Persistence_heat_maps.h

/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
 *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
 *    Author(s):       Pawel Dlotko and Mathieu Carriere
 *
 *    Modifications:
 *      - 2018/04 MC: Add discrete/non-discrete mechanism and non-discrete version
 *
 *    Copyright (C) 2019 Inria
 *
 *    Modification(s):
 *      - YYYY/MM Author: Description of the modification
 */
 
#ifndef PERSISTENCE_HEAT_MAPS_H_
#define PERSISTENCE_HEAT_MAPS_H_
 
// gudhi include
#include <gudhi/read_persistence_from_file.h>
#include <gudhi/common_persistence_representations.h>
 
// standard include
#include <vector>
#include <sstream>
#include <iostream>
#include <cmath>
#include <limits>
#include <algorithm>
#include <utility>
#include <string>
#include <functional>
 
namespace Gudhi {
namespace Persistence_representations {
 
std::vector<std::vector<double> > create_Gaussian_filter(size_t pixel_radius, double sigma) {
  bool dbg = false;
  // we are computing the kernel mask to 2 standard deviations away from the center. We discretize it in a grid of a
  // size 2*pixel_radius times 2*pixel_radius.
 
  double r = 0;
  double sigma_sqr = sigma * sigma;
 
  // sum is for normalization
  double sum = 0;
 
  // initialization of a kernel:
  std::vector<std::vector<double> > kernel(2 * pixel_radius + 1);
  for (size_t i = 0; i != kernel.size(); ++i) {
    std::vector<double> v(2 * pixel_radius + 1, 0);
    kernel[i] = v;
  }
 
  if (dbg) {
    std::clog << "Kernel initialize \n";
    std::clog << "pixel_radius : " << pixel_radius << std::endl;
    std::clog << "kernel.size() : " << kernel.size() << std::endl;
    getchar();
  }
 
  for (int x = -pixel_radius; x <= static_cast<int>(pixel_radius); x++) {
    for (int y = -pixel_radius; y <= static_cast<int>(pixel_radius); y++) {
      double real_x = 2 * sigma * x / pixel_radius;
      double real_y = 2 * sigma * y / pixel_radius;
      r = std::sqrt(real_x * real_x + real_y * real_y);
      kernel[x + pixel_radius][y + pixel_radius] = (exp(-(r * r) / sigma_sqr)) / (3.141592 * sigma_sqr);
      sum += kernel[x + pixel_radius][y + pixel_radius];
    }
  }
 
  // normalize the kernel
  for (size_t i = 0; i != kernel.size(); ++i) {
    for (size_t j = 0; j != kernel[i].size(); ++j) {
      kernel[i][j] /= sum;
    }
  }
 
  if (dbg) {
    std::clog << "Here is the kernel : \n";
    for (size_t i = 0; i != kernel.size(); ++i) {
      for (size_t j = 0; j != kernel[i].size(); ++j) {
        std::clog << kernel[i][j] << " ";
      }
      std::clog << std::endl;
    }
  }
  return kernel;
}
 
/*
 * There are various options to scale the points depending on their location. One can for instance:
 * (1) do nothing (scale all of them with the weight 1), as in the function constant_function
 * (2) Scale them by the distance to the diagonal. This is implemented in function
 * (3) Scale them with the square of their distance to diagonal. This is implemented in function
 * (4) Scale them with
 */
 
class constant_scaling_function {
 public:
  double operator()(const std::pair<double, double>& point_in_diagram) { return 1; }
};
 
class distance_from_diagonal_scaling {
 public:
  double operator()(const std::pair<double, double>& point_in_diagram) {
    // (point_in_diagram.first+point_in_diagram.second)/2.0
    return std::sqrt(std::pow((point_in_diagram.first - (point_in_diagram.first + point_in_diagram.second) / 2.0), 2) +
                     std::pow((point_in_diagram.second - (point_in_diagram.first + point_in_diagram.second) / 2.0), 2));
  }
};
 
class squared_distance_from_diagonal_scaling {
 public:
  double operator()(const std::pair<double, double>& point_in_diagram) {
    return std::pow((point_in_diagram.first - (point_in_diagram.first + point_in_diagram.second) / 2.0), 2) +
           std::pow((point_in_diagram.second - (point_in_diagram.first + point_in_diagram.second) / 2.0), 2);
  }
};
 
class arc_tan_of_persistence_of_point {
 public:
  double operator()(const std::pair<double, double>& point_in_diagram) {
    return atan(point_in_diagram.second - point_in_diagram.first);
  }
};
 
class weight_by_setting_maximal_interval_to_have_length_one {
 public:
  weight_by_setting_maximal_interval_to_have_length_one(double len) : length_of_maximal_interval(len) {}
  double operator()(const std::pair<double, double>& point_in_diagram) {
    return (point_in_diagram.second - point_in_diagram.first) / this->length_of_maximal_interval;
  }
 
 private:
  double length_of_maximal_interval;
};
 
// This class implements the following concepts: Vectorized_topological_data, Topological_data_with_distances,
// Real_valued_topological_data, Topological_data_with_averages, Topological_data_with_scalar_product
template <typename Scalling_of_kernels = constant_scaling_function>
class Persistence_heat_maps {
 public:
  Persistence_heat_maps() {
    Scalling_of_kernels f;
    this->f = f;
    this->erase_below_diagonal = false;
    this->min_ = this->max_ = 0;
    this->set_up_parameters_for_basic_classes();
  }
 
  Persistence_heat_maps(const std::vector<std::pair<double, double> >& interval,
                        std::vector<std::vector<double> > filter = create_Gaussian_filter(5, 1),
                        bool erase_below_diagonal = false, size_t number_of_pixels = 1000,
                        double min_ = std::numeric_limits<double>::max(),
                        double max_ = std::numeric_limits<double>::max());
 
  Persistence_heat_maps(const char* filename, std::vector<std::vector<double> > filter = create_Gaussian_filter(5, 1),
                        bool erase_below_diagonal = false, size_t number_of_pixels = 1000,
                        double min_ = std::numeric_limits<double>::max(),
                        double max_ = std::numeric_limits<double>::max(),
                        unsigned dimension = std::numeric_limits<unsigned>::max());
 
  Persistence_heat_maps(const std::vector<std::pair<double, double> >& interval,
                        const std::function<double(std::pair<double, double>, std::pair<double, double>)>& kernel,
                        size_t number_of_x_pixels, size_t number_of_y_pixels, double min_x = 0, double max_x = 1,
                        double min_y = 0, double max_y = 1);
 
  Persistence_heat_maps(const std::vector<std::pair<double, double> >& interval,
                        const std::function<double(std::pair<double, double>, std::pair<double, double>)>& kernel);
 
  void compute_mean(const std::vector<Persistence_heat_maps*>& maps);
 
  void compute_median(const std::vector<Persistence_heat_maps*>& maps);
 
  void compute_percentage_of_active(const std::vector<Persistence_heat_maps*>& maps, size_t cutoff = 1);
 
  // put to file subroutine
  void print_to_file(const char* filename) const;
 
  void load_from_file(const char* filename);
 
  inline bool check_if_the_same(const Persistence_heat_maps& second) const {
    bool dbg = false;
    if (this->heat_map.size() != second.heat_map.size()) {
      if (dbg)
        std::clog << "this->heat_map.size() : " << this->heat_map.size()
                  << " \n second.heat_map.size() : " << second.heat_map.size() << std::endl;
      return false;
    }
    if (this->min_ != second.min_) {
      if (dbg) std::clog << "this->min_ : " << this->min_ << ", second.min_ : " << second.min_ << std::endl;
      return false;
    }
    if (this->max_ != second.max_) {
      if (dbg) std::clog << "this->max_ : " << this->max_ << ", second.max_ : " << second.max_ << std::endl;
      return false;
    }
    // in the other case we may assume that the persistence images are defined on the same domain.
    return true;
  }
 
  inline double get_min() const { return this->min_; }
 
  inline double get_max() const { return this->max_; }
 
  bool operator==(const Persistence_heat_maps& rhs) const {
    bool dbg = false;
    if (!this->check_if_the_same(rhs)) {
      if (dbg) std::clog << "The domains are not the same \n";
      return false;  // in this case, the domains are not the same, so the maps cannot be the same.
    }
    for (size_t i = 0; i != this->heat_map.size(); ++i) {
      for (size_t j = 0; j != this->heat_map[i].size(); ++j) {
        if (!almost_equal(this->heat_map[i][j], rhs.heat_map[i][j])) {
          if (dbg) {
            std::clog << "this->heat_map[" << i << "][" << j << "] = " << this->heat_map[i][j] << std::endl;
            std::clog << "rhs.heat_map[" << i << "][" << j << "] = " << rhs.heat_map[i][j] << std::endl;
          }
          return false;
        }
      }
    }
    return true;
  }
 
  bool operator!=(const Persistence_heat_maps& rhs) const { return !((*this) == rhs); }
 
  void plot(const char* filename) const;
 
  template <typename Operation_type>
  friend Persistence_heat_maps operation_on_pair_of_heat_maps(const Persistence_heat_maps& first,
                                                              const Persistence_heat_maps& second,
                                                              Operation_type operation) {
    // first check if the heat maps are compatible
    if (!first.check_if_the_same(second)) {
      std::cerr << "Sizes of the heat maps are not compatible. The program will now terminate \n";
      throw "Sizes of the heat maps are not compatible. The program will now terminate \n";
    }
    Persistence_heat_maps result;
    result.min_ = first.min_;
    result.max_ = first.max_;
    result.heat_map.reserve(first.heat_map.size());
    for (size_t i = 0; i != first.heat_map.size(); ++i) {
      std::vector<double> v;
      v.reserve(first.heat_map[i].size());
      for (size_t j = 0; j != first.heat_map[i].size(); ++j) {
        v.push_back(operation(first.heat_map[i][j], second.heat_map[i][j]));
      }
      result.heat_map.push_back(v);
    }
    return result;
  }  // operation_on_pair_of_heat_maps
 
  Persistence_heat_maps multiply_by_scalar(double scalar) const {
    Persistence_heat_maps result;
    result.min_ = this->min_;
    result.max_ = this->max_;
    result.heat_map.reserve(this->heat_map.size());
    for (size_t i = 0; i != this->heat_map.size(); ++i) {
      std::vector<double> v;
      v.reserve(this->heat_map[i].size());
      for (size_t j = 0; j != this->heat_map[i].size(); ++j) {
        v.push_back(this->heat_map[i][j] * scalar);
      }
      result.heat_map.push_back(v);
    }
    return result;
  }
 
  friend Persistence_heat_maps operator+(const Persistence_heat_maps& first, const Persistence_heat_maps& second) {
    return operation_on_pair_of_heat_maps(first, second, std::plus<double>());
  }
  friend Persistence_heat_maps operator-(const Persistence_heat_maps& first, const Persistence_heat_maps& second) {
    return operation_on_pair_of_heat_maps(first, second, std::minus<double>());
  }
  friend Persistence_heat_maps operator*(double scalar, const Persistence_heat_maps& A) {
    return A.multiply_by_scalar(scalar);
  }
  friend Persistence_heat_maps operator*(const Persistence_heat_maps& A, double scalar) {
    return A.multiply_by_scalar(scalar);
  }
  Persistence_heat_maps operator*(double scalar) { return this->multiply_by_scalar(scalar); }
  Persistence_heat_maps operator+=(const Persistence_heat_maps& rhs) {
    *this = *this + rhs;
    return *this;
  }
  Persistence_heat_maps operator-=(const Persistence_heat_maps& rhs) {
    *this = *this - rhs;
    return *this;
  }
  Persistence_heat_maps operator*=(double x) {
    *this = *this * x;
    return *this;
  }
  Persistence_heat_maps operator/=(double x) {
    if (x == 0) throw("In operator /=, division by 0. Program terminated.");
    *this = *this * (1 / x);
    return *this;
  }
 
  // Implementations of functions for various concepts.
 
  std::vector<double> vectorize(int number_of_function) const;
  size_t number_of_vectorize_functions() const { return this->number_of_functions_for_vectorization; }
 
  double project_to_R(int number_of_function) const;
  size_t number_of_projections_to_R() const { return this->number_of_functions_for_projections_to_reals; }
 
  double distance(const Persistence_heat_maps& second_, double power = 1) const;
 
  void compute_average(const std::vector<Persistence_heat_maps*>& to_average);
 
  double compute_scalar_product(const Persistence_heat_maps& second_) const;
 
  // end of implementation of functions needed for concepts.
 
  std::pair<double, double> get_x_range() const { return std::make_pair(this->min_, this->max_); }
 
  std::pair<double, double> get_y_range() const { return this->get_x_range(); }
 
 protected:
  // private methods
  std::vector<std::vector<double> > check_and_initialize_maps(const std::vector<Persistence_heat_maps*>& maps);
  size_t number_of_functions_for_vectorization;
  size_t number_of_functions_for_projections_to_reals;
  void construct(const std::vector<std::pair<double, double> >& intervals_,
                 std::vector<std::vector<double> > filter = create_Gaussian_filter(5, 1),
                 bool erase_below_diagonal = false, size_t number_of_pixels = 1000,
                 double min_ = std::numeric_limits<double>::max(), double max_ = std::numeric_limits<double>::max());
 
  void set_up_parameters_for_basic_classes() {
    this->number_of_functions_for_vectorization = 1;
    this->number_of_functions_for_projections_to_reals = 1;
  }
 
  // Boolean indicating if we are computing persistence image (true) or persistence weighted gaussian kernel (false)
  bool discrete = true;
  std::function<double(std::pair<double, double>, std::pair<double, double>)> kernel;
  std::vector<std::pair<double, double> > interval;
  std::vector<double> weights;
 
  // data
  Scalling_of_kernels f;
  bool erase_below_diagonal;
  double min_;
  double max_;
  std::vector<std::vector<double> > heat_map;
};
 
template <typename Scalling_of_kernels>
Persistence_heat_maps<Scalling_of_kernels>::Persistence_heat_maps(
    const std::vector<std::pair<double, double> >& interval,
    const std::function<double(std::pair<double, double>, std::pair<double, double>)>& kernel,
    size_t number_of_x_pixels, size_t number_of_y_pixels, double min_x, double max_x, double min_y, double max_y) {
  this->discrete = true;
  this->min_ = min_x;
  this->max_ = max_x;
  this->heat_map.resize(number_of_y_pixels);
  double step_x = (max_x - min_x) / (number_of_x_pixels - 1);
  double step_y = (max_y - min_y) / (number_of_y_pixels - 1);
 
  int num_pts = interval.size();
  for (size_t i = 0; i < number_of_y_pixels; i++) {
    double y = min_y + i * step_y;
    this->heat_map[i].reserve(number_of_x_pixels);
    for (size_t j = 0; j < number_of_x_pixels; j++) {
      double x = min_x + j * step_x;
      std::pair<double, double> grid_point(x, y);
      double pixel_value = 0;
      for (int k = 0; k < num_pts; k++) pixel_value += this->f(interval[k]) * kernel(interval[k], grid_point);
      this->heat_map[i].push_back(pixel_value);
    }
  }
  this->set_up_parameters_for_basic_classes();
}
 
template <typename Scalling_of_kernels>
Persistence_heat_maps<Scalling_of_kernels>::Persistence_heat_maps(
    const std::vector<std::pair<double, double> >& interval,
    const std::function<double(std::pair<double, double>, std::pair<double, double>)>& kernel) {
  this->discrete = false;
  this->interval = interval;
  this->kernel = kernel;
  int num_pts = this->interval.size();
  for (int i = 0; i < num_pts; i++) this->weights.push_back(this->f(this->interval[i]));
  this->set_up_parameters_for_basic_classes();
}
 
// if min_ == max_, then the program is requested to set up the values itself based on persistence intervals
template <typename Scalling_of_kernels>
void Persistence_heat_maps<Scalling_of_kernels>::construct(const std::vector<std::pair<double, double> >& intervals_,
                                                           std::vector<std::vector<double> > filter,
                                                           bool erase_below_diagonal, size_t number_of_pixels,
                                                           double min_, double max_) {
  bool dbg = false;
  if (dbg) std::clog << "Entering construct procedure \n";
  Scalling_of_kernels f;
  this->f = f;
 
  if (dbg) std::clog << "min and max passed to construct() procedure: " << min_ << " " << max_ << std::endl;
 
  if (min_ == max_) {
    if (dbg) std::clog << "min and max parameters will be determined based on intervals \n";
    // in this case, we want the program to set up the min_ and max_ values by itself.
    min_ = std::numeric_limits<int>::max();
    max_ = -std::numeric_limits<int>::max();
 
    for (size_t i = 0; i != intervals_.size(); ++i) {
      if (intervals_[i].first < min_) min_ = intervals_[i].first;
      if (intervals_[i].second > max_) max_ = intervals_[i].second;
    }
    // now we have the structure filled in, and moreover we know min_ and max_ values of the interval, so we know the
    // range.
 
    // add some more space:
    min_ -= fabs(max_ - min_) / 100;
    max_ += fabs(max_ - min_) / 100;
  }
 
  if (dbg) {
    std::clog << "min_ : " << min_ << std::endl;
    std::clog << "max_ : " << max_ << std::endl;
    std::clog << "number_of_pixels : " << number_of_pixels << std::endl;
    getchar();
  }
 
  this->min_ = min_;
  this->max_ = max_;
 
  // initialization of the structure heat_map
  std::vector<std::vector<double> > heat_map_;
  for (size_t i = 0; i != number_of_pixels; ++i) {
    std::vector<double> v(number_of_pixels, 0);
    heat_map_.push_back(v);
  }
  this->heat_map = heat_map_;
 
  if (dbg) std::clog << "Done creating of the heat map, now we will fill in the structure \n";
 
  for (size_t pt_nr = 0; pt_nr != intervals_.size(); ++pt_nr) {
    // compute the value of intervals_[pt_nr] in the grid:
    int x_grid =
        static_cast<int>((intervals_[pt_nr].first - this->min_) / (this->max_ - this->min_) * number_of_pixels);
    int y_grid =
        static_cast<int>((intervals_[pt_nr].second - this->min_) / (this->max_ - this->min_) * number_of_pixels);
 
    if (dbg) {
      std::clog << "point : " << intervals_[pt_nr].first << " , " << intervals_[pt_nr].second << std::endl;
      std::clog << "x_grid : " << x_grid << std::endl;
      std::clog << "y_grid : " << y_grid << std::endl;
    }
 
    // x_grid and y_grid gives a center of the kernel. We want to have its lower left corner. To get this, we need to
    // shift x_grid and y_grid by a grid diameter.
    x_grid -= filter.size() / 2;
    y_grid -= filter.size() / 2;
    // note that the numbers x_grid and y_grid may be negative.
 
    if (dbg) {
      std::clog << "After shift : \n";
      std::clog << "x_grid : " << x_grid << std::endl;
      std::clog << "y_grid : " << y_grid << std::endl;
    }
 
    double scaling_value = this->f(intervals_[pt_nr]);
 
    for (size_t i = 0; i != filter.size(); ++i) {
      for (size_t j = 0; j != filter.size(); ++j) {
        // if the point (x_grid+i,y_grid+j) is the correct point in the grid.
        if (((x_grid + i) >= 0) && (x_grid + i < this->heat_map.size()) && ((y_grid + j) >= 0) &&
            (y_grid + j < this->heat_map.size())) {
          if (dbg) {
            std::clog << y_grid + j << " " << x_grid + i << std::endl;
          }
          this->heat_map[y_grid + j][x_grid + i] += scaling_value * filter[i][j];
          if (dbg) {
            std::clog << "Position : (" << x_grid + i << "," << y_grid + j
                      << ") got increased by the value : " << filter[i][j] << std::endl;
          }
        }
      }
    }
  }
 
  // now it remains to cut everything below diagonal if the user wants us to.
  if (erase_below_diagonal) {
    for (size_t i = 0; i != this->heat_map.size(); ++i) {
      for (size_t j = i; j != this->heat_map.size(); ++j) {
        this->heat_map[i][j] = 0;
      }
    }
  }
}  // construct
 
template <typename Scalling_of_kernels>
Persistence_heat_maps<Scalling_of_kernels>::Persistence_heat_maps(
    const std::vector<std::pair<double, double> >& interval, std::vector<std::vector<double> > filter,
    bool erase_below_diagonal, size_t number_of_pixels, double min_, double max_) {
  this->construct(interval, filter, erase_below_diagonal, number_of_pixels, min_, max_);
  this->set_up_parameters_for_basic_classes();
}
 
template <typename Scalling_of_kernels>
Persistence_heat_maps<Scalling_of_kernels>::Persistence_heat_maps(const char* filename,
                                                                  std::vector<std::vector<double> > filter,
                                                                  bool erase_below_diagonal, size_t number_of_pixels,
                                                                  double min_, double max_, unsigned dimension) {
  std::vector<std::pair<double, double> > intervals_;
  if (dimension == std::numeric_limits<unsigned>::max()) {
    intervals_ = read_persistence_intervals_in_one_dimension_from_file(filename);
  } else {
    intervals_ = read_persistence_intervals_in_one_dimension_from_file(filename, dimension);
  }
  this->construct(intervals_, filter, erase_below_diagonal, number_of_pixels, min_, max_);
  this->set_up_parameters_for_basic_classes();
}
 
template <typename Scalling_of_kernels>
std::vector<std::vector<double> > Persistence_heat_maps<Scalling_of_kernels>::check_and_initialize_maps(
    const std::vector<Persistence_heat_maps*>& maps) {
  // checking if all the heat maps are of the same size:
  for (size_t i = 0; i != maps.size(); ++i) {
    if (maps[i]->heat_map.size() != maps[0]->heat_map.size()) {
      std::cerr << "Sizes of Persistence_heat_maps are not compatible. The program will terminate now \n";
      throw "Sizes of Persistence_heat_maps are not compatible. The program will terminate now \n";
    }
    if (maps[i]->heat_map[0].size() != maps[0]->heat_map[0].size()) {
      std::cerr << "Sizes of Persistence_heat_maps are not compatible. The program will terminate now \n";
      throw "Sizes of Persistence_heat_maps are not compatible. The program will terminate now \n";
    }
  }
  std::vector<std::vector<double> > heat_maps(maps[0]->heat_map.size());
  for (size_t i = 0; i != maps[0]->heat_map.size(); ++i) {
    std::vector<double> v(maps[0]->heat_map[0].size(), 0);
    heat_maps[i] = v;
  }
  return heat_maps;
}
 
template <typename Scalling_of_kernels>
void Persistence_heat_maps<Scalling_of_kernels>::compute_median(const std::vector<Persistence_heat_maps*>& maps) {
  std::vector<std::vector<double> > heat_maps = this->check_and_initialize_maps(maps);
 
  std::vector<double> to_compute_median(maps.size());
  for (size_t i = 0; i != heat_maps.size(); ++i) {
    for (size_t j = 0; j != heat_maps[i].size(); ++j) {
      for (size_t map_no = 0; map_no != maps.size(); ++map_no) {
        to_compute_median[map_no] = maps[map_no]->heat_map[i][j];
      }
      std::nth_element(to_compute_median.begin(), to_compute_median.begin() + to_compute_median.size() / 2,
                       to_compute_median.end());
      heat_maps[i][j] = to_compute_median[to_compute_median.size() / 2];
    }
  }
  this->heat_map = heat_maps;
  this->min_ = maps[0]->min_;
  this->max_ = maps[0]->max_;
}
 
template <typename Scalling_of_kernels>
void Persistence_heat_maps<Scalling_of_kernels>::compute_mean(const std::vector<Persistence_heat_maps*>& maps) {
  std::vector<std::vector<double> > heat_maps = this->check_and_initialize_maps(maps);
  for (size_t i = 0; i != heat_maps.size(); ++i) {
    for (size_t j = 0; j != heat_maps[i].size(); ++j) {
      double mean = 0;
      for (size_t map_no = 0; map_no != maps.size(); ++map_no) {
        mean += maps[map_no]->heat_map[i][j];
      }
      heat_maps[i][j] = mean / static_cast<double>(maps.size());
    }
  }
  this->heat_map = heat_maps;
  this->min_ = maps[0]->min_;
  this->max_ = maps[0]->max_;
}
 
template <typename Scalling_of_kernels>
void Persistence_heat_maps<Scalling_of_kernels>::compute_percentage_of_active(
    const std::vector<Persistence_heat_maps*>& maps, size_t cutoff) {
  std::vector<std::vector<double> > heat_maps = this->check_and_initialize_maps(maps);
 
  for (size_t i = 0; i != heat_maps.size(); ++i) {
    for (size_t j = 0; j != heat_maps[i].size(); ++j) {
      size_t number_of_active_levels = 0;
      for (size_t map_no = 0; map_no != maps.size(); ++map_no) {
        if (maps[map_no]->heat_map[i][j]) number_of_active_levels++;
      }
      if (number_of_active_levels > cutoff) {
        heat_maps[i][j] = number_of_active_levels;
      } else {
        heat_maps[i][j] = 0;
      }
    }
  }
  this->heat_map = heat_maps;
  this->min_ = maps[0]->min_;
  this->max_ = maps[0]->max_;
}
 
template <typename Scalling_of_kernels>
void Persistence_heat_maps<Scalling_of_kernels>::plot(const char* filename) const {
  std::ofstream out;
  std::stringstream gnuplot_script;
  gnuplot_script << filename << "_GnuplotScript";
 
  out.open(gnuplot_script.str().c_str());
  out << "plot      '-' matrix with image" << std::endl;
  for (size_t i = 0; i != this->heat_map.size(); ++i) {
    for (size_t j = 0; j != this->heat_map[i].size(); ++j) {
      out << this->heat_map[i][j] << " ";
    }
    out << std::endl;
  }
  out.close();
  std::clog << "To visualize, install gnuplot and type the command: gnuplot -persist -e \"load \'"
            << gnuplot_script.str().c_str() << "\'\"" << std::endl;
}
 
template <typename Scalling_of_kernels>
void Persistence_heat_maps<Scalling_of_kernels>::print_to_file(const char* filename) const {
  std::ofstream out;
  out.open(filename);
 
  // First we store this->min_ and this->max_ values:
  out << this->min_ << " " << this->max_ << std::endl;
  for (size_t i = 0; i != this->heat_map.size(); ++i) {
    for (size_t j = 0; j != this->heat_map[i].size(); ++j) {
      out << this->heat_map[i][j] << " ";
    }
    out << std::endl;
  }
  out.close();
}
 
template <typename Scalling_of_kernels>
void Persistence_heat_maps<Scalling_of_kernels>::load_from_file(const char* filename) {
  bool dbg = false;
 
  std::ifstream in;
  in.open(filename);
 
  // checking if the file exist / if it was open.
  if (!in.good()) {
    std::cerr << "The file : " << filename << " do not exist. The program will now terminate \n";
    throw "The persistence landscape file do not exist. The program will now terminate \n";
  }
 
  // now we read the file one by one.
 
  in >> this->min_ >> this->max_;
  if (dbg) {
    std::clog << "Reading the following values of min and max : " << this->min_ << " , " << this->max_ << std::endl;
  }
 
  std::string temp;
  std::getline(in, temp);
  while (in.good()) {
    std::getline(in, temp);
    std::stringstream lineSS;
    lineSS << temp;
 
    std::vector<double> line_of_heat_map;
    while (lineSS.good()) {
      double point;
 
      lineSS >> point;
      line_of_heat_map.push_back(point);
      if (dbg) {
        std::clog << point << " ";
      }
    }
    if (dbg) {
      std::clog << std::endl;
      getchar();
    }
 
    if (in.good()) this->heat_map.push_back(line_of_heat_map);
  }
  in.close();
  if (dbg) std::clog << "Done \n";
}
 
// Concretizations of virtual methods:
template <typename Scalling_of_kernels>
std::vector<double> Persistence_heat_maps<Scalling_of_kernels>::vectorize(int number_of_function) const {
  std::vector<double> result;
  if (!discrete) {
    std::cerr << "No vectorize method in case of infinite dimensional vectorization" << std::endl;
    return result;
  }
 
  // convert this->heat_map into one large vector:
  size_t size_of_result = 0;
  for (size_t i = 0; i != this->heat_map.size(); ++i) {
    size_of_result += this->heat_map[i].size();
  }
 
  result.reserve(size_of_result);
 
  for (size_t i = 0; i != this->heat_map.size(); ++i) {
    for (size_t j = 0; j != this->heat_map[i].size(); ++j) {
      result.push_back(this->heat_map[i][j]);
    }
  }
 
  return result;
}
 
template <typename Scalling_of_kernels>
double Persistence_heat_maps<Scalling_of_kernels>::distance(const Persistence_heat_maps& second, double power) const {
  if (this->discrete) {
    // first we need to check if (*this) and second are defined on the same domain and have the same dimensions:
    if (!this->check_if_the_same(second)) {
      std::cerr << "The persistence images are of non compatible sizes. We cannot therefore compute distance between "
                   "them. The program will now terminate";
      throw "The persistence images are of non compatible sizes. The program will now terminate";
    }
 
    // if we are here, we know that the two persistence images are defined on the same domain, so we can start
    // computing their distances:
 
    double distance = 0;
    if (power < std::numeric_limits<double>::max()) {
      for (size_t i = 0; i != this->heat_map.size(); ++i) {
        for (size_t j = 0; j != this->heat_map[i].size(); ++j) {
          distance += std::pow(std::fabs(this->heat_map[i][j] - second.heat_map[i][j]), power);
        }
      }
    } else {
      // in this case, we compute max norm distance
      for (size_t i = 0; i != this->heat_map.size(); ++i) {
        for (size_t j = 0; j != this->heat_map[i].size(); ++j) {
          if (distance < std::fabs(this->heat_map[i][j] - second.heat_map[i][j])) {
            distance = std::fabs(this->heat_map[i][j] - second.heat_map[i][j]);
          }
        }
      }
    }
    return distance;
  } else {
    return std::sqrt(this->compute_scalar_product(*this) + second.compute_scalar_product(second) -
                     2 * this->compute_scalar_product(second));
  }
}
 
template <typename Scalling_of_kernels>
double Persistence_heat_maps<Scalling_of_kernels>::project_to_R(int number_of_function) const {
  double result = 0;
  for (size_t i = 0; i != this->heat_map.size(); ++i) {
    for (size_t j = 0; j != this->heat_map[i].size(); ++j) {
      result += this->heat_map[i][j];
    }
  }
  return result;
}
 
template <typename Scalling_of_kernels>
void Persistence_heat_maps<Scalling_of_kernels>::compute_average(
    const std::vector<Persistence_heat_maps*>& to_average) {
  this->compute_mean(to_average);
}
 
template <typename Scalling_of_kernels>
double Persistence_heat_maps<Scalling_of_kernels>::compute_scalar_product(const Persistence_heat_maps& second) const {
  if (discrete) {
    // first we need to check if (*this) and second are defined on the same domain and have the same dimensions:
    if (!this->check_if_the_same(second)) {
      std::cerr << "The persistence images are of non compatible sizes. We cannot therefore compute distance between "
                   "them. The program will now terminate";
      throw "The persistence images are of non compatible sizes. The program will now terminate";
    }
 
    // if we are here, we know that the two persistence images are defined on the same domain, so we can start computing
    // their scalar product:
    double scalar_prod = 0;
    for (size_t i = 0; i != this->heat_map.size(); ++i) {
      for (size_t j = 0; j != this->heat_map[i].size(); ++j) {
        scalar_prod += this->heat_map[i][j] * second.heat_map[i][j];
      }
    }
    return scalar_prod;
  } else {
    int num_pts1 = this->interval.size();
    int num_pts2 = second.interval.size();
    double kernel_val = 0;
    for (int i = 0; i < num_pts1; i++) {
      std::pair<double, double> pi = this->interval[i];
      for (int j = 0; j < num_pts2; j++) {
        std::pair<double, double> pj = second.interval[j];
        kernel_val += this->weights[i] * second.weights[j] * this->kernel(pi, pj);
      }
    }
    return kernel_val;
  }
}
 
}  // namespace Persistence_representations
}  // namespace Gudhi
 
#endif  // PERSISTENCE_HEAT_MAPS_H_