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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) 2015 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_gudhi_stat_H
#define common_gudhi_stat_H
namespace Gudhi
{
namespace Persistence_representations
{
//this file contain an implementation of some common procedures used in Gudhi_stat.
//double epsi = std::numeric_limits<double>::epsilon();
double epsi = 0.000005;
/**
* A procedure used to compare doubles. Typically gien 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 give the user a tolerance on what should be consider equal.
**/
inline bool almost_equal( double a , double b )
{
if ( 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 opposide 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 agguments 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;
//cerr << "Line crossing points : (" << p1.first << "," << p1.second << ") oraz (" << p2.first << "," << p2.second << ") : \n";
//cerr << "a : " << a << " , b : " << b << " , x : " << x << endl;
return -b/a;
}
//landscapes
/**
* This method provides a comparision of points that is used in construction of persistence landscapes. The orderign 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 conputes the line pasing 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 Gudhi_stat
}//namespace Gudhi
#endif
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