Merged trunk into relaxed witness branch

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/relaxed-witness@1579 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: a9ca2e7a968ebf4bb80cfa795965ae78511e8dd4

12 files changed, 114 insertions, 147 deletions

diff --git a/src/Witness_complex/concept/Simplicial_complex.h b/src/Witness_complex/concept/Simplicial_complex_for_witness.h
index d7f3496d..caaf0db6 100644
--- a/src/Witness_complex/concept/Simplicial_complex.h
+++ b/src/Witness_complex/concept/Simplicial_complex_for_witness.h
@@ -20,8 +20,8 @@
  *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
  */
 
-#ifndef CONCEPT_WITNESS_COMPLEX_SIMPLICIAL_COMPLEX_H_
-#define CONCEPT_WITNESS_COMPLEX_SIMPLICIAL_COMPLEX_H_
+#ifndef CONCEPT_WITNESS_COMPLEX_SIMPLICIAL_COMPLEX_FOR_WITNESS_H_
+#define CONCEPT_WITNESS_COMPLEX_SIMPLICIAL_COMPLEX_FOR_WITNESS_H_
 
 namespace Gudhi {
 
@@ -31,7 +31,7 @@ namespace witness_complex {
  * for a type to implement a simplicial complex, 
  * used for example to build a 'Witness_complex'. 
  */
-struct Simplicial_complex {
+struct SimplicialComplexForWitness {
   /** Handle to specify a simplex. */
   typedef unspecified Simplex_handle;
   /** Handle to specify a vertex. Must be a non-negative integer. */
@@ -40,16 +40,11 @@ struct Simplicial_complex {
   /** Returns a Simplex_hanlde that is different from all simplex handles 
    * of the simplices. */
   Simplex_handle null_simplex();
-  /** \brief Returns the number of simplices in the complex.
-   *
-   * Does not count the empty simplex. */
-  size_t num_simplices();
 
   /** \brief Iterator over the simplices of the complex,
    * in an arbitrary order.
    *
    * 'value_type' must be 'Simplex_handle'.*/
-  typedef unspecified Complex_simplex_iterator;
   typedef unspecified Complex_simplex_range;
 
   /**
@@ -71,19 +66,17 @@ struct Simplicial_complex {
    */
   typedef unspecified Insertion_result_type;
 
-  /** \brief Input range of vertices.
-   * 'value_type' must be 'Vertex_handle'. */
-  typedef unspecified Input_vertex_range;
-
   /** \brief Inserts a simplex with vertices from a given range
    *  'vertex_range' in the simplicial complex.
    *  */
+  template< typedef Input_vertex_range >
   Insertion_result_type insert_simplex(Input_vertex_range const & vertex_range);
 
   /** \brief Finds a simplex with vertices given by a range
    *
    * If a simplex exists, its Simplex_handle is returned.
    * Otherwise null_simplex() is returned. */
+  template< typedef Input_vertex_range >
   Simplex_handle find(Input_vertex_range const & vertex_range);
 };
 
@@ -91,4 +84,4 @@ struct Simplicial_complex {
 
 }  // namespace Gudhi
 
-#endif  // CONCEPT_WITNESS_COMPLEX_SIMPLICIAL_COMPLEX_H_
+#endif  // CONCEPT_WITNESS_COMPLEX_SIMPLICIAL_COMPLEX_FOR_WITNESS_H_
diff --git a/src/Witness_complex/include/gudhi/Witness_complex_doc.h b/src/Witness_complex/doc/Witness_complex_doc.h
index e9f78170..60dfd27b 100644
--- a/src/Witness_complex/include/gudhi/Witness_complex_doc.h
+++ b/src/Witness_complex/doc/Witness_complex_doc.h
@@ -6,6 +6,8 @@
 
    \author Siargey Kachanovich
 
+   \image html "Witness_complex_representation.png" "Witness complex representation"
+
    \section Definitions
 
    Witness complex \f$ Wit(W,L) \f$  is a simplicial complex defined on two sets of points in \f$\mathbb{R}^D\f$:
@@ -18,7 +20,9 @@
 
    \f$ \sigma \subset L \f$ is witnessed if there exists a point \f$w \in W\f$ such that 
    w is closer to the vertices of \f$ \sigma \f$ than other points in \f$ L \f$ and all of its faces are witnessed as well. 
-      
+ 
+   The data structure is described in \cite boissonnatmariasimplextreealgorithmica .
+
    \section Implementation
 
    The principal class of this module is Gudhi::Witness_complex.
diff --git a/src/Witness_complex/doc/Witness_complex_representation.png b/src/Witness_complex/doc/Witness_complex_representation.png
new file mode 100644
index 00000000..1d31a490
--- /dev/null
+++ b/src/Witness_complex/doc/Witness_complex_representation.png
diff --git a/src/Witness_complex/example/CMakeLists.txt b/src/Witness_complex/example/CMakeLists.txt
index d6a958b7..4d67e0d0 100644
--- a/src/Witness_complex/example/CMakeLists.txt
+++ b/src/Witness_complex/example/CMakeLists.txt
@@ -1,5 +1,5 @@
 cmake_minimum_required(VERSION 2.6)
-project(GUDHIWitnessComplex)
+project(Witness_complex_examples)
 
 # A simple example
    add_executable( witness_complex_from_file witness_complex_from_file.cpp )
@@ -7,51 +7,10 @@ project(GUDHIWitnessComplex)
 
 if(CGAL_FOUND)
   if (NOT CGAL_VERSION VERSION_LESS 4.6.0)
-    message(STATUS "CGAL version: ${CGAL_VERSION}.")
-
-    include( ${CGAL_USE_FILE} )
-    # In CMakeLists.txt, when include(${CGAL_USE_FILE}), CXX_FLAGS are overwritten.
-    # cf. http://doc.cgal.org/latest/Manual/installation.html#title40
-    # A workaround is to add "-std=c++11" again.
-    # A fix would be to use https://cmake.org/cmake/help/v3.1/prop_gbl/CMAKE_CXX_KNOWN_FEATURES.html 
-    # or even better https://cmake.org/cmake/help/v3.1/variable/CMAKE_CXX_STANDARD.html
-    # but it implies to use cmake version 3.1 at least.
-    if(NOT MSVC)
-      include(CheckCXXCompilerFlag)
-      CHECK_CXX_COMPILER_FLAG(-std=c++11 COMPILER_SUPPORTS_CXX11)
-      if(COMPILER_SUPPORTS_CXX11)
-        set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11")
-      endif()
-    endif()
-    # - End of workaround
-
-    find_package(Eigen3 3.1.0)
     if (EIGEN3_FOUND)
-      message(STATUS "Eigen3 version: ${EIGEN3_VERSION}.")
-      include( ${EIGEN3_USE_FILE} )
-      message(STATUS "Eigen3 use file: ${EIGEN3_USE_FILE}.")
-      include_directories (BEFORE "../../include")
-
       add_executable ( witness_complex_sphere witness_complex_sphere.cpp )
       target_link_libraries(witness_complex_sphere ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
       add_test( witness_complex_sphere_10 ${CMAKE_CURRENT_BINARY_DIR}/witness_complex_sphere 10)   
-      add_executable ( relaxed_witness_persistence relaxed_witness_persistence.cpp )
-      target_link_libraries(relaxed_witness_persistence ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
-      add_test( relaxed_witness_persistence_10 ${CMAKE_CURRENT_BINARY_DIR}/relaxed_witness_persistence 10)   
-      add_executable ( a0_persistence a0_persistence.cpp )
-      target_link_libraries(a0_persistence ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
-      add_test( a0_persistence_10 ${CMAKE_CURRENT_BINARY_DIR}/a0_persistence 10)
-      add_executable ( bench_rwit bench_rwit.cpp )
-      target_link_libraries(bench_rwit ${Boost_SYSTEM_LIBRARY} ${Boost_PROGRAM_OPTIONS_LIBRARY})
-                  
-      add_executable ( relaxed_delaunay relaxed_delaunay.cpp )
-      target_link_libraries(relaxed_delaunay ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
-      add_test( relaxed_delaunay_10 ${CMAKE_CURRENT_BINARY_DIR}/relaxed_delaunay 10)   
-      add_executable ( generate_torus generate_torus.cpp )
-    else()
-      message(WARNING "Eigen3 not found. Version 3.1.0 is required for witness_complex_sphere example.")      
-    endif()
-  else()
-    message(WARNING "CGAL version: ${CGAL_VERSION} is too old to compile witness_complex_sphere example. Version 4.6.0 is required.")
-  endif ()
+    endif(EIGEN3_FOUND)
+  endif (NOT CGAL_VERSION VERSION_LESS 4.6.0)
 endif()
diff --git a/src/Witness_complex/example/witness_complex_from_file.cpp b/src/Witness_complex/example/witness_complex_from_file.cpp
index 77109512..53207ad2 100644
--- a/src/Witness_complex/example/witness_complex_from_file.cpp
+++ b/src/Witness_complex/example/witness_complex_from_file.cpp
@@ -34,14 +34,9 @@
 #include <string>
 #include <vector>
 
-using namespace Gudhi;
-using namespace Gudhi::witness_complex;
-
 typedef std::vector< Vertex_handle > typeVectorVertex;
 typedef std::vector< std::vector <double> > Point_Vector;
 
-typedef Witness_complex< Simplex_tree<> > WitnessComplex;
-
 /**
  * \brief Customized version of read_points
  * which takes into account a possible nbP first line
@@ -68,17 +63,6 @@ read_points_cust(std::string file_name, std::vector< std::vector< double > > & p
   in_file.close();
 }
 
-/** Write a gnuplot readable file.
- *  Data range is a random access range of pairs (arg, value)
- */
-template < typename Data_range >
-void write_data(Data_range & data, std::string filename) {
-  std::ofstream ofs(filename, std::ofstream::out);
-  for (auto entry : data)
-    ofs << entry.first << ", " << entry.second << "\n";
-  ofs.close();
-}
-
 int main(int argc, char * const argv[]) {
   if (argc != 3) {
     std::cerr << "Usage: " << argv[0]
@@ -91,7 +75,7 @@ int main(int argc, char * const argv[]) {
   clock_t start, end;
 
   // Construct the Simplex Tree
-  Simplex_tree<> simplex_tree;
+  Gudhi::Simplex_tree<> simplex_tree;
 
   // Read the point file
   Point_Vector point_vector;
@@ -109,7 +93,7 @@ int main(int argc, char * const argv[]) {
 
   // Compute witness complex
   start = clock();
-  WitnessComplex(knn, simplex_tree, nbL, point_vector[0].size());
+  Gudhi::witness_complex::witness_complex(knn, nbL, point_vector[0].size(), simplex_tree);
   end = clock();
   std::cout << "Witness complex took "
       << static_cast<double>(end - start) / CLOCKS_PER_SEC << " s. \n";
diff --git a/src/Witness_complex/example/witness_complex_sphere.cpp b/src/Witness_complex/example/witness_complex_sphere.cpp
index 1ff35bff..b26c9f36 100644
--- a/src/Witness_complex/example/witness_complex_sphere.cpp
+++ b/src/Witness_complex/example/witness_complex_sphere.cpp
@@ -39,13 +39,6 @@
 
 #include "generators.h"
 
-using namespace Gudhi;
-using namespace Gudhi::witness_complex;
-
-typedef std::vector< Vertex_handle > typeVectorVertex;
-
-typedef Witness_complex< Simplex_tree<> > WitnessComplex;
-
 /** Write a gnuplot readable file.
  *  Data range is a random access range of pairs (arg, value)
  */
@@ -60,15 +53,15 @@ void write_data(Data_range & data, std::string filename) {
 int main(int argc, char * const argv[]) {
   if (argc != 2) {
     std::cerr << "Usage: " << argv[0]
-        << " nbL \n";
+        << " number_of_landmarks \n";
     return 0;
   }
 
-  int nbL = atoi(argv[1]);
+  int number_of_landmarks = atoi(argv[1]);
   clock_t start, end;
 
   // Construct the Simplex Tree
-  Simplex_tree<> simplex_tree;
+  Gudhi::Simplex_tree<> simplex_tree;
 
   std::vector< std::pair<int, double> > l_time;
 
@@ -82,14 +75,15 @@ int main(int argc, char * const argv[]) {
     // Choose landmarks
     start = clock();
     std::vector<std::vector< int > > knn;
-    Gudhi::witness_complex::landmark_choice_by_random_point(point_vector, nbL, knn);
+    Gudhi::witness_complex::landmark_choice_by_random_point(point_vector, number_of_landmarks, knn);
 
     // Compute witness complex
-    WitnessComplex(knn, simplex_tree, nbL, point_vector[0].size());
+    Gudhi::witness_complex::witness_complex(knn, number_of_landmarks, point_vector[0].size(), simplex_tree);
     end = clock();
     double time = static_cast<double>(end - start) / CLOCKS_PER_SEC;
-    std::cout << "Witness complex for " << nbL << " landmarks took "
+    std::cout << "Witness complex for " << number_of_landmarks << " landmarks took "
         << time << " s. \n";
+    std::cout << "Number of simplices is: " << simplex_tree.num_simplices() << "\n";
     l_time.push_back(std::make_pair(nbP, time));
   }
   write_data(l_time, "w_time.dat");
diff --git a/src/Witness_complex/include/gudhi/Landmark_choice_by_furthest_point.h b/src/Witness_complex/include/gudhi/Landmark_choice_by_furthest_point.h
index 47cd888d..df93155b 100644
--- a/src/Witness_complex/include/gudhi/Landmark_choice_by_furthest_point.h
+++ b/src/Witness_complex/include/gudhi/Landmark_choice_by_furthest_point.h
@@ -23,7 +23,10 @@
 #ifndef LANDMARK_CHOICE_BY_FURTHEST_POINT_H_
 #define LANDMARK_CHOICE_BY_FURTHEST_POINT_H_
 
+#include <boost/range/size.hpp>
+
 #include <limits>  // for numeric_limits<>
+#include <iterator>
 #include <algorithm>  // for sort
 #include <vector>
 
@@ -31,13 +34,19 @@ namespace Gudhi {
 
 namespace witness_complex {
 
- typedef std::vector<int> typeVectorVertex;
+  typedef std::vector<int> typeVectorVertex;
 
   /** 
+   *  \ingroup witness_complex
    *  \brief Landmark choice strategy by iteratively adding the furthest witness from the
    *  current landmark set as the new landmark. 
    *  \details It chooses nbL landmarks from a random access range `points` and
    *  writes {witness}*{closest landmarks} matrix in `knn`.
+   *
+   *  The type KNearestNeighbors can be seen as 
+   *  Witness_range<Closest_landmark_range<Vertex_handle>>, where
+   *  Witness_range and Closest_landmark_range are random access ranges 
+   *  
    */
 
   template <typename KNearestNeighbours,
@@ -45,7 +54,7 @@ namespace witness_complex {
   void landmark_choice_by_furthest_point(Point_random_access_range const &points,
                                          int nbL,
                                          KNearestNeighbours &knn) {
-    int nb_points = points.end() - points.begin();
+    int nb_points = boost::size(points);
     assert(nb_points >= nbL);
     // distance matrix witness x landmarks
     std::vector<std::vector<double>> wit_land_dist(nb_points, std::vector<double>());
@@ -59,6 +68,7 @@ namespace witness_complex {
     std::vector< double > dist_to_L(nb_points, infty);  // vector of current distances to L from points
 
     // TODO(SK) Consider using rand_r(...) instead of rand(...) for improved thread safety
+    // or better yet std::uniform_int_distribution
     int rand_int = rand() % nb_points;
     int curr_max_w = rand_int;  // For testing purposes a pseudo-random number is used here
 
@@ -67,7 +77,7 @@ namespace witness_complex {
       chosen_landmarks.push_back(curr_max_w);
       unsigned i = 0;
       for (auto& p : points) {
-        double curr_dist = euclidean_distance(p, *(points.begin() + chosen_landmarks[current_number_of_landmarks]));
+        double curr_dist = euclidean_distance(p, *(std::begin(points) + chosen_landmarks[current_number_of_landmarks]));
         wit_land_dist[i].push_back(curr_dist);
         knn[i].push_back(current_number_of_landmarks);
         if (curr_dist < dist_to_L[i])
@@ -81,9 +91,9 @@ namespace witness_complex {
           curr_max_w = i;
         }
     }
-    for (unsigned i = 0; i < points.size(); ++i)
-      std::sort(knn[i].begin(),
-                knn[i].end(),
+    for (int i = 0; i < nb_points; ++i)
+      std::sort(std::begin(knn[i]),
+                std::end(knn[i]),
                 [&wit_land_dist, i](int a, int b) {
                   return wit_land_dist[i][a] < wit_land_dist[i][b]; });
   }
diff --git a/src/Witness_complex/include/gudhi/Landmark_choice_by_random_point.h b/src/Witness_complex/include/gudhi/Landmark_choice_by_random_point.h
index dc364007..ebf6aad1 100644
--- a/src/Witness_complex/include/gudhi/Landmark_choice_by_random_point.h
+++ b/src/Witness_complex/include/gudhi/Landmark_choice_by_random_point.h
@@ -23,8 +23,11 @@
 #ifndef LANDMARK_CHOICE_BY_RANDOM_POINT_H_
 #define LANDMARK_CHOICE_BY_RANDOM_POINT_H_
 
+#include <boost/range/size.hpp>
+
 #include <queue>  // for priority_queue<>
 #include <utility>  // for pair<>
+#include <iterator>
 #include <vector>
 #include <set>
 
@@ -32,9 +35,17 @@ namespace Gudhi {
 
 namespace witness_complex {
 
-  /** \brief Landmark choice strategy by taking random vertices for landmarks.
+  /**
+   *  \ingroup witness_complex
+   * \brief Landmark choice strategy by taking random vertices for landmarks.
    *  \details It chooses nbL distinct landmarks from a random access range `points`
    *  and outputs a matrix {witness}*{closest landmarks} in knn.
+   *
+   *  The type KNearestNeighbors can be seen as 
+   *  Witness_range<Closest_landmark_range<Vertex_handle>>, where
+   *  Witness_range and Closest_landmark_range are random access ranges and
+   *  Vertex_handle is the label type of a vertex in a simplicial complex.
+   *  Closest_landmark_range needs to have push_back operation.
    */
 
   template <typename KNearestNeighbours,
@@ -42,7 +53,7 @@ namespace witness_complex {
   void landmark_choice_by_random_point(Point_random_access_range const &points,
                                        int nbL,
                                        KNearestNeighbours &knn) {
-    int nbP = points.end() - points.begin();
+    int nbP = boost::size(points);
     assert(nbP >= nbL);
     std::set<int> landmarks;
     int current_number_of_landmarks = 0;  // counter for landmarks
@@ -55,12 +66,12 @@ namespace witness_complex {
       landmarks.insert(chosen_landmark);
     }
 
-    int dim = points.begin()->size();
+    int dim = boost::size(*std::begin(points));
     typedef std::pair<double, int> dist_i;
     typedef bool (*comp)(dist_i, dist_i);
     knn = KNearestNeighbours(nbP);
     for (int points_i = 0; points_i < nbP; points_i++) {
-      std::priority_queue<dist_i, std::vector<dist_i>, comp> l_heap([&](dist_i j1, dist_i j2) {
+      std::priority_queue<dist_i, std::vector<dist_i>, comp> l_heap([](dist_i j1, dist_i j2) {
           return j1.first > j2.first;
         });
       std::set<int>::iterator landmarks_it;
diff --git a/src/Witness_complex/include/gudhi/Witness_complex.h b/src/Witness_complex/include/gudhi/Witness_complex.h
index 34cbc882..489cdf11 100644
--- a/src/Witness_complex/include/gudhi/Witness_complex.h
+++ b/src/Witness_complex/include/gudhi/Witness_complex.h
@@ -28,8 +28,7 @@
 #include <boost/graph/adjacency_list.hpp>
 #include <boost/graph/connected_components.hpp>
 
-#include <boost/container/flat_map.hpp>
-#include <boost/iterator/transform_iterator.hpp>
+#include <boost/range/size.hpp>
 
 #include <gudhi/distance_functions.h>
 
@@ -47,12 +46,13 @@ namespace Gudhi {
 
 namespace witness_complex {
 
-/** 
-    \class Witness_complex
-    \brief Constructs the witness complex for the given set of witnesses and landmarks.
-    \ingroup witness_complex
- */
-template< class Simplicial_complex>
+// /*
+//  *  \private
+//     \class Witness_complex
+//     \brief Constructs the witness complex for the given set of witnesses and landmarks.
+//     \ingroup witness_complex
+//  */
+template< class SimplicialComplex>
 class Witness_complex {
  private:
   struct Active_witness {
@@ -65,13 +65,12 @@ class Witness_complex {
   };
 
  private:
-  typedef typename Simplicial_complex::Simplex_handle Simplex_handle;
-  typedef typename Simplicial_complex::Vertex_handle Vertex_handle;
+  typedef typename SimplicialComplex::Simplex_handle Simplex_handle;
+  typedef typename SimplicialComplex::Vertex_handle Vertex_handle;
 
   typedef std::vector< double > Point_t;
   typedef std::vector< Point_t > Point_Vector;
 
-  // typedef typename Simplicial_complex::Filtration_value Filtration_value;
   typedef std::vector< Vertex_handle > typeVectorVertex;
   typedef std::pair< typeVectorVertex, Filtration_value> typeSimplex;
   typedef std::pair< Simplex_handle, bool > typePairSimplexBool;
@@ -81,19 +80,19 @@ class Witness_complex {
   typedef std::list< Vertex_handle > ActiveWitnessList;
 
  private:
-  int nbL;  // Number of landmarks
-  Simplicial_complex& sc;  // Simplicial complex
+  int nbL_;  // Number of landmarks
+  SimplicialComplex& sc_;  // Simplicial complex
 
  public:
   /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-  /** @name Constructor
+  /* @name Constructor
    */
 
   //@{
 
   // Witness_range<Closest_landmark_range<Vertex_handle>>
 
-  /**
+  /*
    *  \brief Iterative construction of the witness complex.
    *  \details The witness complex is written in sc_ basing on a matrix knn of
    *  nearest neighbours of the form {witnesses}x{landmarks}.
@@ -109,31 +108,29 @@ class Witness_complex {
    */
   template< typename KNearestNeighbors >
   Witness_complex(KNearestNeighbors const & knn,
-                  Simplicial_complex & sc_,
-                  int nbL_,
-                  int dim) : nbL(nbL_), sc(sc_) {
+                  int nbL,
+                  int dim,
+                  SimplicialComplex & sc) : nbL_(nbL), sc_(sc) {
     // Construction of the active witness list
-    int nbW = knn.size();
+    int nbW = boost::size(knn);
     typeVectorVertex vv;
     int counter = 0;
     /* The list of still useful witnesses
      * it will diminuish in the course of iterations
      */
     ActiveWitnessList active_w;  // = new ActiveWitnessList();
-    for (int i = 0; i != nbL; ++i) {
+    for (Vertex_handle i = 0; i != nbL_; ++i) {
       // initial fill of 0-dimensional simplices
       // by doing it we don't assume that landmarks are necessarily witnesses themselves anymore
       counter++;
       vv = {i};
-      sc.insert_simplex(vv);
+      sc_.insert_simplex(vv);
       // TODO(SK) Error if not inserted : normally no need here though
     }
     int k = 1; /* current dimension in iterative construction */
     for (int i = 0; i != nbW; ++i)
       active_w.push_back(i);
-    // std::cout << "Successfully added edges" << std::endl;
     while (!active_w.empty() && k < dim) {
-      // std::cout << "Started the step k=" << k << std::endl;
       typename ActiveWitnessList::iterator it = active_w.begin();
       while (it != active_w.end()) {
         typeVectorVertex simplex_vector;
@@ -142,9 +139,9 @@ class Witness_complex {
         if (ok) {
           for (int i = 0; i != k + 1; ++i)
             simplex_vector.push_back(knn[*it][i]);
-          sc.insert_simplex(simplex_vector, 0.0);
+          sc_.insert_simplex(simplex_vector);
           // TODO(SK) Error if not inserted : normally no need here though
-          it++;
+          ++it;
         } else {
           active_w.erase(it++);  // First increase the iterator and then erase the previous element
         }
@@ -156,15 +153,13 @@ class Witness_complex {
   //@}
 
  private:
-  /** \brief Check if the facets of the k-dimensional simplex witnessed 
+  /* \brief Check if the facets of the k-dimensional simplex witnessed 
    *  by witness witness_id are already in the complex.
    *  inserted_vertex is the handle of the (k+1)-th vertex witnessed by witness_id
    */
   template <typename KNearestNeighbors>
   bool all_faces_in(KNearestNeighbors const &knn, int witness_id, int k) {
-    // std::cout << "All face in with the landmark " << inserted_vertex << std::endl;
     std::vector< Vertex_handle > facet;
-    // Vertex_handle curr_vh = curr_sh->first;
     // CHECK ALL THE FACETS
     for (int i = 0; i != k + 1; ++i) {
       facet = {};
@@ -173,9 +168,8 @@ class Witness_complex {
           facet.push_back(knn[witness_id][j]);
         }
       }  // endfor
-      if (sc.find(facet) == sc.null_simplex())
+      if (sc_.find(facet) == sc_.null_simplex())
         return false;
-      // std::cout << "++++ finished loop safely\n";
     }  // endfor
     return true;
   }
@@ -194,27 +188,25 @@ class Witness_complex {
   }
 
  public:
-  /**
-   *  \brief Verification if every simplex in the complex is witnessed by witnesses in knn.
-   *  \param print_output =true will print the witnesses for each simplex
-   *  \remark Added for debugging purposes.
-   */
+  // /*
+  //  *  \brief Verification if every simplex in the complex is witnessed by witnesses in knn.
+  //  *  \param print_output =true will print the witnesses for each simplex
+  //  *  \remark Added for debugging purposes.
+  //  */
   template< class KNearestNeighbors >
   bool is_witness_complex(KNearestNeighbors const & knn, bool print_output) {
-    // bool final_result = true;
-    for (Simplex_handle sh : sc.complex_simplex_range()) {
+    for (Simplex_handle sh : sc_.complex_simplex_range()) {
       bool is_witnessed = false;
       typeVectorVertex simplex;
       int nbV = 0;  // number of verticed in the simplex
-      for (int v : sc.simplex_vertex_range(sh))
+      for (Vertex_handle v : sc_.simplex_vertex_range(sh))
         simplex.push_back(v);
       nbV = simplex.size();
       for (typeVectorVertex w : knn) {
         bool has_vertices = true;
-        for (int v : simplex)
+        for (Vertex_handle v : simplex)
           if (std::find(w.begin(), w.begin() + nbV, v) == w.begin() + nbV) {
             has_vertices = false;
-            // break;
           }
         if (has_vertices) {
           is_witnessed = true;
@@ -242,6 +234,30 @@ class Witness_complex {
   }
 };
 
+  /**
+   *  \ingroup witness_complex
+   *  \brief Iterative construction of the witness complex.
+   *  \details The witness complex is written in simplicial complex sc_
+   *   basing on a matrix knn of
+   *  nearest neighbours of the form {witnesses}x{landmarks}.
+   *
+   *  The type KNearestNeighbors can be seen as
+   *  Witness_range<Closest_landmark_range<Vertex_handle>>, where
+   *  Witness_range and Closest_landmark_range are random access ranges.
+   *
+   *  Procedure takes into account at most (dim+1)
+   *  first landmarks from each landmark range to construct simplices.
+   *
+   *  Landmarks are supposed to be in [0,nbL_-1]
+   */
+  template <class KNearestNeighbors, class SimplicialComplexForWitness>
+  void witness_complex(KNearestNeighbors const & knn,
+                       int nbL,
+                       int dim,
+                       SimplicialComplexForWitness & sc) {
+    Witness_complex<SimplicialComplexForWitness>(knn, nbL, dim, sc);
+  }
+
 }  // namespace witness_complex
 
 }  // namespace Gudhi
diff --git a/src/Witness_complex/test/CMakeLists.txt b/src/Witness_complex/test/CMakeLists.txt
index 9422c152..bb55b0f1 100644
--- a/src/Witness_complex/test/CMakeLists.txt
+++ b/src/Witness_complex/test/CMakeLists.txt
@@ -1,17 +1,13 @@
 cmake_minimum_required(VERSION 2.6)
-project(GUDHIWitnessComplexUT)
+project(Witness_complex_tests)
 
 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()
 
 add_executable ( simple_witness_complexUT simple_witness_complex.cpp )
diff --git a/src/Witness_complex/test/simple_witness_complex.cpp b/src/Witness_complex/test/simple_witness_complex.cpp
index 7d44b90c..03df78ee 100644
--- a/src/Witness_complex/test/simple_witness_complex.cpp
+++ b/src/Witness_complex/test/simple_witness_complex.cpp
@@ -53,7 +53,7 @@ BOOST_AUTO_TEST_CASE(simple_witness_complex) {
   knn.push_back({5, 0, 1, 3, 6, 2, 4});
   knn.push_back({5, 6, 1, 0, 2, 3, 4});
   knn.push_back({1, 6, 0, 5, 2, 3, 4});
-  WitnessComplex witnessComplex(knn, complex, 7, 7);
+  WitnessComplex witnessComplex(knn, 7, 7, complex);
 
   BOOST_CHECK(witnessComplex.is_witness_complex(knn, false));
 }
diff --git a/src/Witness_complex/test/witness_complex_points.cpp b/src/Witness_complex/test/witness_complex_points.cpp
index cb1639e1..bd3df604 100644
--- a/src/Witness_complex/test/witness_complex_points.cpp
+++ b/src/Witness_complex/test/witness_complex_points.cpp
@@ -52,13 +52,13 @@ BOOST_AUTO_TEST_CASE(witness_complex_points) {
   Simplex_tree complex1;
   Gudhi::witness_complex::landmark_choice_by_random_point(points, 100, knn);
   assert(!knn.empty());
-  WitnessComplex witnessComplex1(knn, complex1, 100, 3);
+  WitnessComplex witnessComplex1(knn, 100, 3, complex1);
   BOOST_CHECK(witnessComplex1.is_witness_complex(knn, b_print_output));
 
   // Second test: furthest choice
   knn.clear();
   Simplex_tree complex2;
   Gudhi::witness_complex::landmark_choice_by_furthest_point(points, 100, knn);
-  WitnessComplex witnessComplex2(knn, complex2, 100, 3);
+  WitnessComplex witnessComplex2(knn, 100, 3, complex2);
   BOOST_CHECK(witnessComplex2.is_witness_complex(knn, b_print_output));
 }