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diff --git a/src/Persistence_representations/include/gudhi/Persistence_heat_maps_exact.h b/src/Persistence_representations/include/gudhi/Persistence_heat_maps_exact.h
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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; double step_y = (max_y - min_y)/res_y;
+
+    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_