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
|
/* 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 <CGAL/Epick_d.h>
#include <CGAL/point_generators_d.h>
#include <CGAL/algorithm.h>
#include <CGAL/assertions.h>
#include <gudhi/Alpha_complex.h>
#include <gudhi/Persistent_cohomology.h>
#include <iostream>
#include <iterator>
#include <vector>
#include <fstream> // for std::ofstream
#include <algorithm> // for std::sort
using Kernel = CGAL::Epick_d< CGAL::Dimension_tag<3> >;
using Point = Kernel::Point_d;
using Alpha_complex = Gudhi::alpha_complex::Alpha_complex<Kernel>;
std::vector<Point> random_points() {
// Instanciate a random point generator
CGAL::Random rng(0);
// Generate "points_number" random points in a vector
std::vector<Point> points;
// Generates 1000 random 3D points on a sphere of radius 4.0
CGAL::Random_points_on_sphere_d<Point> rand_outside(3, 4.0, rng);
CGAL::cpp11::copy_n(rand_outside, 1000, std::back_inserter(points));
// Generates 2000 random 3D points in a sphere of radius 3.0
CGAL::Random_points_in_ball_d<Point> rand_inside(3, 3.0, rng);
CGAL::cpp11::copy_n(rand_inside, 2000, std::back_inserter(points));
return points;
}
/*
* Compare two intervals by dimension, then by length.
*/
struct cmp_intervals_by_dim_then_length {
explicit cmp_intervals_by_dim_then_length(Alpha_complex * sc)
: sc_(sc) { }
template<typename Persistent_interval>
bool operator()(const Persistent_interval & p1, const Persistent_interval & p2) {
if (sc_->dimension(get < 0 > (p1)) == sc_->dimension(get < 0 > (p2)))
return (sc_->filtration(get < 1 > (p1)) - sc_->filtration(get < 0 > (p1))
> sc_->filtration(get < 1 > (p2)) - sc_->filtration(get < 0 > (p2)));
else
return (sc_->dimension(get < 0 > (p1)) > sc_->dimension(get < 0 > (p2)));
}
Alpha_complex* sc_;
};
int main(int argc, char **argv) {
std::vector<Point> points = random_points();
// Alpha complex persistence computation from generated points
Alpha_complex alpha_complex_from_points(points, 0.6);
using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology< Alpha_complex,
Gudhi::persistent_cohomology::Field_Zp >;
Persistent_cohomology pcoh(alpha_complex_from_points);
// initializes the coefficient field for homology - Z/3Z
pcoh.init_coefficients(3);
pcoh.compute_persistent_cohomology(0.2);
// Custom sort and output persistence
cmp_intervals_by_dim_then_length cmp(&alpha_complex_from_points);
auto persistent_pairs = pcoh.get_persistent_pairs();
std::sort(std::begin(persistent_pairs), std::end(persistent_pairs), cmp);
for (auto pair : persistent_pairs) {
std::cout << alpha_complex_from_points.dimension(get<0>(pair)) << " "
<< alpha_complex_from_points.filtration(get<0>(pair)) << " "
<< alpha_complex_from_points.filtration(get<1>(pair)) << std::endl;
}
// Persistent Betti numbers
std::cout << "The persistent Betti numbers in interval [0.40, 0.41] are : ";
for (int dim = 0; dim < alpha_complex_from_points.dimension(); dim++)
std::cout << "b" << dim << " = " << pcoh.persistent_betti_number(dim, 0.40, 0.41) << " ; ";
std::cout << std::endl;
// Betti numbers
std::vector<int> betti_numbers = pcoh.betti_numbers();
std::cout << "The Betti numbers are : ";
for (std::size_t i = 0; i < betti_numbers.size(); i++)
std::cout << "b" << i << " = " << betti_numbers[i] << " ; ";
std::cout << std::endl;
return 0;
}
|
