/* 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
*
* 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
#ifdef GUDHI_USE_TBB
#include
#endif
#include
#include
#include // for numeric_limits
namespace Gudhi {
namespace persistence_diagram {
/** \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 PersistenceDiagrams (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 ? */
double bottleneck_alive() 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;
double b_alive;
};
template
Persistence_graph::Persistence_graph(const Persistence_diagram1 &diag1,
const Persistence_diagram2 &diag2, double e)
: u(), v(), b_alive(0.) {
std::vector u_alive;
std::vector v_alive;
for (auto it = std::begin(diag1); it != std::end(diag1); ++it) {
if (std::get<1>(*it) == std::numeric_limits::infinity())
u_alive.push_back(std::get<0>(*it));
else if (std::get<1>(*it) - std::get<0>(*it) > e)
u.push_back(Internal_point(std::get<0>(*it), std::get<1>(*it), u.size()));
}
for (auto it = std::begin(diag2); it != std::end(diag2); ++it) {
if (std::get<1>(*it) == std::numeric_limits::infinity())
v_alive.push_back(std::get<0>(*it));
else if (std::get<1>(*it) - std::get<0>(*it) > e)
v.push_back(Internal_point(std::get<0>(*it), std::get<1>(*it), v.size()));
}
if (u.size() < v.size())
swap(u, v);
std::sort(u_alive.begin(), u_alive.end());
std::sort(v_alive.begin(), v_alive.end());
if (u_alive.size() != v_alive.size()) {
b_alive = std::numeric_limits::infinity();
} else {
for (auto it_u = u_alive.cbegin(), it_v = v_alive.cbegin(); it_u != u_alive.cend(); ++it_u, ++it_v)
b_alive = (std::max)(b_alive, std::fabs(*it_u - *it_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 double Persistence_graph::bottleneck_alive() const {
return b_alive;
}
inline std::vector Persistence_graph::sorted_distances() const {
std::vector distances;
distances.push_back(0.); // for empty diagrams
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));
}
#ifdef GUDHI_USE_TBB
tbb::parallel_sort(distances.begin(), distances.end());
#else
std::sort(distances.begin(), distances.end());
#endif
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 persistence_diagram
} // namespace Gudhi
#endif // PERSISTENCE_GRAPH_H_