integrated kernel code in pers_representation branch

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/kernels@3249 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 58e77263a0da3674e4699cef832b6d357dcf12e2

10 files changed, 575 insertions, 176 deletions

diff --git a/src/Persistence_representations/include/gudhi/PSSK.h b/src/Persistence_representations/include/gudhi/PSSK.h
index e2d4225e..630f5623 100644
--- a/src/Persistence_representations/include/gudhi/PSSK.h
+++ b/src/Persistence_representations/include/gudhi/PSSK.h
@@ -121,10 +121,10 @@ void PSSK::construct(const std::vector<std::pair<double, double> >& intervals_,
 
   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);
+    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::cerr << "point : " << intervals_[pt_nr].first << " , " << intervals_[pt_nr].second << std::endl;
diff --git a/src/Persistence_representations/include/gudhi/Persistence_heat_maps.h b/src/Persistence_representations/include/gudhi/Persistence_heat_maps.h
index 04dd78ad..a80c3c40 100644
--- a/src/Persistence_representations/include/gudhi/Persistence_heat_maps.h
+++ b/src/Persistence_representations/include/gudhi/Persistence_heat_maps.h
@@ -582,10 +582,10 @@ void Persistence_heat_maps<Scalling_of_kernels>::construct(const std::vector<std
 
   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);
+    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::cerr << "point : " << intervals_[pt_nr].first << " , " << intervals_[pt_nr].second << std::endl;
@@ -743,10 +743,10 @@ void Persistence_heat_maps<Scalling_of_kernels>::compute_percentage_of_active(
 template <typename Scalling_of_kernels>
 void Persistence_heat_maps<Scalling_of_kernels>::plot(const char* filename) const {
   std::ofstream out;
-  std::stringstream ss;
-  ss << filename << "_GnuplotScript";
+  std::stringstream gnuplot_script;
+  gnuplot_script << filename << "_GnuplotScript";
 
-  out.open(ss.str().c_str());
+  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) {
@@ -755,8 +755,8 @@ void Persistence_heat_maps<Scalling_of_kernels>::plot(const char* filename) cons
     out << std::endl;
   }
   out.close();
-  std::cout << "Gnuplot script have been created. Open gnuplot and type load \'" << ss.str().c_str()
-            << "\' to see the picture." << std::endl;
+  std::cout << "To visualize, install gnuplot and type the command: gnuplot -persist -e \"load \'"
+            << gnuplot_script.str().c_str() << "\'\"" << std::endl;
 }
 
 template <typename Scalling_of_kernels>
@@ -797,8 +797,7 @@ void Persistence_heat_maps<Scalling_of_kernels>::load_from_file(const char* file
 
   std::string temp;
   std::getline(in, temp);
-
-  while (!in.eof()) {
+  while (in.good()) {
     std::getline(in, temp);
     std::stringstream lineSS;
     lineSS << temp;
diff --git a/src/Persistence_representations/include/gudhi/Persistence_intervals.h b/src/Persistence_representations/include/gudhi/Persistence_intervals.h
index 525d58a3..3d04d8b7 100644
--- a/src/Persistence_representations/include/gudhi/Persistence_intervals.h
+++ b/src/Persistence_representations/include/gudhi/Persistence_intervals.h
@@ -167,10 +167,10 @@ class Persistence_intervals {
     // this program create a gnuplot script file that allows to plot persistence diagram.
     std::ofstream out;
 
-    std::ostringstream nameSS;
-    nameSS << filename << "_GnuplotScript";
-    std::string nameStr = nameSS.str();
-    out.open(nameStr);
+    std::stringstream gnuplot_script;
+    gnuplot_script << filename << "_GnuplotScript";
+
+    out.open(gnuplot_script.str().c_str());
 
     std::pair<double, double> min_max_values = this->get_x_range();
     if (min_x == max_x) {
@@ -195,8 +195,8 @@ class Persistence_intervals {
 
     out.close();
 
-    std::cout << "Gnuplot script to visualize persistence diagram written to the file: " << nameStr << ". Type load '"
-              << nameStr << "' in gnuplot to visualize." << std::endl;
+    std::cout << "To visualize, install gnuplot and type the command: gnuplot -persist -e \"load \'"
+              << gnuplot_script.str().c_str() << "\'\"" << std::endl;
   }
 
   /**
@@ -402,9 +402,8 @@ std::vector<double> Persistence_intervals::characteristic_function_of_diagram(do
     }
 
     for (size_t pos = beginIt; pos != endIt; ++pos) {
-      result[pos] +=
-          ((x_max - x_min) / static_cast<double>(number_of_bins)) *
-           (this->intervals[i].second - this->intervals[i].first);
+      result[pos] += ((x_max - x_min) / static_cast<double>(number_of_bins)) *
+                     (this->intervals[i].second - this->intervals[i].first);
     }
     if (dbg) {
       std::cerr << "Result at this stage \n";
diff --git a/src/Persistence_representations/include/gudhi/Persistence_intervals_with_distances.h b/src/Persistence_representations/include/gudhi/Persistence_intervals_with_distances.h
index d5ab04b4..79908883 100644
--- a/src/Persistence_representations/include/gudhi/Persistence_intervals_with_distances.h
+++ b/src/Persistence_representations/include/gudhi/Persistence_intervals_with_distances.h
@@ -26,7 +26,6 @@
 #include <gudhi/Persistence_intervals.h>
 #include <gudhi/Bottleneck.h>
 
-
 #include <limits>
 
 namespace Gudhi {
@@ -47,7 +46,7 @@ class Persistence_intervals_with_distances : public Persistence_intervals {
    * The last parameter, tolerance, it is an additiv error of the approimation, set by default to zero.
   **/
   double distance(const Persistence_intervals_with_distances& second, double power = std::numeric_limits<double>::max(),
-                  double tolerance = 0) const {
+                  double tolerance = (std::numeric_limits<double>::min)()) const {
     if (power >= std::numeric_limits<double>::max()) {
       return Gudhi::persistence_diagram::bottleneck_distance(this->intervals, second.intervals, tolerance);
     } else {
diff --git a/src/Persistence_representations/include/gudhi/Persistence_landscape.h b/src/Persistence_representations/include/gudhi/Persistence_landscape.h
index 5c300112..c5aa7867 100644
--- a/src/Persistence_representations/include/gudhi/Persistence_landscape.h
+++ b/src/Persistence_representations/include/gudhi/Persistence_landscape.h
@@ -79,14 +79,16 @@ class Persistence_landscape {
   /**
   * Constructor that takes as an input a vector of birth-death pairs.
   **/
-  Persistence_landscape(const std::vector<std::pair<double, double> >& p, size_t number_of_levels = std::numeric_limits<size_t>::max() );
+  Persistence_landscape(const std::vector<std::pair<double, double> >& p,
+                        size_t number_of_levels = std::numeric_limits<size_t>::max());
 
   /**
        * Constructor that reads persistence intervals from file and creates persistence landscape. The format of the
     *input file is the following: in each line we put birth-death pair. Last line is assumed
        * to be empty. Even if the points within a line are not ordered, they will be ordered while the input is read.
       **/
-  Persistence_landscape(const char* filename, size_t dimension = std::numeric_limits<unsigned>::max() , size_t number_of_levels = std::numeric_limits<size_t>::max() );
+  Persistence_landscape(const char* filename, size_t dimension = std::numeric_limits<unsigned>::max(),
+                        size_t number_of_levels = std::numeric_limits<size_t>::max());
 
   /**
    * This procedure loads a landscape from file. It erase all the data that was previously stored in this landscape.
@@ -285,7 +287,7 @@ class Persistence_landscape {
    *distance, we need to take its absolute value. This is the purpose of this procedure.
   **/
   Persistence_landscape abs();
-  
+
   Persistence_landscape* new_abs();
 
   /**
@@ -453,7 +455,8 @@ class Persistence_landscape {
   size_t number_of_functions_for_vectorization;
   size_t number_of_functions_for_projections_to_reals;
 
-  void construct_persistence_landscape_from_barcode(const std::vector<std::pair<double, double> >& p , size_t number_of_levels = std::numeric_limits<size_t>::max());
+  void construct_persistence_landscape_from_barcode(const std::vector<std::pair<double, double> >& p,
+                                                    size_t number_of_levels = std::numeric_limits<size_t>::max());
   Persistence_landscape multiply_lanscape_by_real_number_not_overwrite(double x) const;
   void multiply_lanscape_by_real_number_overwrite(double x);
   friend double compute_maximal_distance_non_symmetric(const Persistence_landscape& pl1,
@@ -473,7 +476,7 @@ Persistence_landscape::Persistence_landscape(const char* filename, size_t dimens
   } else {
     barcode = read_persistence_intervals_in_one_dimension_from_file(filename);
   }
-  this->construct_persistence_landscape_from_barcode(barcode,number_of_levels);
+  this->construct_persistence_landscape_from_barcode(barcode, number_of_levels);
   this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
 }
 
@@ -506,14 +509,14 @@ bool Persistence_landscape::operator==(const Persistence_landscape& rhs) const {
   return true;
 }
 
-Persistence_landscape::Persistence_landscape(const std::vector<std::pair<double, double> >& p,size_t number_of_levels) {
-  this->construct_persistence_landscape_from_barcode(p,number_of_levels);
+Persistence_landscape::Persistence_landscape(const std::vector<std::pair<double, double> >& p,
+                                             size_t number_of_levels) {
+  this->construct_persistence_landscape_from_barcode(p, number_of_levels);
   this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
 }
 
 void Persistence_landscape::construct_persistence_landscape_from_barcode(
-    const std::vector<std::pair<double, double> >& p, size_t number_of_levels) 
-    {
+    const std::vector<std::pair<double, double> >& p, size_t number_of_levels) {
   bool dbg = false;
   if (dbg) {
     std::cerr << "Persistence_landscape::Persistence_landscape( const std::vector< std::pair< double , double > >& p )"
@@ -648,12 +651,11 @@ void Persistence_landscape::construct_persistence_landscape_from_barcode(
 
     lambda_n.erase(std::unique(lambda_n.begin(), lambda_n.end()), lambda_n.end());
     this->land.push_back(lambda_n);
-    
+
     ++number_of_levels_in_the_landscape;
-    if ( number_of_levels == number_of_levels_in_the_landscape )
-    {
-		break;
-	}
+    if (number_of_levels == number_of_levels_in_the_landscape) {
+      break;
+    }
   }
 }
 
@@ -857,58 +859,47 @@ Persistence_landscape Persistence_landscape::abs() {
   return result;
 }
 
+Persistence_landscape* Persistence_landscape::new_abs() {
+  Persistence_landscape* result = new Persistence_landscape(*this);
+  for (size_t level = 0; level != this->land.size(); ++level) {
+    if (AbsDbg) {
+      std::cout << "level: " << level << std::endl;
+    }
+    std::vector<std::pair<double, double> > lambda_n;
+    lambda_n.push_back(std::make_pair(-std::numeric_limits<int>::max(), 0));
+    for (size_t i = 1; i != this->land[level].size(); ++i) {
+      if (AbsDbg) {
+        std::cout << "this->land[" << level << "][" << i << "] : " << this->land[level][i].first << " "
+                  << this->land[level][i].second << std::endl;
+      }
+      // if a line segment between this->land[level][i-1] and this->land[level][i] crosses the x-axis, then we have to
+      // add one landscape point t o result
+      if ((this->land[level][i - 1].second) * (this->land[level][i].second) < 0) {
+        double zero =
+            find_zero_of_a_line_segment_between_those_two_points(this->land[level][i - 1], this->land[level][i]);
 
-Persistence_landscape* Persistence_landscape::new_abs() 
-{
-	Persistence_landscape* result = new Persistence_landscape(*this);	 
-	for (size_t level = 0; level != this->land.size(); ++level) 
-	{
-		if (AbsDbg) 
-		{
-			std::cout << "level: " << level << std::endl;
-		}
-		std::vector<std::pair<double, double> > lambda_n;
-		lambda_n.push_back(std::make_pair(-std::numeric_limits<int>::max(), 0));
-		for (size_t i = 1; i != this->land[level].size(); ++i) 
-		{
-			if (AbsDbg) 
-			{
-				std::cout << "this->land[" << level << "][" << i << "] : " << this->land[level][i].first << " "
-					  << this->land[level][i].second << std::endl;
-			}
-			// if a line segment between this->land[level][i-1] and this->land[level][i] crosses the x-axis, then we have to
-			// add one landscape point t o result
-			if ((this->land[level][i - 1].second) * (this->land[level][i].second) < 0) {
-			double zero =
-				find_zero_of_a_line_segment_between_those_two_points(this->land[level][i - 1], this->land[level][i]);
-
-			lambda_n.push_back(std::make_pair(zero, 0));
-			lambda_n.push_back(std::make_pair(this->land[level][i].first, fabs(this->land[level][i].second)));
-			if (AbsDbg) 
-			{
-				std::cout << "Adding pair : (" << zero << ",0)" << std::endl;
-				std::cout << "In the same step adding pair : (" << this->land[level][i].first << ","
-						<< fabs(this->land[level][i].second) << ") " << std::endl;
-				std::cin.ignore();
-			}
-			} 
-			else 
-			{
-				lambda_n.push_back(std::make_pair(this->land[level][i].first, fabs(this->land[level][i].second)));
-				if (AbsDbg) 
-				{
-					std::cout << "Adding pair : (" << this->land[level][i].first << "," << fabs(this->land[level][i].second)
-							<< ") " << std::endl;
-					std::cin.ignore();
-				}
-			}
-	   }
-	result->land.push_back(lambda_n);
-	}	
-	return result;
+        lambda_n.push_back(std::make_pair(zero, 0));
+        lambda_n.push_back(std::make_pair(this->land[level][i].first, fabs(this->land[level][i].second)));
+        if (AbsDbg) {
+          std::cout << "Adding pair : (" << zero << ",0)" << std::endl;
+          std::cout << "In the same step adding pair : (" << this->land[level][i].first << ","
+                    << fabs(this->land[level][i].second) << ") " << std::endl;
+          std::cin.ignore();
+        }
+      } else {
+        lambda_n.push_back(std::make_pair(this->land[level][i].first, fabs(this->land[level][i].second)));
+        if (AbsDbg) {
+          std::cout << "Adding pair : (" << this->land[level][i].first << "," << fabs(this->land[level][i].second)
+                    << ") " << std::endl;
+          std::cin.ignore();
+        }
+      }
+    }
+    result->land.push_back(lambda_n);
+  }
+  return result;
 }
 
-
 Persistence_landscape Persistence_landscape::multiply_lanscape_by_real_number_not_overwrite(double x) const {
   std::vector<std::vector<std::pair<double, double> > > result(this->land.size());
   for (size_t dim = 0; dim != this->land.size(); ++dim) {
@@ -954,7 +945,7 @@ void Persistence_landscape::load_landscape_from_file(const char* filename) {
   std::vector<std::pair<double, double> > landscapeAtThisLevel;
 
   bool isThisAFirsLine = true;
-  while (!in.eof()) {
+  while (in.good()) {
     getline(in, line);
     if (!(line.length() == 0 || line[0] == '#')) {
       std::stringstream lineSS;
@@ -1340,10 +1331,9 @@ void Persistence_landscape::plot(const char* filename, double xRangeBegin, doubl
   // this program create a gnuplot script file that allows to plot persistence diagram.
   std::ofstream out;
 
-  std::ostringstream nameSS;
-  nameSS << filename << "_GnuplotScript";
-  std::string nameStr = nameSS.str();
-  out.open(nameStr);
+  std::ostringstream gnuplot_script;
+  gnuplot_script << filename << "_GnuplotScript";
+  out.open(gnuplot_script.str().c_str());
 
   if ((xRangeBegin != std::numeric_limits<double>::max()) || (xRangeEnd != std::numeric_limits<double>::max()) ||
       (yRangeBegin != std::numeric_limits<double>::max()) || (yRangeEnd != std::numeric_limits<double>::max())) {
@@ -1376,8 +1366,8 @@ void Persistence_landscape::plot(const char* filename, double xRangeBegin, doubl
     }
     out << "EOF" << std::endl;
   }
-  std::cout << "Gnuplot script to visualize persistence diagram written to the file: " << nameStr << ". Type load '"
-            << nameStr << "' in gnuplot to visualize." << std::endl;
+  std::cout << "To visualize, install gnuplot and type the command: gnuplot -persist -e \"load \'"
+            << gnuplot_script.str().c_str() << "\'\"" << std::endl;
 }
 
 }  // namespace Persistence_representations
diff --git a/src/Persistence_representations/include/gudhi/Persistence_landscape_on_grid.h b/src/Persistence_representations/include/gudhi/Persistence_landscape_on_grid.h
index 4ceb9bf6..84fd22ed 100644
--- a/src/Persistence_representations/include/gudhi/Persistence_landscape_on_grid.h
+++ b/src/Persistence_representations/include/gudhi/Persistence_landscape_on_grid.h
@@ -1207,10 +1207,9 @@ void Persistence_landscape_on_grid::plot(const char* filename, double min_x, dou
   // this program create a gnuplot script file that allows to plot persistence diagram.
   std::ofstream out;
 
-  std::ostringstream nameSS;
-  nameSS << filename << "_GnuplotScript";
-  std::string nameStr = nameSS.str();
-  out.open(nameStr);
+  std::ostringstream gnuplot_script;
+  gnuplot_script << filename << "_GnuplotScript";
+  out.open(gnuplot_script.str().c_str());
 
   if (min_x == max_x) {
     std::pair<double, double> min_max = compute_minimum_maximum();
@@ -1241,7 +1240,6 @@ void Persistence_landscape_on_grid::plot(const char* filename, double min_x, dou
 
   out << "plot ";
   for (size_t lambda = from; lambda != to; ++lambda) {
-    // out << "     '-' using 1:2 title 'l" << lambda << "' with lp";
     out << "     '-' using 1:2 notitle with lp";
     if (lambda + 1 != to) {
       out << ", \\";
@@ -1261,8 +1259,8 @@ void Persistence_landscape_on_grid::plot(const char* filename, double min_x, dou
     }
     out << "EOF" << std::endl;
   }
-  std::cout << "Gnuplot script to visualize persistence diagram written to the file: " << nameStr << ". Type load '"
-            << nameStr << "' in gnuplot to visualize." << std::endl;
+  std::cout << "To visualize, install gnuplot and type the command: gnuplot -persist -e \"load \'"
+            << gnuplot_script.str().c_str() << "\'\"" << std::endl;
 }
 
 template <typename T>
diff --git a/src/Persistence_representations/include/gudhi/Persistence_vectors.h b/src/Persistence_representations/include/gudhi/Persistence_vectors.h
index 0fb49eee..63577e46 100644
--- a/src/Persistence_representations/include/gudhi/Persistence_vectors.h
+++ b/src/Persistence_representations/include/gudhi/Persistence_vectors.h
@@ -201,7 +201,8 @@ class Vector_distances_in_diagram {
     }
     out << std::endl;
     out.close();
-    std::cout << "To visualize, open gnuplot and type: load \'" << gnuplot_script.str().c_str() << "\'" << std::endl;
+    std::cout << "To visualize, install gnuplot and type the command: gnuplot -persist -e \"load \'"
+              << gnuplot_script.str().c_str() << "\'\"" << std::endl;
   }
 
   /**
@@ -617,9 +618,7 @@ void Vector_distances_in_diagram<F>::load_from_file(const char* filename) {
   }
 
   double number;
-  while (true) {
-    in >> number;
-    if (in.eof()) break;
+  while (in >> number) {
     this->sorted_vector_of_distances.push_back(number);
   }
   in.close();
diff --git a/src/Persistence_representations/include/gudhi/Persistence_weighted_gaussian.h b/src/Persistence_representations/include/gudhi/Persistence_weighted_gaussian.h
new file mode 100644
index 00000000..2884885c
--- /dev/null
+++ b/src/Persistence_representations/include/gudhi/Persistence_weighted_gaussian.h
@@ -0,0 +1,143 @@
+/*    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_WEIGHTED_GAUSSIAN_H_
+#define PERSISTENCE_WEIGHTED_GAUSSIAN_H_
+
+#ifdef GUDHI_USE_TBB
+#include <tbb/parallel_for.h>
+#endif
+
+// gudhi include
+#include <gudhi/read_persistence_from_file.h>
+
+// standard include
+#include <cmath>
+#include <iostream>
+#include <vector>
+#include <limits>
+#include <fstream>
+#include <sstream>
+#include <algorithm>
+#include <string>
+#include <utility>
+#include <functional>
+#include <boost/math/constants/constants.hpp>
+
+double pi = boost::math::constants::pi<double>();
+using PD = std::vector<std::pair<double,double> >;
+
+namespace Gudhi {
+namespace Persistence_representations {
+
+class Persistence_weighted_gaussian{
+
+ protected:
+    PD diagram;
+
+ public:
+
+  Persistence_weighted_gaussian(PD _diagram){diagram = _diagram;}
+  PD get_diagram(){return this->diagram;}
+
+
+  // **********************************
+  // Utils.
+  // **********************************
+
+
+  static double pss_weight(std::pair<double,double> P){
+    if(P.second > P.first)  return 1;
+    else return -1;
+  }
+
+  static double arctan_weight(std::pair<double,double> P){
+    return atan(P.second - P.first);
+  }
+
+  template<class Weight = std::function<double (std::pair<double,double>) > >
+  std::vector<std::pair<double,double> > Fourier_feat(PD D, std::vector<std::pair<double,double> > Z, Weight weight = arctan_weight){
+    int m = D.size(); std::vector<std::pair<double,double> > B; int M = Z.size();
+    for(int i = 0; i < M; i++){
+      double d1 = 0; double d2 = 0; double zx = Z[i].first; double zy = Z[i].second;
+      for(int j = 0; j < m; j++){
+        double x = D[j].first; double y = D[j].second;
+        d1 += weight(D[j])*cos(x*zx + y*zy);
+        d2 += weight(D[j])*sin(x*zx + y*zy);
+      }
+      B.emplace_back(d1,d2);
+    }
+    return B;
+  }
+
+  std::vector<std::pair<double,double> > random_Fourier(double sigma, int M = 1000){
+    std::normal_distribution<double> distrib(0,1); std::vector<std::pair<double,double> > Z; std::random_device rd;
+    for(int i = 0; i < M; i++){
+      std::mt19937 e1(rd()); std::mt19937 e2(rd());
+      double zx = distrib(e1); double zy = distrib(e2);
+      Z.emplace_back(zx/sigma,zy/sigma);
+    }
+    return Z;
+  }
+
+
+
+  // **********************************
+  // Scalar product + distance.
+  // **********************************
+
+
+  template<class Weight = std::function<double (std::pair<double,double>) > >
+  double compute_scalar_product(Persistence_weighted_gaussian second, double sigma, Weight weight = arctan_weight, int m = 1000){
+
+    PD diagram1 = this->diagram; PD diagram2 = second.diagram;
+
+    if(m == -1){
+      int num_pts1 = diagram1.size(); int num_pts2 = diagram2.size(); double k = 0;
+      for(int i = 0; i < num_pts1; i++)
+        for(int j = 0; j < num_pts2; j++)
+          k += weight(diagram1[i])*weight(diagram2[j])*exp(-((diagram1[i].first  - diagram2[j].first)  *  (diagram1[i].first  - diagram2[j].first) +
+                                                             (diagram1[i].second - diagram2[j].second) *  (diagram1[i].second - diagram2[j].second))
+                                                           /(2*sigma*sigma));
+      return k;
+    }
+    else{
+      std::vector<std::pair<double,double> > z =  random_Fourier(sigma, m);
+      std::vector<std::pair<double,double> > b1 = Fourier_feat(diagram1,z,weight);
+      std::vector<std::pair<double,double> > b2 = Fourier_feat(diagram2,z,weight);
+      double d = 0; for(int i = 0; i < m; i++) d += b1[i].first*b2[i].first + b1[i].second*b2[i].second;
+      return d/m;
+    }
+  }
+
+  template<class Weight = std::function<double (std::pair<double,double>) > >
+  double distance(Persistence_weighted_gaussian second, double sigma, Weight weight = arctan_weight, int m = 1000, double power = 1) {
+    return std::pow(this->compute_scalar_product(*this, sigma, weight, m) + second.compute_scalar_product(second, sigma, weight, m)-2*this->compute_scalar_product(second, sigma, weight, m),  power/2.0);
+  }
+
+
+};
+
+}  // namespace Persistence_weighted_gaussian
+}  // namespace Gudhi
+
+#endif  // PERSISTENCE_WEIGHTED_GAUSSIAN_H_
diff --git a/src/Persistence_representations/include/gudhi/Sliced_Wasserstein.h b/src/Persistence_representations/include/gudhi/Sliced_Wasserstein.h
new file mode 100644
index 00000000..4fa6151f
--- /dev/null
+++ b/src/Persistence_representations/include/gudhi/Sliced_Wasserstein.h
@@ -0,0 +1,285 @@
+/*    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 SLICED_WASSERSTEIN_H_
+#define SLICED_WASSERSTEIN_H_
+
+#ifdef GUDHI_USE_TBB
+#include <tbb/parallel_for.h>
+#endif
+
+// gudhi include
+#include <gudhi/read_persistence_from_file.h>
+
+// standard include
+#include <cmath>
+#include <iostream>
+#include <vector>
+#include <limits>
+#include <fstream>
+#include <sstream>
+#include <algorithm>
+#include <string>
+#include <utility>
+#include <functional>
+#include <boost/math/constants/constants.hpp>
+
+double pi = boost::math::constants::pi<double>();
+using PD = std::vector<std::pair<double,double> >;
+
+namespace Gudhi {
+namespace Persistence_representations {
+
+class Sliced_Wasserstein {
+
+ protected:
+    PD diagram;
+
+ public:
+
+  Sliced_Wasserstein(PD _diagram){diagram = _diagram;}
+  PD get_diagram(){return this->diagram;}
+
+
+  // **********************************
+  // Utils.
+  // **********************************
+
+  // Compute the angle formed by two points of a PD
+  double compute_angle(PD diag, int i, int j){
+    std::pair<double,double> vect; double x1,y1, x2,y2;
+    x1 = diag[i].first; y1 = diag[i].second;
+    x2 = diag[j].first; y2 = diag[j].second;
+    if (y1 - y2 > 0){
+      vect.first = y1 - y2;
+      vect.second = x2 - x1;}
+    else{
+      if(y1 - y2 < 0){
+        vect.first = y2 - y1;
+        vect.second = x1 - x2;
+      }
+      else{
+        vect.first = 0;
+        vect.second = abs(x1 - x2);}
+    }
+    double norm = std::sqrt(vect.first*vect.first + vect.second*vect.second);
+    return asin(vect.second/norm);
+  }
+
+  // Compute the integral of |cos()| between alpha and beta, valid only if alpha is in [-pi,pi] and beta-alpha is in [0,pi]
+  double compute_int_cos(const double & alpha, const double & beta){
+    double res = 0;
+    if (alpha >= 0 && alpha <= pi){
+      if (cos(alpha) >= 0){
+        if(pi/2 <= beta){res = 2-sin(alpha)-sin(beta);}
+        else{res = sin(beta)-sin(alpha);}
+      }
+      else{
+        if(1.5*pi <= beta){res = 2+sin(alpha)+sin(beta);}
+        else{res = sin(alpha)-sin(beta);}
+      }
+    }
+    if (alpha >= -pi && alpha <= 0){
+      if (cos(alpha) <= 0){
+        if(-pi/2 <= beta){res = 2+sin(alpha)+sin(beta);}
+        else{res = sin(alpha)-sin(beta);}
+      }
+      else{
+        if(pi/2 <= beta){res = 2-sin(alpha)-sin(beta);}
+        else{res = sin(beta)-sin(alpha);}
+      }
+    }
+    return res;
+  }
+
+  double compute_int(const double & theta1, const double & theta2, const int & p, const int & q, const PD & PD1, const PD & PD2){
+    double norm = std::sqrt(  (PD1[p].first-PD2[q].first)*(PD1[p].first-PD2[q].first) + (PD1[p].second-PD2[q].second)*(PD1[p].second-PD2[q].second)  );
+    double angle1;
+    if (PD1[p].first > PD2[q].first)
+      angle1 = theta1 - asin( (PD1[p].second-PD2[q].second)/norm  );
+    else
+      angle1 = theta1 - asin( (PD2[q].second-PD1[p].second)/norm  );
+    double angle2 = angle1 + theta2 - theta1;
+    double integral = compute_int_cos(angle1,angle2);
+    return norm*integral;
+  }
+
+
+
+
+  // **********************************
+  // Scalar product + distance.
+  // **********************************
+
+  double compute_sliced_wasserstein_distance(Sliced_Wasserstein second, int approx) {
+
+      PD diagram1 = this->diagram; PD diagram2 = second.diagram; double sw = 0;
+
+      if(approx == -1){
+
+        // Add projections onto diagonal.
+        int n1, n2; n1 = diagram1.size(); n2 = diagram2.size(); double max_ordinate = std::numeric_limits<double>::lowest();
+        for (int i = 0; i < n2; i++){
+          max_ordinate = std::max(max_ordinate, diagram2[i].second);
+          diagram1.emplace_back(  (diagram2[i].first+diagram2[i].second)/2, (diagram2[i].first+diagram2[i].second)/2  );
+        }
+        for (int i = 0; i < n1; i++){
+          max_ordinate = std::max(max_ordinate, diagram1[i].second);
+          diagram2.emplace_back(  (diagram1[i].first+diagram1[i].second)/2, (diagram1[i].first+diagram1[i].second)/2  );
+        }
+        int num_pts_dgm = diagram1.size();
+
+        // Slightly perturb the points so that the PDs are in generic positions.
+        int mag = 0; while(max_ordinate > 10){mag++; max_ordinate/=10;}
+        double thresh = pow(10,-5+mag);
+        srand(time(NULL));
+        for (int i = 0; i < num_pts_dgm; i++){
+          diagram1[i].first += thresh*(1.0-2.0*rand()/RAND_MAX); diagram1[i].second += thresh*(1.0-2.0*rand()/RAND_MAX);
+          diagram2[i].first += thresh*(1.0-2.0*rand()/RAND_MAX); diagram2[i].second += thresh*(1.0-2.0*rand()/RAND_MAX);
+        }
+
+        // Compute all angles in both PDs.
+        std::vector<std::pair<double, std::pair<int,int> > > angles1, angles2;
+        for (int i = 0; i < num_pts_dgm; i++){
+          for (int j = i+1; j < num_pts_dgm; j++){
+            double theta1 = compute_angle(diagram1,i,j); double theta2 = compute_angle(diagram2,i,j);
+            angles1.emplace_back(theta1, std::pair<int,int>(i,j));
+            angles2.emplace_back(theta2, std::pair<int,int>(i,j));
+          }
+        }
+
+        // Sort angles.
+        std::sort(angles1.begin(), angles1.end(), [=](std::pair<double, std::pair<int,int> >& p1, const std::pair<double, std::pair<int,int> >& p2){return (p1.first < p2.first);});
+        std::sort(angles2.begin(), angles2.end(), [=](std::pair<double, std::pair<int,int> >& p1, const std::pair<double, std::pair<int,int> >& p2){return (p1.first < p2.first);});
+
+        // Initialize orders of the points of both PDs (given by ordinates when theta = -pi/2).
+        std::vector<int> orderp1, orderp2;
+        for (int i = 0; i < num_pts_dgm; i++){ orderp1.push_back(i); orderp2.push_back(i); }
+        std::sort( orderp1.begin(), orderp1.end(), [=](int i, int j){ if(diagram1[i].second != diagram1[j].second) return (diagram1[i].second < diagram1[j].second); else return (diagram1[i].first > diagram1[j].first); } );
+        std::sort( orderp2.begin(), orderp2.end(), [=](int i, int j){ if(diagram2[i].second != diagram2[j].second) return (diagram2[i].second < diagram2[j].second); else return (diagram2[i].first > diagram2[j].first); } );
+
+        // Find the inverses of the orders.
+        std::vector<int> order1(num_pts_dgm); std::vector<int> order2(num_pts_dgm);
+        for(int i = 0; i < num_pts_dgm; i++)  for (int j = 0; j < num_pts_dgm; j++)  if(orderp1[j] == i){  order1[i] = j; break;  }
+        for(int i = 0; i < num_pts_dgm; i++)  for (int j = 0; j < num_pts_dgm; j++)  if(orderp2[j] == i){  order2[i] = j; break;  }
+
+        // Record all inversions of points in the orders as theta varies along the positive half-disk.
+        std::vector<std::vector<std::pair<int,double> > > anglePerm1(num_pts_dgm);
+        std::vector<std::vector<std::pair<int,double> > > anglePerm2(num_pts_dgm);
+
+        int m1 = angles1.size();
+        for (int i = 0; i < m1; i++){
+          double theta = angles1[i].first; int p = angles1[i].second.first; int q = angles1[i].second.second;
+          anglePerm1[order1[p]].emplace_back(p,theta);
+          anglePerm1[order1[q]].emplace_back(q,theta);
+          int a = order1[p]; int b = order1[q]; order1[p] = b; order1[q] = a;
+        }
+
+        int m2 = angles2.size();
+        for (int i = 0; i < m2; i++){
+          double theta = angles2[i].first; int p = angles2[i].second.first; int q = angles2[i].second.second;
+          anglePerm2[order2[p]].emplace_back(p,theta);
+          anglePerm2[order2[q]].emplace_back(q,theta);
+          int a = order2[p]; int b = order2[q]; order2[p] = b; order2[q] = a;
+        }
+
+        for (int i = 0; i < num_pts_dgm; i++){
+          anglePerm1[order1[i]].emplace_back(i,pi/2);
+          anglePerm2[order2[i]].emplace_back(i,pi/2);
+        }
+
+        // Compute the SW distance with the list of inversions.
+        for (int i = 0; i < num_pts_dgm; i++){
+          std::vector<std::pair<int,double> > u,v; u = anglePerm1[i]; v = anglePerm2[i];
+          double theta1, theta2; theta1 = -pi/2;
+          unsigned int ku, kv; ku = 0; kv = 0; theta2 = std::min(u[ku].second,v[kv].second);
+          while(theta1 != pi/2){
+            if(diagram1[u[ku].first].first != diagram2[v[kv].first].first || diagram1[u[ku].first].second != diagram2[v[kv].first].second)
+              if(theta1 != theta2)
+                sw += compute_int(theta1, theta2, u[ku].first, v[kv].first, diagram1, diagram2);
+            theta1 = theta2;
+            if (  (theta2 == u[ku].second)  &&  ku < u.size()-1  )  ku++;
+            if (  (theta2 == v[kv].second)  &&  kv < v.size()-1  )  kv++;
+            theta2 = std::min(u[ku].second, v[kv].second);
+          }
+        }
+      }
+
+
+      else{
+        double step = pi/approx;
+
+        // Add projections onto diagonal.
+        int n1, n2; n1 = diagram1.size(); n2 = diagram2.size();
+        for (int i = 0; i < n2; i++)
+          diagram1.emplace_back(  (diagram2[i].first + diagram2[i].second)/2,  (diagram2[i].first + diagram2[i].second)/2  );
+        for (int i = 0; i < n1; i++)
+          diagram2.emplace_back(  (diagram1[i].first + diagram1[i].second)/2,  (diagram1[i].first + diagram1[i].second)/2  );
+        int n = diagram1.size();
+
+        // Sort and compare all projections.
+        #ifdef GUDHI_USE_TBB
+          tbb::parallel_for(0, approx, [&](int i){
+            std::vector<std::pair<int,double> > l1, l2;
+            for (int j = 0; j < n; j++){
+              l1.emplace_back(   j, diagram1[j].first*cos(-pi/2+i*step) + diagram1[j].second*sin(-pi/2+i*step)   );
+              l2.emplace_back(   j, diagram2[j].first*cos(-pi/2+i*step) + diagram2[j].second*sin(-pi/2+i*step)   );
+            }
+            std::sort(l1.begin(),l1.end(), [=](const std::pair<int,double> & p1, const std::pair<int,double> & p2){return p1.second < p2.second;});
+            std::sort(l2.begin(),l2.end(), [=](const std::pair<int,double> & p1, const std::pair<int,double> & p2){return p1.second < p2.second;});
+            double f = 0; for (int j = 0; j < n; j++)  f += std::abs(l1[j].second - l2[j].second);
+            sw += f*step;
+          });
+        #else
+          for (int i = 0; i < approx; i++){
+            std::vector<std::pair<int,double> > l1, l2;
+            for (int j = 0; j < n; j++){
+              l1.emplace_back(   j, diagram1[j].first*cos(-pi/2+i*step) + diagram1[j].second*sin(-pi/2+i*step)   );
+              l2.emplace_back(   j, diagram2[j].first*cos(-pi/2+i*step) + diagram2[j].second*sin(-pi/2+i*step)   );
+            }
+            std::sort(l1.begin(),l1.end(), [=](const std::pair<int,double> & p1, const std::pair<int,double> & p2){return p1.second < p2.second;});
+            std::sort(l2.begin(),l2.end(), [=](const std::pair<int,double> & p1, const std::pair<int,double> & p2){return p1.second < p2.second;});
+            double f = 0; for (int j = 0; j < n; j++)  f += std::abs(l1[j].second - l2[j].second);
+            sw += f*step;
+          }
+        #endif
+      }
+
+      return sw/pi;
+  }
+
+
+  double compute_scalar_product(Sliced_Wasserstein second, double sigma, int approx = 100) {
+    return std::exp(-compute_sliced_wasserstein_distance(second, approx)/(2*sigma*sigma));
+  }
+
+  double distance(Sliced_Wasserstein second, double sigma, int approx = 100, double power = 1) {
+    return std::pow(this->compute_scalar_product(*this, sigma, approx) + second.compute_scalar_product(second, sigma, approx)-2*this->compute_scalar_product(second, sigma, approx),  power/2.0);
+  }
+
+
+};
+
+}  // namespace Sliced_Wasserstein
+}  // namespace Gudhi
+
+#endif  // SLICED_WASSERSTEIN_H_
diff --git a/src/Persistence_representations/include/gudhi/read_persistence_from_file.h b/src/Persistence_representations/include/gudhi/read_persistence_from_file.h
index 770da15b..83b89d0e 100644
--- a/src/Persistence_representations/include/gudhi/read_persistence_from_file.h
+++ b/src/Persistence_representations/include/gudhi/read_persistence_from_file.h
@@ -23,6 +23,8 @@
 #ifndef READ_PERSISTENCE_FROM_FILE_H_
 #define READ_PERSISTENCE_FROM_FILE_H_
 
+#include <gudhi/reader_utils.h>
+
 #include <iostream>
 #include <fstream>
 #include <sstream>
@@ -30,7 +32,7 @@
 #include <algorithm>
 #include <string>
 #include <utility>
-#include <gudhi/reader_utils.h>
+#include <limits>  // for std::numeric_limits<>
 
 namespace Gudhi {
 namespace Persistence_representations {
@@ -50,81 +52,66 @@ namespace Persistence_representations {
  * The procedure returns vector of persistence pairs.
 **/
 std::vector<std::pair<double, double> > read_persistence_intervals_in_one_dimension_from_file(
-    std::string const& filename, int dimension = -1, double what_to_substitute_for_infinite_bar = -1) {  
+    std::string const& filename, int dimension = -1, double what_to_substitute_for_infinite_bar = -1) {
   bool dbg = false;
 
   std::string line;
-  std::vector<std::pair<double, double> > barcode_initial = read_persistence_intervals_in_dimension(filename,(int)dimension);
+  std::vector<std::pair<double, double> > barcode_initial =
+      read_persistence_intervals_in_dimension(filename, (int)dimension);
   std::vector<std::pair<double, double> > final_barcode;
-  final_barcode.reserve( barcode_initial.size() );
-  
-  if ( dbg ) 
-  {
-	  std::cerr << "Here are the intervals that we read from the file : \n";
-	  for ( size_t i = 0 ; i != barcode_initial.size() ; ++i )
-	  {
-		  std::cout << barcode_initial[i].first << " " << barcode_initial[i].second << std::endl;
-	  }
-	  getchar();
+  final_barcode.reserve(barcode_initial.size());
+
+  if (dbg) {
+    std::cerr << "Here are the intervals that we read from the file : \n";
+    for (size_t i = 0; i != barcode_initial.size(); ++i) {
+      std::cout << barcode_initial[i].first << " " << barcode_initial[i].second << std::endl;
+    }
+    getchar();
   }
-  
-  for ( size_t i = 0 ; i != barcode_initial.size() ; ++i )
-  {
-	   if ( dbg )
-	   {
-		   std::cout << "COnsidering interval : " << barcode_initial[i].first << " " << barcode_initial[i].second << std::endl;
-	   }
-	   // if ( barcode_initial[i].first == barcode_initial[i].second )
-	   //{
-	   //		if ( dbg )std::cout << "It has zero length \n";
-	   //		continue;//zero length intervals are not relevant, so we skip all of them.
-	   //}
-	
-		if ( barcode_initial[i].first > barcode_initial[i].second )//note that in this case barcode_initial[i].second != std::numeric_limits<double>::infinity()
-		{
-			if ( dbg )std::cout << "Swap and enter \n";
-			//swap them to make sure that birth < death
-			final_barcode.push_back( std::pair<double,double>( barcode_initial[i].second , barcode_initial[i].first ) );
-			continue;
-		}
-		else
-		{
-			if ( barcode_initial[i].second != std::numeric_limits<double>::infinity() )
-			{
-				if ( dbg )std::cout << "Simply enters\n";
-				//in this case, due to the previous conditions we know that barcode_initial[i].first < barcode_initial[i].second, so we put them as they are
-				final_barcode.push_back( std::pair<double,double>( barcode_initial[i].first , barcode_initial[i].second ) );
-			}
-		}
-	
-		if ( (barcode_initial[i].second == std::numeric_limits<double>::infinity() ) && ( what_to_substitute_for_infinite_bar != -1 ) )
-		{								
-			if ( barcode_initial[i].first < what_to_substitute_for_infinite_bar )//if only birth < death.
-			{ 
-				final_barcode.push_back( std::pair<double,double>( barcode_initial[i].first , what_to_substitute_for_infinite_bar ) );
-			}
-		}
-		else
-		{
-			//if the variable what_to_substitute_for_infinite_bar is not set, then we ignore all the infinite bars. 
-		}		
+
+  for (size_t i = 0; i != barcode_initial.size(); ++i) {
+    if (dbg) {
+      std::cout << "COnsidering interval : " << barcode_initial[i].first << " " << barcode_initial[i].second
+                << std::endl;
+    }
+
+    if (barcode_initial[i].first > barcode_initial[i].second) {
+      // note that in this case barcode_initial[i].second != std::numeric_limits<double>::infinity()
+      if (dbg) std::cout << "Swap and enter \n";
+      // swap them to make sure that birth < death
+      final_barcode.push_back(std::pair<double, double>(barcode_initial[i].second, barcode_initial[i].first));
+      continue;
+    } else {
+      if (barcode_initial[i].second != std::numeric_limits<double>::infinity()) {
+        if (dbg) std::cout << "Simply enters\n";
+        // in this case, due to the previous conditions we know that barcode_initial[i].first <
+        // barcode_initial[i].second, so we put them as they are
+        final_barcode.push_back(std::pair<double, double>(barcode_initial[i].first, barcode_initial[i].second));
+      }
+    }
+
+    if ((barcode_initial[i].second == std::numeric_limits<double>::infinity()) &&
+        (what_to_substitute_for_infinite_bar != -1)) {
+      if (barcode_initial[i].first < what_to_substitute_for_infinite_bar)  // if only birth < death.
+      {
+        final_barcode.push_back(
+            std::pair<double, double>(barcode_initial[i].first, what_to_substitute_for_infinite_bar));
+      }
+    } else {
+      // if the variable what_to_substitute_for_infinite_bar is not set, then we ignore all the infinite bars.
+    }
   }
-  
-    
-  if ( dbg ) 
-  {
-	  std::cerr << "Here are the final bars that we are sending further : \n";
-	  for ( size_t i = 0 ; i != final_barcode.size() ; ++i )
-	  {
-		  std::cout << final_barcode[i].first << " " << final_barcode[i].second << std::endl;
-	  }
-	  std::cerr << "final_barcode.size() : " << final_barcode.size() << std::endl;
-	  getchar();
+
+  if (dbg) {
+    std::cerr << "Here are the final bars that we are sending further : \n";
+    for (size_t i = 0; i != final_barcode.size(); ++i) {
+      std::cout << final_barcode[i].first << " " << final_barcode[i].second << std::endl;
+    }
+    std::cerr << "final_barcode.size() : " << final_barcode.size() << std::endl;
+    getchar();
   }
-  
-  
-  
-  return final_barcode;  
+
+  return final_barcode;
 }  // read_persistence_intervals_in_one_dimension_from_file
 
 }  // namespace Persistence_representations