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-rw-r--r--src/Alpha_complex/utilities/CMakeLists.txt58
-rw-r--r--src/Alpha_complex/utilities/alpha_complex_3d_persistence.cpp305
-rw-r--r--src/Alpha_complex/utilities/alpha_complex_persistence.cpp126
-rw-r--r--src/Alpha_complex/utilities/alphacomplex.md127
4 files changed, 616 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..5295f3cd
--- /dev/null
+++ b/src/Alpha_complex/utilities/CMakeLists.txt
@@ -0,0 +1,58 @@
+project(Alpha_complex_utilities)
+
+if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.11.0)
+ add_executable (alpha_complex_persistence alpha_complex_persistence.cpp)
+ target_link_libraries(alpha_complex_persistence ${CGAL_LIBRARY} ${Boost_PROGRAM_OPTIONS_LIBRARY})
+
+ if (TBB_FOUND)
+ target_link_libraries(alpha_complex_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")
+
+ install(TARGETS alpha_complex_persistence DESTINATION bin)
+
+ add_executable(alpha_complex_3d_persistence alpha_complex_3d_persistence.cpp)
+ target_link_libraries(alpha_complex_3d_persistence ${CGAL_LIBRARY} ${Boost_PROGRAM_OPTIONS_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 COMMAND $<TARGET_FILE:alpha_complex_3d_persistence>
+ "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off"
+ "-p" "2" "-m" "0.45" "-o" "safe.pers")
+
+ add_test(NAME Alpha_complex_utilities_exact_alpha_complex_3d COMMAND $<TARGET_FILE:alpha_complex_3d_persistence>
+ "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off"
+ "-p" "2" "-m" "0.45" "-o" "exact.pers" "-e")
+
+ add_test(NAME Alpha_complex_utilities_safe_alpha_complex_3d COMMAND $<TARGET_FILE:alpha_complex_3d_persistence>
+ "${CMAKE_SOURCE_DIR}/data/points/tore3D_300.off"
+ "-p" "2" "-m" "0.45" "-o" "fast.pers" "-f")
+
+ if (DIFF_PATH)
+ add_test(Alpha_complex_utilities_diff_alpha_complex_3d ${DIFF_PATH}
+ "exact.pers" "safe.pers")
+ add_test(Alpha_complex_utilities_diff_alpha_complex_3d ${DIFF_PATH}
+ "fast.pers" "safe.pers")
+ endif()
+
+ add_test(NAME Alpha_complex_utilities_periodic_alpha_complex_3d_persistence COMMAND $<TARGET_FILE:alpha_complex_3d_persistence>
+ "${CMAKE_SOURCE_DIR}/data/points/grid_10_10_10_in_0_1.off"
+ "-c" "${CMAKE_SOURCE_DIR}/data/points/iso_cuboid_3_in_0_1.txt"
+ "-p" "2" "-m" "0")
+
+ add_test(NAME Alpha_complex_utilities_weighted_alpha_complex_3d COMMAND $<TARGET_FILE:alpha_complex_3d_persistence>
+ "${CMAKE_SOURCE_DIR}/data/points/grid_10_10_10_in_0_1.off"
+ "-w" "${CMAKE_SOURCE_DIR}/data/points/grid_10_10_10_in_0_1.weights"
+ "-p" "2" "-m" "0")
+
+ add_test(NAME Alpha_complex_utilities_weighted_periodic_alpha_complex_3d COMMAND $<TARGET_FILE:alpha_complex_3d_persistence>
+ "${CMAKE_SOURCE_DIR}/data/points/grid_10_10_10_in_0_1.off"
+ "-w" "${CMAKE_SOURCE_DIR}/data/points/grid_10_10_10_in_0_1.weights"
+ "-c" "${CMAKE_SOURCE_DIR}/data/points/iso_cuboid_3_in_0_1.txt"
+ "-p" "2" "-m" "0" "-e")
+
+ install(TARGETS alpha_complex_3d_persistence DESTINATION bin)
+
+endif (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.11.0)
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..2272576e
--- /dev/null
+++ b/src/Alpha_complex/utilities/alpha_complex_3d_persistence.cpp
@@ -0,0 +1,305 @@
+/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ * Author(s): Vincent Rouvreau
+ *
+ * Copyright (C) 2014 Inria
+ *
+ * Modification(s):
+ * - YYYY/MM Author: Description of the modification
+ */
+
+#include <boost/program_options.hpp>
+#include <boost/variant.hpp>
+
+#include <gudhi/Alpha_complex_3d.h>
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Persistent_cohomology.h>
+#include <gudhi/Points_3D_off_io.h>
+
+#include <fstream>
+#include <string>
+#include <vector>
+#include <limits> // for numeric_limits<>
+
+// gudhi type definition
+using Simplex_tree = Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_fast_persistence>;
+using Filtration_value = Simplex_tree::Filtration_value;
+using Persistent_cohomology =
+ Gudhi::persistent_cohomology::Persistent_cohomology<Simplex_tree, Gudhi::persistent_cohomology::Field_Zp>;
+
+void program_options(int argc, char *argv[], std::string &off_file_points, bool &exact, bool &safe,
+ std::string &weight_file, std::string &cuboid_file, std::string &output_file_diag,
+ Filtration_value &alpha_square_max_value, int &coeff_field_characteristic,
+ Filtration_value &min_persistence);
+
+bool read_weight_file(const std::string &weight_file, std::vector<double> &weights) {
+ // Read weights information from file
+ std::ifstream weights_ifstr(weight_file);
+ if (weights_ifstr.good()) {
+ double weight = 0.0;
+ // Attempt read the weight in a double format, return false if it fails
+ while (weights_ifstr >> weight) {
+ weights.push_back(weight);
+ }
+ } else {
+ return false;
+ }
+ return true;
+}
+
+bool read_cuboid_file(const std::string &cuboid_file, double &x_min, double &y_min, double &z_min, double &x_max,
+ double &y_max, double &z_max) {
+ // Read weights information from file
+ std::ifstream iso_cuboid_str(cuboid_file);
+ if (iso_cuboid_str.is_open()) {
+ if (!(iso_cuboid_str >> x_min >> y_min >> z_min >> x_max >> y_max >> z_max)) {
+ return false;
+ }
+ } else {
+ return false;
+ }
+ return true;
+}
+
+template <typename AlphaComplex3d>
+std::vector<typename AlphaComplex3d::Point_3> read_off(const std::string &off_file_points) {
+ // Read the OFF file (input file name given as parameter) and triangulate points
+ Gudhi::Points_3D_off_reader<typename AlphaComplex3d::Point_3> off_reader(off_file_points);
+ // Check the read operation was correct
+ if (!off_reader.is_valid()) {
+ std::cerr << "Unable to read OFF file " << off_file_points << std::endl;
+ exit(-1);
+ }
+ return off_reader.get_point_cloud();
+}
+
+int main(int argc, char **argv) {
+ std::string off_file_points;
+ std::string weight_file;
+ std::string cuboid_file;
+ std::string output_file_diag;
+ Filtration_value alpha_square_max_value = 0.;
+ int coeff_field_characteristic = 0;
+ Filtration_value min_persistence = 0.;
+ bool exact_version = false;
+ bool fast_version = false;
+ bool weighted_version = false;
+ bool periodic_version = false;
+
+ program_options(argc, argv, off_file_points, exact_version, fast_version, weight_file, cuboid_file, output_file_diag,
+ alpha_square_max_value, coeff_field_characteristic, min_persistence);
+
+ std::vector<double> weights;
+ if (weight_file != std::string()) {
+ if (!read_weight_file(weight_file, weights)) {
+ std::cerr << "Unable to read weights file " << weight_file << std::endl;
+ exit(-1);
+ }
+ weighted_version = true;
+ }
+
+ double x_min = 0., y_min = 0., z_min = 0., x_max = 0., y_max = 0., z_max = 0.;
+ std::ifstream iso_cuboid_str(argv[3]);
+ if (cuboid_file != std::string()) {
+ if (!read_cuboid_file(cuboid_file, x_min, y_min, z_min, x_max, y_max, z_max)) {
+ std::cerr << "Unable to read cuboid file " << cuboid_file << std::endl;
+ exit(-1);
+ }
+ periodic_version = true;
+ }
+
+ Gudhi::alpha_complex::complexity complexity = Gudhi::alpha_complex::complexity::SAFE;
+ if (exact_version) {
+ if (fast_version) {
+ std::cerr << "You cannot set the exact and the fast version." << std::endl;
+ exit(-1);
+ }
+ complexity = Gudhi::alpha_complex::complexity::EXACT;
+ }
+ if (fast_version) {
+ complexity = Gudhi::alpha_complex::complexity::FAST;
+ }
+
+ Simplex_tree simplex_tree;
+
+ switch (complexity) {
+ case Gudhi::alpha_complex::complexity::FAST:
+ if (weighted_version) {
+ if (periodic_version) {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::FAST, true, true>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points, weights, x_min, y_min, z_min, x_max, y_max, z_max);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ } else {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::FAST, true, false>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points, weights);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ }
+ } else {
+ if (periodic_version) {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::FAST, false, true>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points, x_min, y_min, z_min, x_max, y_max, z_max);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ } else {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::FAST, false, false>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ }
+ }
+ break;
+ case Gudhi::alpha_complex::complexity::EXACT:
+ if (weighted_version) {
+ if (periodic_version) {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, true, true>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points, weights, x_min, y_min, z_min, x_max, y_max, z_max);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ } else {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, true, false>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points, weights);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ }
+ } else {
+ if (periodic_version) {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, false, true>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points, x_min, y_min, z_min, x_max, y_max, z_max);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ } else {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::EXACT, false, false>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ }
+ }
+ break;
+ case Gudhi::alpha_complex::complexity::SAFE:
+ if (weighted_version) {
+ if (periodic_version) {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, true, true>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points, weights, x_min, y_min, z_min, x_max, y_max, z_max);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ } else {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, true, false>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points, weights);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ }
+ } else {
+ if (periodic_version) {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, false, true>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points, x_min, y_min, z_min, x_max, y_max, z_max);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ } else {
+ using Alpha_complex_3d =
+ Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, false, false>;
+ auto points = read_off<Alpha_complex_3d>(off_file_points);
+ Alpha_complex_3d alpha_complex(points);
+ alpha_complex.create_complex(simplex_tree, alpha_square_max_value);
+ }
+ }
+ break;
+ default:
+ std::cerr << "Unknown complexity value " << std::endl;
+ exit(-1);
+ break;
+ }
+
+ // 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);
+
+ // 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, bool &exact, bool &fast,
+ std::string &weight_file, std::string &cuboid_file, 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")(
+ "exact,e", po::bool_switch(&exact),
+ "To activate exact version of Alpha complex 3d (default is false, not available if fast is set)")(
+ "fast,f", po::bool_switch(&fast),
+ "To activate fast version of Alpha complex 3d (default is false, not available if exact is set)")(
+ "weight-file,w", po::value<std::string>(&weight_file)->default_value(std::string()),
+ "Name of file containing a point weights. Format is one weight per line:\n W1\n ...\n Wn ")(
+ "cuboid-file,c", po::value<std::string>(&cuboid_file),
+ "Name of file describing the periodic domain. Format is:\n min_hx min_hy min_hz\n max_hx max_hy max_hz")(
+ "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") || !vm.count("weight-file")) {
+ std::cout << std::endl;
+ std::cout << "Compute the persistent homology with coefficient field Z/pZ \n";
+ std::cout << "of a 3D Alpha complex defined on a set of input points.\n";
+ std::cout << "3D Alpha complex can be safe (by default) exact or fast, weighted and/or periodic\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.\n\n";
+
+ std::cout << "Usage: " << argv[0] << " [options] input-file weight-file\n\n";
+ std::cout << visible << std::endl;
+ exit(-1);
+ }
+}
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..fab7bd30
--- /dev/null
+++ b/src/Alpha_complex/utilities/alpha_complex_persistence.cpp
@@ -0,0 +1,126 @@
+/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ * Author(s): Vincent Rouvreau
+ *
+ * Copyright (C) 2016 Inria
+ *
+ * Modification(s):
+ * - YYYY/MM Author: Description of the modification
+ */
+
+#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;
+ exit(-1);
+ }
+}
diff --git a/src/Alpha_complex/utilities/alphacomplex.md b/src/Alpha_complex/utilities/alphacomplex.md
new file mode 100644
index 00000000..fcd16a3b
--- /dev/null
+++ b/src/Alpha_complex/utilities/alphacomplex.md
@@ -0,0 +1,127 @@
+---
+layout: page
+title: "Alpha complex"
+meta_title: "Alpha complex"
+teaser: ""
+permalink: /alphacomplex/
+---
+{::comment}
+Leave the lines above as it is required by the web site generator 'Jekyll'
+{:/comment}
+
+
+## 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 birth death
+```
+
+where `dim` is the dimension of the homological feature, `birth` and `death`
+are respectively the birth and death of the feature, and `p` is the
+characteristic of the field *Z/pZ* used for homology coefficients (`p` must be
+a prime number).
+
+**Usage**
+
+```
+ alpha_complex_persistence [options] <input OFF file>
+```
+
+where
+`<input OFF file>` is the path to the input point cloud in
+[nOFF ASCII format]({{ site.officialurl }}/doc/latest/fileformats.html#FileFormatsOFF).
+
+**Allowed options**
+
+* `-h [ --help ]` Produce help message
+* `-o [ --output-file ]` Name of file in which the persistence diagram is
+written. Default print in standard output.
+* `-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
+```
+
+N.B.:
+
+* Filtration values are alpha square values.
+
+
+## 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.
+One can use exact computation. It is slower, but it is necessary when points
+are on a grid for instance.
+Alpha complex 3d can be weighted and/or periodic (refer to the
+[CGAL's 3D Periodic Triangulations User Manual](
+https://doc.cgal.org/latest/Periodic_3_triangulation_3/index.html)
+for more details).
+
+The output diagram contains
+one bar per line, written with the convention:
+
+```
+p dim birth death
+```
+
+where `dim` is the dimension of the homological feature, `birth` and `death`
+are respectively the birth and death of the feature, and `p` is the
+characteristic of the field *Z/pZ* used for homology coefficients (`p` must be
+a prime number).
+
+**Usage**
+
+```
+ alpha_complex_3d_persistence [options] <input OFF file>
+```
+
+where `<input OFF file>` is the path to the input point cloud in
+[nOFF ASCII format]({{ site.officialurl }}/doc/latest/fileformats.html#FileFormatsOFF).
+
+**Allowed options**
+
+* `-h [ --help ]` Produce help message
+* `-o [ --output-file ]` Name of file in which the persistence diagram is
+written. Default print in standard output.
+* `-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.
+* `-c [ --cuboid-file ]` is the path to the file describing the periodic domain.
+It must be in the format described
+[here]({{ site.officialurl }}/doc/latest/fileformats.html#FileFormatsIsoCuboid).
+Default version is not periodic.
+* `-w [ --weight-file ]` is the path to the file containing the weights of the
+points (one value per line).
+Default version is not weighted.
+* `-e [ --exact ]` for the exact computation version (not compatible with
+weight and periodic version).
+* `-f [ --fast ]` for the fast computation version.
+
+**Example**
+
+```
+alpha_complex_3d_persistence ../../data/points/tore3D_300.off -p 2 -m 0.45
+```
+
+N.B.:
+
+* `alpha_complex_3d_persistence` only accepts OFF files in dimension 3.
+* Filtration values are alpha square values.
+* Weights values are explained on CGAL
+[Alpha shape](https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title0)
+and
+[Regular triangulation](https://doc.cgal.org/latest/Triangulation_3/index.html#Triangulation3secclassRegulartriangulation) documentation.
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-17 11:21:08 +0000