(const Facet& fct) {
  Vertex_list the_list;
  for (auto i = 0; i < 4; i++) {
    if (fct.second != i) {
#ifdef DEBUG_TRACES
      std::cout << "from facet=[" << i << "]" << fct.first->vertex(i)->point() << std::endl;
#endif  // DEBUG_TRACES
      the_list.push_back(fct.first->vertex(i));
    }
  }
  return the_list;
}

Vertex_list from(const Edge_3& edg) {
  Vertex_list the_list;
  for (auto i = 0; i < 4; i++) {
    if ((edg.second == i) || (edg.third == i)) {
#ifdef DEBUG_TRACES
      std::cout << "from edge[" << i << "]=" << edg.first->vertex(i)->point() << std::endl;
#endif  // DEBUG_TRACES
      the_list.push_back(edg.first->vertex(i));
    }
  }
  return the_list;
}

Vertex_list from(const Alpha_shape_3::Vertex_handle& vh) {
  Vertex_list the_list;
#ifdef DEBUG_TRACES
  std::cout << "from vertex=" << vh->point() << std::endl;
#endif  // DEBUG_TRACES
  the_list.push_back(vh);
  return the_list;
}

void usage(char * const progName) {
  std::cerr << "Usage: " << progName <<
      " path_to_file_graph coeff_field_characteristic[integer > 0] min_persistence[float >= -1.0]\n";
  exit(-1);
}

int main(int argc, char * const argv[]) {
  // program args management
  if (argc != 4) {
    std::cerr << "Error: Number of arguments (" << argc << ") is not correct\n";
    usage(argv[0]);
  }

  int coeff_field_characteristic = 0;
  int returnedScanValue = sscanf(argv[2], "%d", &coeff_field_characteristic);
  if ((returnedScanValue == EOF) || (coeff_field_characteristic <= 0)) {
    std::cerr << "Error: " << argv[2] << " is not correct\n";
    usage(argv[0]);
  }

  Filtration_value min_persistence = 0.0;
  returnedScanValue = sscanf(argv[3], "%lf", &min_persistence);
  if ((returnedScanValue == EOF) || (min_persistence < -1.0)) {
    std::cerr << "Error: " << argv[3] << " is not correct\n";
    usage(argv[0]);
  }

  // Read points from file
  std::string offInputFile(argv[1]);
  // Read the OFF file (input file name given as parameter) and triangulate points
  Gudhi::Points_3D_off_reader<Point_3> off_reader(offInputFile);
  // Check the read operation was correct
  if (!off_reader.is_valid()) {
    std::cerr << "Unable to read file " << offInputFile << std::endl;
    usage(argv[0]);
  }

  // Retrieve the triangulation
  std::vector<Point_3> lp = off_reader.get_point_cloud();

  // Define the periodic cube
  P3DT3 pdt(PK::Iso_cuboid_3(0, 0, 0, 1, 1, 1));
  // Heuristic for inserting large point sets (if pts is reasonably large)
  pdt.insert(lp.begin(), lp.end(), true);
  // As pdt won't be modified anymore switch to 1-sheeted cover if possible
  if (pdt.is_triangulation_in_1_sheet()) pdt.convert_to_1_sheeted_covering();
  std::cout << "Periodic Delaunay computed." << std::endl;

  // alpha shape construction from points. CGAL has a strange behavior in REGULARIZED mode. This is the default mode
  // Maybe need to set it to GENERAL mode
  Alpha_shape_3 as(pdt, 0, Alpha_shape_3::GENERAL);

  // filtration with alpha values from alpha shape
  std::vector<Object> the_objects;
  std::vector<Alpha_value_type> the_alpha_values;

  Dispatch disp = CGAL::dispatch_output<Object, Alpha_value_type>(std::back_inserter(the_objects),
                                                                  std::back_inserter(the_alpha_values));

  as.filtration_with_alpha_values(disp);
#ifdef DEBUG_TRACES
  std::cout << "filtration_with_alpha_values returns : " << the_objects.size() << " objects" << std::endl;
#endif  // DEBUG_TRACES

  Alpha_shape_3::size_type count_vertices = 0;
  Alpha_shape_3::size_type count_edges = 0;
  Alpha_shape_3::size_type count_facets = 0;
  Alpha_shape_3::size_type count_cells = 0;

  // Loop on objects vector
  Vertex_list vertex_list;
  ST simplex_tree;
  Alpha_shape_simplex_tree_map map_cgal_simplex_tree;
  std::vector<Alpha_value_type>::iterator the_alpha_value_iterator = the_alpha_values.begin();
  int dim_max = 0;
  Filtration_value filtration_max = 0.0;
  for (auto object_iterator : the_objects) {
    // Retrieve Alpha shape vertex list from object
    if (const Cell_handle * cell = CGAL::object_cast<Cell_handle>(&object_iterator)) {
      vertex_list = from(*cell);
      count_cells++;
      if (dim_max < 3) {
        // Cell is of dim 3
        dim_max = 3;
      }
    } else if (const Facet * facet = CGAL::object_cast<Facet>(&object_iterator)) {
      vertex_list = from(*facet);
      count_facets++;
      if (dim_max < 2) {
        // Facet is of dim 2
        dim_max = 2;
      }
    } else if (const Edge_3 * edge = CGAL::object_cast<Edge_3>(&object_iterator)) {
      vertex_list = from(*edge);
      count_edges++;
      if (dim_max < 1) {
        // Edge_3 is of dim 1
        dim_max = 1;
      }
    } else if (const Alpha_shape_3::Vertex_handle * vertex =
               CGAL::object_cast<Alpha_shape_3::Vertex_handle>(&object_iterator)) {
      count_vertices++;
      vertex_list = from(*vertex);
    }
    // Construction of the vector of simplex_tree vertex from list of alpha_shapes vertex
    Simplex_tree_vector_vertex the_simplex_tree;
    for (auto the_alpha_shape_vertex : vertex_list) {
      Alpha_shape_simplex_tree_map::iterator the_map_iterator = map_cgal_simplex_tree.find(the_alpha_shape_vertex);
      if (the_map_iterator == map_cgal_simplex_tree.end()) {
        // alpha shape not found
        Simplex_tree_vertex vertex = map_cgal_simplex_tree.size();
#ifdef DEBUG_TRACES
        std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] not found - insert " << vertex << std::endl;
#endif  // DEBUG_TRACES
        the_simplex_tree.push_back(vertex);
        map_cgal_simplex_tree.insert(Alpha_shape_simplex_tree_pair(the_alpha_shape_vertex, vertex));
      } else {
        // alpha shape found
        Simplex_tree_vertex vertex = the_map_iterator->second;
#ifdef DEBUG_TRACES
        std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] found in " << vertex << std::endl;
#endif  // DEBUG_TRACES
        the_simplex_tree.push_back(vertex);
      }
    }
    // Construction of the simplex_tree
    Filtration_value filtr = /*std::sqrt*/(*the_alpha_value_iterator);
#ifdef DEBUG_TRACES
    std::cout << "filtration = " << filtr << std::endl;
#endif  // DEBUG_TRACES
    if (filtr > filtration_max) {
      filtration_max = filtr;
    }
    simplex_tree.insert_simplex(the_simplex_tree, filtr);
    if (the_alpha_value_iterator != the_alpha_values.end())
      ++the_alpha_value_iterator;
    else
      std::cout << "This shall not happen" << std::endl;
  }
  simplex_tree.set_filtration(filtration_max);
  simplex_tree.set_dimension(dim_max);

#ifdef DEBUG_TRACES
  std::cout << "vertices \t\t" << count_vertices << std::endl;
  std::cout << "edges \t\t" << count_edges << std::endl;
  std::cout << "facets \t\t" << count_facets << std::endl;
  std::cout << "cells \t\t" << count_cells << std::endl;


  std::cout << "Information of the Simplex Tree: " << std::endl;
  std::cout << "  Number of vertices = " << simplex_tree.num_vertices() << " ";
  std::cout << "  Number of simplices = " << simplex_tree.num_simplices() << std::endl << std::endl;
  std::cout << "  Dimension = " << simplex_tree.dimension() << " ";
  std::cout << "  filtration = " << simplex_tree.filtration() << std::endl << std::endl;
#endif  // DEBUG_TRACES

#ifdef DEBUG_TRACES
  std::cout << "Iterator on vertices: " << std::endl;
  for (auto vertex : simplex_tree.complex_vertex_range()) {
    std::cout << vertex << " ";
  }
#endif  // DEBUG_TRACES

  // Sort the simplices in the order of the filtration
  simplex_tree.initialize_filtration();

  std::cout << "Simplex_tree dim: " << simplex_tree.dimension() << std::endl;
  // Compute the persistence diagram of the complex
  Persistent_cohomology pcoh(simplex_tree, true);
  // initializes the coefficient field for homology
  pcoh.init_coefficients(coeff_field_characteristic);

  pcoh.compute_persistent_cohomology(min_persistence);

  pcoh.output_diagram();

  return 0;
}