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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: 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 <http://www.gnu.org/licenses/>.
*/
#ifndef BOTTLENECK_H_
#define BOTTLENECK_H_
#include <gudhi/Graph_matching.h>
#include <cmath>
namespace Gudhi {
namespace persistence_diagram {
double bottleneck_distance_approx(Persistence_graph& g, double e) {
double b_lower_bound = 0.;
double b_upper_bound = g.diameter_bound();
const double alpha = std::pow(g.size(), 1. / 5.);
Graph_matching m(g);
Graph_matching biggest_unperfect(g);
while (b_upper_bound - b_lower_bound > 2 * e) {
double step = b_lower_bound + (b_upper_bound - b_lower_bound) / alpha;
if (step <= b_lower_bound || step >= b_upper_bound) // Avoid precision problem
break;
m.set_r(step);
while (m.multi_augment()); // compute a maximum matching (in the graph corresponding to the current r)
if (m.perfect()) {
m = biggest_unperfect;
b_upper_bound = step;
} else {
biggest_unperfect = m;
b_lower_bound = step;
}
}
return (b_lower_bound + b_upper_bound) / 2.;
}
double bottleneck_distance_exact(Persistence_graph& g) {
std::vector<double> sd = g.sorted_distances();
long lower_bound_i = 0;
long upper_bound_i = sd.size() - 1;
const double alpha = std::pow(g.size(), 1. / 5.);
Graph_matching m(g);
Graph_matching biggest_unperfect(g);
while (lower_bound_i != upper_bound_i) {
long step = lower_bound_i + static_cast<long> ((upper_bound_i - lower_bound_i - 1) / alpha);
m.set_r(sd.at(step));
while (m.multi_augment()); // compute a maximum matching (in the graph corresponding to the current r)
if (m.perfect()) {
m = biggest_unperfect;
upper_bound_i = step;
} else {
biggest_unperfect = m;
lower_bound_i = step + 1;
}
}
return sd.at(lower_bound_i);
}
/** \brief Function to use in order to compute the Bottleneck distance between two persistence diagrams (see concepts).
* If the last parameter e is not 0, you get an additive e-approximation, which is a lot faster to compute whatever is
* e.
* Thus, by default, e is a very small positive double, actually the smallest double possible such that the
* floating-point inaccuracies don't lead to a failure of the algorithm.
*
* \ingroup bottleneck_distance
*/
template<typename Persistence_diagram1, typename Persistence_diagram2>
double bottleneck_distance(const Persistence_diagram1 &diag1, const Persistence_diagram2 &diag2,
double e = std::numeric_limits<double>::min()) {
Persistence_graph g(diag1, diag2, e);
if (g.bottleneck_alive() == std::numeric_limits<double>::infinity())
return std::numeric_limits<double>::infinity();
return std::max(g.bottleneck_alive(), e == 0. ? bottleneck_distance_exact(g) : bottleneck_distance_approx(g, e));
}
} // namespace persistence_diagram
} // namespace Gudhi
#endif // BOTTLENECK_H_
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