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
|
/* 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): Pawel Dlotko
*
* Copyright (C) 2016 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/>.
*/
#ifndef COMMON_PERSISTENCE_REPRESENTATIONS_H_
#define COMMON_PERSISTENCE_REPRESENTATIONS_H_
#include <utility>
#include <string>
#include <cmath>
#include <boost/math/constants/constants.hpp>
namespace Gudhi {
namespace Persistence_representations {
// this file contain an implementation of some common procedures used in Persistence_representations.
static constexpr double pi = boost::math::constants::pi<double>();
/**
* In this module, we use the name Persistence_diagram for the representation of a diagram in a vector of pairs of two double.
*/
using Persistence_diagram = std::vector<std::pair<double, double> >;
// double epsi = std::numeric_limits<double>::epsilon();
double epsi = 0.000005;
/**
* A procedure used to compare doubles. Typically given two doubles A and B, comparing A == B is not good idea. In this
* case, we use the procedure almostEqual with the epsi defined at
* the top of the file. Setting up the epsi gives the user a tolerance on what should be consider equal.
**/
inline bool almost_equal(double a, double b) {
if (std::fabs(a - b) < epsi) return true;
return false;
}
// landscapes
/**
* Extra functions needed in construction of barcodes.
**/
double minus_length(std::pair<double, double> a) { return a.first - a.second; }
double birth_plus_deaths(std::pair<double, double> a) { return a.first + a.second; }
// landscapes
/**
* Given two points in R^2, the procedure compute the parameters A and B of the line y = Ax + B that crosses those two points.
**/
std::pair<double, double> compute_parameters_of_a_line(std::pair<double, double> p1, std::pair<double, double> p2) {
double a = (p2.second - p1.second) / (p2.first - p1.first);
double b = p1.second - a * p1.first;
return std::make_pair(a, b);
}
// landscapes
/**
* This procedure given two points which lies on the opposite sides of x axis, compute x for which the line connecting those two points crosses x axis.
**/
double find_zero_of_a_line_segment_between_those_two_points(std::pair<double, double> p1,
std::pair<double, double> p2) {
if (p1.first == p2.first) return p1.first;
if (p1.second * p2.second > 0) {
std::ostringstream errMessage;
errMessage << "In function find_zero_of_a_line_segment_between_those_two_points the arguments are: (" << p1.first
<< "," << p1.second << ") and (" << p2.first << "," << p2.second
<< "). There is no zero in line between those two points. Program terminated.";
std::string errMessageStr = errMessage.str();
const char* err = errMessageStr.c_str();
throw(err);
}
// we assume here, that x \in [ p1.first, p2.first ] and p1 and p2 are points between which we will put the line
// segment
double a = (p2.second - p1.second) / (p2.first - p1.first);
double b = p1.second - a * p1.first;
return -b / a;
}
// landscapes
/**
* This method provides a comparison of points that is used in construction of persistence landscapes. The ordering is
* lexicographical for the first coordinate, and reverse-lexicographical for the second coordinate.
**/
bool compare_points_sorting(std::pair<double, double> f, std::pair<double, double> s) {
if (f.first < s.first) {
return true;
} else { // f.first >= s.first
if (f.first > s.first) {
return false;
} else { // f.first == s.first
if (f.second > s.second) {
return true;
} else {
return false;
}
}
}
}
// landscapes
/**
* This procedure takes two points in R^2 and a double value x. It computes the line parsing through those two points
*and return the value of that linear function at x.
**/
double function_value(std::pair<double, double> p1, std::pair<double, double> p2, double x) {
// we assume here, that x \in [ p1.first, p2.first ] and p1 and p2 are points between which we will put the line
// segment
double a = (p2.second - p1.second) / (p2.first - p1.first);
double b = p1.second - a * p1.first;
return (a * x + b);
}
} // namespace Persistence_representations
} // namespace Gudhi
#endif // COMMON_PERSISTENCE_REPRESENTATIONS_H_
|
