Merge last trunk modifications

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/ST_cythonize@2194 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: a8fa0a9eeb6b7064cb1d3d3780d5ab58818f49ec

8 files changed, 699 insertions, 140 deletions

diff --git a/src/Persistent_cohomology/doc/COPYRIGHT b/src/Persistent_cohomology/doc/COPYRIGHT
new file mode 100644
index 00000000..34345bef
--- /dev/null
+++ b/src/Persistent_cohomology/doc/COPYRIGHT
@@ -0,0 +1,19 @@
+The files of this directory are part of the Gudhi Library. The Gudhi library
+(Geometric Understanding in Higher Dimensions) is a generic C++ library for
+computational topology.
+
+Author(s):       Clément Maria
+
+Copyright (C) 2015  INRIA
+
+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/>.
diff --git a/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h b/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h
index 40dd3f93..e17e5926 100644
--- a/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h
+++ b/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h
@@ -172,6 +172,28 @@ Persistent_cohomology/alpha_complex_3d_persistence.cpp</a> computes the persiste
 2  1 0.0934117 1.00003 
 2  2 0.56444 1.03938 \endcode
 
+\li <a href="_persistent_cohomology_2exact_alpha_complex_3d_persistence_8cpp-example.html">
+Persistent_cohomology/exact_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with
+\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file.
+Here, as CGAL computes the exact values, it is slower, but it is necessary when points are on a grid
+for instance.
+\code $> ./exact_alpha_complex_3d_persistence ../../data/points/sphere3D_pts_on_grid.off 2 0.1 \endcode
+\code Simplex_tree dim: 3
+2  0 0 inf
+2  2 0.0002 0.2028 \endcode
+
+\li <a href="_persistent_cohomology_2weighted_alpha_complex_3d_persistence_8cpp-example.html">
+Persistent_cohomology/weighted_alpha_complex_3d_persistence.cpp</a> computes the persistent homology with
+\f$\mathbb{Z}/2\mathbb{Z}\f$ coefficients of the weighted alpha complex on points sampling from an OFF file
+and a weights file.
+\code $> ./weighted_alpha_complex_3d_persistence ../../data/points/tore3D_300.off
+../../data/points/tore3D_300.weights 2 0.45 \endcode
+\code Simplex_tree dim: 3
+2  -0 0 inf
+2  1 0.0682162 1.0001
+2  1 0.0934117 1.00003
+2  2 0.56444 1.03938 \endcode
+
 \li <a href="_persistent_cohomology_2alpha_complex_persistence_8cpp-example.html">
 Persistent_cohomology/alpha_complex_persistence.cpp</a> computes the persistent homology with
 \f$\mathbb{Z}/p\mathbb{Z}\f$ coefficients of the alpha complex on points sampling from an OFF file.
diff --git a/src/Persistent_cohomology/example/CMakeLists.txt b/src/Persistent_cohomology/example/CMakeLists.txt
index d2a84b1e..20700d86 100644
--- a/src/Persistent_cohomology/example/CMakeLists.txt
+++ b/src/Persistent_cohomology/example/CMakeLists.txt
@@ -34,38 +34,58 @@ endif()
 
 add_test(plain_homology ${CMAKE_CURRENT_BINARY_DIR}/plain_homology)
 add_test(persistence_from_simple_simplex_tree ${CMAKE_CURRENT_BINARY_DIR}/persistence_from_simple_simplex_tree 1 0)
-add_test(rips_distance_matrix ${CMAKE_CURRENT_BINARY_DIR}/rips_distance_matrix_persistence ${CMAKE_SOURCE_DIR}/data/distance_matrix/full_square_distance_matrix.csv -r 1.0 -d 3 -p 3 -m 0)
-add_test(rips_persistence_3 ${CMAKE_CURRENT_BINARY_DIR}/rips_persistence ${CMAKE_SOURCE_DIR}/data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3)
-add_test(rips_persistence_step_by_step_3 ${CMAKE_CURRENT_BINARY_DIR}/rips_persistence_step_by_step ${CMAKE_SOURCE_DIR}/data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3)
-add_test(rips_persistence_via_boundary_matrix_3 ${CMAKE_CURRENT_BINARY_DIR}/rips_persistence_via_boundary_matrix ${CMAKE_SOURCE_DIR}/data/points/Kl.off -r 0.16 -d 3 -p 3 -m 100)
-add_test(persistence_from_file_3_2_0 ${CMAKE_CURRENT_BINARY_DIR}/persistence_from_file ${CMAKE_SOURCE_DIR}/data/filtered_simplicial_complex/bunny_5000_complex.fsc -p 2 -m 0)
-add_test(persistence_from_file_3_3_100 ${CMAKE_CURRENT_BINARY_DIR}/persistence_from_file ${CMAKE_SOURCE_DIR}/data/filtered_simplicial_complex/bunny_5000_complex.fsc -p 3 -m 100)
+add_test(rips_distance_matrix ${CMAKE_CURRENT_BINARY_DIR}/rips_distance_matrix_persistence
+    ${CMAKE_SOURCE_DIR}/data/distance_matrix/full_square_distance_matrix.csv -r 1.0 -d 3 -p 3 -m 0)
+add_test(rips_persistence_3 ${CMAKE_CURRENT_BINARY_DIR}/rips_persistence
+    ${CMAKE_SOURCE_DIR}/data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3)
+add_test(rips_persistence_step_by_step_3 ${CMAKE_CURRENT_BINARY_DIR}/rips_persistence_step_by_step
+    ${CMAKE_SOURCE_DIR}/data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 3)
+add_test(rips_persistence_via_boundary_matrix_3 ${CMAKE_CURRENT_BINARY_DIR}/rips_persistence_via_boundary_matrix
+    ${CMAKE_SOURCE_DIR}/data/points/Kl.off -r 0.16 -d 3 -p 3 -m 100)
+add_test(persistence_from_file_3_2_0 ${CMAKE_CURRENT_BINARY_DIR}/persistence_from_file
+    ${CMAKE_SOURCE_DIR}/data/filtered_simplicial_complex/bunny_5000_complex.fsc -p 2 -m 0)
+add_test(persistence_from_file_3_3_100 ${CMAKE_CURRENT_BINARY_DIR}/persistence_from_file
+    ${CMAKE_SOURCE_DIR}/data/filtered_simplicial_complex/bunny_5000_complex.fsc -p 3 -m 100)
    
 if(GMP_FOUND)
    if(GMPXX_FOUND)
       add_executable(rips_multifield_persistence rips_multifield_persistence.cpp )
-      target_link_libraries(rips_multifield_persistence ${Boost_SYSTEM_LIBRARY} ${Boost_PROGRAM_OPTIONS_LIBRARY} ${GMPXX_LIBRARIES} ${GMP_LIBRARIES})
+      target_link_libraries(rips_multifield_persistence
+          ${Boost_SYSTEM_LIBRARY} ${Boost_PROGRAM_OPTIONS_LIBRARY} ${GMPXX_LIBRARIES} ${GMP_LIBRARIES})
       if (TBB_FOUND)
         target_link_libraries(rips_multifield_persistence ${TBB_LIBRARIES})
       endif(TBB_FOUND)
-   add_test(rips_multifield_persistence_2_71 ${CMAKE_CURRENT_BINARY_DIR}/rips_multifield_persistence ${CMAKE_SOURCE_DIR}/data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 2 -q 71)
+   add_test(rips_multifield_persistence_2_71 ${CMAKE_CURRENT_BINARY_DIR}/rips_multifield_persistence
+       ${CMAKE_SOURCE_DIR}/data/points/tore3D_1307.off -r 0.25 -m 0.5 -d 3 -p 2 -q 71)
    endif(GMPXX_FOUND)
 endif(GMP_FOUND)
 
 if(CGAL_FOUND)
   add_executable(alpha_complex_3d_persistence alpha_complex_3d_persistence.cpp)
   target_link_libraries(alpha_complex_3d_persistence ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
+  add_executable(exact_alpha_complex_3d_persistence exact_alpha_complex_3d_persistence.cpp)
+  target_link_libraries(exact_alpha_complex_3d_persistence ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
+  add_executable(weighted_alpha_complex_3d_persistence weighted_alpha_complex_3d_persistence.cpp)
+  target_link_libraries(weighted_alpha_complex_3d_persistence ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
 
   if (TBB_FOUND)
     target_link_libraries(alpha_complex_3d_persistence ${TBB_LIBRARIES})
+    target_link_libraries(exact_alpha_complex_3d_persistence ${TBB_LIBRARIES})
+    target_link_libraries(weighted_alpha_complex_3d_persistence ${TBB_LIBRARIES})
   endif(TBB_FOUND)
-  add_test(alpha_complex_3d_persistence_2_0_5 ${CMAKE_CURRENT_BINARY_DIR}/alpha_complex_3d_persistence ${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off 2 0.45)
+  add_test(alpha_complex_3d_persistence_2_0_5 ${CMAKE_CURRENT_BINARY_DIR}/alpha_complex_3d_persistence
+      ${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off 2 0.45)
+  add_test(exact_alpha_complex_3d_persistence_2_0_5 ${CMAKE_CURRENT_BINARY_DIR}/exact_alpha_complex_3d_persistence
+      ${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off 2 0.45)
+  add_test(weighted_alpha_complex_3d_persistence_2_0_5 ${CMAKE_CURRENT_BINARY_DIR}/weighted_alpha_complex_3d_persistence
+      ${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off ${CMAKE_SOURCE_DIR}/data/points/tore3D_300.weights 2 0.45)
 
 
   if (NOT CGAL_VERSION VERSION_LESS 4.7.0)
     if (EIGEN3_FOUND)
       add_executable (alpha_complex_persistence alpha_complex_persistence.cpp)
-      target_link_libraries(alpha_complex_persistence  ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY} ${Boost_PROGRAM_OPTIONS_LIBRARY})
+      target_link_libraries(alpha_complex_persistence
+          ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY} ${Boost_PROGRAM_OPTIONS_LIBRARY})
 
       add_executable(periodic_alpha_complex_3d_persistence periodic_alpha_complex_3d_persistence.cpp)
       target_link_libraries(periodic_alpha_complex_3d_persistence ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
@@ -78,8 +98,10 @@ if(CGAL_FOUND)
         target_link_libraries(periodic_alpha_complex_3d_persistence ${TBB_LIBRARIES})
         target_link_libraries(custom_persistence_sort ${TBB_LIBRARIES})
       endif(TBB_FOUND)
-      add_test(alpha_complex_persistence_2_0_45 ${CMAKE_CURRENT_BINARY_DIR}/alpha_complex_persistence ${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off -m 0.45 -p 2)
-      add_test(periodic_alpha_complex_3d_persistence_2_0 ${CMAKE_CURRENT_BINARY_DIR}/periodic_alpha_complex_3d_persistence ${CMAKE_SOURCE_DIR}/data/points/grid_10_10_10_in_0_1.off ${CMAKE_SOURCE_DIR}/data/points/iso_cuboid_3_in_0_1.txt 2 0)
+      add_test(alpha_complex_persistence_2_0_45 ${CMAKE_CURRENT_BINARY_DIR}/alpha_complex_persistence
+          ${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off -m 0.45 -p 2)
+      add_test(periodic_alpha_complex_3d_persistence_2_0 ${CMAKE_CURRENT_BINARY_DIR}/periodic_alpha_complex_3d_persistence
+          ${CMAKE_SOURCE_DIR}/data/points/grid_10_10_10_in_0_1.off ${CMAKE_SOURCE_DIR}/data/points/iso_cuboid_3_in_0_1.txt 2 0)
       add_test(custom_persistence_sort ${CMAKE_CURRENT_BINARY_DIR}/custom_persistence_sort)
     endif(EIGEN3_FOUND)
   endif (NOT CGAL_VERSION VERSION_LESS 4.7.0)
diff --git a/src/Persistent_cohomology/example/alpha_complex_3d_helper.h b/src/Persistent_cohomology/example/alpha_complex_3d_helper.h
new file mode 100644
index 00000000..ceefd2ba
--- /dev/null
+++ b/src/Persistent_cohomology/example/alpha_complex_3d_helper.h
@@ -0,0 +1,76 @@
+/*    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):       Vincent Rouvreau
+ *
+ *    Copyright (C) 2014  INRIA 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 EXAMPLE_PERSISTENT_COHOMOLOGY_ALPHA_COMPLEX_3D_HELPER_H_
+#define EXAMPLE_PERSISTENT_COHOMOLOGY_ALPHA_COMPLEX_3D_HELPER_H_
+
+template<class Vertex_list, class Cell_handle>
+Vertex_list from_cell(const Cell_handle& ch) {
+  Vertex_list the_list;
+  for (auto i = 0; i < 4; i++) {
+#ifdef DEBUG_TRACES
+    std::cout << "from cell[" << i << "]=" << ch->vertex(i)->point() << std::endl;
+#endif  // DEBUG_TRACES
+    the_list.push_back(ch->vertex(i));
+  }
+  return the_list;
+}
+
+template<class Vertex_list, class Facet>
+Vertex_list from_facet(const Facet& fct) {
+  Vertex_list the_list;
+  for (auto i = 0; i < 4; i++) {
+    if (fct.second != i) {
+#ifdef DEBUG_TRACES
+      std::cout << "from facet=[" << i << "]" << fct.first->vertex(i)->point() << std::endl;
+#endif  // DEBUG_TRACES
+      the_list.push_back(fct.first->vertex(i));
+    }
+  }
+  return the_list;
+}
+
+template<class Vertex_list, class Edge_3>
+Vertex_list from_edge(const Edge_3& edg) {
+  Vertex_list the_list;
+  for (auto i = 0; i < 4; i++) {
+    if ((edg.second == i) || (edg.third == i)) {
+#ifdef DEBUG_TRACES
+      std::cout << "from edge[" << i << "]=" << edg.first->vertex(i)->point() << std::endl;
+#endif  // DEBUG_TRACES
+      the_list.push_back(edg.first->vertex(i));
+    }
+  }
+  return the_list;
+}
+
+template<class Vertex_list, class Vertex_handle>
+Vertex_list from_vertex(const Vertex_handle& vh) {
+  Vertex_list the_list;
+#ifdef DEBUG_TRACES
+  std::cout << "from vertex=" << vh->point() << std::endl;
+#endif  // DEBUG_TRACES
+  the_list.push_back(vh);
+  return the_list;
+}
+
+#endif  // EXAMPLE_PERSISTENT_COHOMOLOGY_ALPHA_COMPLEX_3D_HELPER_H_
diff --git a/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp b/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp
index 978dc942..ffb98283 100644
--- a/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp
+++ b/src/Persistent_cohomology/example/alpha_complex_3d_persistence.cpp
@@ -30,6 +30,8 @@
 #include <CGAL/Alpha_shape_3.h>
 #include <CGAL/iterator.h>
 
+#include "alpha_complex_3d_helper.h"
+
 #include <fstream>
 #include <cmath>
 #include <string>
@@ -40,84 +42,39 @@
 #include <vector>
 
 // 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::Triangulation_data_structure_3<Vb, Fb> Tds;
-typedef CGAL::Delaunay_triangulation_3<Kernel, Tds> Triangulation_3;
-typedef CGAL::Alpha_shape_3<Triangulation_3> Alpha_shape_3;
+using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
+using Vb = CGAL::Alpha_shape_vertex_base_3<Kernel>;
+using Fb = CGAL::Alpha_shape_cell_base_3<Kernel>;
+using Tds = CGAL::Triangulation_data_structure_3<Vb, Fb>;
+using Triangulation_3 = CGAL::Delaunay_triangulation_3<Kernel, Tds>;
+using Alpha_shape_3 = CGAL::Alpha_shape_3<Triangulation_3>;
 
 // From file type definition
-typedef Kernel::Point_3 Point_3;
+using Point_3 = Kernel::Point_3;
 
 // filtration with alpha values needed type definition
-typedef Alpha_shape_3::FT Alpha_value_type;
-typedef CGAL::Object Object;
-typedef CGAL::Dispatch_output_iterator<
-CGAL::cpp11::tuple<Object, Alpha_value_type>,
-CGAL::cpp11::tuple<std::back_insert_iterator< std::vector<Object> >,
-    std::back_insert_iterator< std::vector<Alpha_value_type> > > > Dispatch;
-typedef Alpha_shape_3::Cell_handle Cell_handle;
-typedef Alpha_shape_3::Facet Facet;
-typedef Alpha_shape_3::Edge Edge_3;
-typedef std::list<Alpha_shape_3::Vertex_handle> Vertex_list;
+using Alpha_value_type = Alpha_shape_3::FT;
+using Object = CGAL::Object;
+using Dispatch = CGAL::Dispatch_output_iterator<
+          CGAL::cpp11::tuple<Object, Alpha_value_type>,
+          CGAL::cpp11::tuple<std::back_insert_iterator< std::vector<Object> >,
+          std::back_insert_iterator< std::vector<Alpha_value_type> > > >;
+using Cell_handle = Alpha_shape_3::Cell_handle;
+using Facet = Alpha_shape_3::Facet;
+using Edge_3 = Alpha_shape_3::Edge;
+using Vertex_handle = Alpha_shape_3::Vertex_handle;
+using Vertex_list = std::list<Alpha_shape_3::Vertex_handle>;
 
 // gudhi type definition
-typedef Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence> ST;
-typedef ST::Filtration_value Filtration_value;
-typedef ST::Vertex_handle Simplex_tree_vertex;
-typedef std::map<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex > Alpha_shape_simplex_tree_map;
-typedef std::pair<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex> Alpha_shape_simplex_tree_pair;
-typedef std::vector< Simplex_tree_vertex > Simplex_tree_vector_vertex;
-typedef Gudhi::persistent_cohomology::Persistent_cohomology< ST, Gudhi::persistent_cohomology::Field_Zp > PCOH;
-
-Vertex_list from(const Cell_handle& ch) {
-  Vertex_list the_list;
-  for (auto i = 0; i < 4; i++) {
-#ifdef DEBUG_TRACES
-    std::cout << "from cell[" << i << "]=" << ch->vertex(i)->point() << std::endl;
-#endif  // DEBUG_TRACES
-    the_list.push_back(ch->vertex(i));
-  }
-  return the_list;
-}
-
-Vertex_list from(const Facet& fct) {
-  Vertex_list the_list;
-  for (auto i = 0; i < 4; i++) {
-    if (fct.second != i) {
-#ifdef DEBUG_TRACES
-      std::cout << "from facet=[" << i << "]" << fct.first->vertex(i)->point() << std::endl;
-#endif  // DEBUG_TRACES
-      the_list.push_back(fct.first->vertex(i));
-    }
-  }
-  return the_list;
-}
-
-Vertex_list from(const Edge_3& edg) {
-  Vertex_list the_list;
-  for (auto i = 0; i < 4; i++) {
-    if ((edg.second == i) || (edg.third == i)) {
-#ifdef DEBUG_TRACES
-      std::cout << "from edge[" << i << "]=" << edg.first->vertex(i)->point() << std::endl;
-#endif  // DEBUG_TRACES
-      the_list.push_back(edg.first->vertex(i));
-    }
-  }
-  return the_list;
-}
-
-Vertex_list from(const Alpha_shape_3::Vertex_handle& vh) {
-  Vertex_list the_list;
-#ifdef DEBUG_TRACES
-  std::cout << "from vertex=" << vh->point() << std::endl;
-#endif  // DEBUG_TRACES
-  the_list.push_back(vh);
-  return the_list;
-}
-
-void usage(char * const progName) {
+using ST = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
+using Filtration_value = ST::Filtration_value;
+using Simplex_tree_vertex = ST::Vertex_handle;
+using Alpha_shape_simplex_tree_map = std::map<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex >;
+using Alpha_shape_simplex_tree_pair = std::pair<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex>;
+using Simplex_tree_vector_vertex = std::vector< Simplex_tree_vertex >;
+using PCOH = Gudhi::persistent_cohomology::Persistent_cohomology< ST, Gudhi::persistent_cohomology::Field_Zp >;
+
+void usage(const std::string& progName) {
   std::cerr << "Usage: " << progName <<
       " path_to_file_graph coeff_field_characteristic[integer > 0] min_persistence[float >= -1.0]\n";
   exit(-1);
@@ -185,30 +142,29 @@ int main(int argc, char * const argv[]) {
   for (auto object_iterator : the_objects) {
     // Retrieve Alpha shape vertex list from object
     if (const Cell_handle * cell = CGAL::object_cast<Cell_handle>(&object_iterator)) {
-      vertex_list = from(*cell);
+      vertex_list = from_cell<Vertex_list, Cell_handle>(*cell);
       count_cells++;
       if (dim_max < 3) {
         // Cell is of dim 3
         dim_max = 3;
       }
     } else if (const Facet * facet = CGAL::object_cast<Facet>(&object_iterator)) {
-      vertex_list = from(*facet);
+      vertex_list = from_facet<Vertex_list, Facet>(*facet);
       count_facets++;
       if (dim_max < 2) {
         // Facet is of dim 2
         dim_max = 2;
       }
     } else if (const Edge_3 * edge = CGAL::object_cast<Edge_3>(&object_iterator)) {
-      vertex_list = from(*edge);
+      vertex_list = from_edge<Vertex_list, Edge_3>(*edge);
       count_edges++;
       if (dim_max < 1) {
         // Edge_3 is of dim 1
         dim_max = 1;
       }
-    } else if (const Alpha_shape_3::Vertex_handle * vertex =
-               CGAL::object_cast<Alpha_shape_3::Vertex_handle>(&object_iterator)) {
+    } else if (const Vertex_handle * vertex = CGAL::object_cast<Vertex_handle>(&object_iterator)) {
       count_vertices++;
-      vertex_list = from(*vertex);
+      vertex_list = from_vertex<Vertex_list, Vertex_handle>(*vertex);
     }
     // Construction of the vector of simplex_tree vertex from list of alpha_shapes vertex
     Simplex_tree_vector_vertex the_simplex_tree;
diff --git a/src/Persistent_cohomology/example/exact_alpha_complex_3d_persistence.cpp b/src/Persistent_cohomology/example/exact_alpha_complex_3d_persistence.cpp
new file mode 100644
index 00000000..c016a596
--- /dev/null
+++ b/src/Persistent_cohomology/example/exact_alpha_complex_3d_persistence.cpp
@@ -0,0 +1,244 @@
+/*    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):       Vincent Rouvreau
+ *
+ *    Copyright (C) 2014  INRIA 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/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/Alpha_shape_3.h>
+#include <CGAL/iterator.h>
+
+#include "alpha_complex_3d_helper.h"
+
+#include <fstream>
+#include <cmath>
+#include <string>
+#include <tuple>
+#include <map>
+#include <utility>
+#include <list>
+#include <vector>
+
+// Alpha_shape_3 templates type definitions
+using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
+using Exact_tag = CGAL::Tag_true;
+using Vb = CGAL::Alpha_shape_vertex_base_3<Kernel, CGAL::Default, Exact_tag>;
+using Fb = CGAL::Alpha_shape_cell_base_3<Kernel, CGAL::Default, Exact_tag>;
+using Tds = CGAL::Triangulation_data_structure_3<Vb, Fb>;
+using Triangulation_3 = CGAL::Delaunay_triangulation_3<Kernel, Tds>;
+using Alpha_shape_3 = CGAL::Alpha_shape_3<Triangulation_3, Exact_tag>;
+
+// From file type definition
+using Point_3 = Kernel::Point_3;
+
+// filtration with alpha values needed type definition
+using Alpha_value_type = Alpha_shape_3::FT;
+using Object = CGAL::Object;
+using Dispatch = CGAL::Dispatch_output_iterator<
+          CGAL::cpp11::tuple<Object, Alpha_value_type>,
+          CGAL::cpp11::tuple<std::back_insert_iterator< std::vector<Object> >,
+          std::back_insert_iterator< std::vector<Alpha_value_type> > > >;
+using Cell_handle = Alpha_shape_3::Cell_handle;
+using Facet = Alpha_shape_3::Facet;
+using Edge_3 = Alpha_shape_3::Edge;
+using Vertex_handle = Alpha_shape_3::Vertex_handle;
+using Vertex_list = std::list<Vertex_handle>;
+
+// gudhi type definition
+using ST = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
+using Filtration_value = ST::Filtration_value;
+using Simplex_tree_vertex = ST::Vertex_handle;
+using Alpha_shape_simplex_tree_map = std::map<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex >;
+using Alpha_shape_simplex_tree_pair = std::pair<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex>;
+using Simplex_tree_vector_vertex = std::vector< Simplex_tree_vertex >;
+using PCOH = Gudhi::persistent_cohomology::Persistent_cohomology< ST, Gudhi::persistent_cohomology::Field_Zp >;
+
+void usage(char * const progName) {
+  std::cerr << "Usage: " << progName <<
+      " path_to_file_graph coeff_field_characteristic[integer > 0] min_persistence[float >= -1.0]\n";
+  exit(-1);
+}
+
+int main(int argc, char * const argv[]) {
+  // program args management
+  if (argc != 4) {
+    std::cerr << "Error: Number of arguments (" << argc << ") is not correct\n";
+    usage(argv[0]);
+  }
+
+  int coeff_field_characteristic = atoi(argv[2]);
+
+  Filtration_value min_persistence = 0.0;
+  int returnedScanValue = sscanf(argv[3], "%f", &min_persistence);
+  if ((returnedScanValue == EOF) || (min_persistence < -1.0)) {
+    std::cerr << "Error: " << argv[3] << " is not correct\n";
+    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();
+
+  // 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);
+#ifdef DEBUG_TRACES
+  std::cout << "Alpha shape computed in GENERAL mode" << std::endl;
+#endif  // DEBUG_TRACES
+
+  // filtration with alpha values from alpha shape
+  std::vector<Object> the_objects;
+  std::vector<Alpha_value_type> the_alpha_values;
+
+  Dispatch disp = CGAL::dispatch_output<Object, Alpha_value_type>(std::back_inserter(the_objects),
+                                                                  std::back_inserter(the_alpha_values));
+
+  as.filtration_with_alpha_values(disp);
+#ifdef DEBUG_TRACES
+  std::cout << "filtration_with_alpha_values returns : " << the_objects.size() << " objects" << std::endl;
+#endif  // DEBUG_TRACES
+
+  Alpha_shape_3::size_type count_vertices = 0;
+  Alpha_shape_3::size_type count_edges = 0;
+  Alpha_shape_3::size_type count_facets = 0;
+  Alpha_shape_3::size_type count_cells = 0;
+
+  // Loop on objects vector
+  Vertex_list vertex_list;
+  ST simplex_tree;
+  Alpha_shape_simplex_tree_map map_cgal_simplex_tree;
+  std::vector<Alpha_value_type>::iterator the_alpha_value_iterator = the_alpha_values.begin();
+  int dim_max = 0;
+  Filtration_value filtration_max = 0.0;
+  for (auto object_iterator : the_objects) {
+    // Retrieve Alpha shape vertex list from object
+    if (const Cell_handle * cell = CGAL::object_cast<Cell_handle>(&object_iterator)) {
+      vertex_list = from_cell<Vertex_list, Cell_handle>(*cell);
+      count_cells++;
+      if (dim_max < 3) {
+        // Cell is of dim 3
+        dim_max = 3;
+      }
+    } else if (const Facet * facet = CGAL::object_cast<Facet>(&object_iterator)) {
+      vertex_list = from_facet<Vertex_list, Facet>(*facet);
+      count_facets++;
+      if (dim_max < 2) {
+        // Facet is of dim 2
+        dim_max = 2;
+      }
+    } else if (const Edge_3 * edge = CGAL::object_cast<Edge_3>(&object_iterator)) {
+      vertex_list = from_edge<Vertex_list, Edge_3>(*edge);
+      count_edges++;
+      if (dim_max < 1) {
+        // Edge_3 is of dim 1
+        dim_max = 1;
+      }
+    } else if (const Vertex_handle * vertex = CGAL::object_cast<Vertex_handle>(&object_iterator)) {
+      count_vertices++;
+      vertex_list = from_vertex<Vertex_list, Vertex_handle>(*vertex);
+    }
+    // Construction of the vector of simplex_tree vertex from list of alpha_shapes vertex
+    Simplex_tree_vector_vertex the_simplex_tree;
+    for (auto the_alpha_shape_vertex : vertex_list) {
+      Alpha_shape_simplex_tree_map::iterator the_map_iterator = map_cgal_simplex_tree.find(the_alpha_shape_vertex);
+      if (the_map_iterator == map_cgal_simplex_tree.end()) {
+        // alpha shape not found
+        Simplex_tree_vertex vertex = map_cgal_simplex_tree.size();
+#ifdef DEBUG_TRACES
+        std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] not found - insert " << vertex << std::endl;
+#endif  // DEBUG_TRACES
+        the_simplex_tree.push_back(vertex);
+        map_cgal_simplex_tree.insert(Alpha_shape_simplex_tree_pair(the_alpha_shape_vertex, vertex));
+      } else {
+        // alpha shape found
+        Simplex_tree_vertex vertex = the_map_iterator->second;
+#ifdef DEBUG_TRACES
+        std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] found in " << vertex << std::endl;
+#endif  // DEBUG_TRACES
+        the_simplex_tree.push_back(vertex);
+      }
+    }
+    // Construction of the simplex_tree
+    // you can also use the_alpha_value_iterator->exact()
+    Filtration_value filtr = /*std::sqrt*/CGAL::to_double(the_alpha_value_iterator->exact());
+#ifdef DEBUG_TRACES
+    std::cout << "filtration = " << filtr << std::endl;
+#endif  // DEBUG_TRACES
+    if (filtr > filtration_max) {
+      filtration_max = filtr;
+    }
+    simplex_tree.insert_simplex(the_simplex_tree, filtr);
+    if (the_alpha_value_iterator != the_alpha_values.end())
+      ++the_alpha_value_iterator;
+    else
+      std::cout << "This shall not happen" << std::endl;
+  }
+  simplex_tree.set_filtration(filtration_max);
+  simplex_tree.set_dimension(dim_max);
+
+#ifdef DEBUG_TRACES
+  std::cout << "vertices \t\t" << count_vertices << std::endl;
+  std::cout << "edges \t\t" << count_edges << std::endl;
+  std::cout << "facets \t\t" << count_facets << std::endl;
+  std::cout << "cells \t\t" << count_cells << std::endl;
+
+
+  std::cout << "Information of the Simplex Tree: " << std::endl;
+  std::cout << "  Number of vertices = " << simplex_tree.num_vertices() << " ";
+  std::cout << "  Number of simplices = " << simplex_tree.num_simplices() << std::endl << std::endl;
+  std::cout << "  Dimension = " << simplex_tree.dimension() << " ";
+  std::cout << "  filtration = " << simplex_tree.filtration() << std::endl << std::endl;
+#endif  // DEBUG_TRACES
+
+#ifdef DEBUG_TRACES
+  std::cout << "Iterator on vertices: " << std::endl;
+  for (auto vertex : simplex_tree.complex_vertex_range()) {
+    std::cout << vertex << " ";
+  }
+#endif  // DEBUG_TRACES
+
+  // Sort the simplices in the order of the filtration
+  simplex_tree.initialize_filtration();
+
+  std::cout << "Simplex_tree dim: " << simplex_tree.dimension() << std::endl;
+  // Compute the persistence diagram of the complex
+  PCOH pcoh(simplex_tree);
+  // initializes the coefficient field for homology
+  pcoh.init_coefficients(coeff_field_characteristic);
+
+  pcoh.compute_persistent_cohomology(min_persistence);
+
+  pcoh.output_diagram();
+
+  return 0;
+}
diff --git a/src/Persistent_cohomology/example/periodic_alpha_complex_3d_persistence.cpp b/src/Persistent_cohomology/example/periodic_alpha_complex_3d_persistence.cpp
index dbc42706..4f6ea40e 100644
--- a/src/Persistent_cohomology/example/periodic_alpha_complex_3d_persistence.cpp
+++ b/src/Persistent_cohomology/example/periodic_alpha_complex_3d_persistence.cpp
@@ -31,6 +31,8 @@
 #include <CGAL/Alpha_shape_3.h>
 #include <CGAL/iterator.h>
 
+#include "alpha_complex_3d_helper.h"
+
 #include <fstream>
 #include <cmath>
 #include <string>
@@ -67,6 +69,7 @@ using Dispatch = CGAL::Dispatch_output_iterator<
 using Cell_handle = Alpha_shape_3::Cell_handle;
 using Facet = Alpha_shape_3::Facet;
 using Edge_3 = Alpha_shape_3::Edge;
+using Vertex_handle = Alpha_shape_3::Vertex_handle;
 using Vertex_list = std::list<Alpha_shape_3::Vertex_handle>;
 
 // gudhi type definition
@@ -79,52 +82,6 @@ using Simplex_tree_vector_vertex = std::vector< Simplex_tree_vertex >;
 using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<
     ST, Gudhi::persistent_cohomology::Field_Zp >;
 
-Vertex_list from(const Cell_handle& ch) {
-  Vertex_list the_list;
-  for (auto i = 0; i < 4; i++) {
-#ifdef DEBUG_TRACES
-    std::cout << "from cell[" << i << "]=" << ch->vertex(i)->point() << std::endl;
-#endif  // DEBUG_TRACES
-    the_list.push_back(ch->vertex(i));
-  }
-  return the_list;
-}
-
-Vertex_list from(const Facet& fct) {
-  Vertex_list the_list;
-  for (auto i = 0; i < 4; i++) {
-    if (fct.second != i) {
-#ifdef DEBUG_TRACES
-      std::cout << "from facet=[" << i << "]" << fct.first->vertex(i)->point() << std::endl;
-#endif  // DEBUG_TRACES
-      the_list.push_back(fct.first->vertex(i));
-    }
-  }
-  return the_list;
-}
-
-Vertex_list from(const Edge_3& edg) {
-  Vertex_list the_list;
-  for (auto i = 0; i < 4; i++) {
-    if ((edg.second == i) || (edg.third == i)) {
-#ifdef DEBUG_TRACES
-      std::cout << "from edge[" << i << "]=" << edg.first->vertex(i)->point() << std::endl;
-#endif  // DEBUG_TRACES
-      the_list.push_back(edg.first->vertex(i));
-    }
-  }
-  return the_list;
-}
-
-Vertex_list from(const Alpha_shape_3::Vertex_handle& vh) {
-  Vertex_list the_list;
-#ifdef DEBUG_TRACES
-  std::cout << "from vertex=" << vh->point() << std::endl;
-#endif  // DEBUG_TRACES
-  the_list.push_back(vh);
-  return the_list;
-}
-
 void usage(char * const progName) {
   std::cerr << "Usage: " << progName <<
       " path_to_file_graph path_to_iso_cuboid_3_file coeff_field_characteristic[integer > 0] min_persistence[float >= -1.0]\n";
@@ -203,21 +160,21 @@ int main(int argc, char * const argv[]) {
   for (auto object_iterator : the_objects) {
     // Retrieve Alpha shape vertex list from object
     if (const Cell_handle * cell = CGAL::object_cast<Cell_handle>(&object_iterator)) {
-      vertex_list = from(*cell);
+      vertex_list = from_cell<Vertex_list, Cell_handle>(*cell);
       count_cells++;
       if (dim_max < 3) {
         // Cell is of dim 3
         dim_max = 3;
       }
     } else if (const Facet * facet = CGAL::object_cast<Facet>(&object_iterator)) {
-      vertex_list = from(*facet);
+      vertex_list = from_facet<Vertex_list, Facet>(*facet);
       count_facets++;
       if (dim_max < 2) {
         // Facet is of dim 2
         dim_max = 2;
       }
     } else if (const Edge_3 * edge = CGAL::object_cast<Edge_3>(&object_iterator)) {
-      vertex_list = from(*edge);
+      vertex_list = from_edge<Vertex_list, Edge_3>(*edge);
       count_edges++;
       if (dim_max < 1) {
         // Edge_3 is of dim 1
@@ -226,7 +183,7 @@ int main(int argc, char * const argv[]) {
     } else if (const Alpha_shape_3::Vertex_handle * vertex =
                CGAL::object_cast<Alpha_shape_3::Vertex_handle>(&object_iterator)) {
       count_vertices++;
-      vertex_list = from(*vertex);
+      vertex_list = from_vertex<Vertex_list, Vertex_handle>(*vertex);
     }
     // Construction of the vector of simplex_tree vertex from list of alpha_shapes vertex
     Simplex_tree_vector_vertex the_simplex_tree;
diff --git a/src/Persistent_cohomology/example/weighted_alpha_complex_3d_persistence.cpp b/src/Persistent_cohomology/example/weighted_alpha_complex_3d_persistence.cpp
new file mode 100644
index 00000000..5203548a
--- /dev/null
+++ b/src/Persistent_cohomology/example/weighted_alpha_complex_3d_persistence.cpp
@@ -0,0 +1,263 @@
+/*    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):       Vincent Rouvreau
+ *
+ *    Copyright (C) 2014  INRIA
+ *
+ *    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/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/Regular_triangulation_euclidean_traits_3.h>
+#include <CGAL/Regular_triangulation_3.h>
+#include <CGAL/Alpha_shape_3.h>
+#include <CGAL/iterator.h>
+
+#include "alpha_complex_3d_helper.h"
+
+#include <fstream>
+#include <cmath>
+#include <string>
+#include <tuple>
+#include <map>
+#include <utility>
+#include <list>
+#include <vector>
+#include <cstdlib>
+
+// Traits
+using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
+using Gt = CGAL::Regular_triangulation_euclidean_traits_3<Kernel>;
+using Vb = CGAL::Alpha_shape_vertex_base_3<Gt>;
+using Fb = CGAL::Alpha_shape_cell_base_3<Gt>;
+using Tds = CGAL::Triangulation_data_structure_3<Vb, Fb>;
+using Triangulation_3 = CGAL::Regular_triangulation_3<Gt,Tds>;
+using Alpha_shape_3 = CGAL::Alpha_shape_3<Triangulation_3>;
+
+// From file type definition
+using Point_3 = Gt::Bare_point;
+using Weighted_point_3 = Gt::Weighted_point;
+
+// filtration with alpha values needed type definition
+using Alpha_value_type = Alpha_shape_3::FT;
+using Object = CGAL::Object;
+using Dispatch = CGAL::Dispatch_output_iterator<
+          CGAL::cpp11::tuple<Object, Alpha_value_type>,
+          CGAL::cpp11::tuple<std::back_insert_iterator< std::vector<Object> >,
+          std::back_insert_iterator< std::vector<Alpha_value_type> > > >;
+using Cell_handle = Alpha_shape_3::Cell_handle;
+using Facet = Alpha_shape_3::Facet;
+using Edge_3 = Alpha_shape_3::Edge;
+using Vertex_handle = Alpha_shape_3::Vertex_handle;
+using Vertex_list = std::list<Alpha_shape_3::Vertex_handle>;
+
+// gudhi type definition
+using ST = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
+using Filtration_value = ST::Filtration_value;
+using Simplex_tree_vertex = ST::Vertex_handle;
+using Alpha_shape_simplex_tree_map = std::map<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex >;
+using Alpha_shape_simplex_tree_pair = std::pair<Alpha_shape_3::Vertex_handle, Simplex_tree_vertex>;
+using Simplex_tree_vector_vertex = std::vector< Simplex_tree_vertex >;
+using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<
+    ST, Gudhi::persistent_cohomology::Field_Zp >;
+
+void usage(char * const progName) {
+  std::cerr << "Usage: " << progName <<
+      " path_to_file_graph path_to_weight_file coeff_field_characteristic[integer > 0] min_persistence[float >= -1.0]\n";
+  exit(-1);
+}
+
+int main(int argc, char * const argv[]) {
+  // program args management
+  if (argc != 5) {
+    std::cerr << "Error: Number of arguments (" << argc << ") is not correct\n";
+    usage(argv[0]);
+  }
+
+  int coeff_field_characteristic = atoi(argv[3]);
+  Filtration_value min_persistence = strtof(argv[4], nullptr);
+
+  // 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();
+
+  // Read weights information from file
+  std::ifstream weights_ifstr(argv[2]);
+  std::vector<Weighted_point_3> wp;
+  if (weights_ifstr.good()) {
+    double weight = 0.0;
+    std::size_t index = 0;
+    // Attempt read the weight in a double format, return false if it fails
+    while((weights_ifstr >> weight) && (index < lp.size()))
+    {
+      wp.push_back(Weighted_point_3(lp[index], weight));
+      index++;
+    }
+    if (index != lp.size()) {
+      std::cerr << "Bad number of weights in file " << argv[2] << std::endl;
+      usage(argv[0]);
+    }
+  } else {
+    std::cerr << "Unable to read file " << argv[2] << std::endl;
+    usage(argv[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);
+#ifdef DEBUG_TRACES
+  std::cout << "Alpha shape computed in GENERAL mode" << std::endl;
+#endif  // DEBUG_TRACES
+
+  // filtration with alpha values from alpha shape
+  std::vector<Object> the_objects;
+  std::vector<Alpha_value_type> the_alpha_values;
+
+  Dispatch disp = CGAL::dispatch_output<Object, Alpha_value_type>(std::back_inserter(the_objects),
+                                                                  std::back_inserter(the_alpha_values));
+
+  as.filtration_with_alpha_values(disp);
+#ifdef DEBUG_TRACES
+  std::cout << "filtration_with_alpha_values returns : " << the_objects.size() << " objects" << std::endl;
+#endif  // DEBUG_TRACES
+
+  Alpha_shape_3::size_type count_vertices = 0;
+  Alpha_shape_3::size_type count_edges = 0;
+  Alpha_shape_3::size_type count_facets = 0;
+  Alpha_shape_3::size_type count_cells = 0;
+
+  // Loop on objects vector
+  Vertex_list vertex_list;
+  ST simplex_tree;
+  Alpha_shape_simplex_tree_map map_cgal_simplex_tree;
+  std::vector<Alpha_value_type>::iterator the_alpha_value_iterator = the_alpha_values.begin();
+  int dim_max = 0;
+  Filtration_value filtration_max = 0.0;
+  for (auto object_iterator : the_objects) {
+    // Retrieve Alpha shape vertex list from object
+    if (const Cell_handle * cell = CGAL::object_cast<Cell_handle>(&object_iterator)) {
+      vertex_list = from_cell<Vertex_list, Cell_handle>(*cell);
+      count_cells++;
+      if (dim_max < 3) {
+        // Cell is of dim 3
+        dim_max = 3;
+      }
+    } else if (const Facet * facet = CGAL::object_cast<Facet>(&object_iterator)) {
+      vertex_list = from_facet<Vertex_list, Facet>(*facet);
+      count_facets++;
+      if (dim_max < 2) {
+        // Facet is of dim 2
+        dim_max = 2;
+      }
+    } else if (const Edge_3 * edge = CGAL::object_cast<Edge_3>(&object_iterator)) {
+      vertex_list = from_edge<Vertex_list, Edge_3>(*edge);
+      count_edges++;
+      if (dim_max < 1) {
+        // Edge_3 is of dim 1
+        dim_max = 1;
+      }
+    } else if (const Alpha_shape_3::Vertex_handle * vertex =
+               CGAL::object_cast<Alpha_shape_3::Vertex_handle>(&object_iterator)) {
+      count_vertices++;
+      vertex_list = from_vertex<Vertex_list, Vertex_handle>(*vertex);
+    }
+    // Construction of the vector of simplex_tree vertex from list of alpha_shapes vertex
+    Simplex_tree_vector_vertex the_simplex_tree;
+    for (auto the_alpha_shape_vertex : vertex_list) {
+      Alpha_shape_simplex_tree_map::iterator the_map_iterator = map_cgal_simplex_tree.find(the_alpha_shape_vertex);
+      if (the_map_iterator == map_cgal_simplex_tree.end()) {
+        // alpha shape not found
+        Simplex_tree_vertex vertex = map_cgal_simplex_tree.size();
+#ifdef DEBUG_TRACES
+        std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] not found - insert " << vertex << std::endl;
+#endif  // DEBUG_TRACES
+        the_simplex_tree.push_back(vertex);
+        map_cgal_simplex_tree.insert(Alpha_shape_simplex_tree_pair(the_alpha_shape_vertex, vertex));
+      } else {
+        // alpha shape found
+        Simplex_tree_vertex vertex = the_map_iterator->second;
+#ifdef DEBUG_TRACES
+        std::cout << "vertex [" << the_alpha_shape_vertex->point() << "] found in " << vertex << std::endl;
+#endif  // DEBUG_TRACES
+        the_simplex_tree.push_back(vertex);
+      }
+    }
+    // Construction of the simplex_tree
+    Filtration_value filtr = /*std::sqrt*/(*the_alpha_value_iterator);
+#ifdef DEBUG_TRACES
+    std::cout << "filtration = " << filtr << std::endl;
+#endif  // DEBUG_TRACES
+    if (filtr > filtration_max) {
+      filtration_max = filtr;
+    }
+    simplex_tree.insert_simplex(the_simplex_tree, filtr);
+    if (the_alpha_value_iterator != the_alpha_values.end())
+      ++the_alpha_value_iterator;
+    else
+      std::cout << "This shall not happen" << std::endl;
+  }
+  simplex_tree.set_filtration(filtration_max);
+  simplex_tree.set_dimension(dim_max);
+
+#ifdef DEBUG_TRACES
+  std::cout << "vertices \t\t" << count_vertices << std::endl;
+  std::cout << "edges \t\t" << count_edges << std::endl;
+  std::cout << "facets \t\t" << count_facets << std::endl;
+  std::cout << "cells \t\t" << count_cells << std::endl;
+
+
+  std::cout << "Information of the Simplex Tree: " << std::endl;
+  std::cout << "  Number of vertices = " << simplex_tree.num_vertices() << " ";
+  std::cout << "  Number of simplices = " << simplex_tree.num_simplices() << std::endl << std::endl;
+  std::cout << "  Dimension = " << simplex_tree.dimension() << " ";
+  std::cout << "  filtration = " << simplex_tree.filtration() << std::endl << std::endl;
+#endif  // DEBUG_TRACES
+
+#ifdef DEBUG_TRACES
+  std::cout << "Iterator on vertices: " << std::endl;
+  for (auto vertex : simplex_tree.complex_vertex_range()) {
+    std::cout << vertex << " ";
+  }
+#endif  // DEBUG_TRACES
+
+  // Sort the simplices in the order of the filtration
+  simplex_tree.initialize_filtration();
+
+  std::cout << "Simplex_tree dim: " << simplex_tree.dimension() << std::endl;
+  // Compute the persistence diagram of the complex
+  Persistent_cohomology pcoh(simplex_tree, true);
+  // initializes the coefficient field for homology
+  pcoh.init_coefficients(coeff_field_characteristic);
+
+  pcoh.compute_persistent_cohomology(min_persistence);
+
+  pcoh.output_diagram();
+
+  return 0;
+}