1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
|
/* 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): Siddharth Pritam, Vincent Rouvreau
*
* Copyright (C) 2020 Inria
*
* Modification(s):
* - YYYY/MM Author: Description of the modification
*/
#include <gudhi/Flag_complex_edge_collapser.h>
#include <gudhi/Simplex_tree.h>
#include <gudhi/Persistent_cohomology.h>
#include <gudhi/reader_utils.h>
#include <gudhi/graph_simplicial_complex.h>
#include <boost/program_options.hpp>
#include <boost/range/adaptor/transformed.hpp>
using Simplex_tree = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
using Filtration_value = Simplex_tree::Filtration_value;
using Vertex_handle = Simplex_tree::Vertex_handle;
using Filtered_edge = std::tuple<Vertex_handle, Vertex_handle, Filtration_value>;
using Proximity_graph = Gudhi::Proximity_graph<Simplex_tree>;
using Field_Zp = Gudhi::persistent_cohomology::Field_Zp;
using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<Simplex_tree, Field_Zp>;
using Distance_matrix = std::vector<std::vector<Filtration_value>>;
void program_options(int argc, char* argv[], std::string& csv_matrix_file, std::string& filediag,
Filtration_value& threshold, int& dim_max, int& p, int& edge_collapse_iter_nb,
Filtration_value& min_persistence);
int main(int argc, char* argv[]) {
std::string csv_matrix_file;
std::string filediag;
Filtration_value threshold;
int dim_max = 2;
int p;
int edge_collapse_iter_nb;
Filtration_value min_persistence;
program_options(argc, argv, csv_matrix_file, filediag, threshold, dim_max, p, edge_collapse_iter_nb,
min_persistence);
Distance_matrix distances = Gudhi::read_lower_triangular_matrix_from_csv_file<Filtration_value>(csv_matrix_file);
std::cout << "Read the distance matrix successfully, of size: " << distances.size() << std::endl;
Proximity_graph proximity_graph = Gudhi::compute_proximity_graph<Simplex_tree>(boost::irange((size_t)0,
distances.size()),
threshold,
[&distances](size_t i, size_t j) {
return distances[j][i];
});
auto edges_from_graph = boost::adaptors::transform(edges(proximity_graph), [&](auto&&edge){
return std::make_tuple(source(edge, proximity_graph),
target(edge, proximity_graph),
get(Gudhi::edge_filtration_t(), proximity_graph, edge));
});
std::vector<Filtered_edge> edges_list(edges_from_graph.begin(), edges_from_graph.end());
std::vector<Filtered_edge> remaining_edges;
for (int iter = 0; iter < edge_collapse_iter_nb; iter++) {
auto remaining_edges = Gudhi::collapse::flag_complex_collapse_edges(edges_list);
edges_list = std::move(remaining_edges);
remaining_edges.clear();
}
Simplex_tree stree;
for (Vertex_handle vertex = 0; static_cast<std::size_t>(vertex) < distances.size(); vertex++) {
// insert the vertex with a 0. filtration value just like a Rips
stree.insert_simplex({vertex}, 0.);
}
for (auto filtered_edge : edges_list) {
stree.insert_simplex({std::get<0>(filtered_edge), std::get<1>(filtered_edge)}, std::get<2>(filtered_edge));
}
stree.expansion(dim_max);
std::cout << "The complex contains " << stree.num_simplices() << " simplices after collapse. \n";
std::cout << " and has dimension " << stree.dimension() << " \n";
// Sort the simplices in the order of the filtration
stree.initialize_filtration();
// Compute the persistence diagram of the complex
Persistent_cohomology pcoh(stree);
// initializes the coefficient field for homology
pcoh.init_coefficients(3);
pcoh.compute_persistent_cohomology(min_persistence);
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[], std::string& csv_matrix_file, std::string& filediag,
Filtration_value& threshold, int& dim_max, int& p, int& edge_collapse_iter_nb,
Filtration_value& min_persistence) {
namespace po = boost::program_options;
po::options_description hidden("Hidden options");
hidden.add_options()(
"input-file", po::value<std::string>(&csv_matrix_file),
"Name of file containing a distance matrix. Can be square or lower triangular matrix. Separator is ';'.");
po::options_description visible("Allowed options", 100);
visible.add_options()("help,h", "produce help message")(
"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 std::cout")(
"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.")(
"edge-collapse-iterations,i", po::value<int>(&edge_collapse_iter_nb)->default_value(1),
"Number of iterations edge collapse is performed.")(
"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 after edge collapse defined on a set of distance matrix.\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);
}
}
|
