/* 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: Francois Godi
*
* 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 .
*/
#ifndef PERSISTENCE_GRAPH_H_
#define PERSISTENCE_GRAPH_H_
#include
#include
#include
namespace Gudhi {
namespace bottleneck_distance {
/** \internal \brief Structure representing an euclidean bipartite graph containing
* the points from the two persistence diagrams (including the projections).
*
* \ingroup bottleneck_distance
*/
class Persistence_graph {
public:
/** \internal \brief Constructor taking 2 Persistence_Diagrams (concept) as parameters. */
template
Persistence_graph(const Persistence_diagram1& diag1, const Persistence_diagram2& diag2, double e);
/** \internal \brief Is the given point from U the projection of a point in V ? */
bool on_the_u_diagonal(int u_point_index) const;
/** \internal \brief Is the given point from V the projection of a point in U ? */
bool on_the_v_diagonal(int v_point_index) const;
/** \internal \brief Given a point from V, returns the corresponding (projection or projector) point in U. */
int corresponding_point_in_u(int v_point_index) const;
/** \internal \brief Given a point from U, returns the corresponding (projection or projector) point in V. */
int corresponding_point_in_v(int u_point_index) const;
/** \internal \brief Given a point from U and a point from V, returns the distance between those points. */
double distance(int u_point_index, int v_point_index) const;
/** \internal \brief Returns size = |U| = |V|. */
int size() const;
/** \internal \brief Is there as many infinite points (alive components) in both diagrams ? */
bool alive_match() const;
/** \internal \brief Returns the O(n^2) sorted distances between the points. */
std::vector sorted_distances() const;
/** \internal \brief Returns an upper bound for the diameter of the convex hull of all non infinite points */
double diameter_bound() const;
/** \internal \brief Returns the corresponding internal point */
Internal_point get_u_point(int u_point_index) const;
/** \internal \brief Returns the corresponding internal point */
Internal_point get_v_point(int v_point_index) const;
private:
std::vector u;
std::vector v;
int alive_count;
};
template
Persistence_graph::Persistence_graph(const Persistence_diagram1 &diag1,
const Persistence_diagram2 &diag2, double e)
: u(), v(), alive_count(0)
{
for (auto it = diag1.cbegin(); it != diag1.cend(); ++it)
if(it->second == std::numeric_limits::infinity())
alive_count++;
else if (it->second - it->first > e)
u.push_back(Internal_point(std::get<0>(*it), std::get<1>(*it), u.size()));
for (auto it = diag2.cbegin(); it != diag2.cend(); ++it)
if(it->second == std::numeric_limits::infinity())
alive_count--;
else if (it->second - it->first > e)
v.push_back(Internal_point(std::get<0>(*it), std::get<1>(*it), v.size()));
if (u.size() < v.size())
swap(u, v);
}
inline bool Persistence_graph::on_the_u_diagonal(int u_point_index) const {
return u_point_index >= static_cast (u.size());
}
inline bool Persistence_graph::on_the_v_diagonal(int v_point_index) const {
return v_point_index >= static_cast (v.size());
}
inline int Persistence_graph::corresponding_point_in_u(int v_point_index) const {
return on_the_v_diagonal(v_point_index) ?
v_point_index - static_cast (v.size()) : v_point_index + static_cast (u.size());
}
inline int Persistence_graph::corresponding_point_in_v(int u_point_index) const {
return on_the_u_diagonal(u_point_index) ?
u_point_index - static_cast (u.size()) : u_point_index + static_cast (v.size());
}
inline double Persistence_graph::distance(int u_point_index, int v_point_index) const {
if (on_the_u_diagonal(u_point_index) && on_the_v_diagonal(v_point_index))
return 0.;
Internal_point p_u = get_u_point(u_point_index);
Internal_point p_v = get_v_point(v_point_index);
return std::max(std::fabs(p_u.x() - p_v.x()), std::fabs(p_u.y() - p_v.y()));
}
inline int Persistence_graph::size() const {
return static_cast (u.size() + v.size());
}
inline bool Persistence_graph::alive_match() const{
return alive_count==0;
}
inline std::vector Persistence_graph::sorted_distances() const {
std::vector distances;
distances.push_back(0.);
for (int u_point_index = 0; u_point_index < size(); ++u_point_index){
distances.push_back(distance(u_point_index, corresponding_point_in_v(u_point_index)));
for (int v_point_index = 0; v_point_index < size(); ++v_point_index)
distances.push_back(distance(u_point_index, v_point_index));
}
std::sort(distances.begin(), distances.end());
return distances;
}
inline Internal_point Persistence_graph::get_u_point(int u_point_index) const {
if (!on_the_u_diagonal(u_point_index))
return u.at(u_point_index);
Internal_point projector = v.at(corresponding_point_in_v(u_point_index));
double m = (projector.x() + projector.y()) / 2;
return Internal_point(m,m,u_point_index);
}
inline Internal_point Persistence_graph::get_v_point(int v_point_index) const {
if (!on_the_v_diagonal(v_point_index))
return v.at(v_point_index);
Internal_point projector = u.at(corresponding_point_in_u(v_point_index));
double m = (projector.x() + projector.y()) / 2;
return Internal_point(m,m,v_point_index);
}
inline double Persistence_graph::diameter_bound() const {
double max = 0.;
for(auto it = u.cbegin(); it != u.cend(); it++)
max = std::max(max,it->y());
for(auto it = v.cbegin(); it != v.cend(); it++)
max = std::max(max,it->y());
return max;
}
} // namespace bottleneck_distance
} // namespace Gudhi
#endif // PERSISTENCE_GRAPH_H_