84 files changed, 614245 insertions, 17 deletions

diff --git a/CMakeLists.txt b/CMakeLists.txt
index 42a56fdc..d7078489 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -126,6 +126,7 @@ else()
   include_directories(src/Simplex_tree/include/)
   include_directories(src/Skeleton_blocker/include/)
   include_directories(src/Witness_complex/include/)
+  include_directories(src/Gudhi_stat/include/)
 
   add_subdirectory(src/common/example)
   add_subdirectory(src/common/test)
@@ -142,6 +143,8 @@ else()
   add_subdirectory(src/Bitmap_cubical_complex/example)
   add_subdirectory(src/Alpha_complex/example)
   add_subdirectory(src/Alpha_complex/test)
+  add_subdirectory(src/Gudhi_stat/test)
+  add_subdirectory(src/Gudhi_stat/example)
 
   # data points generator
   add_subdirectory(data/points/generator)
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index c7744c49..337079b1 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -108,6 +108,8 @@ else()
   add_subdirectory(example/Bitmap_cubical_complex)
   add_subdirectory(example/Witness_complex)
   add_subdirectory(example/Alpha_complex)
+  add_subdirectory(example/Bottleneck)
+
 
   # data points generator
   add_subdirectory(data/points/generator)
diff --git a/src/Gudhi_stat/doc/documentation.pdf b/src/Gudhi_stat/doc/documentation.pdf
new file mode 100644
index 00000000..829ecd4a
--- /dev/null
+++ b/src/Gudhi_stat/doc/documentation.pdf
diff --git a/src/Gudhi_stat/doc/documentation.tex b/src/Gudhi_stat/doc/documentation.tex
new file mode 100644
index 00000000..30078cd7
--- /dev/null
+++ b/src/Gudhi_stat/doc/documentation.tex
@@ -0,0 +1,200 @@
+%
+\documentclass[11pt]{article}
+\usepackage{amsmath}
+\usepackage{amsthm}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{color}
+\usepackage{graphicx}
+\usepackage{url}
+
+\graphicspath{{./figures/}}
+
+\newcommand{\ds}{\displaystyle}
+\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}
+\newcommand{\mbf}[1]{\mathbf{#1}}
+\newcommand{\mbb}[1]{\mathbb{#1}}
+\newcommand{\R}{\mbb{R}}
+\newcommand{\N}{\mbb{N}}
+\newcommand{\mcal}[1]{\mathcal{#1}}
+\newcommand{\eps}{\varepsilon}
+\newcommand{\set}[1]{\{#1\}}
+%\usepackage{customMath}
+
+\usepackage[top=2.5cm, bottom=3.5cm, left=2.5cm, right=2.5cm]{geometry}
+\parindent=12pt
+\pdfpagewidth 8.5in
+\pdfpageheight 11in
+%
+\renewcommand{\textfraction}{0.05}
+\renewcommand{\topfraction}{0.95}
+\renewcommand{\bottomfraction}{0.05}
+\renewcommand{\floatpagefraction}{0.90}
+%
+\newcommand{\PD}[1]{\textcolor{green}{\textbf{PD}\noindent\textbf{[#1]}}}
+\newcommand{\TS}[1]{\textcolor{blue}{\textbf{TS}\noindent\textbf{[#1]}}}
+\newcommand{\TW}[1]{\textcolor{red}{\textbf{TW}\noindent\textbf{[#1]}}}
+
+\renewcommand{\epsilon}{\varepsilon}
+\DeclareMathOperator{\Ima}{Im}
+
+\newcommand{\norm}[1]{\ensuremath{\left\|#1\right\|}}
+\newcommand{\bdr}[1]{bdr\ #1}
+\newtheorem{theorem}{Theorem}[section]
+\newtheorem{prop}[theorem]{Proposition}
+\newtheorem{lemma}[theorem]{Lemma}
+\newtheorem{cor}[theorem]{Corollary}
+\newtheorem{remark}[theorem]{Remark}
+
+
+\begin{document}
+
+\begin{center}
+\Huge{The gudhi stat doc.\\
+Ver 1.0.}
+\end{center}
+
+
+\section{Idea}
+
+When it comes to the statistics and machine learning, one need only very limited number of operations to be performed on a data to get the results. Let us think of some representation of persistence, of a type $\mathcal{A}$. To perform most of the statistical and machine learning operations one need to be able to compute average of objects of type $\mathcal{A}$ (so that the averaged object is also of a type $\mathcal{A}$). One need to be able to compute distance between objects of a type $\mathcal{A}$, and to compute scalar product of objects of a type $\mathcal{A}$.
+
+To put this statement into a context, let us assume we have two collections $c_1,...,c_n$ and $d_1,...,d_n$ of objects of a type $\mathcal{A}$. We want to verify if the average of those two collections are different by performing bootstrap.
+First of all, we compute averages of those two collections: $C =$ average of $c_1,...,c_n$ and $D =$ average of $d_1,...,d_n$. Note that both $C$ and $D$ are of a type $\mathcal{A}$. Then we compute $d(C,D)$, a distance between $C$ and $D$.
+Later we put the two collections into one bin:\\
+\[B = { c_1,...,c_n,d_1,...,d_n }\]
+Then we shuffle $B$, and we divide the shuffled version of $B$ into two classes: $B_1$ and $B_2$ (in this case, of the same cardinality). Note that again, $B_1$ and $B_2$ are of a type $\mathcal{A}$. We compute their distance $d(B_1,B_2)$. The procedure of shuffling and dividing the set $B$ is repeated $N$ times (where $N$ is reasonably large number).
+Then the p-value of a statement that the averages of  $c_1,...,c_n$ and $d_1,...,d_n$ is approximated by the number of times $d(B_1,B_2) > d(C,D)$ divided by $N$.
+
+As one can see, this procedure can be performed for any type $\mathcal{A}$ which can be averaged, and which allows for computations of distances. The idea of Gudhi\_stat is to take advantage of C++ (and later python) polymorphism and implement a few interfaces:
+\begin{enumerate}
+\item Interface of a representation of persistence that allows averaging (so that the average object is of the same type).
+\item Interface of representation of persistence that allows computations of distances.
+\item Interface of representation of persistence that allows computations of scalar product.
+\end{enumerate}
+
+And then to implement various currently known representations based on those interfaces. At the moment we have the implementation of following classes available (further details of those representations will be discussed later):
+\begin{enumerate}
+\item Exact persistence landscapes (allow averaging, computation of distances and scalar products).
+\item Persistence landscapes on a grid (allow averaging, computation of distances and scalar products).
+\item Persistence heat maps – various representations where one put some weighted or not Gaussian kernel for each point of diagram (allow averaging, computation of distances and scalar products).
+\item Persistence vectors (allow averaging, computation of distances and scalar products).
+\item Persistence diagrams / barcodes (allow computation of distances).
+\end{enumerate}
+
+
+The main aim of this implementation is to be able to implement various statistical methods, both on the level of C++ and python, that operates on the interfaces that are required for that particular method (like, in the example above, the ability of averaging and computations of distances). Given those implementations of statistical methods, we are able to use any of representation that implement athe required collection of interfaces (that includes the future ones that has not been implemented yet). 
+Doing so, we define a computational framework that joins topological methods that uses persistent homology with statistics and machine learning. This framework is very easy to being extend by new representations of persistence, and even more general, but any new type of representation.
+
+Below we are discussing the representations which are currently implemented in Gudhi\_stat:
+
+
+\section{Persistence Landscapes}
+\label{sec:persistence_landscapes}
+Persistence landscapes were originally proposed by Bubenik in~\cite{landscapes1}. Efficient algorithms to compute them rigorously were proposed by Bubenik and D{\l}otko in~\cite{landscapes2}. The idea of persistence landscapes is shortly summarized in below.
+
+To begin with, suppose we are given a point~$(b,d) \in \mathbb{R}^2$ in a
+persistence diagram. With this point, we associate a piecewise
+linear function~$f_{(b,d)} : \mathbb{R} \rightarrow [0,\infty)$, which is
+defined as
+%
+\begin{equation} \label{eq:basicLand}
+  f_{(b,d)}(x) =
+  \left\{ \begin{array}{ccl}
+            0     & \mbox{ if } & x \not\in (b, d) \; , \\[2ex]
+            x - b & \mbox{ if } & x \in \left( b, \frac{b+d}{2}
+              \right] \; , \\[2ex]
+            d - x & \mbox{ if } & x \in \left(\frac{b+d}{2},
+              d \right) \; .
+  \end{array} \right.
+\end{equation}
+
+A \emph{persistence landscape} of the birth-death
+pairs~$(b_i , d_i)$, where $i = 1,\ldots,m$, which constitute the given
+persistence diagram is the sequence of functions $\lambda_k : \mathbb{R}
+\rightarrow [0,\infty)$ for $k \in \mathbb{N}$, where~$\lambda_k(x)$
+denotes the $k^{\rm th}$ largest value of the numbers~$f_{(b_i,d_i)}(x)$,
+for $i = 1, \ldots, m$, and we define $\lambda_k(x) = 0$ if $k > m$.
+Equivalently, this sequence of functions can be combined into a single
+function $L : \mathbb{N} \times \mathbb{R} \to [0,\infty)$ of two
+variables, if we define $L(k,t) = \lambda_k(t)$.
+
+The detailed description of algorithms used to compute persistence landscapes can be found in~\cite{landscapes2}. Note that this implementation provides exact representation of landscapes. That have many advantages, but also a few drawbacks. For instance, as discussed in~\cite{landscapes2}, the exact representation of landscape may be of quadratic size with respect to the input persistence diagram. It may therefore happen that, for very large diagrams, using this representation may be memory--prohibitive. In such a case, there are two possible ways to proceed:
+\begin{enumerate}
+\item Use non exact representation on a grid described in the Section~\ref{sec:landscapes_on_grid}.
+\item Compute just a number of initial nonzero landscapes. This option is available from C++ level. 
+\end{enumerate}
+
+
+
+\section{Persistence Landscapes on a grid}
+\label{sec:landscapes_on_grid}
+This is an alternative representation of persistence landscapes defined in the Section~\ref{sec:persistence_landscapes}. Unlike in the Section~\ref{sec:persistence_landscapes} we build a non--exact representation by sampling persistence landscape on a finite, equally distributed grid of points. Since, the persistence landscapes that originate from persistence diagrams have slope $1$ or $-1$, we have an estimate of an error made in between grid points by such a sampling. We do not have a similar estimation when a landscape is obtained from averaging process. 
+
+Due to a lack of rigorous description of the algorithms in the literature, we are giving a short discussion of them in below. Persistence landscapes are being represented by vector of vectors of real numbers. Assume that i-th vector consist of $n_i$ numbers sorted from larger to smaller. They represent the values of the functions $\lambda_1,\ldots,\lambda_{n_i}$ ($\lambda_{n_i+1}$ and further are zero) on the i-th point of a grid. 
+
+When averaging two persistence landscapes represented by a grid, we simply compute point-wise averages of the entries of corresponding vectors\footnote{In this whole section we assume that if one vector is shorter than another, we extend the shorter one with zeros so that they have the same length.}
+
+Computations of distances between two persistence landscapes on a grid is not much different than in the rigorous case. In this case, we sum up the distances between the same levels of corresponding landscapes. For fixed level, we approximate the landscapes between the corresponding constitutive points of landscapes by linear functions, and compute the $L^p$ distance between them.
+
+Similarly as in case of distance, when computing the scalar product of two persistence landscapes on a grid, we sum up the scalar products of corresponding levels of landscapes. For each level, we assume that the persistence landscape on a grid between two grid points is approximated by linear function. Therefore to compute scalar product of two corresponding levels of landscapes, we sum up the integrals of products of line segments for every pair of constitutive grid points. 
+
+Note that for this representation we need to specify a few parameters:
+\begin{enumerate}
+\item Begin and end point of a grid (real numbers)
+
+\item Number of points in a grid.
+\end{enumerate}
+
+Note that the same representation is used in TDA R-package~\cite{tda}.
+
+\section{Persistence heat maps}
+This is a general class of discrete structures which are based on idea of placing a Gaussian kernel in the points of persistence diagrams. This idea appeared in work by many authors along the last 15 years. As far as we know this idea was firstly described in the work of Bologna group in~\cite{bologna1} and~\cite{bologna2}. Later it has been described by Colorado State University group in~\cite{Henry}. The presented paper in the first time provide a discussion of stability of the representation. Also, the same ideas are used in construction of two recent kernels used for machine learning:~\cite{yasu} and~\cite{uli}. Both the kernel's construction uses interesting ideas to ensure stability of the representation with respect to Wasserstein metric. In the kernel presented in~\cite{yasu}, a scaling function is used to multiply the Gaussian kernel in the way that the points close to diagonal got low weight and consequently do not have a big influence on the resulting total distribution. In~\cite{uli} for every point $(b,d)$ two Gaussian kernels are added. First, with a weight one in a point $(b,d)$, and the second, with the weight $-1$ for a point $(b,d)$. In both cases, the representations are stable with respect to 1-Wasserstein distance.
+
+In Gudhi\_stat we currently implement all the structures described above. The base of this implementation is 2-dimensional arrays of pixels. Each pixel have assigned a real value which is a sum of values of distributions induced by each point of the persistence diagram. 
+
+The parameters of the structure are as follows:
+\begin{enumerate}
+\item Size of the image (we always assume that the images are square).
+\item A filter: in practice a square matrix of a size $2k+1 \times 2k+1$. By default, this is a Gaussian kernel, but any other can be used instead.
+\item The box $[x_0,x_1]\times [y_0,y_1]$ bounding the domain of the persistence image. 
+\item Scaling function (each Gaussian kernel at point $(p,q)$ gets multiplied by the value of this function at the point $(p,q)$. 
+\item A boolean value determining if the space below diagonal should be erased or not. 
+\end{enumerate}
+
+\section{Persistence vectors}
+This is a representation of persistent homology in a form of a vector which was designed for an application in 3d graphic in~\cite{vectors}. Below we provide a short description of this representation.
+
+Given a persistence diagram $D = \{ (b_i,d_i) \}$, for every pair of birth--death points $(b_1,d_1)$ and $(b_2,d_2)$ we compute the following three distances:
+\begin{enumerate}
+\item $d( (b_1,d_1) , (b_2,d_2) )$.
+\item $d( (b_1,d_1) , (\frac{b_1,d_1}{2},\frac{b_1,d_1}{2}) )$.
+\item $d( (b_2,d_2) , (\frac{b_2,d_2}{2},\frac{b_2,d_2}{2}) )$.
+\end{enumerate}
+We pick the smallest of those and add it to a vector. The obtained vector of numbers is then sorted in decreasing order. This way we obtain a \emph{persistence vector} representing the diagram.
+
+Given two persistence vectors, the computation of distances, averages and scalar products is straightforward. Average is simply a coordinate-wise average of a collection of vectors. In this section we assume that the vectors are extended by zeros if they are of a different size. To compute distances we compute absolute value of differences between coordinates. A scalar product is a sum of products of values at the corresponding positions of two vectors. 
+
+
+\begin{thebibliography}{99}
+\bibitem{landscapes1}  P. Bubenik, Statistical topological data analysis using persistence landscapes, Journal of Machine Learning Research, 16 (2015), 77–102.
+
+\bibitem{landscapes2} P. Bubenik, P. Dlotko, A persistence landscapes toolbox for topological statistics. Journal of Symbolic Computation.
+
+\bibitem{tda} B. Fasy, J. Kim, F. Lecci, C. Maria, Introduction to the R package TDA, arXiv:1411.1830.
+
+\bibitem{bologna1} P. Donatini, P. Frosini, A. Lovato, Size functions for signature recognition, Proceedings of SPIE, Vision Geometry VII, vol. 3454
+(1998).
+
+\bibitem{bologna2} M. Ferri, P. Frosini, A. Lovato, C. Zambelli, Point selection: A new comparison scheme for size functions (With an application to monogram recognition), Proceedings Third Asian Conference on Computer Vision, Lecture Notes in Computer Science 1351.
+
+\bibitem{Henry} H. Adams, S. Chepushtanova, T. Emerson, E. Hanson, M. Kirby, F. Motta, R. Neville, C. Peterson, P. Shipman, L. Ziegelmeier, Persistence Images: A Stable Vector Representation of Persistent Homology, arXiv:1507.06217.
+
+\bibitem{yasu} G. Kusano, K. Fukumizu, Y. Hiraoka, Persistence weighted Gaussian kernel for topological data analysis, arXiv:1601.01741.
+
+\bibitem{uli} J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, A Stable Multi-Scale Kernel for Topological Machine Learning, arXiv:1412.6821.
+
+\bibitem{vectors} M. Carrière, S. Oudot, M. Ovsjanikov, Stable Topological Signatures for Points on 3D Shapes., Proc. Sympos. on Geometry Processing, July 2015.
+
+\end{thebibliography}
+\end{document}
\ No newline at end of file
diff --git a/src/Gudhi_stat/example/CMakeLists.txt b/src/Gudhi_stat/example/CMakeLists.txt
new file mode 100644
index 00000000..613e4d26
--- /dev/null
+++ b/src/Gudhi_stat/example/CMakeLists.txt
@@ -0,0 +1,119 @@
+cmake_minimum_required(VERSION 2.6)
+project(GUDHI_STAT)
+
+add_executable ( persistence_landscape_on_grid persistence_landscape_on_grid.cpp )
+target_link_libraries(persistence_landscape_on_grid ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( persistence_landscape persistence_landscape.cpp )
+target_link_libraries(persistence_landscape ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( persistence_intervals persistence_intervals.cpp )
+target_link_libraries(persistence_intervals ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( vector_representation vector_representation.cpp )
+target_link_libraries(vector_representation ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( persistence_heat_maps persistence_heat_maps.cpp )
+target_link_libraries(persistence_heat_maps ${Boost_SYSTEM_LIBRARY})
+
+
+##UTILITIES:
+
+#persitence diagrams
+add_executable ( plot_persistence_intervals utilities/persistence_intervals/plot_persistence_intervals.cpp )
+target_link_libraries( plot_persistence_intervals ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( compute_birth_death_range_in_persistence_diagram utilities/persistence_intervals/compute_birth_death_range_in_persistence_diagram.cpp )
+target_link_libraries( compute_birth_death_range_in_persistence_diagram ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( compute_number_of_dominant_intervals utilities/persistence_intervals/compute_number_of_dominant_intervals.cpp )
+target_link_libraries( compute_number_of_dominant_intervals ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( plot_histogram_of_intervals_lengths utilities/persistence_intervals/plot_histogram_of_intervals_lengths.cpp )
+target_link_libraries( plot_histogram_of_intervals_lengths ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( plot_persistence_Betti_numebrs utilities/persistence_intervals/plot_persistence_Betti_numebrs.cpp )
+target_link_libraries( plot_persistence_Betti_numebrs ${Boost_SYSTEM_LIBRARY})
+
+#when we have bottleneck and wasserstein distance computations, add suitable programs here.
+
+
+#persitence landscapes
+add_executable ( average_landscapes utilities/persistence_landscapes/average_landscapes.cpp )
+target_link_libraries(average_landscapes ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( create_landscapes utilities/persistence_landscapes/create_landscapes.cpp )
+target_link_libraries(create_landscapes ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( plot_landscapes utilities/persistence_landscapes/plot_landscapes.cpp )
+target_link_libraries(plot_landscapes ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( compute_distance_of_landscapes utilities/persistence_landscapes/compute_distance_of_landscapes.cpp )
+target_link_libraries(compute_distance_of_landscapes ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( compute_scalar_product_of_landscapes utilities/persistence_landscapes/compute_scalar_product_of_landscapes.cpp )
+target_link_libraries(compute_scalar_product_of_landscapes ${Boost_SYSTEM_LIBRARY})
+
+#persitence landscapes on a grid
+add_executable ( average_landscapes_on_grid utilities/persistence_landscapes_on_grid/average_landscapes_on_grid.cpp )
+target_link_libraries(average_landscapes_on_grid ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( create_landscapes_on_grid utilities/persistence_landscapes_on_grid/create_landscapes_on_grid.cpp )
+target_link_libraries(create_landscapes_on_grid ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( plot_landscapes_on_grid utilities/persistence_landscapes_on_grid/plot_landscapes_on_grid.cpp )
+target_link_libraries(plot_landscapes_on_grid ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( compute_distance_of_landscapes_on_grid utilities/persistence_landscapes_on_grid/compute_distance_of_landscapes_on_grid.cpp )
+target_link_libraries(compute_distance_of_landscapes_on_grid ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( compute_scalar_product_of_landscapes_on_grid utilities/persistence_landscapes_on_grid/compute_scalar_product_of_landscapes_on_grid.cpp )
+target_link_libraries(compute_scalar_product_of_landscapes_on_grid ${Boost_SYSTEM_LIBRARY})
+
+#persitence heat maps
+add_executable ( average_persistence_heat_maps utilities/persistence_heat_maps/average_persistence_heat_maps.cpp )
+target_link_libraries(average_persistence_heat_maps ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( create_persistence_heat_maps utilities/persistence_heat_maps/create_persistence_heat_maps.cpp )
+target_link_libraries(create_persistence_heat_maps ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( plot_persistence_heat_map utilities/persistence_heat_maps/plot_persistence_heat_map.cpp )
+target_link_libraries(plot_persistence_heat_map ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( compute_distance_of_persistence_heat_maps utilities/persistence_heat_maps/compute_distance_of_persistence_heat_maps.cpp )
+target_link_libraries(compute_distance_of_persistence_heat_maps ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( compute_scalar_product_of_persistence_heat_maps utilities/persistence_heat_maps/compute_scalar_product_of_persistence_heat_maps.cpp )
+target_link_libraries(compute_scalar_product_of_persistence_heat_maps ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( create_pssk utilities/persistence_heat_maps/create_pssk.cpp )
+target_link_libraries(create_pssk ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( create_persistence_heat_maps_weighted_by_distance_from_diagonal utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_distance_from_diagonal.cpp )
+target_link_libraries(create_persistence_heat_maps_weighted_by_distance_from_diagonal ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( create_persistence_heat_maps_weighted_by_squared_distance_from_diagonal utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_squared_distance_from_diagonal.cpp )
+target_link_libraries(create_persistence_heat_maps_weighted_by_squared_distance_from_diagonal ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( create_persistence_heat_maps_weighted_by_arctan_of_their_persistence utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_arctan_of_their_persistence.cpp )
+target_link_libraries(create_persistence_heat_maps_weighted_by_arctan_of_their_persistence ${Boost_SYSTEM_LIBRARY})
+
+
+#persitence vectors
+add_executable ( average_persistence_vectors utilities/persistence_vectors/average_persistence_vectors.cpp )
+target_link_libraries(average_persistence_vectors ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( create_persistence_vectors utilities/persistence_vectors/create_persistence_vectors.cpp )
+target_link_libraries(create_persistence_vectors ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( compute_distance_of_persistence_vectors utilities/persistence_vectors/compute_distance_of_persistence_vectors.cpp )
+target_link_libraries(compute_distance_of_persistence_vectors ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( compute_scalar_product_of_persistence_vectors utilities/persistence_vectors/compute_scalar_product_of_persistence_vectors.cpp )
+target_link_libraries(compute_scalar_product_of_persistence_vectors ${Boost_SYSTEM_LIBRARY})
+
+add_executable ( plot_persistence_vectors utilities/persistence_vectors/plot_persistence_vectors.cpp )
+target_link_libraries(plot_persistence_vectors ${Boost_SYSTEM_LIBRARY})
+
+
+
diff --git a/src/Gudhi_stat/example/persistence_heat_maps.cpp b/src/Gudhi_stat/example/persistence_heat_maps.cpp
new file mode 100644
index 00000000..cd0c4113
--- /dev/null
+++ b/src/Gudhi_stat/example/persistence_heat_maps.cpp
@@ -0,0 +1,196 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/reader_utils.h>
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_heat_maps.h>
+
+#include <iostream>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+
+double epsilon = 0.0000005;
+
+using namespace std;
+
+	
+int main( int argc , char** argv )
+{
+	//if ( argc != 2 )
+	//{
+	//	cout << "To run this program, please provide the name of a file with persistence diagram \n";
+	//	return 1;
+	//}
+	
+/*
+	std::vector< std::pair< double,double > > intervals;
+	intervals.push_back( std::make_pair(0.5,0.5) );	
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(5,1);		
+	Persistence_heat_maps p( intervals , filter ,  constant_function, false , 100 , 0 , 1 );
+	p.plot( "heat_map_1" );
+
+	
+	std::vector< std::pair< double,double > > intervals2;
+	intervals2.push_back( std::make_pair(7,12) );		
+	Persistence_heat_maps q( intervals2 , filter ,  constant_function, false , 100 , 0 , 10 );
+	q.plot( "heat_map_2" );
+*/
+/*
+	std::vector< std::pair< double,double > > intervals;
+	intervals.push_back( std::make_pair(0.5,0.5) );	
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(5,1);		
+	Persistence_heat_maps p( intervals , filter ,  constant_function, false , 10 , 0 , 1 );
+	p.write_to_file( "aaa" );
+	
+	Persistence_heat_maps q;
+	q.load_from_file( "aaa" );
+	
+	cerr << ( p == q ) << endl;
+	*/
+
+/*
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(30,1);		
+	Persistence_heat_maps p( "file_with_diagram" , filter ,  constant_function, false , 100 , 0 , 1 );
+	p.plot( "heat_map_1" );
+*/ 
+	 
+/*   
+   //test to construct persistence heat map:
+    std::vector< std::vector<double> > filter = create_Gaussian_filter(100,1);		
+	Persistence_heat_maps p( "file_with_diagram" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	p.print_to_file( "persistence_heat_map_from_file_with_diagram" );
+	
+	Persistence_heat_maps q;
+	q.load_from_file( "persistence_heat_map_from_file_with_diagram" );	
+	
+	cerr << (p == q) << endl;
+*/
+/*
+	//test of computations of a mean:
+	std::vector< std::pair< double,double > > intervals;
+	intervals.push_back( std::make_pair(5,5) );	
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(5,1);		
+	Persistence_heat_maps p( intervals , filter ,  constant_function, false , 100 , 0 , 10 );
+	p.plot( "heat_map_1" );
+
+	
+	std::vector< std::pair< double,double > > intervals2;
+	intervals2.push_back( std::make_pair(7,7) );		
+	Persistence_heat_maps q( intervals2 , filter ,  constant_function, false , 100 , 0 , 10 );
+	q.plot( "heat_map_2" );
+	
+	
+	std::vector< Abs_Topological_data_with_averages* > to_average;
+	to_average.push_back( (Abs_Topological_data_with_averages*)(&p) );
+	to_average.push_back( (Abs_Topological_data_with_averages*)(&q) );
+	Persistence_heat_maps av;	
+	av.compute_average( to_average );
+	av.plot( "average" );
+*/
+
+/*
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(30,1);	
+	Persistence_heat_maps p( "file_with_diagram" , filter ,  constant_function, false , 1000 , 0 , 10 );
+	Persistence_heat_maps q( "file_with_diagram_1" , filter ,  constant_function, false , 1000 , 0 , 10 );
+	Persistence_heat_maps r( "file_with_diagram_2" , filter ,  constant_function, false , 1000 , 0 , 10 );
+	
+	std::vector< Abs_Topological_data_with_averages* > to_average;
+	to_average.push_back( (Abs_Topological_data_with_averages*)(&p) );
+	to_average.push_back( (Abs_Topological_data_with_averages*)(&q) );
+	to_average.push_back( (Abs_Topological_data_with_averages*)(&r) );
+	Persistence_heat_maps av;	
+	av.compute_average( to_average );
+	
+	av.print_to_file( "template_average_of_heat_maps" );
+*/	
+
+/*
+	std::vector< std::pair< double,double > > intervals;
+	intervals.push_back( std::make_pair(5,5) );	
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(5,1);		
+	Persistence_heat_maps p( intervals , filter ,  constant_function, false , 10 , 0 , 10 );
+	p.plot( "heat_map_1" );
+	
+	std::vector< std::pair< double,double > > intervals2;
+	intervals2.push_back( std::make_pair(7,7) );		
+	Persistence_heat_maps q( intervals2 , filter ,  constant_function, false , 10 , 0 , 10 );
+	q.plot( "heat_map_2" );
+	
+	std::vector< Persistence_heat_maps* > to_compute_median;
+	to_compute_median.push_back( &p );
+	to_compute_median.push_back( &q );	
+	Persistence_heat_maps median;	
+	median.compute_median( to_compute_median );
+	median.plot( "median" );
+*/
+
+/*
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(30,1);	
+	Persistence_heat_maps p( "file_with_diagram" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps q( "file_with_diagram_1" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps r( "file_with_diagram_2" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	
+	std::vector< Persistence_heat_maps* > to_compute_median;
+	to_compute_median.push_back( &p );
+	to_compute_median.push_back( &q );
+	to_compute_median.push_back( &r );
+	Persistence_heat_maps median;	
+	median.compute_median( to_compute_median );
+	
+	median.print_to_file( "template_median_of_heat_maps" );
+*/
+
+
+
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(30,1);	
+	Persistence_heat_maps p( "file_with_diagram" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps q( "file_with_diagram_1" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps r( "file_with_diagram_2" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	
+	std::vector< Persistence_heat_maps* > to_compute_percentage_of_active;
+	to_compute_percentage_of_active.push_back( &p );
+	to_compute_percentage_of_active.push_back( &q );
+	to_compute_percentage_of_active.push_back( &r );
+	Persistence_heat_maps percentage_of_active;	
+	percentage_of_active.compute_percentage_of_active( to_compute_percentage_of_active , 0.1 );
+	
+	percentage_of_active.print_to_file( "template_percentage_of_active_of_heat_maps" );
+	//percentage_of_active.plot( "template_percentage_of_active_of_heat_maps" );
+	
+	
+
+	
+	return 0;
+}
+
+
+
+
+
+
+
diff --git a/src/Gudhi_stat/example/persistence_intervals.cpp b/src/Gudhi_stat/example/persistence_intervals.cpp
new file mode 100644
index 00000000..cbd4020d
--- /dev/null
+++ b/src/Gudhi_stat/example/persistence_intervals.cpp
@@ -0,0 +1,114 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/reader_utils.h>
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_intervals.h>
+
+#include <iostream>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+using namespace std;
+
+	
+int main( int argc , char** argv )
+{
+	if ( argc != 2 )
+	{
+		cout << "To run this program, please provide the name of a file with persistence diagram \n";
+		return 1;
+	}
+	
+	Persistence_intervals p( argv[1] );
+	std::pair<double,double> min_max_ = p.min_max();	
+	cout << "Birth-death range : " <<  min_max_.first << " " << min_max_.second << endl;
+	
+	
+	std::vector<double> dominant_ten_intervals_length = p.length_of_dominant_intervals(10);
+	cout << "Lendth of ten dominant intervals : " << endl;	
+	for ( size_t i = 0 ; i != dominant_ten_intervals_length.size() ; ++i )
+	{
+		cout << dominant_ten_intervals_length[i] << endl;
+	}
+	
+	std::vector< std::pair<double,double> > ten_dominant_intervals = p.dominant_intervals( 10 );	
+	cout << "Here are the dominant intervals : " << endl;
+	for ( size_t i = 0 ; i != ten_dominant_intervals.size() ; ++i )
+	{
+		cout << "( " << ten_dominant_intervals[i].first<< "," << ten_dominant_intervals[i].second << endl;
+	}
+	
+	std::vector< size_t > histogram = p.histograms_of_lengths( 10  );
+	cout << "Here is the histogram of barcode's length : " << endl;
+	for ( size_t i = 0 ; i != histogram.size() ; ++i )
+	{
+		cout << histogram[i]  << " ";
+	}		
+	cout << endl;
+
+	
+	std::vector< size_t > cumulative_histogram = p.cumulative_histograms_of_lengths( 10  );
+	cout<< "Cumuative histogram : " << endl;	
+	for ( size_t i = 0 ; i != cumulative_histogram.size() ; ++i )
+	{
+		cout << cumulative_histogram[i] << " ";
+	}		
+	cout << endl;
+
+	std::vector< double  > char_funct_diag = p.characteristic_function_of_diagram( min_max_.first , min_max_.second );	
+	cout << "Characteristic function of diagram : " << endl;
+	for ( size_t i = 0 ; i != char_funct_diag.size() ; ++i )
+	{
+		cout << char_funct_diag[i] << " ";
+	}		
+	cout << endl;
+
+	std::vector< double  > cumul_char_funct_diag = p.cumulative_characteristic_function_of_diagram( min_max_.first , min_max_.second );
+	cout << "Cumulative characteristic function of diagram : " << endl;
+	for ( size_t i = 0 ; i != cumul_char_funct_diag.size() ; ++i )
+	{		
+		cout << cumul_char_funct_diag[i] << " ";
+	}	
+	cout << endl;
+
+	cout << "Persistence Betti numbers \n";
+	std::vector< std::pair< double , size_t > > pbns = p.compute_persistent_betti_numbers();	
+	for ( size_t i = 0 ; i != pbns.size() ; ++i )
+	{
+		cout <<  pbns[i].first << " " << pbns[i].second << endl;	
+	}
+	
+	return 0;
+}
+
+
+
+
+
+
+
diff --git a/src/Gudhi_stat/example/persistence_landscape.cpp b/src/Gudhi_stat/example/persistence_landscape.cpp
new file mode 100644
index 00000000..a5b726c7
--- /dev/null
+++ b/src/Gudhi_stat/example/persistence_landscape.cpp
@@ -0,0 +1,167 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+
+
+int main( int argc , char** argv )
+{
+	
+	if ( argc != 2 )
+	{
+		std::cerr << "To run this program, please provide a name of a file with persistence landscape \n";
+		//return 1;
+	}		
+	Persistence_landscape p("../test/data/file_with_diagram");
+	
+	Persistence_landscape q;
+	q.load_landscape_from_file( "file_with_landscape_from_file_with_diagram" );
+	
+	if ( p != q )
+	{
+		cout << "Not equal \n";
+	}
+	
+	double integral = p.compute_integral_of_landscape();
+	cout << "integral : " << integral <<endl;
+	
+	//compute integral for each level separatelly
+	for ( size_t level = 0 ; level != p.size() ; ++level )
+	{
+		cout << p.compute_integral_of_landscape( level ) << endl;
+	}
+	
+	//compute integral of p-th power of landscspe
+	for ( size_t power = 0 ; power != 5 ; ++power ) 
+	{
+		cout << p.compute_integral_of_landscape( power ) << endl;
+	}
+	
+	cout << "Value of level 1 at 0 : " <<  p.compute_value_at_a_given_point(1,0.0) << endl;
+	cout << "Value of level 1  at 1 : " <<  p.compute_value_at_a_given_point(1,0.1) << endl;
+	cout << "Value of level 1  at 2 : " <<  p.compute_value_at_a_given_point(1,0.2) << endl;
+	cout << "Value of level 1  at 3 : " <<  p.compute_value_at_a_given_point(1,0.3) << endl;
+	
+		
+	cout << "Value of level 2 at 0 : " <<  p.compute_value_at_a_given_point(2,0.0) << endl;
+	cout << "Value of level 2  at 1 : " <<  p.compute_value_at_a_given_point(2,0.1) << endl;
+	cout << "Value of level 2  at 2 : " <<  p.compute_value_at_a_given_point(2,0.2) << endl;
+	cout << "Value of level 2  at 3 : " <<  p.compute_value_at_a_given_point(2,0.3) << endl;
+	
+		
+	cout << "Value of level 3 at 0 : " <<  p.compute_value_at_a_given_point(3,0.0) << endl;
+	cout << "Value of level 3  at 1 : " <<  p.compute_value_at_a_given_point(3,0.1) << endl;
+	cout << "Value of level 3  at 2 : " <<  p.compute_value_at_a_given_point(3,0.2) << endl;
+	cout << "Value of level 3  at 3 : " <<  p.compute_value_at_a_given_point(3,0.3) << endl;
+	
+	
+	
+	Persistence_landscape second;
+	second.load_landscape_from_file("file_with_landscape_from_file_with_diagram_1" );
+	
+	Persistence_landscape sum = p + second;
+	Persistence_landscape difference = p - second;
+	Persistence_landscape multiply_by_scalar = 10*p;
+	
+	//sum.print_to_file("sum");
+	//difference.print_to_file("difference");
+	//multiply_by_scalar.print_to_file("multiply_by_scalar");
+	
+	Persistence_landscape template_sum;
+	template_sum.load_landscape_from_file( "sum" );
+	Persistence_landscape template_difference;
+	template_difference.load_landscape_from_file( "difference" );
+	Persistence_landscape template_multiply_by_scalar;
+	template_multiply_by_scalar.load_landscape_from_file( "multiply_by_scalar" );
+	
+	if ( sum != template_sum )
+	{
+		cerr << "Problem with sums \n";
+	}
+	if ( difference != template_difference )
+	{
+		cerr << "Problem with differences \n";
+	}
+	if ( multiply_by_scalar != template_multiply_by_scalar )
+	{
+		cerr << "Problem with multiplication by scalar \n";
+	}
+	
+	
+	
+	cout << "Maximum : " << p.compute_maximum() << endl;
+	
+	cout << "L^1 norm : " << p.compute_norm_of_landscape(1) << endl;
+	cout << "L^2 norm : " << p.compute_norm_of_landscape(2) << endl;
+	cout << "L^3 norm : " << p.compute_norm_of_landscape(3) << endl;	
+	
+	
+	cout << "L^1 distance : " << compute_discance_of_landscapes(p,sum,1) << endl;
+	cout << "L^2 distance : " << compute_discance_of_landscapes(p,sum,2) << endl;
+	cout << "L^infty distance : " << compute_discance_of_landscapes(p,sum,-1) << endl;
+	
+	{
+		Persistence_landscape p( "../test/data/file_with_diagram" );
+		Persistence_landscape q( "../test/data/file_with_diagram_1" );
+		std::vector< Abs_Topological_data_with_averages* > to_average;
+		to_average.push_back( &p );
+		to_average.push_back( &q );
+		Persistence_landscape av;
+		av.compute_average( to_average );
+	
+		Persistence_landscape template_average;
+		template_average.load_landscape_from_file( "average" );
+		if ( template_average != av )
+		{
+			cerr << "We have a problem with average \n";
+		}
+	}
+	
+	
+	{
+		Persistence_landscape p( "../test/data/file_with_diagram" );
+		Persistence_landscape q( "../test/data/file_with_diagram_1" );
+		cout << "L^1 distance : " <<  p.distance( &q ) << endl;
+		cout << "L^2 distance : " <<  p.distance( &q , 2) << endl;
+		cout << "L^infty distance : " <<  p.distance( &q , -1 ) << endl;
+	}
+	
+	
+	{
+		Persistence_landscape p( "../test/data/file_with_diagram" );
+		Persistence_landscape q( "../test/data/file_with_diagram_1" );
+		cout << "Scalar product : " <<  p.compute_scalar_product( &q ) << endl;		
+	}
+
+	
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/persistence_landscape_on_grid.cpp b/src/Gudhi_stat/example/persistence_landscape_on_grid.cpp
new file mode 100644
index 00000000..2807d76f
--- /dev/null
+++ b/src/Gudhi_stat/example/persistence_landscape_on_grid.cpp
@@ -0,0 +1,147 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape_on_grid.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+
+
+int main( int argc , char** argv )
+{
+	/*
+	Persistence_landscape_on_grid l( "file_with_diagram_1" , 100 );
+	l.print_to_file( "landscape_from_file_with_diagram_1" );
+	
+	Persistence_landscape_on_grid g;
+	g.load_landscape_from_file( "landscape_from_file_with_diagram_1" );
+	
+	cerr << ( l == g );
+	*/
+	
+	/*
+	Persistence_landscape_on_grid l( "file_with_diagram_1" , 100 );
+	cerr << l << endl;
+	cerr << l.compute_integral_of_landscape() << endl;
+	*/
+	 
+	 /*
+	 Persistence_landscape_on_grid p( "file_with_diagram_1" , 100 );	
+	 for ( size_t level = 0 ; level != 30 ; ++level )
+	 {
+		 double integral = p.compute_integral_of_landscape( level );
+		 cerr << integral << endl;
+	 }
+	 */
+	 
+	 /*
+	 Persistence_landscape_on_grid p( "file_with_diagram_1" , 100 );	
+	 for ( size_t power = 0 ; power != 5 ; ++power )
+	 {
+		 double integral = p.compute_integral_of_landscape( (double)power );
+		 cerr << integral << endl;
+	 }
+	 */
+	 
+	 /*
+	 Persistence_landscape_on_grid p( "file_with_diagram_1" , 100 );	
+	 double x = 0.0012321;
+	 double dx = 0.05212;
+	 for ( size_t i = 0 ; i != 10 ; ++i )
+	 {  		
+		cerr << p.compute_value_at_a_given_point(10,x) << endl;
+		x += dx;
+	 }
+	 */
+	 
+	 /*	
+	Persistence_landscape_on_grid p( "file_with_diagram_1",100 );	
+	Persistence_landscape_on_grid second("file_with_diagram_1",100 );		
+	Persistence_landscape_on_grid sum = p + second;
+	Persistence_landscape_on_grid difference = p - second;
+	Persistence_landscape_on_grid multiply_by_scalar = 10*p;
+	sum.print_to_file( "sum_on_grid_test" );
+	difference.print_to_file( "difference_on_grid_test" );
+	multiply_by_scalar.print_to_file( "multiply_by_scalar_on_grid_test" );
+	*/
+	
+	
+	/*	
+	Persistence_landscape_on_grid p( "file_with_diagram_1" , 0 , 1 , 100 );
+	Persistence_landscape_on_grid second("file_with_diagram_1", 0 , 1 , 100 );	
+	Persistence_landscape_on_grid sum = p + second;
+	
+	cerr << "max : " << p.compute_maximum() << endl;
+	cerr << "1-norm : " << p.compute_norm_of_landscape(1) << endl;
+	cerr << "2-norm : " << p.compute_norm_of_landscape(2) << endl;
+	cerr << "3-norm : " << p.compute_norm_of_landscape(3) << endl;
+	
+	cerr <<  compute_discance_of_landscapes_on_grid(p,sum,1) << endl;
+	cerr <<  compute_discance_of_landscapes_on_grid(p,sum,2) << endl;
+	cerr <<  compute_discance_of_landscapes_on_grid(p,sum,-1)  << endl;
+	*/
+	
+	/*
+	Persistence_landscape_on_grid p( "file_with_diagram", 0,1,100 );
+	Persistence_landscape_on_grid q( "file_with_diagram_1", 0,1,100 );	
+	std::vector< Abs_Topological_data_with_averages* > to_average;
+	to_average.push_back( &p );
+	to_average.push_back( &q );
+	Persistence_landscape_on_grid av;	
+	av.compute_average( to_average );
+	av.print_to_file("average_on_a_grid");
+
+	Persistence_landscape_on_grid template_average;
+	template_average.load_landscape_from_file( "average_on_a_grid" );
+	if ( template_average == av )
+	{
+		cerr << "OK OK \n";
+	}*/
+	
+	/*
+	Persistence_landscape_on_grid p( "file_with_diagram" , 0,1,10000);
+	Persistence_landscape_on_grid q( "file_with_diagram_1" , 0,1,10000);
+	cerr <<  p.distance( &q )<< endl;
+	cerr <<  p.distance( &q , 2 ) << endl;
+	cerr <<  p.distance( &q , -1 ) << endl;
+	*/
+	
+
+	Persistence_landscape_on_grid p( "file_with_diagram", 0,1,10000 );
+	Persistence_landscape_on_grid q( "file_with_diagram_1", 0,1,10000 );
+	
+	//std::vector< std::pair< double,double > > aa;
+	//aa.push_back( std::make_pair( 0,1 ) );
+	//Persistence_landscape_on_grid p( aa, 0,1,10 );
+	//Persistence_landscape_on_grid q( aa, 0,1,10 );
+	cerr <<  p.compute_scalar_product( &q ) << endl;
+
+		
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_heat_maps/average_persistence_heat_maps.cpp b/src/Gudhi_stat/example/utilities/persistence_heat_maps/average_persistence_heat_maps.cpp
new file mode 100644
index 00000000..d90e78e1
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_heat_maps/average_persistence_heat_maps.cpp
@@ -0,0 +1,73 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_heat_maps.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program computes average persistence landscape of persistence landscapes created based on persistence diagrams provided as an input. Please call this program with the names of files with persistence diagrams \n";
+	std::vector< const char* > filenames;
+	
+	if ( argc == 1 )
+	{
+		std::cout << "No input files given, the program will now terminate \n";
+		return 1;
+	}
+	
+	for ( int i = 1 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	
+	std::cout << "Creating persistence landscapes...\n";
+	std::vector< Abs_Topological_data_with_averages* > maps;
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		Persistence_heat_maps* l = new Persistence_heat_maps;
+		l->load_from_file( filenames[i] );
+		maps.push_back( (Abs_Topological_data_with_averages*)l );
+	}
+	
+	Persistence_heat_maps av;
+	av.compute_average( maps );
+	
+	av.print_to_file( "average.mps" );
+	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		delete maps[i];
+	}
+	
+	std::cout << "Done \n";
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_heat_maps/compute_distance_of_persistence_heat_maps.cpp b/src/Gudhi_stat/example/utilities/persistence_heat_maps/compute_distance_of_persistence_heat_maps.cpp
new file mode 100644
index 00000000..10d6f04c
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_heat_maps/compute_distance_of_persistence_heat_maps.cpp
@@ -0,0 +1,107 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_heat_maps.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program compute dsitance of persistence landscapes stored in a file (the file needs to be created beforehand). \n";	
+	std::cout << "The first parameter of a program is an interger p. The program compute L^p distance of the two landscapes. For L^infty distance choose p = -1. \n";
+	std::cout << "The remaining parameters of this programs are names of files with persistence landscapes.\n";
+	
+	if ( argc < 3 )
+	{
+		std::cout << "Wrong number of parameters, the program will now terminate \n";
+		return 1;
+	}
+	
+	int p = atoi( argv[1] );
+
+	std::vector< const char* > filenames;
+	for ( int i = 2 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	std::vector< Abs_Topological_data_with_distances* > maps;
+	maps.reserve( filenames.size() );
+	for ( size_t file_no = 0 ; file_no != filenames.size() ; ++file_no )
+	{
+		Persistence_heat_maps* l = new Persistence_heat_maps;
+		l->load_from_file( filenames[file_no] );
+		maps.push_back( (Abs_Topological_data_with_distances*)l );
+	}
+		
+	//and now we will compute the scalar product of landscapes.
+	
+	//first we prepare an array:
+	std::vector< std::vector< double > > distance( filenames.size() );
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		std::vector< double > v( filenames.size() , 0 );
+		distance[i] = v;
+	}
+	
+	//and now we can compute the distnaces:
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		for ( size_t j = i ; j != filenames.size() ; ++j )
+		{
+			distance[i][j] = distance[j][i] = ((Persistence_heat_maps*)maps[i])->distance( maps[j] , p ) ;
+		}
+	}
+	
+	//and now output the result to the screen and a file:
+	ofstream out;
+	out.open( "distance" );
+	for ( size_t i = 0 ; i != distance.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != distance.size() ; ++j )
+		{
+			cout << distance[i][j] << " ";
+			out << distance[i][j] << " ";
+		}
+		cout << endl;
+		out << endl;
+	}
+	out.close();
+		
+	return 0;
+}
+
+
+
+
+
+
+	
diff --git a/src/Gudhi_stat/example/utilities/persistence_heat_maps/compute_scalar_product_of_persistence_heat_maps.cpp b/src/Gudhi_stat/example/utilities/persistence_heat_maps/compute_scalar_product_of_persistence_heat_maps.cpp
new file mode 100644
index 00000000..cd529f10
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_heat_maps/compute_scalar_product_of_persistence_heat_maps.cpp
@@ -0,0 +1,91 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_heat_maps.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program compute scalar product of persistence landscapes stored in a file (the file needs to be created beforehand). \n";	
+	std::cout << "The parameters of this programs are names of files with persistence landscapes.\n";
+
+	std::vector< const char* > filenames;
+	for ( int i = 1 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	std::vector< Persistence_heat_maps* > maps;
+	maps.reserve( filenames.size() );
+	for ( size_t file_no = 0 ; file_no != filenames.size() ; ++file_no )
+	{
+		Persistence_heat_maps* l = new Persistence_heat_maps;
+		l->load_from_file( filenames[file_no] );
+		maps.push_back( l );
+	}
+		
+	//and now we will compute the scalar product of landscapes.
+	
+	//first we prepare an array:
+	std::vector< std::vector< double > > scalar_product( filenames.size() );
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		std::vector< double > v( filenames.size() , 0 );
+		scalar_product[i] = v;
+	}
+	
+	//and now we can compute the scalar product:
+	for ( size_t i = 0 ; i != maps.size() ; ++i )
+	{
+		for ( size_t j = i ; j != maps.size() ; ++j )
+		{
+			scalar_product[i][j] = scalar_product[j][i] = ((Persistence_heat_maps*)maps[i])->compute_scalar_product( maps[j] ) ;
+		}
+	}
+	
+	//and now output the result to the screen and a file:
+	ofstream out;
+	out.open( "scalar_product" );
+	for ( size_t i = 0 ; i != scalar_product.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != scalar_product.size() ; ++j )
+		{
+			cout << scalar_product[i][j] << " ";
+			out << scalar_product[i][j] << " ";
+		}
+		cout << endl;
+		out << endl;
+	}
+	out.close();
+		
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps.cpp b/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps.cpp
new file mode 100644
index 00000000..3d8dc2e8
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps.cpp
@@ -0,0 +1,79 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_heat_maps.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program creates persistence heat map of diagrams provided as an input.\n";
+	std::cout << "The first parameter of a program is an integer, a size of a grid.\n";
+	std::cout << "The second and third parameters are min and max of the grid. If you want those numbers to be computed based on the data, set them both to -1 \n";
+	std::cerr << "The fourth parameter is an integer, the standard deviation of a gaussian kernel expressed in a number of pixels \n";
+	std::cout << "The remaining parameters are the names of files with persistence diagrams. \n";
+	
+	if ( argc < 5 )
+	{
+		std::cout << "Wrong parameter list, the program will now terminate \n";
+		return 1;
+	}
+	
+	size_t size_of_grid = (size_t)atoi( argv[1] );
+	double min_ = atof( argv[2] );
+	double max_ = atof( argv[3] );
+	size_t stdiv = atof( argv[4] );
+	
+	std::vector< const char* > filenames;
+	for ( int i = 5 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+
+	
+	
+	std::cout << "Creating persistence heat maps...\n";	
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(stdiv,1);
+	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{		
+		std::cout << "Creating a heat map based on a file : " << filenames[i] << std::endl;
+		Persistence_heat_maps l( filenames[i] , filter, constant_function, false , size_of_grid , min_ , max_ );		
+		
+		std::stringstream ss;
+		ss << filenames[i] << ".mps";
+		l.print_to_file( ss.str().c_str() );
+	}
+	std::cout << "Done \n";
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_arctan_of_their_persistence.cpp b/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_arctan_of_their_persistence.cpp
new file mode 100644
index 00000000..253320ff
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_arctan_of_their_persistence.cpp
@@ -0,0 +1,79 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_heat_maps.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program creates persistence heat map of diagrams provided as an input. The Gaussian kernels are weighted by the arcus tangens of their persistence.\n";
+	std::cout << "The first parameter of a program is an integer, a size of a grid.\n";
+	std::cout << "The second and third parameters are min and max of the grid. If you want those numbers to be computed based on the data, set them both to -1 \n";
+	std::cerr << "The fourth parameter is an integer, the standard deviation of a gaussian kernel expressed in a number of pixels \n";
+	std::cout << "The remaining parameters are the names of files with persistence diagrams. \n";
+	
+	if ( argc < 5 )
+	{
+		std::cout << "Wrong parameter list, the program will now terminate \n";
+		return 1;
+	}
+	
+	size_t size_of_grid = (size_t)atoi( argv[1] );
+	double min_ = atof( argv[2] );
+	double max_ = atof( argv[3] );
+	size_t stdiv = atof( argv[4] );
+	
+	std::vector< const char* > filenames;
+	for ( int i = 5 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+
+	
+	
+	std::cout << "Creating persistence heat maps...\n";	
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(stdiv,1);
+	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{		
+		std::cout << "Creating a heat map based on a file : " << filenames[i] << std::endl;
+		Persistence_heat_maps l( filenames[i] , filter, arc_tan_of_persistence_of_point, false , size_of_grid , min_ , max_ );		
+		
+		std::stringstream ss;
+		ss << filenames[i] << ".mps";
+		l.print_to_file( ss.str().c_str() );
+	}
+	std::cout << "Done \n";
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_distance_from_diagonal.cpp b/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_distance_from_diagonal.cpp
new file mode 100644
index 00000000..d7f4fbdd
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_distance_from_diagonal.cpp
@@ -0,0 +1,79 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_heat_maps.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program creates persistence heat map of diagrams provided as an input. The Gaussian kernels are weighted by the distance of a center from the diagonal.\n";
+	std::cout << "The first parameter of a program is an integer, a size of a grid.\n";
+	std::cout << "The second and third parameters are min and max of the grid. If you want those numbers to be computed based on the data, set them both to -1 \n";
+	std::cerr << "The fourth parameter is an integer, the standard deviation of a gaussian kernel expressed in a number of pixels \n";
+	std::cout << "The remaining parameters are the names of files with persistence diagrams. \n";
+	
+	if ( argc < 5 )
+	{
+		std::cout << "Wrong parameter list, the program will now terminate \n";
+		return 1;
+	}
+	
+	size_t size_of_grid = (size_t)atoi( argv[1] );
+	double min_ = atof( argv[2] );
+	double max_ = atof( argv[3] );
+	size_t stdiv = atof( argv[4] );
+	
+	std::vector< const char* > filenames;
+	for ( int i = 5 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+
+	
+	
+	std::cout << "Creating persistence heat maps...\n";	
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(stdiv,1);
+	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{		
+		std::cout << "Creating a heat map based on a file : " << filenames[i] << std::endl;
+		Persistence_heat_maps l( filenames[i] , filter, distance_from_diagonal, false , size_of_grid , min_ , max_ );		
+		
+		std::stringstream ss;
+		ss << filenames[i] << ".mps";
+		l.print_to_file( ss.str().c_str() );
+	}
+	std::cout << "Done \n";
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_squared_distance_from_diagonal.cpp b/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_squared_distance_from_diagonal.cpp
new file mode 100644
index 00000000..eac0d067
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_persistence_heat_maps_weighted_by_squared_distance_from_diagonal.cpp
@@ -0,0 +1,79 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_heat_maps.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program creates persistence heat map of diagrams provided as an input. The Gaussian kernels are weighted by the square of distance of a center from the diagonal.\n";
+	std::cout << "The first parameter of a program is an integer, a size of a grid.\n";
+	std::cout << "The second and third parameters are min and max of the grid. If you want those numbers to be computed based on the data, set them both to -1 \n";
+	std::cerr << "The fourth parameter is an integer, the standard deviation of a gaussian kernel expressed in a number of pixels \n";
+	std::cout << "The remaining parameters are the names of files with persistence diagrams. \n";
+	
+	if ( argc < 5 )
+	{
+		std::cout << "Wrong parameter list, the program will now terminate \n";
+		return 1;
+	}
+	
+	size_t size_of_grid = (size_t)atoi( argv[1] );
+	double min_ = atof( argv[2] );
+	double max_ = atof( argv[3] );
+	size_t stdiv = atof( argv[4] );
+	
+	std::vector< const char* > filenames;
+	for ( int i = 5 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+
+	
+	
+	std::cout << "Creating persistence heat maps...\n";	
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(stdiv,1);
+	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{		
+		std::cout << "Creating a heat map based on a file : " << filenames[i] << std::endl;
+		Persistence_heat_maps l( filenames[i] , filter, squared_distance_from_diagonal, false , size_of_grid , min_ , max_ );		
+		
+		std::stringstream ss;
+		ss << filenames[i] << ".mps";
+		l.print_to_file( ss.str().c_str() );
+	}
+	std::cout << "Done \n";
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_pssk.cpp b/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_pssk.cpp
new file mode 100644
index 00000000..ccd884ec
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_heat_maps/create_pssk.cpp
@@ -0,0 +1,77 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/PSSK.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program creates PSSK of diagrams provided as an input.\n";
+	std::cout << "The first parameter of a program is an integer, a size of a grid.\n";
+	std::cout << "The second and third parameters are min and max of the grid. If you want those numbers to be computed based on the data, set them both to -1 \n";
+	std::cerr << "The fourth parameter is an integer, the standard deviation of a gaussian kernel expressed in a number of pixels \n";
+	std::cout << "The remaining parameters are the names of files with persistence diagrams. \n";
+	
+	if ( argc < 5 )
+	{
+		std::cout << "Wrong parameter list, the program will now terminate \n";
+		return 1;
+	}
+	
+	size_t size_of_grid = (size_t)atoi( argv[1] );
+	double min_ = atof( argv[2] );
+	double max_ = atof( argv[3] );
+	size_t stdiv = atof( argv[4] );
+	
+	std::vector< const char* > filenames;
+	for ( int i = 5 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}	
+	
+	std::cout << "Creating persistence heat maps...\n";	
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(stdiv,1);	
+	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{		
+		std::cout << "Creating a heat map based on a file : " << filenames[i] << std::endl;
+		PSSK l( filenames[i] , filter , size_of_grid , min_ , max_ );		
+		
+		std::stringstream ss;
+		ss << filenames[i] << ".pssk";
+		l.print_to_file( ss.str().c_str() );
+	}
+	std::cout << "Done \n";
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_heat_maps/plot_persistence_heat_map.cpp b/src/Gudhi_stat/example/utilities/persistence_heat_maps/plot_persistence_heat_map.cpp
new file mode 100644
index 00000000..b85a502b
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_heat_maps/plot_persistence_heat_map.cpp
@@ -0,0 +1,44 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_heat_maps.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program plot persistence landscape stored in a file (the file needs to be created beforehand). Please call the code with the name of a landsape file \n";	
+	Persistence_heat_maps l;
+	l.load_from_file( argv[1] );		
+	l.plot( argv[1] );	
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_intervals/aaa b/src/Gudhi_stat/example/utilities/persistence_intervals/aaa
new file mode 100644
index 00000000..5aed2ec0
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_intervals/aaa
@@ -0,0 +1,51 @@
+0.254583	0.837489
+0.25491	0.410985
+0.262238	0.405964
+0.233498	0.338685
+0.253282	0.344571
+0.249923	0.339748
+0.179532	0.263873
+0.247402	0.323782
+0.181315	0.249492
+0.160746	0.22547
+0.170367	0.232149
+0.192048	0.253065
+0.27298	0.333994
+0.202383	0.260308
+0.278325	0.329157
+0.176624	0.226215
+0.200184	0.249281
+0.275607	0.323516
+0.178408	0.224032
+0.319435	0.362706
+0.184347	0.226301
+0.19342	0.23356
+0.143554	0.180648
+0.313975	0.34917
+0.260887	0.29465
+0.206395	0.23344
+0.272846	0.298156
+0.222294	0.246925
+0.272951	0.295696
+0.235421	0.257957
+0.277907	0.29913
+0.16591	0.186925
+0.223042	0.243167
+0.435025	0.454885
+0.151992	0.169807
+0.138011	0.155776
+0.218083	0.235837
+0.219364	0.237079
+0.297063	0.313899
+0.282666	0.298727
+0.24199	0.256381
+0.302722	0.316677
+0.160453	0.174076
+0.157689	0.169984
+0.192957	0.204705
+0.153738	0.165306
+0.226448	0.237898
+0.243627	0.252613
+0.210126	0.21907
+0.172082	0.177708
+0.232291	0.234521
diff --git a/src/Gudhi_stat/example/utilities/persistence_intervals/aaa_Gnuplot_script b/src/Gudhi_stat/example/utilities/persistence_intervals/aaa_Gnuplot_script
new file mode 100644
index 00000000..3ff83e9c
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_intervals/aaa_Gnuplot_script
@@ -0,0 +1,208 @@
+set xrange [0.131016 : 0.844554]
+set yrange [0 : 16.16]
+plot '-' using 1:2 notitle with lp 
+0.138011 0
+0.138011 1
+0.143554 1
+0.143554 2
+0.151992 2
+0.151992 3
+0.153738 3
+0.153738 4
+0.155776 4
+0.155776 3
+0.157689 3
+0.157689 4
+0.160453 4
+0.160453 5
+0.160746 5
+0.160746 6
+0.165306 6
+0.165306 5
+0.16591 5
+0.16591 6
+0.169807 6
+0.169807 5
+0.169984 5
+0.169984 4
+0.170367 4
+0.170367 5
+0.172082 5
+0.172082 6
+0.174076 6
+0.174076 5
+0.176624 5
+0.176624 6
+0.177708 6
+0.177708 5
+0.178408 5
+0.178408 6
+0.179532 6
+0.179532 7
+0.180648 7
+0.180648 6
+0.181315 6
+0.181315 7
+0.184347 7
+0.184347 8
+0.186925 8
+0.186925 7
+0.192048 7
+0.192048 8
+0.192957 8
+0.192957 9
+0.19342 9
+0.19342 10
+0.200184 10
+0.200184 11
+0.202383 11
+0.202383 12
+0.204705 12
+0.204705 11
+0.206395 11
+0.206395 12
+0.210126 12
+0.210126 13
+0.218083 13
+0.218083 14
+0.21907 14
+0.21907 13
+0.219364 13
+0.219364 14
+0.222294 14
+0.222294 15
+0.223042 15
+0.223042 16
+0.224032 16
+0.224032 15
+0.22547 15
+0.22547 14
+0.226215 14
+0.226215 13
+0.226301 13
+0.226301 12
+0.226448 12
+0.226448 13
+0.232149 13
+0.232149 12
+0.232291 12
+0.232291 13
+0.23344 13
+0.23344 12
+0.233498 12
+0.233498 13
+0.23356 13
+0.23356 12
+0.234521 12
+0.234521 11
+0.235421 11
+0.235421 12
+0.235837 12
+0.235837 11
+0.237079 11
+0.237079 10
+0.237898 10
+0.237898 9
+0.24199 9
+0.24199 10
+0.243167 10
+0.243167 9
+0.243627 9
+0.243627 10
+0.246925 10
+0.246925 9
+0.247402 9
+0.247402 10
+0.249281 10
+0.249281 9
+0.249492 9
+0.249492 8
+0.249923 8
+0.249923 9
+0.252613 9
+0.252613 8
+0.253065 8
+0.253065 7
+0.253282 7
+0.253282 8
+0.254583 8
+0.254583 9
+0.25491 9
+0.25491 10
+0.256381 10
+0.256381 9
+0.257957 9
+0.257957 8
+0.260308 8
+0.260308 7
+0.260887 7
+0.260887 8
+0.262238 8
+0.262238 9
+0.263873 9
+0.263873 8
+0.272846 8
+0.272846 9
+0.272951 9
+0.272951 10
+0.27298 10
+0.27298 11
+0.275607 11
+0.275607 12
+0.277907 12
+0.277907 13
+0.278325 13
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+0.282666 14
+0.282666 15
+0.29465 15
+0.29465 14
+0.295696 14
+0.295696 13
+0.297063 13
+0.297063 14
+0.298156 14
+0.298156 13
+0.298727 13
+0.298727 12
+0.29913 12
+0.29913 11
+0.302722 11
+0.302722 12
+0.313899 12
+0.313899 11
+0.313975 11
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+0.316677 12
+0.316677 11
+0.319435 11
+0.319435 12
+0.323516 12
+0.323516 11
+0.323782 11
+0.323782 10
+0.329157 10
+0.329157 9
+0.333994 9
+0.333994 8
+0.338685 8
+0.338685 7
+0.339748 7
+0.339748 6
+0.344571 6
+0.344571 5
+0.34917 5
+0.34917 4
+0.362706 4
+0.362706 3
+0.405964 3
+0.405964 2
+0.410985 2
+0.410985 1
+0.435025 1
+0.435025 2
+0.454885 2
+0.454885 1
+0.837489 1
+0.837489 0
+
diff --git a/src/Gudhi_stat/example/utilities/persistence_intervals/compute_birth_death_range_in_persistence_diagram.cpp b/src/Gudhi_stat/example/utilities/persistence_intervals/compute_birth_death_range_in_persistence_diagram.cpp
new file mode 100644
index 00000000..dba0984a
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_intervals/compute_birth_death_range_in_persistence_diagram.cpp
@@ -0,0 +1,72 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/reader_utils.h>
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_intervals.h>
+
+#include <iostream>
+#include <vector>
+#include <limits>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+using namespace std;
+
+
+int main( int argc , char** argv )
+{
+	//std::cout << "This program compute minimum birth and the maximum death time for a collection of persistence intervals \n";
+	//if ( argc != 2 )
+	//{
+	//	cout << "To run this program, please provide the name of a file with persistence diagram \n";
+	//	return 1;
+	//}
+	//Persistence_intervals p( argv[1] );
+	//std::pair<double,double> min_max_ = p.min_max();
+	//cout << "Birth-death range : min: " <<  min_max_.first << ", max: " << min_max_.second << endl;
+	
+	std::vector< const char* > filenames;
+	for ( int i = 1 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	
+	double min_ = std::numeric_limits<double>::max();
+	double max_ = -std::numeric_limits<double>::max();
+	
+	for ( size_t file_no = 0 ; file_no != filenames.size() ; ++file_no )
+	{
+		std::cout << "Creating diagram based on a file : " << filenames[file_no] << std::endl;
+		Persistence_intervals p( filenames[file_no] );
+		std::pair<double,double> min_max_ = p.min_max();
+		if ( min_max_.first < min_ )min_ = min_max_.first;
+		if ( min_max_.second > max_ )max_ = min_max_.second;
+	}
+	cout << "Birth-death range : min: " <<  min_ << ", max: " << max_ << endl;
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_intervals/compute_number_of_dominant_intervals.cpp b/src/Gudhi_stat/example/utilities/persistence_intervals/compute_number_of_dominant_intervals.cpp
new file mode 100644
index 00000000..6e6a9c88
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_intervals/compute_number_of_dominant_intervals.cpp
@@ -0,0 +1,57 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/reader_utils.h>
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_intervals.h>
+
+#include <iostream>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+using namespace std;
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program compute the dominant intervals. A number of intervals to be displayed is a parameter of this program. \n";
+	if ( argc != 3 )
+	{
+		cout << "To run this program, please provide the name of a file with persistence diagram and number of dominant intervals you would like to get \n";
+		return 1;
+	}
+
+	Persistence_intervals p( argv[1] );
+	std::vector< std::pair<double,double> > dominant_intervals = p.dominant_intervals( atoi( argv[2] ) );
+	cout << "Here are the dominant intervals : " << endl;
+	for ( size_t i = 0 ; i != dominant_intervals.size() ; ++i )
+	{
+		cout << " " << dominant_intervals[i].first<< "," << dominant_intervals[i].second  << " "<< endl;
+	}
+	
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_intervals/plot_histogram_of_intervals_lengths.cpp b/src/Gudhi_stat/example/utilities/persistence_intervals/plot_histogram_of_intervals_lengths.cpp
new file mode 100644
index 00000000..dd2f3f99
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_intervals/plot_histogram_of_intervals_lengths.cpp
@@ -0,0 +1,69 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/reader_utils.h>
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_intervals.h>
+
+#include <iostream>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+using namespace std;
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program compute a histogram of barcode's length. A number of bins in the histogram is a parameter of this program. \n";
+	if ( argc != 3 )
+	{
+		cout << "To run this program, please provide the name of a file with persistence diagram and number of dominant intervals you would like to get \n";
+		return 1;
+	}
+
+	Persistence_intervals p( argv[1] );
+	std::vector< std::pair<double,double> > dominant_intervals = p.dominant_intervals( atoi( argv[2] ) );
+	std::vector< size_t > histogram = p.histograms_of_lengths( 10  );
+	
+	std::stringstream gnuplot_script;
+	gnuplot_script << argv[1] << "_Gnuplot_script";
+	ofstream out;
+	out.open( gnuplot_script.str().c_str() );
+	
+	out << "set style data histogram" << std::endl;
+	out << "set style histogram cluster gap 1" << std::endl;
+	out << "set style fill solid border -1" << std::endl;
+	out << "plot '-' notitle" << std::endl;    
+	for ( size_t i = 0 ; i != histogram.size() ; ++i )
+	{
+		out << histogram[i]  << std::endl;
+	}		
+	out << endl;
+	std::cout << "To vizualize, open gnuplot and type: load \'" << gnuplot_script.str().c_str() << "\'" <<  std::endl;	
+	out.close();	
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_intervals/plot_persistence_Betti_numebrs.cpp b/src/Gudhi_stat/example/utilities/persistence_intervals/plot_persistence_Betti_numebrs.cpp
new file mode 100644
index 00000000..33ff7bce
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_intervals/plot_persistence_Betti_numebrs.cpp
@@ -0,0 +1,93 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/reader_utils.h>
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_intervals.h>
+
+#include <iostream>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+using namespace std;
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program compute a plot of persistence Betti numbers. The input parameter is a file with persistence intervals. \n";
+	if ( argc != 2 )
+	{
+		cout << "To run this program, please provide the name of a file with persistence diagram and number of dominant intervals you would like to get \n";
+		return 1;
+	}
+	
+	
+	
+	std::stringstream gnuplot_script;
+	gnuplot_script << argv[1] << "_Gnuplot_script";
+	ofstream out;
+	out.open( gnuplot_script.str().c_str() );
+	
+	Persistence_intervals p( argv[1] );
+	std::vector< std::pair< double , size_t > > pbns = p.compute_persistent_betti_numbers();	
+	
+	//set up the ranges so that we see the image well.
+	double xRangeBegin = pbns[0].first;
+	double xRangeEnd = pbns[ pbns.size()-1 ].first;
+	double yRangeBegin = 0;
+	double yRangeEnd = 0;
+	for ( size_t i = 0 ; i != pbns.size() ; ++i )
+	{
+		if ( pbns[i].second > yRangeEnd )yRangeEnd = pbns[i].second;
+	}
+	xRangeBegin -= (xRangeEnd -xRangeBegin)/100.0;
+	xRangeEnd += (xRangeEnd -xRangeBegin)/100.0;
+	yRangeEnd += yRangeEnd/100;
+	
+	
+	out << "set xrange [" << xRangeBegin << " : " << xRangeEnd << "]" << endl;
+    out << "set yrange [" << yRangeBegin << " : " << yRangeEnd << "]" << endl;	
+	out << "plot '-' using 1:2 notitle with lp " << std::endl;    
+	double previous_y = 0;
+	for ( size_t i = 0 ; i != pbns.size() ; ++i )
+	{
+		out << pbns[i].first << " " << previous_y << endl;
+		out << pbns[i].first << " " << pbns[i].second << std::endl;
+		previous_y = pbns[i].second;
+	}		
+	out << endl;
+	out.close();
+	
+	//for ( size_t i = 0 ; i != pbns.size() ; ++i )
+	//{
+	//	cout << pbns[i].first << " " << pbns[i].second << std::endl;
+	//}	
+	
+	std::cout << "To vizualize, open gnuplot and type: load \'" << gnuplot_script.str().c_str() << "\'" << std::endl;
+			
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_intervals/plot_persistence_intervals.cpp b/src/Gudhi_stat/example/utilities/persistence_intervals/plot_persistence_intervals.cpp
new file mode 100644
index 00000000..c4dd7284
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_intervals/plot_persistence_intervals.cpp
@@ -0,0 +1,59 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/reader_utils.h>
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_intervals.h>
+
+#include <iostream>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+
+double epsilon = 0.0000005;
+
+using namespace std;
+
+	
+int main( int argc , char** argv )
+{
+	if ( argc != 2 )
+	{
+		cout << "To run this program, please provide the name of a file with persistence diagram \n";
+		return 1;
+	}
+	Persistence_intervals b( argv[1] );
+	b.plot( argv[1] );
+	return 0;
+}
+
+
+
+
+
+
+
diff --git a/src/Gudhi_stat/example/utilities/persistence_landscapes/average_landscapes.cpp b/src/Gudhi_stat/example/utilities/persistence_landscapes/average_landscapes.cpp
new file mode 100644
index 00000000..418244d2
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_landscapes/average_landscapes.cpp
@@ -0,0 +1,75 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program computes average persistence landscape of persistence landscapes created based on persistence diagrams provided as an input (you must create them first).\n"; 
+	std::cout << "Please call this program with the names of files with persistence landscapes. The program will create a persistence landscape which will be their average \n";
+	std::vector< const char* > filenames;
+	
+	if ( argc == 1 )
+	{
+		std::cout << "No input files given, the program will now terminate \n";
+		return 1;
+	}
+	
+	for ( int i = 1 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	
+	std::cout << "Creating persistence landscapes...\n";
+	std::vector< Abs_Topological_data_with_averages* > lands;
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		Persistence_landscape* l = new Persistence_landscape;
+		l->load_landscape_from_file( filenames[i] );
+		lands.push_back( (Abs_Topological_data_with_averages*)l );
+	}
+	
+	Persistence_landscape av;
+	av.compute_average( lands );
+	
+	av.print_to_file( "average.land" );
+	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		delete lands[i];
+	}
+	
+	std::cout << "Done \n";
+
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_landscapes/compute_distance_of_landscapes.cpp b/src/Gudhi_stat/example/utilities/persistence_landscapes/compute_distance_of_landscapes.cpp
new file mode 100644
index 00000000..12a4b3bd
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_landscapes/compute_distance_of_landscapes.cpp
@@ -0,0 +1,109 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program compute distance of persistence landscapes stored in a file (the file needs to be created beforehand). \n";	
+	std::cout << "The first parameter of a program is an interger p. The program compute L^p distance of the given landscapes. For L^infty distance choose p = -1. \n";
+	std::cout << "The remaining parameters of this programs are names of files with persistence landscapes.";
+	
+	if ( argc < 3 )
+	{
+		std::cout << "Wrong number of parameters, the program will now terminate \n";
+		return 1;
+	}
+	
+	int p = atoi( argv[1] );
+
+	std::vector< const char* > filenames;
+	for ( int i = 2 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	std::vector< Persistence_landscape > landscaspes;
+	landscaspes.reserve( filenames.size() );
+	for ( size_t file_no = 0 ; file_no != filenames.size() ; ++file_no )
+	{
+		std::cout << "Loading persistence landscape from a file : " << filenames[file_no] << std::endl;
+		Persistence_landscape l;
+		l.load_landscape_from_file( filenames[file_no] );
+		landscaspes.push_back( l );
+	}
+		
+	//and now we will compute the scalar product of landscapes.
+	
+	//first we prepare an array:
+	std::vector< std::vector< double > > distance( filenames.size() );
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		std::vector< double > v( filenames.size() , 0 );
+		distance[i] = v;
+	}
+	
+	//and now we can compute the distances:
+	for ( size_t i = 0 ; i != landscaspes.size() ; ++i )
+	{
+		for ( size_t j = i ; j != landscaspes.size() ; ++j )
+		{			
+			distance[i][j] = distance[j][i] = compute_discance_of_landscapes( landscaspes[i], landscaspes[j] , p ) ;
+			
+		}
+	}
+	
+	//and now output the result to the screen and a file:
+	ofstream out;
+	out.open( "distance" );
+	for ( size_t i = 0 ; i != distance.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != distance.size() ; ++j )
+		{
+			cout << distance[i][j] << " ";
+			out << distance[i][j] << " ";
+		}
+		cout << endl;
+		out << endl;
+	}
+	out.close();
+		
+	return 0;
+}
+
+
+
+
+
+
+	
diff --git a/src/Gudhi_stat/example/utilities/persistence_landscapes/compute_scalar_product_of_landscapes.cpp b/src/Gudhi_stat/example/utilities/persistence_landscapes/compute_scalar_product_of_landscapes.cpp
new file mode 100644
index 00000000..ac64a798
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_landscapes/compute_scalar_product_of_landscapes.cpp
@@ -0,0 +1,92 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program compute scalar product of persistence landscapes stored in a file (the file needs to be created beforehand). \n";	
+	std::cout << "The parameters of this programs are names of files with persistence landscapes.\n";
+
+	std::vector< const char* > filenames;
+	for ( int i = 1 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	std::vector< Persistence_landscape > landscaspes;
+	landscaspes.reserve( filenames.size() );
+	for ( size_t file_no = 0 ; file_no != filenames.size() ; ++file_no )
+	{
+		std::cout << "Reading persistence landscape from a file : " << filenames[file_no] << std::endl;
+		Persistence_landscape l;
+		l.load_landscape_from_file( filenames[file_no] );
+		landscaspes.push_back( l );
+	}
+		
+	//and now we will compute the scalar product of landscapes.
+	
+	//first we prepare an array:
+	std::vector< std::vector< double > > scalar_product( filenames.size() );
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		std::vector< double > v( filenames.size() , 0 );
+		scalar_product[i] = v;
+	}
+	
+	//and now we can compute the scalar product:
+	for ( size_t i = 0 ; i != landscaspes.size() ; ++i )
+	{
+		for ( size_t j = i ; j != landscaspes.size() ; ++j )
+		{
+			scalar_product[i][j] = scalar_product[j][i] = compute_inner_product( landscaspes[i], landscaspes[j] ) ;
+		}
+	}
+	
+	//and now output the result to the screen and a file:
+	ofstream out;
+	out.open( "scalar_product" );
+	for ( size_t i = 0 ; i != scalar_product.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != scalar_product.size() ; ++j )
+		{
+			cout << scalar_product[i][j] << " ";
+			out << scalar_product[i][j] << " ";
+		}
+		cout << endl;
+		out << endl;
+	}
+	out.close();
+		
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_landscapes/create_landscapes.cpp b/src/Gudhi_stat/example/utilities/persistence_landscapes/create_landscapes.cpp
new file mode 100644
index 00000000..5152a033
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_landscapes/create_landscapes.cpp
@@ -0,0 +1,56 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program creates persistence landscapes of diagrams provided as an input. Please call this program with the names of files with persistence diagrams \n";
+	std::vector< const char* > filenames;
+	for ( int i = 1 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	
+	std::cout << "Creating persistence landscapes...\n";	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		Persistence_landscape l( filenames[i] , 1 );
+		std::stringstream ss;
+		ss << filenames[i] << ".land";
+		l.print_to_file( ss.str().c_str() );
+	}
+	std::cout << "Done \n";
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_landscapes/plot_landscapes.cpp b/src/Gudhi_stat/example/utilities/persistence_landscapes/plot_landscapes.cpp
new file mode 100644
index 00000000..559fc096
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_landscapes/plot_landscapes.cpp
@@ -0,0 +1,50 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program plot persistence landscape stored in a file (the file needs to be created beforehand). Please call the code with the name of a landsape file \n";	
+	Persistence_landscape l;
+	l.load_landscape_from_file( argv[1] );
+	
+	std::stringstream ss;
+	ss << argv[1] << "_gnuplot_script";
+	l.plot( ss.str().c_str() );
+	
+	std::cout << "Done \n";
+		
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/average_landscapes_on_grid.cpp b/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/average_landscapes_on_grid.cpp
new file mode 100644
index 00000000..7c3b8db2
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/average_landscapes_on_grid.cpp
@@ -0,0 +1,74 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape_on_grid.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program computes average persistence landscape on grid of persistence landscapes on grid created based on persistence diagrams provided as an input. Please call this program with the names of files with persistence diagrams \n";
+	std::vector< const char* > filenames;
+	
+	if ( argc == 1 )
+	{
+		std::cout << "No input files given, the program will now terminate \n";
+		return 1;
+	}
+	
+	for ( int i = 1 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	
+	std::cout << "Creating persistence landscapes...\n";
+	std::vector< Abs_Topological_data_with_averages* > lands;
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		Persistence_landscape_on_grid* l = new Persistence_landscape_on_grid;
+		l->load_landscape_from_file( filenames[i] );
+		lands.push_back( (Abs_Topological_data_with_averages*)l );
+	}
+	
+	Persistence_landscape_on_grid av;
+	av.compute_average( lands );
+	
+	av.print_to_file( "average.g_land" );
+	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		delete lands[i];
+	}
+	
+	std::cout << "Done \n";
+
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/compute_distance_of_landscapes_on_grid.cpp b/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/compute_distance_of_landscapes_on_grid.cpp
new file mode 100644
index 00000000..20cb52c9
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/compute_distance_of_landscapes_on_grid.cpp
@@ -0,0 +1,107 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape_on_grid.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program compute dsitance of persistence landscapes on grid stored in a file (the file needs to be created beforehand). \n";	
+	std::cout << "The first parameter of a program is an interger p. The program compute L^p distance of the the landscapes on grid. For L^infty distance choose p = -1. \n";
+	std::cout << "The remaining parameters of this programs are names of files with persistence landscapes on grid.\n";
+	
+	if ( argc < 3 )
+	{
+		std::cout << "Wrong number of parameters, the program will now terminate \n";
+		return 1;
+	}
+	
+	int p = atoi( argv[1] );
+
+	std::vector< const char* > filenames;
+	for ( int i = 2 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	std::vector< Persistence_landscape_on_grid > landscaspes;
+	landscaspes.reserve( filenames.size() );
+	for ( size_t file_no = 0 ; file_no != filenames.size() ; ++file_no )
+	{
+		Persistence_landscape_on_grid l;
+		l.load_landscape_from_file( filenames[file_no] );
+		landscaspes.push_back( l );
+	}
+		
+	//and now we will compute the scalar product of landscapes.
+	
+	//first we prepare an array:
+	std::vector< std::vector< double > > distance( filenames.size() );
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		std::vector< double > v( filenames.size() , 0 );
+		distance[i] = v;
+	}
+	
+	//and now we can compute the scalar product:
+	for ( size_t i = 0 ; i != landscaspes.size() ; ++i )
+	{
+		for ( size_t j = i ; j != landscaspes.size() ; ++j )
+		{
+			distance[i][j] = distance[j][i] = compute_discance_of_landscapes_on_grid( landscaspes[i], landscaspes[j] , p ) ;
+		}
+	}
+	
+	//and now output the result to the screen and a file:
+	ofstream out;
+	out.open( "distance" );
+	for ( size_t i = 0 ; i != distance.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != distance.size() ; ++j )
+		{
+			cout << distance[i][j] << " ";
+			out << distance[i][j] << " ";
+		}
+		cout << endl;
+		out << endl;
+	}
+	out.close();
+		
+	return 0;
+}
+
+
+
+
+
+
+	
diff --git a/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/compute_scalar_product_of_landscapes_on_grid.cpp b/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/compute_scalar_product_of_landscapes_on_grid.cpp
new file mode 100644
index 00000000..056710ff
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/compute_scalar_product_of_landscapes_on_grid.cpp
@@ -0,0 +1,91 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape_on_grid.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program compute scalar product of persistence landscapes on grid stored in a file (the file needs to be created beforehand). \n";	
+	std::cout << "The parameters of this programs are names of files with persistence landscapes on grid.\n";
+
+	std::vector< const char* > filenames;
+	for ( int i = 1 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	std::vector< Persistence_landscape_on_grid > landscaspes;
+	landscaspes.reserve( filenames.size() );
+	for ( size_t file_no = 0 ; file_no != filenames.size() ; ++file_no )
+	{
+		Persistence_landscape_on_grid l;
+		l.load_landscape_from_file( filenames[file_no] );
+		landscaspes.push_back( l );
+	}
+		
+	//and now we will compute the scalar product of landscapes.
+	
+	//first we prepare an array:
+	std::vector< std::vector< double > > scalar_product( filenames.size() );
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		std::vector< double > v( filenames.size() , 0 );
+		scalar_product[i] = v;
+	}
+	
+	//and now we can compute the scalar product:
+	for ( size_t i = 0 ; i != landscaspes.size() ; ++i )
+	{
+		for ( size_t j = i ; j != landscaspes.size() ; ++j )
+		{
+			scalar_product[i][j] = scalar_product[j][i] = compute_inner_product( landscaspes[i], landscaspes[j] ) ;
+		}
+	}
+	
+	//and now output the result to the screen and a file:
+	ofstream out;
+	out.open( "scalar_product" );
+	for ( size_t i = 0 ; i != scalar_product.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != scalar_product.size() ; ++j )
+		{
+			cout << scalar_product[i][j] << " ";
+			out << scalar_product[i][j] << " ";
+		}
+		cout << endl;
+		out << endl;
+	}
+	out.close();
+		
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/create_landscapes_on_grid.cpp b/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/create_landscapes_on_grid.cpp
new file mode 100644
index 00000000..2ac74eb3
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/create_landscapes_on_grid.cpp
@@ -0,0 +1,80 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape_on_grid.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program creates persistence landscape on grid of diagrams provided as an input.\n";
+	std::cout << "The first parameter of a program is an integer, a size of a grid.\n";
+	std::cout << "The second and third parameters are min and max of the grid. If you want those numbers to be computed based on the data, set them both to -1 \n";
+	std::cout << "The remaining parameters are the names of files with persistence diagrams. \n";
+	
+	if ( argc < 4 )
+	{
+		std::cout << "Wrong parameter list, the program will now terminate \n";
+		return 1;
+	}
+	
+	size_t size_of_grid = (size_t)atoi( argv[1] );
+	double min_ = atof( argv[2] );
+	double max_ = atof( argv[3] );
+	
+	std::vector< const char* > filenames;
+	for ( int i = 4 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	
+	std::cout << "Creating persistence landscapes...\n";	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		std::cout << "Creating persistence landscape on a grid based on a file : " << filenames[i] << std::endl;
+		Persistence_landscape_on_grid l;
+		if ( (min_ != -1) || (max_ != -1) )
+		{
+			l = Persistence_landscape_on_grid( filenames[i] , min_ , max_ , size_of_grid );
+		}
+		else
+		{
+			//(min_ == -1) && (max_ == -1), in this case the program will find min_ and max_ based on the data.
+			l = Persistence_landscape_on_grid( filenames[i] , size_of_grid );
+		}		
+		std::stringstream ss;
+		ss << filenames[i] << ".g_land";
+		l.print_to_file( ss.str().c_str() );
+	}
+	std::cout << "Done \n";
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/plot_landscapes_on_grid.cpp b/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/plot_landscapes_on_grid.cpp
new file mode 100644
index 00000000..54b8367b
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_landscapes_on_grid/plot_landscapes_on_grid.cpp
@@ -0,0 +1,55 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape_on_grid.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program plot persistence landscape on grid stored in a file (the file needs to be created beforehand). Please call the code with the name of a landsape on grid file \n";	
+	if ( argc == 1 )
+	{
+		std::cout << "Wrong parameters of a program call, the program will now terminate \n";
+		return 1;
+	}
+	Persistence_landscape_on_grid l;
+	l.load_landscape_from_file( argv[1] );
+	
+	std::stringstream ss;
+	ss << argv[1] << "_gnuplot_script";
+	l.plot( ss.str().c_str() );
+	
+	std::cout << "Done \n";
+		
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_vectors/average_persistence_vectors.cpp b/src/Gudhi_stat/example/utilities/persistence_vectors/average_persistence_vectors.cpp
new file mode 100644
index 00000000..1b269e9c
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_vectors/average_persistence_vectors.cpp
@@ -0,0 +1,75 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Vector_distances_in_diagram.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program computes average persistence vector of persistence vectors created based on persistence diagrams provided as an input. \n";
+	std::cout << "Please call this program with the names of files with persistence diagrams \n";
+	std::vector< const char* > filenames;
+	
+	if ( argc == 1 )
+	{
+		std::cout << "No input files given, the program will now terminate \n";
+		return 1;
+	}
+	
+	for ( int i = 1 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	
+	std::cout << "Reading persistence vectors...\n";
+	std::vector< Abs_Topological_data_with_averages* > lands;
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{		
+		Vector_distances_in_diagram< euclidean_distance<double> >* l = new Vector_distances_in_diagram< euclidean_distance<double> >;
+		l->load_from_file( filenames[i] );
+		lands.push_back( (Abs_Topological_data_with_averages*)l );
+	}
+	
+	Vector_distances_in_diagram< euclidean_distance<double> > av;
+	av.compute_average( lands );
+	
+	av.print_to_file( "average.vect" );
+	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		delete lands[i];
+	}
+	
+	std::cout << "Done \n";
+
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_vectors/compute_distance_of_persistence_vectors.cpp b/src/Gudhi_stat/example/utilities/persistence_vectors/compute_distance_of_persistence_vectors.cpp
new file mode 100644
index 00000000..72026497
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_vectors/compute_distance_of_persistence_vectors.cpp
@@ -0,0 +1,108 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Vector_distances_in_diagram.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program compute distance of persistence vectors stored in a file (the file needs to be created beforehand). \n";	
+	std::cout << "The first parameter of a program is an interger p. The program compute l^p distance of the vectors. For l^infty distance choose p = -1. \n";
+	std::cout << "The remaining parameters of this programs are names of files with persistence vectors.\n";
+	
+	if ( argc < 3 )
+	{
+		std::cout << "Wrong number of parameters, the program will now terminate \n";
+		return 1;
+	}
+	
+	int p = atoi( argv[1] );
+
+	std::vector< const char* > filenames;
+	for ( int i = 2 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	std::vector< Vector_distances_in_diagram< euclidean_distance<double> >* > vectors;
+	vectors.reserve( filenames.size() );
+	for ( size_t file_no = 0 ; file_no != filenames.size() ; ++file_no )
+	{
+		//cerr << filenames[file_no] << endl;
+		Vector_distances_in_diagram< euclidean_distance<double> >* l = new Vector_distances_in_diagram< euclidean_distance<double> >;
+		l->load_from_file( filenames[file_no] );
+		vectors.push_back( l );
+	}
+		
+	//and now we will compute the scalar product of landscapes.
+	
+	//first we prepare an array:
+	std::vector< std::vector< double > > distance( filenames.size() );
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		std::vector< double > v( filenames.size() , 0 );
+		distance[i] = v;
+	}
+		
+	//and now we can compute the distances:
+	for ( size_t i = 0 ; i != vectors.size() ; ++i )
+	{
+		for ( size_t j = i+1 ; j != vectors.size() ; ++j )
+		{
+			distance[i][j] = distance[j][i] = ((Vector_distances_in_diagram< euclidean_distance<double> >*)vectors[i])->distance( vectors[j] , p ) ;
+		}
+	}
+	
+	//and now output the result to the screen and a file:
+	ofstream out;
+	out.open( "distance" );
+	for ( size_t i = 0 ; i != distance.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != distance.size() ; ++j )
+		{
+			cout << distance[i][j] << " ";
+			out << distance[i][j] << " ";
+		}
+		cout << endl;
+		out << endl;
+	}
+	out.close();
+		
+	return 0;
+}
+
+
+
+
+
+
+	
diff --git a/src/Gudhi_stat/example/utilities/persistence_vectors/compute_scalar_product_of_persistence_vectors.cpp b/src/Gudhi_stat/example/utilities/persistence_vectors/compute_scalar_product_of_persistence_vectors.cpp
new file mode 100644
index 00000000..16192d52
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_vectors/compute_scalar_product_of_persistence_vectors.cpp
@@ -0,0 +1,97 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Vector_distances_in_diagram.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program compute scalar product of persistence vectors stored in a file (the file needs to be created beforehand). \n";	
+	std::cout << "The parameters of this programs are names of files with persistence vectors.\n";
+
+	std::vector< const char* > filenames;
+	for ( int i = 1 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	std::vector< Vector_distances_in_diagram< euclidean_distance<double> >* > vectors;
+	vectors.reserve( filenames.size() );
+	for ( size_t file_no = 0 ; file_no != filenames.size() ; ++file_no )
+	{
+		Vector_distances_in_diagram< euclidean_distance<double> >* l = new Vector_distances_in_diagram< euclidean_distance<double> >;
+		l->load_from_file( filenames[file_no] );
+		vectors.push_back( l );
+	}
+		
+	//and now we will compute the scalar product of landscapes.
+	
+	//first we prepare an array:
+	std::vector< std::vector< double > > scalar_product( filenames.size() );
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		std::vector< double > v( filenames.size() , 0 );
+		scalar_product[i] = v;
+	}
+	
+	//and now we can compute the scalar product:
+	for ( size_t i = 0 ; i != vectors.size() ; ++i )
+	{
+		for ( size_t j = i ; j != vectors.size() ; ++j )
+		{
+			scalar_product[i][j] = scalar_product[j][i] = ((Vector_distances_in_diagram< euclidean_distance<double> >*)vectors[i])->compute_scalar_product( vectors[j] ) ;
+		}
+	}
+	
+	//and now output the result to the screen and a file:
+	ofstream out;
+	out.open( "scalar_product" );
+	for ( size_t i = 0 ; i != scalar_product.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != scalar_product.size() ; ++j )
+		{
+			cout << scalar_product[i][j] << " ";
+			out << scalar_product[i][j] << " ";
+		}
+		cout << endl;
+		out << endl;
+	}
+	out.close();
+	
+	//cleaning up
+	for ( size_t i = 0 ; i != vectors.size() ; ++i )
+	{
+		delete vectors[i];
+	}
+		
+	return 0;
+}
diff --git a/src/Gudhi_stat/example/utilities/persistence_vectors/create_persistence_vectors.cpp b/src/Gudhi_stat/example/utilities/persistence_vectors/create_persistence_vectors.cpp
new file mode 100644
index 00000000..99015e41
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_vectors/create_persistence_vectors.cpp
@@ -0,0 +1,57 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Vector_distances_in_diagram.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program creates persistence vectors of diagrams provided as an input. Please call this program with the names of files with persistence diagrams \n";
+	std::vector< const char* > filenames;
+	for ( int i = 1 ; i < argc ; ++i )
+	{
+		filenames.push_back( argv[i] );
+	}
+	
+	for ( size_t i = 0 ; i != filenames.size() ; ++i )
+	{
+		std::cerr << "Creatign persistence vectors based on a file : " << filenames[i] << std::endl;
+		Vector_distances_in_diagram< euclidean_distance<double> > l( filenames[i] , -1 );				
+		std::stringstream ss;
+		ss << filenames[i] << ".vect";
+		l.print_to_file( ss.str().c_str() );
+	}
+	std::cout << "Done \n";
+	return 0;
+}
+
diff --git a/src/Gudhi_stat/example/utilities/persistence_vectors/plot_persistence_vectors.cpp b/src/Gudhi_stat/example/utilities/persistence_vectors/plot_persistence_vectors.cpp
new file mode 100644
index 00000000..ad6c06e2
--- /dev/null
+++ b/src/Gudhi_stat/example/utilities/persistence_vectors/plot_persistence_vectors.cpp
@@ -0,0 +1,51 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Vector_distances_in_diagram.h>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+#include <iostream>
+#include <sstream>
+
+
+int main( int argc , char** argv )
+{
+	std::cout << "This program create a Gnuplot script to plot persistence vector. Please call this program with the name of file with persistence vector. \n";
+	if ( argc != 2 )
+	{
+		std::cout << "Wrong number of parameters, the program will now terminate. \n";
+		return 1;
+	}
+	Vector_distances_in_diagram< euclidean_distance<double> > l;
+	l.load_from_file( argv[1] );
+	l.plot( argv[1] );
+	
+	return 0;
+}
+
diff --git a/src/Gudhi_stat/example/vector_representation.cpp b/src/Gudhi_stat/example/vector_representation.cpp
new file mode 100644
index 00000000..358de1b0
--- /dev/null
+++ b/src/Gudhi_stat/example/vector_representation.cpp
@@ -0,0 +1,77 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#include <gudhi/concretizations/Vector_distances_in_diagram.h>
+#include <iostream>
+
+
+#include <gudhi/reader_utils.h>
+#include <vector>
+#include <cmath>
+#include <iomanip>
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+using namespace std;
+
+
+double epsilon = 0.000005;
+
+
+
+int main( int argc , char** argv )
+{
+	if ( argc < 2 )
+	{
+		cout << "To run this program, please provide the name of a file with persistence diagram. If you provide two files, we will do distance, scalar produc and average computations \n";
+		return 1;
+	}
+	
+	Vector_distances_in_diagram< euclidean_distance<double> > p( argv[1] , 100 );
+	cout << "This is a vector corresponding to the input persistence diagram : \n";	
+	cout << p << endl;
+
+
+
+	if ( argc == 3 )
+	{
+		Vector_distances_in_diagram< euclidean_distance<double> > p_prime( argv[2] , 100);	
+		
+		cout << "p_prime : " <<p_prime << endl;
+			
+		cout << "Distance between input persistence diagrams : " << p.distance( (Abs_Topological_data_with_distances*)(&p_prime) ) << endl;	
+		std::vector< Abs_Topological_data_with_averages* > to_average;
+		to_average.push_back( (Abs_Topological_data_with_averages*)(&p) );
+		to_average.push_back( (Abs_Topological_data_with_averages*)(&p_prime) );
+	
+		Vector_distances_in_diagram< euclidean_distance<double> > average; 
+		average.compute_average( to_average );
+	
+		cout << "Here is an average : " << average << endl;
+	}
+	return 0;
+}
+
+
diff --git a/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Real_valued_topological_data.h b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Real_valued_topological_data.h
new file mode 100644
index 00000000..9b313e62
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Real_valued_topological_data.h
@@ -0,0 +1,54 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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 Abs_Real_valued_topological_data_H_
+#define Abs_Real_valued_topological_data_H_
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+
+namespace Gudhi 
+{
+namespace Gudhi_stat 
+{
+
+
+
+/**
+* This is specialization of a topological data class allows computing various real-valued characterizations of topological data.
+**/
+
+class Abs_Real_valued_topological_data : public virtual Abs_Topological_data
+{
+public:
+	 Abs_Real_valued_topological_data():number_of_functions_for_projections_to_reals(0){} 
+	 Abs_Real_valued_topological_data( size_t number_of_functions_ ):number_of_functions_for_projections_to_reals(number_of_functions_){} 
+	 size_t number_of_projections_to_R(){return this->number_of_functions_for_projections_to_reals;};
+     virtual double project_to_R( int number_of_function ) = 0;
+     virtual ~Abs_Real_valued_topological_data(){}
+protected:
+	size_t number_of_functions_for_projections_to_reals;
+};
+
+}//namespace Gudhi_stat
+}//namespace Gudhi 
+
+#endif
diff --git a/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data.h b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data.h
new file mode 100644
index 00000000..0e3db722
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data.h
@@ -0,0 +1,47 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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 ABS_Topological_data_H_
+//#define ABS_Topological_data_H_
+
+#pragma once
+
+namespace Gudhi 
+{
+namespace Gudhi_stat 
+{
+
+/**
+* This is an abstract container to store topological information. Most typically, this information will be some representation of persistent homology.
+**/
+
+class Abs_Topological_data
+{
+//public:
+//    Abs_Topological_data(){};
+//protected:
+};
+
+}//namespace Gudhi_stat
+}//namespace Gudhi 
+
+//#endif
diff --git a/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data_with_averages.h b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data_with_averages.h
new file mode 100644
index 00000000..88220e73
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data_with_averages.h
@@ -0,0 +1,62 @@
+
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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 Abs_Topological_data_with_averages_H_
+#define Abs_Topological_data_with_averages_H_
+
+namespace Gudhi 
+{
+namespace Gudhi_stat 
+{
+	
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+
+
+/**
+* This is an abstract container to store topological information. Most typically, this information will be some representation of persistent homology.
+**/
+
+class Abs_Topological_data_with_averages : public virtual Abs_Topological_data
+{
+public:
+    Abs_Topological_data_with_averages(){};
+    
+    //options: 
+    //1) Function returns void, take std::vector< Abs_Topological_data_with_averages* > and change the object underneeth to the average of this vector.
+    //2) Function returns  Abs_Topological_data*, and compute the average of all the objects in the vector, plus (*this). 
+    //virtual Abs_Topological_data* compute_average( std::vector< Abs_Topological_data_with_averages* > to_average ) = 0;
+    //At the moment I will try to implement option (1). 
+    virtual void compute_average( std::vector< Abs_Topological_data_with_averages* > to_average ) = 0;
+    virtual ~Abs_Topological_data_with_averages(){}
+protected:
+};
+
+
+}//namespace Gudhi_stat
+}//namespace Gudhi 
+
+
+ 
+
+
+#endif
diff --git a/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data_with_distances.h b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data_with_distances.h
new file mode 100644
index 00000000..2725c2c6
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data_with_distances.h
@@ -0,0 +1,51 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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 Abs_Topological_data_with_distances_H_
+#define Abs_Topological_data_with_distances_H_
+
+namespace Gudhi 
+{
+namespace Gudhi_stat 
+{
+
+//with this path it do not find the files
+//#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include "Abs_Topological_data.h"
+
+/**
+* This is an abstract container to store topological information. Most typically, this information will be some representation of persistent homology.
+**/
+
+class Abs_Topological_data_with_distances : public virtual Abs_Topological_data
+{
+public:
+    Abs_Topological_data_with_distances(){};
+    virtual double distance( const Abs_Topological_data_with_distances* second , double power = 1) = 0;
+    virtual ~Abs_Topological_data_with_distances(){}
+protected:
+};
+
+}//namespace Gudhi_stat
+}//namespace Gudhi 
+
+#endif
diff --git a/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data_with_scalar_product.h b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data_with_scalar_product.h
new file mode 100644
index 00000000..b5e5b175
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Topological_data_with_scalar_product.h
@@ -0,0 +1,49 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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 Abs_Topological_data_with_scalar_product_H
+#define Abs_Topological_data_with_scalar_product_H_
+
+namespace Gudhi 
+{
+namespace Gudhi_stat 
+{
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+
+/**
+* This is an abstract container to store topological information. Most typically, this information will be some representation of persistent homology.
+**/
+
+class Abs_Topological_data_with_scalar_product : public virtual Abs_Topological_data
+{
+public:
+    Abs_Topological_data_with_scalar_product(){};
+    virtual double compute_scalar_product( const Abs_Topological_data_with_scalar_product* second ) = 0;
+    virtual ~Abs_Topological_data_with_scalar_product(){}
+protected:
+};
+
+}//namespace Gudhi_stat
+}//namespace Gudhi 
+
+#endif
diff --git a/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Vectorized_topological_data.h b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Vectorized_topological_data.h
new file mode 100644
index 00000000..df423688
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/abstract_classes/Abs_Vectorized_topological_data.h
@@ -0,0 +1,60 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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 Abs_Vectorized_topological_data_H_
+#define Abs_Vectorized_topological_data_H_
+
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+
+namespace Gudhi 
+{
+namespace Gudhi_stat 
+{
+
+//with this path it do not find the files
+//#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include "Abs_Topological_data.h"
+#include <vector>
+
+using namespace std;
+
+/**
+* This is specialization of a topological data class that allows to create vectors based on topological data.
+**/
+
+class Abs_Vectorized_topological_data  :  public virtual Abs_Topological_data 	
+{
+public:
+    Abs_Vectorized_topological_data():where_to_cut(10){}
+    Abs_Vectorized_topological_data( size_t where_to_cut ):where_to_cut(where_to_cut){}
+    size_t number_of_vectorize_functions(){return number_of_functions_for_vectorization;}
+    virtual std::vector<double> vectorize( int number_of_function ) = 0;
+    virtual ~Abs_Vectorized_topological_data(){}
+protected:
+    size_t number_of_functions_for_vectorization;
+    size_t where_to_cut;
+};
+
+}//namespace Gudhi_stat
+}//namespace Gudhi 
+
+#endif
diff --git a/src/Gudhi_stat/include/gudhi/common.h b/src/Gudhi_stat/include/gudhi/common.h
new file mode 100644
index 00000000..d573a92a
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/common.h
@@ -0,0 +1,39 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+#pragma once 
+ //this file contain an implementation of some common procedures used in Gudhi_stat.
+
+ //double epsi = std::numeric_limits<double>::epsilon();
+double epsi = 0.000005;
+
+
+/**
+ *  A procedure used to compare doubles. Typically gien two doubles A and B, comparing A == B is not good idea. In this case, we use the procedure almostEqual with the epsi defined at
+ *  the top of the file. Setting up the epsi give the user a tolerance on what should be consider equal.
+**/
+inline bool almost_equal( double a , double b )
+{
+    if ( fabs(a-b) < epsi )
+        return true;
+    return false;
+}
diff --git a/src/Gudhi_stat/include/gudhi/concretizations/PSSK.h b/src/Gudhi_stat/include/gudhi/concretizations/PSSK.h
new file mode 100644
index 00000000..61597ee2
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/concretizations/PSSK.h
@@ -0,0 +1,173 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+#pragma once
+#ifndef PSSK_H
+#define PSSK_H
+
+//gudhi include
+#include <gudhi/concretizations/Persistence_heat_maps.h>
+
+
+namespace Gudhi
+{
+namespace Gudhi_stat
+{
+
+/**
+* This is a version of a representation presented in https://arxiv.org/abs/1412.6821
+* In that paper the authors are using the representation just to compute kernel. Over here, we extend the usability by far.
+* Note that the version presented here is not exact, since we are discretizing the kernel.
+* The only difference with respect to the original class is the method of creation. We have full (square) image, and for every point (p,q), we add a kernel at (p,q) and the negative kernel
+* at (q,p)
+**/
+
+class PSSK : public Persistence_heat_maps
+{
+public:
+	PSSK():Persistence_heat_maps(){}
+	
+	PSSK(const std::vector< std::pair< double,double > >  & interval , std::vector< std::vector<double> > filter = create_Gaussian_filter(5,1) , size_t number_of_pixels = 1000 , double min_ = -1 , double max_ = -1 )
+	:Persistence_heat_maps()
+	{
+		this->construct( interval  , filter , number_of_pixels , min_ , max_ );
+	}
+	
+	 
+	 PSSK( const char* filename , std::vector< std::vector<double> > filter = create_Gaussian_filter(5,1) , size_t number_of_pixels = 1000 , double min_ = -1 , double max_ = -1  ):
+	    Persistence_heat_maps()
+	    {
+			std::vector< std::pair< double , double > > intervals_ = read_standard_file( filename );         
+			this->construct( intervals_ , filter , number_of_pixels , min_ , max_ );
+		}
+
+protected:
+	void construct( const std::vector< std::pair<double,double> >& intervals_  , 
+					std::vector< std::vector<double> > filter = create_Gaussian_filter(5,1),
+                    size_t number_of_pixels = 1000 , double min_ = -1 , double max_ = -1 );
+};
+
+//if min_ == max_, then the program is requested to set up the values itself based on persistence intervals
+void PSSK::construct( const std::vector< std::pair<double,double> >& intervals_  ,  
+									   std::vector< std::vector<double> > filter,
+									   size_t number_of_pixels , double min_ , double max_ )
+{	
+    bool dbg = false;       
+    if ( dbg ){std::cerr << "Entering construct procedure \n";getchar();}
+
+    if ( min_ == max_ )
+    {
+        //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 )
+	{
+		cerr << "min_ : " << min_ << endl;
+		cerr << "max_ : " << max_ << endl;
+		cerr << "number_of_pixels : " << number_of_pixels << endl;
+		getchar();
+	}
+
+    this->min_ = min_;
+    this->max_ = max_;    
+    this->scalling_function_with_respect_to_distance_from_diagonal = scalling_function_with_respect_to_distance_from_diagonal;
+
+
+    //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)cerr << "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 = (int)((intervals_[pt_nr].first - this->min_)/( this->max_-this->min_ )*number_of_pixels);
+		int y_grid = (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 << endl;
+			std::cerr << "x_grid : " << x_grid << endl;
+			std::cerr << "y_grid : " << y_grid << endl;
+		}
+		
+		//x_grid and y_grid gives a center of the kernel. We want to have its lower left cordner. 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::cerr << "After shift : \n";;
+			std::cerr << "x_grid : " << x_grid << endl;
+			std::cerr << "y_grid : " << y_grid << endl;
+			std::cerr << "filter.size() : " << filter.size() << std::endl;
+			getchar();
+		}					
+
+		
+		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::cerr << y_grid+j << " " <<  x_grid+i << std::endl;}
+					this->heat_map[ y_grid+j ][ x_grid+i ] += filter[i][j];
+					this->heat_map[ x_grid+i ][ y_grid+j ] += -filter[i][j];
+				}
+			}
+		}
+		
+	}
+}//construct
+
+
+#endif
+
+}//namespace Gudhi_stat
+}//namespace Gudhi
diff --git a/src/Gudhi_stat/include/gudhi/concretizations/Persistence_heat_maps.h b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_heat_maps.h
new file mode 100644
index 00000000..afb0da87
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_heat_maps.h
@@ -0,0 +1,781 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+ 
+//standard include
+#include <vector>
+#include <sstream>
+#include <iostream>
+#include <cmath>
+#include <limits>
+#include <vector>
+#include <algorithm>
+
+//gudhi include
+#include <gudhi/abstract_classes/Abs_Vectorized_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_averages.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_distances.h>
+#include <gudhi/abstract_classes/Abs_Real_valued_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_scalar_product.h>
+#include <gudhi/concretizations/read_persitence_from_file.h>
+#include <gudhi/common.h>
+
+
+
+using namespace std;
+
+namespace Gudhi
+{
+namespace Gudhi_stat
+{
+
+
+/**
+ * This is a simple procedure to create n by n (or 2*pixel_radius times 2*pixel_radius.
+**/ 
+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::cerr << "Kernel initalize \n";	
+		cerr << "pixel_radius : " << pixel_radius << endl; 
+		std::cerr << "kernel.size() : " << kernel.size() << endl;
+		getchar();
+	}
+ 
+    for (int x = -pixel_radius; x <= (int)pixel_radius; x++)
+    {
+        for(int y = -pixel_radius; y <= (int)pixel_radius; y++)
+        {			
+			double real_x = 2*sigma*x/pixel_radius;
+			double real_y = 2*sigma*y/pixel_radius;						
+            r = 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::cerr << "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::cerr << kernel[i][j] << " ";
+			}
+			std::cerr << std::endl;
+		}
+	}
+    return kernel;
+}
+
+
+/**
+ * There are various options to scale the poits 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 
+**/ 
+
+double constant_function( const std::pair< double , double >& point_in_diagram )
+{	
+	return 1;
+}
+
+double distance_from_diagonal( const std::pair< double , double >& point_in_diagram )
+{
+	//(point_in_diagram.first+point_in_diagram.second)/2.0
+	return sqrt( pow((point_in_diagram.first-(point_in_diagram.first+point_in_diagram.second)/2.0),2) + pow((point_in_diagram.second-(point_in_diagram.first+point_in_diagram.second)/2.0),2)  );
+}
+
+double squared_distance_from_diagonal( const std::pair< double , double >& point_in_diagram )
+{
+	return pow((point_in_diagram.first-(point_in_diagram.first+point_in_diagram.second)/2.0),2) + pow((point_in_diagram.second-(point_in_diagram.first+point_in_diagram.second)/2.0),2);
+}
+
+double arc_tan_of_persistence_of_point( const std::pair< double , double >& point_in_diagram )
+{
+	return atan( point_in_diagram.second - point_in_diagram.first );
+}
+
+
+
+
+class Persistence_heat_maps :
+								public Abs_Vectorized_topological_data ,
+								public Abs_Topological_data_with_distances ,
+								public Abs_Real_valued_topological_data,
+								public Abs_Topological_data_with_averages,
+								public Abs_Topological_data_with_scalar_product
+{
+public:
+    /**
+     * The default constructor. A scaling function from the diagonal is set up to a constant function. The image is not erased below the diagonal. The gaussian have diameter 5. 	 
+    **/ 
+	Persistence_heat_maps()
+	{
+		this->scalling_function_with_respect_to_distance_from_diagonal = constant_function;
+		this->erase_below_diagonal = false;		
+		this->min_ = this->max_ = 0;
+		this->set_up_parameters_for_basic_classes();
+	};
+	
+	/**
+	 * Construction that takes at the input the following parameters:
+	 * (1) A vector of pairs of doubles (representing persistence intervals). All other parameters are optional. They are:
+	 * (2) a Gausian filter generated by create_Gaussian_filter filter (the default value of this vaiable is a Gaussian filter of a radius 5), 
+	 * (3) a scaling function (constant by default). This function allows to put a different weights to points depending on their position, in particular, depending on their distance from diagonal, 
+	 * (4) a boolean value which determines if the area of image below diagonal should, or should not be erased (it will be erased by default). 
+	 * (5) a number of pixels in each direction (set to 1000 by default). 
+	 * (6) a min x and y value of points that are to be taken into account. By default it is set to -1, in which case the program compute the values based on the data,
+	 * (6) a max x and y value of points that are to be taken into account. By default it is set to -1, in which case the program compute the values based on the data.
+	**/  
+    Persistence_heat_maps( const std::vector< std::pair< double,double > >  & interval , std::vector< std::vector<double> > filter = create_Gaussian_filter(5,1) ,  double (*scalling_function_with_respect_to_distance_from_diagonal)( const std::pair< double , double >& point_in_diagram ) = constant_function, bool erase_below_diagonal = false , size_t number_of_pixels = 1000 , double min_ = -1 , double max_ = -1  );
+    
+    /**
+	 * Construction that takes at the input a name of a file with persistence intervals, a filter (radius 5 by default), a scaling function (constant by default), a boolean value which determines if the area of image below diagonal should, or should not be erased (should by default). The next parameter is the number of pixels in each direction (set to 1000 by default). and min and max values of images (both set to -1 by defaulet. If this is the case, the program will pick the right values based on the data).
+	**/  
+	/**
+	 * Construction that takes at the input the following parameters:
+	 * (1) A a name of a file with persistence intervals. The file shold be readable by the function read_standard_file. All other parameters are optional. They are:
+	 * (2) a Gausian filter generated by create_Gaussian_filter filter (the default value of this vaiable is a Gaussian filter of a radius 5), 
+	 * (3) a scaling function (constant by default). This function allows to put a different weights to points depending on their position, in particular, depending on their distance from diagonal, 
+	 * (4) a boolean value which determines if the area of image below diagonal should, or should not be erased (it will be erased by default). 
+	 * (5) a number of pixels in each direction (set to 1000 by default). 
+	 * (6) a min x and y value of points that are to be taken into account. By default it is set to -1, in which case the program compute the values based on the data,
+	 * (6) a max x and y value of points that are to be taken into account. By default it is set to -1, in which case the program compute the values based on the data.
+	**/ 	
+    Persistence_heat_maps( const char* filename , std::vector< std::vector<double> > filter = create_Gaussian_filter(5,1) , double (*scalling_function_with_respect_to_distance_from_diagonal)( const std::pair< double , double >& point_in_diagram ) = constant_function, bool erase_below_diagonal = false , size_t number_of_pixels = 1000 , double min_ = -1 , double max_ = -1  );
+
+	
+	/**
+	 * Compute a mean value of a collection of heat maps and store it in the current object. Note that all the persistence maps send in a vector to this procedure need to have the same parameters. 
+	 * If this is not the case, the program will throw an exception. 
+	**/ 
+	void compute_mean( const std::vector<Persistence_heat_maps*>& maps );
+	
+	/**
+	 * Compute a median value of a collection of heat maps and store it in the current object. Note that all the persistence maps send in a vector to this procedure need to have the same parameters. 
+	 * If this is not the case, the program will throw an exception. 
+	**/ 
+	void compute_median( const std::vector<Persistence_heat_maps*>& maps );	
+	
+	/**
+	 * Compute a percentage of active (i.e) values above the cutoff of a collection of heat maps. 
+	**/ 
+	void compute_percentage_of_active( const std::vector<Persistence_heat_maps*>& maps , size_t cutoff = 1 );
+    
+    //put to file subroutine
+    /**
+     * The function outputs the perssitence image to a text file. The format as follow:
+     * In the first line, the values min and max of the image are stored
+     * In the next lines, we have the persistence images in a form of a bitmap image. 
+    **/
+    void print_to_file( const char* filename );
+    
+    /**
+     * A function that load a heat map from file to the current object (and arase qhatever was stored in the current object before).
+    **/
+    void load_from_file( const char* filename );
+    
+    
+    /**
+     * The procedure checks if min_, max_ and this->heat_maps sizes are the same. 
+    **/ 
+    inline bool check_if_the_same( const Persistence_heat_maps& second  )
+    {
+		bool dbg = false;
+		if ( this->heat_map.size() != second.heat_map.size() )
+		{
+			if ( dbg )std::cerr << "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::cerr << "this->min_ : " << this->min_ << ", second.min_ : " << second.min_ << std::endl;
+			return false;
+		}
+		if ( this->max_ != second.max_ )
+		{
+			if ( dbg )std::cerr << "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;
+	}
+	
+	
+	/**
+	 * Return minimal range value of persistent image.
+	**/ 
+	inline double gimme_min(){return this->min_;}
+
+	/**
+	 * Return maximal range value of persistent image.
+	**/ 
+	inline double gimme_max(){return this->max_;}
+	
+	
+	/**
+	 * Operator == to check if to persistence heat maps are the same.
+	**/ 
+	bool operator == ( const Persistence_heat_maps& rhs )
+	{
+		bool dbg = false;
+		if ( !this->check_if_the_same(rhs) )
+		{
+			if ( dbg )std::cerr << "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::cerr << "this->heat_map[" << i << "][" << j << "] = " << this->heat_map[i][j] << std::endl;
+						std::cerr << "rhs.heat_map[" << i << "][" << j << "] = " << rhs.heat_map[i][j] << std::endl;						
+					}
+					return false;
+				}
+			}
+		}
+		return true;
+	}
+	
+	/**
+	 * Operator != to check if to persistence heat maps are different.
+	**/ 
+	bool operator != ( const Persistence_heat_maps& rhs )
+	{
+		return !( (*this) == rhs );
+	}
+    
+    
+    /**
+     * A function to generate a gnuplot script to vizualize the persistent image.  
+    **/
+    void plot( const char* filename );
+    
+    
+    //Concretizations of virtual methods:    
+    std::vector<double> vectorize( int number_of_function );
+	double distance( const Abs_Topological_data_with_distances* second_ , double power = 1);
+	double project_to_R( int number_of_function );	
+	void compute_average( std::vector< Abs_Topological_data_with_averages* > to_average );	
+	double compute_scalar_product( const Abs_Topological_data_with_scalar_product* second_ );
+	
+protected:
+	//private methods
+	std::vector< std::vector<double> > check_and_initialize_maps( const std::vector<Persistence_heat_maps*>& maps );
+    void construct( const std::vector< std::pair<double,double> >& intervals_  , 
+					std::vector< std::vector<double> > filter = create_Gaussian_filter(5,1),
+                    double (*scalling_function_with_respect_to_distance_from_diagonal)( const std::pair< double , double >& point_in_diagram ) = constant_function, 
+                    bool erase_below_diagonal = false , size_t number_of_pixels = 1000 , double min_ = -1 , double max_ = -1 );
+                    
+	void set_up_parameters_for_basic_classes()
+	{
+		this->number_of_functions_for_vectorization = 1;
+		this->number_of_functions_for_projections_to_reals = 1;
+	}
+    
+    //data    
+    double (*scalling_function_with_respect_to_distance_from_diagonal)( const std::pair< double , double >& point_in_diagram );    
+    bool erase_below_diagonal;
+    double min_;
+    double max_;
+    std::vector< std::vector< double > > heat_map;    
+};
+
+
+//if min_ == max_, then the program is requested to set up the values itself based on persistence intervals
+void Persistence_heat_maps::construct( const std::vector< std::pair<double,double> >& intervals_  ,  
+									   std::vector< std::vector<double> > filter,
+									   double (*scalling_function_with_respect_to_distance_from_diagonal)( const std::pair< double , double >& point_in_diagram ), 
+									   bool erase_below_diagonal , size_t number_of_pixels , double min_ , double max_ )
+{
+    bool dbg = false;       
+    if ( dbg )std::cerr << "Entering construct procedure \n";
+
+    if ( min_ == max_ )
+    {
+        //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 )
+	{
+		cerr << "min_ : " << min_ << endl;
+		cerr << "max_ : " << max_ << endl;
+		cerr << "number_of_pixels : " << number_of_pixels << endl;
+		getchar();
+	}
+
+    this->min_ = min_;
+    this->max_ = max_;    
+    this->scalling_function_with_respect_to_distance_from_diagonal = scalling_function_with_respect_to_distance_from_diagonal;
+
+
+    //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)cerr << "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 = (int)((intervals_[pt_nr].first - this->min_)/( this->max_-this->min_ )*number_of_pixels);
+		int y_grid = (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 << endl;
+			std::cerr << "x_grid : " << x_grid << endl;
+			std::cerr << "y_grid : " << y_grid << endl;
+		}
+		
+		//x_grid and y_grid gives a center of the kernel. We want to have its lower left cordner. 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::cerr << "After shift : \n";;
+			std::cerr << "x_grid : " << x_grid << endl;
+			std::cerr << "y_grid : " << y_grid << endl;
+		}
+				
+		double scaling_value = this->scalling_function_with_respect_to_distance_from_diagonal(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::cerr << 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::cerr << "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
+
+
+Persistence_heat_maps::Persistence_heat_maps( const std::vector< std::pair< double,double > >  & interval , 
+											  std::vector< std::vector<double> > filter,  
+											  double (*scalling_function_with_respect_to_distance_from_diagonal)( const std::pair< double , double >& point_in_diagram ), 
+											  bool erase_below_diagonal , size_t number_of_pixels , double min_ , double max_ )
+{
+    this->construct( interval ,  filter ,  scalling_function_with_respect_to_distance_from_diagonal, erase_below_diagonal , number_of_pixels , min_ , max_ );
+    this->set_up_parameters_for_basic_classes();
+}
+
+
+Persistence_heat_maps::Persistence_heat_maps( const char* filename , 
+											  std::vector< std::vector<double> > filter, 
+											  double (*scalling_function_with_respect_to_distance_from_diagonal)( const std::pair< double , double >& point_in_diagram ), 
+											  bool erase_below_diagonal , size_t number_of_pixels  , double min_ , double max_ )
+{    
+    std::vector< std::pair< double , double > > intervals_ = read_standard_file( filename );           
+    this->construct( intervals_ ,  filter ,  scalling_function_with_respect_to_distance_from_diagonal, erase_below_diagonal , number_of_pixels , min_ , max_ );
+    this->set_up_parameters_for_basic_classes();
+}
+
+
+
+std::vector< std::vector<double> > Persistence_heat_maps::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;
+}
+
+
+void Persistence_heat_maps::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_;
+}
+
+
+
+void Persistence_heat_maps::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/(double)maps.size();
+        }       
+    }
+	this->heat_map = heat_maps;
+	this->min_ = maps[0]->min_;
+	this->max_ = maps[0]->max_;
+}
+
+
+
+
+void Persistence_heat_maps::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_;
+}
+
+
+
+void Persistence_heat_maps::plot( const char* filename )
+{
+	ofstream out;
+	std::stringstream ss;
+	ss << filename << "_Gnuplot_script";
+	
+    out.open( ss.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 << 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; 
+}
+
+
+
+void Persistence_heat_maps::print_to_file( const char* filename )
+{
+
+	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 << endl;
+    }
+	out.close();
+}
+
+
+void Persistence_heat_maps::load_from_file( const char* filename )
+{
+	bool dbg = false;	
+	
+	ifstream in;
+	in.open( filename );
+	
+	//checking if the file exist / if it was open. 
+	if ( !( access( filename, F_OK ) != -1 ) )
+	{
+		cerr << "The file : " << filename << " do not exist. The program will now terminate \n";
+		throw "The file from which you are trying to read the persistence landscape 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::cerr << "Reading the following values of min and max : " << this->min_ << " , " << this->max_ << std::endl;
+	}
+
+	std::string temp;
+	std::getline(in, temp);
+         
+	while (!in.eof())
+	{
+		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::cout << point << " ";
+			}
+		}
+		if ( dbg )
+		{
+			std::cout << std::endl;
+			getchar();
+		}
+
+		if ( in.good() )this->heat_map.push_back( line_of_heat_map );
+	}	
+	in.close();
+	if ( dbg )std::cout << "Done \n";
+}
+
+
+//Concretizations of virtual methods:    
+std::vector<double> Persistence_heat_maps::vectorize( int number_of_function )
+{
+	//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();
+	}
+	
+	std::vector< double > result;
+	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;
+}
+
+double Persistence_heat_maps::distance( const Abs_Topological_data_with_distances* second_ , double power )
+{		
+	Persistence_heat_maps* second = (Persistence_heat_maps*)second_;
+	
+	//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 noncompatible sizes. We cannot therefore compute distance between them. The program will now terminate";
+		throw "The persistence images are of noncompatible sizes. We cannot therefore compute distance between them. The program will now terminate";
+	}
+	
+	//if we are here, we know that the two persistence iomages are defined on the same domain, so we can start computing their distances:
+	
+	double distance = 0;
+	for ( size_t i = 0 ; i != this->heat_map.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != this->heat_map[i].size() ; ++j )
+		{
+			distance += pow( abs(this->heat_map[i][j] - second->heat_map[i][j]) , power );
+		}
+	}
+	return distance;
+}
+
+double Persistence_heat_maps::project_to_R( int number_of_function )
+{
+	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;
+}
+
+void Persistence_heat_maps::compute_average( std::vector< Abs_Topological_data_with_averages* > to_average )
+{
+	std::vector<Persistence_heat_maps*> maps;
+	maps.reserve( to_average.size() );
+	for ( size_t i = 0 ; i != to_average.size() ; ++i )
+	{
+		maps.push_back( (Persistence_heat_maps*)to_average[i] );
+	}					
+	this->compute_mean( maps );
+}
+
+double Persistence_heat_maps::compute_scalar_product( const Abs_Topological_data_with_scalar_product* second_ )
+{
+	Persistence_heat_maps* second = (Persistence_heat_maps*)second_;
+	
+	//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 noncompatible sizes. We cannot therefore compute distance between them. The program will now terminate";
+		throw "The persistence images are of noncompatible sizes. We cannot therefore compute distance between them. The program will now terminate";
+	}
+	
+	//if we are here, we know that the two persistence iomages 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;
+}
+
+
+
+
+}//namespace Gudhi_stat
+}//namespace Gudhi
diff --git a/src/Gudhi_stat/include/gudhi/concretizations/Persistence_intervals.h b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_intervals.h
new file mode 100644
index 00000000..e0db0070
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_intervals.h
@@ -0,0 +1,637 @@
+/*    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):       Pawel Dlotko

+ *

+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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_intervals_H_

+#define Persistence_intervals_H_

+

+//gudhi include

+#include <gudhi/abstract_classes/Abs_Vectorized_topological_data.h>

+#include <gudhi/abstract_classes/Abs_Topological_data_with_distances.h>

+#include <gudhi/abstract_classes/Abs_Real_valued_topological_data.h>

+#include <gudhi/concretizations/read_persitence_from_file.h>

+

+//standard include

+#include <limits>

+#include <iostream>

+#include <fstream>

+#include <vector>

+#include <algorithm>

+#include <climits>

+#include <cmath>

+

+namespace Gudhi 

+{

+namespace Gudhi_stat 

+{

+

+class Persistence_intervals : public Abs_Vectorized_topological_data , public Abs_Topological_data_with_distances, public Abs_Real_valued_topological_data

+{

+public:	   

+	/**

+	 * This is a constructor of a class Persistence_intervals from a text file. Each line of the input file is supposed to contain two numbers of a type doube (or convertable to double)

+	 * representing the birth and the death of the persistence interval. If the pairs are not sorted so that birth <= death, then the constructor will sort then that way. 

+	**/ 

+    Persistence_intervals( const char* filename );

+    

+    /**

+     * This is a constructor of a class Persistence_intervals from a vector of pairs. Each pair is assumed to represent a persistence interval. We assume that the first elemnets of pairs 

+     * are smaller or equal the second elements of pairs.

+    **/ 

+    Persistence_intervals( const std::vector< std::pair< double,double > >& intervals );

+

+	/**

+	 * The procedure returns a pair the first element of which is the leftmost end of the interval, and the second element of which is the rightmost end of the interval.  

+	**/

+    std::pair<double,double> min_max();

+

+	/**

+	 * Procedure that compute the vector of lengths of the dominant (i.e. the longest) persistence intervals. The list is truncated at the parameter of the call where_to_cut (set by default to 100).

+	**/ 

+    std::vector<double> length_of_dominant_intervals( size_t where_to_cut = 100 );

+    

+    

+    /**

+	 * Procedure that compute the vector of the dominant (i.e. the longest) persistence intervals. The parameter of the procedure (set by default to 100) is the number of dominant intervals returned by the procedure.

+	**/ 

+    std::vector< std::pair<double,double> > dominant_intervals( size_t where_to_cut = 100 );

+    

+    /**

+	 * Procedure to compute a histogram of interva's length. A histogram is a block plot. The number of blocks is determined by the first parameter of the function (set by default to 10). 

+	 * For the sake of argument let us assume that the length of the longest interval is 1 and the number of bins is 10. In this case the i-th block correspond to a range between i-1/10 and i10. 

+	 * The vale of a block supported at the interval is the number of persistence intervals of a length between x_0 and x_1.

+	**/

+    std::vector< size_t > histograms_of_lengths( size_t number_of_bins = 10  );

+    

+    /**

+     * Based on a histogram of intervals lengts computed by the function histograms_of_lengths H the procedure below computes the cumulative histogram. The i-th position of the resulting histogram

+     * is the sume of values of H for the positions from 0 to i. 

+    **/

+    std::vector< size_t > cumulative_histograms_of_lengths( size_t number_of_bins = 10 );

+    

+    /**

+     * In this procedure we assume that each barcode is a characteristic function of a hight equal to its length. The persistence diagram is a sum of such a functions. The procedure below construct a function being a 

+     * sum of the characteristic functions of persistence intervals. The first two parameters are the range in which the function is to be computed and the last parameter is the number of bins in 

+     * the discretization of the interval [_min,_max].

+    **/ 

+    std::vector< double > characteristic_function_of_diagram( double x_min , double x_max , size_t number_of_bins = 10 );

+    

+    /**

+     * Cumulative version of the function characteristic_function_of_diagram

+    **/ 

+    std::vector< double > cumulative_characteristic_function_of_diagram( double x_min , double x_max , size_t number_of_bins = 10 );

+    

+    /**

+     * Compute the funtion of persistence Betti numbers. The returned value is a vector of pair. First element of each pair is a place where persistence Betti numbers change. 

+     * Second element of each pair is the value of Persistence Betti numbers at that point.  

+    **/ 

+    std::vector< std::pair< double , size_t > > compute_persistent_betti_numbers();

+    

+    /**

+     *This is a non optimal procedure that compute vector of distances from each point of diagram to its k-th nearest neighbor (k is a parameted of the program). The resulting vector is by default truncated to 10 

+     *elements (this value can be changed by using the second parameter of the program). The points are returned in order from the ones which are farthest away from their k-th nearest neighbors. 

+    **/

+    std::vector< double > k_n_n( size_t k  , size_t where_to_cut = 10 );

+

+	/**

+     * Operator that send the diagram to a stream. 

+    **/    

+    friend ostream& operator << ( ostream& out , const Persistence_intervals& intervals )

+    {

+        for ( size_t i = 0 ; i != intervals.intervals.size() ; ++i )

+        {

+            out << intervals.intervals[i].first << " " << intervals.intervals[i].second << endl;

+        }

+        return out;

+    }

+    

+    /**

+     * Generating gnuplot script to plot the interval. 

+    **/

+    void plot( const char* filename ) 

+    {

+		//this program create a gnuplot script file that allows to plot persistence diagram.

+		ofstream out;

+		

+		std::ostringstream nameSS;

+		nameSS << filename << "_GnuplotScript";

+		std::string nameStr = nameSS.str();

+		out.open( (char*)nameStr.c_str() );

+		std::pair<double,double> min_max_values = this->min_max();

+		out << "set xrange [" << min_max_values.first - 0.1*(min_max_values.second-min_max_values.first) << " : " << min_max_values.second + 0.1*(min_max_values.second-min_max_values.first) << " ]" << endl;

+		out << "set yrange [" << min_max_values.first - 0.1*(min_max_values.second-min_max_values.first) << " : " << min_max_values.second + 0.1*(min_max_values.second-min_max_values.first) << " ]" << endl;

+		out << "plot '-' using 1:2 notitle \"" << filename << "\", \\" << endl;

+		out << "     '-' using 1:2 notitle with lp" << endl;

+		for ( size_t i = 0 ; i != this->intervals.size() ; ++i )

+		{

+			out << this->intervals[i].first << " " << this->intervals[i].second << endl;

+		}

+		out << "EOF" << endl;

+		out << min_max_values.first - 0.1*(min_max_values.second-min_max_values.first) << " " << min_max_values.first - 0.1*(min_max_values.second-min_max_values.first) << endl;

+		out << min_max_values.second + 0.1*(min_max_values.second-min_max_values.first) << " " << min_max_values.second + 0.1*(min_max_values.second-min_max_values.first) << endl;

+			

+		out.close();

+		

+		cout << "Gnuplot script to visualize persistence diagram written to the file: " << nameStr << ". Type load '" << nameStr << "' in gnuplot to visualize." << endl;

+	}

+

+	/**

+     * Return a familly of vectors obtained from the persistence diagram. The i-th vector consist of the lenfth of i dominant persistence intervals. 

+    **/

+    std::vector<double> vectorize( int number_of_function )//comment: in this case, number_of_functions (a static member of Abs_Vectorized_topological_data cannot be set a priori. 

+															//In this cas, maybe it is better not to make this parameter static.

+    {

+        return this->length_of_dominant_intervals( number_of_function );

+    }

+

+	/**

+     * Retun numbr of points in the diagram.

+    **/

+    size_t size()const{return this->intervals.size();}

+    

+    /**

+     * Return the persistence interval at the given position. Note that intervals are not sorted with respect to their lengths. 

+    **/

+    inline std::pair< double,double > operator [](size_t i)

+    {

+        if ( i >= this->intervals.size() )throw("Index out of range! Operator [], one_d_gaussians class\n");

+        return this->intervals[i];

+    }

+    

+    /**

+     *Computations of distance from the current persistnce diagram to the persistence diagram given as a parameter of this function.

+     *The last parameter, power, is here in case we would like to compute p=th Wasserstein distance. At the moment, for the bottleneck distances, it will be ignored.

+    **/

+    double distance( const Abs_Topological_data_with_distances* second , double power = 1) 

+    {

+		return 1;

+		//waiting for Francois Godi for the code. We will compute here the Bottleneck distnace. 

+	}

+	

+	/**

+	 * This is a simple function projectig the persistence intervals to a real number. The function we use here is a sum of squared lendgths of intervals. It can be naturally interpreted as

+	 * sum of step function, where the step hight it equal to the length of the interval.

+	 **/ 

+	double project_to_R( int number_of_function );

+	

+    

+    //For visualization use output from vectorize and build histograms. 

+     std::vector< std::pair< double,double > > output_for_visualization()

+    {

+		return this->intervals;

+	}

+

+protected:

+	

+	void set_up_numbers_of_functions_for_vectorization_and_projections_to_reals()

+	{

+		//warning, this function can be only called after filling in the intervals vector.

+		this->number_of_functions_for_vectorization = this->intervals.size();

+		this->number_of_functions_for_projections_to_reals = 1;

+	}

+

+    std::vector< std::pair< double,double > > intervals;    

+};

+

+

+Persistence_intervals::Persistence_intervals( const char* filename )

+{

+    //bool dbg = false;

+    //ifstream in;

+    //in.open( filename );

+

+    //if ( !in.good() )

+    //{

+    //    throw("File with the persistence diagram do not exist, the program will now terminate.\n");

+    //}

+

+    //while ( true )

+    //{

+    //    double first;

+    //    double second;

+    //    in >> first >> second;

+

+    //    if ( first > second )

+    //    {

+    //        double buf = first;

+    //        first = second;

+    //        second = buf;

+    //    }

+

+    //    if ( in.eof() )break;

+    //    this->intervals.push_back( std::make_pair( first,second ) );

+    //    if ( dbg )

+    //    {

+    //        cerr << "Adding interval [ " << first << " , " << second << " ]\n";

+    //        getchar();

+    //    }

+    //}

+    //in.close();

+    //standard file with barcode

+    std::vector< std::pair< double , double > > barcode = read_standard_file( filename );    

+    //gudhi file with barcode

+    //std::vector< std::pair< double , double > > barcode = read_gudhi_file( filename , dimension );   

+    

+    this->intervals = barcode;

+    this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();

+}//Persistence_intervals

+

+

+Persistence_intervals::Persistence_intervals( const std::vector< std::pair< double , double > >& intervals_ )

+{

+	std::vector< std::pair< double,double > > aaa( intervals_ );

+    this->intervals = aaa;

+    this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();

+}

+

+

+std::vector< double > Persistence_intervals::length_of_dominant_intervals( size_t where_to_cut )

+{

+	this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();

+    std::vector< double > result( this->intervals.size() );

+    for ( size_t i = 0 ; i != this->intervals.size() ; ++i )

+    {

+        result[i] = this->intervals[i].second - this->intervals[i].first;

+    }

+    std::sort( result.begin() , result.end() ,  std::greater<double>() );

+

+

+    result.resize( std::min(where_to_cut,result.size()) );

+    return result;

+}//length_of_dominant_intervals

+

+

+

+bool compare( const std::pair< size_t , double >& first , const std::pair< size_t , double >& second )

+{

+	return first.second > second.second;

+}

+

+

+std::vector< std::pair<double,double> > Persistence_intervals::dominant_intervals( size_t where_to_cut )

+{

+	bool dbg = false;

+	std::vector< std::pair< size_t , double > > position_length_vector( this->intervals.size() );

+	for ( size_t i = 0 ; i != this->intervals.size() ; ++i )

+    {

+        position_length_vector[i] = std::make_pair( i , this->intervals[i].second - this->intervals[i].first );

+    }

+    

+    std::sort( position_length_vector.begin() , position_length_vector.end() , compare );

+

+	std::vector< std::pair<double,double> > result;

+	result.reserve( std::min( where_to_cut , position_length_vector.size() ) );

+	

+	for ( size_t i = 0 ; i != std::min( where_to_cut , position_length_vector.size() ) ; ++i )

+	{

+		result.push_back( this->intervals[ position_length_vector[i].first ] );

+		if ( dbg )cerr << "Position : " << position_length_vector[i].first << " length : " << position_length_vector[i].second << endl;

+	}

+	

+	return result;

+}//dominant_intervals

+

+

+std::vector< size_t > Persistence_intervals::histograms_of_lengths( size_t number_of_bins )

+{

+    bool dbg = false;

+

+    if ( dbg )cerr << "this->intervals.size() : " << this->intervals.size() << endl;

+    //first find the length of the longest interval:

+    double lengthOfLongest = 0;

+    for ( size_t i = 0  ; i != this->intervals.size() ; ++i )

+    {

+        if ( (this->intervals[i].second - this->intervals[i].first) > lengthOfLongest )

+        {

+            lengthOfLongest = this->intervals[i].second - this->intervals[i].first;

+        }

+    }

+

+    if ( dbg ){cerr << "lengthOfLongest : " << lengthOfLongest << endl;}

+

+	//this is a container we will use to store the resulting histogram

+    std::vector< size_t > result( number_of_bins + 1 , 0 );

+    

+    //for every persistence interval in our collection.

+    for ( size_t i = 0  ; i != this->intervals.size() ; ++i )

+    {

+		//compute its length relative to the length of the dominant interval:

+        double relative_length_of_this_interval = (this->intervals[i].second - this->intervals[i].first)/lengthOfLongest;

+        

+        //given the relative length (between 0 and 1) compute to which bin should it contribute. 

+        size_t position = (size_t)(relative_length_of_this_interval*number_of_bins);

+        

+        

+        ++result[position];

+        

+        if ( dbg )

+        {

+            cerr << "i : " << i << endl;

+            cerr << "Interval : [" << this->intervals[i].first << " , " << this->intervals[i].second << " ] \n";

+            cerr << "relative_length_of_this_interval : " << relative_length_of_this_interval << endl;

+            cerr << "position : " << position << endl;

+            getchar();

+        }

+    }

+

+    

+    if ( dbg ){for ( size_t i = 0 ; i != result.size() ; ++i )cerr << result[i] << endl;}

+    return result;

+}

+

+

+std::vector< size_t > Persistence_intervals::cumulative_histograms_of_lengths( size_t number_of_bins )

+{

+    std::vector< size_t > histogram = this->histograms_of_lengths( number_of_bins );

+    std::vector< size_t > result( histogram.size() );

+

+    size_t sum = 0;

+    for ( size_t i = 0 ; i != histogram.size() ; ++i )

+    {

+        sum += histogram[i];

+        result[i] = sum;

+    }

+    return result;

+}

+

+

+std::vector< double > Persistence_intervals::characteristic_function_of_diagram( double x_min , double x_max , size_t number_of_bins )

+{

+    bool dbg = false;

+

+    std::vector< double > result( number_of_bins );

+    std::fill( result.begin() , result.end() , 0 );

+

+    for ( size_t i = 0 ; i != this->intervals.size() ; ++i )

+    {

+        if ( dbg )

+        {

+            cerr << "Interval : " << this->intervals[i].first << " , " << this->intervals[i].second << endl;

+        }

+

+        size_t beginIt = 0;

+        if ( this->intervals[i].first < x_min )beginIt = 0;

+        if ( this->intervals[i].first >= x_max )beginIt = result.size();

+        if ( ( this->intervals[i].first > x_min ) && ( this->intervals[i].first < x_max ) )

+        {

+            beginIt = number_of_bins*(this->intervals[i].first-x_min)/(x_max - x_min);

+        }

+

+        size_t endIt;

+        if ( this->intervals[i].second < x_min )endIt = 0;

+        if ( this->intervals[i].second >= x_max )endIt = result.size();

+        if ( ( this->intervals[i].second > x_min ) && ( this->intervals[i].second < x_max ) )

+        {

+            endIt = number_of_bins*( this->intervals[i].second - x_min )/(x_max - x_min);

+        }

+

+        if ( beginIt > endIt ){beginIt = endIt;}

+

+        if ( dbg )

+        {

+            cerr << "beginIt : " << beginIt << endl;

+            cerr << "endIt : " << endIt << endl;

+        }

+

+

+        for ( size_t pos = beginIt ; pos != endIt ; ++pos )

+        {

+            result[pos] += ( (x_max - x_min)/(double)number_of_bins ) * ( this->intervals[i].second - this->intervals[i].first );

+        }

+        //cerr << "x_max : " << x_max << " x_min : " << x_min << " , number_of_bins : " << number_of_bins << " this->intervals[i].second : " << this->intervals[i].second <<  " this->intervals[i].first : " << this->intervals[i].first << endl;

+        if ( dbg )

+        {

+            cerr << "Result at this stage \n";

+            for ( size_t aa = 0 ; aa != result.size() ; ++aa )

+            {

+                cerr << result[aa] << " ";

+            }

+            cerr << endl;

+            //getchar();

+        }

+    }

+    return result;

+}//characteristic_function_of_diagram

+

+

+

+std::vector< double > Persistence_intervals::cumulative_characteristic_function_of_diagram( double x_min , double x_max , size_t number_of_bins )

+{

+    std::vector< double > intsOfBars = this->characteristic_function_of_diagram( x_min , x_max , number_of_bins );    

+    std::vector< double > result( intsOfBars.size() );

+    double sum = 0;

+    for ( size_t i = 0 ; i != intsOfBars.size() ; ++i )

+    {

+        sum += intsOfBars[i];

+        result[i] = sum;

+    }

+    return result;

+}//cumulative_characteristic_function_of_diagram

+

+

+template <typename T>

+bool compare_first_element_of_pair( const std::pair< T , bool >& f, const std::pair< T , bool >& s )

+{

+    return (f.first < s.first);

+}

+

+

+std::vector< std::pair< double , size_t > > Persistence_intervals::compute_persistent_betti_numbers()

+{	

+    std::vector< std::pair< double , bool > > places_where_pbs_change( 2*this->intervals.size() );

+

+    for ( size_t i = 0 ; i != this->intervals.size() ; ++i )

+    {

+        places_where_pbs_change[2*i] = std::make_pair( this->intervals[i].first , true );

+        places_where_pbs_change[2*i+1] = std::make_pair( this->intervals[i].second , false );

+    }

+

+    std::sort( places_where_pbs_change.begin() , places_where_pbs_change.end() , compare_first_element_of_pair<double> );

+    size_t pbn = 0;

+    std::vector< std::pair< double , size_t > > pbns( places_where_pbs_change.size() );

+    for ( size_t i = 0 ; i != places_where_pbs_change.size() ; ++i )

+    {

+        if ( places_where_pbs_change[i].second == true )

+        {

+            ++pbn;

+        }

+        else

+        {

+            --pbn;

+        }

+        pbns[i] = std::make_pair( places_where_pbs_change[i].first , pbn );

+    }    

+    return pbns;

+}

+

+

+

+

+

+

+inline double compute_euclidean_distance( const std::pair< double,double > & f , const std::pair< double,double > & s )

+{

+    return sqrt( (f.first-s.first)*(f.first-s.first) + (f.second-s.second)*(f.second-s.second) );

+}

+

+

+std::vector< double > Persistence_intervals::k_n_n( size_t k , size_t where_to_cut )

+{

+    bool dbg = false;

+    if ( dbg )

+    {

+        cerr << "Here are the intervals : \n";

+        for ( size_t i = 0 ; i != this->intervals.size() ; ++i )

+        {

+            cerr << "[ " << this->intervals[i].first << " , " << this->intervals[i].second << "] \n";

+        }

+        getchar();

+    }

+

+    std::vector< double > result;

+    //compute all to all distance between point in the diagram. Also, consider points in the diagonal with the infinite multiplicity.

+    std::vector< std::vector< double > > distances( this->intervals.size() );

+    for ( size_t i = 0 ; i != this->intervals.size() ; ++i )

+    {

+        std::vector<double> aa(this->intervals.size());

+        std::fill( aa.begin() , aa.end() , 0 );

+        distances[i] = aa;

+    }

+    std::vector< double > distances_from_diagonal( this->intervals.size() );

+    std::fill( distances_from_diagonal.begin() , distances_from_diagonal.end() , 0 );

+
    for ( size_t i = 0 ; i != this->intervals.size() ; ++i )

+    {

+        std::vector< double > distancesFromI;

+        for ( size_t j = i+1 ; j != this->intervals.size() ; ++j )

+        {

+            distancesFromI.push_back( compute_euclidean_distance( this->intervals[i] , this->intervals[j] ) );

+        }

+        //distances.push_back( distancesFromI );

+        //also add a distance from this guy to daigonal:

+        double distanceToDiagonal = compute_euclidean_distance( this->intervals[i] , std::make_pair( 0.5*(this->intervals[i].first + this->intervals[i].second) , 0.5*(this->intervals[i].first + this->intervals[i].second) ) );

+        distances_from_diagonal[i] = distanceToDiagonal;

+

+        if ( dbg )

+        {

+            cerr << "Here are the distances form the point : [" << this->intervals[i].first << " , " << this->intervals[i].second << "] in the diagram \n";

+            for ( size_t aa = 0 ; aa != distancesFromI.size() ; ++aa )

+            {

+                cerr << "To : " << i+aa << " : " << distancesFromI[aa] << " ";

+            }

+            cerr << endl;

+            getchar();

+        }

+

+        //filling in the distances matrix:

+        for ( size_t j = i+1 ; j != this->intervals.size() ; ++j  )

+        {

+            distances[i][j] = distancesFromI[j-i-1];

+            distances[j][i] = distancesFromI[j-i-1];

+        }

+    }

+    if ( dbg )

+    {

+        cerr << "Here is the distance matrix : \n";

+        for ( size_t i = 0 ; i != distances.size() ; ++i )

+        {

+            for ( size_t j = 0 ; j != distances.size() ; ++j )

+            {

+                cerr << distances[i][j] << " ";

+            }

+            cerr << endl;

+        }

+        cerr << endl << endl << "And here are the distances to the diagonal : " << endl;

+        for ( size_t i = 0 ; i != distances_from_diagonal. size() ; ++i )

+        {

+            cerr << distances_from_diagonal[i] << " ";

+        }

+        cerr << endl << endl;

+        getchar();

+    }

+

+    for ( size_t i = 0 ; i != this->intervals.size() ; ++i )

+    {

+        std::vector< double > distancesFromI = distances[i];

+        distancesFromI.push_back( distances_from_diagonal[i] );

+

+        //sort it:

+        std::sort( distancesFromI.begin() , distancesFromI.end() , std::greater<double>() );

+

+        if ( k > distancesFromI.size() )

+        {

+            if ( dbg )

+            {

+                cerr << "There are not enough neighbors in your set. We set the result to plus infty \n";

+            }

+            result.push_back( std::numeric_limits<double>::max() );

+        }

+        else

+        {

+            if ( distances_from_diagonal[i] > distancesFromI[k] )

+            {

+                if ( dbg )

+                {

+                    cerr << "The k-th n.n. is on a diagonal. Therefore we set up a distance to diagonal \n";

+                }

+                result.push_back( distances_from_diagonal[i] );

+            }

+            else

+            {

+                result.push_back( distancesFromI[k] );

+            }

+        }

+    }

+    std::sort( result.begin() , result.end() , std::greater<double>() );

+    result.resize( std::min( result.size() , where_to_cut ) );

+

+    return result;
+}

+

+

+std::pair<double,double> Persistence_intervals::min_max()

+{

+    double min_ = std::numeric_limits<int>::max();

+    double max_ = -std::numeric_limits<int>::max();

+    for ( size_t i = 0 ; i != this->intervals.size() ; ++i )

+    {

+        if ( this->intervals[i].first < min_ )min_ = this->intervals[i].first;

+        if ( this->intervals[i].second > max_ )max_ = this->intervals[i].second;

+    }

+    return std::make_pair( min_ , max_ );

+}

+

+double Persistence_intervals::project_to_R( int number_of_function )

+{

+	double result = 0;

+	

+	for ( size_t i = 0 ; i != this->intervals.size() ; ++i )

+	{

+		result += ( this->intervals[i].second - this->intervals[i].first )*( this->intervals[i].second - this->intervals[i].first );

+	}

+	

+	return result;

+}

+

+

+}//namespace gudhi stat

+}//namespace gudhi

+

+#endif

diff --git a/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscape.h b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscape.h
new file mode 100644
index 00000000..82ee5878
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscape.h
@@ -0,0 +1,1508 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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_landscapes_H
+#define Persistence_landscapes_H
+
+//standard include
+#include <cmath>
+#include <iostream>
+#include <vector>
+#include <limits>
+#include <fstream>
+#include <sstream>
+#include <algorithm>
+#include <unistd.h>
+
+
+//gudhi include
+#include <gudhi/abstract_classes/Abs_Vectorized_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_averages.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_distances.h>
+#include <gudhi/abstract_classes/Abs_Real_valued_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_scalar_product.h>
+#include <gudhi/concretizations/read_persitence_from_file.h>
+#include <gudhi/common.h>
+using namespace std;
+
+
+
+
+namespace Gudhi
+{
+namespace Gudhi_stat
+{
+
+
+
+
+
+
+/**
+ * Extra functions needed in construction of barcodes.
+**/
+double minus_length( std::pair<double,double> a )
+{
+    return a.first-a.second;
+}
+double birth_plus_deaths( std::pair<double,double> a )
+{
+    return a.first+a.second;
+}
+
+
+
+/**
+ * Given two points in R^2, the procedure compute the parameters A and B of the line y = Ax + B that crosses those two points.
+**/
+std::pair<double,double> compute_parameters_of_a_line( std::pair<double,double> p1 , std::pair<double,double> p2 )
+{
+    double a = (p2.second-p1.second)/( p2.first - p1.first );
+    double b = p1.second - a*p1.first;
+    return std::make_pair(a,b);
+}
+
+/**
+ * This procedure given two points which lies on the opposide sides of x axis, compute x for which the line connecting those two points crosses x axis.
+**/
+double find_zero_of_a_line_segment_between_those_two_points ( std::pair<double,double> p1, std::pair<double,double> p2 )
+{
+    if ( p1.first == p2.first )return p1.first;
+    if ( p1.second*p2.second > 0 )
+    {
+        std::ostringstream errMessage;
+        errMessage <<"In function find_zero_of_a_line_segment_between_those_two_points the agguments are: (" << p1.first << "," << p1.second << ") and (" << p2.first << "," << p2.second << "). There is no zero in line between those two points. Program terminated.";
+        std::string errMessageStr = errMessage.str();
+        const char* err = errMessageStr.c_str();
+        throw(err);
+    }
+    //we assume here, that x \in [ p1.first, p2.first ] and p1 and p2 are points between which we will put the line segment
+    double a = (p2.second - p1.second)/(p2.first - p1.first);
+    double b = p1.second - a*p1.first;
+    //cerr << "Line crossing points : (" << p1.first << "," << p1.second << ") oraz (" << p2.first << "," << p2.second << ") : \n";
+    //cerr << "a : " << a << " , b : " << b << " , x : " << x << endl;
+    return -b/a;
+}
+
+
+
+
+/**
+ * Lexicographical ordering of points	.
+**/
+bool compare_points_sorting( std::pair<double,double> f, std::pair<double,double> s )
+{
+    if ( f.first < s.first )
+    {
+        return true;
+    }
+    else
+    {//f.first >= s.first
+        if ( f.first > s.first )
+        {
+            return false;
+        }
+        else
+        {//f.first == s.first
+            if ( f.second > s.second )
+            {
+                return true;
+            }
+            else
+            {
+                return false;
+            }
+        }
+    }
+}
+
+
+
+/**
+ * This procedure takes two points in R^2 and a double value x. It conputes the line pasing through those two points and return the value of that linear function at x.
+**/
+double function_value ( std::pair<double,double> p1, std::pair<double,double> p2 , double x )
+{
+    //we assume here, that x \in [ p1.first, p2.first ] and p1 and p2 are points between which we will put the line segment
+    double a = (p2.second - p1.second)/(p2.first - p1.first);
+    double b = p1.second - a*p1.first;
+    return (a*x+b);
+}
+
+
+
+
+
+/**
+ * A clas implementing persistence landascpes data structures. For theroretical desciritpion, please consult a paper ''Statistical topological data analysis using persistence landscapes'' by Peter Bubenik.
+ * For details of algorithms, please consult ''A persistence landscapes toolbox for topological statistics'' by Peter Bubenik and Pawel Dlotko.
+ * Persistence landscapes allow vertorization, computations of distances, computations of projections to Real, computations of averages and scalar products. Therefore they implement suitable interfaces.
+**/
+class Persistence_landscape :
+								public Abs_Vectorized_topological_data ,
+								public Abs_Topological_data_with_distances,
+								public Abs_Real_valued_topological_data,
+								public Abs_Topological_data_with_averages,
+								public Abs_Topological_data_with_scalar_product
+{
+public:
+	/**
+	 * Default constructor.
+	**/
+    Persistence_landscape()
+    {
+		this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
+	}
+
+    /**
+	 * Constructor that takes as an input a vector of birth-death pairs.
+	**/
+    Persistence_landscape( const std::vector< std::pair< double , double > >& p );
+
+    /**
+	 * Assignement operator.
+	**/
+    Persistence_landscape& operator=( const Persistence_landscape& org );
+
+    /**
+	 * Copy constructor.
+	**/
+    Persistence_landscape(const Persistence_landscape&);
+
+    /**
+	 * 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 = 0);
+
+
+
+    /**
+     * This procedure loads a landscape from file. It erase all the data that was previously stored in this landscape.
+    **/
+    void load_landscape_from_file( const char* filename );
+
+
+    /**
+     * The procedure stores a landscape to a file. The file can be later used by a procedure load_landscape_from_file.
+    **/
+    void print_to_file( const char* filename )const;
+
+
+
+	/**
+	 * This function compute integral of the landscape (defined formally as sum of integrals on R of all landscape functions)
+	**/
+    double compute_integral_of_landscape()const;
+
+
+    /**
+	 * This function compute integral of the 'level'-level of a landscape.
+	**/
+    double compute_integral_of_landscape( size_t level )const;
+
+
+    /**
+	 * This function compute integral of the landscape p-th power of a landscape (defined formally as sum of integrals on R of p-th powers of all landscape functions)
+	**/
+	double compute_integral_of_landscape( double p )const;//this function compute integral of p-th power of landscape.
+
+
+    /**
+     * A function that computes the value of a landscape at a given point. The parameters of the function are: unsigned level and double x.
+     * The procedure will compute the value of the level-landscape at the point x.
+    **/
+    double compute_value_at_a_given_point( unsigned level , double x )const;
+
+    /**
+     * Writing landscape into a stream. A i-th level landscape starts with a string "lambda_i". Then the discontinuity points of the landscapes follows.
+     * Shall those points be joined with lines, we will obtain the i-th landscape function.
+    **/
+    friend std::ostream& operator<<(std::ostream& out, Persistence_landscape& land );
+
+
+
+
+
+	/**
+	 * A function that compute sum of two landscapes.
+	**/
+    friend Persistence_landscape add_two_landscapes ( const Persistence_landscape& land1 ,  const Persistence_landscape& land2 )
+    {
+        return operation_on_pair_of_landscapes< std::plus<double> >(land1,land2);
+    }
+
+    /**
+	 * A function that compute difference of two landscapes.
+	**/
+    friend Persistence_landscape subtract_two_landscapes ( const Persistence_landscape& land1 ,  const Persistence_landscape& land2 )
+    {
+        return operation_on_pair_of_landscapes< std::minus<double> >(land1,land2);
+    }
+
+	/**
+	 * An operator +, that compute sum of two landscapes.
+	**/
+    friend Persistence_landscape operator+( const Persistence_landscape& first , const Persistence_landscape& second )
+    {
+        return add_two_landscapes( first,second );
+    }
+
+	/**
+	 * An operator -, that compute difference of two landscapes.
+	**/
+    friend Persistence_landscape operator-( const Persistence_landscape& first , const Persistence_landscape& second )
+    {
+        return subtract_two_landscapes( first,second );
+    }
+
+	/**
+	 * An operator * that allows multipilication of a landscape by a real number.
+	**/
+    friend Persistence_landscape operator*( const Persistence_landscape& first , double con )
+    {
+        return first.multiply_lanscape_by_real_number_not_overwrite(con);
+    }
+
+	/**
+	 * An operator * that allows multipilication of a landscape by a real number (order of parameters swapped).
+	**/
+    friend Persistence_landscape operator*( double con , const Persistence_landscape& first  )
+    {
+        return first.multiply_lanscape_by_real_number_not_overwrite(con);
+    }
+
+	/**
+	 * Operator +=. The second parameter is persistnece landwscape.
+	**/
+    Persistence_landscape operator += ( const Persistence_landscape& rhs )
+    {
+        *this = *this + rhs;
+        return *this;
+    }
+
+	/**
+	 * Operator -=. The second parameter is persistnece landwscape.
+	**/
+    Persistence_landscape operator -= ( const Persistence_landscape& rhs )
+    {
+        *this = *this - rhs;
+        return *this;
+    }
+
+
+	/**
+	 * Operator *=. The second parameter is a real number by which the y values of all landscape functions are multiplied. The x-values remain unchanged. 
+	**/
+    Persistence_landscape operator *= ( double x )
+    {
+        *this = *this*x;
+        return *this;
+    }
+
+	/**
+	 * Operator /=. The second parameter is a real number.
+	**/
+    Persistence_landscape operator /= ( double x )
+    {
+        if ( x == 0 )throw( "In operator /=, division by 0. Program terminated." );
+        *this = *this * (1/x);
+        return *this;
+    }
+
+	/**
+	 * An operator to compare two persistence landscapes.
+	**/
+    bool operator == ( const Persistence_landscape& rhs  )const;
+
+
+    /**
+	 * An operator to compare two persistence landscapes.
+	**/
+    bool operator != ( const Persistence_landscape& rhs  )const
+    {
+		return !((*this) == rhs);
+	}
+
+
+	/**
+	 * Computations of maximum (y) value of landscape.
+	**/
+    double compute_maximum()const
+    {
+        double maxValue = 0;
+        if ( this->land.size() )
+        {
+            maxValue = -std::numeric_limits<int>::max();
+            for ( size_t i = 0 ; i != this->land[0].size() ; ++i )
+            {
+                if ( this->land[0][i].second > maxValue )maxValue = this->land[0][i].second;
+            }
+        }
+        return maxValue;
+    }
+
+	/**
+	 * Computations of a L^i norm of landscape, where i is the input parameter.
+	**/
+    double compute_norm_of_landscape( double i )
+    {
+        Persistence_landscape l;
+        if ( i != -1 )
+        {
+            return compute_discance_of_landscapes(*this,l,i);
+        }
+        else
+        {
+            return compute_max_norm_discance_of_landscapes(*this,l);
+        }
+    }
+
+	/**
+ 	 * An operator to compute the value of a landscape in the level 'level' at the argument 'x'.
+	**/
+    double operator()(unsigned level,double x)const{return this->compute_value_at_a_given_point(level,x);}
+
+	/**
+	 * Computations of L^{\infty} distance between two landscapes.
+	**/
+    friend double compute_max_norm_discance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second );
+    //friend double compute_max_norm_discance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second , unsigned& nrOfLand , double&x , double& y1, double& y2 );
+
+
+	/**
+	 * Computations of L^{p} distance between two landscapes. p is the parameter of the procedure.
+	**/
+    friend double compute_discance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second , int p );
+
+
+
+	/**
+	 * Function to compute absolute value of a PL function. The representation of persistence landscapes allow to store general PL-function. When computing distance betwen two landscapes, we compute difference between
+	 * them. In this case, a general PL-function with negative value can appear as a result. Then in order to compute distance, we need to take its absolute value. This is the purpose of this procedure.
+	**/
+    Persistence_landscape abs();
+
+	/**
+	 * Computes the number of landscape functions.
+	**/
+    size_t size()const{return this->land.size(); }
+
+	/**
+	 *  Computate maximal value of lambda-level landscape.
+	**/
+    double find_max( unsigned lambda )const;
+
+	/**
+	 * Function to compute inner (scalar) product of two landscapes.
+	**/
+    friend double compute_inner_product( const Persistence_landscape& l1 , const Persistence_landscape& l2 );
+
+
+
+
+	//concretization of abstract functions:
+
+	/**
+	 * The number of projections to R is defined to the number of nonzero landscape functions. I-th projection is an integral of i-th landscape function over whole R.
+	**/
+    double project_to_R( int number_of_function )
+    {
+		return this->compute_integral_of_landscape( (size_t)number_of_function );
+	}
+
+    std::vector<double> vectorize( int number_of_function )
+    {
+		//TODO, think of something smarter over here
+		std::vector<double> v;
+		if ( (size_t)number_of_function > this->land.size() )
+		{
+			return v;
+		}
+		v.reserve( this->land[number_of_function].size() );
+		for ( size_t i = 0 ; i != this->land[number_of_function].size() ; ++i )
+		{
+			v.push_back( this->land[number_of_function][i].second );
+		}
+		return v;
+	}
+    void compute_average( std::vector< Abs_Topological_data_with_averages* > to_average )
+    {
+		bool dbg = false;
+
+		std::vector< Persistence_landscape* > nextLevelMerge( to_average.size() );
+        for ( size_t i = 0 ; i != to_average.size() ; ++i )
+        {
+            nextLevelMerge[i] = (Persistence_landscape*)to_average[i];
+        }
+        bool is_this_first_level = true;//in the loop, we will create dynamically a unmber of intermediate complexes. We have to clean that up, but we cannot erase the initial andscapes we have
+										//to average. In this case, we simply check if the nextLevelMerge are the input landscapes or the ones created in that loop by usig this extra variable.
+
+        while ( nextLevelMerge.size() != 1 )
+        {
+            if ( dbg ){cerr << "nextLevelMerge.size() : " << nextLevelMerge.size() << endl;}
+            std::vector< Persistence_landscape* > nextNextLevelMerge;
+            nextNextLevelMerge.reserve( to_average.size() );
+            for ( size_t i = 0 ; i < nextLevelMerge.size() ; i=i+2 )
+            {
+                if ( dbg ){cerr << "i : " << i << endl;}
+                Persistence_landscape* l = new Persistence_landscape;
+                if ( i+1 != nextLevelMerge.size() )
+                {
+                    (*l) = (*nextLevelMerge[i])+(*nextLevelMerge[i+1]);
+                }
+                else
+                {
+                    (*l) = *nextLevelMerge[i];
+                }
+                nextNextLevelMerge.push_back( l );
+            }
+            if ( dbg ){cerr << "After this iteration \n";}
+
+            if ( !is_this_first_level )
+            {
+				//deallocate the memory if the vector nextLevelMerge do not consist of the initial landscapes
+				for ( size_t i = 0 ; i != nextLevelMerge.size() ; ++i )
+				{
+					delete nextLevelMerge[i];
+				}
+			}
+			is_this_first_level = false;
+            nextLevelMerge.swap(nextNextLevelMerge);
+        }
+        (*this) = (*nextLevelMerge[0]);
+        (*this) *= 1/( (double)to_average.size() );
+	}
+
+
+    double distance( const Abs_Topological_data_with_distances* second , double power = 1 )
+    {
+		if ( power != -1 )
+		{
+			return compute_discance_of_landscapes( *this , *((Persistence_landscape*)second) , power );
+		}
+		else
+		{
+			return compute_max_norm_discance_of_landscapes( *this , *((Persistence_landscape*)second) );
+		}
+	}
+
+
+	double compute_scalar_product( const Abs_Topological_data_with_scalar_product* second )
+	{
+		return compute_inner_product( (*this) , *((Persistence_landscape*)second) );
+	}
+
+
+	std::vector< std::vector< std::pair<double,double> > > output_for_visualization()
+	{
+		return this->land;
+	}
+	
+	
+	//a function used to create a gnuplot script for visualization of landscapes
+	void plot( const char* filename ,int from = -1, int to = -1 ,  double xRangeBegin = -1 , double xRangeEnd = -1 , double yRangeBegin = -1 , double yRangeEnd = -1 );
+
+
+protected:
+    std::vector< std::vector< std::pair<double,double> > > land;
+
+    void construct_persistence_landscape_from_barcode( const std::vector< std::pair< double , double > > & p );
+    Persistence_landscape multiply_lanscape_by_real_number_not_overwrite( double x )const;
+    void multiply_lanscape_by_real_number_overwrite( double x );
+    template < typename oper > friend Persistence_landscape operation_on_pair_of_landscapes ( const Persistence_landscape& land1 ,  const Persistence_landscape& land2 );
+    friend double compute_maximal_distance_non_symmetric( const Persistence_landscape& pl1, const Persistence_landscape& pl2 );
+
+    void set_up_numbers_of_functions_for_vectorization_and_projections_to_reals()
+	{
+		//warning, this function can be only called after filling in the intervals vector.
+		this->number_of_functions_for_vectorization = this->land.size();
+		this->number_of_functions_for_projections_to_reals = this->land.size();
+	}
+};
+
+
+Persistence_landscape::Persistence_landscape(const Persistence_landscape& oryginal)
+{
+    //std::cerr << "Running copy constructor \n";
+    std::vector< std::vector< std::pair<double,double> > > land( oryginal.land.size() );
+    for ( size_t i = 0 ; i != oryginal.land.size() ; ++i )
+    {
+        land[i].insert( land[i].end() , oryginal.land[i].begin() , oryginal.land[i].end() );
+    }
+    this->land = land;
+    this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
+}
+
+
+
+
+
+Persistence_landscape::Persistence_landscape(const char* filename , size_t dimension)
+{
+    bool dbg = false;
+
+    if ( dbg )
+    {
+        std::cerr << "Using constructor : Persistence_landscape(char* filename)" << std::endl;
+    }   
+    //standard file with barcode
+    std::vector< std::pair< double , double > > barcode = read_standard_file( filename );    
+    //gudhi file with barcode
+    //std::vector< std::pair< double , double > > barcode = read_gudhi_file( filename , dimension );        
+	this->construct_persistence_landscape_from_barcode( barcode );
+	this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
+}
+
+
+bool operatorEqualDbg = false;
+bool Persistence_landscape::operator == ( const Persistence_landscape& rhs  )const
+{
+    if ( this->land.size() != rhs.land.size() )
+    {
+        if (operatorEqualDbg)std::cerr << "1\n";
+        return false;
+    }
+    for ( size_t level = 0 ; level != this->land.size() ; ++level )
+    {
+        if ( this->land[level].size() != rhs.land[level].size() )
+        {
+            if (operatorEqualDbg)std::cerr << "this->land[level].size() : " << this->land[level].size() <<  "\n";
+            if (operatorEqualDbg)std::cerr << "rhs.land[level].size() : " << rhs.land[level].size() <<  "\n";
+            if (operatorEqualDbg)std::cerr << "2\n";
+            return false;
+        }
+        for ( size_t i = 0 ; i != this->land[level].size() ; ++i )
+        {
+            if ( !( almost_equal(this->land[level][i].first , rhs.land[level][i].first) && almost_equal(this->land[level][i].second , rhs.land[level][i].second) ) )
+            {
+				//cerr<< this->land[level][i].first << " , " <<  rhs.land[level][i].first << " and " << this->land[level][i].second << " , " << rhs.land[level][i].second << endl;
+                if (operatorEqualDbg)std::cerr << "this->land[level][i] : " << this->land[level][i].first << " " << this->land[level][i].second << "\n";
+                if (operatorEqualDbg)std::cerr << "rhs.land[level][i] : " << rhs.land[level][i].first << " " << rhs.land[level][i].second	 << "\n";
+                if (operatorEqualDbg)std::cerr << "3\n";
+                return false;
+            }
+        }
+    }
+    return true;
+}
+
+
+Persistence_landscape& Persistence_landscape::operator=( const Persistence_landscape& oryginal )
+{
+    std::vector< std::vector< std::pair<double,double> > > land( oryginal.land.size() );
+    for ( size_t i = 0 ; i != oryginal.land.size() ; ++i )
+    {
+        land[i].insert( land[i].end() , oryginal.land[i].begin() , oryginal.land[i].end() );
+    }
+    this->land = land;
+    return *this;
+}
+
+
+
+Persistence_landscape::Persistence_landscape( const std::vector< std::pair< double , double > > & p )
+{
+    this->construct_persistence_landscape_from_barcode( p );
+    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 )
+{
+	bool dbg = false;
+    if ( dbg ){cerr << "Persistence_landscape::Persistence_landscape( const std::vector< std::pair< double , double > >& p )" << endl;}
+
+	//this is a general algorithm to construct persistence landscapes.
+	std::vector< std::pair<double,double> > bars;
+	bars.insert( bars.begin() , p.begin() , p.end() );
+	std::sort( bars.begin() , bars.end() , compare_points_sorting );
+
+	if (dbg)
+	{
+		std::cerr << "Bars : \n";
+		for ( size_t i = 0 ; i != bars.size() ; ++i )
+		{
+			std::cerr << bars[i].first << " " << bars[i].second << "\n";
+		}
+		getchar();
+	}
+
+	std::vector< std::pair<double,double> > characteristicPoints(p.size());
+	for ( size_t i = 0 ; i != bars.size() ; ++i )
+	{
+		characteristicPoints[i] = std::make_pair((bars[i].first+bars[i].second)/2.0 , (bars[i].second - bars[i].first)/2.0);
+	}
+	std::vector< std::vector< std::pair<double,double> > > Persistence_landscape;
+	while ( !characteristicPoints.empty() )
+	{
+		if(dbg)
+		{
+			for ( size_t i = 0 ; i != characteristicPoints.size() ; ++i )
+			{
+				std::cout << "("  << characteristicPoints[i].first << " " << characteristicPoints[i].second << ")\n";
+			}
+			std::cin.ignore();
+		}
+
+		std::vector< std::pair<double,double> > lambda_n;
+		lambda_n.push_back( std::make_pair( -std::numeric_limits<int>::max() , 0 ) );
+		lambda_n.push_back( std::make_pair(minus_length(characteristicPoints[0]),0) );
+		lambda_n.push_back( characteristicPoints[0] );
+
+		if (dbg)
+		{
+			std::cerr << "1 Adding to lambda_n : (" << -std::numeric_limits<int>::max() << " " << 0  << ") , (" << minus_length(characteristicPoints[0]) << " " << 0 << ") , (" << characteristicPoints[0].first << " " << characteristicPoints[0].second << ") \n";
+		}
+
+		size_t i = 1;
+		std::vector< std::pair<double,double> >  newCharacteristicPoints;
+		while ( i < characteristicPoints.size() )
+		{
+			size_t p = 1;
+			if ( (minus_length(characteristicPoints[i]) >= minus_length(lambda_n[lambda_n.size()-1])) && (birth_plus_deaths(characteristicPoints[i]) > birth_plus_deaths(lambda_n[lambda_n.size()-1])) )
+			{
+				if ( minus_length(characteristicPoints[i]) < birth_plus_deaths(lambda_n[lambda_n.size()-1]) )
+				{
+					std::pair<double,double> point = std::make_pair( (minus_length(characteristicPoints[i])+birth_plus_deaths(lambda_n[lambda_n.size()-1]))/2 , (birth_plus_deaths(lambda_n[lambda_n.size()-1])-minus_length(characteristicPoints[i]))/2 );
+					lambda_n.push_back( point );
+					if (dbg)
+					{
+						std::cerr << "2 Adding to lambda_n : (" << point.first << " " << point.second << ")\n";
+					}
+
+
+					if ( dbg )
+					{
+						std::cerr << "characteristicPoints[i+p] : " << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << "\n";
+						std::cerr << "point : " << point.first << " " << point.second << "\n";
+						getchar();
+					}
+
+					while ( (i+p < characteristicPoints.size() ) && ( almost_equal(minus_length(point),minus_length(characteristicPoints[i+p])) ) && ( birth_plus_deaths(point) <= birth_plus_deaths(characteristicPoints[i+p]) ) )
+					{
+						newCharacteristicPoints.push_back( characteristicPoints[i+p] );
+						if (dbg)
+						{
+							std::cerr << "3.5 Adding to newCharacteristicPoints : (" << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << ")\n";
+							getchar();
+						}
+						++p;
+					}
+
+
+					newCharacteristicPoints.push_back( point );
+					if (dbg)
+					{
+						std::cerr << "4 Adding to newCharacteristicPoints : (" << point.first << " " << point.second << ")\n";
+					}
+
+
+					while ( (i+p < characteristicPoints.size() ) && ( minus_length(point) <= minus_length(characteristicPoints[i+p]) ) && (birth_plus_deaths(point)>=birth_plus_deaths(characteristicPoints[i+p])) )
+					{
+						newCharacteristicPoints.push_back( characteristicPoints[i+p] );
+						if (dbg)
+						{
+							std::cerr << "characteristicPoints[i+p] : " << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << "\n";
+							std::cerr << "point : " << point.first << " " << point.second << "\n";
+							std::cerr << "characteristicPoints[i+p] birth and death : " << minus_length(characteristicPoints[i+p]) << " , " << birth_plus_deaths(characteristicPoints[i+p]) << "\n";
+							std::cerr << "point birth and death : " << minus_length(point) << " , " << birth_plus_deaths(point) << "\n";
+
+							std::cerr << "3 Adding to newCharacteristicPoints : (" << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << ")\n";
+							getchar();
+						}
+						++p;
+					}
+
+				}
+				else
+				{
+					lambda_n.push_back( std::make_pair( birth_plus_deaths(lambda_n[lambda_n.size()-1]) , 0 ) );
+					lambda_n.push_back( std::make_pair( minus_length(characteristicPoints[i]) , 0 ) );
+					if (dbg)
+					{
+						std::cerr << "5 Adding to lambda_n : (" << birth_plus_deaths(lambda_n[lambda_n.size()-1]) << " " <<  0 << ")\n";
+						std::cerr << "5 Adding to lambda_n : (" << minus_length(characteristicPoints[i]) << " " << 0  << ")\n";
+					}
+				}
+				lambda_n.push_back( characteristicPoints[i] );
+				if (dbg)
+				{
+					std::cerr << "6 Adding to lambda_n : (" << characteristicPoints[i].first << " " << characteristicPoints[i].second << ")\n";
+				}
+			}
+			else
+			{
+				newCharacteristicPoints.push_back( characteristicPoints[i] );
+				if (dbg)
+				{
+					std::cerr << "7 Adding to newCharacteristicPoints : (" << characteristicPoints[i].first << " " << characteristicPoints[i].second << ")\n";
+				}
+			}
+			i = i+p;
+		}
+		lambda_n.push_back( std::make_pair(birth_plus_deaths(lambda_n[lambda_n.size()-1]),0) );
+		lambda_n.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) );
+
+		characteristicPoints = newCharacteristicPoints;
+
+		lambda_n.erase(std::unique(lambda_n.begin(), lambda_n.end()), lambda_n.end());
+		this->land.push_back( lambda_n );
+	}
+}
+
+
+
+//this function find maximum of lambda_n
+double Persistence_landscape::find_max( unsigned lambda )const
+{
+    if ( this->land.size() < lambda )return 0;
+    double maximum = -std::numeric_limits<int>::max();
+    for ( size_t i = 0 ; i != this->land[lambda].size() ; ++i )
+    {
+        if ( this->land[lambda][i].second > maximum )maximum = this->land[lambda][i].second;
+    }
+    return maximum;
+}
+
+
+double Persistence_landscape::compute_integral_of_landscape()const
+{
+    double result = 0;
+    for ( size_t i = 0 ; i != this->land.size() ; ++i )
+    {
+        for ( size_t nr = 2 ; nr != this->land[i].size()-1 ; ++nr )
+        {
+            //it suffices to compute every planar integral and then sum them ap for each lambda_n
+            result += 0.5*( this->land[i][nr].first - this->land[i][nr-1].first )*(this->land[i][nr].second + this->land[i][nr-1].second);
+        }
+    }
+    return result;
+}
+
+double Persistence_landscape::compute_integral_of_landscape( size_t  level )const
+{
+    double result = 0;
+    if ( level >= this->land.size() )
+    {
+		//this landscape function is constantly equal 0, so is the intergral.
+		return result;
+	}
+	//also negative landscapes are assumed to be zero.
+	if ( level < 0 )return 0;
+
+	for ( size_t nr = 2 ; nr != this->land[ level ].size()-1 ; ++nr )
+	{
+		//it suffices to compute every planar integral and then sum them ap for each lambda_n
+		result += 0.5*( this->land[ level ][nr].first - this->land[ level ][nr-1].first )*(this->land[ level ][nr].second + this->land[ level ][nr-1].second);
+	}
+
+    return result;
+}
+
+
+double Persistence_landscape::compute_integral_of_landscape( double p )const
+{
+	bool dbg = false;
+    double result = 0;
+    for ( size_t i = 0 ; i != this->land.size() ; ++i )
+    {
+        for ( size_t nr = 2 ; nr != this->land[i].size()-1 ; ++nr )
+        {
+            if (dbg)std::cout << "nr : " << nr << "\n";
+            //In this interval, the landscape has a form f(x) = ax+b. We want to compute integral of (ax+b)^p = 1/a * (ax+b)^{p+1}/(p+1)
+            std::pair<double,double> coef = compute_parameters_of_a_line( this->land[i][nr] , this->land[i][nr-1] );
+            double a = coef.first;
+            double b = coef.second;
+
+            if (dbg)std::cout << "(" << this->land[i][nr].first << "," << this->land[i][nr].second << ") , " << this->land[i][nr-1].first << "," << this->land[i][nr].second << ")" << std::endl;
+            if ( this->land[i][nr].first == this->land[i][nr-1].first )continue;
+            if ( a != 0 )
+            {
+                result += 1/(a*(p+1)) * ( pow((a*this->land[i][nr].first+b),p+1) - pow((a*this->land[i][nr-1].first+b),p+1));
+            }
+            else
+            {
+                result += ( this->land[i][nr].first - this->land[i][nr-1].first )*( pow(this->land[i][nr].second,p) );
+            }
+            if ( dbg )
+            {
+                std::cout << "a : " <<a << " , b : " << b << std::endl;
+                std::cout << "result : " << result << std::endl;
+            }
+        }
+        //if (compute_integral_of_landscapeDbg) std::cin.ignore();
+    }
+    return result;
+}
+
+
+//this is O(log(n)) algorithm, where n is number of points in this->land.
+double Persistence_landscape::compute_value_at_a_given_point( unsigned level , double x )const
+{
+	bool compute_value_at_a_given_pointDbg = false;
+    //in such a case lambda_level = 0.
+    if ( level > this->land.size() ) return 0;
+
+    //we know that the points in this->land[level] are ordered according to x coordinate. Therefore, we can find the point by using bisection:
+    unsigned coordBegin = 1;
+    unsigned coordEnd = this->land[level].size()-2;
+
+    if ( compute_value_at_a_given_pointDbg )
+    {
+        std::cerr << "Tutaj \n";
+        std::cerr << "x : " << x << "\n";
+        std::cerr << "this->land[level][coordBegin].first : " << this->land[level][coordBegin].first << "\n";
+        std::cerr << "this->land[level][coordEnd].first : " << this->land[level][coordEnd].first << "\n";
+    }
+
+    //in this case x is outside the support of the landscape, therefore the value of the landscape is 0.
+    if ( x <= this->land[level][coordBegin].first )return 0;
+    if ( x >= this->land[level][coordEnd].first )return 0;
+
+    if (compute_value_at_a_given_pointDbg)std::cerr << "Entering to the while loop \n";
+
+    while ( coordBegin+1 != coordEnd )
+    {
+        if (compute_value_at_a_given_pointDbg)
+        {
+            std::cerr << "coordBegin : " << coordBegin << "\n";
+            std::cerr << "coordEnd : " << coordEnd << "\n";
+            std::cerr << "this->land[level][coordBegin].first : " << this->land[level][coordBegin].first << "\n";
+            std::cerr << "this->land[level][coordEnd].first : " << this->land[level][coordEnd].first << "\n";
+        }
+
+
+        unsigned newCord = (unsigned)floor((coordEnd+coordBegin)/2.0);
+
+        if (compute_value_at_a_given_pointDbg)
+        {
+            std::cerr << "newCord : " << newCord << "\n";
+            std::cerr << "this->land[level][newCord].first : " << this->land[level][newCord].first << "\n";
+            std::cin.ignore();
+        }
+
+        if ( this->land[level][newCord].first <= x )
+        {
+            coordBegin = newCord;
+            if ( this->land[level][newCord].first == x )return this->land[level][newCord].second;
+        }
+        else
+        {
+            coordEnd = newCord;
+        }
+    }
+
+    if (compute_value_at_a_given_pointDbg)
+    {
+        std::cout << "x : " << x << " is between : " << this->land[level][coordBegin].first << " a  " << this->land[level][coordEnd].first << "\n";
+        std::cout << "the y coords are : " << this->land[level][coordBegin].second << " a  " << this->land[level][coordEnd].second << "\n";
+        std::cerr << "coordBegin : " << coordBegin << "\n";
+        std::cerr << "coordEnd : " << coordEnd << "\n";
+        std::cin.ignore();
+    }
+    return function_value( this->land[level][coordBegin] , this->land[level][coordEnd] , x );
+}
+
+std::ostream& operator<<(std::ostream& out, Persistence_landscape& land )
+{
+    for ( size_t level = 0 ; level != land.land.size() ; ++level )
+    {
+        out << "Lambda_" << level << ":" << std::endl;
+        for ( size_t i = 0 ; i != land.land[level].size() ; ++i )
+        {
+            if ( land.land[level][i].first == -std::numeric_limits<int>::max() )
+            {
+                out << "-inf";
+            }
+            else
+            {
+                if ( land.land[level][i].first == std::numeric_limits<int>::max() )
+                {
+                    out << "+inf";
+                }
+                else
+                {
+                    out << land.land[level][i].first;
+                }
+            }
+            out << " , " << land.land[level][i].second << std::endl;
+        }
+    }
+    return out;
+}
+
+
+
+
+void Persistence_landscape::multiply_lanscape_by_real_number_overwrite( double x )
+{
+    for ( size_t dim = 0 ; dim != this->land.size() ; ++dim )
+    {
+        for ( size_t i = 0 ; i != this->land[dim].size() ; ++i )
+        {
+             this->land[dim][i].second *= x;
+        }
+    }
+}
+
+bool AbsDbg = false;
+Persistence_landscape Persistence_landscape::abs()
+{
+    Persistence_landscape result;
+    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 oresult
+            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;
+}
+
+
+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 )
+    {
+        std::vector< std::pair<double,double> > lambda_dim( this->land[dim].size() );
+        for ( size_t i = 0 ; i != this->land[dim].size() ; ++i )
+        {
+            lambda_dim[i] = std::make_pair( this->land[dim][i].first , x*this->land[dim][i].second );
+        }
+        result[dim] = lambda_dim;
+    }
+    Persistence_landscape res;
+    //CHANGE
+    //res.land = result;
+    res.land.swap(result);
+    return res;
+}//multiply_lanscape_by_real_number_overwrite
+
+
+void Persistence_landscape::print_to_file( const char* filename )const
+{
+    std::ofstream write;
+    write.open(filename);
+    for ( size_t dim = 0 ; dim != this->land.size() ; ++dim )
+    {
+        write << "#lambda_" << dim << std::endl;
+        for ( size_t i = 1 ; i != this->land[dim].size()-1 ; ++i )
+        {
+            write << this->land[dim][i].first << "  " << this->land[dim][i].second << std::endl;
+        }
+    }
+    write.close();
+}
+
+void Persistence_landscape::load_landscape_from_file( const char* filename )
+{
+	bool dbg = false;
+	//removing the current content of the persistence landscape.
+	this->land.clear();
+
+
+	//this constructor reads persistence landscape form a file. This file have to be created by this software beforehead
+    std::ifstream in;
+    in.open( filename );
+	if ( !( access( filename, F_OK ) != -1 ) )
+	{
+		cerr << "The file : " << filename << " do not exist. The program will now terminate \n";
+		throw "The file from which you are trying to read the persistence landscape do not exist. The program will now terminate \n";
+	}
+
+    std::string line;
+    std::vector< std::pair<double,double> > landscapeAtThisLevel;
+
+    bool isThisAFirsLine = true;
+    while ( !in.eof() )
+    {
+        getline(in,line);
+        if ( !(line.length() == 0 || line[0] == '#') )
+        {
+            std::stringstream lineSS;
+            lineSS << line;
+            double beginn, endd;
+            lineSS >> beginn;
+            lineSS >> endd;
+            landscapeAtThisLevel.push_back( std::make_pair( beginn , endd ) );
+            if (dbg){std::cerr << "Reading a pont : " << beginn << " , " << endd << std::endl;}
+        }
+        else
+        {
+            if (dbg)
+            {
+                std::cout << "IGNORE LINE\n";
+                getchar();
+            }
+            if ( !isThisAFirsLine )
+            {
+                landscapeAtThisLevel.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) );
+                this->land.push_back(landscapeAtThisLevel);
+                std::vector< std::pair<double,double> > newLevelOdLandscape;
+                landscapeAtThisLevel.swap(newLevelOdLandscape);
+            }
+            landscapeAtThisLevel.push_back( std::make_pair( -std::numeric_limits<int>::max() , 0 ) );
+            isThisAFirsLine = false;
+        }
+	}
+	if ( landscapeAtThisLevel.size() > 1 )
+    {
+        //seems that the last line of the file is not finished with the newline sign. We need to put what we have in landscapeAtThisLevel to the constructed landscape.
+        landscapeAtThisLevel.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) );
+        this->land.push_back(landscapeAtThisLevel);
+    }
+
+    in.close();
+}
+
+
+template < typename T >
+Persistence_landscape operation_on_pair_of_landscapes ( const Persistence_landscape& land1 ,  const Persistence_landscape& land2 )
+{
+	bool operation_on_pair_of_landscapesDBG = false;
+    if ( operation_on_pair_of_landscapesDBG ){std::cout << "operation_on_pair_of_landscapes\n";std::cin.ignore();}
+    Persistence_landscape result;
+    std::vector< std::vector< std::pair<double,double> > > land( std::max( land1.land.size() , land2.land.size() ) );
+    result.land = land;
+    T oper;
+
+    for ( size_t i = 0 ; i != std::min( land1.land.size() , land2.land.size() ) ; ++i )
+    {
+        std::vector< std::pair<double,double> > lambda_n;
+        size_t p = 0;
+        size_t q = 0;
+        while ( (p+1 < land1.land[i].size()) && (q+1 < land2.land[i].size()) )
+        {
+            if ( operation_on_pair_of_landscapesDBG )
+            {
+                std::cerr << "p : " << p << "\n";
+                std::cerr << "q : " << q << "\n";
+                std::cout << "land1.land[i][p].first : " << land1.land[i][p].first << "\n";
+                std::cout << "land2.land[i][q].first : " << land2.land[i][q].first << "\n";
+            }
+
+            if ( land1.land[i][p].first < land2.land[i][q].first )
+            {
+                if ( operation_on_pair_of_landscapesDBG )
+                {
+                    std::cout << "first \n";
+                    std::cout << " function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) : "<<  function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) << "\n";
+                    //std::cout << "oper( " << land1.land[i][p].second <<"," << function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) << " : " << oper( land1.land[i][p].second , function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) ) << "\n";
+                }
+                lambda_n.push_back( 
+									std::make_pair( 
+									              land1.land[i][p].first , 
+									              oper( (double)land1.land[i][p].second , function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) ) 
+												  ) 
+								  );
+                ++p;
+                continue;
+            }
+            if ( land1.land[i][p].first > land2.land[i][q].first )
+            {
+                if ( operation_on_pair_of_landscapesDBG )
+                {
+                    std::cout << "Second \n";
+                    std::cout << "function_value("<< land1.land[i][p-1].first << " " << land1.land[i][p-1].second <<" ,"<< land1.land[i][p].first << " " << land1.land[i][p].second <<", " << land2.land[i][q].first<<" ) : " << function_value( land1.land[i][p-1] , land1.land[i][p-1] ,land2.land[i][q].first ) << "\n";
+                    std::cout << "oper( " << function_value( land1.land[i][p] , land1.land[i][p-1] ,land2.land[i][q].first ) <<"," << land2.land[i][q].second <<" : " << oper( land2.land[i][q].second , function_value( land1.land[i][p] , land1.land[i][p-1] ,land2.land[i][q].first ) ) << "\n";
+                }
+                lambda_n.push_back( std::make_pair( land2.land[i][q].first , oper( function_value( land1.land[i][p] , land1.land[i][p-1] ,land2.land[i][q].first ) , land2.land[i][q].second )  )  );
+                ++q;
+                continue;
+            }
+            if ( land1.land[i][p].first == land2.land[i][q].first )
+            {
+                if (operation_on_pair_of_landscapesDBG)std::cout << "Third \n";
+                lambda_n.push_back( std::make_pair( land2.land[i][q].first , oper( land1.land[i][p].second , land2.land[i][q].second ) ) );
+                ++p;++q;
+            }
+            if (operation_on_pair_of_landscapesDBG){std::cout << "Next iteration \n";getchar();}
+        }
+        while ( (p+1 < land1.land[i].size())&&(q+1 >= land2.land[i].size()) )
+        {
+            if (operation_on_pair_of_landscapesDBG)
+            {
+                std::cout << "New point : " << land1.land[i][p].first << "  oper(land1.land[i][p].second,0) : " <<  oper(land1.land[i][p].second,0) << std::endl;
+            }
+            lambda_n.push_back( std::make_pair(land1.land[i][p].first , oper(land1.land[i][p].second,0) ) );
+            ++p;
+        }
+        while ( (p+1 >= land1.land[i].size())&&(q+1 < land2.land[i].size()) )
+        {
+            if (operation_on_pair_of_landscapesDBG)
+            {
+                std::cout << "New point : " << land2.land[i][q].first << " oper(0,land2.land[i][q].second) : " <<  oper(0,land2.land[i][q].second) << std::endl;
+            }
+            lambda_n.push_back( std::make_pair(land2.land[i][q].first , oper(0,land2.land[i][q].second) ) );
+            ++q;
+        }
+        lambda_n.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) );
+        //CHANGE
+        //result.land[i] = lambda_n;
+        result.land[i].swap(lambda_n);
+    }
+    if ( land1.land.size() > std::min( land1.land.size() , land2.land.size() ) )
+    {
+        if (operation_on_pair_of_landscapesDBG){std::cout << "land1.land.size() > std::min( land1.land.size() , land2.land.size() )" << std::endl;}
+        for ( size_t i = std::min( land1.land.size() , land2.land.size() ) ; i != std::max( land1.land.size() , land2.land.size() ) ; ++i )
+        {
+            std::vector< std::pair<double,double> > lambda_n( land1.land[i] );
+            for ( size_t nr = 0 ; nr != land1.land[i].size() ; ++nr )
+            {
+                lambda_n[nr] = std::make_pair( land1.land[i][nr].first , oper( land1.land[i][nr].second , 0 ) );
+            }
+            //CHANGE
+            //result.land[i] = lambda_n;
+            result.land[i].swap(lambda_n);
+        }
+    }
+    if ( land2.land.size() > std::min( land1.land.size() , land2.land.size() ) )
+    {
+        if (operation_on_pair_of_landscapesDBG){std::cout << "( land2.land.size() > std::min( land1.land.size() , land2.land.size() ) ) " << std::endl;}
+        for ( size_t i = std::min( land1.land.size() , land2.land.size() ) ; i != std::max( land1.land.size() , land2.land.size() ) ; ++i )
+        {
+            std::vector< std::pair<double,double> > lambda_n( land2.land[i] );
+            for ( size_t nr = 0 ; nr != land2.land[i].size() ; ++nr )
+            {
+                lambda_n[nr] = std::make_pair( land2.land[i][nr].first , oper( 0 , land2.land[i][nr].second ) );
+            }
+            //CHANGE
+            //result.land[i] = lambda_n;
+            result.land[i].swap(lambda_n);
+        }
+    }
+    if ( operation_on_pair_of_landscapesDBG ){std::cout << "operation_on_pair_of_landscapes\n";std::cin.ignore();}
+    return result;
+}//operation_on_pair_of_landscapes
+
+
+
+double compute_maximal_distance_non_symmetric( const Persistence_landscape& pl1, const Persistence_landscape& pl2 )
+{
+    bool dbg = false;
+    if (dbg)std::cerr << " compute_maximal_distance_non_symmetric \n";
+    //this distance is not symmetric. It compute ONLY distance between inflection points of pl1 and pl2.
+    double maxDist = 0;
+    size_t minimalNumberOfLevels = std::min( pl1.land.size() , pl2.land.size() );
+    for ( size_t level = 0 ; level != minimalNumberOfLevels ; ++ level )
+    {
+        if (dbg)
+        {
+            std::cerr << "Level : " << level << std::endl;
+            std::cerr << "PL1 : \n";
+            for ( size_t i = 0 ; i  != pl1.land[level].size() ; ++i )
+            {
+                std::cerr << "(" <<pl1.land[level][i].first << "," << pl1.land[level][i].second << ") \n";
+            }
+            std::cerr << "PL2 : \n";
+            for ( size_t i = 0 ; i  != pl2.land[level].size() ; ++i )
+            {
+                std::cerr << "(" <<pl2.land[level][i].first << "," << pl2.land[level][i].second << ") \n";
+            }
+            std::cin.ignore();
+        }
+
+        int p2Count = 0;
+        for ( size_t i = 1 ; i != pl1.land[level].size()-1 ; ++i ) //w tym przypadku nie rozwarzam punktow w nieskocznosci
+        {
+            while ( true )
+            {
+                if (  (pl1.land[level][i].first>=pl2.land[level][p2Count].first) && (pl1.land[level][i].first<=pl2.land[level][p2Count+1].first)  )break;
+                p2Count++;
+            }
+            double val = fabs( function_value( pl2.land[level][p2Count] , pl2.land[level][p2Count+1] , pl1.land[level][i].first ) - pl1.land[level][i].second);
+            if ( maxDist <= val )maxDist = val;
+
+            if (dbg)
+            {
+                std::cerr << pl1.land[level][i].first <<"in [" << pl2.land[level][p2Count].first << "," <<  pl2.land[level][p2Count+1].first <<"] \n";
+                std::cerr << "pl1[level][i].second : " << pl1.land[level][i].second << std::endl;
+                std::cerr << "function_value( pl2[level][p2Count] , pl2[level][p2Count+1] , pl1[level][i].first ) : " << function_value( pl2.land[level][p2Count] , pl2.land[level][p2Count+1] , pl1.land[level][i].first ) << std::endl;
+                std::cerr << "val : "  << val << std::endl;
+                std::cin.ignore();
+            }
+        }
+    }
+
+    if (dbg)std::cerr << "minimalNumberOfLevels : " << minimalNumberOfLevels << std::endl;
+
+    if ( minimalNumberOfLevels < pl1.land.size() )
+    {
+        for ( size_t level = minimalNumberOfLevels ; level != pl1.land.size() ; ++ level )
+        {
+            for ( size_t i = 0 ; i != pl1.land[level].size() ; ++i )
+            {
+                if (dbg)std::cerr << "pl1[level][i].second  : " << pl1.land[level][i].second << std::endl;
+                if ( maxDist < pl1.land[level][i].second )maxDist = pl1.land[level][i].second;
+            }
+        }
+    }
+    return maxDist;
+}
+
+
+
+
+double compute_discance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second , int p )
+{
+	bool dbg = false;
+    //This is what we want to compute: (\int_{- \infty}^{+\infty}| first-second |^p)^(1/p). We will do it one step at a time:
+
+    //first-second :
+    Persistence_landscape lan = first-second;
+
+    //| first-second |:
+    lan = lan.abs();
+    
+    if ( dbg ){cerr << "Abs of difference ; " << lan << endl;getchar();}
+    
+	if ( p != -1 )
+	{
+		//\int_{- \infty}^{+\infty}| first-second |^p
+		double result;
+		if ( p != 1 )
+		{
+			if ( dbg )std::cerr << "Power != 1, compute integral to the power p\n";
+			result = lan.compute_integral_of_landscape( (double)p );
+		}
+		else
+		{
+			if ( dbg )std::cerr << "Power = 1, compute integral \n";
+			result = lan.compute_integral_of_landscape();
+		}
+		//(\int_{- \infty}^{+\infty}| first-second |^p)^(1/p)
+		return pow( result , 1/(double)p );
+	}
+	else
+	{
+		//p == -1
+		if ( dbg )std::cerr << "Power = -1, compute maximum \n";
+		return lan.compute_maximum();
+	}
+}
+
+double compute_max_norm_discance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second )
+{
+    return std::max( compute_maximal_distance_non_symmetric(first,second) , compute_maximal_distance_non_symmetric(second,first) );
+}
+
+
+bool comparePairsForMerging( std::pair< double , unsigned > first , std::pair< double , unsigned > second )
+{
+    return (first.first < second.first);
+}
+
+
+
+
+double compute_inner_product( const Persistence_landscape& l1 , const Persistence_landscape& l2 )
+{
+    bool dbg = false;
+    double result = 0;
+
+    for ( size_t level = 0 ; level != std::min( l1.size() , l2.size() ) ; ++level )
+    {
+        if ( dbg ){cerr << "Computing inner product for a level : " << level << endl;getchar();}
+        if ( l1.land[level].size() * l2.land[level].size() == 0 )continue;
+
+        //endpoints of the interval on which we will compute the inner product of two locally linear functions:
+        double x1 = -std::numeric_limits<int>::max();
+        double x2;
+        if ( l1.land[level][1].first < l2.land[level][1].first )
+        {
+            x2 = l1.land[level][1].first;
+        }
+        else
+        {
+            x2 = l2.land[level][1].first;
+        }
+
+        //iterators for the landscapes l1 and l2
+        size_t l1It = 0;
+        size_t l2It = 0;
+
+        while ( (l1It < l1.land[level].size()-1) && (l2It < l2.land[level].size()-1) )
+        {
+            //compute the value of a inner product on a interval [x1,x2]
+
+            double a,b,c,d;
+
+			if ( l1.land[level][l1It+1].first != l1.land[level][l1It].first )
+			{
+				a = (l1.land[level][l1It+1].second - l1.land[level][l1It].second)/(l1.land[level][l1It+1].first - l1.land[level][l1It].first);
+			}
+			else
+			{
+				a = 0;
+			}
+            b = l1.land[level][l1It].second - a*l1.land[level][l1It].first;
+            if ( l2.land[level][l2It+1].first != l2.land[level][l2It].first )
+            {
+				c = (l2.land[level][l2It+1].second - l2.land[level][l2It].second)/(l2.land[level][l2It+1].first - l2.land[level][l2It].first);
+			}
+			else
+			{
+				c = 0;
+			}
+            d = l2.land[level][l2It].second - c*l2.land[level][l2It].first;
+
+            double contributionFromThisPart
+            =
+            (a*c*x2*x2*x2/3 + (a*d+b*c)*x2*x2/2 + b*d*x2) - (a*c*x1*x1*x1/3 + (a*d+b*c)*x1*x1/2 + b*d*x1);
+
+            result += contributionFromThisPart;
+
+            if ( dbg )
+            {
+                cerr << "[l1.land[level][l1It].first,l1.land[level][l1It+1].first] : " << l1.land[level][l1It].first << " , " << l1.land[level][l1It+1].first << endl;
+                cerr << "[l2.land[level][l2It].first,l2.land[level][l2It+1].first] : " << l2.land[level][l2It].first << " , " << l2.land[level][l2It+1].first << endl;
+                cerr << "a : " << a << ", b : " << b << " , c: " << c << ", d : " << d << endl;
+                cerr << "x1 : " << x1 << " , x2 : " << x2 << endl;
+                cerr << "contributionFromThisPart : " << contributionFromThisPart << endl;
+                cerr << "result : " << result << endl;
+                getchar();
+            }
+
+            //we have two intervals in which functions are constant:
+            //[l1.land[level][l1It].first , l1.land[level][l1It+1].first]
+            //and
+            //[l2.land[level][l2It].first , l2.land[level][l2It+1].first]
+            //We also have an interval [x1,x2]. Since the intervals in the landscapes cover the whole R, then it is clear that x2
+            //is either l1.land[level][l1It+1].first of l2.land[level][l2It+1].first or both. Lets test it.
+            if ( x2 == l1.land[level][l1It+1].first )
+            {
+                if ( x2 == l2.land[level][l2It+1].first )
+                {
+                    //in this case, we increment both:
+                    ++l2It;
+                    if ( dbg ){cerr << "Incrementing both \n";}
+                }
+                else
+                {
+                    if ( dbg ){cerr << "Incrementing first \n";}
+                }
+                ++l1It;
+            }
+            else
+            {
+                //in this case we increment l2It
+                ++l2It;
+                if ( dbg ){cerr << "Incrementing second \n";}
+            }
+            //Now, we shift x1 and x2:
+            x1 = x2;
+            if ( l1.land[level][l1It+1].first < l2.land[level][l2It+1].first )
+            {
+                x2 = l1.land[level][l1It+1].first;
+            }
+            else
+            {
+                x2 = l2.land[level][l2It+1].first;
+            }
+
+        }
+
+    }
+    return result;
+}
+
+
+void Persistence_landscape::plot( const char* filename , int from, int to , double xRangeBegin , double xRangeEnd , double yRangeBegin , double yRangeEnd )
+{
+    //this program create a gnuplot script file that allows to plot persistence diagram.
+    ofstream out;
+
+    std::ostringstream nameSS;
+    nameSS << filename << "_GnuplotScript";
+    std::string nameStr = nameSS.str();
+    out.open( (char*)nameStr.c_str() );
+
+    if ( (xRangeBegin != -1) || (xRangeEnd != -1) || (yRangeBegin != -1) || (yRangeEnd != -1)  )
+    {
+        out << "set xrange [" << xRangeBegin << " : " << xRangeEnd << "]" << endl;
+        out << "set yrange [" << yRangeBegin << " : " << yRangeEnd << "]" << endl;
+    }
+
+    if ( from == -1 ){from = 0;}
+    if ( to == -1 ){to = this->land.size();}
+
+    out << "plot ";
+    for ( size_t lambda= std::min((size_t)from,this->land.size()) ; lambda != std::min((size_t)to,this->land.size()) ; ++lambda )
+    {
+        //out << "     '-' using 1:2 title 'l" << lambda << "' with lp";
+        out << "     '-' using 1:2 notitle with lp";
+        if ( lambda+1 != std::min((size_t)to,this->land.size()) )
+        {
+            out << ", \\";
+        }
+        out << endl;
+    }
+
+    for ( size_t lambda= std::min((size_t)from,this->land.size()) ; lambda != std::min((size_t)to,this->land.size()) ; ++lambda )
+    {
+        for ( size_t i = 1 ; i != this->land[lambda].size()-1 ; ++i )
+        {
+            out << this->land[lambda][i].first << " " << this->land[lambda][i].second << endl;
+        }
+        out << "EOF" << endl;
+    }
+    cout << "Gnuplot script to visualize persistence diagram written to the file: " << nameStr << ". Type load '" << nameStr << "' in gnuplot to visualize." << endl;
+}
+
+
+
+
+}//namespace gudhi stat
+}//namespace gudhi
+
+
+#endif
diff --git a/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscape_on_grid.h b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscape_on_grid.h
new file mode 100644
index 00000000..7afd515d
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscape_on_grid.h
@@ -0,0 +1,1255 @@
+#ifndef Persistence_landscape_on_grid_H_
+#define Persistence_landscape_on_grid_H_
+
+ 
+//standard include
+#include <iostream>
+#include <vector>
+#include <limits>
+#include <fstream>
+#include <sstream>
+#include <algorithm>
+#include <unistd.h>
+#include <cmath>
+
+
+//gudhi include
+#include <gudhi/abstract_classes/Abs_Vectorized_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_averages.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_distances.h>
+#include <gudhi/abstract_classes/Abs_Real_valued_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_scalar_product.h>
+#include <gudhi/concretizations/read_persitence_from_file.h>
+
+
+
+using namespace std;
+
+
+namespace Gudhi
+{
+namespace Gudhi_stat
+{
+
+/**
+ * Given two points in R^2, the procedure compute the parameters A and B of the line y = Ax + B that crosses those two points.
+**/
+std::pair<double,double> compute_parameters_of_a_line( std::pair<double,double> p1 , std::pair<double,double> p2 )
+{
+    double a = (p2.second-p1.second)/( p2.first - p1.first );
+    double b = p1.second - a*p1.first;
+    return std::make_pair(a,b);
+}
+
+struct greater
+{
+    template<class T>
+    bool operator()(T const &a, T const &b) const { return a > b; }
+};
+
+//double epsi = std::numeric_limits<double>::epsilon();
+double epsi = 0.000005;
+
+
+/**
+ *  A procedure used to compare doubles. Typically gien two doubles A and B, comparing A == B is not good idea. In this case, we use the procedure almostEqual with the epsi defined at
+ *  the top of the file. Setting up the epsi give the user a tolerance on what should be consider equal.
+**/
+inline bool almost_equal( double a , double b )
+{
+    if ( fabs(a-b) < epsi )
+        return true;
+    return false;
+}
+
+
+
+
+class Persistence_landscape_on_grid  :
+								public Abs_Vectorized_topological_data ,
+								public Abs_Topological_data_with_distances,
+								public Abs_Real_valued_topological_data,
+								public Abs_Topological_data_with_averages,
+								public Abs_Topological_data_with_scalar_product
+{
+public:
+	/**
+	 * Default constructor.
+	**/
+    Persistence_landscape_on_grid()
+    {
+		this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
+		this->grid_min = this->grid_max = 0;
+	}
+
+    /**
+	 * Constructor that takes as an input a vector of birth-death pairs.
+	**/
+    Persistence_landscape_on_grid( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ );
+
+    /**
+	 * Assignement operator.
+	**/
+    Persistence_landscape_on_grid& operator=( const Persistence_landscape_on_grid& org );
+
+    /**
+	 * Copy constructor.
+	**/
+    Persistence_landscape_on_grid(const Persistence_landscape_on_grid&);
+
+    /**
+	 * 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. The additional parameters of this procedure are: ranges of grid, resoltion of a grid
+	 * and the dimension of intervals that are need to be read from a file (in case of Gudhi format files). 
+	**/
+    Persistence_landscape_on_grid(const char* filename , double grid_min_, double grid_max_ , size_t number_of_points_ , size_t dimension_ = 0 );
+        
+    /**
+	 * 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. The additional parameter is the resoution of a grid. The remaning parameters are 
+	 * calculated based on data. 
+	**/
+    Persistence_landscape_on_grid(const char* filename , size_t number_of_points );
+
+
+    /**
+     * This procedure loads a landscape from file. It erase all the data that was previously stored in this landscape.
+    **/
+    void load_landscape_from_file( const char* filename );
+
+
+    /**
+     * The procedure stores a landscape to a file. The file can be later used by a procedure load_landscape_from_file.
+    **/
+    void print_to_file( const char* filename )const;
+
+
+
+	/**
+	 * This function compute integral of the landscape (defined formally as sum of integrals on R of all landscape functions)
+	**/
+    double compute_integral_of_landscape()const
+    {
+		size_t maximal_level = this->number_of_nonzero_levels();
+		double result = 0;
+		for ( size_t i = 0 ; i != maximal_level ; ++i )
+		{
+			result += this->compute_integral_of_landscape(i);
+		}
+		return result;
+	}
+
+
+    /**
+	 * This function compute integral of the 'level'-level of a landscape.
+	**/
+    double compute_integral_of_landscape( size_t level )const
+    {
+		bool dbg = false;
+		double result = 0;		
+		double dx = (this->grid_max - this->grid_min)/(double)(this->values_of_landscapes.size()-1);
+		
+		if ( dbg )
+		{			
+			cerr << "this->grid_max : " << this->grid_max << endl;
+			cerr << "this->grid_min : " << this->grid_min << endl;
+			cerr << "this->values_of_landscapes.size() : " << this->values_of_landscapes.size() << endl;
+			getchar();
+		}
+		
+		
+		double previous_x = this->grid_min-dx;
+		double previous_y = 0;
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			double current_x = previous_x + dx;
+			double current_y = 0;
+			if ( this->values_of_landscapes[i].size() > level )current_y = this->values_of_landscapes[i][level];
+		
+			if ( dbg )
+			{
+				cerr << "this->values_of_landscapes[i].size() : " << this->values_of_landscapes[i].size() << " , level : " << level << endl;	
+				if ( this->values_of_landscapes[i].size() > level )cerr << "this->values_of_landscapes[i][level] : " << this->values_of_landscapes[i][level] << endl;
+				cerr << "previous_y : " << previous_y << endl;
+				cerr << "current_y : " << current_y << endl;
+				cerr << "dx : " << dx << endl;
+				cerr << "0.5*dx*( previous_y + current_y ); " << 0.5*dx*( previous_y + current_y ) << endl;
+			}
+			
+			result += 0.5*dx*( previous_y + current_y );			
+			previous_x = current_x;
+			previous_y = current_y;
+		}
+		return result;
+	}
+
+	/**
+	 * This function compute integral of the landscape p-th power of a landscape (defined formally as sum of integrals on R of p-th powers of all landscape functions)
+	**/
+	double compute_integral_of_landscape( double p )const
+	{
+		size_t maximal_level = this->number_of_nonzero_levels();
+		double result = 0;
+		for ( size_t i = 0 ; i != maximal_level ; ++i )
+		{
+			result += this->compute_integral_of_landscape(p,i);
+		}
+		return result;
+	}
+
+    /**
+	 * This function compute integral of the landscape p-th power of a level of a landscape (defined formally as sum of integrals on R of p-th powers of all landscape functions)
+	**/	
+	double compute_integral_of_landscape( double p , size_t level )const
+	{
+		bool dbg = false;
+		
+		double result = 0;				
+		double dx = (this->grid_max - this->grid_min)/(double)(this->values_of_landscapes.size()-1);		
+		double previous_x = this->grid_min;
+		double previous_y = 0;
+		if ( this->values_of_landscapes[0].size() > level )previous_y = this->values_of_landscapes[0][level];
+		
+		if ( dbg )
+		{
+			cerr << "dx : " << dx << endl;
+			cerr << "previous_x : " << previous_x << endl;
+			cerr << "previous_y : " << previous_y << endl;
+			cerr << "power : " << p << endl;
+			getchar();
+		}
+		
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			double current_x = previous_x + dx;
+			double current_y = 0;
+			if ( this->values_of_landscapes[i].size() > level )current_y = this->values_of_landscapes[i][level];
+			
+			if ( dbg )cerr << "current_y : " << current_y << endl;
+			
+			if ( current_y == previous_y )continue; 
+			
+			std::pair<double,double> coef = compute_parameters_of_a_line( std::make_pair( previous_x , previous_y ) , std::make_pair( current_x , current_y ) );
+			double a = coef.first;
+			double b = coef.second;
+			
+			if ( dbg )
+			{
+				cerr << "A line passing through points : (" << previous_x << "," << previous_y << ") and (" << current_x << "," << current_y << ") is : " << a << "x+" << b << endl;
+			}
+			
+			//In this interval, the landscape has a form f(x) = ax+b. We want to compute integral of (ax+b)^p = 1/a * (ax+b)^{p+1}/(p+1)
+			double value_to_add = 0;
+			if ( a != 0 )
+			{			
+				value_to_add = 1/(a*(p+1)) * ( pow((a*current_x+b),p+1) - pow((a*previous_x+b),p+1));				
+			}
+			else
+			{
+				value_to_add = ( current_x - previous_x )*( pow(b,p) );
+			}				
+			result += value_to_add;
+			if ( dbg )
+			{
+				cerr << "Increasing result by : " << value_to_add << endl;
+				cerr << "restult : " << result << endl;
+				getchar();
+			}		
+			previous_x = current_x;
+			previous_y = current_y;
+		}		
+		if ( dbg )cerr << "The total result is : " << result << endl;
+		return result;
+	}
+	
+	/**
+     * Writing landscape into a stream. A i-th level landscape starts with a string "lambda_i". Then the discontinuity points of the landscapes follows.
+     * Shall those points be joined with lines, we will obtain the i-th landscape function.
+    **/
+    friend std::ostream& operator<<(std::ostream& out, const Persistence_landscape_on_grid& land )
+	{
+		double dx = (land.grid_max - land.grid_min)/(double)(land.values_of_landscapes.size()-1);
+		double x = land.grid_min;
+		for ( size_t i = 0 ; i != land.values_of_landscapes.size() ; ++i )
+		{
+			out << x << " : ";
+			for ( size_t j = 0 ; j != land.values_of_landscapes[i].size() ; ++j )
+			{
+				out << land.values_of_landscapes[i][j] << " ";
+			}
+			out << endl;
+			x += dx;
+		}
+		return out;
+	}
+
+
+    /**
+     * A function that computes the value of a landscape at a given point. The parameters of the function are: unsigned level and double x.
+     * The procedure will compute the value of the level-landscape at the point x.
+    **/
+    double compute_value_at_a_given_point( unsigned level , double x )const
+    {
+		bool dbg = false;
+		if ( (x < this->grid_min) || (x > this->grid_max) )return 0;
+		
+		//find a position of a vector closest to x:
+		double dx = (this->grid_max - this->grid_min)/(double)(this->values_of_landscapes.size()-1);
+		size_t position = size_t((x-this->grid_min)/dx);
+		
+		if ( dbg )
+		{
+			std::cerr << "This is a procedure compute_value_at_a_given_point \n";
+			std::cerr << "level : " << level << endl;
+			std::cerr << "x : " << x << endl;
+			std::cerr << "psoition : " << position << endl;
+		}
+		//check if we are not exacly in the grid point:
+		if ( almost_equal( position*dx+ this->grid_min ,  x) )
+		{
+			if ( this->values_of_landscapes[position].size() < level )
+			{
+				return this->values_of_landscapes[position][level];
+			}
+			else
+			{
+				return 0;
+			}
+		}
+		//in the other case, approximate with a line:
+		std::pair<double,double> line;
+		if ( (this->values_of_landscapes[position].size() > level) && (this->values_of_landscapes[position+1].size() > level) )
+		{
+			line = compute_parameters_of_a_line( std::make_pair( position*dx+ this->grid_min , this->values_of_landscapes[position][level] ) , std::make_pair( (position+1)*dx+ this->grid_min , this->values_of_landscapes[position+1][level] ) );
+		}
+		else
+		{
+			if ( (this->values_of_landscapes[position].size() > level) || (this->values_of_landscapes[position+1].size() > level) )
+			{
+				if ( (this->values_of_landscapes[position].size() > level) )
+				{
+						line = compute_parameters_of_a_line( std::make_pair( position*dx+ this->grid_min , this->values_of_landscapes[position][level] ) , std::make_pair( (position+1)*dx+ this->grid_min , 0 ) );
+				}
+				else
+				{
+					//(this->values_of_landscapes[position+1].size() > level)
+					line = compute_parameters_of_a_line( std::make_pair( position*dx+ this->grid_min , 0 ) , std::make_pair( (position+1)*dx+ this->grid_min , this->values_of_landscapes[position+1][level] ) );	
+				}
+			}
+			else
+			{
+				return 0;
+			}
+		}
+		//compute the value of the linear function parametrized by line on a point x:
+		return line.first*x+line.second;
+	}
+    
+
+	/**
+	 * A function that compute sum of two landscapes.
+	**/
+    friend Persistence_landscape_on_grid add_two_landscapes ( const Persistence_landscape_on_grid& land1 ,  const Persistence_landscape_on_grid& land2 )
+    {
+        return operation_on_pair_of_landscapes_on_grid< std::plus<double> >(land1,land2);
+    }
+
+    /**
+	 * A function that compute difference of two landscapes.
+	**/
+    friend Persistence_landscape_on_grid subtract_two_landscapes ( const Persistence_landscape_on_grid& land1 ,  const Persistence_landscape_on_grid& land2 )
+    {
+        return operation_on_pair_of_landscapes_on_grid< std::minus<double> >(land1,land2);
+    }
+
+	/**
+	 * An operator +, that compute sum of two landscapes.
+	**/
+    friend Persistence_landscape_on_grid operator+( const Persistence_landscape_on_grid& first , const Persistence_landscape_on_grid& second )
+    {
+        return add_two_landscapes( first,second );
+    }
+
+	/**
+	 * An operator -, that compute difference of two landscapes.
+	**/
+    friend Persistence_landscape_on_grid operator-( const Persistence_landscape_on_grid& first , const Persistence_landscape_on_grid& second )
+    {
+        return subtract_two_landscapes( first,second );
+    }
+
+	/**
+	 * An operator * that allows multipilication of a landscape by a real number.
+	**/
+    friend Persistence_landscape_on_grid operator*( const Persistence_landscape_on_grid& first , double con )
+    {
+        return first.multiply_lanscape_by_real_number_not_overwrite(con);
+    }
+
+	/**
+	 * An operator * that allows multipilication of a landscape by a real number (order of parameters swapped).
+	**/
+    friend Persistence_landscape_on_grid operator*( double con , const Persistence_landscape_on_grid& first  )
+    {
+        return first.multiply_lanscape_by_real_number_not_overwrite(con);
+    }
+
+	friend bool check_if_defined_on_the_same_domain( const Persistence_landscape_on_grid& land1, const Persistence_landscape_on_grid& land2 )
+	{
+		if ( land1.values_of_landscapes.size() != land2.values_of_landscapes.size() )return false;
+		if ( land1.grid_min != land2.grid_min )return false;
+		if ( land1.grid_max != land2.grid_max )return false;
+		return true;
+	}
+
+	/**
+	 * Operator +=. The second parameter is persistnece landwscape.
+	**/
+    Persistence_landscape_on_grid operator += ( const Persistence_landscape_on_grid& rhs )
+    {
+        *this = *this + rhs;
+        return *this;
+    }
+
+	/**
+	 * Operator -=. The second parameter is persistnece landwscape.
+	**/
+    Persistence_landscape_on_grid operator -= ( const Persistence_landscape_on_grid& rhs )
+    {
+        *this = *this - rhs;
+        return *this;
+    }
+
+
+	/**
+	 * Operator *=. The second parameter is a real number by which the y values of all landscape functions are multiplied. The x-values remain unchanged. 
+	**/
+    Persistence_landscape_on_grid operator *= ( double x )
+    {
+        *this = *this*x;
+        return *this;
+    }
+
+	/**
+	 * Operator /=. The second parameter is a real number.
+	**/
+    Persistence_landscape_on_grid operator /= ( double x )
+    {
+        if ( x == 0 )throw( "In operator /=, division by 0. Program terminated." );
+        *this = *this * (1/x);
+        return *this;
+    }
+
+	/**
+	 * An operator to compare two persistence landscapes.
+	**/
+    bool operator == ( const Persistence_landscape_on_grid& rhs  )const
+    {
+		bool dbg = true;
+		if ( ! this->values_of_landscapes.size() == rhs.values_of_landscapes.size() )
+		{
+			if (dbg) cerr << "values_of_landscapes of incompatable sizes\n";
+			return false;
+		}
+		if ( !almost_equal( this->grid_min , rhs.grid_min ) )
+		{
+			if (dbg) cerr << "grid_min not equal\n";
+			return false; 
+		}
+		if ( !almost_equal(this->grid_max,rhs.grid_max ) )
+		{	
+			if (dbg) cerr << "grid_max not equal\n";
+			return false;		
+		}
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{					
+			for ( size_t aa = 0 ; aa != this->values_of_landscapes[i].size() ; ++aa )
+			{
+				if ( !almost_equal( this->values_of_landscapes[i][aa]  , rhs.values_of_landscapes[i][aa]  ) )
+				{					
+					if (dbg) 
+					{
+						cerr << "Problem in the position : " << i << " of values_of_landscapes. \n";
+						cerr << this->values_of_landscapes[i][aa]   << " " <<  rhs.values_of_landscapes[i][aa] << endl;
+					}
+					return false;
+				}
+			}				
+		}	
+		return true;
+	}
+
+
+    /**
+	 * An operator to compare two persistence landscapes.
+	**/
+    bool operator != ( const Persistence_landscape_on_grid& rhs  )const
+    {
+		return !((*this) == rhs);
+	}
+
+
+	/**
+	 * Computations of maximum (y) value of landscape.
+	**/
+    double compute_maximum()const
+    {
+       //since the function can only be entirely positive or negative, the maximal value will be an extremal value in the arrays:
+		double max_value = -std::numeric_limits<double>::max();
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			if ( this->values_of_landscapes[i].size() )
+			{
+				if ( this->values_of_landscapes[i][0] > max_value )max_value = this->values_of_landscapes[i][0];
+				if ( this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ] > max_value )max_value = this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ];
+			}
+		}
+		return max_value;        
+    }
+    
+    /**
+	 * Computations of minimum and maximum value of landscape.
+	**/
+    std::pair<double,double> compute_minimum_maximum()const
+    {        
+       //since the function can only be entirely positive or negative, the maximal value will be an extremal value in the arrays:
+		double max_value = -std::numeric_limits<double>::max();
+		double min_value = 0;
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			if ( this->values_of_landscapes[i].size() )
+			{
+				if ( this->values_of_landscapes[i][0] > max_value )max_value = this->values_of_landscapes[i][0];
+				if ( this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ] > max_value )max_value = this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ];
+				
+				if ( this->values_of_landscapes[i][0] < min_value )min_value = this->values_of_landscapes[i][0];
+				if ( this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ] < min_value )min_value = this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ];
+			}
+		}
+		return std::make_pair(min_value , max_value);
+    }
+    
+    /**
+     * This function computes maximal lambda for which lambda-level landscape is nonzero.
+    **/
+    size_t number_of_nonzero_levels()const
+    {
+		size_t result = 0;
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			if ( this->values_of_landscapes[i].size() > result )result = this->values_of_landscapes[i].size();
+		}
+		return result;
+	}
+
+	/**
+	 * Computations of a L^i norm of landscape, where i is the input parameter.
+	**/
+    double compute_norm_of_landscape( double i )
+    {
+		std::vector< std::pair< double , double > > p;
+        Persistence_landscape_on_grid l(p,this->grid_min,this->grid_max,this->values_of_landscapes.size()-1);       
+        
+        if ( i != -1 )
+        {
+            return compute_discance_of_landscapes_on_grid(*this,l,i);
+        }
+        else
+        {
+            return compute_max_norm_discance_of_landscapes(*this,l);
+        }
+    }
+
+	/**
+ 	 * An operator to compute the value of a landscape in the level 'level' at the argument 'x'.
+	**/
+    double operator()(unsigned level,double x)const{return this->compute_value_at_a_given_point(level,x);}
+
+	/**
+	 * Computations of L^{\infty} distance between two landscapes.
+	**/
+    friend double compute_max_norm_discance_of_landscapes( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& second );
+    //friend double compute_max_norm_discance_of_landscapes( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& second , unsigned& nrOfLand , double&x , double& y1, double& y2 );
+
+
+
+
+	/**
+	 * Function to compute absolute value of a PL function. The representation of persistence landscapes allow to store general PL-function. When computing distance betwen two landscapes, we compute difference between
+	 * them. In this case, a general PL-function with negative value can appear as a result. Then in order to compute distance, we need to take its absolute value. This is the purpose of this procedure.
+	**/
+    void abs()
+    {
+		//Be careful here. We assume that the functions are either entirely positive or negative. They do not change signs. That is why I can implemnt abs in the way presented below:
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			for ( size_t j = 0 ; j != this->values_of_landscapes[i].size() ; ++j )
+			{
+				this->values_of_landscapes[i][j] = std::abs( this->values_of_landscapes[i][j] );
+			}
+		}
+	}
+
+	/**
+	 * Computes the number of landscape functions.
+	**/
+    size_t size()const{return this->number_of_nonzero_levels(); }
+
+	/**
+	 *  Computate maximal value of lambda-level landscape.
+	**/
+    double find_max( unsigned lambda )const
+    {		
+		double max_value = -std::numeric_limits<double>::max();
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			if ( this->values_of_landscapes[i].size() > lambda )
+			{
+				if ( this->values_of_landscapes[i][lambda] > max_value )max_value = this->values_of_landscapes[i][lambda];				
+			}
+		}
+		return max_value;
+	}
+
+	/**
+	 * Function to compute inner (scalar) product of two landscapes.
+	**/
+    friend double compute_inner_product( const Persistence_landscape_on_grid& l1 , const Persistence_landscape_on_grid& l2 )
+    {
+		if ( !check_if_defined_on_the_same_domain(l1,l2) )throw "Landscapes are not defined on the same grid, the program will now terminate";
+		size_t maximal_level = l1.number_of_nonzero_levels();
+		double result = 0;
+		for ( size_t i = 0 ; i != maximal_level ; ++i )
+		{
+			result += compute_inner_product(l1,l2,i);
+		}
+		return result;
+	}
+
+	
+	
+	/**
+	 * Function to compute inner (scalar) product of given levels of two landscapes.
+	**/
+    friend double compute_inner_product( const Persistence_landscape_on_grid& l1 , const Persistence_landscape_on_grid& l2 , size_t level )
+    {
+		bool dbg = false;
+		
+		if ( !check_if_defined_on_the_same_domain(l1,l2) )throw "Landscapes are not defined on the same grid, the program will now terminate";
+		double result = 0;
+		
+		double dx = (l1.grid_max - l1.grid_min)/(double)(l1.values_of_landscapes.size()-1);
+		
+		double previous_x = l1.grid_min-dx;
+		double previous_y_l1 = 0;
+		double previous_y_l2 = 0;
+		for ( size_t i = 0 ; i != l1.values_of_landscapes.size() ; ++i )
+		{
+			if ( dbg )std::cerr << "i : " << i << std::endl;
+			
+			double current_x = previous_x + dx;
+			double current_y_l1 = 0;
+			if ( l1.values_of_landscapes[i].size() > level )current_y_l1 = l1.values_of_landscapes[i][level];
+			
+			double current_y_l2 = 0;
+			if ( l2.values_of_landscapes[i].size() > level )current_y_l2 = l2.values_of_landscapes[i][level];
+			
+			if ( dbg )
+			{
+				std::cerr << "previous_x  : " << previous_x << std::endl;
+				std::cerr << "previous_y_l1 : " << previous_y_l1 << std::endl;
+				std::cerr << "current_y_l1 : " << current_y_l1 << std::endl;
+				std::cerr << "previous_y_l2 : " << previous_y_l2 << std::endl;
+				std::cerr << "current_y_l2 : " << current_y_l2 << std::endl;
+			}
+			
+			std::pair<double,double> l1_coords = compute_parameters_of_a_line( std::make_pair( previous_x , previous_y_l1 ) , std::make_pair( current_x , current_y_l1 ) );			
+			std::pair<double,double> l2_coords = compute_parameters_of_a_line( std::make_pair( previous_x , previous_y_l2 ) , std::make_pair( current_x , current_y_l2 ) );
+			
+			//let us assume that the first line is of a form y = ax+b, and the second one is of a form y = cx + d. Then here are a,b,c,d:
+			double a = l1_coords.first;
+			double b = l1_coords.second;
+			
+			double c = l2_coords.first;
+			double d = l2_coords.second;
+			
+			if ( dbg )
+			{
+				std::cerr << "Here are the formulas for a line: \n";
+				std::cerr << "a : " << a << std::endl;
+				std::cerr << "b : " << b << std::endl;
+				std::cerr << "c : " << c << std::endl;
+				std::cerr << "d : " << d << std::endl;				
+			}
+			
+			//now, to compute the inner product in this interval we need to compute the integral of (ax+b)(cx+d) = acx^2 + (ad+bc)x + bd in the interval from previous_x to current_x:
+			//The integal is ac/3*x^3 + (ac+bd)/2*x^2 + bd*x
+		
+			double added_value = (a*c/3*current_x*current_x*current_x + (a*d+b*c)/2*current_x*current_x + b*d*current_x)-
+			          (a*c/3*previous_x*previous_x*previous_x + (a*d+b*c)/2*previous_x*previous_x + b*d*previous_x);
+
+			if ( dbg )
+			{
+				std::cerr << "Value of the integral on the left end ie : " << previous_x << " is : " <<  a*c/3*previous_x*previous_x*previous_x + (a*d+b*c)/2*previous_x*previous_x + b*d*previous_x << std::endl;
+				std::cerr << "Value of the integral on the right end i.e. : " << current_x << " is " << a*c/3*current_x*current_x*current_x + (a*d+b*c)/2*current_x*current_x + b*d*current_x << std::endl;
+			}
+		
+			result += added_value;
+			
+			if ( dbg )
+			{
+				std::cerr << "added_value : " << added_value << std::endl;
+				std::cerr << "result : " << result << std::endl;
+				getchar();
+			}
+			
+			
+			previous_x = current_x;
+			previous_y_l1 = current_y_l1;
+			previous_y_l2 = current_y_l2;
+			
+		}		
+		return result;
+	}
+
+
+
+
+	//concretization of abstract functions:
+
+	/**
+	 * The number of projections to R is defined to the number of nonzero landscape functions. I-th projection is an integral of i-th landscape function over whole R.
+	**/
+    double project_to_R( int number_of_function )
+    {
+		return this->compute_integral_of_landscape( (size_t)number_of_function );
+	}
+
+    std::vector<double> vectorize( int number_of_function )
+    {
+		//TODO, think of something smarter over here
+		if ( ( number_of_function < 0 ) || ( (size_t)number_of_function >= this->values_of_landscapes.size() ) )
+		{
+			throw "Wrong number of function\n";
+		}
+		std::vector<double> v = this->values_of_landscapes[ number_of_function ];
+		return v;
+	}
+	
+	/**
+	 * A function to compute averaged persistence landscape on a grid, based on vector of persistence landscapes on grid (projected to Abs_Topological_data_with_averages*, since this is a concretization of a virtual method.
+	**/  
+    void compute_average( std::vector< Abs_Topological_data_with_averages* > to_average )
+    {
+		
+		bool dbg = false;
+		//After execution of this procedure, the average is supposed to be in the current object. To make sure that this is the case, we need to do some cleaning first.
+		this->values_of_landscapes.clear();
+		this->grid_min = this->grid_max = 0;
+		
+		//if there is nothing to averate, then the average is a zero landscape. 
+		if ( to_average.size() == 0 )return;
+		
+		//now we need to check if the grids in all objects of to_average are the same:
+		for ( size_t i = 0 ; i != to_average.size() ; ++i )
+		{	
+			if ( !check_if_defined_on_the_same_domain(*((Persistence_landscape_on_grid*)(to_average[0])),*((Persistence_landscape_on_grid*)(to_average[i]))) )throw "Two grids are not compatible"; 				
+		}
+		
+		this->values_of_landscapes = std::vector< std::vector<double> >( ((Persistence_landscape_on_grid*)(to_average[0]))->values_of_landscapes.size() );
+		this->grid_min = ((Persistence_landscape_on_grid*)(to_average[0]))->grid_min;
+		this->grid_max = ((Persistence_landscape_on_grid*)(to_average[0]))->grid_max;
+		
+		if ( dbg )
+		{
+			cerr << "Computations of average. The data from the current landscape have been cleared. We are ready to do the computations. \n";
+		}
+						
+		//for every point in the grid:
+		for ( size_t grid_point = 0 ; grid_point != ((Persistence_landscape_on_grid*)(to_average[0]))->values_of_landscapes.size() ; ++grid_point )
+		{
+			
+			//set up a vector of the correct size:
+			size_t maximal_size_of_vector = 0;
+			for ( size_t land_no = 0 ; land_no != to_average.size() ; ++land_no )
+			{
+				if ( ((Persistence_landscape_on_grid*)(to_average[land_no]))->values_of_landscapes[grid_point].size() > maximal_size_of_vector )
+				maximal_size_of_vector = ((Persistence_landscape_on_grid*)(to_average[land_no]))->values_of_landscapes[grid_point].size();
+			}
+			this->values_of_landscapes[grid_point] = std::vector<double>( maximal_size_of_vector );
+			
+			if ( dbg )
+			{
+				cerr << "We are considering the point : " << grid_point << " of the grid. In this point, there are at most : " << maximal_size_of_vector << " nonzero landscape functions \n";
+			}
+		
+			//and compute an arythmetic average:
+			for ( size_t land_no = 0 ; land_no != to_average.size() ; ++land_no )
+			{
+				//summing:				
+				for ( size_t i = 0 ; i != ((Persistence_landscape_on_grid*)(to_average[land_no]))->values_of_landscapes[grid_point].size() ; ++i )
+				{
+					//compute the average in a smarter way.
+					this->values_of_landscapes[grid_point][i] += ((Persistence_landscape_on_grid*)(to_average[land_no]))->values_of_landscapes[grid_point][i];
+				}								
+			}
+			//normalizing:
+			for ( size_t i = 0 ; i != this->values_of_landscapes[grid_point].size() ; ++i )
+			{
+				this->values_of_landscapes[grid_point][i] /= (double)to_average.size();
+			}			 
+		}
+	}//compute_average
+	
+	
+	/**
+	 * Computations of L^{p} distance between two landscapes on a grid. p is the parameter of the procedure.
+	**/
+	friend double compute_discance_of_landscapes_on_grid( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& second , int p )
+	{		
+		bool dbg = false;
+		//This is what we want to compute: (\int_{- \infty}^{+\infty}| first-second |^p)^(1/p). We will do it one step at a time:
+
+		if ( dbg )
+		{
+			cerr << "first : " << first << endl;
+			cerr << "second : " << second << endl;
+			getchar();
+		}
+
+		//first-second :
+		Persistence_landscape_on_grid lan = first-second;
+		
+		if ( dbg )
+		{
+			cerr << "Difference : " << lan << endl;
+		}
+
+		//| first-second |:
+		lan.abs();
+		
+		if ( dbg )
+		{
+			cerr << "Abs : " << lan << endl;
+		}
+		
+		if ( p != -1 )
+		{
+			//\int_{- \infty}^{+\infty}| first-second |^p
+			double result;
+			if ( p != 1 )
+			{
+				if (dbg){cerr << "p : " << p << endl; getchar();}
+				result = lan.compute_integral_of_landscape( (double)p );				
+				if (dbg){cerr << "integral : " << result << endl;getchar();}
+			}
+			else
+			{
+				result = lan.compute_integral_of_landscape();			
+				if (dbg){cerr << "integral, wihtout power : " << result << endl;getchar();}
+			}
+			//(\int_{- \infty}^{+\infty}| first-second |^p)^(1/p)
+			return pow( result , 1/(double)p );
+		}
+		else
+		{
+			//p == -1
+			return lan.compute_maximum();
+		}
+	}
+
+	/**
+	* A function to compute distance between persistence landscape on a grid.
+	* The parameter of this functionis a persistence landscapes on grid (projected to Abs_Topological_data_with_averages*, since this is a concretization of a virtual method.
+	**/
+    double distance( const Abs_Topological_data_with_distances* second , double power = 1 )
+    {
+		if ( power != -1 )
+		{
+			return compute_discance_of_landscapes_on_grid( *this , *((Persistence_landscape_on_grid*)second) , power );
+		}
+		else
+		{
+			return compute_max_norm_discance_of_landscapes( *this , *((Persistence_landscape_on_grid*)second) );
+		}
+	}
+
+	/**
+	* A function to compute scalar product of persistence landscape on a grid.
+	* The parameter of this functionis a persistence landscapes on grid (projected to Abs_Topological_data_with_averages*, since this is a concretization of a virtual method.
+	**/
+	double compute_scalar_product( const Abs_Topological_data_with_scalar_product* second )
+	{
+		return compute_inner_product( (*this) , *((Persistence_landscape_on_grid*)second) );
+	}
+
+
+	/**
+	* A function that returns values of landsapes. It can be used for vizualization
+	**/
+	std::vector< std::vector< double > > output_for_visualization()
+	{
+		return this->values_of_landscapes;
+	}
+	
+	/**
+	* function used to create a gnuplot script for visualization of landscapes
+	**/ 
+	void plot( const char* filename , size_t from_ = std::numeric_limits<size_t>::max(), size_t to_ = std::numeric_limits<size_t>::max() );
+
+
+protected:
+	double grid_min;
+	double grid_max;
+	std::vector< std::vector< double > > values_of_landscapes;
+	
+	void set_up_numbers_of_functions_for_vectorization_and_projections_to_reals()
+	{
+		//warning, this function can be only called after filling in the values_of_landscapes vector.
+		this->number_of_functions_for_vectorization = this->values_of_landscapes.size();
+		this->number_of_functions_for_projections_to_reals = this->values_of_landscapes.size();
+	}
+	
+	void set_up_values_of_landscapes( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ );
+	template < typename oper > friend Persistence_landscape_on_grid operation_on_pair_of_landscapes_on_grid( const Persistence_landscape_on_grid& land1 ,  const Persistence_landscape_on_grid& land2 );
+	Persistence_landscape_on_grid multiply_lanscape_by_real_number_not_overwrite( double x )const;
+};
+
+
+void Persistence_landscape_on_grid::set_up_values_of_landscapes( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ )
+{
+	bool dbg = false;
+	if ( dbg )
+	{
+		std::cerr << "Here is the procedure : set_up_values_of_landscapes. The parameters are : grid_min_ : " << grid_min_ << ", grid_max_ : " << grid_max_ << ", number_of_points_ : " << number_of_points_ << endl;
+		//getchar();
+		std::cerr << "Here are the intervals at our disposal : \n";
+		for ( size_t i = 0 ; i != p.size() ; ++i )
+		{
+			std::cerr << p[i].first << " , " << p[i].second << endl;
+		} 
+	}
+	
+	if ( (grid_min_ == std::numeric_limits<double>::max()) || (grid_min_ == std::numeric_limits<double>::max()) )
+	{
+		//in this case, we need to find grid_min_ and grid_min_ based 
+	}
+	
+	this->values_of_landscapes = std::vector< std::vector< double > >( number_of_points_+1 );
+	this->grid_min = grid_min_;
+	this->grid_max = grid_max_;
+	
+	if ( grid_max_ <= grid_min_ )
+	{
+		throw "Wrong parameters of grid_min and grid_max given to the procedure. THe grid have negative, or zero size. The program will now terminate.\n";
+	}
+	
+	double dx = ( grid_max_ - grid_min_ )/(double)(number_of_points_);		
+	//for every interval in the diagram:
+	for ( size_t int_no = 0 ; int_no != p.size() ; ++int_no )
+	{		
+		size_t grid_interval_begin = (p[int_no].first-grid_min_)/dx;
+		size_t grid_interval_end = (p[int_no].second-grid_min_)/dx;
+		size_t grid_interval_midpoint = (size_t)(0.5*(grid_interval_begin+grid_interval_end));
+		
+		if ( dbg )
+		{
+			cerr << "Considering an interval : " << p[int_no].first << "," << p[int_no].second << endl;
+		
+			std::cerr << "grid_interval_begin : " << grid_interval_begin << std::endl;
+			std::cerr << "grid_interval_end : " << grid_interval_end << std::endl;
+			std::cerr << "grid_interval_midpoint : " << grid_interval_midpoint << std::endl;	
+		}
+		
+		double landscape_value = dx;
+		for ( size_t i = grid_interval_begin+1 ; i < grid_interval_midpoint ; ++i )
+		{
+			if ( dbg )
+			{
+				std::cerr << "Adding landscape value (going up) for a point : " << i << " equal : " << landscape_value << std::endl;
+			}
+			this->values_of_landscapes[i].push_back( landscape_value );
+			landscape_value += dx;
+		}
+		for ( size_t i = grid_interval_midpoint ; i <= grid_interval_end ; ++i )
+		{						
+			if ( landscape_value > 0 ) 
+			{ 
+				this->values_of_landscapes[i].push_back( landscape_value );	
+				if ( dbg )
+				{				
+					std::cerr << "AAdding landscape value (going down) for a point : " << i << " equal : " << landscape_value << std::endl;
+				}
+			}
+			landscape_value -= dx;	
+		}  
+	}
+	
+	//and now we need to sort the valuesL
+	for ( size_t pt = 0 ; pt != this->values_of_landscapes.size() ; ++pt )
+	{
+		std::sort( this->values_of_landscapes[pt].begin() , this->values_of_landscapes[pt].end() , greater() );	
+	}
+}//set_up_values_of_landscapes
+
+Persistence_landscape_on_grid::Persistence_landscape_on_grid( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ )
+{
+	this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ );
+}//Persistence_landscape_on_grid
+
+Persistence_landscape_on_grid& Persistence_landscape_on_grid::operator=( const Persistence_landscape_on_grid& org )
+{
+	this->grid_min = org.grid_min;
+	this->grid_max = org.grid_max;
+	this->values_of_landscapes = org.values_of_landscapes;
+	return (*this);
+}//operator=
+
+Persistence_landscape_on_grid::Persistence_landscape_on_grid(const Persistence_landscape_on_grid& org)
+{
+	this->grid_min = org.grid_min;
+	this->grid_max = org.grid_max;
+	this->values_of_landscapes = org.values_of_landscapes;
+}//copy constructor
+
+Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename , double grid_min_, double grid_max_ , size_t number_of_points_ , size_t dimension )
+{
+	//standard file with barcode
+    std::vector< std::pair< double , double > > p = read_standard_file( filename );    
+    //gudhi file with barcode
+    //std::vector< std::pair< double , double > > p = read_gudhi_file( filename , dimension );        
+	
+	this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ );
+}
+
+Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename , size_t number_of_points_ )
+{
+	//standard file with barcode
+    std::vector< std::pair< double , double > > p = read_standard_file( filename );    
+    //gudhi file with barcode
+    //std::vector< std::pair< double , double > > p = read_gudhi_file( filename , dimension );     
+    
+    double grid_min_ = std::numeric_limits<double>::max();
+    double grid_max_ = -std::numeric_limits<double>::max();
+    for ( size_t i = 0 ; i != p.size() ; ++i )
+    {
+		if ( p[i].first < grid_min_ )grid_min_ = p[i].first;
+		if ( p[i].second > grid_max_ )grid_max_ = p[i].second;
+	}	
+	this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ );
+}
+
+void Persistence_landscape_on_grid::load_landscape_from_file( const char* filename )
+{
+	//check if the file exist.
+	if ( !( access( filename, F_OK ) != -1 ) )
+	{
+		cerr << "The file : " << filename << " do not exist. The program will now terminate \n";
+		throw "The file from which you are trying to read the persistence landscape do not exist. The program will now terminate \n";
+	}	
+	std::ifstream in;
+	in.open( filename );
+	
+	size_t number_of_points_in_the_grid = 0;
+	in >> this->grid_min >> this->grid_max >> number_of_points_in_the_grid;
+	
+	std::vector< std::vector< double > > v(number_of_points_in_the_grid);
+	std::string line;
+	std::getline(in, line);
+	double number;
+	for ( size_t i = 0 ; i != number_of_points_in_the_grid ; ++i )
+	{
+		//read a line of a file and convert it to a vector.
+		std::vector< double > vv;		
+		std::getline(in, line);		
+		//cerr << "Reading line : " << line << endl;getchar();		
+		std::istringstream stream(line);
+		while (stream >> number)
+		{
+			vv.push_back(number);
+		}		
+		v[i] = vv;
+	}
+	this->values_of_landscapes = v;
+	in.close();
+}
+
+void Persistence_landscape_on_grid::print_to_file( const char* filename )const
+{
+	std::ofstream out;
+	out.open( filename );
+	
+	//first we store the parameters of the grid:
+	out << grid_min << std::endl << grid_max << std::endl << this->values_of_landscapes.size() << std::endl;
+	
+	//and now in the following lines, the values of this->values_of_landscapes for the following arguments:
+	for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != this->values_of_landscapes[i].size() ; ++j )
+		{
+			out << this->values_of_landscapes[i][j] << " ";
+		}
+		out << std::endl;
+	}
+	
+	out.close();
+}
+
+void Persistence_landscape_on_grid::plot( const char* filename , size_t from_ , size_t to_ )
+{		
+    //this program create a gnuplot script file that allows to plot persistence diagram.
+    ofstream out;
+
+    std::ostringstream nameSS;
+    nameSS << filename << "_GnuplotScript";
+    std::string nameStr = nameSS.str();
+    out.open( (char*)nameStr.c_str() );
+
+    std::pair<double,double> min_max = compute_minimum_maximum();
+    out << "set xrange [" << this->grid_min << " : " << this->grid_max << "]" << endl;
+    out << "set yrange [" << min_max.first << " : " << min_max.second << "]" << endl;
+    
+    size_t number_of_nonzero_levels = this->number_of_nonzero_levels();
+    double dx = ( this->grid_max - this->grid_min )/((double)this->values_of_landscapes.size()-1);
+    
+    
+    size_t from = 0;
+    if ( from_ != std::numeric_limits<size_t>::max() )
+    {
+		if ( from_ < number_of_nonzero_levels )
+		{
+			from = from_;
+		}
+		else
+		{
+			return;
+		}
+	}	
+	size_t to = number_of_nonzero_levels;
+	if ( to_ != std::numeric_limits<size_t>::max() )
+    {
+		if ( to_ < number_of_nonzero_levels )
+		{
+			to = to_;
+		}
+	}
+    
+    
+    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 << ", \\";
+        }
+        out << endl;
+    }
+    
+    for ( size_t lambda = from ; lambda != to ; ++lambda )
+    {
+		double point = this->grid_min;
+        for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+        {
+			double value = 0;
+			if ( this->values_of_landscapes[i].size() > lambda )			
+			{
+				value = this->values_of_landscapes[i][lambda];
+			}
+            out << point << " " << value << endl;
+            point += dx;
+        }
+        out << "EOF" << endl;
+    }
+    cout << "Gnuplot script to visualize persistence diagram written to the file: " << nameStr << ". Type load '" << nameStr << "' in gnuplot to visualize." << endl;
+}
+
+template < typename T > 
+Persistence_landscape_on_grid operation_on_pair_of_landscapes_on_grid ( const Persistence_landscape_on_grid& land1 ,  const Persistence_landscape_on_grid& land2 )
+{
+	//first we need to check if the domains are the same:
+	if ( !check_if_defined_on_the_same_domain(land1,land2) )throw "Two grids are not compatible"; 	
+	
+	T oper;
+	Persistence_landscape_on_grid result;
+	result.values_of_landscapes = std::vector< std::vector< double > >( land1.values_of_landscapes.size()  );
+	result.grid_min = land1.grid_min;
+	result.grid_max = land1.grid_max;
+	
+	//now we perorm the operations:
+	for ( size_t grid_point = 0 ; grid_point != land1.values_of_landscapes.size() ; ++grid_point )
+	{
+		result.values_of_landscapes[grid_point] = std::vector< double >( std::max( land1.values_of_landscapes[grid_point].size() , land2.values_of_landscapes[grid_point].size() ) );
+		for ( size_t lambda = 0 ; lambda != std::max( land1.values_of_landscapes[grid_point].size() , land2.values_of_landscapes[grid_point].size() ) ; ++lambda )
+		{
+			double value1 = 0;
+			double value2 = 0;
+			if ( lambda < land1.values_of_landscapes[grid_point].size() )value1 = land1.values_of_landscapes[grid_point][lambda];
+			if ( lambda < land2.values_of_landscapes[grid_point].size() )value2 = land2.values_of_landscapes[grid_point][lambda];
+			result.values_of_landscapes[grid_point][lambda] = oper( value1 , value2 );
+		}
+	}
+	
+	return result;
+}
+
+Persistence_landscape_on_grid Persistence_landscape_on_grid::multiply_lanscape_by_real_number_not_overwrite( double x )const
+{
+	Persistence_landscape_on_grid result;
+	result.values_of_landscapes = std::vector< std::vector< double > >( this->values_of_landscapes.size()  );
+	result.grid_min = this->grid_min;
+	result.grid_max = this->grid_max;
+	
+	for ( size_t grid_point = 0 ; grid_point != this->values_of_landscapes.size() ; ++grid_point )
+	{
+		result.values_of_landscapes[grid_point] = std::vector< double >( this->values_of_landscapes[grid_point].size() );
+		for ( size_t i = 0 ; i != this->values_of_landscapes[grid_point].size() ; ++i )
+		{
+			result.values_of_landscapes[grid_point][i] = x*this->values_of_landscapes[grid_point][i];
+		}
+	}
+	
+	return result;
+}
+
+double compute_max_norm_discance_of_landscapes( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& second )
+{
+	double result = 0;
+	
+	//first we need to check if first and second is defined on the same domain"
+	if ( !check_if_defined_on_the_same_domain(first, second) )throw "Two grids are not compatible"; 
+	
+	for ( size_t i = 0 ; i != first.values_of_landscapes.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != std::min( first.values_of_landscapes[i].size() , second.values_of_landscapes[i].size() ) ; ++j )
+		{
+			if ( result < abs( first.values_of_landscapes[i][j] - second.values_of_landscapes[i][j] ) )
+			{
+				result = abs( first.values_of_landscapes[i][j] - second.values_of_landscapes[i][j] );
+			}
+		}
+		if ( first.values_of_landscapes[i].size() == std::min( first.values_of_landscapes[i].size() , second.values_of_landscapes[i].size() ) )
+		{
+			for ( size_t j = first.values_of_landscapes[i].size() ; j != second.values_of_landscapes[i].size() ; ++j )
+			{
+				if ( result < second.values_of_landscapes[i][j] )result = second.values_of_landscapes[i][j];
+			}
+		}
+		if ( second.values_of_landscapes[i].size() == std::min( first.values_of_landscapes[i].size() , second.values_of_landscapes[i].size() ) )
+		{
+			for ( size_t j = second.values_of_landscapes[i].size() ; j != first.values_of_landscapes[i].size() ; ++j )
+			{
+				if ( result < first.values_of_landscapes[i][j] )result = first.values_of_landscapes[i][j];
+			}
+		}
+	}  
+	return result;
+}
+
+
+
+}//namespace Gudhi_stat
+}//namespace Gudhi
+
+#endif
diff --git a/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscapes.h b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscapes.h
new file mode 100644
index 00000000..b6266375
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscapes.h
@@ -0,0 +1,1487 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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_landscapes_H
+#define Persistence_landscapes_H
+
+//standard include
+#include <cmath>
+#include <iostream>
+#include <vector>
+#include <limits>
+#include <fstream>
+#include <sstream>
+#include <algorithm>
+#include <unistd.h>
+
+
+//gudhi include
+#include <gudhi/abstract_classes/Abs_Vectorized_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_averages.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_distances.h>
+#include <gudhi/abstract_classes/Abs_Real_valued_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_scalar_product.h>
+#include <gudhi/concretizations/read_persitence_from_file.h>
+#include <gudhi/common.h>
+using namespace std;
+
+
+
+
+namespace Gudhi
+{
+namespace Gudhi_stat
+{
+
+
+
+
+
+
+/**
+ * Extra functions needed in construction of barcodes.
+**/
+double minus_length( std::pair<double,double> a )
+{
+    return a.first-a.second;
+}
+double birth_plus_deaths( std::pair<double,double> a )
+{
+    return a.first+a.second;
+}
+
+
+
+/**
+ * Given two points in R^2, the procedure compute the parameters A and B of the line y = Ax + B that crosses those two points.
+**/
+std::pair<double,double> compute_parameters_of_a_line( std::pair<double,double> p1 , std::pair<double,double> p2 )
+{
+    double a = (p2.second-p1.second)/( p2.first - p1.first );
+    double b = p1.second - a*p1.first;
+    return std::make_pair(a,b);
+}
+
+/**
+ * This procedure given two points which lies on the opposide sides of x axis, compute x for which the line connecting those two points crosses x axis.
+**/
+double find_zero_of_a_line_segment_between_those_two_points ( std::pair<double,double> p1, std::pair<double,double> p2 )
+{
+    if ( p1.first == p2.first )return p1.first;
+    if ( p1.second*p2.second > 0 )
+    {
+        std::ostringstream errMessage;
+        errMessage <<"In function find_zero_of_a_line_segment_between_those_two_points the agguments are: (" << p1.first << "," << p1.second << ") and (" << p2.first << "," << p2.second << "). There is no zero in line between those two points. Program terminated.";
+        std::string errMessageStr = errMessage.str();
+        const char* err = errMessageStr.c_str();
+        throw(err);
+    }
+    //we assume here, that x \in [ p1.first, p2.first ] and p1 and p2 are points between which we will put the line segment
+    double a = (p2.second - p1.second)/(p2.first - p1.first);
+    double b = p1.second - a*p1.first;
+    //cerr << "Line crossing points : (" << p1.first << "," << p1.second << ") oraz (" << p2.first << "," << p2.second << ") : \n";
+    //cerr << "a : " << a << " , b : " << b << " , x : " << x << endl;
+    return -b/a;
+}
+
+
+
+
+/**
+ * Lexicographical ordering of points	.
+**/
+bool compare_points_sorting( std::pair<double,double> f, std::pair<double,double> s )
+{
+    if ( f.first < s.first )
+    {
+        return true;
+    }
+    else
+    {//f.first >= s.first
+        if ( f.first > s.first )
+        {
+            return false;
+        }
+        else
+        {//f.first == s.first
+            if ( f.second > s.second )
+            {
+                return true;
+            }
+            else
+            {
+                return false;
+            }
+        }
+    }
+}
+
+
+
+/**
+ * This procedure takes two points in R^2 and a double value x. It conputes the line pasing through those two points and return the value of that linear function at x.
+**/
+double function_value ( std::pair<double,double> p1, std::pair<double,double> p2 , double x )
+{
+    //we assume here, that x \in [ p1.first, p2.first ] and p1 and p2 are points between which we will put the line segment
+    double a = (p2.second - p1.second)/(p2.first - p1.first);
+    double b = p1.second - a*p1.first;
+    return (a*x+b);
+}
+
+
+
+
+
+/**
+ * A clas implementing persistence landascpes data structures. For theroretical desciritpion, please consult a paper ''Statistical topological data analysis using persistence landscapes'' by Peter Bubenik.
+ * For details of algorithms, please consult ''A persistence landscapes toolbox for topological statistics'' by Peter Bubenik and Pawel Dlotko.
+ * Persistence landscapes allow vertorization, computations of distances, computations of projections to Real, computations of averages and scalar products. Therefore they implement suitable interfaces.
+**/
+class Persistence_landscape :
+								public Abs_Vectorized_topological_data ,
+								public Abs_Topological_data_with_distances,
+								public Abs_Real_valued_topological_data,
+								public Abs_Topological_data_with_averages,
+								public Abs_Topological_data_with_scalar_product
+{
+public:
+	/**
+	 * Default constructor.
+	**/
+    Persistence_landscape()
+    {
+		this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
+	}
+
+    /**
+	 * Constructor that takes as an input a vector of birth-death pairs.
+	**/
+    Persistence_landscape( const std::vector< std::pair< double , double > >& p );
+
+    /**
+	 * Assignement operator.
+	**/
+    Persistence_landscape& operator=( const Persistence_landscape& org );
+
+    /**
+	 * Copy constructor.
+	**/
+    Persistence_landscape(const Persistence_landscape&);
+
+    /**
+	 * 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 = 0);
+
+
+
+    /**
+     * This procedure loads a landscape from file. It erase all the data that was previously stored in this landscape.
+    **/
+    void load_landscape_from_file( const char* filename );
+
+
+    /**
+     * The procedure stores a landscape to a file. The file can be later used by a procedure load_landscape_from_file.
+    **/
+    void print_to_file( const char* filename )const;
+
+
+
+	/**
+	 * This function compute integral of the landscape (defined formally as sum of integrals on R of all landscape functions)
+	**/
+    double compute_integral_of_landscape()const;
+
+
+    /**
+	 * This function compute integral of the 'level'-level of a landscape.
+	**/
+    double compute_integral_of_landscape( size_t level )const;
+
+
+    /**
+	 * This function compute integral of the landscape p-th power of a landscape (defined formally as sum of integrals on R of p-th powers of all landscape functions)
+	**/
+	double compute_integral_of_landscape( double p )const;//this function compute integral of p-th power of landscape.
+
+
+    /**
+     * A function that computes the value of a landscape at a given point. The parameters of the function are: unsigned level and double x.
+     * The procedure will compute the value of the level-landscape at the point x.
+    **/
+    double compute_value_at_a_given_point( unsigned level , double x )const;
+
+    /**
+     * Writing landscape into a stream. A i-th level landscape starts with a string "lambda_i". Then the discontinuity points of the landscapes follows.
+     * Shall those points be joined with lines, we will obtain the i-th landscape function.
+    **/
+    friend std::ostream& operator<<(std::ostream& out, Persistence_landscape& land );
+
+
+
+
+
+	/**
+	 * A function that compute sum of two landscapes.
+	**/
+    friend Persistence_landscape add_two_landscapes ( const Persistence_landscape& land1 ,  const Persistence_landscape& land2 )
+    {
+        return operation_on_pair_of_landscapes< std::plus<double> >(land1,land2);
+    }
+
+    /**
+	 * A function that compute difference of two landscapes.
+	**/
+    friend Persistence_landscape subtract_two_landscapes ( const Persistence_landscape& land1 ,  const Persistence_landscape& land2 )
+    {
+        return operation_on_pair_of_landscapes< std::minus<double> >(land1,land2);
+    }
+
+	/**
+	 * An operator +, that compute sum of two landscapes.
+	**/
+    friend Persistence_landscape operator+( const Persistence_landscape& first , const Persistence_landscape& second )
+    {
+        return add_two_landscapes( first,second );
+    }
+
+	/**
+	 * An operator -, that compute difference of two landscapes.
+	**/
+    friend Persistence_landscape operator-( const Persistence_landscape& first , const Persistence_landscape& second )
+    {
+        return subtract_two_landscapes( first,second );
+    }
+
+	/**
+	 * An operator * that allows multipilication of a landscape by a real number.
+	**/
+    friend Persistence_landscape operator*( const Persistence_landscape& first , double con )
+    {
+        return first.multiply_lanscape_by_real_number_not_overwrite(con);
+    }
+
+	/**
+	 * An operator * that allows multipilication of a landscape by a real number (order of parameters swapped).
+	**/
+    friend Persistence_landscape operator*( double con , const Persistence_landscape& first  )
+    {
+        return first.multiply_lanscape_by_real_number_not_overwrite(con);
+    }
+
+	/**
+	 * Operator +=. The second parameter is persistnece landwscape.
+	**/
+    Persistence_landscape operator += ( const Persistence_landscape& rhs )
+    {
+        *this = *this + rhs;
+        return *this;
+    }
+
+	/**
+	 * Operator -=. The second parameter is persistnece landwscape.
+	**/
+    Persistence_landscape operator -= ( const Persistence_landscape& rhs )
+    {
+        *this = *this - rhs;
+        return *this;
+    }
+
+
+	/**
+	 * Operator *=. The second parameter is a real number by which the y values of all landscape functions are multiplied. The x-values remain unchanged. 
+	**/
+    Persistence_landscape operator *= ( double x )
+    {
+        *this = *this*x;
+        return *this;
+    }
+
+	/**
+	 * Operator /=. The second parameter is a real number.
+	**/
+    Persistence_landscape operator /= ( double x )
+    {
+        if ( x == 0 )throw( "In operator /=, division by 0. Program terminated." );
+        *this = *this * (1/x);
+        return *this;
+    }
+
+	/**
+	 * An operator to compare two persistence landscapes.
+	**/
+    bool operator == ( const Persistence_landscape& rhs  )const;
+
+
+    /**
+	 * An operator to compare two persistence landscapes.
+	**/
+    bool operator != ( const Persistence_landscape& rhs  )const
+    {
+		return !((*this) == rhs);
+	}
+
+
+	/**
+	 * Computations of maximum (y) value of landscape.
+	**/
+    double compute_maximum()const
+    {
+        double maxValue = 0;
+        if ( this->land.size() )
+        {
+            maxValue = -std::numeric_limits<int>::max();
+            for ( size_t i = 0 ; i != this->land[0].size() ; ++i )
+            {
+                if ( this->land[0][i].second > maxValue )maxValue = this->land[0][i].second;
+            }
+        }
+        return maxValue;
+    }
+
+	/**
+	 * Computations of a L^i norm of landscape, where i is the input parameter.
+	**/
+    double compute_norm_of_landscape( double i )
+    {
+        Persistence_landscape l;
+        if ( i != -1 )
+        {
+            return compute_discance_of_landscapes(*this,l,i);
+        }
+        else
+        {
+            return compute_max_norm_discance_of_landscapes(*this,l);
+        }
+    }
+
+	/**
+ 	 * An operator to compute the value of a landscape in the level 'level' at the argument 'x'.
+	**/
+    double operator()(unsigned level,double x)const{return this->compute_value_at_a_given_point(level,x);}
+
+	/**
+	 * Computations of L^{\infty} distance between two landscapes.
+	**/
+    friend double compute_max_norm_discance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second );
+    //friend double compute_max_norm_discance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second , unsigned& nrOfLand , double&x , double& y1, double& y2 );
+
+
+	/**
+	 * Computations of L^{p} distance between two landscapes. p is the parameter of the procedure.
+	**/
+    friend double compute_discance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second , int p );
+
+
+
+	/**
+	 * Function to compute absolute value of a PL function. The representation of persistence landscapes allow to store general PL-function. When computing distance betwen two landscapes, we compute difference between
+	 * them. In this case, a general PL-function with negative value can appear as a result. Then in order to compute distance, we need to take its absolute value. This is the purpose of this procedure.
+	**/
+    Persistence_landscape abs();
+
+	/**
+	 * Computes the number of landscape functions.
+	**/
+    size_t size()const{return this->land.size(); }
+
+	/**
+	 *  Computate maximal value of lambda-level landscape.
+	**/
+    double find_max( unsigned lambda )const;
+
+	/**
+	 * Function to compute inner (scalar) product of two landscapes.
+	**/
+    friend double compute_inner_product( const Persistence_landscape& l1 , const Persistence_landscape& l2 );
+
+
+
+
+	//concretization of abstract functions:
+
+	/**
+	 * The number of projections to R is defined to the number of nonzero landscape functions. I-th projection is an integral of i-th landscape function over whole R.
+	**/
+    double project_to_R( int number_of_function )
+    {
+		return this->compute_integral_of_landscape( (size_t)number_of_function );
+	}
+
+    std::vector<double> vectorize( int number_of_function )
+    {
+		//TODO, think of something smarter over here
+		std::vector<double> v;
+		if ( (size_t)number_of_function > this->land.size() )
+		{
+			return v;
+		}
+		v.reserve( this->land[number_of_function].size() );
+		for ( size_t i = 0 ; i != this->land[number_of_function].size() ; ++i )
+		{
+			v.push_back( this->land[number_of_function][i].second );
+		}
+		return v;
+	}
+    void compute_average( std::vector< Abs_Topological_data_with_averages* > to_average )
+    {
+		bool dbg = false;
+
+		std::vector< Persistence_landscape* > nextLevelMerge( to_average.size() );
+        for ( size_t i = 0 ; i != to_average.size() ; ++i )
+        {
+            nextLevelMerge[i] = (Persistence_landscape*)to_average[i];
+        }
+        bool is_this_first_level = true;//in the loop, we will create dynamically a unmber of intermediate complexes. We have to clean that up, but we cannot erase the initial andscapes we have
+										//to average. In this case, we simply check if the nextLevelMerge are the input landscapes or the ones created in that loop by usig this extra variable.
+
+        while ( nextLevelMerge.size() != 1 )
+        {
+            if ( dbg ){cerr << "nextLevelMerge.size() : " << nextLevelMerge.size() << endl;}
+            std::vector< Persistence_landscape* > nextNextLevelMerge;
+            nextNextLevelMerge.reserve( to_average.size() );
+            for ( size_t i = 0 ; i < nextLevelMerge.size() ; i=i+2 )
+            {
+                if ( dbg ){cerr << "i : " << i << endl;}
+                Persistence_landscape* l = new Persistence_landscape;
+                if ( i+1 != nextLevelMerge.size() )
+                {
+                    (*l) = (*nextLevelMerge[i])+(*nextLevelMerge[i+1]);
+                }
+                else
+                {
+                    (*l) = *nextLevelMerge[i];
+                }
+                nextNextLevelMerge.push_back( l );
+            }
+            if ( dbg ){cerr << "After this iteration \n";}
+
+            if ( !is_this_first_level )
+            {
+				//deallocate the memory if the vector nextLevelMerge do not consist of the initial landscapes
+				for ( size_t i = 0 ; i != nextLevelMerge.size() ; ++i )
+				{
+					delete nextLevelMerge[i];
+				}
+			}
+			is_this_first_level = false;
+            nextLevelMerge.swap(nextNextLevelMerge);
+        }
+        (*this) = (*nextLevelMerge[0]);
+        (*this) *= 1/( (double)to_average.size() );
+	}
+
+
+    double distance( const Abs_Topological_data_with_distances* second , double power = 1 )
+    {
+		if ( power != -1 )
+		{
+			return compute_discance_of_landscapes( *this , *((Persistence_landscape*)second) , power );
+		}
+		else
+		{
+			return compute_max_norm_discance_of_landscapes( *this , *((Persistence_landscape*)second) );
+		}
+	}
+
+
+	double compute_scalar_product( const Abs_Topological_data_with_scalar_product* second )
+	{
+		return compute_inner_product( (*this) , *((Persistence_landscape*)second) );
+	}
+
+
+	std::vector< std::vector< std::pair<double,double> > > output_for_visualization()
+	{
+		return this->land;
+	}
+	
+	
+	//a function used to create a gnuplot script for visualization of landscapes
+	void plot( const char* filename ,int from = -1, int to = -1 ,  double xRangeBegin = -1 , double xRangeEnd = -1 , double yRangeBegin = -1 , double yRangeEnd = -1 );
+
+
+private:
+    std::vector< std::vector< std::pair<double,double> > > land;
+
+    void construct_persistence_landscape_from_barcode( const std::vector< std::pair< double , double > > & p );
+    Persistence_landscape multiply_lanscape_by_real_number_not_overwrite( double x )const;
+    void multiply_lanscape_by_real_number_overwrite( double x );
+    template < typename oper > friend Persistence_landscape operation_on_pair_of_landscapes ( const Persistence_landscape& land1 ,  const Persistence_landscape& land2 );
+    friend double compute_maximal_distance_non_symmetric( const Persistence_landscape& pl1, const Persistence_landscape& pl2 );
+
+    void set_up_numbers_of_functions_for_vectorization_and_projections_to_reals()
+	{
+		//warning, this function can be only called after filling in the intervals vector.
+		this->number_of_functions_for_vectorization = this->land.size();
+		this->number_of_functions_for_projections_to_reals = this->land.size();
+	}
+};
+
+
+Persistence_landscape::Persistence_landscape(const Persistence_landscape& oryginal)
+{
+    //std::cerr << "Running copy constructor \n";
+    std::vector< std::vector< std::pair<double,double> > > land( oryginal.land.size() );
+    for ( size_t i = 0 ; i != oryginal.land.size() ; ++i )
+    {
+        land[i].insert( land[i].end() , oryginal.land[i].begin() , oryginal.land[i].end() );
+    }
+    this->land = land;
+    this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
+}
+
+
+
+
+
+Persistence_landscape::Persistence_landscape(const char* filename , size_t dimension)
+{
+    bool dbg = false;
+
+    if ( dbg )
+    {
+        std::cerr << "Using constructor : Persistence_landscape(char* filename)" << std::endl;
+    }   
+    //standard file with barcode
+    std::vector< std::pair< double , double > > barcode = read_standard_file( filename );    
+    //gudhi file with barcode
+    //std::vector< std::pair< double , double > > barcode = read_gudhi_file( filename , dimension );        
+	this->construct_persistence_landscape_from_barcode( barcode );
+	this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
+}
+
+
+bool operatorEqualDbg = false;
+bool Persistence_landscape::operator == ( const Persistence_landscape& rhs  )const
+{
+    if ( this->land.size() != rhs.land.size() )
+    {
+        if (operatorEqualDbg)std::cerr << "1\n";
+        return false;
+    }
+    for ( size_t level = 0 ; level != this->land.size() ; ++level )
+    {
+        if ( this->land[level].size() != rhs.land[level].size() )
+        {
+            if (operatorEqualDbg)std::cerr << "this->land[level].size() : " << this->land[level].size() <<  "\n";
+            if (operatorEqualDbg)std::cerr << "rhs.land[level].size() : " << rhs.land[level].size() <<  "\n";
+            if (operatorEqualDbg)std::cerr << "2\n";
+            return false;
+        }
+        for ( size_t i = 0 ; i != this->land[level].size() ; ++i )
+        {
+            if ( !( almost_equal(this->land[level][i].first , rhs.land[level][i].first) && almost_equal(this->land[level][i].second , rhs.land[level][i].second) ) )
+            {
+				//cerr<< this->land[level][i].first << " , " <<  rhs.land[level][i].first << " and " << this->land[level][i].second << " , " << rhs.land[level][i].second << endl;
+                if (operatorEqualDbg)std::cerr << "this->land[level][i] : " << this->land[level][i].first << " " << this->land[level][i].second << "\n";
+                if (operatorEqualDbg)std::cerr << "rhs.land[level][i] : " << rhs.land[level][i].first << " " << rhs.land[level][i].second	 << "\n";
+                if (operatorEqualDbg)std::cerr << "3\n";
+                return false;
+            }
+        }
+    }
+    return true;
+}
+
+
+Persistence_landscape& Persistence_landscape::operator=( const Persistence_landscape& oryginal )
+{
+    std::vector< std::vector< std::pair<double,double> > > land( oryginal.land.size() );
+    for ( size_t i = 0 ; i != oryginal.land.size() ; ++i )
+    {
+        land[i].insert( land[i].end() , oryginal.land[i].begin() , oryginal.land[i].end() );
+    }
+    this->land = land;
+    return *this;
+}
+
+
+
+Persistence_landscape::Persistence_landscape( const std::vector< std::pair< double , double > > & p )
+{
+    this->construct_persistence_landscape_from_barcode( p );
+    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 )
+{
+	bool dbg = false;
+    if ( dbg ){cerr << "Persistence_landscape::Persistence_landscape( const std::vector< std::pair< double , double > >& p )" << endl;}
+
+	//this is a general algorithm to construct persistence landscapes.
+	std::vector< std::pair<double,double> > bars;
+	bars.insert( bars.begin() , p.begin() , p.end() );
+	std::sort( bars.begin() , bars.end() , compare_points_sorting );
+
+	if (dbg)
+	{
+		std::cerr << "Bars : \n";
+		for ( size_t i = 0 ; i != bars.size() ; ++i )
+		{
+			std::cerr << bars[i].first << " " << bars[i].second << "\n";
+		}
+		getchar();
+	}
+
+	std::vector< std::pair<double,double> > characteristicPoints(p.size());
+	for ( size_t i = 0 ; i != bars.size() ; ++i )
+	{
+		characteristicPoints[i] = std::make_pair((bars[i].first+bars[i].second)/2.0 , (bars[i].second - bars[i].first)/2.0);
+	}
+	std::vector< std::vector< std::pair<double,double> > > Persistence_landscape;
+	while ( !characteristicPoints.empty() )
+	{
+		if(dbg)
+		{
+			for ( size_t i = 0 ; i != characteristicPoints.size() ; ++i )
+			{
+				std::cout << "("  << characteristicPoints[i].first << " " << characteristicPoints[i].second << ")\n";
+			}
+			std::cin.ignore();
+		}
+
+		std::vector< std::pair<double,double> > lambda_n;
+		lambda_n.push_back( std::make_pair( -std::numeric_limits<int>::max() , 0 ) );
+		lambda_n.push_back( std::make_pair(minus_length(characteristicPoints[0]),0) );
+		lambda_n.push_back( characteristicPoints[0] );
+
+		if (dbg)
+		{
+			std::cerr << "1 Adding to lambda_n : (" << -std::numeric_limits<int>::max() << " " << 0  << ") , (" << minus_length(characteristicPoints[0]) << " " << 0 << ") , (" << characteristicPoints[0].first << " " << characteristicPoints[0].second << ") \n";
+		}
+
+		size_t i = 1;
+		std::vector< std::pair<double,double> >  newCharacteristicPoints;
+		while ( i < characteristicPoints.size() )
+		{
+			size_t p = 1;
+			if ( (minus_length(characteristicPoints[i]) >= minus_length(lambda_n[lambda_n.size()-1])) && (birth_plus_deaths(characteristicPoints[i]) > birth_plus_deaths(lambda_n[lambda_n.size()-1])) )
+			{
+				if ( minus_length(characteristicPoints[i]) < birth_plus_deaths(lambda_n[lambda_n.size()-1]) )
+				{
+					std::pair<double,double> point = std::make_pair( (minus_length(characteristicPoints[i])+birth_plus_deaths(lambda_n[lambda_n.size()-1]))/2 , (birth_plus_deaths(lambda_n[lambda_n.size()-1])-minus_length(characteristicPoints[i]))/2 );
+					lambda_n.push_back( point );
+					if (dbg)
+					{
+						std::cerr << "2 Adding to lambda_n : (" << point.first << " " << point.second << ")\n";
+					}
+
+
+					if ( dbg )
+					{
+						std::cerr << "characteristicPoints[i+p] : " << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << "\n";
+						std::cerr << "point : " << point.first << " " << point.second << "\n";
+						getchar();
+					}
+
+					while ( (i+p < characteristicPoints.size() ) && ( almost_equal(minus_length(point),minus_length(characteristicPoints[i+p])) ) && ( birth_plus_deaths(point) <= birth_plus_deaths(characteristicPoints[i+p]) ) )
+					{
+						newCharacteristicPoints.push_back( characteristicPoints[i+p] );
+						if (dbg)
+						{
+							std::cerr << "3.5 Adding to newCharacteristicPoints : (" << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << ")\n";
+							getchar();
+						}
+						++p;
+					}
+
+
+					newCharacteristicPoints.push_back( point );
+					if (dbg)
+					{
+						std::cerr << "4 Adding to newCharacteristicPoints : (" << point.first << " " << point.second << ")\n";
+					}
+
+
+					while ( (i+p < characteristicPoints.size() ) && ( minus_length(point) <= minus_length(characteristicPoints[i+p]) ) && (birth_plus_deaths(point)>=birth_plus_deaths(characteristicPoints[i+p])) )
+					{
+						newCharacteristicPoints.push_back( characteristicPoints[i+p] );
+						if (dbg)
+						{
+							std::cerr << "characteristicPoints[i+p] : " << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << "\n";
+							std::cerr << "point : " << point.first << " " << point.second << "\n";
+							std::cerr << "characteristicPoints[i+p] birth and death : " << minus_length(characteristicPoints[i+p]) << " , " << birth_plus_deaths(characteristicPoints[i+p]) << "\n";
+							std::cerr << "point birth and death : " << minus_length(point) << " , " << birth_plus_deaths(point) << "\n";
+
+							std::cerr << "3 Adding to newCharacteristicPoints : (" << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << ")\n";
+							getchar();
+						}
+						++p;
+					}
+
+				}
+				else
+				{
+					lambda_n.push_back( std::make_pair( birth_plus_deaths(lambda_n[lambda_n.size()-1]) , 0 ) );
+					lambda_n.push_back( std::make_pair( minus_length(characteristicPoints[i]) , 0 ) );
+					if (dbg)
+					{
+						std::cerr << "5 Adding to lambda_n : (" << birth_plus_deaths(lambda_n[lambda_n.size()-1]) << " " <<  0 << ")\n";
+						std::cerr << "5 Adding to lambda_n : (" << minus_length(characteristicPoints[i]) << " " << 0  << ")\n";
+					}
+				}
+				lambda_n.push_back( characteristicPoints[i] );
+				if (dbg)
+				{
+					std::cerr << "6 Adding to lambda_n : (" << characteristicPoints[i].first << " " << characteristicPoints[i].second << ")\n";
+				}
+			}
+			else
+			{
+				newCharacteristicPoints.push_back( characteristicPoints[i] );
+				if (dbg)
+				{
+					std::cerr << "7 Adding to newCharacteristicPoints : (" << characteristicPoints[i].first << " " << characteristicPoints[i].second << ")\n";
+				}
+			}
+			i = i+p;
+		}
+		lambda_n.push_back( std::make_pair(birth_plus_deaths(lambda_n[lambda_n.size()-1]),0) );
+		lambda_n.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) );
+
+		characteristicPoints = newCharacteristicPoints;
+
+		lambda_n.erase(std::unique(lambda_n.begin(), lambda_n.end()), lambda_n.end());
+		this->land.push_back( lambda_n );
+	}
+}
+
+
+
+//this function find maximum of lambda_n
+double Persistence_landscape::find_max( unsigned lambda )const
+{
+    if ( this->land.size() < lambda )return 0;
+    double maximum = -std::numeric_limits<int>::max();
+    for ( size_t i = 0 ; i != this->land[lambda].size() ; ++i )
+    {
+        if ( this->land[lambda][i].second > maximum )maximum = this->land[lambda][i].second;
+    }
+    return maximum;
+}
+
+
+double Persistence_landscape::compute_integral_of_landscape()const
+{
+    double result = 0;
+    for ( size_t i = 0 ; i != this->land.size() ; ++i )
+    {
+        for ( size_t nr = 2 ; nr != this->land[i].size()-1 ; ++nr )
+        {
+            //it suffices to compute every planar integral and then sum them ap for each lambda_n
+            result += 0.5*( this->land[i][nr].first - this->land[i][nr-1].first )*(this->land[i][nr].second + this->land[i][nr-1].second);
+        }
+    }
+    return result;
+}
+
+double Persistence_landscape::compute_integral_of_landscape( size_t  level )const
+{
+    double result = 0;
+    if ( level >= this->land.size() )
+    {
+		//this landscape function is constantly equal 0, so is the intergral.
+		return result;
+	}
+	//also negative landscapes are assumed to be zero.
+	if ( level < 0 )return 0;
+
+	for ( size_t nr = 2 ; nr != this->land[ level ].size()-1 ; ++nr )
+	{
+		//it suffices to compute every planar integral and then sum them ap for each lambda_n
+		result += 0.5*( this->land[ level ][nr].first - this->land[ level ][nr-1].first )*(this->land[ level ][nr].second + this->land[ level ][nr-1].second);
+	}
+
+    return result;
+}
+
+
+bool compute_integral_of_landscapeDbg = false;
+double Persistence_landscape::compute_integral_of_landscape( double p )const
+{
+    double result = 0;
+    for ( size_t i = 0 ; i != this->land.size() ; ++i )
+    {
+        for ( size_t nr = 2 ; nr != this->land[i].size()-1 ; ++nr )
+        {
+            if (compute_integral_of_landscapeDbg)std::cout << "nr : " << nr << "\n";
+            //In this interval, the landscape has a form f(x) = ax+b. We want to compute integral of (ax+b)^p = 1/a * (ax+b)^{p+1}/(p+1)
+            std::pair<double,double> coef = compute_parameters_of_a_line( this->land[i][nr] , this->land[i][nr-1] );
+            double a = coef.first;
+            double b = coef.second;
+
+            if (compute_integral_of_landscapeDbg)std::cout << "(" << this->land[i][nr].first << "," << this->land[i][nr].second << ") , " << this->land[i][nr-1].first << "," << this->land[i][nr].second << ")" << std::endl;
+            if ( this->land[i][nr].first == this->land[i][nr-1].first )continue;
+            if ( a != 0 )
+            {
+                result += 1/(a*(p+1)) * ( pow((a*this->land[i][nr].first+b),p+1) - pow((a*this->land[i][nr-1].first+b),p+1));
+            }
+            else
+            {
+                result += ( this->land[i][nr].first - this->land[i][nr-1].first )*( pow(this->land[i][nr].second,p) );
+            }
+            if ( compute_integral_of_landscapeDbg )
+            {
+                std::cout << "a : " <<a << " , b : " << b << std::endl;
+                std::cout << "result : " << result << std::endl;
+            }
+        }
+        //if (compute_integral_of_landscapeDbg) std::cin.ignore();
+    }
+    return result;
+}
+
+
+//this is O(log(n)) algorithm, where n is number of points in this->land.
+double Persistence_landscape::compute_value_at_a_given_point( unsigned level , double x )const
+{
+	bool compute_value_at_a_given_pointDbg = false;
+    //in such a case lambda_level = 0.
+    if ( level > this->land.size() ) return 0;
+
+    //we know that the points in this->land[level] are ordered according to x coordinate. Therefore, we can find the point by using bisection:
+    unsigned coordBegin = 1;
+    unsigned coordEnd = this->land[level].size()-2;
+
+    if ( compute_value_at_a_given_pointDbg )
+    {
+        std::cerr << "Tutaj \n";
+        std::cerr << "x : " << x << "\n";
+        std::cerr << "this->land[level][coordBegin].first : " << this->land[level][coordBegin].first << "\n";
+        std::cerr << "this->land[level][coordEnd].first : " << this->land[level][coordEnd].first << "\n";
+    }
+
+    //in this case x is outside the support of the landscape, therefore the value of the landscape is 0.
+    if ( x <= this->land[level][coordBegin].first )return 0;
+    if ( x >= this->land[level][coordEnd].first )return 0;
+
+    if (compute_value_at_a_given_pointDbg)std::cerr << "Entering to the while loop \n";
+
+    while ( coordBegin+1 != coordEnd )
+    {
+        if (compute_value_at_a_given_pointDbg)
+        {
+            std::cerr << "coordBegin : " << coordBegin << "\n";
+            std::cerr << "coordEnd : " << coordEnd << "\n";
+            std::cerr << "this->land[level][coordBegin].first : " << this->land[level][coordBegin].first << "\n";
+            std::cerr << "this->land[level][coordEnd].first : " << this->land[level][coordEnd].first << "\n";
+        }
+
+
+        unsigned newCord = (unsigned)floor((coordEnd+coordBegin)/2.0);
+
+        if (compute_value_at_a_given_pointDbg)
+        {
+            std::cerr << "newCord : " << newCord << "\n";
+            std::cerr << "this->land[level][newCord].first : " << this->land[level][newCord].first << "\n";
+            std::cin.ignore();
+        }
+
+        if ( this->land[level][newCord].first <= x )
+        {
+            coordBegin = newCord;
+            if ( this->land[level][newCord].first == x )return this->land[level][newCord].second;
+        }
+        else
+        {
+            coordEnd = newCord;
+        }
+    }
+
+    if (compute_value_at_a_given_pointDbg)
+    {
+        std::cout << "x : " << x << " is between : " << this->land[level][coordBegin].first << " a  " << this->land[level][coordEnd].first << "\n";
+        std::cout << "the y coords are : " << this->land[level][coordBegin].second << " a  " << this->land[level][coordEnd].second << "\n";
+        std::cerr << "coordBegin : " << coordBegin << "\n";
+        std::cerr << "coordEnd : " << coordEnd << "\n";
+        std::cin.ignore();
+    }
+    return function_value( this->land[level][coordBegin] , this->land[level][coordEnd] , x );
+}
+
+std::ostream& operator<<(std::ostream& out, Persistence_landscape& land )
+{
+    for ( size_t level = 0 ; level != land.land.size() ; ++level )
+    {
+        out << "Lambda_" << level << ":" << std::endl;
+        for ( size_t i = 0 ; i != land.land[level].size() ; ++i )
+        {
+            if ( land.land[level][i].first == -std::numeric_limits<int>::max() )
+            {
+                out << "-inf";
+            }
+            else
+            {
+                if ( land.land[level][i].first == std::numeric_limits<int>::max() )
+                {
+                    out << "+inf";
+                }
+                else
+                {
+                    out << land.land[level][i].first;
+                }
+            }
+            out << " , " << land.land[level][i].second << std::endl;
+        }
+    }
+    return out;
+}
+
+
+
+
+void Persistence_landscape::multiply_lanscape_by_real_number_overwrite( double x )
+{
+    for ( size_t dim = 0 ; dim != this->land.size() ; ++dim )
+    {
+        for ( size_t i = 0 ; i != this->land[dim].size() ; ++i )
+        {
+             this->land[dim][i].second *= x;
+        }
+    }
+}
+
+bool AbsDbg = false;
+Persistence_landscape Persistence_landscape::abs()
+{
+    Persistence_landscape result;
+    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 oresult
+            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;
+}
+
+
+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 )
+    {
+        std::vector< std::pair<double,double> > lambda_dim( this->land[dim].size() );
+        for ( size_t i = 0 ; i != this->land[dim].size() ; ++i )
+        {
+            lambda_dim[i] = std::make_pair( this->land[dim][i].first , x*this->land[dim][i].second );
+        }
+        result[dim] = lambda_dim;
+    }
+    Persistence_landscape res;
+    //CHANGE
+    //res.land = result;
+    res.land.swap(result);
+    return res;
+}//multiply_lanscape_by_real_number_overwrite
+
+
+void Persistence_landscape::print_to_file( const char* filename )const
+{
+    std::ofstream write;
+    write.open(filename);
+    for ( size_t dim = 0 ; dim != this->land.size() ; ++dim )
+    {
+        write << "#lambda_" << dim << std::endl;
+        for ( size_t i = 1 ; i != this->land[dim].size()-1 ; ++i )
+        {
+            write << this->land[dim][i].first << "  " << this->land[dim][i].second << std::endl;
+        }
+    }
+    write.close();
+}
+
+void Persistence_landscape::load_landscape_from_file( const char* filename )
+{
+	bool dbg = false;
+	//removing the current content of the persistence landscape.
+	this->land.clear();
+
+
+	//this constructor reads persistence landscape form a file. This file have to be created by this software beforehead
+    std::ifstream in;
+    in.open( filename );
+	if ( !( access( filename, F_OK ) != -1 ) )
+	{
+		cerr << "The file : " << filename << " do not exist. The program will now terminate \n";
+		throw "The file from which you are trying to read the persistence landscape do not exist. The program will now terminate \n";
+	}
+
+    std::string line;
+    std::vector< std::pair<double,double> > landscapeAtThisLevel;
+
+    bool isThisAFirsLine = true;
+    while ( !in.eof() )
+    {
+        getline(in,line);
+        if ( !(line.length() == 0 || line[0] == '#') )
+        {
+            std::stringstream lineSS;
+            lineSS << line;
+            double beginn, endd;
+            lineSS >> beginn;
+            lineSS >> endd;
+            landscapeAtThisLevel.push_back( std::make_pair( beginn , endd ) );
+            if (dbg){std::cerr << "Reading a pont : " << beginn << " , " << endd << std::endl;}
+        }
+        else
+        {
+            if (dbg)
+            {
+                std::cout << "IGNORE LINE\n";
+                getchar();
+            }
+            if ( !isThisAFirsLine )
+            {
+                landscapeAtThisLevel.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) );
+                this->land.push_back(landscapeAtThisLevel);
+                std::vector< std::pair<double,double> > newLevelOdLandscape;
+                landscapeAtThisLevel.swap(newLevelOdLandscape);
+            }
+            landscapeAtThisLevel.push_back( std::make_pair( -std::numeric_limits<int>::max() , 0 ) );
+            isThisAFirsLine = false;
+        }
+	}
+	if ( landscapeAtThisLevel.size() > 1 )
+    {
+        //seems that the last line of the file is not finished with the newline sign. We need to put what we have in landscapeAtThisLevel to the constructed landscape.
+        landscapeAtThisLevel.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) );
+        this->land.push_back(landscapeAtThisLevel);
+    }
+
+    in.close();
+}
+
+
+template < typename T >
+Persistence_landscape operation_on_pair_of_landscapes ( const Persistence_landscape& land1 ,  const Persistence_landscape& land2 )
+{
+	bool operation_on_pair_of_landscapesDBG = false;
+    if ( operation_on_pair_of_landscapesDBG ){std::cout << "operation_on_pair_of_landscapes\n";std::cin.ignore();}
+    Persistence_landscape result;
+    std::vector< std::vector< std::pair<double,double> > > land( std::max( land1.land.size() , land2.land.size() ) );
+    result.land = land;
+    T oper;
+
+    for ( size_t i = 0 ; i != std::min( land1.land.size() , land2.land.size() ) ; ++i )
+    {
+        std::vector< std::pair<double,double> > lambda_n;
+        size_t p = 0;
+        size_t q = 0;
+        while ( (p+1 < land1.land[i].size()) && (q+1 < land2.land[i].size()) )
+        {
+            if ( operation_on_pair_of_landscapesDBG )
+            {
+                std::cerr << "p : " << p << "\n";
+                std::cerr << "q : " << q << "\n";
+                std::cout << "land1.land[i][p].first : " << land1.land[i][p].first << "\n";
+                std::cout << "land2.land[i][q].first : " << land2.land[i][q].first << "\n";
+            }
+
+            if ( land1.land[i][p].first < land2.land[i][q].first )
+            {
+                if ( operation_on_pair_of_landscapesDBG )
+                {
+                    std::cout << "first \n";
+                    std::cout << " function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) : "<<  function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) << "\n";
+                    //std::cout << "oper( " << land1.land[i][p].second <<"," << function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) << " : " << oper( land1.land[i][p].second , function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) ) << "\n";
+                }
+                lambda_n.push_back( 
+									std::make_pair( 
+									              land1.land[i][p].first , 
+									              oper( (double)land1.land[i][p].second , function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) ) 
+												  ) 
+								  );
+                ++p;
+                continue;
+            }
+            if ( land1.land[i][p].first > land2.land[i][q].first )
+            {
+                if ( operation_on_pair_of_landscapesDBG )
+                {
+                    std::cout << "Second \n";
+                    std::cout << "function_value("<< land1.land[i][p-1].first << " " << land1.land[i][p-1].second <<" ,"<< land1.land[i][p].first << " " << land1.land[i][p].second <<", " << land2.land[i][q].first<<" ) : " << function_value( land1.land[i][p-1] , land1.land[i][p-1] ,land2.land[i][q].first ) << "\n";
+                    std::cout << "oper( " << function_value( land1.land[i][p] , land1.land[i][p-1] ,land2.land[i][q].first ) <<"," << land2.land[i][q].second <<" : " << oper( land2.land[i][q].second , function_value( land1.land[i][p] , land1.land[i][p-1] ,land2.land[i][q].first ) ) << "\n";
+                }
+                lambda_n.push_back( std::make_pair( land2.land[i][q].first , oper( function_value( land1.land[i][p] , land1.land[i][p-1] ,land2.land[i][q].first ) , land2.land[i][q].second )  )  );
+                ++q;
+                continue;
+            }
+            if ( land1.land[i][p].first == land2.land[i][q].first )
+            {
+                if (operation_on_pair_of_landscapesDBG)std::cout << "Third \n";
+                lambda_n.push_back( std::make_pair( land2.land[i][q].first , oper( land1.land[i][p].second , land2.land[i][q].second ) ) );
+                ++p;++q;
+            }
+            if (operation_on_pair_of_landscapesDBG){std::cout << "Next iteration \n";getchar();}
+        }
+        while ( (p+1 < land1.land[i].size())&&(q+1 >= land2.land[i].size()) )
+        {
+            if (operation_on_pair_of_landscapesDBG)
+            {
+                std::cout << "New point : " << land1.land[i][p].first << "  oper(land1.land[i][p].second,0) : " <<  oper(land1.land[i][p].second,0) << std::endl;
+            }
+            lambda_n.push_back( std::make_pair(land1.land[i][p].first , oper(land1.land[i][p].second,0) ) );
+            ++p;
+        }
+        while ( (p+1 >= land1.land[i].size())&&(q+1 < land2.land[i].size()) )
+        {
+            if (operation_on_pair_of_landscapesDBG)
+            {
+                std::cout << "New point : " << land2.land[i][q].first << " oper(0,land2.land[i][q].second) : " <<  oper(0,land2.land[i][q].second) << std::endl;
+            }
+            lambda_n.push_back( std::make_pair(land2.land[i][q].first , oper(0,land2.land[i][q].second) ) );
+            ++q;
+        }
+        lambda_n.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) );
+        //CHANGE
+        //result.land[i] = lambda_n;
+        result.land[i].swap(lambda_n);
+    }
+    if ( land1.land.size() > std::min( land1.land.size() , land2.land.size() ) )
+    {
+        if (operation_on_pair_of_landscapesDBG){std::cout << "land1.land.size() > std::min( land1.land.size() , land2.land.size() )" << std::endl;}
+        for ( size_t i = std::min( land1.land.size() , land2.land.size() ) ; i != std::max( land1.land.size() , land2.land.size() ) ; ++i )
+        {
+            std::vector< std::pair<double,double> > lambda_n( land1.land[i] );
+            for ( size_t nr = 0 ; nr != land1.land[i].size() ; ++nr )
+            {
+                lambda_n[nr] = std::make_pair( land1.land[i][nr].first , oper( land1.land[i][nr].second , 0 ) );
+            }
+            //CHANGE
+            //result.land[i] = lambda_n;
+            result.land[i].swap(lambda_n);
+        }
+    }
+    if ( land2.land.size() > std::min( land1.land.size() , land2.land.size() ) )
+    {
+        if (operation_on_pair_of_landscapesDBG){std::cout << "( land2.land.size() > std::min( land1.land.size() , land2.land.size() ) ) " << std::endl;}
+        for ( size_t i = std::min( land1.land.size() , land2.land.size() ) ; i != std::max( land1.land.size() , land2.land.size() ) ; ++i )
+        {
+            std::vector< std::pair<double,double> > lambda_n( land2.land[i] );
+            for ( size_t nr = 0 ; nr != land2.land[i].size() ; ++nr )
+            {
+                lambda_n[nr] = std::make_pair( land2.land[i][nr].first , oper( 0 , land2.land[i][nr].second ) );
+            }
+            //CHANGE
+            //result.land[i] = lambda_n;
+            result.land[i].swap(lambda_n);
+        }
+    }
+    if ( operation_on_pair_of_landscapesDBG ){std::cout << "operation_on_pair_of_landscapes\n";std::cin.ignore();}
+    return result;
+}//operation_on_pair_of_landscapes
+
+
+
+double compute_maximal_distance_non_symmetric( const Persistence_landscape& pl1, const Persistence_landscape& pl2 )
+{
+    bool dbg = false;
+    if (dbg)std::cerr << " compute_maximal_distance_non_symmetric \n";
+    //this distance is not symmetric. It compute ONLY distance between inflection points of pl1 and pl2.
+    double maxDist = 0;
+    size_t minimalNumberOfLevels = std::min( pl1.land.size() , pl2.land.size() );
+    for ( size_t level = 0 ; level != minimalNumberOfLevels ; ++ level )
+    {
+        if (dbg)
+        {
+            std::cerr << "Level : " << level << std::endl;
+            std::cerr << "PL1 : \n";
+            for ( size_t i = 0 ; i  != pl1.land[level].size() ; ++i )
+            {
+                std::cerr << "(" <<pl1.land[level][i].first << "," << pl1.land[level][i].second << ") \n";
+            }
+            std::cerr << "PL2 : \n";
+            for ( size_t i = 0 ; i  != pl2.land[level].size() ; ++i )
+            {
+                std::cerr << "(" <<pl2.land[level][i].first << "," << pl2.land[level][i].second << ") \n";
+            }
+            std::cin.ignore();
+        }
+
+        int p2Count = 0;
+        for ( size_t i = 1 ; i != pl1.land[level].size()-1 ; ++i ) //w tym przypadku nie rozwarzam punktow w nieskocznosci
+        {
+            while ( true )
+            {
+                if (  (pl1.land[level][i].first>=pl2.land[level][p2Count].first) && (pl1.land[level][i].first<=pl2.land[level][p2Count+1].first)  )break;
+                p2Count++;
+            }
+            double val = fabs( function_value( pl2.land[level][p2Count] , pl2.land[level][p2Count+1] , pl1.land[level][i].first ) - pl1.land[level][i].second);
+            if ( maxDist <= val )maxDist = val;
+
+            if (dbg)
+            {
+                std::cerr << pl1.land[level][i].first <<"in [" << pl2.land[level][p2Count].first << "," <<  pl2.land[level][p2Count+1].first <<"] \n";
+                std::cerr << "pl1[level][i].second : " << pl1.land[level][i].second << std::endl;
+                std::cerr << "function_value( pl2[level][p2Count] , pl2[level][p2Count+1] , pl1[level][i].first ) : " << function_value( pl2.land[level][p2Count] , pl2.land[level][p2Count+1] , pl1.land[level][i].first ) << std::endl;
+                std::cerr << "val : "  << val << std::endl;
+                std::cin.ignore();
+            }
+        }
+    }
+
+    if (dbg)std::cerr << "minimalNumberOfLevels : " << minimalNumberOfLevels << std::endl;
+
+    if ( minimalNumberOfLevels < pl1.land.size() )
+    {
+        for ( size_t level = minimalNumberOfLevels ; level != pl1.land.size() ; ++ level )
+        {
+            for ( size_t i = 0 ; i != pl1.land[level].size() ; ++i )
+            {
+                if (dbg)std::cerr << "pl1[level][i].second  : " << pl1.land[level][i].second << std::endl;
+                if ( maxDist < pl1.land[level][i].second )maxDist = pl1.land[level][i].second;
+            }
+        }
+    }
+    return maxDist;
+}
+
+
+
+
+double compute_discance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second , int p )
+{
+    //This is what we want to compute: (\int_{- \infty}^{+\infty}| first-second |^p)^(1/p). We will do it one step at a time:
+
+    //first-second :
+    Persistence_landscape lan = first-second;
+
+    //| first-second |:
+    lan = lan.abs();
+	if ( p != -1 )
+	{
+		//\int_{- \infty}^{+\infty}| first-second |^p
+		double result;
+		if ( p != 1 )
+		{
+			result = lan.compute_integral_of_landscape( (double)p );
+		}
+		else
+		{
+			result = lan.compute_integral_of_landscape();
+		}
+
+		//(\int_{- \infty}^{+\infty}| first-second |^p)^(1/p)
+		return pow( result , 1/(double)p );
+	}
+	else
+	{
+		//p == -1
+		return lan.compute_maximum();
+	}
+}
+
+double compute_max_norm_discance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second )
+{
+    return std::max( compute_maximal_distance_non_symmetric(first,second) , compute_maximal_distance_non_symmetric(second,first) );
+}
+
+
+bool comparePairsForMerging( std::pair< double , unsigned > first , std::pair< double , unsigned > second )
+{
+    return (first.first < second.first);
+}
+
+
+
+
+double compute_inner_product( const Persistence_landscape& l1 , const Persistence_landscape& l2 )
+{
+    bool dbg = false;
+    double result = 0;
+
+    for ( size_t level = 0 ; level != std::min( l1.size() , l2.size() ) ; ++level )
+    {
+        if ( dbg ){cerr << "Computing inner product for a level : " << level << endl;getchar();}
+        if ( l1.land[level].size() * l2.land[level].size() == 0 )continue;
+
+        //endpoints of the interval on which we will compute the inner product of two locally linear functions:
+        double x1 = -std::numeric_limits<int>::max();
+        double x2;
+        if ( l1.land[level][1].first < l2.land[level][1].first )
+        {
+            x2 = l1.land[level][1].first;
+        }
+        else
+        {
+            x2 = l2.land[level][1].first;
+        }
+
+        //iterators for the landscapes l1 and l2
+        size_t l1It = 0;
+        size_t l2It = 0;
+
+        while ( (l1It < l1.land[level].size()-1) && (l2It < l2.land[level].size()-1) )
+        {
+            //compute the value of a inner product on a interval [x1,x2]
+
+            double a,b,c,d;
+
+            a = (l1.land[level][l1It+1].second - l1.land[level][l1It].second)/(l1.land[level][l1It+1].first - l1.land[level][l1It].first);
+            b = l1.land[level][l1It].second - a*l1.land[level][l1It].first;
+            c = (l2.land[level][l2It+1].second - l2.land[level][l2It].second)/(l2.land[level][l2It+1].first - l2.land[level][l2It].first);
+            d = l2.land[level][l2It].second - c*l2.land[level][l2It].first;
+
+            double contributionFromThisPart
+            =
+            (a*c*x2*x2*x2/3 + (a*d+b*c)*x2*x2/2 + b*d*x2) - (a*c*x1*x1*x1/3 + (a*d+b*c)*x1*x1/2 + b*d*x1);
+
+            result += contributionFromThisPart;
+
+            if ( dbg )
+            {
+                cerr << "[l1.land[level][l1It].first,l1.land[level][l1It+1].first] : " << l1.land[level][l1It].first << " , " << l1.land[level][l1It+1].first << endl;
+                cerr << "[l2.land[level][l2It].first,l2.land[level][l2It+1].first] : " << l2.land[level][l2It].first << " , " << l2.land[level][l2It+1].first << endl;
+                cerr << "a : " << a << ", b : " << b << " , c: " << c << ", d : " << d << endl;
+                cerr << "x1 : " << x1 << " , x2 : " << x2 << endl;
+                cerr << "contributionFromThisPart : " << contributionFromThisPart << endl;
+                cerr << "result : " << result << endl;
+                getchar();
+            }
+
+            //we have two intervals in which functions are constant:
+            //[l1.land[level][l1It].first , l1.land[level][l1It+1].first]
+            //and
+            //[l2.land[level][l2It].first , l2.land[level][l2It+1].first]
+            //We also have an interval [x1,x2]. Since the intervals in the landscapes cover the whole R, then it is clear that x2
+            //is either l1.land[level][l1It+1].first of l2.land[level][l2It+1].first or both. Lets test it.
+            if ( x2 == l1.land[level][l1It+1].first )
+            {
+                if ( x2 == l2.land[level][l2It+1].first )
+                {
+                    //in this case, we increment both:
+                    ++l2It;
+                    if ( dbg ){cerr << "Incrementing both \n";}
+                }
+                else
+                {
+                    if ( dbg ){cerr << "Incrementing first \n";}
+                }
+                ++l1It;
+            }
+            else
+            {
+                //in this case we increment l2It
+                ++l2It;
+                if ( dbg ){cerr << "Incrementing second \n";}
+            }
+            //Now, we shift x1 and x2:
+            x1 = x2;
+            if ( l1.land[level][l1It+1].first < l2.land[level][l2It+1].first )
+            {
+                x2 = l1.land[level][l1It+1].first;
+            }
+            else
+            {
+                x2 = l2.land[level][l2It+1].first;
+            }
+
+        }
+
+    }
+    return result;
+}
+
+
+void Persistence_landscape::plot( const char* filename , int from, int to , double xRangeBegin , double xRangeEnd , double yRangeBegin , double yRangeEnd )
+{
+    //this program create a gnuplot script file that allows to plot persistence diagram.
+    ofstream out;
+
+    std::ostringstream nameSS;
+    nameSS << filename << "_GnuplotScript";
+    std::string nameStr = nameSS.str();
+    out.open( (char*)nameStr.c_str() );
+
+    if ( (xRangeBegin != -1) || (xRangeEnd != -1) || (yRangeBegin != -1) || (yRangeEnd != -1)  )
+    {
+        out << "set xrange [" << xRangeBegin << " : " << xRangeEnd << "]" << endl;
+        out << "set yrange [" << yRangeBegin << " : " << yRangeEnd << "]" << endl;
+    }
+
+    if ( from == -1 ){from = 0;}
+    if ( to == -1 ){to = this->land.size();}
+
+    out << "plot ";
+    for ( size_t lambda= std::min((size_t)from,this->land.size()) ; lambda != std::min((size_t)to,this->land.size()) ; ++lambda )
+    {
+        out << "     '-' using 1:2 title 'l" << lambda << "' with lp";
+        if ( lambda+1 != std::min((size_t)to,this->land.size()) )
+        {
+            out << ", \\";
+        }
+        out << endl;
+    }
+
+    for ( size_t lambda= std::min((size_t)from,this->land.size()) ; lambda != std::min((size_t)to,this->land.size()) ; ++lambda )
+    {
+        for ( size_t i = 1 ; i != this->land[lambda].size()-1 ; ++i )
+        {
+            out << this->land[lambda][i].first << " " << this->land[lambda][i].second << endl;
+        }
+        out << "EOF" << endl;
+    }
+    cout << "Gnuplot script to visualize persistence diagram written to the file: " << nameStr << ". Type load '" << nameStr << "' in gnuplot to visualize." << endl;
+}
+
+
+
+
+}//namespace gudhi stat
+}//namespace gudhi
+
+
+#endif
diff --git a/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscapes_on_grid.h b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscapes_on_grid.h
new file mode 100644
index 00000000..5d2ccef9
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscapes_on_grid.h
@@ -0,0 +1,1221 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+#pragma once
+#ifndef Persistence_landscape_on_grid_on_grid_H
+#define Persistence_landscape_on_grid_on_grid_H
+
+//standard include
+#include <iostream>
+#include <vector>
+#include <limits>
+#include <fstream>
+#include <sstream>
+#include <algorithm>
+#include <unistd.h>
+#include <cmath>
+
+
+//gudhi include
+#include <gudhi/abstract_classes/Abs_Vectorized_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_averages.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_distances.h>
+#include <gudhi/abstract_classes/Abs_Real_valued_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_scalar_product.h>
+#include <gudhi/concretizations/read_persitence_from_file.h>
+
+
+
+using namespace std;
+
+
+namespace Gudhi
+{
+namespace Gudhi_stat
+{
+
+/**
+ * Given two points in R^2, the procedure compute the parameters A and B of the line y = Ax + B that crosses those two points.
+**/
+std::pair<double,double> compute_parameters_of_a_line( std::pair<double,double> p1 , std::pair<double,double> p2 )
+{
+    double a = (p2.second-p1.second)/( p2.first - p1.first );
+    double b = p1.second - a*p1.first;
+    return std::make_pair(a,b);
+}
+
+struct greater
+{
+    template<class T>
+    bool operator()(T const &a, T const &b) const { return a > b; }
+};
+
+//double epsi = std::numeric_limits<double>::epsilon();
+double epsi = 0.000005;
+
+
+/**
+ *  A procedure used to compare doubles. Typically gien two doubles A and B, comparing A == B is not good idea. In this case, we use the procedure almostEqual with the epsi defined at
+ *  the top of the file. Setting up the epsi give the user a tolerance on what should be consider equal.
+**/
+inline bool almost_equal( double a , double b )
+{
+    if ( fabs(a-b) < epsi )
+        return true;
+    return false;
+}
+
+
+
+
+class Persistence_landscape_on_grid  :
+								public Abs_Vectorized_topological_data ,
+								public Abs_Topological_data_with_distances,
+								public Abs_Real_valued_topological_data,
+								public Abs_Topological_data_with_averages,
+								public Abs_Topological_data_with_scalar_product
+{
+public:
+	/**
+	 * Default constructor.
+	**/
+    Persistence_landscape_on_grid()
+    {
+		this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
+		this->grid_min = this->grid_max = 0;
+	}
+
+    /**
+	 * Constructor that takes as an input a vector of birth-death pairs.
+	**/
+    Persistence_landscape_on_grid( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ );
+
+    /**
+	 * Assignement operator.
+	**/
+    Persistence_landscape_on_grid& operator=( const Persistence_landscape_on_grid& org );
+
+    /**
+	 * Copy constructor.
+	**/
+    Persistence_landscape_on_grid(const Persistence_landscape_on_grid&);
+
+    /**
+	 * 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. The additional parameters of this procedure are: ranges of grid, resoltion of a grid
+	 * and the dimension of intervals that are need to be read from a file (in case of Gudhi format files). 
+	**/
+    Persistence_landscape_on_grid(const char* filename , double grid_min_, double grid_max_ , size_t number_of_points_ , size_t dimension_ = 0 );
+        
+    /**
+	 * 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. The additional parameter is the resoution of a grid. The remaning parameters are 
+	 * calculated based on data. 
+	**/
+    Persistence_landscape_on_grid(const char* filename , size_t number_of_points );
+
+
+    /**
+     * This procedure loads a landscape from file. It erase all the data that was previously stored in this landscape.
+    **/
+    void load_landscape_from_file( const char* filename );
+
+
+    /**
+     * The procedure stores a landscape to a file. The file can be later used by a procedure load_landscape_from_file.
+    **/
+    void print_to_file( const char* filename )const;
+
+
+
+	/**
+	 * This function compute integral of the landscape (defined formally as sum of integrals on R of all landscape functions)
+	**/
+    double compute_integral_of_landscape()const
+    {
+		size_t maximal_level = this->number_of_nonzero_levels();
+		double result = 0;
+		for ( size_t i = 0 ; i != maximal_level ; ++i )
+		{
+			result += this->compute_integral_of_landscape(i);
+		}
+		return result;
+	}
+
+
+    /**
+	 * This function compute integral of the 'level'-level of a landscape.
+	**/
+    double compute_integral_of_landscape( size_t level )const
+    {
+		bool dbg = false;
+		double result = 0;		
+		double dx = (this->grid_max - this->grid_min)/(double)(this->values_of_landscapes.size()-1);
+		
+		if ( dbg )
+		{			
+			cerr << "this->grid_max : " << this->grid_max << endl;
+			cerr << "this->grid_min : " << this->grid_min << endl;
+			cerr << "this->values_of_landscapes.size() : " << this->values_of_landscapes.size() << endl;
+			getchar();
+		}
+		
+		
+		double previous_x = this->grid_min-dx;
+		double previous_y = 0;
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			double current_x = previous_x + dx;
+			double current_y = 0;
+			if ( this->values_of_landscapes[i].size() > level )current_y = this->values_of_landscapes[i][level];
+		
+			if ( dbg )
+			{
+				cerr << "this->values_of_landscapes[i].size() : " << this->values_of_landscapes[i].size() << " , level : " << level << endl;	
+				if ( this->values_of_landscapes[i].size() > level )cerr << "this->values_of_landscapes[i][level] : " << this->values_of_landscapes[i][level] << endl;
+				cerr << "previous_y : " << previous_y << endl;
+				cerr << "current_y : " << current_y << endl;
+				cerr << "dx : " << dx << endl;
+				cerr << "0.5*dx*( previous_y + current_y ); " << 0.5*dx*( previous_y + current_y ) << endl;
+			}
+			
+			result += 0.5*dx*( previous_y + current_y );			
+			previous_x = current_x;
+			previous_y = current_y;
+		}
+		return result;
+	}
+
+	/**
+	 * This function compute integral of the landscape p-th power of a landscape (defined formally as sum of integrals on R of p-th powers of all landscape functions)
+	**/
+	double compute_integral_of_landscape( double p )const
+	{
+		size_t maximal_level = this->number_of_nonzero_levels();
+		double result = 0;
+		for ( size_t i = 0 ; i != maximal_level ; ++i )
+		{
+			result += this->compute_integral_of_landscape(p,i);
+		}
+		return result;
+	}
+
+    /**
+	 * This function compute integral of the landscape p-th power of a level of a landscape (defined formally as sum of integrals on R of p-th powers of all landscape functions)
+	**/	
+	double compute_integral_of_landscape( double p , size_t level )const
+	{
+		bool dbg = false;
+		
+		double result = 0;				
+		double dx = (this->grid_max - this->grid_min)/(double)(this->values_of_landscapes.size()-1);		
+		double previous_x = this->grid_min;
+		double previous_y = 0;
+		if ( this->values_of_landscapes[0].size() > level )previous_y = this->values_of_landscapes[0][level];
+		
+		if ( dbg )
+		{
+			cerr << "dx : " << dx << endl;
+			cerr << "previous_x : " << previous_x << endl;
+			cerr << "previous_y : " << previous_y << endl;
+			cerr << "power : " << p << endl;
+			getchar();
+		}
+		
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			double current_x = previous_x + dx;
+			double current_y = 0;
+			if ( this->values_of_landscapes[i].size() > level )current_y = this->values_of_landscapes[i][level];
+			
+			if ( dbg )cerr << "current_y : " << current_y << endl;
+			
+			if ( current_y == previous_y )continue; 
+			
+			std::pair<double,double> coef = compute_parameters_of_a_line( std::make_pair( previous_x , previous_y ) , std::make_pair( current_x , current_y ) );
+			double a = coef.first;
+			double b = coef.second;
+			
+			if ( dbg )
+			{
+				cerr << "A line passing through points : (" << previous_x << "," << previous_y << ") and (" << current_x << "," << current_y << ") is : " << a << "x+" << b << endl;
+			}
+			
+			//In this interval, the landscape has a form f(x) = ax+b. We want to compute integral of (ax+b)^p = 1/a * (ax+b)^{p+1}/(p+1)
+			double value_to_add = 0;
+			if ( a != 0 )
+			{			
+				value_to_add = 1/(a*(p+1)) * ( pow((a*current_x+b),p+1) - pow((a*previous_x+b),p+1));				
+			}
+			else
+			{
+				value_to_add = ( current_x - previous_x )*( pow(b,p) );
+			}				
+			result += value_to_add;
+			if ( dbg )
+			{
+				cerr << "Increasing result by : " << value_to_add << endl;
+				cerr << "restult : " << result << endl;
+				getchar();
+			}		
+			previous_x = current_x;
+			previous_y = current_y;
+		}		
+		if ( dbg )cerr << "The total result is : " << result << endl;
+		return result;
+	}
+	
+	/**
+     * Writing landscape into a stream. A i-th level landscape starts with a string "lambda_i". Then the discontinuity points of the landscapes follows.
+     * Shall those points be joined with lines, we will obtain the i-th landscape function.
+    **/
+    friend std::ostream& operator<<(std::ostream& out, const Persistence_landscape_on_grid& land )
+	{
+		double dx = (land.grid_max - land.grid_min)/(double)(land.values_of_landscapes.size()-1);
+		double x = land.grid_min;
+		for ( size_t i = 0 ; i != land.values_of_landscapes.size() ; ++i )
+		{
+			out << x << " : ";
+			for ( size_t j = 0 ; j != land.values_of_landscapes[i].size() ; ++j )
+			{
+				out << land.values_of_landscapes[i][j] << " ";
+			}
+			out << endl;
+			x += dx;
+		}
+		return out;
+	}
+
+
+    /**
+     * A function that computes the value of a landscape at a given point. The parameters of the function are: unsigned level and double x.
+     * The procedure will compute the value of the level-landscape at the point x.
+    **/
+    double compute_value_at_a_given_point( unsigned level , double x )const
+    {
+		bool dbg = false;
+		if ( (x < this->grid_min) || (x > this->grid_max) )return 0;
+		
+		//find a position of a vector closest to x:
+		double dx = (this->grid_max - this->grid_min)/(double)(this->values_of_landscapes.size()-1);
+		size_t position = size_t((x-this->grid_min)/dx);
+		
+		if ( dbg )
+		{
+			std::cerr << "This is a procedure compute_value_at_a_given_point \n";
+			std::cerr << "level : " << level << endl;
+			std::cerr << "x : " << x << endl;
+			std::cerr << "psoition : " << position << endl;
+		}
+		//check if we are not exacly in the grid point:
+		if ( almost_equal( position*dx+ this->grid_min ,  x) )
+		{
+			if ( this->values_of_landscapes[position].size() < level )
+			{
+				return this->values_of_landscapes[position][level];
+			}
+			else
+			{
+				return 0;
+			}
+		}
+		//in the other case, approximate with a line:
+		std::pair<double,double> line;
+		if ( (this->values_of_landscapes[position].size() > level) && (this->values_of_landscapes[position+1].size() > level) )
+		{
+			line = compute_parameters_of_a_line( std::make_pair( position*dx+ this->grid_min , this->values_of_landscapes[position][level] ) , std::make_pair( (position+1)*dx+ this->grid_min , this->values_of_landscapes[position+1][level] ) );
+		}
+		else
+		{
+			if ( (this->values_of_landscapes[position].size() > level) || (this->values_of_landscapes[position+1].size() > level) )
+			{
+				if ( (this->values_of_landscapes[position].size() > level) )
+				{
+						line = compute_parameters_of_a_line( std::make_pair( position*dx+ this->grid_min , this->values_of_landscapes[position][level] ) , std::make_pair( (position+1)*dx+ this->grid_min , 0 ) );
+				}
+				else
+				{
+					//(this->values_of_landscapes[position+1].size() > level)
+					line = compute_parameters_of_a_line( std::make_pair( position*dx+ this->grid_min , 0 ) , std::make_pair( (position+1)*dx+ this->grid_min , this->values_of_landscapes[position+1][level] ) );	
+				}
+			}
+			else
+			{
+				return 0;
+			}
+		}
+		//compute the value of the linear function parametrized by line on a point x:
+		return line.first*x+line.second;
+	}
+    
+
+	/**
+	 * A function that compute sum of two landscapes.
+	**/
+    friend Persistence_landscape_on_grid add_two_landscapes ( const Persistence_landscape_on_grid& land1 ,  const Persistence_landscape_on_grid& land2 )
+    {
+        return operation_on_pair_of_landscapes_on_grid< std::plus<double> >(land1,land2);
+    }
+
+    /**
+	 * A function that compute difference of two landscapes.
+	**/
+    friend Persistence_landscape_on_grid subtract_two_landscapes ( const Persistence_landscape_on_grid& land1 ,  const Persistence_landscape_on_grid& land2 )
+    {
+        return operation_on_pair_of_landscapes_on_grid< std::minus<double> >(land1,land2);
+    }
+
+	/**
+	 * An operator +, that compute sum of two landscapes.
+	**/
+    friend Persistence_landscape_on_grid operator+( const Persistence_landscape_on_grid& first , const Persistence_landscape_on_grid& second )
+    {
+        return add_two_landscapes( first,second );
+    }
+
+	/**
+	 * An operator -, that compute difference of two landscapes.
+	**/
+    friend Persistence_landscape_on_grid operator-( const Persistence_landscape_on_grid& first , const Persistence_landscape_on_grid& second )
+    {
+        return subtract_two_landscapes( first,second );
+    }
+
+	/**
+	 * An operator * that allows multipilication of a landscape by a real number.
+	**/
+    friend Persistence_landscape_on_grid operator*( const Persistence_landscape_on_grid& first , double con )
+    {
+        return first.multiply_lanscape_by_real_number_not_overwrite(con);
+    }
+
+	/**
+	 * An operator * that allows multipilication of a landscape by a real number (order of parameters swapped).
+	**/
+    friend Persistence_landscape_on_grid operator*( double con , const Persistence_landscape_on_grid& first  )
+    {
+        return first.multiply_lanscape_by_real_number_not_overwrite(con);
+    }
+
+	friend bool check_if_defined_on_the_same_domain( const Persistence_landscape_on_grid& land1, const Persistence_landscape_on_grid& land2 )
+	{
+		if ( land1.values_of_landscapes.size() != land2.values_of_landscapes.size() )return false;
+		if ( land1.grid_min != land2.grid_min )return false;
+		if ( land1.grid_max != land2.grid_max )return false;
+		return true;
+	}
+
+	/**
+	 * Operator +=. The second parameter is persistnece landwscape.
+	**/
+    Persistence_landscape_on_grid operator += ( const Persistence_landscape_on_grid& rhs )
+    {
+        *this = *this + rhs;
+        return *this;
+    }
+
+	/**
+	 * Operator -=. The second parameter is persistnece landwscape.
+	**/
+    Persistence_landscape_on_grid operator -= ( const Persistence_landscape_on_grid& rhs )
+    {
+        *this = *this - rhs;
+        return *this;
+    }
+
+
+	/**
+	 * Operator *=. The second parameter is a real number by which the y values of all landscape functions are multiplied. The x-values remain unchanged. 
+	**/
+    Persistence_landscape_on_grid operator *= ( double x )
+    {
+        *this = *this*x;
+        return *this;
+    }
+
+	/**
+	 * Operator /=. The second parameter is a real number.
+	**/
+    Persistence_landscape_on_grid operator /= ( double x )
+    {
+        if ( x == 0 )throw( "In operator /=, division by 0. Program terminated." );
+        *this = *this * (1/x);
+        return *this;
+    }
+
+	/**
+	 * An operator to compare two persistence landscapes.
+	**/
+    bool operator == ( const Persistence_landscape_on_grid& rhs  )const
+    {
+		bool dbg = true;
+		if ( ! this->values_of_landscapes.size() == rhs.values_of_landscapes.size() )
+		{
+			if (dbg) cerr << "values_of_landscapes of incompatable sizes\n";
+			return false;
+		}
+		if ( !almost_equal( this->grid_min , rhs.grid_min ) )
+		{
+			if (dbg) cerr << "grid_min not equal\n";
+			return false; 
+		}
+		if ( !almost_equal(this->grid_max,rhs.grid_max ) )
+		{	
+			if (dbg) cerr << "grid_max not equal\n";
+			return false;		
+		}
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{					
+			for ( size_t aa = 0 ; aa != this->values_of_landscapes[i].size() ; ++aa )
+			{
+				if ( !almost_equal( this->values_of_landscapes[i][aa]  , rhs.values_of_landscapes[i][aa]  ) )
+				{					
+					if (dbg) 
+					{
+						cerr << "Problem in the position : " << i << " of values_of_landscapes. \n";
+						cerr << this->values_of_landscapes[i][aa]   << " " <<  rhs.values_of_landscapes[i][aa] << endl;
+					}
+					return false;
+				}
+			}				
+		}	
+		return true;
+	}
+
+
+    /**
+	 * An operator to compare two persistence landscapes.
+	**/
+    bool operator != ( const Persistence_landscape_on_grid& rhs  )const
+    {
+		return !((*this) == rhs);
+	}
+
+
+	/**
+	 * Computations of maximum (y) value of landscape.
+	**/
+    double compute_maximum()const
+    {
+       //since the function can only be entirely positive or negative, the maximal value will be an extremal value in the arrays:
+		double max_value = -std::numeric_limits<double>::max();
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			if ( this->values_of_landscapes[i].size() )
+			{
+				if ( this->values_of_landscapes[i][0] > max_value )max_value = this->values_of_landscapes[i][0];
+				if ( this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ] > max_value )max_value = this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ];
+			}
+		}
+		return max_value;        
+    }
+    
+    /**
+	 * Computations of minimum and maximum value of landscape.
+	**/
+    std::pair<double,double> compute_minimum_maximum()const
+    {        
+       //since the function can only be entirely positive or negative, the maximal value will be an extremal value in the arrays:
+		double max_value = -std::numeric_limits<double>::max();
+		double min_value = 0;
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			if ( this->values_of_landscapes[i].size() )
+			{
+				if ( this->values_of_landscapes[i][0] > max_value )max_value = this->values_of_landscapes[i][0];
+				if ( this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ] > max_value )max_value = this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ];
+				
+				if ( this->values_of_landscapes[i][0] < min_value )min_value = this->values_of_landscapes[i][0];
+				if ( this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ] < min_value )min_value = this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ];
+			}
+		}
+		return std::make_pair(min_value , max_value);
+    }
+    
+    /**
+     * This function computes maximal lambda for which lambda-level landscape is nonzero.
+    **/
+    size_t number_of_nonzero_levels()const
+    {
+		size_t result = 0;
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			if ( this->values_of_landscapes[i].size() > result )result = this->values_of_landscapes[i].size();
+		}
+		return result;
+	}
+
+	/**
+	 * Computations of a L^i norm of landscape, where i is the input parameter.
+	**/
+    double compute_norm_of_landscape( double i )
+    {
+		std::vector< std::pair< double , double > > p;
+        Persistence_landscape_on_grid l(p,this->grid_min,this->grid_max,this->values_of_landscapes.size()-1);       
+        
+        if ( i != -1 )
+        {
+            return compute_discance_of_landscapes_on_grid(*this,l,i);
+        }
+        else
+        {
+            return compute_max_norm_discance_of_landscapes(*this,l);
+        }
+    }
+
+	/**
+ 	 * An operator to compute the value of a landscape in the level 'level' at the argument 'x'.
+	**/
+    double operator()(unsigned level,double x)const{return this->compute_value_at_a_given_point(level,x);}
+
+	/**
+	 * Computations of L^{\infty} distance between two landscapes.
+	**/
+    friend double compute_max_norm_discance_of_landscapes( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& second );
+    //friend double compute_max_norm_discance_of_landscapes( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& second , unsigned& nrOfLand , double&x , double& y1, double& y2 );
+
+
+
+
+	/**
+	 * Function to compute absolute value of a PL function. The representation of persistence landscapes allow to store general PL-function. When computing distance betwen two landscapes, we compute difference between
+	 * them. In this case, a general PL-function with negative value can appear as a result. Then in order to compute distance, we need to take its absolute value. This is the purpose of this procedure.
+	**/
+    void abs()
+    {
+		//Be careful here. We assume that the functions are either entirely positive or negative. They do not change signs. That is why I can implemnt abs in the way presented below:
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			for ( size_t j = 0 ; j != this->values_of_landscapes[i].size() ; ++j )
+			{
+				this->values_of_landscapes[i][j] = std::abs( this->values_of_landscapes[i][j] );
+			}
+		}
+	}
+
+	/**
+	 * Computes the number of landscape functions.
+	**/
+    size_t size()const{return this->number_of_nonzero_levels(); }
+
+	/**
+	 *  Computate maximal value of lambda-level landscape.
+	**/
+    double find_max( unsigned lambda )const
+    {		
+		double max_value = -std::numeric_limits<double>::max();
+		for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+		{
+			if ( this->values_of_landscapes[i].size() > lambda )
+			{
+				if ( this->values_of_landscapes[i][lambda] > max_value )max_value = this->values_of_landscapes[i][lambda];				
+			}
+		}
+		return max_value;
+	}
+
+	/**
+	 * Function to compute inner (scalar) product of two landscapes.
+	**/
+    friend double compute_inner_product( const Persistence_landscape_on_grid& l1 , const Persistence_landscape_on_grid& l2 )
+    {
+		if ( !check_if_defined_on_the_same_domain(l1,l2) )throw "Landscapes are not defined on the same grid, the program will now terminate";
+		size_t maximal_level = l1.number_of_nonzero_levels();
+		double result = 0;
+		for ( size_t i = 0 ; i != maximal_level ; ++i )
+		{
+			result += compute_inner_product(l1,l2,i);
+		}
+		return result;
+	}
+
+	
+	
+//SOMETHIND IS WRONG OVER HERE!!! THE SCALAR PRODUC DEPENDS A LOT ON THE RESOLUTION OF A GRID> THIS SHOULD NOT BE LIKE THIS!!!
+	/**
+	 * Function to compute inner (scalar) product of given levels of two landscapes.
+	**/
+    friend double compute_inner_product( const Persistence_landscape_on_grid& l1 , const Persistence_landscape_on_grid& l2 , size_t level )
+    {
+		if ( !check_if_defined_on_the_same_domain(l1,l2) )throw "Landscapes are not defined on the same grid, the program will now terminate";
+		double result = 0;
+		
+		double dx = (l1.grid_max - l1.grid_min)/(double)(l1.values_of_landscapes.size()-1);
+		
+		double previous_x = l1.grid_min-dx;
+		double previous_y_l1 = 0;
+		double previous_y_l2 = 0;
+		for ( size_t i = 0 ; i != l1.values_of_landscapes.size() ; ++i )
+		{
+			double current_x = previous_x + dx;
+			double current_y_l1 = 0;
+			if ( l1.values_of_landscapes[i].size() > level )current_y_l1 = l1.values_of_landscapes[i][level];
+			
+			double current_y_l2 = 0;
+			if ( l2.values_of_landscapes[i].size() > level )current_y_l2 = l2.values_of_landscapes[i][level];
+			
+			std::pair<double,double> l1_coords = compute_parameters_of_a_line( std::make_pair( previous_x , previous_y_l1 ) , std::make_pair( current_x , current_y_l1 ) );			
+			std::pair<double,double> l2_coords = compute_parameters_of_a_line( std::make_pair( previous_x , previous_y_l2 ) , std::make_pair( current_x , current_y_l2 ) );
+			
+			//let us assume that the first line is of a form y = ax+b, and the second one is of a form y = cx + d. Then here are a,b,c,d:
+			double a = l1_coords.first;
+			double b = l1_coords.second;
+			
+			double c = l2_coords.first;
+			double d = l2_coords.second;
+			
+			//now, to compute the inner product in this interval we need to compute the integral of (ax+b)(cx+d) = acx^2 + (ad+bc)x + bd in the interval from previous_x to current_x:
+			//The integal is ac/3*x^3 + (ac+bd)/2*x^2 + bd*x
+		
+			result += a*c/3*current_x*current_x*current_x + (a*c+b*d)/2*current_x*current_x + b*d*current_x-
+			          a*c/3*previous_x*previous_x*previous_x + (a*c+b*d)/2*previous_x*previous_x + b*d*previous_x;
+			
+			previous_x = current_x;
+			previous_y_l1 = current_y_l1;
+			previous_y_l2 = current_y_l2;
+			
+		}		
+		return result;
+	}
+
+
+
+
+	//concretization of abstract functions:
+
+	/**
+	 * The number of projections to R is defined to the number of nonzero landscape functions. I-th projection is an integral of i-th landscape function over whole R.
+	**/
+    double project_to_R( int number_of_function )
+    {
+		return this->compute_integral_of_landscape( (size_t)number_of_function );
+	}
+
+    std::vector<double> vectorize( int number_of_function )
+    {
+		//TODO, think of something smarter over here
+		if ( ( number_of_function < 0 ) || ( (size_t)number_of_function >= this->values_of_landscapes.size() ) )
+		{
+			throw "Wrong number of function\n";
+		}
+		std::vector<double> v = this->values_of_landscapes[ number_of_function ];
+		return v;
+	}
+    void compute_average( std::vector< Abs_Topological_data_with_averages* > to_average )
+    {
+		
+		bool dbg = false;
+		//After execution of this procedure, the average is supposed to be in the current object. To make sure that this is the case, we need to do some cleaning first.
+		this->values_of_landscapes.clear();
+		this->grid_min = this->grid_max = 0;
+		
+		//if there is nothing to averate, then the average is a zero landscape. 
+		if ( to_average.size() == 0 )return;
+		
+		//now we need to check if the grids in all objects of to_average are the same:
+		for ( size_t i = 0 ; i != to_average.size() ; ++i )
+		{	
+			if ( !check_if_defined_on_the_same_domain(*((Persistence_landscape_on_grid*)(to_average[0])),*((Persistence_landscape_on_grid*)(to_average[i]))) )throw "Two grids are not compatible"; 				
+		}
+		
+		this->values_of_landscapes = std::vector< std::vector<double> >( ((Persistence_landscape_on_grid*)(to_average[0]))->values_of_landscapes.size() );
+		this->grid_min = ((Persistence_landscape_on_grid*)(to_average[0]))->grid_min;
+		this->grid_max = ((Persistence_landscape_on_grid*)(to_average[0]))->grid_max;
+		
+		if ( dbg )
+		{
+			cerr << "Computations of average. The data from the current landscape have been cleared. We are ready to do the computations. \n";
+		}
+						
+		//for every point in the grid:
+		for ( size_t grid_point = 0 ; grid_point != ((Persistence_landscape_on_grid*)(to_average[0]))->values_of_landscapes.size() ; ++grid_point )
+		{
+			
+			//set up a vector of the correct size:
+			size_t maximal_size_of_vector = 0;
+			for ( size_t land_no = 0 ; land_no != to_average.size() ; ++land_no )
+			{
+				if ( ((Persistence_landscape_on_grid*)(to_average[land_no]))->values_of_landscapes[grid_point].size() > maximal_size_of_vector )
+				maximal_size_of_vector = ((Persistence_landscape_on_grid*)(to_average[land_no]))->values_of_landscapes[grid_point].size();
+			}
+			this->values_of_landscapes[grid_point] = std::vector<double>( maximal_size_of_vector );
+			
+			if ( dbg )
+			{
+				cerr << "We are considering the point : " << grid_point << " of the grid. In this point, there are at most : " << maximal_size_of_vector << " nonzero landscape functions \n";
+			}
+		
+			//and compute an arythmetic average:
+			for ( size_t land_no = 0 ; land_no != to_average.size() ; ++land_no )
+			{
+				//summing:				
+				for ( size_t i = 0 ; i != ((Persistence_landscape_on_grid*)(to_average[land_no]))->values_of_landscapes[grid_point].size() ; ++i )
+				{
+					//compute the average in a smarter way.
+					this->values_of_landscapes[grid_point][i] += ((Persistence_landscape_on_grid*)(to_average[land_no]))->values_of_landscapes[grid_point][i];
+				}								
+			}
+			//normalizing:
+			for ( size_t i = 0 ; i != this->values_of_landscapes[grid_point].size() ; ++i )
+			{
+				this->values_of_landscapes[grid_point][i] /= (double)to_average.size();
+			}			 
+		}
+	}//compute_average
+	
+	
+	/**
+	 * Computations of L^{p} distance between two landscapes on a grid. p is the parameter of the procedure.
+	**/
+	friend double compute_discance_of_landscapes_on_grid( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& second , int p )
+	{		
+		bool dbg = false;
+		//This is what we want to compute: (\int_{- \infty}^{+\infty}| first-second |^p)^(1/p). We will do it one step at a time:
+
+		if ( dbg )
+		{
+			cerr << "first : " << first << endl;
+			cerr << "second : " << second << endl;
+			getchar();
+		}
+
+		//first-second :
+		Persistence_landscape_on_grid lan = first-second;
+		
+		if ( dbg )
+		{
+			cerr << "Difference : " << lan << endl;
+		}
+
+		//| first-second |:
+		lan.abs();
+		
+		if ( dbg )
+		{
+			cerr << "Abs : " << lan << endl;
+		}
+		
+		if ( p != -1 )
+		{
+			//\int_{- \infty}^{+\infty}| first-second |^p
+			double result;
+			if ( p != 1 )
+			{
+				if (dbg){cerr << "p : " << p << endl; getchar();}
+				result = lan.compute_integral_of_landscape( (double)p );				
+				if (dbg){cerr << "integral : " << result << endl;getchar();}
+			}
+			else
+			{
+				result = lan.compute_integral_of_landscape();			
+				if (dbg){cerr << "integral, wihtout power : " << result << endl;getchar();}
+			}
+			//(\int_{- \infty}^{+\infty}| first-second |^p)^(1/p)
+			return pow( result , 1/(double)p );
+		}
+		else
+		{
+			//p == -1
+			return lan.compute_maximum();
+		}
+	}
+
+
+    double distance( const Abs_Topological_data_with_distances* second , double power = 1 )
+    {
+		if ( power != -1 )
+		{
+			return compute_discance_of_landscapes_on_grid( *this , *((Persistence_landscape_on_grid*)second) , power );
+		}
+		else
+		{
+			return compute_max_norm_discance_of_landscapes( *this , *((Persistence_landscape_on_grid*)second) );
+		}
+	}
+
+
+	double compute_scalar_product( const Abs_Topological_data_with_scalar_product* second )
+	{
+		return compute_inner_product( (*this) , *((Persistence_landscape_on_grid*)second) );
+	}
+
+
+	std::vector< std::vector< double > > output_for_visualization()
+	{
+		return this->values_of_landscapes;
+	}
+	
+	
+	//a function used to create a gnuplot script for visualization of landscapes
+	void plot( const char* filename , size_t from_ = std::numeric_limits<size_t>::max(), size_t to_ = std::numeric_limits<size_t>::max() );
+
+
+private:
+	double grid_min;
+	double grid_max;
+	std::vector< std::vector< double > > values_of_landscapes;
+	
+	void set_up_numbers_of_functions_for_vectorization_and_projections_to_reals()
+	{
+		//warning, this function can be only called after filling in the values_of_landscapes vector.
+		this->number_of_functions_for_vectorization = this->values_of_landscapes.size();
+		this->number_of_functions_for_projections_to_reals = this->values_of_landscapes.size();
+	}
+	
+	void set_up_values_of_landscapes( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ );
+	template < typename oper > friend Persistence_landscape_on_grid operation_on_pair_of_landscapes_on_grid( const Persistence_landscape_on_grid& land1 ,  const Persistence_landscape_on_grid& land2 );
+	Persistence_landscape_on_grid multiply_lanscape_by_real_number_not_overwrite( double x )const;
+};
+
+
+void Persistence_landscape_on_grid::set_up_values_of_landscapes( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ )
+{
+	bool dbg = false;
+	if ( dbg )
+	{
+		std::cerr << "Here is the procedure : set_up_values_of_landscapes. The parameters are : grid_min_ : " << grid_min_ << ", grid_max_ : " << grid_max_ << ", number_of_points_ : " << number_of_points_ << endl;
+		//getchar();
+		std::cerr << "Here are the intervals at our disposal : \n";
+		for ( size_t i = 0 ; i != p.size() ; ++i )
+		{
+			std::cerr << p[i].first << " , " << p[i].second << endl;
+		} 
+	}
+	
+	this->values_of_landscapes = std::vector< std::vector< double > >( number_of_points_+1 );
+	this->grid_min = grid_min_;
+	this->grid_max = grid_max_;
+	
+	if ( grid_max_ <= grid_min_ )
+	{
+		throw "Wrong parameters of grid_min and grid_max given to the procedure. THe grid have negative, or zero size. The program will now terminate.\n";
+	}
+	
+	double dx = ( grid_max_ - grid_min_ )/(double)(number_of_points_);		
+	//for every interval in the diagram:
+	for ( size_t int_no = 0 ; int_no != p.size() ; ++int_no )
+	{		
+		size_t grid_interval_begin = (p[int_no].first-grid_min_)/dx;
+		size_t grid_interval_end = (p[int_no].second-grid_min_)/dx;
+		size_t grid_interval_midpoint = (size_t)(0.5*(grid_interval_begin+grid_interval_end));
+		
+		if ( dbg )
+		{
+			cerr << "Considering an interval : " << p[int_no].first << "," << p[int_no].second << endl;
+		
+			std::cerr << "grid_interval_begin : " << grid_interval_begin << std::endl;
+			std::cerr << "grid_interval_end : " << grid_interval_end << std::endl;
+			std::cerr << "grid_interval_midpoint : " << grid_interval_midpoint << std::endl;	
+		}
+		
+		double landscape_value = dx;
+		for ( size_t i = grid_interval_begin+1 ; i < grid_interval_midpoint ; ++i )
+		{
+			if ( dbg )
+			{
+				std::cerr << "Adding landscape value (going up) for a point : " << i << " equal : " << landscape_value << std::endl;
+			}
+			this->values_of_landscapes[i].push_back( landscape_value );
+			landscape_value += dx;
+		}
+		for ( size_t i = grid_interval_midpoint ; i <= grid_interval_end ; ++i )
+		{						
+			if ( landscape_value > 0 ) 
+			{ 
+				this->values_of_landscapes[i].push_back( landscape_value );	
+				if ( dbg )
+				{				
+					std::cerr << "AAdding landscape value (going down) for a point : " << i << " equal : " << landscape_value << std::endl;
+				}
+			}
+			landscape_value -= dx;	
+		}  
+	}
+	
+	//and now we need to sort the valuesL
+	for ( size_t pt = 0 ; pt != this->values_of_landscapes.size() ; ++pt )
+	{
+		std::sort( this->values_of_landscapes[pt].begin() , this->values_of_landscapes[pt].end() , greater() );	
+	}
+}//set_up_values_of_landscapes
+
+Persistence_landscape_on_grid::Persistence_landscape_on_grid( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ )
+{
+	this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ );
+}//Persistence_landscape_on_grid
+
+Persistence_landscape_on_grid& Persistence_landscape_on_grid::operator=( const Persistence_landscape_on_grid& org )
+{
+	this->grid_min = org.grid_min;
+	this->grid_max = org.grid_max;
+	this->values_of_landscapes = org.values_of_landscapes;
+	return (*this);
+}//operator=
+
+Persistence_landscape_on_grid::Persistence_landscape_on_grid(const Persistence_landscape_on_grid& org)
+{
+	this->grid_min = org.grid_min;
+	this->grid_max = org.grid_max;
+	this->values_of_landscapes = org.values_of_landscapes;
+}//copy constructor
+
+Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename , double grid_min_, double grid_max_ , size_t number_of_points_ , size_t dimension )
+{
+	//standard file with barcode
+    std::vector< std::pair< double , double > > p = read_standard_file( filename );    
+    //gudhi file with barcode
+    //std::vector< std::pair< double , double > > p = read_gudhi_file( filename , dimension );        
+	
+	this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ );
+}
+
+Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename , size_t number_of_points_ )
+{
+	//standard file with barcode
+    std::vector< std::pair< double , double > > p = read_standard_file( filename );    
+    //gudhi file with barcode
+    //std::vector< std::pair< double , double > > p = read_gudhi_file( filename , dimension );     
+    
+    double grid_min_ = std::numeric_limits<double>::max();
+    double grid_max_ = -std::numeric_limits<double>::max();
+    for ( size_t i = 0 ; i != p.size() ; ++i )
+    {
+		if ( p[i].first < grid_min_ )grid_min_ = p[i].first;
+		if ( p[i].second > grid_max_ )grid_max_ = p[i].second;
+	}	
+	this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ );
+}
+
+void Persistence_landscape_on_grid::load_landscape_from_file( const char* filename )
+{
+	//check if the file exist.
+	if ( !( access( filename, F_OK ) != -1 ) )
+	{
+		cerr << "The file : " << filename << " do not exist. The program will now terminate \n";
+		throw "The file from which you are trying to read the persistence landscape do not exist. The program will now terminate \n";
+	}	
+	std::ifstream in;
+	in.open( filename );
+	
+	size_t number_of_points_in_the_grid = 0;
+	in >> this->grid_min >> this->grid_max >> number_of_points_in_the_grid;
+	
+	std::vector< std::vector< double > > v(number_of_points_in_the_grid);
+	std::string line;
+	std::getline(in, line);
+	double number;
+	for ( size_t i = 0 ; i != number_of_points_in_the_grid ; ++i )
+	{
+		//read a line of a file and convert it to a vector.
+		std::vector< double > vv;		
+		std::getline(in, line);		
+		//cerr << "Reading line : " << line << endl;getchar();		
+		std::istringstream stream(line);
+		while (stream >> number)
+		{
+			vv.push_back(number);
+		}		
+		v[i] = vv;
+	}
+	this->values_of_landscapes = v;
+	in.close();
+}
+
+void Persistence_landscape_on_grid::print_to_file( const char* filename )const
+{
+	std::ofstream out;
+	out.open( filename );
+	
+	//first we store the parameters of the grid:
+	out << grid_min << std::endl << grid_max << std::endl << this->values_of_landscapes.size() << std::endl;
+	
+	//and now in the following lines, the values of this->values_of_landscapes for the following arguments:
+	for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != this->values_of_landscapes[i].size() ; ++j )
+		{
+			out << this->values_of_landscapes[i][j] << " ";
+		}
+		out << std::endl;
+	}
+	
+	out.close();
+}
+
+void Persistence_landscape_on_grid::plot( const char* filename , size_t from_ , size_t to_ )
+{		
+    //this program create a gnuplot script file that allows to plot persistence diagram.
+    ofstream out;
+
+    std::ostringstream nameSS;
+    nameSS << filename << "_GnuplotScript";
+    std::string nameStr = nameSS.str();
+    out.open( (char*)nameStr.c_str() );
+
+    std::pair<double,double> min_max = compute_minimum_maximum();
+    out << "set xrange [" << this->grid_min << " : " << this->grid_max << "]" << endl;
+    out << "set yrange [" << min_max.first << " : " << min_max.second << "]" << endl;
+    
+    size_t number_of_nonzero_levels = this->number_of_nonzero_levels();
+    double dx = ( this->grid_max - this->grid_min )/((double)this->values_of_landscapes.size()-1);
+    
+    
+    size_t from = 0;
+    if ( from_ != std::numeric_limits<size_t>::max() )
+    {
+		if ( from_ < number_of_nonzero_levels )
+		{
+			from = from_;
+		}
+		else
+		{
+			return;
+		}
+	}	
+	size_t to = number_of_nonzero_levels;
+	if ( to_ != std::numeric_limits<size_t>::max() )
+    {
+		if ( to_ < number_of_nonzero_levels )
+		{
+			to = to_;
+		}
+	}
+    
+    
+    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 << ", \\";
+        }
+        out << endl;
+    }
+    
+    for ( size_t lambda = from ; lambda != to ; ++lambda )
+    {
+		double point = this->grid_min;
+        for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i )
+        {
+			double value = 0;
+			if ( this->values_of_landscapes[i].size() > lambda )			
+			{
+				value = this->values_of_landscapes[i][lambda];
+			}
+            out << point << " " << value << endl;
+            point += dx;
+        }
+        out << "EOF" << endl;
+    }
+    cout << "Gnuplot script to visualize persistence diagram written to the file: " << nameStr << ". Type load '" << nameStr << "' in gnuplot to visualize." << endl;
+}
+
+template < typename T > 
+Persistence_landscape_on_grid operation_on_pair_of_landscapes_on_grid ( const Persistence_landscape_on_grid& land1 ,  const Persistence_landscape_on_grid& land2 )
+{
+	//first we need to check if the domains are the same:
+	if ( !check_if_defined_on_the_same_domain(land1,land2) )throw "Two grids are not compatible"; 	
+	
+	T oper;
+	Persistence_landscape_on_grid result;
+	result.values_of_landscapes = std::vector< std::vector< double > >( land1.values_of_landscapes.size()  );
+	result.grid_min = land1.grid_min;
+	result.grid_max = land1.grid_max;
+	
+	//now we perorm the operations:
+	for ( size_t grid_point = 0 ; grid_point != land1.values_of_landscapes.size() ; ++grid_point )
+	{
+		result.values_of_landscapes[grid_point] = std::vector< double >( std::max( land1.values_of_landscapes[grid_point].size() , land2.values_of_landscapes[grid_point].size() ) );
+		for ( size_t lambda = 0 ; lambda != std::max( land1.values_of_landscapes[grid_point].size() , land2.values_of_landscapes[grid_point].size() ) ; ++lambda )
+		{
+			double value1 = 0;
+			double value2 = 0;
+			if ( lambda < land1.values_of_landscapes[grid_point].size() )value1 = land1.values_of_landscapes[grid_point][lambda];
+			if ( lambda < land2.values_of_landscapes[grid_point].size() )value2 = land2.values_of_landscapes[grid_point][lambda];
+			result.values_of_landscapes[grid_point][lambda] = oper( value1 , value2 );
+		}
+	}
+	
+	return result;
+}
+
+Persistence_landscape_on_grid Persistence_landscape_on_grid::multiply_lanscape_by_real_number_not_overwrite( double x )const
+{
+	Persistence_landscape_on_grid result;
+	result.values_of_landscapes = std::vector< std::vector< double > >( this->values_of_landscapes.size()  );
+	result.grid_min = this->grid_min;
+	result.grid_max = this->grid_max;
+	
+	for ( size_t grid_point = 0 ; grid_point != this->values_of_landscapes.size() ; ++grid_point )
+	{
+		result.values_of_landscapes[grid_point] = std::vector< double >( this->values_of_landscapes[grid_point].size() );
+		for ( size_t i = 0 ; i != this->values_of_landscapes[grid_point].size() ; ++i )
+		{
+			result.values_of_landscapes[grid_point][i] = x*this->values_of_landscapes[grid_point][i];
+		}
+	}
+	
+	return result;
+}
+
+double compute_max_norm_discance_of_landscapes( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& second )
+{
+	double result = 0;
+	
+	//first we need to check if first and second is defined on the same domain"
+	if ( !check_if_defined_on_the_same_domain(first, second) )throw "Two grids are not compatible"; 
+	
+	for ( size_t i = 0 ; i != first.values_of_landscapes.size() ; ++i )
+	{
+		for ( size_t j = 0 ; j != std::min( first.values_of_landscapes[i].size() , second.values_of_landscapes[i].size() ) ; ++j )
+		{
+			if ( result < abs( first.values_of_landscapes[i][j] - second.values_of_landscapes[i][j] ) )
+			{
+				result = abs( first.values_of_landscapes[i][j] - second.values_of_landscapes[i][j] );
+			}
+		}
+		if ( first.values_of_landscapes[i].size() == std::min( first.values_of_landscapes[i].size() , second.values_of_landscapes[i].size() ) )
+		{
+			for ( size_t j = first.values_of_landscapes[i].size() ; j != second.values_of_landscapes[i].size() ; ++j )
+			{
+				if ( result < second.values_of_landscapes[i][j] )result = second.values_of_landscapes[i][j];
+			}
+		}
+		if ( second.values_of_landscapes[i].size() == std::min( first.values_of_landscapes[i].size() , second.values_of_landscapes[i].size() ) )
+		{
+			for ( size_t j = second.values_of_landscapes[i].size() ; j != first.values_of_landscapes[i].size() ; ++j )
+			{
+				if ( result < first.values_of_landscapes[i][j] )result = first.values_of_landscapes[i][j];
+			}
+		}
+	}  
+	return result;
+}
+
+
+
+}//namespace Gudhi_stat
+}//namespace Gudhi
+
+#endif
diff --git a/src/Gudhi_stat/include/gudhi/concretizations/Vector_distances_in_diagram.h b/src/Gudhi_stat/include/gudhi/concretizations/Vector_distances_in_diagram.h
new file mode 100644
index 00000000..5870c652
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/concretizations/Vector_distances_in_diagram.h
@@ -0,0 +1,617 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+#pragma once
+#ifndef Vector_distances_in_diagram_H
+#define Vector_distances_in_diagram_H
+
+#include <fstream>
+#include <cmath>
+#include <algorithm>
+#include <iostream>
+#include <limits>
+
+
+
+#include <gudhi/abstract_classes/Abs_Vectorized_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_averages.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_distances.h>
+#include <gudhi/abstract_classes/Abs_Real_valued_topological_data.h>
+#include <gudhi/abstract_classes/Abs_Topological_data_with_scalar_product.h>
+#include <gudhi/concretizations/read_persitence_from_file.h>
+#include <gudhi/common.h>
+using namespace std;
+
+namespace Gudhi 
+{
+namespace Gudhi_stat 
+{
+
+
+template <typename T>
+struct euclidean_distance
+{
+    double operator() ( const std::pair< T,T >& f , const std::pair<T,T>& s )
+    {
+        return  sqrt( (f.first-s.first)*(f.first-s.first) + (f.second-s.second)*(f.second-s.second) );
+    }
+};
+
+template <typename T>
+struct maximum_distance
+{
+    double operator() ( const std::pair< T,T >& f , const std::pair<T,T>& s )
+    {
+        return  std::min( fabs( f.first - s.first ) , fabs( f.second - s.second ) );
+    }
+};
+
+
+/**
+* This is an implementation of idea presented in the paper by Steve, Matthew and Max. The parameter of the class is the class that computes distance used to construct the vectors. The typical function is
+* either Eucludean of maximum (Manhattan) distance. 
+**/
+
+template <typename F>
+class Vector_distances_in_diagram : 
+									public Abs_Vectorized_topological_data, 
+									public Abs_Topological_data_with_distances, 
+									public Abs_Real_valued_topological_data, 
+									public Abs_Topological_data_with_averages, 
+									public Abs_Topological_data_with_scalar_product
+{
+public:
+	/**
+	* The default constructor.  
+	**/
+    Vector_distances_in_diagram(){};
+        
+    /**
+	* The constructor that takes as an input a multiset of persistence intervals (given as vector of birth-death pairs). The second parameter is the desiered length of the output vectors. 
+	**/
+    Vector_distances_in_diagram( std::vector< std::pair< double , double > > intervals , size_t where_to_cut );
+    
+    /**
+	* The constructor taking as an input a file with birth-death pairs. The second parameter is the desiered length of the output vectors. 
+	**/
+    Vector_distances_in_diagram( const char* filename , size_t where_to_cut );
+
+	/**
+	 *  Assignement operator.
+	**/ 
+    Vector_distances_in_diagram<F>& operator =( const Vector_distances_in_diagram& org );
+
+
+	/**
+	 *  Copy constructor. 
+	**/
+    Vector_distances_in_diagram( const Vector_distances_in_diagram& org );
+	
+	/**
+	 *  Writing to a stream. 
+	**/
+	template <typename K>
+    friend ostream& operator << ( ostream& out , const Vector_distances_in_diagram<K>& d )
+    {
+        for ( size_t i = 0 ; i != std::min( d.sorted_vector_of_distnaces.size() , d.where_to_cut) ; ++i )
+        {
+            out << d.sorted_vector_of_distnaces[i] << " ";
+        }
+        return out;
+    }
+
+	/**
+	* This procedure gives the value of a vector on a given position.  
+	**/ 
+    inline double vector_in_position( size_t position )
+    {
+        if ( position >= this->sorted_vector_of_distnaces.size() )throw("Wrong position in accessing Vector_distances_in_diagram::sorted_vector_of_distnaces\n");
+        return this->sorted_vector_of_distnaces[position];
+    }
+
+	/**
+	 * Return a size of a vector. 
+	**/
+    inline size_t size()const{return this->sorted_vector_of_distnaces.size();}
+    
+    /**
+	 * Write a vector to a file.
+	**/
+    void write_to_file( const char* filename );
+    
+     /**
+	 * Write a vector to a file.
+	**/
+    void print_to_file( const char* filename )
+    {
+		this->write_to_file( filename );
+	}  
+    
+    /**
+	 * Loading a vector to a file.
+	**/
+    void load_from_file( const char* filename );
+    
+    /**
+     * Comparision operators:
+    **/ 
+    bool operator == ( const Vector_distances_in_diagram& second )
+    {
+		if ( this->sorted_vector_of_distnaces.size() != second.sorted_vector_of_distnaces.size() )return false;
+		for ( size_t i = 0 ; i != this->sorted_vector_of_distnaces.size() ; ++i )
+		{
+			if ( !almost_equal(this->sorted_vector_of_distnaces[i] , second.sorted_vector_of_distnaces[i]) )return false;
+		}
+		return true;
+	}
+	
+	bool operator != ( const Vector_distances_in_diagram& second )
+    {
+		return !( *this == second );
+	}
+    
+    //concretization of abstract methods:
+     /**
+     * Compute projection to real numbers of persistence vector. 
+    **/
+    double project_to_R( int number_of_function );
+    
+    /**
+     * Compute a vectorization of a persistent vectors.
+    **/
+    std::vector<double> vectorize( int number_of_function );
+    
+    /**
+     * Compute a average of two persistent vectors.
+    **/
+    void compute_average( std::vector< Abs_Topological_data_with_averages* > to_average );
+    
+    /**
+     * Compute a distance of two persistent vectors.
+    **/
+    double distance( const Abs_Topological_data_with_distances* second , double power = 1);
+    
+    /**
+     * Compute a scalar product of two persistent vectors.
+    **/ 
+    double compute_scalar_product( const Abs_Topological_data_with_scalar_product* second );
+    
+    /**
+    * For visualization use output from vectorize and build histograms. 
+    **/
+    std::vector< double > output_for_visualization()
+    {
+		return this->sorted_vector_of_distnaces;
+	}
+	
+	/**
+	 * Create a gnuplot script to vizualize the data structure. 
+	 **/ 
+	void plot( const char* filename )
+	{
+		std::stringstream gnuplot_script;
+		gnuplot_script << filename << "_Gnuplot_script";
+		ofstream out;
+		out.open( gnuplot_script.str().c_str() );
+		out << "set style data histogram" << std::endl;
+		out << "set style histogram cluster gap 1" << std::endl;
+		out << "set style fill solid border -1" << std::endl;
+		out << "plot '-' notitle" << std::endl;    
+		for ( size_t i = 0 ; i != this->sorted_vector_of_distnaces.size() ; ++i )
+		{
+			out << this->sorted_vector_of_distnaces[i]  << std::endl;
+		}		
+		out << endl;
+		out.close();
+		std::cout << "To vizualize, open gnuplot and type: load \'" << gnuplot_script.str().c_str() << "\'" <<  std::endl;			
+	}
+    
+
+private:
+    std::vector< std::pair< double , double > > intervals;
+    std::vector< double > sorted_vector_of_distnaces;
+
+    void compute_sorted_vector_of_distnaces_via_heap( size_t where_to_cut );
+    void compute_sorted_vector_of_distnaces_via_vector_sorting( size_t where_to_cut );
+    
+    Vector_distances_in_diagram( const std::vector< double >& sorted_vector_of_distnaces_ ):sorted_vector_of_distnaces(sorted_vector_of_distnaces_)
+    {
+		this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
+	}
+    
+    void set_up_numbers_of_functions_for_vectorization_and_projections_to_reals()
+	{		
+		//warning, this function can be only called after filling in the intervals vector.
+		this->number_of_functions_for_vectorization = this->sorted_vector_of_distnaces.size();
+		this->number_of_functions_for_projections_to_reals = this->sorted_vector_of_distnaces.size();
+	}
+};
+
+
+template <typename F>
+Vector_distances_in_diagram<F>::Vector_distances_in_diagram( std::vector< std::pair< double,double > > intervals_ , size_t where_to_cut ):Abs_Vectorized_topological_data(where_to_cut)
+{    
+    std::vector< std::pair< double,double > > i( intervals_ );
+    this->intervals = i;
+    //this->compute_sorted_vector_of_distnaces_via_heap( where_to_cut );
+    this->compute_sorted_vector_of_distnaces_via_vector_sorting(where_to_cut);
+    this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
+}
+
+template <typename F>
+Vector_distances_in_diagram<F>::Vector_distances_in_diagram( const Vector_distances_in_diagram<F>& org )
+{
+    std::vector< std::pair< double,double > > inter( org.intervals );
+    this->intervals = inter;
+    std::vector< double > sorted_vector_of_distnaces( org.sorted_vector_of_distnaces );
+    this->sorted_vector_of_distnaces = sorted_vector_of_distnaces;
+    set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();
+}
+
+
+template <typename F>
+Vector_distances_in_diagram<F>& Vector_distances_in_diagram<F>::operator =( const Vector_distances_in_diagram& org )
+{
+    std::vector< std::pair< double , double > > inter( org.intervals );
+    this->intervals = inter;
+    std::vector< double > sorted_vector_of_distnaces( org.sorted_vector_of_distnaces );
+    this->sorted_vector_of_distnaces = sorted_vector_of_distnaces;
+    return *this;
+}
+
+
+template <typename F>
+Vector_distances_in_diagram<F>::Vector_distances_in_diagram( const char* filename , size_t where_to_cut  ):Abs_Vectorized_topological_data(where_to_cut)
+{   	
+    //standard file with barcode
+    std::vector< std::pair< double , double > > intervals = read_standard_file( filename );    
+    //gudhi file with barcode
+    //std::vector< std::pair< double , double > > intervals = read_gudhi_file( filename , dimension );    
+     
+    this->intervals = intervals;
+    this->compute_sorted_vector_of_distnaces_via_heap( where_to_cut );
+    //this->compute_sorted_vector_of_distnaces_via_vector_sorting( where_to_cut );
+    set_up_numbers_of_functions_for_vectorization_and_projections_to_reals();  
+}
+
+template < typename F>
+void Vector_distances_in_diagram<F>::compute_sorted_vector_of_distnaces_via_heap( size_t where_to_cut )
+{
+
+    bool dbg = false;
+    if ( dbg )
+    {
+        cerr << "Here are the intervals : \n";
+        for ( size_t i = 0 ; i != this->intervals.size() ; ++i )
+        {
+            cerr << this->intervals[i].first << " , " << this->intervals[i].second << endl;
+        }
+    }       
+	where_to_cut = std::min(where_to_cut , (size_t)(0.5 * this->intervals.size() * ( this->intervals.size() - 1 ) + this->intervals.size()));
+
+    std::vector< double > heap( where_to_cut , std::numeric_limits<int>::max() );
+    std::make_heap (heap.begin(),heap.end());
+    F f;
+
+	//for every pair of points in the diagram, compute the minimum of their distance, and distance of those points from diagonal	
+    for ( size_t i = 0 ; i < this->intervals.size() ; ++i )
+    {
+        for ( size_t j = i+1 ; j < this->intervals.size() ; ++j )
+        {			
+            double value = std::min(
+                                f( this->intervals[i] , this->intervals[j] ),                               
+                                std::min(
+                                        f( this->intervals[i] , std::make_pair( 0.5*(this->intervals[i].first+this->intervals[i].second) , 0.5*(this->intervals[i].first+this->intervals[i].second) ) ),
+                                        f( this->intervals[j] , std::make_pair( 0.5*(this->intervals[j].first+this->intervals[j].second) , 0.5*(this->intervals[j].first+this->intervals[j].second) ) )                                
+                                        )    
+                                );
+
+							if ( dbg )
+							{
+								cerr << "Value : " << value << endl;
+								cerr << "heap.front() : " << heap.front() << endl;
+								getchar();
+							}
+
+            if ( -value < heap.front() )
+            {
+                if ( dbg ){cerr << "Replacing : " << heap.front() << " with : " << -value << endl;getchar();}
+                //remove the first element from the heap
+                std::pop_heap (heap.begin(),heap.end());
+                //heap.pop_back();
+                //and put value there instead:
+                //heap.push_back(-value);
+                heap[ where_to_cut-1 ] = -value;
+                std::push_heap (heap.begin(),heap.end());
+            }
+        }
+    }
+    
+    //now add distances of all points from diagonal   
+    for ( size_t i = 0 ; i < this->intervals.size() ; ++i )
+    {
+		double value = f( this->intervals[i] , std::make_pair( 0.5*(this->intervals[i].first+this->intervals[i].second) , 0.5*(this->intervals[i].first+this->intervals[i].second) ) );
+		if ( -value < heap.front() )
+            {
+                //cerr << "Replacing : " << heap.front() << " with : " << -value << endl;getchar();
+                //remove the first element from the heap
+                std::pop_heap (heap.begin(),heap.end());
+                //heap.pop_back();
+                //and put value there instead:
+                //heap.push_back(-value);
+                heap[ where_to_cut-1 ] = -value;
+                std::push_heap (heap.begin(),heap.end());
+            }
+	}
+	 
+    
+    std::sort_heap (heap.begin(),heap.end());
+    for ( size_t i = 0 ; i != heap.size() ; ++i )
+    {
+        if ( heap[i] == std::numeric_limits<int>::max() )
+        {
+            heap[i] = 0;
+        }
+        else
+        {
+            heap[i] *= -1;
+        }
+    }
+    
+    if ( dbg )
+    {
+		std::cerr << "This is the heap after all the operations :\n";
+		for ( size_t i = 0 ; i != heap.size() ; ++i )
+		{
+			std::cout << heap[i] << " ";
+		} 
+		std::cout << endl;
+	} 
+
+    this->sorted_vector_of_distnaces = heap;
+}
+
+
+
+
+template < typename F>
+void Vector_distances_in_diagram<F>::compute_sorted_vector_of_distnaces_via_vector_sorting( size_t where_to_cut )
+{		
+	std::vector< double > distances;	
+	distances.reserve( (size_t)(0.5 * this->intervals.size() * ( this->intervals.size() - 1 ) + this->intervals.size()) );
+    F f;
+
+	//for every pair of points in the diagram, compute the minimum of their distance, and distance of those points from diagonal	
+    for ( size_t i = 0 ; i < this->intervals.size() ; ++i )
+    {
+		//add distance of i-th point in the diagram from the diagonal to the distances vector
+		distances.push_back( f( this->intervals[i] , std::make_pair( 0.5*(this->intervals[i].first+this->intervals[i].second) , 0.5*(this->intervals[i].first+this->intervals[i].second) ) )  );
+        for ( size_t j = i+1 ; j < this->intervals.size() ; ++j )
+        {
+            double value = std::min(
+                                f( this->intervals[i] , this->intervals[j] ),                               
+                                std::min(
+                                        f( this->intervals[i] , std::make_pair( 0.5*(this->intervals[i].first+this->intervals[i].second) , 0.5*(this->intervals[i].first+this->intervals[i].second) ) ),
+                                        f( this->intervals[j] , std::make_pair( 0.5*(this->intervals[j].first+this->intervals[j].second) , 0.5*(this->intervals[j].first+this->intervals[j].second) ) )                                
+                                        )    
+                                );
+            distances.push_back( value );
+            
+        }
+    }
+    std::sort( distances.begin() , distances.end() , std::greater<double>() );    
+    if ( distances.size() > where_to_cut )distances.resize( where_to_cut );       
+    
+    this->sorted_vector_of_distnaces =  distances;
+}
+
+
+
+//concretization of abstract methods:
+template <typename F>
+double Vector_distances_in_diagram<F>::project_to_R( int number_of_function )
+{
+	if ( number_of_function > this->number_of_functions_for_projections_to_reals )throw "Wrong index of a function in a method Vector_distances_in_diagram<F>::project_to_R";
+	if ( number_of_function < 0 )throw "Wrong index of a function in a method Vector_distances_in_diagram<F>::project_to_R";
+	
+	double result = 0;
+	for ( size_t i = 0 ; i != number_of_function ; ++i )
+	{
+		result += sorted_vector_of_distnaces[i];
+	}
+	return result;
+}
+
+template <typename F>
+void Vector_distances_in_diagram<F>::compute_average( std::vector< Abs_Topological_data_with_averages* > to_average )
+{
+	
+	if ( to_average.size() == 0 )
+	{
+		(*this) = Vector_distances_in_diagram<F>();
+		return;
+	}
+	
+	size_t maximal_length_of_vector = 0;
+	for ( size_t i = 0 ; i != to_average.size() ; ++i )
+	{
+		Vector_distances_in_diagram<F>* current = (Vector_distances_in_diagram<F>*)to_average[i];
+		if ( current->sorted_vector_of_distnaces.size() > maximal_length_of_vector )
+		{
+			maximal_length_of_vector = current->sorted_vector_of_distnaces.size();
+		}
+	}
+	
+	//cerr << "maximal_length_of_vector  : " << maximal_length_of_vector << endl;
+	
+	std::vector< double > av(  maximal_length_of_vector , 0 );
+	for ( size_t i = 0 ; i != to_average.size() ; ++i )
+	{
+		Vector_distances_in_diagram<F>* current = (Vector_distances_in_diagram<F>*)to_average[i];
+		for ( size_t j = 0  ; j != current->sorted_vector_of_distnaces.size() ; ++j )
+		{
+			av[j] += current->sorted_vector_of_distnaces[j];
+		}
+	}
+	
+	for ( size_t i = 0 ; i != maximal_length_of_vector ; ++i )
+	{
+		av[i] /= (double)to_average.size();
+	}
+	this->sorted_vector_of_distnaces = av;
+	this->where_to_cut = av.size();
+}
+
+template <typename F>
+double Vector_distances_in_diagram<F>::distance( const Abs_Topological_data_with_distances* second , double power )
+{
+	bool dbg = false;
+	
+	if ( dbg )
+	{
+		std::cerr << "Entering double Vector_distances_in_diagram<F>::distance( const Abs_Topological_data_with_distances* second , double power ) procedure \n";
+		std::cerr << "Power : " << power << std::endl;
+		std::cerr << "This : " << *this << std::endl;
+		std::cerr << "second : " << *((Vector_distances_in_diagram<F>*)second) << std::endl;
+	}
+	
+	Vector_distances_in_diagram<F>* second_ = ((Vector_distances_in_diagram<F>*)second);
+	
+	
+	double result = 0;
+	for ( size_t i = 0 ; i != std::min(this->sorted_vector_of_distnaces.size(), second_->sorted_vector_of_distnaces.size())  ; ++i )
+	{
+		if ( power == 1 )
+		{
+			if ( dbg )
+			{
+				cerr << "|" << this->sorted_vector_of_distnaces[i] << " -  " << second_->sorted_vector_of_distnaces[i] << " |  : " << fabs( this->sorted_vector_of_distnaces[i] - second_->sorted_vector_of_distnaces[i] ) << endl;
+			}
+			result += fabs( this->sorted_vector_of_distnaces[i] - second_->sorted_vector_of_distnaces[i] );
+		}
+		else
+		{
+			result += std::pow( fabs( this->sorted_vector_of_distnaces[i] - second_->sorted_vector_of_distnaces[i] ) , power );
+			if ( dbg )
+			{
+				cerr << "| " << this->sorted_vector_of_distnaces[i] << " - " << second_->sorted_vector_of_distnaces[i]  << " : " << fabs( this->sorted_vector_of_distnaces[i] - second_->sorted_vector_of_distnaces[i] ) << endl;
+			}
+		}
+	}
+	if ( this->sorted_vector_of_distnaces.size() != second_->sorted_vector_of_distnaces.size() )
+	{
+		if ( this->sorted_vector_of_distnaces.size() > second_->sorted_vector_of_distnaces.size() )
+		{
+			for ( size_t i = second_->sorted_vector_of_distnaces.size() ; i != this->sorted_vector_of_distnaces.size() ; ++i )			
+			{
+				result += fabs( this->sorted_vector_of_distnaces[i] );
+			}
+		}
+		else
+		{
+			//this->sorted_vector_of_distnaces.size() < second_->sorted_vector_of_distnaces.size()
+			for ( size_t i = this->sorted_vector_of_distnaces.size() ; i != second_->sorted_vector_of_distnaces.size() ; ++i )			
+			{
+				result += fabs( second_->sorted_vector_of_distnaces[i] );
+			}			
+		}
+	}
+	
+	
+	if ( power != 1 )
+	{
+		result = std::pow( result , (1.0/power) );
+	}
+	return result;
+}
+    
+template < typename F>
+std::vector<double> Vector_distances_in_diagram<F>::vectorize( int number_of_function )
+{
+	if ( number_of_function > this->number_of_functions_for_vectorization )throw "Wrong index of a function in a method Vector_distances_in_diagram<F>::vectorize";
+	if ( number_of_function < 0 )throw "Wrong index of a function in a method Vector_distances_in_diagram<F>::vectorize";
+	
+    std::vector< double > result( std::min( (size_t)number_of_function , this->sorted_vector_of_distnaces.size() ) );
+    for ( size_t i = 0 ; i != std::min( (size_t)number_of_function , this->sorted_vector_of_distnaces.size() ) ; ++i )
+    {
+        result[i] = this->sorted_vector_of_distnaces[i];
+    }
+    return result;
+}
+
+
+template < typename F>
+void Vector_distances_in_diagram<F>::write_to_file( const char* filename )
+{
+	std::ofstream out;
+	out.open( filename );
+	
+	for ( size_t i = 0 ; i != this->sorted_vector_of_distnaces.size() ; ++i )
+	{
+		out << this->sorted_vector_of_distnaces[i] << " ";
+	}
+	
+	out.close();
+}
+
+template < typename F>
+void Vector_distances_in_diagram<F>::load_from_file( const char* filename )
+{
+	//check if the file exist.
+	if ( !( access( filename, F_OK ) != -1 ) )
+	{
+		cerr << "The file : " << filename << " do not exist. The program will now terminate \n";
+		throw "The file from which you are trying to read the persistence landscape do not exist. The program will now terminate \n";
+	}	
+	std::ifstream in;
+	in.open( filename );
+	
+	double number;
+	while ( true )
+	{		
+		in >> number;
+		if ( in.eof() )break;
+		this->sorted_vector_of_distnaces.push_back(number);
+	}	
+	in.close();
+}
+
+template < typename F>
+double Vector_distances_in_diagram<F>::compute_scalar_product( const Abs_Topological_data_with_scalar_product* second )
+{
+	Vector_distances_in_diagram<F>* second_vector = (Vector_distances_in_diagram<F>*)second;
+		
+	double result = 0;
+	for ( size_t i = 0 ; i != std::min(this->sorted_vector_of_distnaces.size(),second_vector->sorted_vector_of_distnaces.size()) ; ++i )
+	{
+		result += this->sorted_vector_of_distnaces[i] * second_vector->sorted_vector_of_distnaces[i];
+	}
+	return result;
+}
+
+
+
+}//namespace Gudhi_stat 
+}//namespace Gudhi
+
+
+#endif // Vector_distances_in_diagram_H
diff --git a/src/Gudhi_stat/include/gudhi/concretizations/read_persitence_from_file.h b/src/Gudhi_stat/include/gudhi/concretizations/read_persitence_from_file.h
new file mode 100644
index 00000000..d2e6ec3c
--- /dev/null
+++ b/src/Gudhi_stat/include/gudhi/concretizations/read_persitence_from_file.h
@@ -0,0 +1,136 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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 Read_Persitence_From_File_H
+#define Read_Persitence_From_File_H
+
+#include <iostream>
+#include <fstream>
+#include <sstream>
+#include <unistd.h>
+
+
+namespace Gudhi
+{
+namespace Gudhi_stat
+{
+
+
+std::vector< std::pair< double , double > > read_standard_file( const char* filename )
+{
+	bool dbg = false;
+	
+	std::ifstream in;
+    in.open( filename );
+    if ( !( access( filename, F_OK ) != -1 ) )
+	{
+		std::cerr << "The file : " << filename << " do not exist. The program will now terminate \n";
+		throw "The file from which you are trying to read the persistence landscape do not exist. The program will now terminate \n";
+	}
+
+    std::string line;
+    std::vector< std::pair<double,double> > barcode;
+
+    while (!in.eof())
+    {
+        getline(in,line);
+        if ( !(line.length() == 0 || line[0] == '#') )
+        {
+            std::stringstream lineSS;
+            lineSS << line;
+            double beginn, endd;
+            lineSS >> beginn;
+            lineSS >> endd;
+            if ( beginn > endd )
+            {
+                double b = beginn;
+                beginn = endd;
+                endd = b;
+            }
+            barcode.push_back( std::make_pair( beginn , endd ) );
+            if (dbg)
+            {
+				std::cerr << beginn << " , " << endd << std::endl;
+			}
+        }
+	}
+	in.close();
+	return barcode;
+}//read_standard_file
+
+std::vector< std::pair< double , double > > read_gudhi_file( const char* filename , size_t dimension = 0 )
+{
+	bool dbg = false;
+	std::ifstream in;
+    in.open( filename );
+
+    std::string line;
+    std::vector< std::pair<double,double> > barcode;
+
+    while (!in.eof())
+    {
+        getline(in,line);
+        if ( !(line.length() == 0 || line[0] == '#') )
+        {
+			if ( line.find("inf") != std::string::npos )
+			{
+				if ( dbg )
+				{
+					std::cerr << "This line: " << line << " contains infinite interval. We will skip it. \n";
+				}
+				continue;
+			}
+            std::stringstream lineSS;
+            lineSS << line;
+            double beginn, endd, field, dim;
+            lineSS >> field;
+            lineSS >> dim;
+            lineSS >> beginn;
+            lineSS >> endd;
+            if ( beginn > endd )
+            {
+                double b = beginn;
+                beginn = endd;
+                endd = b;
+            }
+            if ( dim == dimension )
+            { 
+				barcode.push_back( std::make_pair( beginn , endd ) );
+				if (dbg)
+				{
+					std::cerr << beginn << " , " << endd << std::endl;
+				}
+			}
+        }
+	}
+	in.close();
+	return barcode;
+}//read_gudhi_file
+
+}//namespace Gudhi_stat
+}//namespace Gudhi
+
+
+
+
+#endif
diff --git a/src/Gudhi_stat/test/CMakeLists.txt b/src/Gudhi_stat/test/CMakeLists.txt
new file mode 100644
index 00000000..292549f8
--- /dev/null
+++ b/src/Gudhi_stat/test/CMakeLists.txt
@@ -0,0 +1,67 @@
+cmake_minimum_required(VERSION 2.6)
+project(GUDHI_STAT_CCUT)
+
+if (GCOVR_PATH)
+  # for gcovr to make coverage reports - Corbera Jenkins plugin
+  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fprofile-arcs -ftest-coverage")
+  set(CMAKE_CXX_FLAGS_DEBUG "${CMAKE_CXX_FLAGS_DEBUG} -fprofile-arcs -ftest-coverage")	
+  set(CMAKE_CXX_FLAGS_RELEASE "${CMAKE_CXX_FLAGS_RELEASE} -fprofile-arcs -ftest-coverage")
+endif()
+if (GPROF_PATH)
+  # for gprof to make coverage reports - Jenkins
+  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -pg")
+  set(CMAKE_CXX_FLAGS_DEBUG "${CMAKE_CXX_FLAGS_DEBUG} -pg")
+  set(CMAKE_CXX_FLAGS_RELEASE "${CMAKE_CXX_FLAGS_RELEASE} -pg")
+endif()
+
+# copy data directory for tests purpose
+file(COPY data DESTINATION ${CMAKE_CURRENT_BINARY_DIR}/)
+
+add_executable ( persistence_intervals_test persistence_intervals_test.cpp )
+target_link_libraries(persistence_intervals_test ${Boost_SYSTEM_LIBRARY} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY})
+
+# Unitary tests
+add_test(NAME persistence_intervals_test
+  COMMAND ${CMAKE_CURRENT_BINARY_DIR}/persistence_intervals_test	 
+  # XML format for Jenkins xUnit plugin 
+  --log_format=XML --log_sink=${CMAKE_SOURCE_DIR}/persistence_intervals_UT.xml --log_level=test_suite --report_level=no)
+
+
+add_executable ( vector_representation_test vector_representation_test.cpp )
+target_link_libraries(vector_representation_test ${Boost_SYSTEM_LIBRARY} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY})
+
+# Unitary tests
+add_test(NAME vector_representation_test
+  COMMAND ${CMAKE_CURRENT_BINARY_DIR}/vector_representation_test
+  # XML format for Jenkins xUnit plugin 
+  --log_format=XML --log_sink=${CMAKE_SOURCE_DIR}/vector_representation_UT.xml --log_level=test_suite --report_level=no)
+
+
+add_executable ( persistence_lanscapes_test persistence_lanscapes_test.cpp )
+target_link_libraries(persistence_lanscapes_test ${Boost_SYSTEM_LIBRARY} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY})
+
+# Unitary tests
+add_test(NAME persistence_lanscapes_test
+  COMMAND ${CMAKE_CURRENT_BINARY_DIR}/persistence_lanscapes_test
+  # XML format for Jenkins xUnit plugin 
+  --log_format=XML --log_sink=${CMAKE_SOURCE_DIR}/persistence_lanscapes_UT.xml --log_level=test_suite --report_level=no)
+
+
+add_executable ( persistence_lanscapes_on_grid_test persistence_lanscapes_on_grid_test.cpp )
+target_link_libraries(persistence_lanscapes_on_grid_test ${Boost_SYSTEM_LIBRARY} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY})
+
+# Unitary tests
+add_test(NAME persistence_lanscapes_on_grid_test
+  COMMAND ${CMAKE_CURRENT_BINARY_DIR}/persistence_lanscapes_on_grid_test
+  # XML format for Jenkins xUnit plugin 
+  --log_format=XML --log_sink=${CMAKE_SOURCE_DIR}/persistence_lanscapes_on_grid_UT.xml --log_level=test_suite --report_level=no)
+
+
+add_executable ( persistence_heat_maps_test persistence_heat_maps_test.cpp )
+target_link_libraries(persistence_heat_maps_test ${Boost_SYSTEM_LIBRARY} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY})
+
+# Unitary tests
+add_test(NAME persistence_heat_maps_test
+  COMMAND ${CMAKE_CURRENT_BINARY_DIR}/persistence_heat_maps_test
+  # XML format for Jenkins xUnit plugin
+  --log_format=XML --log_sink=${CMAKE_SOURCE_DIR}/persistence_heat_maps_UT.xml --log_level=test_suite --report_level=no)
diff --git a/src/Gudhi_stat/test/data/aaaa b/src/Gudhi_stat/test/data/aaaa
new file mode 100644
index 00000000..41069a90
--- /dev/null
+++ b/src/Gudhi_stat/test/data/aaaa
@@ -0,0 +1,104 @@
+0
+1
+101
+0.005 
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diff --git a/src/Gudhi_stat/test/data/average b/src/Gudhi_stat/test/data/average
new file mode 100644
index 00000000..275f6bfc
--- /dev/null
+++ b/src/Gudhi_stat/test/data/average
@@ -0,0 +1,148611 @@
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+0.508229  0.397693
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+0.541697  0.394687
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+0.551764  0.389673
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+0.56849  0.380773
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+0.966553  0.0257846
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+0.997421  0
+#lambda_3
+0.00296489  0
+0.00737515  0.00220513
+0.00842527  0.00168007
+0.0212389  0.00808686
+0.0212923  0.00806015
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+0.3778  0.304632
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+0.996833  0
+#lambda_4
+0.00506514  0
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+0.0084787  0.00165335
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+0.0213945  0.00800906
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+#lambda_5
+0.005172  0
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+0.994855  0
+#lambda_6
+0.00537637  0
+0.00858089  0.00160226
+0.00919041  0.0012975
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+0.994053  0
+#lambda_7
+0.00659542  0
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+#lambda_8
+0.0066006  0
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diff --git a/src/Gudhi_stat/test/data/average_of_persistence_vectors b/src/Gudhi_stat/test/data/average_of_persistence_vectors
new file mode 100644
index 00000000..c7078160
--- /dev/null
+++ b/src/Gudhi_stat/test/data/average_of_persistence_vectors
@@ -0,0 +1 @@
+3.53553 3.53553 2.82843 0.707107 0.707107 0.707107 
\ No newline at end of file
diff --git a/src/Gudhi_stat/test/data/average_on_a_grid b/src/Gudhi_stat/test/data/average_on_a_grid
new file mode 100644
index 00000000..4dd66f81
--- /dev/null
+++ b/src/Gudhi_stat/test/data/average_on_a_grid
@@ -0,0 +1,104 @@
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diff --git a/src/Gudhi_stat/test/data/difference b/src/Gudhi_stat/test/data/difference
new file mode 100644
index 00000000..aab93608
--- /dev/null
+++ b/src/Gudhi_stat/test/data/difference
@@ -0,0 +1,148611 @@
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+0.54603  -0.0146758
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+0.636462  -0.00899078
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+0.967347  -0.00388445
+0.96765  -0.00448995
+0.994537  -0.00448995
+0.999027  0
+#lambda_1
+0.00144702  0
+0.0307676  -0.0293206
+0.0707351  -0.0293206
+0.0725442  -0.0257024
+0.133967  -0.0257025
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+0.534084  -0.0335956
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+0.998422  0
+#lambda_2
+0.00267455  0
+0.00722998  -0.00455543
+0.00737515  -0.00441026
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+0.0212389  -0.0161737
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+0.997421  0
+#lambda_3
+0.00296489  0
+0.00737515  -0.00441026
+0.00842527  -0.00336013
+0.0212389  -0.0161737
+0.0212923  -0.0161203
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+0.996833  0
+#lambda_4
+0.00506514  0
+0.00842527  -0.00336013
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+0.99558  0
+#lambda_5
+0.005172  0
+0.0084787  -0.0033067
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+0.994855  0
+#lambda_6
+0.00537637  0
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+0.994053  0
+#lambda_7
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diff --git a/src/Gudhi_stat/test/data/difference_on_grid_test b/src/Gudhi_stat/test/data/difference_on_grid_test
new file mode 100644
index 00000000..13506d75
--- /dev/null
+++ b/src/Gudhi_stat/test/data/difference_on_grid_test
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diff --git a/src/Gudhi_stat/test/data/file_with_diagram b/src/Gudhi_stat/test/data/file_with_diagram
new file mode 100644
index 00000000..81d8a3bf
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diff --git a/src/Gudhi_stat/test/data/file_with_diagram_2 b/src/Gudhi_stat/test/data/file_with_diagram_2
new file mode 100644
index 00000000..608a1878
--- /dev/null
+++ b/src/Gudhi_stat/test/data/file_with_diagram_2
@@ -0,0 +1,435 @@
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diff --git a/src/Gudhi_stat/test/data/file_with_landscape_from_file_with_diagram b/src/Gudhi_stat/test/data/file_with_landscape_from_file_with_diagram
new file mode 100644
index 00000000..c5c492c9
--- /dev/null
+++ b/src/Gudhi_stat/test/data/file_with_landscape_from_file_with_diagram
@@ -0,0 +1,817 @@
+#lambda_0
+0.0290362  0
+0.273076  0.24404
+0.276873  0.240242
+0.329297  0.292665
+0.36328  0.258682
+0.485629  0.38103
+0.490689  0.375971
+0.54603  0.431313
+0.631171  0.346172
+0.63642  0.351422
+0.640956  0.346887
+0.644303  0.350234
+0.994537  0
+#lambda_1
+0.0307676  0
+0.133967  0.103199
+0.136898  0.100267
+0.276873  0.240242
+0.310857  0.206258
+0.36328  0.258682
+0.36834  0.253622
+0.490689  0.375971
+0.500148  0.366511
+0.534084  0.400446
+0.590941  0.343589
+0.612036  0.364684
+0.630859  0.345861
+0.631171  0.346172
+0.635706  0.341637
+0.640956  0.346887
+0.879378  0.108465
+0.88052  0.109607
+0.990127  0
+#lambda_2
+0.0366312  0
+0.136898  0.100267
+0.145814  0.0913521
+0.188411  0.13395
+0.21348  0.108881
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+0.315917  0.201199
+0.36834  0.253622
+0.372727  0.249235
+0.376471  0.252978
+0.381543  0.247906
+0.500148  0.366511
+0.508229  0.358431
+0.528049  0.37825
+0.549487  0.356812
+0.551764  0.359089
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+0.635394  0.341325
+0.635706  0.341637
+0.816147  0.161196
+0.81754  0.162589
+0.875521  0.104608
+0.879378  0.108465
+0.987842  0
+#lambda_3
+0.0544614  0
+0.145814  0.0913521
+0.170882  0.0662834
+0.21348  0.108881
+0.21854  0.103822
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+0.546453  0.353778
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+0.576826  0.329474
+0.579102  0.33175
+0.597925  0.312927
+0.609764  0.324766
+0.6143  0.320231
+0.635394  0.341325
+0.815835  0.160884
+0.816147  0.161196
+0.874128  0.103215
+0.875521  0.104608
+0.980129  0
+#lambda_4
+0.0920033  0
+0.162167  0.0701632
+0.168464  0.0638655
+0.170882  0.0662834
+0.175942  0.061224
+0.21854  0.103822
+0.222927  0.0994343
+0.320304  0.196811
+0.325376  0.191739
+0.3778  0.244162
+0.38588  0.236082
+0.389624  0.239826
+0.410259  0.21919
+0.490951  0.299882
+0.491334  0.299498
+0.529248  0.337412
+0.529667  0.336992
+0.546453  0.353778
+0.573792  0.32644
+0.576826  0.329474
+0.595649  0.31065
+0.597925  0.312927
+0.60246  0.308392
+0.6143  0.320231
+0.652776  0.281755
+0.659416  0.288395
+0.746537  0.201275
+0.752208  0.206946
+0.807053  0.152102
+0.815835  0.160884
+0.873816  0.102903
+0.874128  0.103215
+0.977343  0
+#lambda_5
+0.104599  0
+0.168464  0.0638655
+0.173524  0.058806
+0.175942  0.061224
+0.180329  0.0568366
+0.222927  0.0994343
+0.227999  0.0943619
+0.325376  0.191739
+0.333457  0.183659
+0.38588  0.236082
+0.406516  0.215446
+0.410259  0.21919
+0.410391  0.219058
+0.45834  0.267007
+0.458592  0.266755
+0.491334  0.299498
+0.491754  0.299079
+0.529667  0.336992
+0.557006  0.309654
+0.573792  0.32644
+0.592615  0.307616
+0.595649  0.31065
+0.600184  0.306115
+0.60246  0.308392
+0.640936  0.269916
+0.652776  0.281755
+0.739896  0.194634
+0.746537  0.201275
+0.801381  0.14643
+0.807053  0.152102
+0.865034  0.0941206
+0.873816  0.102903
+0.976719  0
+#lambda_6
+0.114718  0
+0.173524  0.058806
+0.177911  0.0544186
+0.180329  0.0568366
+0.185402  0.0517641
+0.227999  0.0943619
+0.23608  0.0862815
+0.333457  0.183659
+0.354092  0.163023
+0.406516  0.215446
+0.406648  0.215314
+0.410391  0.219058
+0.410643  0.218807
+0.458592  0.266755
+0.459011  0.266336
+0.491754  0.299079
+0.519092  0.27174
+0.557006  0.309654
+0.56704  0.299619
+0.578509  0.311088
+0.587298  0.3023
+0.592615  0.307616
+0.59715  0.303081
+0.600184  0.306115
+0.63866  0.267639
+0.640936  0.269916
+0.728057  0.182795
+0.739896  0.194634
+0.794741  0.13979
+0.801381  0.14643
+0.859362  0.0884492
+0.865034  0.0941206
+0.916025  0.0431291
+0.924275  0.0513791
+0.975654  0
+#lambda_7
+0.117379  0
+0.127589  0.0102096
+0.130645  0.00715284
+0.177911  0.0544186
+0.182984  0.0493461
+0.185402  0.0517641
+0.193482  0.0436837
+0.23608  0.0862815
+0.240402  0.0819591
+0.323826  0.165383
+0.340139  0.14907
+0.354092  0.163023
+0.354224  0.162891
+0.406648  0.215314
+0.406899  0.215063
+0.410643  0.218807
+0.411062  0.218387
+0.459011  0.266336
+0.486349  0.238998
+0.519092  0.27174
+0.529127  0.261706
+0.56704  0.299619
+0.575829  0.290831
+0.587298  0.3023
+0.591833  0.297764
+0.59715  0.303081
+0.611692  0.288539
+0.6135  0.290348
+0.637434  0.266413
+0.63866  0.267639
+0.725781  0.180518
+0.728057  0.182795
+0.782901  0.127951
+0.794741  0.13979
+0.852722  0.0818087
+0.859362  0.0884492
+0.910354  0.0374576
+0.916025  0.0431291
+0.959154  0
+#lambda_8
+0.123493  0
+0.130645  0.00715284
+0.135718  0.00208036
+0.182984  0.0493461
+0.191064  0.0412657
+0.193482  0.0436837
+0.197804  0.0393613
+0.240402  0.0819591
+0.256715  0.065646
+0.340139  0.14907
+0.340271  0.148938
+0.354224  0.162891
+0.354476  0.16264
+0.406899  0.215063
+0.407318  0.214643
+0.411062  0.218387
+0.432004  0.197446
+0.478291  0.243732
+0.484687  0.237336
+0.486349  0.238998
+0.496384  0.228963
+0.529127  0.261706
+0.537777  0.253055
+0.569195  0.284473
+0.569333  0.284335
+0.575829  0.290831
+0.580364  0.286295
+0.591833  0.297764
+0.606375  0.283223
+0.611692  0.288539
+0.635626  0.264605
+0.637434  0.266413
+0.724555  0.179293
+0.725781  0.180518
+0.780625  0.125674
+0.782901  0.127951
+0.840883  0.0699695
+0.852722  0.0818087
+0.891918  0.0426129
+0.897031  0.0477262
+0.908827  0.0359304
+0.910354  0.0374576
+0.947812  0
+#lambda_9
+0.133638  0
+0.135718  0.00208036
+0.137798  0
+0.149798  0
+0.191064  0.0412657
+0.195386  0.0369434
+0.197804  0.0393613
+0.214117  0.0230483
+0.256715  0.065646
+0.256847  0.065514
+0.340271  0.148938
+0.340523  0.148687
+0.354476  0.16264
+0.354895  0.16222
+0.407318  0.214643
+0.42826  0.193702
+0.432004  0.197446
+0.438401  0.191049
+0.484687  0.237336
+0.494722  0.227301
+0.496384  0.228963
+0.505034  0.220313
+0.537777  0.253055
+0.537915  0.252917
+0.569333  0.284335
+0.573869  0.2798
+0.580364  0.286295
+0.594906  0.271754
+0.606375  0.283223
+0.630309  0.259288
+0.635626  0.264605
+0.722747  0.177484
+0.724555  0.179293
+0.779399  0.124448
+0.780625  0.125674
+0.838606  0.067693
+0.840883  0.0699695
+0.880078  0.0307738
+0.891918  0.0426129
+0.903713  0.0308171
+0.908827  0.0359304
+0.944757  0
+#lambda_10
+0.155421  0
+0.187662  0.0322402
+0.189172  0.0307294
+0.195386  0.0369434
+0.211699  0.0206303
+0.214117  0.0230483
+0.214249  0.0229162
+0.256847  0.065514
+0.257099  0.0652625
+0.340523  0.148687
+0.340942  0.148267
+0.354895  0.16222
+0.36777  0.149345
+0.402826  0.184401
+0.410893  0.176334
+0.42826  0.193702
+0.434657  0.187305
+0.438401  0.191049
+0.448435  0.181014
+0.494722  0.227301
+0.503372  0.218651
+0.505034  0.220313
+0.505173  0.220174
+0.537915  0.252917
+0.542451  0.248382
+0.573869  0.2798
+0.58841  0.265258
+0.594906  0.271754
+0.61884  0.247819
+0.630309  0.259288
+0.71743  0.172168
+0.722747  0.177484
+0.777591  0.12264
+0.779399  0.124448
+0.83738  0.0664671
+0.838606  0.067693
+0.877802  0.0284973
+0.880078  0.0307738
+0.891874  0.0189779
+0.903713  0.0308171
+0.93453  0
+#lambda_11
+0.158443  0
+0.189172  0.0307294
+0.205486  0.0144164
+0.211699  0.0206303
+0.211832  0.0204983
+0.214249  0.0229162
+0.214501  0.0226647
+0.257099  0.0652625
+0.257518  0.0648432
+0.340942  0.148267
+0.353817  0.135392
+0.36777  0.149345
+0.375837  0.141279
+0.410893  0.176334
+0.417289  0.169937
+0.434657  0.187305
+0.444691  0.177271
+0.448435  0.181014
+0.448771  0.180678
+0.477632  0.209539
+0.485947  0.201225
+0.503372  0.218651
+0.503511  0.218512
+0.505173  0.220174
+0.509708  0.215639
+0.542451  0.248382
+0.556992  0.23384
+0.58841  0.265258
+0.612345  0.241324
+0.61884  0.247819
+0.705961  0.160699
+0.71743  0.172168
+0.772274  0.117323
+0.777591  0.12264
+0.835572  0.064659
+0.83738  0.0664671
+0.876576  0.0272714
+0.877802  0.0284973
+0.889598  0.0167015
+0.891874  0.0189779
+0.910852  0
+#lambda_12
+0.176956  0
+0.180095  0.00313879
+0.183234  0
+0.191069  0
+0.205486  0.0144164
+0.205618  0.0142844
+0.211832  0.0204983
+0.212083  0.0202468
+0.214501  0.0226647
+0.21492  0.0222454
+0.257518  0.0648432
+0.270393  0.0519679
+0.353817  0.135392
+0.361884  0.127326
+0.375837  0.141279
+0.382234  0.134882
+0.417289  0.169937
+0.427324  0.159903
+0.444691  0.177271
+0.445028  0.176934
+0.448771  0.180678
+0.457086  0.172364
+0.485947  0.201225
+0.486085  0.201087
+0.503511  0.218512
+0.508046  0.213977
+0.509708  0.215639
+0.52425  0.201097
+0.556992  0.23384
+0.580927  0.209906
+0.612345  0.241324
+0.699465  0.154203
+0.705961  0.160699
+0.760805  0.105854
+0.772274  0.117323
+0.830255  0.0593421
+0.835572  0.064659
+0.874768  0.0254633
+0.876576  0.0272714
+0.888372  0.0154756
+0.889598  0.0167015
+0.906299  0
+#lambda_13
+0.191333  0
+0.205618  0.0142844
+0.205869  0.0140328
+0.212083  0.0202468
+0.212502  0.0198274
+0.21492  0.0222454
+0.222865  0.0143007
+0.243649  0.0350847
+0.24858  0.0301542
+0.270393  0.0519679
+0.27846  0.0439015
+0.361884  0.127326
+0.368281  0.120929
+0.382234  0.134882
+0.392268  0.124847
+0.427324  0.159903
+0.42766  0.159567
+0.445028  0.176934
+0.453342  0.16862
+0.457086  0.172364
+0.457224  0.172226
+0.486085  0.201087
+0.49062  0.196551
+0.508046  0.213977
+0.522588  0.199435
+0.52425  0.201097
+0.548184  0.177163
+0.580927  0.209906
+0.668047  0.122785
+0.699465  0.154203
+0.75431  0.0993589
+0.760805  0.105854
+0.818786  0.0478731
+0.830255  0.0593421
+0.869451  0.0201464
+0.874768  0.0254633
+0.886564  0.0136675
+0.888372  0.0154756
+0.903847  0
+#lambda_14
+0.191836  0
+0.205869  0.0140328
+0.206288  0.0136135
+0.212502  0.0198274
+0.220447  0.0118827
+0.222865  0.0143007
+0.227796  0.00937014
+0.24858  0.0301542
+0.256646  0.0220878
+0.27846  0.0439015
+0.284857  0.0375047
+0.368281  0.120929
+0.378315  0.110894
+0.392268  0.124847
+0.392604  0.124511
+0.42766  0.159567
+0.435974  0.151253
+0.453342  0.16862
+0.45348  0.168482
+0.457224  0.172226
+0.461759  0.16769
+0.49062  0.196551
+0.496732  0.190439
+0.501661  0.195368
+0.510091  0.186939
+0.522588  0.199435
+0.546522  0.175501
+0.548184  0.177163
+0.635305  0.0900423
+0.668047  0.122785
+0.69674  0.0940929
+0.711929  0.109282
+0.738081  0.0831299
+0.75431  0.0993589
+0.812291  0.0413778
+0.818786  0.0478731
+0.857982  0.00867738
+0.869451  0.0201464
+0.881247  0.00835057
+0.886564  0.0136675
+0.900231  0
+#lambda_15
+0.192675  0
+0.206288  0.0136135
+0.214233  0.00566879
+0.220447  0.0118827
+0.225378  0.00695217
+0.227796  0.00937014
+0.235862  0.00130373
+0.256646  0.0220878
+0.263043  0.015691
+0.284857  0.0375047
+0.294891  0.0274702
+0.378315  0.110894
+0.378651  0.110558
+0.392604  0.124511
+0.400919  0.116197
+0.435974  0.151253
+0.436113  0.151114
+0.45348  0.168482
+0.458015  0.163947
+0.461759  0.16769
+0.467871  0.161578
+0.496732  0.190439
+0.505162  0.18201
+0.510091  0.186939
+0.534025  0.163005
+0.546522  0.175501
+0.633643  0.0883803
+0.635305  0.0900423
+0.663997  0.0613501
+0.69674  0.0940929
+0.722892  0.0679409
+0.738081  0.0831299
+0.796062  0.0251487
+0.812291  0.0413778
+0.851487  0.00218203
+0.857982  0.00867738
+0.866659  0
+0.872896  0
+0.881247  0.00835057
+0.889597  0
+#lambda_16
+0.208564  0
+0.214233  0.00566879
+0.219164  0.000738249
+0.225378  0.00695217
+0.23233  0
+0.234558  0
+0.235862  0.00130373
+0.237166  0
+0.247352  0
+0.263043  0.015691
+0.273077  0.00565653
+0.294891  0.0274702
+0.295227  0.0271341
+0.378651  0.110558
+0.386966  0.102244
+0.400919  0.116197
+0.401057  0.116059
+0.436113  0.151114
+0.440648  0.146579
+0.458015  0.163947
+0.464127  0.157834
+0.467871  0.161578
+0.476301  0.153149
+0.505162  0.18201
+0.529096  0.158075
+0.534025  0.163005
+0.621146  0.0758838
+0.633643  0.0883803
+0.662335  0.0596881
+0.663997  0.0613501
+0.690149  0.035198
+0.722892  0.0679409
+0.780873  0.00995978
+0.796062  0.0251487
+0.821211  0
+0.849305  0
+0.851487  0.00218203
+0.853669  0
+#lambda_17
+0.218425  0
+0.219164  0.000738249
+0.219902  0
+0.267421  0
+0.273077  0.00565653
+0.273413  0.00532039
+0.295227  0.0271341
+0.303541  0.0188198
+0.386966  0.102244
+0.387104  0.102106
+0.401057  0.116059
+0.405592  0.111523
+0.440648  0.146579
+0.44676  0.140467
+0.464127  0.157834
+0.472557  0.149405
+0.476301  0.153149
+0.500235  0.129214
+0.529096  0.158075
+0.616217  0.0709547
+0.621146  0.0758838
+0.645033  0.0519969
+0.647105  0.0540688
+0.65191  0.0492634
+0.662335  0.0596881
+0.686402  0.035621
+0.686539  0.0357586
+0.688624  0.0336736
+0.690149  0.035198
+0.704418  0.0209288
+0.720922  0.0374331
+0.758355  0
+0.770913  0
+0.780873  0.00995978
+0.790833  0
+#lambda_18
+0.268093  0
+0.273413  0.00532039
+0.278734  0
+0.284722  0
+0.303541  0.0188198
+0.30368  0.0186815
+0.387104  0.102106
+0.391639  0.0975703
+0.405592  0.111523
+0.411704  0.105411
+0.44676  0.140467
+0.45519  0.132037
+0.472557  0.149405
+0.496491  0.125471
+0.500235  0.129214
+0.500922  0.128527
+0.510982  0.138587
+0.597416  0.0521537
+0.616217  0.0709547
+0.640104  0.0470677
+0.645033  0.0519969
+0.649838  0.0471916
+0.65191  0.0492634
+0.675977  0.0251964
+0.686402  0.035621
+0.688487  0.033536
+0.688624  0.0336736
+0.702894  0.0194043
+0.704418  0.0209288
+0.721485  0.00386195
+0.724166  0.00654325
+0.73071  0
+#lambda_19
+0.284998  0
+0.30368  0.0186815
+0.308215  0.0141462
+0.391639  0.0975703
+0.397751  0.0914582
+0.411704  0.105411
+0.420134  0.0969815
+0.45519  0.132037
+0.479124  0.108103
+0.496491  0.125471
+0.497179  0.124783
+0.500922  0.128527
+0.587356  0.0420936
+0.597416  0.0521537
+0.621303  0.0282668
+0.640104  0.0470677
+0.644909  0.0422624
+0.649838  0.0471916
+0.673905  0.0231246
+0.675977  0.0251964
+0.678062  0.0231114
+0.688487  0.033536
+0.702756  0.0192668
+0.702894  0.0194043
+0.71996  0.00233748
+0.721485  0.00386195
+0.725347  0
+#lambda_20
+0.294069  0
+0.308215  0.0141462
+0.314327  0.00803414
+0.397751  0.0914582
+0.406181  0.0830285
+0.420134  0.0969815
+0.444068  0.0730472
+0.479124  0.108103
+0.479811  0.107416
+0.497179  0.124783
+0.583612  0.0383499
+0.587356  0.0420936
+0.611243  0.0182066
+0.621303  0.0282668
+0.626108  0.0234615
+0.644909  0.0422624
+0.668976  0.0181954
+0.673905  0.0231246
+0.67599  0.0210396
+0.678062  0.0231114
+0.692331  0.00884218
+0.702756  0.0192668
+0.719823  0.00219994
+0.71996  0.00233748
+0.722298  0
+#lambda_21
+0.306293  0
+0.314327  0.00803414
+0.322361  0
+0.323152  0
+0.406181  0.0830285
+0.430115  0.0590942
+0.444068  0.0730472
+0.444755  0.07236
+0.479811  0.107416
+0.566245  0.0209823
+0.583612  0.0383499
+0.607499  0.0144629
+0.611243  0.0182066
+0.616048  0.0134013
+0.626108  0.0234615
+0.64957  0
+0.650781  0
+0.668976  0.0181954
+0.671061  0.0161104
+0.67599  0.0210396
+0.69026  0.00677034
+0.692331  0.00884218
+0.701174  0
+0.717623  0
+0.719823  0.00219994
+0.722023  0
+#lambda_22
+0.371021  0
+0.430115  0.0590942
+0.430802  0.0584071
+0.444755  0.07236
+0.476326  0.0407894
+0.484101  0.0485642
+0.532665  0
+0.545262  0
+0.566245  0.0209823
+0.587227  0
+0.593036  0
+0.607499  0.0144629
+0.612304  0.0096576
+0.616048  0.0134013
+0.617247  0.0122027
+0.620882  0.0158375
+0.636719  0
+0.654951  0
+0.671061  0.0161104
+0.68533  0.00184115
+0.69026  0.00677034
+0.69703  0
+#lambda_23
+0.372395  0
+0.430802  0.0584071
+0.462373  0.0268364
+0.476326  0.0407894
+0.500342  0.0167732
+0.502883  0.0193141
+0.522197  0
+0.602647  0
+0.612304  0.0096576
+0.613503  0.00845896
+0.617247  0.0122027
+0.629449  0
+0.683489  0
+0.68533  0.00184115
+0.687172  0
+#lambda_24
+0.387744  0
+0.425327  0.0375838
+0.449224  0.0136873
+0.462373  0.0268364
+0.486389  0.00282021
+0.500342  0.0167732
+0.517115  0
+0.605044  0
+0.613503  0.00845896
+0.621962  0
+#lambda_25
+0.435537  0
+0.449224  0.0136873
+0.462911  0
+0.483569  0
+0.486389  0.00282021
+0.489209  0
diff --git a/src/Gudhi_stat/test/data/file_with_landscape_from_file_with_diagram_1 b/src/Gudhi_stat/test/data/file_with_landscape_from_file_with_diagram_1
new file mode 100644
index 00000000..075dbd8a
--- /dev/null
+++ b/src/Gudhi_stat/test/data/file_with_landscape_from_file_with_diagram_1
@@ -0,0 +1,147820 @@
+#lambda_0
+0.00115996  0
+0.0705916  0.0694316
+0.0707351  0.0692881
+0.297446  0.295999
+0.299309  0.294137
+0.443232  0.43806
+0.462177  0.419114
+0.507542  0.464478
+0.536031  0.435989
+0.547048  0.447006
+0.571679  0.422374
+0.573069  0.423764
+0.636462  0.360371
+0.637257  0.361165
+0.967347  0.0310745
+0.96765  0.031377
+0.999027  0
+#lambda_1
+0.00144702  0
+0.0707351  0.0692881
+0.0725442  0.067479
+0.292533  0.287468
+0.292586  0.287414
+0.299309  0.294137
+0.30002  0.293425
+0.399923  0.393327
+0.399925  0.393325
+0.429631  0.423031
+0.43268  0.419982
+0.444423  0.431725
+0.445313  0.430835
+0.447291  0.432814
+0.461584  0.418521
+0.462177  0.419114
+0.466162  0.415129
+0.469657  0.418624
+0.476828  0.411452
+0.515923  0.450547
+0.533256  0.433214
+0.536031  0.435989
+0.544472  0.427548
+0.552128  0.435203
+0.562598  0.424733
+0.56277  0.424905
+0.56849  0.419185
+0.571679  0.422374
+0.635073  0.358981
+0.636462  0.360371
+0.758486  0.238348
+0.758779  0.238642
+0.966847  0.030574
+0.967347  0.0310745
+0.998422  0
+#lambda_2
+0.00267455  0
+0.00722998  0.00455543
+0.00737515  0.00441026
+0.0201887  0.0172238
+0.0212389  0.0161737
+0.0725442  0.067479
+0.0725976  0.0674256
+0.292586  0.287414
+0.293298  0.286702
+0.30002  0.293425
+0.300023  0.293422
+0.399925  0.393325
+0.402974  0.390276
+0.43268  0.419982
+0.43357  0.419092
+0.445313  0.430835
+0.459606  0.416542
+0.461584  0.418521
+0.465569  0.414536
+0.466162  0.415129
+0.473334  0.407958
+0.476828  0.411452
+0.479777  0.408504
+0.517273  0.446
+0.531657  0.431615
+0.533256  0.433214
+0.541697  0.424773
+0.544472  0.427548
+0.554943  0.417077
+0.562598  0.424733
+0.568318  0.419013
+0.56849  0.419185
+0.581603  0.406072
+0.583463  0.407932
+0.633743  0.357651
+0.635073  0.358981
+0.67059  0.323463
+0.671354  0.324227
+0.757859  0.237721
+0.758486  0.238348
+0.966553  0.0302801
+0.966847  0.030574
+0.997421  0
+#lambda_3
+0.00296489  0
+0.00737515  0.00441026
+0.00842527  0.00336013
+0.0212389  0.0161737
+0.0212923  0.0161203
+0.0725976  0.0674256
+0.0726998  0.0673234
+0.171718  0.166341
+0.172327  0.165732
+0.293298  0.286702
+0.2933  0.2867
+0.300023  0.293422
+0.303072  0.290373
+0.402974  0.390276
+0.403864  0.389386
+0.43357  0.419092
+0.447863  0.404799
+0.459606  0.416542
+0.463591  0.412557
+0.465569  0.414536
+0.472741  0.407365
+0.473334  0.407958
+0.476282  0.405009
+0.479777  0.408504
+0.488307  0.399973
+0.504029  0.415694
+0.509882  0.409841
+0.531657  0.431615
+0.540099  0.423174
+0.541697  0.424773
+0.552168  0.414302
+0.554943  0.417077
+0.560392  0.411628
+0.566359  0.417595
+0.566629  0.417324
+0.568318  0.419013
+0.581431  0.4059
+0.581603  0.406072
+0.631883  0.355792
+0.633743  0.357651
+0.669261  0.322134
+0.67059  0.323463
+0.757096  0.236958
+0.757859  0.237721
+0.965927  0.0296537
+0.966553  0.0302801
+0.996833  0
+#lambda_4
+0.00506514  0
+0.00842527  0.00336013
+0.0084787  0.0033067
+0.0212923  0.0161203
+0.0213945  0.0160181
+0.0726998  0.0673234
+0.0733093  0.0667139
+0.172327  0.165732
+0.17233  0.165729
+0.2933  0.2867
+0.296349  0.283651
+0.303072  0.290373
+0.303615  0.289831
+0.347829  0.334045
+0.348176  0.333698
+0.403864  0.389386
+0.418157  0.375093
+0.447863  0.404799
+0.451848  0.400814
+0.463591  0.412557
+0.470762  0.405386
+0.472741  0.407365
+0.475689  0.404416
+0.476282  0.405009
+0.480844  0.400447
+0.481994  0.401596
+0.485962  0.397628
+0.488307  0.399973
+0.489664  0.398616
+0.502837  0.411789
+0.507334  0.407292
+0.509882  0.409841
+0.517945  0.401778
+0.519617  0.40345
+0.519996  0.403071
+0.540099  0.423174
+0.550569  0.412704
+0.552168  0.414302
+0.557617  0.408853
+0.560392  0.411628
+0.560663  0.411357
+0.566629  0.417324
+0.579742  0.404211
+0.581431  0.4059
+0.631711  0.355619
+0.631883  0.355792
+0.651446  0.336228
+0.65299  0.337772
+0.668945  0.321818
+0.669261  0.322134
+0.730257  0.261137
+0.731195  0.262075
+0.756704  0.236566
+0.757096  0.236958
+0.939787  0.0542663
+0.940188  0.0546669
+0.965564  0.0292908
+0.965927  0.0296537
+0.99558  0
+#lambda_5
+0.005172  0
+0.0084787  0.0033067
+0.00858089  0.00320452
+0.0213945  0.0160181
+0.022004  0.0154086
+0.0733093  0.0667139
+0.0733119  0.0667113
+0.17233  0.165729
+0.172611  0.165448
+0.218037  0.210874
+0.220805  0.208106
+0.296349  0.283651
+0.296892  0.283108
+0.303615  0.289831
+0.303961  0.289484
+0.348176  0.333698
+0.349208  0.332666
+0.365193  0.348651
+0.366784  0.34706
+0.371799  0.352074
+0.3775  0.346373
+0.409323  0.378196
+0.410706  0.376813
+0.411742  0.377849
+0.416327  0.373264
+0.418157  0.375093
+0.419187  0.374063
+0.431725  0.3866
+0.434679  0.383646
+0.451848  0.400814
+0.453922  0.39874
+0.456869  0.401687
+0.461966  0.39659
+0.470762  0.405386
+0.47371  0.402438
+0.475689  0.404416
+0.480251  0.399854
+0.480844  0.400447
+0.484813  0.396479
+0.485962  0.397628
+0.487319  0.396271
+0.489664  0.398616
+0.491816  0.396465
+0.501371  0.406021
+0.503717  0.403675
+0.507334  0.407292
+0.515397  0.399229
+0.517945  0.401778
+0.518324  0.401399
+0.519996  0.403071
+0.520813  0.402253
+0.534608  0.416048
+0.544261  0.406396
+0.550569  0.412704
+0.556018  0.407254
+0.557617  0.408853
+0.557888  0.408582
+0.560663  0.411357
+0.573776  0.398244
+0.579742  0.404211
+0.591169  0.392784
+0.592845  0.39446
+0.631698  0.355606
+0.631711  0.355619
+0.651274  0.336056
+0.651446  0.336228
+0.667401  0.320274
+0.668945  0.321818
+0.729941  0.260821
+0.730257  0.261137
+0.755766  0.235628
+0.756704  0.236566
+0.939395  0.0538746
+0.939787  0.0542663
+0.965163  0.0288902
+0.965564  0.0292908
+0.994855  0
+#lambda_6
+0.00537637  0
+0.00858089  0.00320452
+0.00919041  0.00259499
+0.022004  0.0154086
+0.0220066  0.015406
+0.0733119  0.0667113
+0.0735929  0.0664303
+0.172611  0.165448
+0.175379  0.16268
+0.220805  0.208106
+0.221191  0.20772
+0.229702  0.216231
+0.229859  0.216075
+0.296892  0.283108
+0.297239  0.282761
+0.303961  0.289484
+0.304994  0.288452
+0.349208  0.332666
+0.350799  0.331075
+0.366784  0.34706
+0.372486  0.341358
+0.3775  0.346373
+0.378883  0.34499
+0.410706  0.376813
+0.415291  0.372228
+0.416327  0.373264
+0.417358  0.372233
+0.419187  0.374063
+0.422142  0.371108
+0.434679  0.383646
+0.436753  0.381571
+0.453922  0.39874
+0.459019  0.393643
+0.461966  0.39659
+0.464915  0.393642
+0.47371  0.402438
+0.478273  0.397875
+0.480251  0.399854
+0.482661  0.397444
+0.482973  0.397756
+0.484532  0.396197
+0.484813  0.396479
+0.48617  0.395121
+0.487319  0.396271
+0.48947  0.394119
+0.491816  0.396465
+0.494161  0.394119
+0.503717  0.403675
+0.51178  0.395612
+0.515397  0.399229
+0.515775  0.398851
+0.518324  0.401399
+0.519142  0.400582
+0.520813  0.402253
+0.530466  0.392601
+0.544261  0.406396
+0.54971  0.400946
+0.556018  0.407254
+0.556289  0.406984
+0.557888  0.408582
+0.563057  0.403413
+0.563935  0.404291
+0.571879  0.396347
+0.573776  0.398244
+0.57552  0.3965
+0.580129  0.401108
+0.589811  0.391426
+0.591169  0.392784
+0.630023  0.353931
+0.631698  0.355606
+0.651261  0.336043
+0.651274  0.336056
+0.667229  0.320102
+0.667401  0.320274
+0.728397  0.259278
+0.729941  0.260821
+0.75545  0.235312
+0.755766  0.235628
+0.938458  0.0529368
+0.939395  0.0538746
+0.964771  0.0284985
+0.965163  0.0288902
+0.994053  0
+#lambda_7
+0.00659542  0
+0.00919041  0.00259499
+0.00919301  0.0025924
+0.0220066  0.015406
+0.0222876  0.015125
+0.0735929  0.0664303
+0.0750937  0.0649295
+0.107045  0.0968812
+0.107603  0.0963232
+0.15977  0.14849
+0.160479  0.147781
+0.175379  0.16268
+0.175765  0.162294
+0.221191  0.20772
+0.221347  0.207563
+0.229859  0.216075
+0.230205  0.215728
+0.297239  0.282761
+0.298271  0.281729
+0.304994  0.288452
+0.306585  0.286861
+0.350799  0.331075
+0.356501  0.325373
+0.372486  0.341358
+0.373868  0.339976
+0.378883  0.34499
+0.383468  0.340405
+0.415291  0.372228
+0.416322  0.371197
+0.417358  0.372233
+0.420312  0.369279
+0.422142  0.371108
+0.424216  0.369034
+0.436753  0.381571
+0.44185  0.376474
+0.459019  0.393643
+0.461967  0.390695
+0.464915  0.393642
+0.469477  0.389079
+0.478273  0.397875
+0.480683  0.395465
+0.482661  0.397444
+0.48422  0.395885
+0.484532  0.396197
+0.485889  0.39484
+0.48617  0.395121
+0.488321  0.39297
+0.48947  0.394119
+0.491816  0.391774
+0.494161  0.394119
+0.502224  0.386057
+0.51178  0.395612
+0.512158  0.395234
+0.515775  0.398851
+0.516593  0.398033
+0.519142  0.400582
+0.528794  0.390929
+0.530466  0.392601
+0.535916  0.387151
+0.54971  0.400946
+0.549981  0.400676
+0.556289  0.406984
+0.561458  0.401814
+0.563057  0.403413
+0.571001  0.395469
+0.571879  0.396347
+0.573623  0.394603
+0.57552  0.3965
+0.585202  0.386818
+0.589811  0.391426
+0.628664  0.352573
+0.630023  0.353931
+0.649586  0.334368
+0.651261  0.336043
+0.667216  0.320089
+0.667229  0.320102
+0.728225  0.259106
+0.728397  0.259278
+0.753906  0.233768
+0.75545  0.235312
+0.938142  0.0526208
+0.938458  0.0529368
+0.963834  0.0275608
+0.964771  0.0284985
+0.99327  0
+#lambda_8
+0.0066006  0
+0.00919301  0.0025924
+0.00947401  0.0023114
+0.0222876  0.015125
+0.0233589  0.0140537
+0.0541778  0.0448725
+0.0546073  0.0444431
+0.0750937  0.0649295
+0.0756517  0.0643715
+0.107603  0.0963232
+0.108313  0.095614
+0.160479  0.147781
+0.160866  0.147394
+0.175765  0.162294
+0.175921  0.162137
+0.221347  0.207563
+0.221694  0.207217
+0.230205  0.215728
+0.231238  0.214695
+0.298271  0.281729
+0.299862  0.280138
+0.306585  0.286861
+0.312286  0.281159
+0.356501  0.325373
+0.357883  0.323991
+0.373868  0.339976
+0.378454  0.33539
+0.383468  0.340405
+0.384499  0.339374
+0.416322  0.371197
+0.419276  0.368243
+0.420312  0.369279
+0.422387  0.367204
+0.424216  0.369034
+0.429313  0.363937
+0.44185  0.376474
+0.444799  0.373526
+0.461967  0.390695
+0.46653  0.386132
+0.469477  0.389079
+0.471887  0.386669
+0.480683  0.395465
+0.482241  0.393907
+0.48422  0.395885
+0.485577  0.394528
+0.485889  0.39484
+0.48804  0.392689
+0.488321  0.39297
+0.490667  0.390625
+0.491816  0.391774
+0.499878  0.383711
+0.502224  0.386057
+0.502603  0.385678
+0.512158  0.395234
+0.512976  0.394416
+0.516593  0.398033
+0.526246  0.38838
+0.528794  0.390929
+0.534244  0.385479
+0.535916  0.387151
+0.536186  0.386881
+0.549981  0.400676
+0.55515  0.395506
+0.561458  0.401814
+0.569402  0.393871
+0.571001  0.395469
+0.572745  0.393725
+0.573623  0.394603
+0.577387  0.390839
+0.578142  0.391595
+0.584061  0.385676
+0.585202  0.386818
+0.618453  0.353567
+0.62001  0.355124
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+#lambda_9
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+#lambda_10
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+#lambda_11
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+#lambda_12
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+#lambda_13
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+#lambda_14
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+#lambda_15
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+#lambda_16
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+#lambda_17
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diff --git a/src/Gudhi_stat/test/data/landscape_from_file_with_diagram_1 b/src/Gudhi_stat/test/data/landscape_from_file_with_diagram_1
new file mode 100644
index 00000000..bc0e34b4
--- /dev/null
+++ b/src/Gudhi_stat/test/data/landscape_from_file_with_diagram_1
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+0.0199573 0.0199573 0.0199573 0.0199573 0.0199573 0.00997867 0.00997867 0.00997867 0.00997867 0.00997867 
+0.00997867 
diff --git a/src/Gudhi_stat/test/data/multiply_by_scalar b/src/Gudhi_stat/test/data/multiply_by_scalar
new file mode 100644
index 00000000..924d696a
--- /dev/null
+++ b/src/Gudhi_stat/test/data/multiply_by_scalar
@@ -0,0 +1,817 @@
+#lambda_0
+0.0290362  0
+0.273076  2.4404
+0.276873  2.40242
+0.329297  2.92665
+0.36328  2.58682
+0.485629  3.8103
+0.490689  3.75971
+0.54603  4.31313
+0.631171  3.46172
+0.63642  3.51422
+0.640956  3.46887
+0.644303  3.50234
+0.994537  0
+#lambda_1
+0.0307676  0
+0.133967  1.03199
+0.136898  1.00267
+0.276873  2.40242
+0.310857  2.06258
+0.36328  2.58682
+0.36834  2.53622
+0.490689  3.75971
+0.500148  3.66511
+0.534084  4.00446
+0.590941  3.43589
+0.612036  3.64684
+0.630859  3.45861
+0.631171  3.46172
+0.635706  3.41637
+0.640956  3.46887
+0.879378  1.08465
+0.88052  1.09607
+0.990127  0
+#lambda_2
+0.0366312  0
+0.136898  1.00267
+0.145814  0.913521
+0.188411  1.3395
+0.21348  1.08881
+0.310857  2.06258
+0.315917  2.01199
+0.36834  2.53622
+0.372727  2.49235
+0.376471  2.52978
+0.381543  2.47906
+0.500148  3.66511
+0.508229  3.58431
+0.528049  3.7825
+0.549487  3.56812
+0.551764  3.59089
+0.579102  3.3175
+0.590941  3.43589
+0.609764  3.24766
+0.630859  3.45861
+0.635394  3.41325
+0.635706  3.41637
+0.816147  1.61196
+0.81754  1.62589
+0.875521  1.04608
+0.879378  1.08465
+0.987842  0
+#lambda_3
+0.0544614  0
+0.145814  0.913521
+0.170882  0.662834
+0.21348  1.08881
+0.21854  1.03822
+0.315917  2.01199
+0.320304  1.96811
+0.372727  2.49235
+0.3778  2.44162
+0.381543  2.47906
+0.389624  2.39826
+0.508229  3.58431
+0.529248  3.37412
+0.546034  3.54197
+0.546453  3.53778
+0.549487  3.56812
+0.576826  3.29474
+0.579102  3.3175
+0.597925  3.12927
+0.609764  3.24766
+0.6143  3.20231
+0.635394  3.41325
+0.815835  1.60884
+0.816147  1.61196
+0.874128  1.03215
+0.875521  1.04608
+0.980129  0
+#lambda_4
+0.0920033  0
+0.162167  0.701632
+0.168464  0.638655
+0.170882  0.662834
+0.175942  0.61224
+0.21854  1.03822
+0.222927  0.994343
+0.320304  1.96811
+0.325376  1.91739
+0.3778  2.44162
+0.38588  2.36082
+0.389624  2.39826
+0.410259  2.1919
+0.490951  2.99882
+0.491334  2.99498
+0.529248  3.37412
+0.529667  3.36992
+0.546453  3.53778
+0.573792  3.2644
+0.576826  3.29474
+0.595649  3.1065
+0.597925  3.12927
+0.60246  3.08392
+0.6143  3.20231
+0.652776  2.81755
+0.659416  2.88395
+0.746537  2.01275
+0.752208  2.06946
+0.807053  1.52102
+0.815835  1.60884
+0.873816  1.02903
+0.874128  1.03215
+0.977343  0
+#lambda_5
+0.104599  0
+0.168464  0.638655
+0.173524  0.58806
+0.175942  0.61224
+0.180329  0.568366
+0.222927  0.994343
+0.227999  0.943619
+0.325376  1.91739
+0.333457  1.83659
+0.38588  2.36082
+0.406516  2.15446
+0.410259  2.1919
+0.410391  2.19058
+0.45834  2.67007
+0.458592  2.66755
+0.491334  2.99498
+0.491754  2.99079
+0.529667  3.36992
+0.557006  3.09654
+0.573792  3.2644
+0.592615  3.07616
+0.595649  3.1065
+0.600184  3.06115
+0.60246  3.08392
+0.640936  2.69916
+0.652776  2.81755
+0.739896  1.94634
+0.746537  2.01275
+0.801381  1.4643
+0.807053  1.52102
+0.865034  0.941206
+0.873816  1.02903
+0.976719  0
+#lambda_6
+0.114718  0
+0.173524  0.58806
+0.177911  0.544186
+0.180329  0.568366
+0.185402  0.517641
+0.227999  0.943619
+0.23608  0.862815
+0.333457  1.83659
+0.354092  1.63023
+0.406516  2.15446
+0.406648  2.15314
+0.410391  2.19058
+0.410643  2.18807
+0.458592  2.66755
+0.459011  2.66336
+0.491754  2.99079
+0.519092  2.7174
+0.557006  3.09654
+0.56704  2.99619
+0.578509  3.11088
+0.587298  3.023
+0.592615  3.07616
+0.59715  3.03081
+0.600184  3.06115
+0.63866  2.67639
+0.640936  2.69916
+0.728057  1.82795
+0.739896  1.94634
+0.794741  1.3979
+0.801381  1.4643
+0.859362  0.884492
+0.865034  0.941206
+0.916025  0.431291
+0.924275  0.513791
+0.975654  0
+#lambda_7
+0.117379  0
+0.127589  0.102096
+0.130645  0.0715284
+0.177911  0.544186
+0.182984  0.493461
+0.185402  0.517641
+0.193482  0.436837
+0.23608  0.862815
+0.240402  0.819591
+0.323826  1.65383
+0.340139  1.4907
+0.354092  1.63023
+0.354224  1.62891
+0.406648  2.15314
+0.406899  2.15063
+0.410643  2.18807
+0.411062  2.18387
+0.459011  2.66336
+0.486349  2.38998
+0.519092  2.7174
+0.529127  2.61706
+0.56704  2.99619
+0.575829  2.90831
+0.587298  3.023
+0.591833  2.97764
+0.59715  3.03081
+0.611692  2.88539
+0.6135  2.90348
+0.637434  2.66413
+0.63866  2.67639
+0.725781  1.80518
+0.728057  1.82795
+0.782901  1.27951
+0.794741  1.3979
+0.852722  0.818087
+0.859362  0.884492
+0.910354  0.374576
+0.916025  0.431291
+0.959154  0
+#lambda_8
+0.123493  0
+0.130645  0.0715284
+0.135718  0.0208036
+0.182984  0.493461
+0.191064  0.412657
+0.193482  0.436837
+0.197804  0.393613
+0.240402  0.819591
+0.256715  0.65646
+0.340139  1.4907
+0.340271  1.48938
+0.354224  1.62891
+0.354476  1.6264
+0.406899  2.15063
+0.407318  2.14643
+0.411062  2.18387
+0.432004  1.97446
+0.478291  2.43732
+0.484687  2.37336
+0.486349  2.38998
+0.496384  2.28963
+0.529127  2.61706
+0.537777  2.53055
+0.569195  2.84473
+0.569333  2.84335
+0.575829  2.90831
+0.580364  2.86295
+0.591833  2.97764
+0.606375  2.83223
+0.611692  2.88539
+0.635626  2.64605
+0.637434  2.66413
+0.724555  1.79293
+0.725781  1.80518
+0.780625  1.25674
+0.782901  1.27951
+0.840883  0.699695
+0.852722  0.818087
+0.891918  0.426129
+0.897031  0.477262
+0.908827  0.359304
+0.910354  0.374576
+0.947812  0
+#lambda_9
+0.133638  0
+0.135718  0.0208036
+0.137798  0
+0.149798  0
+0.191064  0.412657
+0.195386  0.369434
+0.197804  0.393613
+0.214117  0.230483
+0.256715  0.65646
+0.256847  0.65514
+0.340271  1.48938
+0.340523  1.48687
+0.354476  1.6264
+0.354895  1.6222
+0.407318  2.14643
+0.42826  1.93702
+0.432004  1.97446
+0.438401  1.91049
+0.484687  2.37336
+0.494722  2.27301
+0.496384  2.28963
+0.505034  2.20313
+0.537777  2.53055
+0.537915  2.52917
+0.569333  2.84335
+0.573869  2.798
+0.580364  2.86295
+0.594906  2.71754
+0.606375  2.83223
+0.630309  2.59288
+0.635626  2.64605
+0.722747  1.77484
+0.724555  1.79293
+0.779399  1.24448
+0.780625  1.25674
+0.838606  0.67693
+0.840883  0.699695
+0.880078  0.307738
+0.891918  0.426129
+0.903713  0.308171
+0.908827  0.359304
+0.944757  0
+#lambda_10
+0.155421  0
+0.187662  0.322402
+0.189172  0.307294
+0.195386  0.369434
+0.211699  0.206303
+0.214117  0.230483
+0.214249  0.229162
+0.256847  0.65514
+0.257099  0.652625
+0.340523  1.48687
+0.340942  1.48267
+0.354895  1.6222
+0.36777  1.49345
+0.402826  1.84401
+0.410893  1.76334
+0.42826  1.93702
+0.434657  1.87305
+0.438401  1.91049
+0.448435  1.81014
+0.494722  2.27301
+0.503372  2.18651
+0.505034  2.20313
+0.505173  2.20174
+0.537915  2.52917
+0.542451  2.48382
+0.573869  2.798
+0.58841  2.65258
+0.594906  2.71754
+0.61884  2.47819
+0.630309  2.59288
+0.71743  1.72168
+0.722747  1.77484
+0.777591  1.2264
+0.779399  1.24448
+0.83738  0.664671
+0.838606  0.67693
+0.877802  0.284973
+0.880078  0.307738
+0.891874  0.189779
+0.903713  0.308171
+0.93453  0
+#lambda_11
+0.158443  0
+0.189172  0.307294
+0.205486  0.144164
+0.211699  0.206303
+0.211832  0.204983
+0.214249  0.229162
+0.214501  0.226647
+0.257099  0.652625
+0.257518  0.648432
+0.340942  1.48267
+0.353817  1.35392
+0.36777  1.49345
+0.375837  1.41279
+0.410893  1.76334
+0.417289  1.69937
+0.434657  1.87305
+0.444691  1.77271
+0.448435  1.81014
+0.448771  1.80678
+0.477632  2.09539
+0.485947  2.01225
+0.503372  2.18651
+0.503511  2.18512
+0.505173  2.20174
+0.509708  2.15639
+0.542451  2.48382
+0.556992  2.3384
+0.58841  2.65258
+0.612345  2.41324
+0.61884  2.47819
+0.705961  1.60699
+0.71743  1.72168
+0.772274  1.17323
+0.777591  1.2264
+0.835572  0.64659
+0.83738  0.664671
+0.876576  0.272714
+0.877802  0.284973
+0.889598  0.167015
+0.891874  0.189779
+0.910852  0
+#lambda_12
+0.176956  0
+0.180095  0.0313879
+0.183234  0
+0.191069  0
+0.205486  0.144164
+0.205618  0.142844
+0.211832  0.204983
+0.212083  0.202468
+0.214501  0.226647
+0.21492  0.222454
+0.257518  0.648432
+0.270393  0.519679
+0.353817  1.35392
+0.361884  1.27326
+0.375837  1.41279
+0.382234  1.34882
+0.417289  1.69937
+0.427324  1.59903
+0.444691  1.77271
+0.445028  1.76934
+0.448771  1.80678
+0.457086  1.72364
+0.485947  2.01225
+0.486085  2.01087
+0.503511  2.18512
+0.508046  2.13977
+0.509708  2.15639
+0.52425  2.01097
+0.556992  2.3384
+0.580927  2.09906
+0.612345  2.41324
+0.699465  1.54203
+0.705961  1.60699
+0.760805  1.05854
+0.772274  1.17323
+0.830255  0.593421
+0.835572  0.64659
+0.874768  0.254633
+0.876576  0.272714
+0.888372  0.154756
+0.889598  0.167015
+0.906299  0
+#lambda_13
+0.191333  0
+0.205618  0.142844
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+0.243649  0.350847
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+0.462911  0
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+0.486389  0.0282021
+0.489209  0
diff --git a/src/Gudhi_stat/test/data/multiply_by_scalar_on_grid_test b/src/Gudhi_stat/test/data/multiply_by_scalar_on_grid_test
new file mode 100644
index 00000000..b400b49d
--- /dev/null
+++ b/src/Gudhi_stat/test/data/multiply_by_scalar_on_grid_test
@@ -0,0 +1,104 @@
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diff --git a/src/Gudhi_stat/test/data/persistence_heat_map_from_file_with_diagram b/src/Gudhi_stat/test/data/persistence_heat_map_from_file_with_diagram
new file mode 100644
index 00000000..c4903ebe
--- /dev/null
+++ b/src/Gudhi_stat/test/data/persistence_heat_map_from_file_with_diagram
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5.28879e-05 5.32848e-05 5.37419e-05 5.42592e-05 5.48367e-05 5.5474e-05 5.61708e-05 5.69262e-05 5.77394e-05 5.86094e-05 5.95348e-05 6.05143e-05 6.15461e-05 6.26284e-05 6.37592e-05 6.49364e-05 6.61574e-05 6.74198e-05 6.87208e-05 7.00577e-05 7.14273e-05 7.28265e-05 7.42521e-05 7.57005e-05 7.71684e-05 7.86521e-05 8.01478e-05 8.16517e-05 8.31601e-05 8.46688e-05 8.61741e-05 8.76718e-05 8.91579e-05 9.06284e-05 9.20792e-05 9.35063e-05 9.49057e-05 9.62735e-05 9.76057e-05 9.88985e-05 0.000100148 0.000101351 0.000102504 0.000103603 0.000104645 0.000105626 0.000106545 0.000107397 0.00010818 0.000108893 0.000108386 0.000109039 0.000109607 0.00011009 0.000110487 0.000110797 0.000111019 0.000111152 0.000111197 0.000111152 0.000111019 0.000110797 0.000110487 0.00011009 0.000109607 0.000109039 0.000108386 0.000107652 0.000106837 0.000105943 0.000104973 0.000103928 0.000102812 0.000101626 0.000102652 0.000101524 0.00010035 9.9131e-05 9.78728e-05 9.6579e-05 9.52536e-05 9.3901e-05 9.25253e-05 9.1131e-05 8.97225e-05 8.83041e-05 8.68804e-05 8.54558e-05 8.40347e-05 8.26217e-05 8.12211e-05 7.98373e-05 7.84746e-05 7.71373e-05 7.58295e-05 7.45553e-05 7.33188e-05 7.21238e-05 7.0974e-05 6.9873e-05 6.88245e-05 6.78316e-05 6.68975e-05 6.60254e-05 6.52179e-05 6.44778e-05 6.38075e-05 6.32092e-05 6.26851e-05 6.2237e-05 6.18665e-05 6.15751e-05 6.13641e-05 6.12343e-05 6.11865e-05 6.12213e-05 6.13391e-05 6.15397e-05 6.18233e-05 6.21892e-05 6.26369e-05 6.31656e-05 6.37742e-05 6.44614e-05 6.52256e-05 6.60651e-05 6.69779e-05 6.79618e-05 6.90145e-05 7.01334e-05 7.13155e-05 7.25581e-05 7.38578e-05 7.52113e-05 7.66152e-05 7.80657e-05 7.9559e-05 8.10912e-05 8.2658e-05 8.42554e-05 8.5879e-05 8.75242e-05 8.91867e-05 9.08618e-05 9.25449e-05 9.42313e-05 9.59161e-05 9.75948e-05 9.92624e-05 0.000100914 0.000102546 0.000104152 0.000105728 0.000107971 0.000109532 0.000111054 0.000112532 0.000113963 0.000115343 0.000114788 0.000116201 0.000117542 0.000118809 0.000119999 0.00012111 0.00012214 0.000123087 0.000123949 0.000124726 0.000125416 0.000126017 0.00012653 0.000126953 0.000127287 0.000127531 0.000127686 0.000129621 0.000129753 0.000129809 0.000129791 0.000129699 0.000129538 0.000129309 0.000129014 0.000128658 0.000128242 0.00012777 0.000127246 0.000126673 0.000126055 0.000125396 0.000124701 0.000123972 0.000123215 0.000122434 0.000121632 0.000120816 0.000119989 0.000119155 0.000118319 0.000117486 0.00011666 0.000115845 0.000115045 0.000114265 0.000113509 0.00011278 0.000112083 0.00011142 0.000110796 0.000110213 0.000109676 0.000109185 0.000108745 0.000108358 0.000108025 0.000107748 0.00010753 0.000107372 0.000107274 0.000107238 0.000107264 0.000107352 0.000107503 0.000107716 0.00010799 0.000108326 0.000108721 0.000109174 0.000109684 0.000110249 0.000110867 0.000111535 0.000112251 0.000113012 0.000113815 0.000114657 0.000115534 0.000116443 0.00011738 0.000118342 0.000119324 0.000120322 0.000121332 0.000122349 0.00012337 0.000124391 0.000125405 0.00012641 0.0001274 0.000128372 0.00012932 0.000130241 0.00013113 0.000131984 0.000132797 0.000133565 0.000134286 0.000134955 0.000135569 0.000136124 0.000136617 0.000137045 0.000137404 0.000137693 0.000137909 0.000138049 0.000138112 0.000138096 0.000137999 0.000137819 0.000137557 0.00013721 0.000136779 0.000136263 0.00013356 0.000133037 0.000132419 0.000131706 0.0001309 0.000130003 0.000129016 0.000127941 0.000126781 0.000125538 0.000124215 0.000122814 0.000121339 0.000119792 0.000118176 0.000116496 0.000114753 0.000112951 0.000111095 0.000109187 0.000107232 0.000105233 0.000103193 0.000101117 9.90078e-05 9.68698e-05 9.47066e-05 9.25219e-05 9.03193e-05 8.81026e-05 8.58754e-05 8.36412e-05 8.14034e-05 7.91656e-05 7.69309e-05 7.47025e-05 7.24837e-05 7.02773e-05 6.80864e-05 6.59135e-05 6.37614e-05 6.16327e-05 5.95295e-05 5.74543e-05 5.54091e-05 5.3396e-05 5.14166e-05 4.94727e-05 4.7566e-05 4.56976e-05 4.38691e-05 4.20814e-05 4.03356e-05 3.86326e-05 3.6973e-05 3.53576e-05 3.37867e-05 3.22608e-05 3.07801e-05 2.93447e-05 2.79547e-05 2.661e-05 2.53104e-05 2.40557e-05 2.28456e-05 2.16796e-05 2.05572e-05 1.94778e-05 1.84408e-05 1.74455e-05 1.64911e-05 1.55768e-05 1.47019e-05 1.38653e-05 1.30661e-05 1.23035e-05 1.15764e-05 1.08837e-05 1.02246e-05 8.95044e-06 8.40564e-06 7.88768e-06 7.39573e-06 6.92891e-06 6.48637e-06 6.06723e-06 5.67064e-06 5.29574e-06 4.94167e-06 4.60758e-06 4.29264e-06 3.99603e-06 3.71695e-06 3.45459e-06 3.20818e-06 2.97696e-06 2.7602e-06 2.55717e-06 2.36719e-06 2.18956e-06 2.02365e-06 1.86881e-06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
diff --git a/src/Gudhi_stat/test/data/sum b/src/Gudhi_stat/test/data/sum
new file mode 100644
index 00000000..79480306
--- /dev/null
+++ b/src/Gudhi_stat/test/data/sum
@@ -0,0 +1,148611 @@
+#lambda_0
+0.00115996  0
+0.0290362  0.0278763
+0.0705916  0.110987
+0.0707351  0.110987
+0.273076  0.515668
+0.276873  0.515668
+0.297446  0.556814
+0.299309  0.556815
+0.329297  0.61679
+0.36328  0.61679
+0.443232  0.776693
+0.462177  0.776692
+0.485629  0.823596
+0.490689  0.823596
+0.507542  0.857302
+0.536031  0.857302
+0.54603  0.877301
+0.547048  0.877301
+0.571679  0.828038
+0.573069  0.828038
+0.631171  0.711835
+0.63642  0.711835
+0.636462  0.711751
+0.637257  0.71175
+0.640956  0.704353
+0.644303  0.704353
+0.967347  0.0582646
+0.96765  0.0582641
+0.994537  0.00448995
+0.999027  0
+#lambda_1
+0.00144702  0
+0.0307676  0.0293206
+0.0707351  0.109256
+0.0725442  0.109256
+0.133967  0.232101
+0.136898  0.232101
+0.276873  0.51205
+0.292533  0.51205
+0.292586  0.511943
+0.299309  0.511943
+0.30002  0.51052
+0.310857  0.51052
+0.36328  0.615366
+0.36834  0.615366
+0.399923  0.678532
+0.399925  0.678532
+0.429631  0.737944
+0.43268  0.737944
+0.444423  0.76143
+0.445313  0.76143
+0.447291  0.765387
+0.461584  0.765387
+0.462177  0.766573
+0.466162  0.766573
+0.469657  0.773563
+0.476828  0.773562
+0.490689  0.801283
+0.500148  0.801283
+0.515923  0.832832
+0.533256  0.832832
+0.534084  0.834488
+0.536031  0.834488
+0.544472  0.817606
+0.552128  0.817605
+0.562598  0.796665
+0.56277  0.796665
+0.56849  0.785225
+0.571679  0.785225
+0.590941  0.746701
+0.612036  0.746702
+0.630859  0.709056
+0.631171  0.709056
+0.635073  0.701251
+0.635706  0.701251
+0.636462  0.702764
+0.640956  0.702764
+0.758486  0.467704
+0.758779  0.467705
+0.879378  0.226508
+0.88052  0.226508
+0.966847  0.0538541
+0.967347  0.0538546
+0.990127  0.00829479
+0.998422  0
+#lambda_2
+0.00267455  0
+0.00722998  0.00455543
+0.00737515  0.00441026
+0.0201887  0.0172238
+0.0212389  0.0161737
+0.0366312  0.031566
+0.0725442  0.103392
+0.0725976  0.103392
+0.136898  0.231994
+0.145814  0.231994
+0.188411  0.317189
+0.21348  0.317189
+0.292586  0.475401
+0.293298  0.475401
+0.30002  0.488846
+0.300023  0.488846
+0.310857  0.510514
+0.315917  0.510514
+0.36834  0.615362
+0.372727  0.615362
+0.376471  0.622849
+0.381543  0.622849
+0.399925  0.659612
+0.402974  0.659612
+0.43268  0.719024
+0.43357  0.719024
+0.445313  0.74251
+0.459606  0.74251
+0.461584  0.746467
+0.465569  0.746467
+0.466162  0.747653
+0.473334  0.747654
+0.476828  0.754642
+0.479777  0.754643
+0.500148  0.795386
+0.508229  0.795386
+0.517273  0.813475
+0.528049  0.813474
+0.531657  0.806257
+0.533256  0.806257
+0.541697  0.789375
+0.544472  0.789375
+0.549487  0.779345
+0.551764  0.779345
+0.554943  0.772986
+0.562598  0.772987
+0.568318  0.761547
+0.56849  0.761547
+0.579102  0.740323
+0.581603  0.740323
+0.583463  0.744043
+0.590941  0.744043
+0.609764  0.706396
+0.630859  0.706396
+0.633743  0.700627
+0.635073  0.700627
+0.635394  0.699985
+0.635706  0.699985
+0.67059  0.630216
+0.671354  0.630216
+0.757859  0.457205
+0.758486  0.457205
+0.816147  0.341883
+0.81754  0.341883
+0.875521  0.22592
+0.879378  0.22592
+0.966553  0.0515693
+0.966847  0.0515692
+0.987842  0.00957878
+0.997421  0
+#lambda_3
+0.00296489  0
+0.00737515  0.00441026
+0.00842527  0.00336013
+0.0212389  0.0161737
+0.0212923  0.0161203
+0.0544614  0.0492894
+0.0725976  0.0855618
+0.0726998  0.0855618
+0.145814  0.231789
+0.170882  0.231789
+0.171718  0.23346
+0.172327  0.23346
+0.21348  0.315766
+0.21854  0.315766
+0.293298  0.465282
+0.2933  0.465282
+0.300023  0.478727
+0.303072  0.478727
+0.315917  0.504416
+0.320304  0.504416
+0.372727  0.609264
+0.3778  0.609264
+0.381543  0.616751
+0.389624  0.616751
+0.402974  0.643452
+0.403864  0.643452
+0.43357  0.702864
+0.447863  0.702864
+0.459606  0.72635
+0.463591  0.72635
+0.465569  0.730307
+0.472741  0.730308
+0.473334  0.731494
+0.476282  0.731493
+0.479777  0.738483
+0.488307  0.738482
+0.504029  0.769925
+0.508229  0.769925
+0.509882  0.766618
+0.529248  0.766617
+0.531657  0.771436
+0.540099  0.771437
+0.541697  0.774634
+0.546034  0.774634
+0.546453  0.773795
+0.549487  0.773795
+0.552168  0.768433
+0.554943  0.768433
+0.560392  0.757535
+0.566359  0.757535
+0.566629  0.756994
+0.568318  0.756994
+0.576826  0.739979
+0.579102  0.739979
+0.581431  0.735321
+0.581603  0.735321
+0.597925  0.702677
+0.609764  0.702677
+0.6143  0.693606
+0.631883  0.693606
+0.633743  0.697325
+0.635394  0.697325
+0.669261  0.629592
+0.67059  0.629592
+0.757096  0.456581
+0.757859  0.456581
+0.815835  0.340629
+0.816147  0.340629
+0.874128  0.224667
+0.875521  0.224667
+0.965927  0.0438553
+0.966553  0.0438557
+0.980129  0.0167045
+0.996833  0
+#lambda_4
+0.00506514  0
+0.00842527  0.00336013
+0.0084787  0.0033067
+0.0212923  0.0161203
+0.0213945  0.0160181
+0.0726998  0.0673234
+0.0733093  0.0667139
+0.0920033  0.085408
+0.162167  0.225735
+0.168464  0.225735
+0.170882  0.230571
+0.172327  0.230571
+0.17233  0.230565
+0.175942  0.230565
+0.21854  0.315761
+0.222927  0.315761
+0.2933  0.456507
+0.296349  0.456507
+0.303072  0.469952
+0.303615  0.469953
+0.320304  0.503331
+0.325376  0.503331
+0.347829  0.548236
+0.348176  0.548236
+0.3778  0.607484
+0.38588  0.607484
+0.389624  0.614971
+0.403864  0.614971
+0.410259  0.602181
+0.418157  0.602181
+0.447863  0.661593
+0.451848  0.661593
+0.463591  0.685079
+0.470762  0.685079
+0.472741  0.689037
+0.475689  0.689036
+0.476282  0.690222
+0.480844  0.690222
+0.481994  0.692521
+0.485962  0.692521
+0.488307  0.697211
+0.489664  0.697211
+0.490951  0.699785
+0.491334  0.699785
+0.502837  0.72279
+0.507334  0.72279
+0.509882  0.727887
+0.517945  0.727887
+0.519617  0.731231
+0.519996  0.731231
+0.529248  0.749734
+0.529667  0.749734
+0.540099  0.770598
+0.546453  0.770598
+0.550569  0.762366
+0.552168  0.762365
+0.557617  0.751467
+0.560392  0.751467
+0.560663  0.750925
+0.566629  0.750926
+0.573792  0.736601
+0.576826  0.736601
+0.579742  0.730768
+0.581431  0.730768
+0.595649  0.702332
+0.597925  0.702332
+0.60246  0.693262
+0.6143  0.693262
+0.631711  0.658438
+0.631883  0.658439
+0.651446  0.619312
+0.652776  0.619312
+0.65299  0.619741
+0.659416  0.619742
+0.668945  0.600685
+0.669261  0.600685
+0.730257  0.478692
+0.731195  0.478692
+0.746537  0.448008
+0.752208  0.448008
+0.756704  0.439016
+0.757096  0.439016
+0.807053  0.339103
+0.815835  0.339103
+0.873816  0.22314
+0.874128  0.22314
+0.939787  0.0918221
+0.940188  0.0918217
+0.965564  0.0410696
+0.965927  0.0410695
+0.977343  0.0182376
+0.99558  0
+#lambda_5
+0.005172  0
+0.0084787  0.0033067
+0.00858089  0.00320452
+0.0213945  0.0160181
+0.022004  0.0154086
+0.0733093  0.0667139
+0.0733119  0.0667113
+0.104599  0.0979981
+0.168464  0.225729
+0.17233  0.225729
+0.172611  0.225167
+0.173524  0.225167
+0.175942  0.230003
+0.180329  0.230003
+0.218037  0.305418
+0.220805  0.305418
+0.222927  0.309662
+0.227999  0.309662
+0.296349  0.446362
+0.296892  0.446362
+0.303615  0.459808
+0.303961  0.459807
+0.325376  0.502638
+0.333457  0.502638
+0.348176  0.532076
+0.349208  0.532076
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+#lambda_9
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+#lambda_10
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diff --git a/src/Gudhi_stat/test/data/sum_on_grid_test b/src/Gudhi_stat/test/data/sum_on_grid_test
new file mode 100644
index 00000000..dcdef053
--- /dev/null
+++ b/src/Gudhi_stat/test/data/sum_on_grid_test
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diff --git a/src/Gudhi_stat/test/data/template_average_of_heat_maps b/src/Gudhi_stat/test/data/template_average_of_heat_maps
new file mode 100644
index 00000000..c533057f
--- /dev/null
+++ b/src/Gudhi_stat/test/data/template_average_of_heat_maps
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diff --git a/src/Gudhi_stat/test/persistence_heat_maps_test.cpp b/src/Gudhi_stat/test/persistence_heat_maps_test.cpp
new file mode 100644
index 00000000..505b1912
--- /dev/null
+++ b/src/Gudhi_stat/test/persistence_heat_maps_test.cpp
@@ -0,0 +1,238 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#define BOOST_TEST_DYN_LINK
+#define BOOST_TEST_MODULE "gudhi_stat"
+#include <boost/test/unit_test.hpp>
+#include <gudhi/reader_utils.h>
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_heat_maps.h>
+
+#include <iostream>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+using namespace std;
+
+
+	
+
+BOOST_AUTO_TEST_CASE(check_construction_of_heat_maps) 
+{	
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(100,1);		
+	Persistence_heat_maps p( "data/file_with_diagram" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	p.print_to_file( "data/persistence_heat_map_from_file_with_diagram" );
+	
+	Persistence_heat_maps q;
+	q.load_from_file( "data/persistence_heat_map_from_file_with_diagram" );	
+		
+	BOOST_CHECK( p == q );
+}
+
+
+BOOST_AUTO_TEST_CASE(check_averages_of_heat_maps) 
+{
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(30,1);	
+	Persistence_heat_maps p( "data/file_with_diagram" , filter ,  constant_function, false , 1000 , 0 , 10 );
+	Persistence_heat_maps q( "data/file_with_diagram_1" , filter ,  constant_function, false , 1000 , 0 , 10 );
+	Persistence_heat_maps r( "data/file_with_diagram_2" , filter ,  constant_function, false , 1000 , 0 , 10 );
+	
+	std::vector< Abs_Topological_data_with_averages* > to_average;
+	to_average.push_back( (Abs_Topological_data_with_averages*)(&p) );
+	to_average.push_back( (Abs_Topological_data_with_averages*)(&q) );
+	to_average.push_back( (Abs_Topological_data_with_averages*)(&r) );
+	Persistence_heat_maps av;	
+	av.compute_average( to_average );
+	
+	Persistence_heat_maps template_average;
+	template_average.load_from_file( "data/template_average_of_heat_maps" );
+	
+	BOOST_CHECK( av == template_average );
+}
+
+
+BOOST_AUTO_TEST_CASE(check_median_of_heat_maps) 
+{
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(30,1);	
+	Persistence_heat_maps p( "data/file_with_diagram" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps q( "data/file_with_diagram_1" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps r( "data/file_with_diagram_2" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	
+	std::vector< Persistence_heat_maps* > to_compute_median;
+	to_compute_median.push_back( &p );
+	to_compute_median.push_back( &q );
+	to_compute_median.push_back( &r );
+	Persistence_heat_maps median;	
+	median.compute_median( to_compute_median );
+	
+	Persistence_heat_maps template_median;
+	template_median.load_from_file( "data/template_median_of_heat_maps" );
+	
+	BOOST_CHECK( median == template_median );	
+}
+
+
+BOOST_AUTO_TEST_CASE(check_compute_percentage_of_active_of_heat_maps) 
+{
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(30,1);	
+	Persistence_heat_maps p( "data/file_with_diagram" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps q( "data/file_with_diagram_1" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps r( "data/file_with_diagram_2" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	
+	std::vector< Persistence_heat_maps* > to_compute_percentage_of_active;
+	to_compute_percentage_of_active.push_back( &p );
+	to_compute_percentage_of_active.push_back( &q );
+	to_compute_percentage_of_active.push_back( &r );
+	Persistence_heat_maps percentage_of_active;	
+	percentage_of_active.compute_percentage_of_active( to_compute_percentage_of_active , 0.1 );
+	
+	Persistence_heat_maps template_percentage_of_active;
+	template_percentage_of_active.load_from_file( "data/template_percentage_of_active_of_heat_maps" );
+	
+	BOOST_CHECK( percentage_of_active == template_percentage_of_active );	
+}
+
+BOOST_AUTO_TEST_CASE(check_vectorize_for_heat_maps) 
+{
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(30,1);	
+	Persistence_heat_maps p( "data/file_with_diagram" , filter ,  constant_function, false , 5 , 0 , 1 );
+	
+	std::vector<double> p_vect_template;
+	
+	p_vect_template.push_back(0.0606728);
+	p_vect_template.push_back(0.0610023); 
+	p_vect_template.push_back(0.0607978 );
+	p_vect_template.push_back(0.0600647 );
+	p_vect_template.push_back(0.0588224 );
+	p_vect_template.push_back(0.0619829 );
+	p_vect_template.push_back(0.0623218 );
+	p_vect_template.push_back(0.0621152 );
+	p_vect_template.push_back(0.0613686 );
+	p_vect_template.push_back(0.0601016 );
+	p_vect_template.push_back(0.0627679 );
+	p_vect_template.push_back(0.0631134 );
+	p_vect_template.push_back(0.0629066 );
+	p_vect_template.push_back(0.0621528 );
+	p_vect_template.push_back(0.0608719 );
+	p_vect_template.push_back(0.0630073 );
+	p_vect_template.push_back(0.0633564 );
+	p_vect_template.push_back(0.0631511 );
+	p_vect_template.push_back(0.0623968 );
+	p_vect_template.push_back(0.0611132 );
+	p_vect_template.push_back(0.0626947 );
+	p_vect_template.push_back(0.0630445 );
+	p_vect_template.push_back(0.0628425 );
+	p_vect_template.push_back(0.0620941 );
+	p_vect_template.push_back(0.060819);
+	
+	std::vector<double> p_vect = p.vectorize(0);
+	for ( size_t i = 0 ; i != p_vect.size() ; ++i )
+	{
+		BOOST_CHECK( almost_equal( p_vect_template[i] , p_vect[i] ) );
+	}	
+}
+
+
+BOOST_AUTO_TEST_CASE(check_distance_for_heat_maps) 
+{
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(30,1);	
+	Persistence_heat_maps p( "data/file_with_diagram" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps q( "data/file_with_diagram_1" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps r( "data/file_with_diagram_2" , filter ,  constant_function, false , 1000 , 0 , 1 );
+
+	//cerr << p.distance( (Abs_Topological_data_with_distances*)&p ) << endl;
+	//cerr << p.distance( (Abs_Topological_data_with_distances*)&q ) << endl;
+	//cerr << p.distance( (Abs_Topological_data_with_distances*)&r ) << endl;	
+	//cerr << q.distance( (Abs_Topological_data_with_distances*)&p ) << endl;
+	//cerr << q.distance( (Abs_Topological_data_with_distances*)&q ) << endl;
+	//cerr << q.distance( (Abs_Topological_data_with_distances*)&r ) << endl;	
+	//cerr << r.distance( (Abs_Topological_data_with_distances*)&p ) << endl;
+	//cerr << r.distance( (Abs_Topological_data_with_distances*)&q ) << endl;
+	//cerr << r.distance( (Abs_Topological_data_with_distances*)&r ) << endl;	
+	//0         624.183   415.815
+	//624.183   0         528.06Z
+	//415.815   528.066   0
+
+	BOOST_CHECK( fabs( p.distance( (Abs_Topological_data_with_distances*)&p ) - 0) < 0.0005);
+	BOOST_CHECK( fabs( p.distance( (Abs_Topological_data_with_distances*)&q ) - 624.183)< 0.0005);
+	BOOST_CHECK( fabs( p.distance( (Abs_Topological_data_with_distances*)&r ) - 415.815)< 0.0005);
+	BOOST_CHECK( fabs( q.distance( (Abs_Topological_data_with_distances*)&p ) - 624.183)< 0.0005);
+	BOOST_CHECK( fabs( q.distance( (Abs_Topological_data_with_distances*)&q ) - 0)< 0.0005);
+	BOOST_CHECK( fabs( q.distance( (Abs_Topological_data_with_distances*)&r ) - 528.066)< 0.0005);
+	BOOST_CHECK( fabs( r.distance( (Abs_Topological_data_with_distances*)&p ) - 415.815)< 0.0005);
+	BOOST_CHECK( fabs( r.distance( (Abs_Topological_data_with_distances*)&q ) - 528.066)< 0.0005);
+	BOOST_CHECK( fabs( r.distance( (Abs_Topological_data_with_distances*)&r ) - 0)< 0.0005);
+}
+
+
+
+BOOST_AUTO_TEST_CASE(check_projections_to_R_for_heat_maps) 
+{
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(30,1);	
+	Persistence_heat_maps p( "data/file_with_diagram" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps q( "data/file_with_diagram_1" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps r( "data/file_with_diagram_2" , filter ,  constant_function, false , 1000 , 0 , 1 );
+
+	//cerr << p.project_to_R(0) << endl;
+	//cerr << q.project_to_R(0) << endl;
+	//cerr << r.project_to_R(0) << endl;
+
+	BOOST_CHECK( fabs( p.project_to_R(0) - 44.3308 )< 0.0005);
+	BOOST_CHECK( fabs( q.project_to_R(0) - 650.568 )< 0.0005);
+	BOOST_CHECK( fabs( r.project_to_R(0) - 429.287 )< 0.0005);
+}
+
+
+BOOST_AUTO_TEST_CASE(check_scalar_products_for_heat_maps) 
+{
+	std::vector< std::vector<double> > filter = create_Gaussian_filter(30,1);	
+	Persistence_heat_maps p( "data/file_with_diagram" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps q( "data/file_with_diagram_1" , filter ,  constant_function, false , 1000 , 0 , 1 );
+	Persistence_heat_maps r( "data/file_with_diagram_2" , filter ,  constant_function, false , 1000 , 0 , 1 );
+
+	//cerr << p.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&p ) << endl;
+	//cerr << p.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&q ) << endl;
+	//cerr << p.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&r ) << endl;
+	//cerr << q.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&p ) << endl;
+	//cerr << q.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&q ) << endl;
+	//cerr << q.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&r ) << endl;	
+	//cerr << r.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&p ) << endl;
+	//cerr << r.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&q ) << endl;
+	//cerr << r.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&r ) << endl;
+	
+
+	BOOST_CHECK( fabs( p.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&p ) - 0.0345687 )< 0.0005);
+	BOOST_CHECK( fabs( p.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&q ) - 0.0509357 )< 0.0005);
+	BOOST_CHECK( fabs( p.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&r ) - 0.0375608 )< 0.0005);
+	BOOST_CHECK( fabs( q.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&p ) - 0.0509357 )< 0.0005);
+	BOOST_CHECK( fabs( q.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&q ) - 1.31293 )< 0.0005);
+	BOOST_CHECK( fabs( q.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&r ) - 0.536799)< 0.0005);
+	BOOST_CHECK( fabs( r.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&p ) - 0.0375608)< 0.0005);
+	BOOST_CHECK( fabs( r.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&q ) - 0.536799)< 0.0005);
+	BOOST_CHECK( fabs( r.compute_scalar_product( (Abs_Topological_data_with_scalar_product*)&r ) - 0.672907)< 0.0005);
+	
+}
diff --git a/src/Gudhi_stat/test/persistence_intervals_test.cpp b/src/Gudhi_stat/test/persistence_intervals_test.cpp
new file mode 100644
index 00000000..70e20ed0
--- /dev/null
+++ b/src/Gudhi_stat/test/persistence_intervals_test.cpp
@@ -0,0 +1,345 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#define BOOST_TEST_DYN_LINK
+#define BOOST_TEST_MODULE "gudhi_stat"
+#include <boost/test/unit_test.hpp>
+#include <gudhi/reader_utils.h>
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include "gudhi/concretizations/Persistence_intervals.h"
+
+#include <iostream>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+
+double epsilon = 0.0000005;
+
+using namespace std;
+
+	
+
+
+//cout << "Left most end of the interval : " << min_max_.first << endl;
+//cout << "Right most end of the interval : " << min_max_.second << endl;
+BOOST_AUTO_TEST_CASE(check_min_max_function) 
+{
+	Persistence_intervals p( "data/file_with_diagram" );
+	std::pair<double,double> min_max_ = p.min_max();
+	
+	//cout << min_max_.first << " " << min_max_.second << endl;getchar();
+	
+	BOOST_CHECK( fabs ( min_max_.first - 0.0290362 ) <= epsilon );
+	BOOST_CHECK( fabs ( min_max_.second - 0.994537 ) <= epsilon );
+}
+
+
+
+
+
+BOOST_AUTO_TEST_CASE(check_length_of_dominant_intervals) 
+{
+	Persistence_intervals p( "data/file_with_diagram" );
+	std::vector<double> dominant_ten_intervals_length = p.length_of_dominant_intervals(10);
+	std::vector< double > dominant_intervals_length;
+	dominant_intervals_length.push_back(0.862625);
+	dominant_intervals_length.push_back(0.800893);
+	dominant_intervals_length.push_back(0.762061);
+	dominant_intervals_length.push_back(0.756501);
+	dominant_intervals_length.push_back(0.729367);
+	dominant_intervals_length.push_back(0.718177);
+	dominant_intervals_length.push_back(0.708395);
+	dominant_intervals_length.push_back(0.702844);
+	dominant_intervals_length.push_back(0.700468);
+	dominant_intervals_length.push_back(0.622177);
+	for ( size_t i = 0 ; i != dominant_ten_intervals_length.size() ; ++i )
+	{
+		BOOST_CHECK( fabs ( dominant_ten_intervals_length[i] - dominant_intervals_length[i] ) <= epsilon );
+	}
+}
+BOOST_AUTO_TEST_CASE(check_dominant_intervals) 
+{
+	Persistence_intervals p( "data/file_with_diagram" );
+	std::vector< std::pair<double,double> > ten_dominant_intervals = p.dominant_intervals( 10 );
+	
+	std::vector< std::pair<double,double> > templ;
+	templ.push_back( std::pair<double,double>( 0.114718,0.977343) );
+	templ.push_back( std::pair<double,double>( 0.133638,0.93453) );
+	templ.push_back( std::pair<double,double>( 0.104599,0.866659) );
+	templ.push_back( std::pair<double,double>( 0.149798,0.906299) );
+	templ.push_back( std::pair<double,double>( 0.247352,0.976719) );
+	templ.push_back( std::pair<double,double>( 0.192675,0.910852) );
+	templ.push_back( std::pair<double,double>( 0.191836,0.900231) );
+	templ.push_back( std::pair<double,double>( 0.284998,0.987842) );
+	templ.push_back( std::pair<double,double>( 0.294069,0.994537) );
+	templ.push_back( std::pair<double,double>( 0.267421,0.889597) );
+		
+	for ( size_t i = 0 ; i != ten_dominant_intervals.size() ; ++i )
+	{
+		BOOST_CHECK( fabs ( ten_dominant_intervals[i].first - templ[i].first ) <= epsilon );
+		BOOST_CHECK( fabs ( ten_dominant_intervals[i].second - templ[i].second ) <= epsilon );
+	}
+}
+
+BOOST_AUTO_TEST_CASE(check_histograms_of_lengths) 
+{
+	Persistence_intervals p( "data/file_with_diagram" );
+	std::vector< size_t > histogram = p.histograms_of_lengths( 10  );
+	std::vector< size_t > template_histogram;
+	template_histogram.push_back(10); 
+	template_histogram.push_back(5); 
+	template_histogram.push_back(3); 
+	template_histogram.push_back(4); 
+	template_histogram.push_back(4); 
+	template_histogram.push_back(3); 
+	template_histogram.push_back(6);
+	template_histogram.push_back(1); 
+	template_histogram.push_back(7);
+	template_histogram.push_back(1); 
+	template_histogram.push_back(1);		
+	for ( size_t i = 0 ; i != histogram.size() ; ++i )
+	{
+		BOOST_CHECK( fabs ( histogram[i] - template_histogram[i] ) <= epsilon );
+	}		
+}
+
+BOOST_AUTO_TEST_CASE(check_cumulative_histograms_of_lengths) 
+{
+	Persistence_intervals p( "data/file_with_diagram" );
+	std::vector< size_t > cumulative_histogram = p.cumulative_histograms_of_lengths( 10  );
+	std::vector< size_t > template_cumulative_histogram;
+	template_cumulative_histogram.push_back(10); 
+	template_cumulative_histogram.push_back(15); 
+	template_cumulative_histogram.push_back(18);
+	template_cumulative_histogram.push_back(22); 
+	template_cumulative_histogram.push_back(26); 
+	template_cumulative_histogram.push_back(29); 
+	template_cumulative_histogram.push_back(35); 
+	template_cumulative_histogram.push_back(36); 
+	template_cumulative_histogram.push_back(43); 
+	template_cumulative_histogram.push_back(44); 
+	template_cumulative_histogram.push_back(45);
+	
+	for ( size_t i = 0 ; i != cumulative_histogram.size() ; ++i )
+	{
+		BOOST_CHECK( fabs ( cumulative_histogram[i] - template_cumulative_histogram[i] ) <= epsilon );
+	}		
+}	
+BOOST_AUTO_TEST_CASE(check_characteristic_function_of_diagram) 
+{
+	Persistence_intervals p( "data/file_with_diagram" );
+	std::pair<double,double> min_max_ = p.min_max();
+	std::vector< double  > char_funct_diag = p.characteristic_function_of_diagram( min_max_.first , min_max_.second );	
+	std::vector< double > template_char_funct_diag;
+	template_char_funct_diag.push_back(	0.370665	);
+	template_char_funct_diag.push_back(	0.84058	);
+	template_char_funct_diag.push_back(	1.24649	);
+	template_char_funct_diag.push_back(	1.3664	);
+	template_char_funct_diag.push_back(	1.34032	);
+	template_char_funct_diag.push_back(	1.31904	);
+	template_char_funct_diag.push_back(	1.14076	);
+	template_char_funct_diag.push_back(	0.991259	);
+	template_char_funct_diag.push_back(	0.800714	);
+	template_char_funct_diag.push_back(	0.0676303	);
+
+	for ( size_t i = 0 ; i != char_funct_diag.size() ; ++i )
+	{
+		//cout << char_funct_diag[i] << endl;
+		if ( fabs ( char_funct_diag[i] - template_char_funct_diag[i] ) >= 0.0001  )
+		{
+			cout << "Boost test fail  check_characteristic_function_of_diagram : " << endl;
+			cerr << char_funct_diag[i] << " " << template_char_funct_diag[i] << endl;
+			cerr << fabs ( char_funct_diag[i] - template_char_funct_diag[i] ) << endl;
+			cerr << 0.0001 << endl;
+			getchar();
+		}
+		BOOST_CHECK( fabs ( char_funct_diag[i] - template_char_funct_diag[i] ) <= 0.0001 );
+	}		
+}	
+
+
+BOOST_AUTO_TEST_CASE(check_cumulative_characteristic_function_of_diagram) 
+{
+	Persistence_intervals p( "data/file_with_diagram" );
+	std::pair<double,double> min_max_ = p.min_max();
+	std::vector< double  > cumul_char_funct_diag = p.cumulative_characteristic_function_of_diagram( min_max_.first , min_max_.second );
+	std::vector< double > template_char_funct_diag_cumul;		
+	
+	template_char_funct_diag_cumul.push_back(0.370665);
+	template_char_funct_diag_cumul.push_back(1.21125);
+	template_char_funct_diag_cumul.push_back(2.45774);
+	template_char_funct_diag_cumul.push_back(3.82414);
+	template_char_funct_diag_cumul.push_back(5.16446);
+	template_char_funct_diag_cumul.push_back(6.4835);
+	template_char_funct_diag_cumul.push_back(7.62426);
+	template_char_funct_diag_cumul.push_back(8.61552);
+	template_char_funct_diag_cumul.push_back(9.41623);
+	template_char_funct_diag_cumul.push_back(9.48386);
+
+	for ( size_t i = 0 ; i != cumul_char_funct_diag.size() ; ++i )
+	{		
+		//cout << cumul_char_funct_diag[i] << endl;
+		BOOST_CHECK( fabs (cumul_char_funct_diag[i] - template_char_funct_diag_cumul[i] ) <= 0.0001 );
+	}	
+}
+
+
+BOOST_AUTO_TEST_CASE(check_compute_persistent_betti_numbers) 
+{
+	Persistence_intervals p( "data/file_with_diagram" );
+	std::vector< std::pair< double , double > > pbns;
+	pbns.push_back(make_pair<double,double>(	0.0290362,1	));
+	pbns.push_back(make_pair<double,double>(	0.0307676,2	));
+	pbns.push_back(make_pair<double,double>(	0.0366312,3	));
+	pbns.push_back(make_pair<double,double>(	0.0544614,4	));
+	pbns.push_back(make_pair<double,double>(	0.0920033,5	));
+	pbns.push_back(make_pair<double,double>(	0.104599,6	));
+	pbns.push_back(make_pair<double,double>(	0.114718,7	));
+	pbns.push_back(make_pair<double,double>(	0.117379,8	));
+	pbns.push_back(make_pair<double,double>(	0.123493,9	));
+	pbns.push_back(make_pair<double,double>(	0.133638,10	));
+	pbns.push_back(make_pair<double,double>(	0.137798,9	));
+	pbns.push_back(make_pair<double,double>(	0.149798,10	));
+	pbns.push_back(make_pair<double,double>(	0.155421,11	));
+	pbns.push_back(make_pair<double,double>(	0.158443,12	));
+	pbns.push_back(make_pair<double,double>(	0.176956,13	));
+	pbns.push_back(make_pair<double,double>(	0.183234,12	));
+	pbns.push_back(make_pair<double,double>(	0.191069,13	));
+	pbns.push_back(make_pair<double,double>(	0.191333,14	));
+	pbns.push_back(make_pair<double,double>(	0.191836,15	));
+	pbns.push_back(make_pair<double,double>(	0.192675,16	));
+	pbns.push_back(make_pair<double,double>(	0.208564,17	));
+	pbns.push_back(make_pair<double,double>(	0.218425,18	));
+	pbns.push_back(make_pair<double,double>(	0.219902,17	));
+	pbns.push_back(make_pair<double,double>(	0.23233,16	));
+	pbns.push_back(make_pair<double,double>(	0.234558,17	));
+	pbns.push_back(make_pair<double,double>(	0.237166,16	));
+	pbns.push_back(make_pair<double,double>(	0.247352,17	));
+	pbns.push_back(make_pair<double,double>(	0.267421,18	));
+	pbns.push_back(make_pair<double,double>(	0.268093,19	));
+	pbns.push_back(make_pair<double,double>(	0.278734,18	));
+	pbns.push_back(make_pair<double,double>(	0.284722,19	));
+	pbns.push_back(make_pair<double,double>(	0.284998,20	));
+	pbns.push_back(make_pair<double,double>(	0.294069,21	));
+	pbns.push_back(make_pair<double,double>(	0.306293,22	));
+	pbns.push_back(make_pair<double,double>(	0.322361,21	));
+	pbns.push_back(make_pair<double,double>(	0.323152,22	));
+	pbns.push_back(make_pair<double,double>(	0.371021,23	));
+	pbns.push_back(make_pair<double,double>(	0.372395,24	));
+	pbns.push_back(make_pair<double,double>(	0.387744,25	));
+	pbns.push_back(make_pair<double,double>(	0.435537,26	));
+	pbns.push_back(make_pair<double,double>(	0.462911,25	));
+	pbns.push_back(make_pair<double,double>(	0.483569,26	));
+	pbns.push_back(make_pair<double,double>(	0.489209,25	));
+	pbns.push_back(make_pair<double,double>(	0.517115,24	));
+	pbns.push_back(make_pair<double,double>(	0.522197,23	));
+	pbns.push_back(make_pair<double,double>(	0.532665,22	));
+	pbns.push_back(make_pair<double,double>(	0.545262,23	));
+	pbns.push_back(make_pair<double,double>(	0.587227,22	));
+	pbns.push_back(make_pair<double,double>(	0.593036,23	));
+	pbns.push_back(make_pair<double,double>(	0.602647,24	));
+	pbns.push_back(make_pair<double,double>(	0.605044,25	));
+	pbns.push_back(make_pair<double,double>(	0.621962,24	));
+	pbns.push_back(make_pair<double,double>(	0.629449,23	));
+	pbns.push_back(make_pair<double,double>(	0.636719,22	));
+	pbns.push_back(make_pair<double,double>(	0.64957,21	));
+	pbns.push_back(make_pair<double,double>(	0.650781,22	));
+	pbns.push_back(make_pair<double,double>(	0.654951,23	));
+	pbns.push_back(make_pair<double,double>(	0.683489,24	));
+	pbns.push_back(make_pair<double,double>(	0.687172,23	));
+	pbns.push_back(make_pair<double,double>(	0.69703,22	));
+	pbns.push_back(make_pair<double,double>(	0.701174,21	));
+	pbns.push_back(make_pair<double,double>(	0.717623,22	));
+	pbns.push_back(make_pair<double,double>(	0.722023,21	));
+	pbns.push_back(make_pair<double,double>(	0.722298,20	));
+	pbns.push_back(make_pair<double,double>(	0.725347,19	));
+	pbns.push_back(make_pair<double,double>(	0.73071,18	));
+	pbns.push_back(make_pair<double,double>(	0.758355,17	));
+	pbns.push_back(make_pair<double,double>(	0.770913,18	));
+	pbns.push_back(make_pair<double,double>(	0.790833,17	));
+	pbns.push_back(make_pair<double,double>(	0.821211,16	));
+	pbns.push_back(make_pair<double,double>(	0.849305,17	));
+	pbns.push_back(make_pair<double,double>(	0.853669,16	));
+	pbns.push_back(make_pair<double,double>(	0.866659,15	));
+	pbns.push_back(make_pair<double,double>(	0.872896,16	));
+	pbns.push_back(make_pair<double,double>(	0.889597,15	));
+	pbns.push_back(make_pair<double,double>(	0.900231,14	));
+	pbns.push_back(make_pair<double,double>(	0.903847,13	));
+	pbns.push_back(make_pair<double,double>(	0.906299,12	));
+	pbns.push_back(make_pair<double,double>(	0.910852,11	));
+	pbns.push_back(make_pair<double,double>(	0.93453,10	));
+	pbns.push_back(make_pair<double,double>(	0.944757,9	));
+	pbns.push_back(make_pair<double,double>(	0.947812,8	));
+	pbns.push_back(make_pair<double,double>(	0.959154,7	));
+	pbns.push_back(make_pair<double,double>(	0.975654,6	));
+	pbns.push_back(make_pair<double,double>(	0.976719,5	));
+	pbns.push_back(make_pair<double,double>(	0.977343,4	));
+	pbns.push_back(make_pair<double,double>(	0.980129,3	));
+	pbns.push_back(make_pair<double,double>(	0.987842,2	));
+	pbns.push_back(make_pair<double,double>(	0.990127,1	));
+	pbns.push_back(make_pair<double,double>(	0.994537,0	));
+
+
+
+
+	std::vector< std::pair< double , size_t > > pbns_new = p.compute_persistent_betti_numbers();	
+	for ( size_t i = 0 ; i != pbns.size() ; ++i )
+	{
+		//cout << pbns_new[i].first << "," << pbns_new[i].second << endl;
+		BOOST_CHECK( fabs ( pbns[i].first - pbns_new[i].first ) <= epsilon );		
+		BOOST_CHECK( fabs ( pbns[i].second - pbns_new[i].second ) <= epsilon );
+	}
+}
+
+
+
+BOOST_AUTO_TEST_CASE(check_k_n_n) 
+{
+	Persistence_intervals p( "data/file_with_diagram" );
+	std::vector< double > knn = p.k_n_n( 5 );	
+	std::vector< double > knn_template;
+	knn_template.push_back(	1.04208	);
+	knn_template.push_back(	1.00344	);
+	knn_template.push_back(	0.979395	);
+	knn_template.push_back(	0.890643	);
+	knn_template.push_back(	0.874769	);
+	knn_template.push_back(	0.845787	);
+	knn_template.push_back(	0.819713	);
+	knn_template.push_back(	0.803984	);
+	knn_template.push_back(	0.799864	);
+	knn_template.push_back(	0.786945	);
+		
+	for ( size_t i = 0 ; i != knn.size() ; ++i )
+	{
+		//cout << knn[i] << endl;
+		BOOST_CHECK( fabs ( knn[i] - knn_template[i] ) <= 0.000005 );
+	}
+}
+
+
+
+
diff --git a/src/Gudhi_stat/test/persistence_lanscapes_on_grid_test.cpp b/src/Gudhi_stat/test/persistence_lanscapes_on_grid_test.cpp
new file mode 100644
index 00000000..7d0b58a5
--- /dev/null
+++ b/src/Gudhi_stat/test/persistence_lanscapes_on_grid_test.cpp
@@ -0,0 +1,254 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#define BOOST_TEST_DYN_LINK
+#define BOOST_TEST_MODULE "gudhi_stat"
+#include <boost/test/unit_test.hpp>
+#include <gudhi/reader_utils.h>
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape_on_grid.h>
+
+#include <iostream>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+
+double epsilon = 0.0000005;
+
+using namespace std;
+
+
+	
+
+BOOST_AUTO_TEST_CASE(check_construction_of_landscape) 
+{	
+	Persistence_landscape_on_grid l( "data/file_with_diagram_1" , 100 );
+	l.print_to_file( "landscape_from_file_with_diagram_1" );
+	
+	Persistence_landscape_on_grid g;
+	g.load_landscape_from_file( "landscape_from_file_with_diagram_1" );
+	
+	BOOST_CHECK( l == g );
+}
+
+
+BOOST_AUTO_TEST_CASE(check_computations_of_integrals) 
+{
+	Persistence_landscape_on_grid p( "data/file_with_diagram_1" , 100 );	
+	double integral = p.compute_integral_of_landscape();
+	//cerr << "integral : " << integral << endl;getchar();
+	BOOST_CHECK( fabs( integral - 27.343 ) <= 0.00005 );
+}
+
+
+BOOST_AUTO_TEST_CASE(check_computations_of_integrals_for_each_level_separatelly) 
+{
+	Persistence_landscape_on_grid p( "data/file_with_diagram_1" , 100 );	
+	
+	std::vector< double > integrals_fir_different_levels;	
+	//integrals_fir_different_levels.push_back();
+	integrals_fir_different_levels.push_back(0.241168);
+	integrals_fir_different_levels.push_back(0.239276);
+	integrals_fir_different_levels.push_back(0.237882);
+	integrals_fir_different_levels.push_back(0.235193);
+	integrals_fir_different_levels.push_back(0.230115);
+	integrals_fir_different_levels.push_back(0.227626);
+	integrals_fir_different_levels.push_back(0.226132);
+	integrals_fir_different_levels.push_back(0.223643);
+	integrals_fir_different_levels.push_back(0.221651);
+	integrals_fir_different_levels.push_back(0.220556);
+	integrals_fir_different_levels.push_back(0.21727);
+	integrals_fir_different_levels.push_back(0.215976);
+	integrals_fir_different_levels.push_back(0.213685);
+	integrals_fir_different_levels.push_back(0.211993);
+	integrals_fir_different_levels.push_back(0.2102);
+	integrals_fir_different_levels.push_back(0.208707);
+	integrals_fir_different_levels.push_back(0.207014);
+	integrals_fir_different_levels.push_back(0.205122);
+	integrals_fir_different_levels.push_back(0.204226);
+	integrals_fir_different_levels.push_back(0.202633);
+
+	
+	for ( size_t level = 0 ; level != integrals_fir_different_levels.size() ; ++level )
+	{
+		double integral = p.compute_integral_of_landscape( level );		
+		//cerr << integral << endl;
+		BOOST_CHECK( fabs( integral - integrals_fir_different_levels[level] ) <= 0.00005 );
+	}	
+	
+}
+
+
+
+BOOST_AUTO_TEST_CASE(check_computations_of_integrals_of_powers_of_landscape) 
+{
+	Persistence_landscape_on_grid p( "data/file_with_diagram_1" , 100 );	
+	
+	std::vector<double> integrals_fir_different_powers;
+	integrals_fir_different_powers.push_back(	0.241168);
+	integrals_fir_different_powers.push_back(	0.239276);
+	integrals_fir_different_powers.push_back(	0.237882);
+	integrals_fir_different_powers.push_back(	0.235193);
+	integrals_fir_different_powers.push_back(	0.23011);
+ 
+	for ( size_t power = 0 ; power != 5 ; ++power ) 
+	{
+		double integral = p.compute_integral_of_landscape( power );
+		//cerr << integral << endl;
+		BOOST_CHECK( fabs( integral - integrals_fir_different_powers[power] ) <= 0.00001 );
+	}
+}
+
+
+BOOST_AUTO_TEST_CASE(check_computations_of_values_on_different_points) 
+{
+	Persistence_landscape_on_grid p( "data/file_with_diagram_1" , 100 );	
+
+	std::vector< double > results_level_0;	
+	results_level_0.push_back(0.00997867);
+	results_level_0.push_back(0.0521921);
+	results_level_0.push_back(0.104312);
+	results_level_0.push_back(0.156432);
+	results_level_0.push_back(0.208552);
+	results_level_0.push_back(0.260672);
+	results_level_0.push_back(0.312792);
+	results_level_0.push_back(0.364912);
+	results_level_0.push_back(0.417032);
+	results_level_0.push_back(0.429237);
+	
+	std::vector< double > results_level_10;
+	results_level_10.push_back(7.21433e-05);
+	results_level_10.push_back(0.0422135);
+	results_level_10.push_back(0.0943335);
+	results_level_10.push_back(0.146453);
+	results_level_10.push_back(0.198573);
+	results_level_10.push_back(0.240715);
+	results_level_10.push_back(0.272877);
+	results_level_10.push_back(0.324997);
+	results_level_10.push_back(0.359232);
+	results_level_10.push_back(0.379344);
+	
+	double x = 0.0012321;
+	 double dx = 0.05212;
+	 for ( size_t i = 0 ; i != 10 ; ++i )
+	 {  		
+		BOOST_CHECK( almost_equal( p.compute_value_at_a_given_point(0,x) , results_level_0[i] ) );
+		BOOST_CHECK( almost_equal( p.compute_value_at_a_given_point(10,x) , results_level_10[i] ) );
+		x += dx;
+	 }
+}
+
+
+BOOST_AUTO_TEST_CASE(check_computations_sum_differences_and_multiplications) 
+{	
+	Persistence_landscape_on_grid p( "data/file_with_diagram_1" ,100 );	
+	Persistence_landscape_on_grid second("data/file_with_diagram_1" , 100 );	
+	
+	Persistence_landscape_on_grid sum = p + second;
+	Persistence_landscape_on_grid difference = p - second;
+	Persistence_landscape_on_grid multiply_by_scalar = 10*p;	;
+
+	
+	Persistence_landscape_on_grid template_sum;
+	template_sum.load_landscape_from_file( "data/sum_on_grid_test" );
+	
+	Persistence_landscape_on_grid template_difference;
+	template_difference.load_landscape_from_file( "data/difference_on_grid_test" );
+	
+	Persistence_landscape_on_grid template_multiply_by_scalar;
+	template_multiply_by_scalar.load_landscape_from_file( "data/multiply_by_scalar_on_grid_test" );
+	
+	BOOST_CHECK( sum == template_sum );
+	BOOST_CHECK( difference == template_difference );
+	BOOST_CHECK( multiply_by_scalar == template_multiply_by_scalar );		
+}
+
+
+
+BOOST_AUTO_TEST_CASE(check_computations_of_maxima_and_norms) 
+{	
+	Persistence_landscape_on_grid p( "data/file_with_diagram_1" , 0 , 1 , 100 );	
+	Persistence_landscape_on_grid second("data/file_with_diagram_2" , 0 , 1 , 100 );	
+	Persistence_landscape_on_grid sum = p + second;
+	
+	//cerr << p.compute_maximum() << endl;
+	//cerr <<  p.compute_norm_of_landscape(1) << endl;
+	//cerr << p.compute_norm_of_landscape(2) << endl;
+	//cerr <<  p.compute_norm_of_landscape(3) << endl;
+	//cerr <<  compute_discance_of_landscapes_on_grid(p,sum,1) << endl;
+	//cerr <<  compute_discance_of_landscapes_on_grid(p,sum,2) << endl;
+	//cerr <<  compute_discance_of_landscapes_on_grid(p,sum,-1)  << endl;
+	
+	BOOST_CHECK( fabs( p.compute_maximum() - 0.46 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_norm_of_landscape(1) - 27.3373 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_norm_of_landscape(2) - 1.84143 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_norm_of_landscape(3) - 0.927067 ) <= 0.00001 );
+	BOOST_CHECK( fabs( compute_discance_of_landscapes_on_grid(p,sum,1) - 16.8519 ) <= 0.00005 );	
+	BOOST_CHECK( fabs( compute_discance_of_landscapes_on_grid(p,sum,2) - 1.44542 ) <= 0.00001 );
+	BOOST_CHECK( fabs(compute_discance_of_landscapes_on_grid(p,sum,-1) - 0.45 ) <= 0.00001 );		
+}
+
+
+
+
+BOOST_AUTO_TEST_CASE(check_computations_of_averages) 
+{
+	Persistence_landscape_on_grid p( "data/file_with_diagram", 0,1,100 );
+	Persistence_landscape_on_grid q( "data/file_with_diagram_1", 0,1,100 );	
+	std::vector< Abs_Topological_data_with_averages* > to_average;
+	to_average.push_back( &p );
+	to_average.push_back( &q );
+	Persistence_landscape_on_grid av;	
+	av.compute_average( to_average );
+	
+	Persistence_landscape_on_grid template_average;
+	template_average.load_landscape_from_file( "data/average_on_a_grid" );
+	BOOST_CHECK ( template_average == av );
+}
+
+
+
+
+BOOST_AUTO_TEST_CASE(check_computations_of_distances)
+{
+	Persistence_landscape_on_grid p( "data/file_with_diagram", 0,1,10000 );
+	Persistence_landscape_on_grid q( "data/file_with_diagram_1", 0,1,10000 );
+	BOOST_CHECK( fabs( p.distance( &q )- 25.5779) <= 0.00005 );	
+	BOOST_CHECK( fabs( p.distance( &q , 2) - 2.04891) <= 0.00001 );	
+	BOOST_CHECK( fabs( p.distance( &q , -1 )-0.359		 ) <= 0.00001 );
+}
+	
+
+BOOST_AUTO_TEST_CASE(check_computations_of_scalar_product)
+{
+	Persistence_landscape_on_grid p( "data/file_with_diagram" , 0,1,10000);
+	Persistence_landscape_on_grid q( "data/file_with_diagram_1", 0,1,10000 );
+	//std::cerr << p.compute_scalar_product( &q ) << std::endl;
+	BOOST_CHECK( almost_equal(  p.compute_scalar_product( &q ) , p.compute_scalar_product( &q ) ) );	
+}
+
+
diff --git a/src/Gudhi_stat/test/persistence_lanscapes_test.cpp b/src/Gudhi_stat/test/persistence_lanscapes_test.cpp
new file mode 100644
index 00000000..8a7d0ce1
--- /dev/null
+++ b/src/Gudhi_stat/test/persistence_lanscapes_test.cpp
@@ -0,0 +1,224 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+
+#define BOOST_TEST_DYN_LINK
+#define BOOST_TEST_MODULE "gudhi_stat"
+#include <boost/test/unit_test.hpp>
+#include <gudhi/reader_utils.h>
+#include <gudhi/abstract_classes/Abs_Topological_data.h>
+#include <gudhi/concretizations/Persistence_landscape.h>
+
+#include <iostream>
+
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+
+double epsilon = 0.0000005;
+
+using namespace std;
+
+	
+
+BOOST_AUTO_TEST_CASE(check_construction_of_landscape) 
+{	
+	Persistence_landscape p( "data/file_with_diagram" );
+	
+	Persistence_landscape q;
+	q.load_landscape_from_file( "data/file_with_landscape_from_file_with_diagram" );
+		
+	BOOST_CHECK( p == q );
+}
+
+
+BOOST_AUTO_TEST_CASE(check_computations_of_integrals) 
+{
+	Persistence_landscape p( "data/file_with_diagram" );	
+	double integral = p.compute_integral_of_landscape();
+	//cerr << integral  << " " << 2.34992 << endl;
+	BOOST_CHECK( fabs( integral - 2.34992 ) <= 0.00001 );
+}
+
+
+BOOST_AUTO_TEST_CASE(check_computations_of_integrals_for_each_level_separatelly) 
+{
+	Persistence_landscape p( "data/file_with_diagram" );	
+	
+	std::vector< double > integrals_fir_different_levels;
+	integrals_fir_different_levels.push_back(	0.216432	);
+	integrals_fir_different_levels.push_back(	0.204763	);
+	integrals_fir_different_levels.push_back(	0.188793	);
+	integrals_fir_different_levels.push_back(	0.178856	);
+	integrals_fir_different_levels.push_back(	0.163142	);
+	integrals_fir_different_levels.push_back(	0.155015	);
+	integrals_fir_different_levels.push_back(	0.143046	);
+	integrals_fir_different_levels.push_back(	0.133765	);
+	integrals_fir_different_levels.push_back(	0.123531	);
+	integrals_fir_different_levels.push_back(	0.117393	);
+	integrals_fir_different_levels.push_back(	0.111269	);
+	integrals_fir_different_levels.push_back(	0.104283	);
+	integrals_fir_different_levels.push_back(	0.0941308	);
+	integrals_fir_different_levels.push_back(	0.0811208	);
+	integrals_fir_different_levels.push_back(	0.0679001	);
+	integrals_fir_different_levels.push_back(	0.0580801	);
+	integrals_fir_different_levels.push_back(	0.0489647	);
+	integrals_fir_different_levels.push_back(	0.0407936	);
+	integrals_fir_different_levels.push_back(	0.0342599	);
+	integrals_fir_different_levels.push_back(	0.02896	);
+	integrals_fir_different_levels.push_back(	0.0239881	);
+	integrals_fir_different_levels.push_back(	0.0171792	);
+	integrals_fir_different_levels.push_back(	0.0071511	);
+	integrals_fir_different_levels.push_back(	0.00462067	);
+	integrals_fir_different_levels.push_back(	0.00229033	);
+	integrals_fir_different_levels.push_back(	0.000195296	);
+
+
+	
+	
+	for ( size_t level = 0 ; level != p.size() ; ++level )
+	{
+		double integral = p.compute_integral_of_landscape( level );
+		BOOST_CHECK( fabs( integral - integrals_fir_different_levels[level] ) <= 0.00001 );
+	}
+	
+}
+
+BOOST_AUTO_TEST_CASE(check_computations_of_integrals_of_powers_of_landscape) 
+{
+	Persistence_landscape p( "data/file_with_diagram" );	
+	
+	std::vector<double> integrals_fir_different_powers;
+ 	integrals_fir_different_powers.push_back(	0.216432	);
+	integrals_fir_different_powers.push_back(	0.204763	);
+	integrals_fir_different_powers.push_back(	0.188793	);
+	integrals_fir_different_powers.push_back(	0.178856	);
+	integrals_fir_different_powers.push_back(	0.163142	);
+	
+	for ( size_t power = 0 ; power != 5 ; ++power ) 
+	{
+		double integral = p.compute_integral_of_landscape( power );
+		BOOST_CHECK( fabs( integral - integrals_fir_different_powers[power] ) <= 0.00001 );
+	}
+}
+
+BOOST_AUTO_TEST_CASE(check_computations_of_values_on_different_points) 
+{
+	Persistence_landscape p( "data/file_with_diagram" );	
+	
+	
+	BOOST_CHECK( fabs( p.compute_value_at_a_given_point(1,0.0)  ) <= 0.00001 );
+	BOOST_CHECK( fabs(  p.compute_value_at_a_given_point(1,0.1) - 0.0692324 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_value_at_a_given_point(1,0.2) - 0.163369 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_value_at_a_given_point(1,0.3) - 0.217115 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_value_at_a_given_point(2,0.0) ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_value_at_a_given_point(2,0.1) - 0.0633688 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_value_at_a_given_point(2,0.2) - 0.122361 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_value_at_a_given_point(2,0.3) - 0.195401 ) <= 0.00001 );			
+	BOOST_CHECK( fabs( p.compute_value_at_a_given_point(3,0.0)  ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_value_at_a_given_point(3,0.1) - 0.0455386 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_value_at_a_given_point(3,0.2) - 0.0954012 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_value_at_a_given_point(3,0.3) - 0.185282 ) <= 0.00001 );
+}
+
+
+BOOST_AUTO_TEST_CASE(check_computations_sum_differences_and_multiplications) 
+{	
+	Persistence_landscape p( "data/file_with_diagram" );	
+	Persistence_landscape second;
+	second.load_landscape_from_file("data/file_with_landscape_from_file_with_diagram_1" );
+	
+	Persistence_landscape sum = p + second;
+	Persistence_landscape difference = p - second;
+	Persistence_landscape multiply_by_scalar = 10*p;
+
+	
+	Persistence_landscape template_sum;
+	template_sum.load_landscape_from_file( "data/sum" );
+	
+	Persistence_landscape template_difference;
+	template_difference.load_landscape_from_file( "data/difference" );
+	
+	Persistence_landscape template_multiply_by_scalar;
+	template_multiply_by_scalar.load_landscape_from_file( "data/multiply_by_scalar" );
+	
+	BOOST_CHECK( sum == template_sum );
+	BOOST_CHECK( difference == template_difference );
+	BOOST_CHECK( multiply_by_scalar == template_multiply_by_scalar );		
+}
+
+
+
+BOOST_AUTO_TEST_CASE(check_computations_of_maxima_and_norms) 
+{	
+	Persistence_landscape p( "data/file_with_diagram" );	
+	Persistence_landscape second;
+	second.load_landscape_from_file("data/file_with_landscape_from_file_with_diagram_1" );	
+	Persistence_landscape sum = p + second;
+	
+	BOOST_CHECK( fabs( p.compute_maximum() - 0.431313 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_norm_of_landscape(1) - 2.34992 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_norm_of_landscape(2) - 0.706095 ) <= 0.00001 );
+	BOOST_CHECK( fabs( p.compute_norm_of_landscape(3) - 0.501867 ) <= 0.00001 );
+	BOOST_CHECK( fabs( compute_discance_of_landscapes(p,sum,1) - 27.9323 ) <= 0.00005 );	
+	BOOST_CHECK( fabs( compute_discance_of_landscapes(p,sum,2) - 2.35199 ) <= 0.00001 );
+	BOOST_CHECK( fabs(compute_discance_of_landscapes(p,sum,-1) - 0.464478 ) <= 0.00001 );		
+}
+
+BOOST_AUTO_TEST_CASE(check_computations_of_averages) 
+{
+	Persistence_landscape p( "data/file_with_diagram" );
+	Persistence_landscape q( "data/file_with_diagram_1" );
+	std::vector< Abs_Topological_data_with_averages* > to_average;
+	to_average.push_back( &p );
+	to_average.push_back( &q );
+	Persistence_landscape av;
+	av.compute_average( to_average );
+
+	Persistence_landscape template_average;
+	template_average.load_landscape_from_file( "data/average" );
+	BOOST_CHECK ( template_average == av );
+}
+
+
+
+
+BOOST_AUTO_TEST_CASE(check_computations_of_distances)
+{
+	Persistence_landscape p( "data/file_with_diagram" );
+	Persistence_landscape q( "data/file_with_diagram_1" );
+	BOOST_CHECK( fabs( p.distance( &q )- 25.5824) <= 0.00005 );	
+	BOOST_CHECK( fabs( p.distance( &q , 2) - 2.12636 ) <= 0.00001 );	
+	BOOST_CHECK( fabs( p.distance( &q , -1 )-0.359068 ) <= 0.00001 );	
+}
+	
+
+BOOST_AUTO_TEST_CASE(check_computations_of_scalar_product)
+{
+	Persistence_landscape p( "data/file_with_diagram" );
+	Persistence_landscape q( "data/file_with_diagram_1" );
+	BOOST_CHECK( fabs(  p.compute_scalar_product( &q ) - 0.754498 ) <= 0.00001 );	
+}
+
diff --git a/src/Gudhi_stat/test/vector_representation_test.cpp b/src/Gudhi_stat/test/vector_representation_test.cpp
new file mode 100644
index 00000000..e87d1b23
--- /dev/null
+++ b/src/Gudhi_stat/test/vector_representation_test.cpp
@@ -0,0 +1,354 @@
+/*    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):       Pawel Dlotko
+ *
+ *    Copyright (C) 2015  INRIA Sophia-Saclay (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/>.
+ */
+
+
+#include <gudhi/concretizations/Vector_distances_in_diagram.h>
+#include <gudhi/common.h>
+#include <iostream>
+
+#define BOOST_TEST_DYN_LINK
+#define BOOST_TEST_MODULE "gudhi_stat"
+#include <boost/test/unit_test.hpp>
+#include <gudhi/reader_utils.h>
+#include <vector>
+#include <cmath>
+#include <iomanip>
+
+
+using namespace Gudhi;
+using namespace Gudhi::Gudhi_stat;
+
+using namespace std;
+
+
+
+
+
+
+BOOST_AUTO_TEST_CASE(check_read_write_to_files) 
+{
+	std::vector< std::pair<double,double> > intervals;
+	intervals.push_back( std::make_pair(2,3) );
+	intervals.push_back( std::make_pair(4,7) );
+	intervals.push_back( std::make_pair(9,10) );
+	intervals.push_back( std::make_pair(3,11) );
+	Vector_distances_in_diagram< euclidean_distance<double> > p( intervals , -1 );
+	p.write_to_file( "test_vector_representation_write_read" );
+	
+	Vector_distances_in_diagram< euclidean_distance<double> > q;
+	q.load_from_file( "test_vector_representation_write_read" );
+	
+	BOOST_CHECK( p == q );
+	
+}
+
+
+BOOST_AUTO_TEST_CASE(check_sortev_vector_distances_template) 
+{	
+	Vector_distances_in_diagram< euclidean_distance<double> > p( "data/file_with_diagram" , 100 );
+	std::vector< double > sortev_vector_distances_template;
+
+	sortev_vector_distances_template.push_back(	0.609968	);
+	sortev_vector_distances_template.push_back(	0.566317	);
+	sortev_vector_distances_template.push_back(	0.538858	);
+	sortev_vector_distances_template.push_back(	0.534927	);
+	sortev_vector_distances_template.push_back(	0.515741	);
+	sortev_vector_distances_template.push_back(	0.507828	);
+	sortev_vector_distances_template.push_back(	0.500911	);
+	sortev_vector_distances_template.push_back(	0.496986	);
+	sortev_vector_distances_template.push_back(	0.495306	);
+	sortev_vector_distances_template.push_back(	0.439945	);
+	sortev_vector_distances_template.push_back(	0.424097	);
+	sortev_vector_distances_template.push_back(	0.413891	);
+	sortev_vector_distances_template.push_back(	0.413891	);
+	sortev_vector_distances_template.push_back(	0.413891	);
+	sortev_vector_distances_template.push_back(	0.412621	);
+	sortev_vector_distances_template.push_back(	0.410613	);
+	sortev_vector_distances_template.push_back(	0.407853	);
+	sortev_vector_distances_template.push_back(	0.407853	);
+	sortev_vector_distances_template.push_back(	0.402306	);
+	sortev_vector_distances_template.push_back(	0.401937	);
+	sortev_vector_distances_template.push_back(	0.377605	);
+	sortev_vector_distances_template.push_back(	0.363859	);
+	sortev_vector_distances_template.push_back(	0.357765	);
+	sortev_vector_distances_template.push_back(	0.357765	);
+	sortev_vector_distances_template.push_back(	0.357765	);
+	sortev_vector_distances_template.push_back(	0.357765	);
+	sortev_vector_distances_template.push_back(	0.357765	);
+	sortev_vector_distances_template.push_back(	0.353401	);
+	sortev_vector_distances_template.push_back(	0.348004	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.345124	);
+	sortev_vector_distances_template.push_back(	0.34469	);
+	sortev_vector_distances_template.push_back(	0.339466	);
+	sortev_vector_distances_template.push_back(	0.33935	);
+	sortev_vector_distances_template.push_back(	0.32834	);
+	sortev_vector_distances_template.push_back(	0.327276	);
+	sortev_vector_distances_template.push_back(	0.318626	);
+	sortev_vector_distances_template.push_back(	0.318082	);
+	sortev_vector_distances_template.push_back(	0.30603	);
+	sortev_vector_distances_template.push_back(	0.30525	);
+	sortev_vector_distances_template.push_back(	0.297308	);
+	sortev_vector_distances_template.push_back(	0.296333	);
+	sortev_vector_distances_template.push_back(	0.296333	);
+	sortev_vector_distances_template.push_back(	0.296333	);
+	sortev_vector_distances_template.push_back(	0.296333	);
+	sortev_vector_distances_template.push_back(	0.293372	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.292666	);
+	sortev_vector_distances_template.push_back(	0.29029	);
+	sortev_vector_distances_template.push_back(	0.290218	);
+	sortev_vector_distances_template.push_back(	0.289782	);
+	sortev_vector_distances_template.push_back(	0.288128	);
+	sortev_vector_distances_template.push_back(	0.286416	);
+	sortev_vector_distances_template.push_back(	0.285969	);
+	sortev_vector_distances_template.push_back(	0.282046	);
+	sortev_vector_distances_template.push_back(	0.28154	);
+	sortev_vector_distances_template.push_back(	0.281085	);
+	sortev_vector_distances_template.push_back(	0.280227	);
+	sortev_vector_distances_template.push_back(	0.279273	);
+	sortev_vector_distances_template.push_back(	0.278936	);
+	sortev_vector_distances_template.push_back(	0.278706	);
+	sortev_vector_distances_template.push_back(	0.278507	);
+	sortev_vector_distances_template.push_back(	0.278097	);
+	sortev_vector_distances_template.push_back(	0.276293	);
+	sortev_vector_distances_template.push_back(	0.276293	);
+	sortev_vector_distances_template.push_back(	0.276293	);
+	sortev_vector_distances_template.push_back(	0.276293	);
+	sortev_vector_distances_template.push_back(	0.276293	);
+	sortev_vector_distances_template.push_back(	0.276293	);
+	sortev_vector_distances_template.push_back(	0.276293	);
+	sortev_vector_distances_template.push_back(	0.276293	);
+	sortev_vector_distances_template.push_back(	0.276293	);
+	sortev_vector_distances_template.push_back(	0.276169	);
+	sortev_vector_distances_template.push_back(	0.270563	);
+	sortev_vector_distances_template.push_back(	0.264009	);
+
+
+ 
+	size_t proj_no = p.number_of_vectorize_functions();
+	std::vector< double > aa = p.vectorize(proj_no);
+	
+	for ( size_t i = 0 ; i != aa.size() ; ++i )	
+	{		
+		BOOST_CHECK( almost_equal( sortev_vector_distances_template[i] , aa[i] ) );
+	}
+}	
+
+
+
+
+BOOST_AUTO_TEST_CASE(check_projections_to_R) 
+{
+	Vector_distances_in_diagram< euclidean_distance<double> > p( "data/file_with_diagram" , 100 );
+	std::vector< double > proj;
+	proj.push_back(	0	);
+	proj.push_back(	0.6099679993	);
+	proj.push_back(	1.176284775	);
+	proj.push_back(	1.715142954	);
+	proj.push_back(	2.25006986	);
+	proj.push_back(	2.765810506	);
+	proj.push_back(	3.273638431	);
+	proj.push_back(	3.774549309	);
+	proj.push_back(	4.271535042	);
+	proj.push_back(	4.766840875	);
+	proj.push_back(	5.206786149	);
+	proj.push_back(	5.63088295	);
+	proj.push_back(	6.04477433	);
+	proj.push_back(	6.45866571	);
+	proj.push_back(	6.87255709	);
+	proj.push_back(	7.285177939	);
+	proj.push_back(	7.695791381	);
+	proj.push_back(	8.103643945	);
+	proj.push_back(	8.511496508	);
+	proj.push_back(	8.913802775	);
+	proj.push_back(	9.315740229	);
+	proj.push_back(	9.693344927	);
+	proj.push_back(	10.0572035	);
+	proj.push_back(	10.41496899	);
+	proj.push_back(	10.77273448	);
+	proj.push_back(	11.13049996	);
+	proj.push_back(	11.48826545	);
+	proj.push_back(	11.84603094	);
+	proj.push_back(	12.19943233	);
+	proj.push_back(	12.5474364	);
+	proj.push_back(	12.89256042	);
+	proj.push_back(	13.23768444	);
+	proj.push_back(	13.58280846	);
+	proj.push_back(	13.92793248	);
+	proj.push_back(	14.2730565	);
+	proj.push_back(	14.61818051	);
+	proj.push_back(	14.96330453	);
+	proj.push_back(	15.30842855	);
+	proj.push_back(	15.65355257	);
+	proj.push_back(	15.99867659	);
+	proj.push_back(	16.34380061	);
+	proj.push_back(	16.68892462	);
+	proj.push_back(	17.03404864	);
+	proj.push_back(	17.37917266	);
+	proj.push_back(	17.7238622	);
+	proj.push_back(	18.06332781	);
+	proj.push_back(	18.40267754	);
+	proj.push_back(	18.73101759	);
+	proj.push_back(	19.05829313	);
+	proj.push_back(	19.3769189	);
+	proj.push_back(	19.69500045	);
+	proj.push_back(	20.0010306	);
+	proj.push_back(	20.30628026	);
+	proj.push_back(	20.60358868	);
+	proj.push_back(	20.89992192	);
+	proj.push_back(	21.19625516	);
+	proj.push_back(	21.4925884	);
+	proj.push_back(	21.78892164	);
+	proj.push_back(	22.08229394	);
+	proj.push_back(	22.37495987	);
+	proj.push_back(	22.66762581	);
+	proj.push_back(	22.96029174	);
+	proj.push_back(	23.25295768	);
+	proj.push_back(	23.54562361	);
+	proj.push_back(	23.83828955	);
+	proj.push_back(	24.13095549	);
+	proj.push_back(	24.42362142	);
+	proj.push_back(	24.71628736	);
+	proj.push_back(	25.00895329	);
+	proj.push_back(	25.30161923	);
+	proj.push_back(	25.59428516	);
+	proj.push_back(	25.8869511	);
+	proj.push_back(	26.17961703	);
+	proj.push_back(	26.47228297	);
+	proj.push_back(	26.76257262	);
+	proj.push_back(	27.05279049	);
+	proj.push_back(	27.34257265	);
+	proj.push_back(	27.63070097	);
+	proj.push_back(	27.91711687	);
+	proj.push_back(	28.20308566	);
+	proj.push_back(	28.48513176	);
+	proj.push_back(	28.76667161	);
+	proj.push_back(	29.04775635	);
+	proj.push_back(	29.32798359	);
+	proj.push_back(	29.60725702	);
+	proj.push_back(	29.88619335	);
+	proj.push_back(	30.16489915	);
+	proj.push_back(	30.44340655	);
+	proj.push_back(	30.72150329	);
+	proj.push_back(	30.99779604	);
+	proj.push_back(	31.27408878	);
+	proj.push_back(	31.55038153	);
+	proj.push_back(	31.82667427	);
+	proj.push_back(	32.10296702	);
+	proj.push_back(	32.37925976	);
+	proj.push_back(	32.6555525	);
+	proj.push_back(	32.93184525	);
+	proj.push_back(	33.20813799	);
+	proj.push_back(	33.48430662	);
+	proj.push_back(	33.7548692	);
+
+	for ( size_t proj_no = 0 ; proj_no != p.number_of_projections_to_R() ; ++proj_no )	 
+	{		
+		//cout << std::setprecision(10)  << 	p.project_to_R(proj_no) << endl;
+		BOOST_CHECK( almost_equal( p.project_to_R(proj_no) , proj[proj_no] ) );
+	}
+}
+
+
+
+
+
+BOOST_AUTO_TEST_CASE(check_distance_computations) 
+{
+	Vector_distances_in_diagram< euclidean_distance<double> > p( "data/file_with_diagram" , 100 );
+	Vector_distances_in_diagram< euclidean_distance<double> > p_prime( "data/file_with_diagram" , 10 );	
+	std::vector< std::pair<double,double> > intervals(10);
+	intervals[0] = std::pair<double,double>( 1,2 );
+	intervals[1] = std::pair<double,double>( 3,4 );
+	intervals[2] = std::pair<double,double>( 5,6 );
+	intervals[3] = std::pair<double,double>( 7,8 );
+	intervals[4] = std::pair<double,double>( 9,10 );
+	intervals[5] = std::pair<double,double>( 11,12 );
+	intervals[6] = std::pair<double,double>( 13,14 );
+	intervals[7] = std::pair<double,double>( 15,16 );
+	intervals[8] = std::pair<double,double>( 17,18 );
+	intervals[9] = std::pair<double,double>( 19,20 );		
+	Vector_distances_in_diagram< euclidean_distance<double> > p_bis( intervals , 10 );	
+	//cerr << "p_prime.distance( (Abs_Topological_data_with_distances*)(&p_bis) , 1 ) : " << p_prime.distance( (Abs_Topological_data_with_distances*)(&p_bis) , 1 ) << endl;	
+	BOOST_CHECK( almost_equal ( p_prime.distance( (Abs_Topological_data_with_distances*)(&p_bis) , 1 ) , 1.86428 ) );		
+}
+
+
+
+BOOST_AUTO_TEST_CASE(check_compute_average) 
+{
+	Vector_distances_in_diagram< euclidean_distance<double> > p( "data/file_with_diagram" , 100 );
+	//compute average 
+	std::vector< std::pair<double,double> > i1(3);
+	i1[0] = std::pair<double,double>( 1,2 );
+	i1[1] = std::pair<double,double>( 3,8 );
+	i1[2] = std::pair<double,double>( 1,6 );
+	
+	std::vector< std::pair<double,double> > i2(3);
+	i2[0] = std::pair<double,double>( 2,9 );
+	i2[1] = std::pair<double,double>( 2,15);
+	i2[2] = std::pair<double,double>( 6,17 );
+	
+	Vector_distances_in_diagram< euclidean_distance<double> > A( i1 , -1 );
+	Vector_distances_in_diagram< euclidean_distance<double> > B( i1 , -1 );
+	
+	std::vector< Abs_Topological_data_with_averages* > to_average;
+	to_average.push_back( (Abs_Topological_data_with_averages*)(&A) );
+	to_average.push_back( (Abs_Topological_data_with_averages*)(&B) );
+	
+	Vector_distances_in_diagram< euclidean_distance<double> > average; 
+	average.compute_average( to_average );
+	
+	Vector_distances_in_diagram< euclidean_distance<double> > template_average; 
+	template_average.load_from_file( "data/average_of_persistence_vectors" );
+		
+	BOOST_CHECK( template_average == average );
+	
+}
+
+
diff --git a/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp b/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp
index 48fbb91a..20142ab2 100644
--- a/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp
+++ b/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp
@@ -22,11 +22,11 @@
 
 #include <gudhi/Simplex_tree.h>
 #include <gudhi/Persistent_cohomology.h>
-#include <gudhi/Points_3D_off_io.h>
 #include <boost/variant.hpp>
 
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
-#include <CGAL/Delaunay_triangulation_3.h>
+#include <CGAL/Regular_triangulation_3.h>
+#include <CGAL/Regular_triangulation_euclidean_traits_3.h>
 #include <CGAL/Alpha_shape_3.h>
 #include <CGAL/iterator.h>
 
@@ -41,10 +41,11 @@
 
 // Alpha_shape_3 templates type definitions
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
-typedef CGAL::Alpha_shape_vertex_base_3<Kernel> Vb;
-typedef CGAL::Alpha_shape_cell_base_3<Kernel> Fb;
+typedef CGAL::Regular_triangulation_euclidean_traits_3<Kernel> Gt;
+typedef CGAL::Alpha_shape_vertex_base_3<Gt> Vb;
+typedef CGAL::Alpha_shape_cell_base_3<Gt> Fb;
 typedef CGAL::Triangulation_data_structure_3<Vb, Fb> Tds;
-typedef CGAL::Delaunay_triangulation_3<Kernel, Tds> Triangulation_3;
+typedef CGAL::Regular_triangulation_3<Gt, Tds> Triangulation_3;
 typedef CGAL::Alpha_shape_3<Triangulation_3> Alpha_shape_3;
 
 // From file type definition
@@ -138,18 +139,11 @@ int main(int argc, char * const argv[]) {
     usage(argv[0]);
   }
 
-  // Read points from file
-  std::string offInputFile(argv[1]);
-  // Read the OFF file (input file name given as parameter) and triangulate points
-  Gudhi::Points_3D_off_reader<Point_3> off_reader(offInputFile);
-  // Check the read operation was correct
-  if (!off_reader.is_valid()) {
-    std::cerr << "Unable to read file " << offInputFile << std::endl;
-    usage(argv[0]);
-  }
-
-  // Retrieve the triangulation
-  std::vector<Point_3> lp = off_reader.get_point_cloud();
+  std::vector<Gt::Weighted_point> lp;
+  lp.emplace_back(Point_3(0,0,0),0);
+  lp.emplace_back(Point_3(0,0,1),0);
+  lp.emplace_back(Point_3(0,1,0),.2);
+  lp.emplace_back(Point_3(1,0,0),0);
 
   // alpha shape construction from points. CGAL has a strange behavior in REGULARIZED mode.
   Alpha_shape_3 as(lp.begin(), lp.end(), 0, Alpha_shape_3::GENERAL);