Document utilies in README files using Markdown + move/rename some utilities

Only missing doc for now: Garland_heckbert

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/add_utils_in_gudhi_v2@2752 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: 7ba0113762b6622130835dc9e372acfae29c2db8

6 files changed, 879 insertions, 0 deletions

diff --git a/src/Alpha_complex/utilities/CMakeLists.txt b/src/Alpha_complex/utilities/CMakeLists.txt
new file mode 100644
index 00000000..69dbc28a
--- /dev/null
+++ b/src/Alpha_complex/utilities/CMakeLists.txt
@@ -0,0 +1,37 @@
+cmake_minimum_required(VERSION 2.6)
+project(Alpha_complex_utilities)
+
+if(CGAL_FOUND)
+  add_executable(alpha_complex_3d_persistence alpha_complex_3d_persistence.cpp)
+  target_link_libraries(alpha_complex_3d_persistence ${CGAL_LIBRARY})
+
+  if (TBB_FOUND)
+    target_link_libraries(alpha_complex_3d_persistence ${TBB_LIBRARIES})
+  endif(TBB_FOUND)
+  add_test(NAME Alpha_complex_utilities_alpha_complex_3d_persistence COMMAND $<TARGET_FILE:alpha_complex_3d_persistence>
+      "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off" "2" "0.45")
+
+  install(TARGETS alpha_complex_3d_persistence DESTINATION bin)
+
+  if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.7.0)
+    add_executable (alpha_complex_persistence alpha_complex_persistence.cpp)
+    target_link_libraries(alpha_complex_persistence
+        ${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 ${CGAL_LIBRARY})
+
+    if (TBB_FOUND)
+      target_link_libraries(alpha_complex_persistence ${TBB_LIBRARIES})
+      target_link_libraries(periodic_alpha_complex_3d_persistence ${TBB_LIBRARIES})
+    endif(TBB_FOUND)
+    add_test(NAME Alpha_complex_utilities_alpha_complex_persistence COMMAND $<TARGET_FILE:alpha_complex_persistence>
+        "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off" "-p" "2" "-m" "0.45")
+    add_test(NAME Alpha_complex_utilities_periodic_alpha_complex_3d_persistence COMMAND $<TARGET_FILE:periodic_alpha_complex_3d_persistence>
+        "${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")
+
+    install(TARGETS alpha_complex_persistence DESTINATION bin)
+    install(TARGETS periodic_alpha_complex_3d_persistence DESTINATION bin)
+
+  endif (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.7.0)
+endif(CGAL_FOUND)
diff --git a/src/Alpha_complex/utilities/README b/src/Alpha_complex/utilities/README
new file mode 100644
index 00000000..30e1b187
--- /dev/null
+++ b/src/Alpha_complex/utilities/README
@@ -0,0 +1,131 @@
+# Alpha_complex #
+
+## `alpha_complex_3d_persistence` ##
+This program computes the persistent homology with coefficient field Z/pZ of the 3D alpha complex built from a 3D point cloud. The output diagram contains one bar per line, written with the convention:
+
+`p dim b d`
+
+where `dim` is the dimension of the homological feature, `b` and `d` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p = p1*...*pr` is the product of prime numbers *pi* such that the homology feature exists in homology with *Z/piZ* coefficients).
+
+**Usage**
+`alpha_complex_3d_persistence <input OFF file> <p> <min_persistence>` 
+where
+`<input OFF file>` is the path to the input point cloud in OFF format.
+`<p>` is the characteristic p of the coefficient field *Z/pZ* for computing homology. It must be a stricly positive integer.
+`<min_persistence>` is the minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals. It must be a floating-point number >= -1.
+
+**Example**
+`alpha_complex_3d_persistence ../../data/points/tore3D_300.off 2 0.45`
+
+outputs:
+```
+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 
+```
+
+Here we retrieve expected Betti numbers on a tore 3D:
+```
+Betti numbers[0] = 1
+Betti numbers[1] = 2
+Betti numbers[2] = 1
+```
+
+N.B.: 
+* `alpha_complex_3d_persistence` only accepts OFF files in dimension 3.
+* Filtration values are alpha square values.
+
+
+
+
+## `periodic_alpha_complex_3d_persistence` ##
+This program computes the persistent homology with coefficient field Z/pZ of the 3D periodic alpha complex built from a 3D point cloud. The output diagram contains one bar per line, written with the convention:
+
+`p dim b d`
+
+where `dim` is the dimension of the homological feature, `b` and `d` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p = p1*...*pr` is the product of prime numbers *pi* such that the homology feature exists in homology with *Z/piZ* coefficients).
+
+**Usage**
+`periodic_alpha_complex_3d_persistence <input OFF file> <p> <min_persistence>`
+where
+`<input OFF file>` is the path to the input point cloud in OFF format.
+`<p>` is the characteristic p of the coefficient field *Z/pZ* for computing homology. It must be a stricly positive integer.
+`<min_persistence>` is the minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals. It must be a floating-point number >= -1.
+
+**Example**
+`periodic_alpha_complex_3d_persistence ../../data/points/grid_10_10_10_in_0_1.off ../../data/points/iso_cuboid_3_in_0_1.txt 3 1.0`
+
+outputs:
+```
+Periodic Delaunay computed.
+Simplex_tree dim: 3
+3  0 0 inf 
+3  1 0.0025 inf 
+3  1 0.0025 inf 
+3  1 0.0025 inf 
+3  2 0.005 inf 
+3  2 0.005 inf 
+3  2 0.005 inf 
+3  3 0.0075 inf 
+```
+
+Here we retrieve expected Betti numbers on an 3D iso-oriented cuboids:
+```
+Betti numbers[0] = 1
+Betti numbers[1] = 3
+Betti numbers[2] = 3
+Betti numbers[3] = 1
+```
+
+N.B.: 
+* `periodic_alpha_complex_3d_persistence` only accepts OFF files in dimension 3.
+* In this example, the periodic cube is hard coded to { x = [0,1]; y = [0,1]; z = [0,1] }
+* Filtration values are alpha square values.
+
+
+
+
+
+## `alpha_complex_persistence` ##
+This program computes the persistent homology with coefficient field Z/pZ of the dD alpha complex built from a dD point cloud. The output diagram contains one bar per line, written with the convention:
+
+`p dim b d`
+
+where `dim` is the dimension of the homological feature, `b` and `d` are respectively the birth and death of the feature, and `p` is the characteristic of the field *Z/pZ* used for homology coefficients (`p = p1*...*pr` is the product of prime numbers pi such that the homology feature exists in homology with Z/piZ coefficients).
+
+**Usage**
+`alpha_complex_persistence [options] <OFF input file>`
+
+**Allowed options**
+
+* `-h [ --help ]` Produce help message
+* `-o [ --output-file ]` Name of file in which the persistence diagram is written. By default, print in std::cout.
+* `-r [ --max-alpha-square-value ]` (default = inf) Maximal alpha square value for the Alpha complex construction.
+* `-p [ --field-charac ]` (default = 11)     Characteristic p of the coefficient field Z/pZ for computing homology.
+* `-m [ --min-persistence ]` (default = 0) Minimal lifetime of homology feature to be recorded. Enter a negative value to see zero length intervals.
+
+**Example**
+`alpha_complex_persistence -r 32 -p 2 -m 0.45 ../../data/points/tore3D_300.off`
+
+outputs:
+```
+Alpha complex is of dimension 3 - 9273 simplices - 300 vertices.
+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 
+```
+
+Here we retrieve expected Betti numbers on a tore 3D:
+```
+Betti numbers[0] = 1
+Betti numbers[1] = 2
+Betti numbers[2] = 1
+```
+
+N.B.: 
+* `alpha_complex_persistence` only accepts OFF files in dimension d.
+* Filtration values are alpha square values.
diff --git a/src/Alpha_complex/utilities/alpha_complex_3d_helper.h b/src/Alpha_complex/utilities/alpha_complex_3d_helper.h
new file mode 100644
index 00000000..7865e4ec
--- /dev/null
+++ b/src/Alpha_complex/utilities/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 ALPHA_COMPLEX_3D_HELPER_H_
+#define 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  // ALPHA_COMPLEX_3D_HELPER_H_
diff --git a/src/Alpha_complex/utilities/alpha_complex_3d_persistence.cpp b/src/Alpha_complex/utilities/alpha_complex_3d_persistence.cpp
new file mode 100644
index 00000000..f63ff0f6
--- /dev/null
+++ b/src/Alpha_complex/utilities/alpha_complex_3d_persistence.cpp
@@ -0,0 +1,242 @@
+/*    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 <boost/variant.hpp>
+
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Persistent_cohomology.h>
+#include <gudhi/Points_3D_off_io.h>
+
+#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 <fstream>
+#include <cmath>
+#include <string>
+#include <tuple>
+#include <map>
+#include <utility>
+#include <list>
+#include <vector>
+
+#include "alpha_complex_3d_helper.h"
+
+// Alpha_shape_3 templates type definitions
+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
+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<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 PCOH = Gudhi::persistent_cohomology::Persistent_cohomology< ST, Gudhi::persistent_cohomology::Field_Zp >;
+
+void usage(const std::string& progName) {
+  std::cerr << "Usage:\n" << progName << " path_to_OFF_file coeff_field_characteristic[integer " <<
+               "> 0] min_persistence[float >= -1.0]\n";
+  std::cerr << "  path_to_OFF_file is the path to your points cloud in OFF format.\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
+    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_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() << " ";
+#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/Alpha_complex/utilities/alpha_complex_persistence.cpp b/src/Alpha_complex/utilities/alpha_complex_persistence.cpp
new file mode 100644
index 00000000..9e84e91f
--- /dev/null
+++ b/src/Alpha_complex/utilities/alpha_complex_persistence.cpp
@@ -0,0 +1,125 @@
+#include <boost/program_options.hpp>
+
+#include <CGAL/Epick_d.h>
+
+#include <gudhi/Alpha_complex.h>
+#include <gudhi/Persistent_cohomology.h>
+// to construct a simplex_tree from alpha complex
+#include <gudhi/Simplex_tree.h>
+
+#include <iostream>
+#include <string>
+#include <limits>  // for numeric_limits
+
+using Simplex_tree = Gudhi::Simplex_tree<>;
+using Filtration_value = Simplex_tree::Filtration_value;
+
+void program_options(int argc, char * argv[]
+                     , std::string & off_file_points
+                     , std::string & output_file_diag
+                     , Filtration_value & alpha_square_max_value
+                     , int & coeff_field_characteristic
+                     , Filtration_value & min_persistence);
+
+int main(int argc, char **argv) {
+  std::string off_file_points;
+  std::string output_file_diag;
+  Filtration_value alpha_square_max_value;
+  int coeff_field_characteristic;
+  Filtration_value min_persistence;
+
+  program_options(argc, argv, off_file_points, output_file_diag, alpha_square_max_value,
+                  coeff_field_characteristic, min_persistence);
+
+  // ----------------------------------------------------------------------------
+  // Init of an alpha complex from an OFF file
+  // ----------------------------------------------------------------------------
+  using Kernel = CGAL::Epick_d< CGAL::Dynamic_dimension_tag >;
+  Gudhi::alpha_complex::Alpha_complex<Kernel> alpha_complex_from_file(off_file_points);
+
+  Simplex_tree simplex;
+  if (alpha_complex_from_file.create_complex(simplex, alpha_square_max_value)) {
+    // ----------------------------------------------------------------------------
+    // Display information about the alpha complex
+    // ----------------------------------------------------------------------------
+    std::cout << "Simplicial complex is of dimension " << simplex.dimension() <<
+        " - " << simplex.num_simplices() << " simplices - " <<
+        simplex.num_vertices() << " vertices." << std::endl;
+
+    // Sort the simplices in the order of the filtration
+    simplex.initialize_filtration();
+
+    std::cout << "Simplex_tree dim: " << simplex.dimension() << std::endl;
+    // Compute the persistence diagram of the complex
+    Gudhi::persistent_cohomology::Persistent_cohomology< Simplex_tree,
+        Gudhi::persistent_cohomology::Field_Zp > pcoh(simplex);
+    // initializes the coefficient field for homology
+    pcoh.init_coefficients(coeff_field_characteristic);
+
+    pcoh.compute_persistent_cohomology(min_persistence);
+
+    // Output the diagram in filediag
+    if (output_file_diag.empty()) {
+      pcoh.output_diagram();
+    } else {
+      std::cout << "Result in file: " << output_file_diag << std::endl;
+      std::ofstream out(output_file_diag);
+      pcoh.output_diagram(out);
+      out.close();
+    }
+  }
+
+  return 0;
+}
+
+void program_options(int argc, char * argv[]
+                     , std::string & off_file_points
+                     , std::string & output_file_diag
+                     , Filtration_value & alpha_square_max_value
+                     , int & coeff_field_characteristic
+                     , Filtration_value & min_persistence) {
+  namespace po = boost::program_options;
+  po::options_description hidden("Hidden options");
+  hidden.add_options()
+      ("input-file", po::value<std::string>(&off_file_points),
+       "Name of file containing a point set. Format is one point per line:   X1 ... Xd ");
+
+  po::options_description visible("Allowed options", 100);
+  visible.add_options()
+      ("help,h", "produce help message")
+      ("output-file,o", po::value<std::string>(&output_file_diag)->default_value(std::string()),
+       "Name of file in which the persistence diagram is written. Default print in std::cout")
+      ("max-alpha-square-value,r",
+      po::value<Filtration_value>(&alpha_square_max_value)->default_value(std::numeric_limits<Filtration_value>::infinity()),
+       "Maximal alpha square value for the Alpha complex construction.")
+      ("field-charac,p", po::value<int>(&coeff_field_characteristic)->default_value(11),
+       "Characteristic p of the coefficient field Z/pZ for computing homology.")
+      ("min-persistence,m", po::value<Filtration_value>(&min_persistence),
+       "Minimal lifetime of homology feature to be recorded. Default is 0. Enter a negative value to see zero length intervals");
+
+  po::positional_options_description pos;
+  pos.add("input-file", 1);
+
+  po::options_description all;
+  all.add(visible).add(hidden);
+
+  po::variables_map vm;
+  po::store(po::command_line_parser(argc, argv).
+            options(all).positional(pos).run(), vm);
+  po::notify(vm);
+
+  if (vm.count("help") || !vm.count("input-file")) {
+    std::cout << std::endl;
+    std::cout << "Compute the persistent homology with coefficient field Z/pZ \n";
+    std::cout << "of an Alpha complex defined on a set of input points.\n \n";
+    std::cout << "The output diagram contains one bar per line, written with the convention: \n";
+    std::cout << "   p   dim b d \n";
+    std::cout << "where dim is the dimension of the homological feature,\n";
+    std::cout << "b and d are respectively the birth and death of the feature and \n";
+    std::cout << "p is the characteristic of the field Z/pZ used for homology coefficients." << std::endl << std::endl;
+
+    std::cout << "Usage: " << argv[0] << " [options] input-file" << std::endl << std::endl;
+    std::cout << visible << std::endl;
+    std::abort();
+  }
+}
diff --git a/src/Alpha_complex/utilities/periodic_alpha_complex_3d_persistence.cpp b/src/Alpha_complex/utilities/periodic_alpha_complex_3d_persistence.cpp
new file mode 100644
index 00000000..8140a3c5
--- /dev/null
+++ b/src/Alpha_complex/utilities/periodic_alpha_complex_3d_persistence.cpp
@@ -0,0 +1,268 @@
+/*    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 <boost/variant.hpp>
+
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Persistent_cohomology.h>
+#include <gudhi/Points_3D_off_io.h>
+
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Periodic_3_Delaunay_triangulation_traits_3.h>
+#include <CGAL/Periodic_3_Delaunay_triangulation_3.h>
+#include <CGAL/Alpha_shape_3.h>
+#include <CGAL/iterator.h>
+
+#include <fstream>
+#include <cmath>
+#include <string>
+#include <tuple>
+#include <map>
+#include <utility>
+#include <list>
+#include <vector>
+#include <cstdlib>
+
+#include "alpha_complex_3d_helper.h"
+
+// Traits
+using K = CGAL::Exact_predicates_inexact_constructions_kernel;
+using PK = CGAL::Periodic_3_Delaunay_triangulation_traits_3<K>;
+// Vertex type
+using DsVb = CGAL::Periodic_3_triangulation_ds_vertex_base_3<>;
+using Vb = CGAL::Triangulation_vertex_base_3<PK, DsVb>;
+using AsVb = CGAL::Alpha_shape_vertex_base_3<PK, Vb>;
+// Cell type
+using DsCb = CGAL::Periodic_3_triangulation_ds_cell_base_3<>;
+using Cb = CGAL::Triangulation_cell_base_3<PK, DsCb>;
+using AsCb = CGAL::Alpha_shape_cell_base_3<PK, Cb>;
+using Tds = CGAL::Triangulation_data_structure_3<AsVb, AsCb>;
+using P3DT3 = CGAL::Periodic_3_Delaunay_triangulation_3<PK, Tds>;
+using Alpha_shape_3 = CGAL::Alpha_shape_3<P3DT3>;
+using Point_3 = PK::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<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:\n" << progName << " path_to_OFF_file path_to_iso_cuboid_3_file coeff_field_characteristic[" <<
+               "integer > 0] min_persistence[float >= -1.0]\n" <<
+               "  path_to_OFF_file is the path to your points cloud in OFF format.\n" <<
+               "  path_to_iso_cuboid_3_file is the path to the iso cuboid file with the following format :\n" <<
+               "    x_min y_min z_min x_max y_max z_max\n" <<
+               "  In this example, the periodic cube will be " <<
+               "{ x = [x_min,x_max]; y = [y_min,y_max]; z = [z_min,z_max] }.\n" <<
+               "  For more information, please refer to\n" <<
+               "    https://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Iso__cuboid__3.html\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]);
+  }
+
+  // Read iso_cuboid_3 information from file
+  std::ifstream iso_cuboid_str(argv[2]);
+  double x_min, y_min, z_min, x_max, y_max, z_max;
+  if (iso_cuboid_str.good()) {
+    iso_cuboid_str >> x_min >> y_min >> z_min >> x_max >> y_max >> z_max;
+  } else {
+    std::cerr << "Unable to read file " << argv[2] << std::endl;
+    usage(argv[0]);
+  }
+
+  // Retrieve the triangulation
+  std::vector<Point_3> lp = off_reader.get_point_cloud();
+
+  // Define the periodic cube
+  P3DT3 pdt(PK::Iso_cuboid_3(x_min, y_min, z_min, x_max, y_max, z_max));
+  // Heuristic for inserting large point sets (if pts is reasonably large)
+  pdt.insert(lp.begin(), lp.end(), true);
+  // As pdt won't be modified anymore switch to 1-sheeted cover if possible
+  if (pdt.is_triangulation_in_1_sheet()) pdt.convert_to_1_sheeted_covering();
+  std::cout << "Periodic Delaunay computed." << std::endl;
+
+  // alpha shape construction from points. CGAL has a strange behavior in REGULARIZED mode. This is the default mode
+  // Maybe need to set it to GENERAL mode
+  Alpha_shape_3 as(pdt, 0, Alpha_shape_3::GENERAL);
+
+  // 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_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() << " ";
+#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;
+}