common_persistence_representations.h

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/*    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):       Pawel Dlotko
 *
 *    Copyright (C) 2016 Inria
 *
 *    Modification(s):
 *      - 2025/06 Hannah Schreiber: Various small bug fixes (missing `inline`s, `DEBUG_TRACES`s etc.)
 *      - YYYY/MM Author: Description of the modification
 */

 
#ifndef COMMON_PERSISTENCE_REPRESENTATIONS_H_
#define COMMON_PERSISTENCE_REPRESENTATIONS_H_
 
#include <stdexcept>  // std::invalid_argument
#include <utility>    // std::pair, std::make_pair
#include <sstream>    // std::ostringstream
#include <cmath>      // std::fabs
#include <vector>
 
#include <boost/math/constants/constants.hpp>
 
namespace Gudhi {
namespace Persistence_representations {

using Persistence_diagram = std::vector<std::pair<double, double> >;

inline constexpr double pi = boost::math::constants::pi<double>();
 
// TODO: I don't think this is a good idea? Having modifiable global variables like that.
// But the description of `almost_equal` shows that it is the intended use.
// At the same time, it seems to be the only method using it. Can we not add it as an argument instead?
inline double epsi = 0.000005;

inline bool almost_equal(double a, double b)
{
  if (std::fabs(a - b) < epsi) return true;
  return false;
}
 
// landscapes
inline constexpr double minus_length(const std::pair<double, double>& a) { return a.first - a.second; }

inline constexpr double birth_plus_deaths(const std::pair<double, double>& a) { return a.first + a.second; }
 
// landscapes
inline constexpr bool compare_points_sorting(const std::pair<double, double>& f, const 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;
      }
    }
  }
}
 
// TODO: the following methods are mostly used with `std::make_pair` as argument in `Persistence_landscape(_on_grid)".
// If called often, it would be more effective to have a (double, double, double, double) version instead.
 
// landscapes
inline std::pair<double, double> compute_parameters_of_a_line(const std::pair<double, double>& p1,
                                                              const std::pair<double, double>& p2)
{
  const double a = (p2.second - p1.second) / (p2.first - p1.first);
  const double b = p1.second - a * p1.first;
  return std::make_pair(a, b);
}
 
// landscapes
inline double find_zero_of_a_line_segment_between_those_two_points(const std::pair<double, double>& p1,
                                                                   const 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.";
    throw std::invalid_argument(errMessage.str());
  }
  // we assume here, that x \in [ p1.first, p2.first ] and p1 and p2 are points between which we will put the line
  // segment
  const auto [a, b] = compute_parameters_of_a_line(p1, p2);
  return -b / a;
}
 
// landscapes
inline double function_value(const std::pair<double, double>& p1, const 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
  const auto [a, b] = compute_parameters_of_a_line(p1, p2);
  return (a * x + b);
}
 
}  // namespace Persistence_representations
}  // namespace Gudhi
 
#endif  // COMMON_PERSISTENCE_REPRESENTATIONS_H_