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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(s): Mathieu Carriere
*
* Copyright (C) 2018 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 PERSISTENCE_HEAT_MAPS_EXACT_H_
#define PERSISTENCE_HEAT_MAPS_EXACT_H_
// gudhi include
#include <gudhi/read_persistence_from_file.h>
#include <gudhi/common_persistence_representations.h>
#include <gudhi/Weight_functions.h>
#include <gudhi/Debug_utils.h>
// standard include
#include <cmath>
#include <iostream>
#include <vector>
#include <limits>
#include <fstream>
#include <sstream>
#include <algorithm>
#include <string>
#include <utility>
#include <functional>
namespace Gudhi {
namespace Persistence_representations {
/**
* \class Persistence_heat_maps_exact gudhi/Persistence_heat_maps_exact.h
* \brief A class implementing exact persistence heat maps.
*
* \ingroup Persistence_representations
*
* \details
*
* In this class, we propose a way to approximate persistence heat maps, or persistence surfaces, by centering weighted Gaussians on each point of the persistence diagram, and evaluating these (exact) weighted Gaussian functions
* on the pixels of a 2D grid. Note that this scheme is different from the one proposed in Persistence_heat_maps, which first maps the points of the diagram to a 2D grid, and then evaluates the (approximate) weighted Gaussian functions.
* Hence, the difference is that we do not modify the diagram in this implementation, but the code can be slower to run.
**/
class Persistence_heat_maps_exact {
protected:
Persistence_diagram diagram;
int res_x, res_y;
double min_x, max_x, min_y, max_y;
Weight weight;
double sigma;
public:
/** \brief Persistence_heat_maps_exact constructor.
* \ingroup Persistence_heat_maps_exact
*
* @param[in] _diagram persistence diagram.
* @param[in] _min_x minimum value of pixel abscissa.
* @param[in] _max_x maximum value of pixel abscissa.
* @param[in] _res_x number of pixels for the x-direction.
* @param[in] _min_y minimum value of pixel ordinate.
* @param[in] _max_y maximum value of pixel ordinate.
* @param[in] _res_y number of pixels for the y-direction.
* @param[in] _weight weight function for the Gaussians.
* @param[in] _sigma bandwidth parameter for the Gaussians.
*
*/
Persistence_heat_maps_exact(const Persistence_diagram & _diagram, double _min_x = 0.0, double _max_x = 1.0, int _res_x = 10, double _min_y = 0.0, double _max_y = 1.0, int _res_y = 10, const Weight & _weight = arctan_weight(1,1), double _sigma = 1.0){
diagram = _diagram; min_x = _min_x; max_x = _max_x; res_x = _res_x; min_y = _min_y; max_y = _max_y; res_y = _res_y, weight = _weight; sigma = _sigma;
}
/** \brief Computes the persistence image of a diagram.
* \ingroup Persistence_heat_maps_exact
*
*/
std::vector<std::vector<double> > vectorize() const {
std::vector<std::vector<double> > im; for(int i = 0; i < res_y; i++) im.emplace_back();
double step_x = (max_x - min_x)/(res_x - 1); double step_y = (max_y - min_y)/(res_y - 1);
int num_pts = diagram.size();
for(int i = 0; i < res_y; i++){
double y = min_y + i*step_y;
for(int j = 0; j < res_x; j++){
double x = min_x + j*step_x;
double pixel_value = 0;
for(int k = 0; k < num_pts; k++){
double px = diagram[k].first; double py = diagram[k].second;
pixel_value += weight(std::pair<double,double>(px,py)) * std::exp( -((x-px)*(x-px) + (y-(py-px))*(y-(py-px))) / (2*sigma*sigma) ) / (sigma*std::sqrt(2*pi));
}
im[i].push_back(pixel_value);
}
}
return im;
}
}; // class Persistence_heat_maps_exact
} // namespace Persistence_representations
} // namespace Gudhi
#endif // PERSISTENCE_HEAT_MAPS_EXACT_H_
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