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/* 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 (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/>.
*/
#ifndef COMMON_PERSISTENCE_REPRESENTATIONS_H_
#define COMMON_PERSISTENCE_REPRESENTATIONS_H_
#include <utility>
#include <string>
#include <cmath>
namespace Gudhi {
namespace Persistence_representations {
// this file contain an implementation of some common procedures used in Persistence_representations.
// 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_
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