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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 (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 BOTTLENECK_H_
#define BOTTLENECK_H_
#include <gudhi/Graph_matching.h>
namespace Gudhi {
namespace bottleneck_distance {
template<typename Persistence_diagram1, typename Persistence_diagram2>
double compute_exactly(const Persistence_diagram1 &diag1, const Persistence_diagram2 &diag2) {
Persistence_graph g(diag1, diag2, 0.);
std::vector<double> sd(g.sorted_distances());
int idmin = 0;
int idmax = sd.size() - 1;
// alpha can change the complexity
double alpha = pow(sd.size(), 0.25);
Graph_matching m(g);
Graph_matching biggest_unperfect(g);
while (idmin != idmax) {
int step = static_cast<int>((idmax - idmin) / alpha);
m.set_r(sd.at(idmin + step));
while (m.multi_augment());
//The above while compute a maximum matching (according to the r setted before)
if (m.perfect()) {
idmax = idmin + step;
m = biggest_unperfect;
} else {
biggest_unperfect = m;
idmin = idmin + step + 1;
}
}
return sd.at(idmin);
}
/** \brief Function to use in order to compute the Bottleneck distance between two persistence diagrams.
* If the last parameter e is not 0 (default value if not explicited), you get an additive e-approximation.
*
* \ingroup bottleneck_distance
*/
template<typename Persistence_diagram1, typename Persistence_diagram2>
double compute(const Persistence_diagram1 &diag1, const Persistence_diagram2 &diag2, double e=0.) {
if(e == 0.)
return compute_exactly(diag1, diag2);
Persistence_graph g(diag1, diag2, e);
int in = g.diameter_bound()/e + 1;
int idmin = 0;
int idmax = in;
// alpha can change the complexity
double alpha = pow(in, 0.10);
Graph_matching m(g);
Graph_matching biggest_unperfect(g);
while (idmin != idmax) {
int step = static_cast<int>((idmax - idmin) / alpha);
m.set_r(e*(idmin + step));
while (m.multi_augment());
//The above while compute a maximum matching (according to the r setted before)
if (m.perfect()) {
idmax = idmin + step;
m = biggest_unperfect;
} else {
biggest_unperfect = m;
idmin = idmin + step + 1;
}
}
return e*(idmin);
}
} // namespace bottleneck_distance
} // namespace Gudhi
#endif // BOTTLENECK_H_
/* Dichotomic version
template<typename Persistence_diagram1, typename Persistence_diagram2>
double compute(const Persistence_diagram1 &diag1, const Persistence_diagram2 &diag2, double e) {
if(e< std::numeric_limits<double>::min())
return compute_exactly(diag1, diag2);
G::initialize(diag1, diag2, e);
double d = 0.;
double f = G::diameter();
while (f-d > e){
Graph_matching m;
m.set_r((d+f)/2.);
while (m.multi_augment());
//The above while compute a maximum matching (according to the r setted before)
if (m.perfect())
f = (d+f)/2.;
else
d= (d+f)/2.;
}
return d;
} */
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