Merge last trunk modifications

add Py test for subsampling
Add choose_n_furthest from off file


git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/ST_cythonize@1810 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: a23746a3dd427edc958b375f9f0ac4b4d2901fcb

11 files changed, 325 insertions, 88 deletions

diff --git a/biblio/how_to_cite_gudhi.bib b/biblio/how_to_cite_gudhi.bib
index 7e1eac4f..03c05728 100644
--- a/biblio/how_to_cite_gudhi.bib
+++ b/biblio/how_to_cite_gudhi.bib
@@ -33,7 +33,7 @@
 , year =        2015
 }
 
-@incollection{gudhi:Skeleton-Blocker
+@incollection{gudhi:SkeletonBlocker
 , author =  "David Salinas"
 , title =   "Skeleton-Blocker"
 , publisher =  "{GUDHI Editorial Board}"
@@ -42,7 +42,7 @@
 , year =        2015
 }
 
-@incollection{gudhi:Alpha complex
+@incollection{gudhi:AlphaComplex
 , author =  "Vincent Rouvreau"
 , title =   "Alpha complex"
 , publisher =  "{GUDHI Editorial Board}"
@@ -51,7 +51,7 @@
 , year =        2015
 }
 
-@incollection{gudhi:Cubical complex
+@incollection{gudhi:CubicalComplex
 , author =  "Pawel Dlotko"
 , title =   "Cubical complex"
 , publisher =  "{GUDHI Editorial Board}"
@@ -60,7 +60,7 @@
 , year =        2015
 }
 
-@incollection{gudhi:Witness complex
+@incollection{gudhi:WitnessComplex
 , author =  "Siargey Kachanovich"
 , title =   "Witness complex"
 , publisher =  "{GUDHI Editorial Board}"
@@ -69,8 +69,8 @@
 , year =        2015
 }
 
-@incollection{gudhi:Subsampling
-, author =  "Cl\'ement Jamin"
+@incollection{gudhi:SubSampling
+, author =  "Cl\'ement Jamin, Siargey Kachanovich"
 , title =   "Subsampling"
 , publisher =  "{GUDHI Editorial Board}"
 , booktitle =   "{GUDHI} User and Reference Manual"
@@ -78,7 +78,7 @@
 , year =        2016
 }
 
-@incollection{gudhi:Spatial searching
+@incollection{gudhi:SpatialSearching
 , author =  "Cl\'ement Jamin"
 , title =   "Spatial searching"
 , publisher =  "{GUDHI Editorial Board}"
@@ -87,7 +87,7 @@
 , year =        2016
 }
 
-@incollection{gudhi:Tangential complex
+@incollection{gudhi:TangentialComplex
 , author =  "Cl\'ement Jamin"
 , title =   "Tangential complex"
 , publisher =  "{GUDHI Editorial Board}"
diff --git a/src/Alpha_complex/include/gudhi/Alpha_complex.h b/src/Alpha_complex/include/gudhi/Alpha_complex.h
index f2a222c1..9d5a9bad 100644
--- a/src/Alpha_complex/include/gudhi/Alpha_complex.h
+++ b/src/Alpha_complex/include/gudhi/Alpha_complex.h
@@ -171,35 +171,58 @@ class Alpha_complex {
     return vertex_handle_to_iterator_.at(vertex)->point();
   }
 
+  /** \brief number_of_vertices returns the number of vertices (same as the number of points).
+   *
+   * @return The number of vertices.
+   */
+  const std::size_t number_of_vertices() const {
+    return vertex_handle_to_iterator_.size();
+  }
+
  private:
   template<typename InputPointRange >
   void init_from_range(const InputPointRange& points) {
     auto first = std::begin(points);
     auto last = std::end(points);
-    // point_dimension function initialization
-    Point_Dimension point_dimension = kernel_.point_dimension_d_object();
-
-    // Delaunay triangulation is point dimension.
-    triangulation_ = new Delaunay_triangulation(point_dimension(*first));
-
-    std::vector<Point_d> point_cloud(first, last);
-
-    // Creates a vector {0, 1, ..., N-1}
-    std::vector<std::ptrdiff_t> indices(boost::counting_iterator<std::ptrdiff_t>(0),
-                                        boost::counting_iterator<std::ptrdiff_t>(point_cloud.size()));
-
-    typedef boost::iterator_property_map<typename std::vector<Point_d>::iterator,
-                                         CGAL::Identity_property_map<std::ptrdiff_t>> Point_property_map;
-    typedef CGAL::Spatial_sort_traits_adapter_d<Kernel, Point_property_map> Search_traits_d;
-    
-    CGAL::spatial_sort(indices.begin(), indices.end(), Search_traits_d(std::begin(point_cloud)));
-
-    typename Delaunay_triangulation::Full_cell_handle hint;
-    for (auto index : indices) {
-      typename Delaunay_triangulation::Vertex_handle pos = triangulation_->insert(point_cloud[index], hint);
-      // Save index value as data to retrieve it after insertion
-      pos->data() = index;
-      hint = pos->full_cell();
+
+    if (first != last) {
+      // point_dimension function initialization
+      Point_Dimension point_dimension = kernel_.point_dimension_d_object();
+
+      // Delaunay triangulation is point dimension.
+      triangulation_ = new Delaunay_triangulation(point_dimension(*first));
+
+      std::vector<Point_d> point_cloud(first, last);
+  
+      // Creates a vector {0, 1, ..., N-1}
+      std::vector<std::ptrdiff_t> indices(boost::counting_iterator<std::ptrdiff_t>(0),
+                                          boost::counting_iterator<std::ptrdiff_t>(point_cloud.size()));
+  
+      typedef boost::iterator_property_map<typename std::vector<Point_d>::iterator,
+                                           CGAL::Identity_property_map<std::ptrdiff_t>> Point_property_map;
+      typedef CGAL::Spatial_sort_traits_adapter_d<Kernel, Point_property_map> Search_traits_d;
+  
+      CGAL::spatial_sort(indices.begin(), indices.end(), Search_traits_d(std::begin(point_cloud)));
+  
+      typename Delaunay_triangulation::Full_cell_handle hint;
+      for (auto index : indices) {
+        typename Delaunay_triangulation::Vertex_handle pos = triangulation_->insert(point_cloud[index], hint);
+        // Save index value as data to retrieve it after insertion
+        pos->data() = index;
+        hint = pos->full_cell();
+      }
+      // --------------------------------------------------------------------------------------------
+      // double map to retrieve simplex tree vertex handles from CGAL vertex iterator and vice versa
+      // Loop on triangulation vertices list
+      for (CGAL_vertex_iterator vit = triangulation_->vertices_begin(); vit != triangulation_->vertices_end(); ++vit) {
+        if (!triangulation_->is_infinite(*vit)) {
+#ifdef DEBUG_TRACES
+          std::cout << "Vertex insertion - " << vit->data() << " -> " << vit->point() << std::endl;
+#endif  // DEBUG_TRACES
+          vertex_handle_to_iterator_.emplace(vit->data(), vit);
+        }
+      }
+      // --------------------------------------------------------------------------------------------
     }
   }
 
@@ -248,19 +271,6 @@ class Alpha_complex {
     complex.set_dimension(triangulation_->maximal_dimension());
 
     // --------------------------------------------------------------------------------------------
-    // double map to retrieve simplex tree vertex handles from CGAL vertex iterator and vice versa
-    // Loop on triangulation vertices list
-    for (CGAL_vertex_iterator vit = triangulation_->vertices_begin(); vit != triangulation_->vertices_end(); ++vit) {
-      if (!triangulation_->is_infinite(*vit)) {
-#ifdef DEBUG_TRACES
-        std::cout << "Vertex insertion - " << vit->data() << " -> " << vit->point() << std::endl;
-#endif  // DEBUG_TRACES
-        vertex_handle_to_iterator_.emplace(vit->data(), vit);
-      }
-    }
-    // --------------------------------------------------------------------------------------------
-
-    // --------------------------------------------------------------------------------------------
     // Simplex_tree construction from loop on triangulation finite full cells list
     if (triangulation_->number_of_vertices() > 0) {
       for (auto cit = triangulation_->finite_full_cells_begin(); cit != triangulation_->finite_full_cells_end(); ++cit) {
diff --git a/src/Alpha_complex/test/Alpha_complex_unit_test.cpp b/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
index fc53eeeb..7380547f 100644
--- a/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
+++ b/src/Alpha_complex/test/Alpha_complex_unit_test.cpp
@@ -36,12 +36,17 @@
 // to construct a simplex_tree from Delaunay_triangulation
 #include <gudhi/graph_simplicial_complex.h>
 #include <gudhi/Simplex_tree.h>
+#include <boost/mpl/list.hpp>
 
 // Use dynamic_dimension_tag for the user to be able to set dimension
 typedef CGAL::Epick_d< CGAL::Dynamic_dimension_tag > Kernel_d;
+// Use static dimension_tag for the user not to be able to set dimension
+typedef CGAL::Epick_d< CGAL::Dimension_tag<2> > Kernel_s;
 // The triangulation uses the default instantiation of the TriangulationDataStructure template parameter
 
-BOOST_AUTO_TEST_CASE(ALPHA_DOC_OFF_file) {
+typedef boost::mpl::list<Kernel_d, Kernel_s> list_of_kernel_variants;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(Alpha_complex_from_OFF_file, TestedKernel, list_of_kernel_variants) {
   // ----------------------------------------------------------------------------
   //
   // Init of an alpha-complex from a OFF file
@@ -52,7 +57,11 @@ BOOST_AUTO_TEST_CASE(ALPHA_DOC_OFF_file) {
   std::cout << "========== OFF FILE NAME = " << off_file_name << " - alpha²=" <<
       max_alpha_square_value << "==========" << std::endl;
 
-  Gudhi::alpha_complex::Alpha_complex<Kernel_d> alpha_complex_from_file(off_file_name);
+  Gudhi::alpha_complex::Alpha_complex<TestedKernel> alpha_complex_from_file(off_file_name);
+
+  std::cout << "alpha_complex_from_points.number_of_vertices()=" << alpha_complex_from_file.number_of_vertices()
+      << std::endl;
+  BOOST_CHECK(alpha_complex_from_file.number_of_vertices() == 7);
 
   Gudhi::Simplex_tree<> simplex_tree_60;
   BOOST_CHECK(alpha_complex_from_file.create_complex(simplex_tree_60, max_alpha_square_value));
@@ -60,6 +69,10 @@ BOOST_AUTO_TEST_CASE(ALPHA_DOC_OFF_file) {
   std::cout << "simplex_tree_60.dimension()=" << simplex_tree_60.dimension() << std::endl;
   BOOST_CHECK(simplex_tree_60.dimension() == 2);
 
+  std::cout << "alpha_complex_from_points.number_of_vertices()=" << alpha_complex_from_file.number_of_vertices()
+      << std::endl;
+  BOOST_CHECK(alpha_complex_from_file.number_of_vertices() == 7);
+
   std::cout << "simplex_tree_60.num_vertices()=" << simplex_tree_60.num_vertices() << std::endl;
   BOOST_CHECK(simplex_tree_60.num_vertices() == 7);
 
@@ -87,13 +100,12 @@ bool are_almost_the_same(float a, float b) {
   return std::fabs(a - b) < std::numeric_limits<float>::epsilon();
 }
 
-// Use dynamic_dimension_tag for the user to be able to set dimension
-typedef CGAL::Epick_d< CGAL::Dimension_tag<4> > Kernel_s;
-typedef Kernel_s::Point_d Point;
-typedef std::vector<Point> Vector_of_points;
-
+// Use static dimension_tag for the user not to be able to set dimension
+typedef CGAL::Epick_d< CGAL::Dimension_tag<4> > Kernel_4;
+typedef Kernel_4::Point_d Point_4;
+typedef std::vector<Point_4> Vector_4_Points;
 
-bool is_point_in_list(Vector_of_points points_list, Point point) {
+bool is_point_in_list(Vector_4_Points points_list, Point_4 point) {
   for (auto& point_in_list : points_list) {
     if (point_in_list == point) {
       return true;  // point found
@@ -106,26 +118,30 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_from_points) {
   // ----------------------------------------------------------------------------
   // Init of a list of points
   // ----------------------------------------------------------------------------
-  Vector_of_points points;
+  Vector_4_Points points;
   std::vector<double> coords = { 0.0, 0.0, 0.0, 1.0 };
-  points.push_back(Point(coords.begin(), coords.end()));
+  points.push_back(Point_4(coords.begin(), coords.end()));
   coords = { 0.0, 0.0, 1.0, 0.0 };
-  points.push_back(Point(coords.begin(), coords.end()));
+  points.push_back(Point_4(coords.begin(), coords.end()));
   coords = { 0.0, 1.0, 0.0, 0.0 };
-  points.push_back(Point(coords.begin(), coords.end()));
+  points.push_back(Point_4(coords.begin(), coords.end()));
   coords = { 1.0, 0.0, 0.0, 0.0 };
-  points.push_back(Point(coords.begin(), coords.end()));
+  points.push_back(Point_4(coords.begin(), coords.end()));
 
   // ----------------------------------------------------------------------------
   // Init of an alpha complex from the list of points
   // ----------------------------------------------------------------------------
-  Gudhi::alpha_complex::Alpha_complex<Kernel_s> alpha_complex_from_points(points);
+  Gudhi::alpha_complex::Alpha_complex<Kernel_4> alpha_complex_from_points(points);
 
   std::cout << "========== Alpha_complex_from_points ==========" << std::endl;
 
   Gudhi::Simplex_tree<> simplex_tree;
   BOOST_CHECK(alpha_complex_from_points.create_complex(simplex_tree));
   
+  std::cout << "alpha_complex_from_points.number_of_vertices()=" << alpha_complex_from_points.number_of_vertices()
+      << std::endl;
+  BOOST_CHECK(alpha_complex_from_points.number_of_vertices() == points.size());
+
   // Another way to check num_simplices
   std::cout << "Iterator on alpha complex simplices in the filtration order, with [filtration value]:" << std::endl;
   int num_simplices = 0;
@@ -167,22 +183,22 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_from_points) {
     }
   }
 
-  Point p0 = alpha_complex_from_points.get_point(0);
+  Point_4 p0 = alpha_complex_from_points.get_point(0);
   std::cout << "alpha_complex_from_points.get_point(0)=" << p0 << std::endl;
   BOOST_CHECK(4 == p0.dimension());
   BOOST_CHECK(is_point_in_list(points, p0));
 
-  Point p1 = alpha_complex_from_points.get_point(1);
+  Point_4 p1 = alpha_complex_from_points.get_point(1);
   std::cout << "alpha_complex_from_points.get_point(1)=" << p1 << std::endl;
   BOOST_CHECK(4 == p1.dimension());
   BOOST_CHECK(is_point_in_list(points, p1));
 
-  Point p2 = alpha_complex_from_points.get_point(2);
+  Point_4 p2 = alpha_complex_from_points.get_point(2);
   std::cout << "alpha_complex_from_points.get_point(2)=" << p2 << std::endl;
   BOOST_CHECK(4 == p2.dimension());
   BOOST_CHECK(is_point_in_list(points, p2));
 
-  Point p3 = alpha_complex_from_points.get_point(3);
+  Point_4 p3 = alpha_complex_from_points.get_point(3);
   std::cout << "alpha_complex_from_points.get_point(3)=" << p3 << std::endl;
   BOOST_CHECK(4 == p3.dimension());
   BOOST_CHECK(is_point_in_list(points, p3));
@@ -236,31 +252,35 @@ BOOST_AUTO_TEST_CASE(Alpha_complex_from_points) {
 
 }
 
-BOOST_AUTO_TEST_CASE(Alpha_complex_from_empty_points) {
+BOOST_AUTO_TEST_CASE_TEMPLATE(Alpha_complex_from_empty_points, TestedKernel, list_of_kernel_variants) {
+  std::cout << "========== Alpha_complex_from_empty_points ==========" << std::endl;
+
   // ----------------------------------------------------------------------------
-  // Init of a list of points
+  // Init of an empty list of points
   // ----------------------------------------------------------------------------
-  Vector_of_points points;
+  std::vector<typename TestedKernel::Point_d> points;
 
   // ----------------------------------------------------------------------------
   // Init of an alpha complex from the list of points
   // ----------------------------------------------------------------------------
-  Gudhi::alpha_complex::Alpha_complex<Kernel_s> alpha_complex_from_points(points);
+  Gudhi::alpha_complex::Alpha_complex<TestedKernel> alpha_complex_from_points(points);
 
-  std::cout << "========== Alpha_complex_from_empty_points ==========" << std::endl;
+  // Test to the limit
+  BOOST_CHECK_THROW (alpha_complex_from_points.get_point(0), std::out_of_range);
 
   Gudhi::Simplex_tree<> simplex_tree;
-  BOOST_CHECK(alpha_complex_from_points.create_complex(simplex_tree));
+  BOOST_CHECK(!alpha_complex_from_points.create_complex(simplex_tree));
   
+  std::cout << "alpha_complex_from_points.number_of_vertices()=" << alpha_complex_from_points.number_of_vertices()
+      << std::endl;
+  BOOST_CHECK(alpha_complex_from_points.number_of_vertices() == points.size());
+
   std::cout << "simplex_tree.num_simplices()=" << simplex_tree.num_simplices() << std::endl;
   BOOST_CHECK(simplex_tree.num_simplices() == 0);
 
   std::cout << "simplex_tree.dimension()=" << simplex_tree.dimension() << std::endl;
-  BOOST_CHECK(simplex_tree.dimension() == 4);
+  BOOST_CHECK(simplex_tree.dimension() == -1);
   
   std::cout << "simplex_tree.num_vertices()=" << simplex_tree.num_vertices() << std::endl;
   BOOST_CHECK(simplex_tree.num_vertices() == 0);
-
-  // Test to the limit
-  BOOST_CHECK_THROW (alpha_complex_from_points.get_point(0), std::out_of_range);
 }
diff --git a/src/Subsampling/include/gudhi/choose_n_farthest_points.h b/src/Subsampling/include/gudhi/choose_n_farthest_points.h
index 40c7808d..9b45c640 100644
--- a/src/Subsampling/include/gudhi/choose_n_farthest_points.h
+++ b/src/Subsampling/include/gudhi/choose_n_farthest_points.h
@@ -60,10 +60,15 @@ void choose_n_farthest_points(Kernel const &k,
                               std::size_t final_size,
                               std::size_t starting_point,
                               OutputIterator output_it) {
-  typename Kernel::Squared_distance_d sqdist = k.squared_distance_d_object();
-
   std::size_t nb_points = boost::size(input_pts);
-  assert(nb_points >= final_size);
+  if (final_size > nb_points)
+    final_size = nb_points;
+
+  // Tests to the limit
+  if (final_size < 1)
+    return;
+
+  typename Kernel::Squared_distance_d sqdist = k.squared_distance_d_object();
 
   std::size_t current_number_of_landmarks = 0;  // counter for landmarks
   const double infty = std::numeric_limits<double>::infinity();  // infinity (see next entry)
@@ -107,11 +112,16 @@ void choose_n_farthest_points(Kernel const& k,
                               Point_container const &input_pts,
                               unsigned final_size,
                               OutputIterator output_it) {
+  // Tests to the limit
+  if ((final_size < 1) || (input_pts.size() == 0))
+    return;
+
   // Choose randomly the first landmark
   std::random_device rd;
   std::mt19937 gen(rd());
-  std::uniform_int_distribution<> dis(1, 6);
-  int starting_point = dis(gen);
+  std::uniform_int_distribution<> dis(0, (input_pts.size() - 1));
+  std::size_t starting_point = dis(gen);
+
   choose_n_farthest_points(k, input_pts, final_size, starting_point, output_it);
 }
 
diff --git a/src/Subsampling/test/test_choose_n_farthest_points.cpp b/src/Subsampling/test/test_choose_n_farthest_points.cpp
index d064899a..0bc0dff4 100644
--- a/src/Subsampling/test/test_choose_n_farthest_points.cpp
+++ b/src/Subsampling/test/test_choose_n_farthest_points.cpp
@@ -39,18 +39,65 @@ typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K;
 typedef typename K::FT FT;
 typedef typename K::Point_d Point_d;
 
-BOOST_AUTO_TEST_CASE(test_choose_farthest_point) {
+typedef boost::mpl::list<CGAL::Epick_d<CGAL::Dynamic_dimension_tag>, CGAL::Epick_d<CGAL::Dimension_tag<4>>> list_of_tested_kernels;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(test_choose_farthest_point, Kernel, list_of_tested_kernels) {
+  typedef typename Kernel::FT FT;
+  typedef typename Kernel::Point_d Point_d;
   std::vector< Point_d > points, landmarks;
   // Add grid points (625 points)
   for (FT i = 0; i < 5; i += 1.0)
     for (FT j = 0; j < 5; j += 1.0)
       for (FT k = 0; k < 5; k += 1.0)
-        for (FT l = 0; l < 5; l += 1.0)
-          points.push_back(Point_d(std::vector<FT>({i, j, k, l})));
+        for (FT l = 0; l < 5; l += 1.0) {
+          std::vector<FT> point({i, j, k, l});
+          points.push_back(Point_d(point.begin(), point.end()));
+        }
 
   landmarks.clear();
-  K k;
+  Kernel k;
   Gudhi::subsampling::choose_n_farthest_points(k, points, 100, std::back_inserter(landmarks));
 
   BOOST_CHECK(landmarks.size() == 100);
+  for (auto landmark : landmarks)
+  {
+    // Check all landmarks are in points
+    BOOST_CHECK(std::find (points.begin(), points.end(), landmark) != points.end());
+  }
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE(test_choose_farthest_point_limits, Kernel, list_of_tested_kernels) {
+  typedef typename Kernel::FT FT;
+  typedef typename Kernel::Point_d Point_d;
+  std::vector< Point_d > points, landmarks;
+  landmarks.clear();
+  Kernel k;
+  // Choose -1 farthest points in an empty point cloud
+  Gudhi::subsampling::choose_n_farthest_points(k, points, -1, std::back_inserter(landmarks));
+  BOOST_CHECK(landmarks.size() == 0);
+  landmarks.clear();
+  // Choose 0 farthest points in an empty point cloud
+  Gudhi::subsampling::choose_n_farthest_points(k, points, 0, std::back_inserter(landmarks));
+  BOOST_CHECK(landmarks.size() == 0);
+  landmarks.clear();
+  // Choose 1 farthest points in an empty point cloud
+  Gudhi::subsampling::choose_n_farthest_points(k, points, 1, std::back_inserter(landmarks));
+  BOOST_CHECK(landmarks.size() == 0);
+  landmarks.clear();
+
+  std::vector<FT> point({0.0, 0.0, 0.0, 0.0});
+  points.push_back(Point_d(point.begin(), point.end()));
+  // Choose -1 farthest points in an empty point cloud
+  Gudhi::subsampling::choose_n_farthest_points(k, points, -1, std::back_inserter(landmarks));
+  BOOST_CHECK(landmarks.size() == 1);
+  landmarks.clear();
+  // Choose 0 farthest points in a one point cloud
+  Gudhi::subsampling::choose_n_farthest_points(k, points, 0, std::back_inserter(landmarks));
+  BOOST_CHECK(landmarks.size() == 0);
+  landmarks.clear();
+  // Choose 1 farthest points in a one point cloud
+  Gudhi::subsampling::choose_n_farthest_points(k, points, 1, std::back_inserter(landmarks));
+  BOOST_CHECK(landmarks.size() == 1);
+  landmarks.clear();
+
 }
diff --git a/src/Tangential_complex/benchmark/CMakeLists.txt b/src/Tangential_complex/benchmark/CMakeLists.txt
index a217d6e6..56dd8128 100644
--- a/src/Tangential_complex/benchmark/CMakeLists.txt
+++ b/src/Tangential_complex/benchmark/CMakeLists.txt
@@ -16,7 +16,7 @@ if(CGAL_FOUND)
     if (EIGEN3_FOUND)
       add_executable(Tangential_complex_benchmark benchmark_tc.cpp)
       target_link_libraries(Tangential_complex_benchmark 
-		${Boost_DATE_TIME_LIBRARY} ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
+        ${Boost_DATE_TIME_LIBRARY} ${Boost_SYSTEM_LIBRARY} ${CGAL_LIBRARY})
       if (TBB_FOUND)
         target_link_libraries(Tangential_complex_benchmark ${TBB_LIBRARIES})
       endif(TBB_FOUND)
diff --git a/src/cython/CMakeLists.txt b/src/cython/CMakeLists.txt
index c2026682..998908e7 100644
--- a/src/cython/CMakeLists.txt
+++ b/src/cython/CMakeLists.txt
@@ -47,7 +47,7 @@ if(PYTHON_PATH AND CYTHON_PATH)
     file(COPY include DESTINATION ${CMAKE_CURRENT_BINARY_DIR})
     file(COPY cython DESTINATION ${CMAKE_CURRENT_BINARY_DIR})
     file(COPY test DESTINATION ${CMAKE_CURRENT_BINARY_DIR})
-    
+
     if (CGAL_FOUND)
       if (NOT CGAL_VERSION VERSION_LESS 4.8.1)
           # If CGAL_VERSION >= 4.8.1, include subsampling
diff --git a/src/cython/cython/alpha_complex.pyx b/src/cython/cython/alpha_complex.pyx
index 56cf925c..6b27594a 100644
--- a/src/cython/cython/alpha_complex.pyx
+++ b/src/cython/cython/alpha_complex.pyx
@@ -62,7 +62,7 @@ cdef class AlphaComplex:
     cdef Alpha_complex_interface * thisptr
 
     # Fake constructor that does nothing but documenting the constructor
-    def __init__(self, points=None, off_file=''):
+    def __init__(self, points=[], off_file=''):
         """AlphaComplex constructor.
 
         :param points: A list of points in d-Dimension.
diff --git a/src/cython/cython/subsampling.pyx b/src/cython/cython/subsampling.pyx
index e59e0c6a..5ca38099 100644
--- a/src/cython/cython/subsampling.pyx
+++ b/src/cython/cython/subsampling.pyx
@@ -32,6 +32,42 @@ __license__ = "GPL v3"
 
 cdef extern from "Subsampling_interface.h" namespace "Gudhi::subsampling":
     vector[vector[double]] subsampling_n_farthest_points(vector[vector[double]] points, unsigned nb_points)
+    vector[vector[double]] subsampling_n_farthest_points(vector[vector[double]] points, unsigned nb_points, unsigned starting_point)
+    vector[vector[double]] subsampling_n_farthest_points_from_file(string off_file, unsigned nb_points)
+    vector[vector[double]] subsampling_n_farthest_points_from_file(string off_file, unsigned nb_points, unsigned starting_point)
 
-def choose_n_farthest_points(points, nb_points):
-    subsampling_n_farthest_points(points, nb_points)
+def choose_n_farthest_points(points=[], off_file='', nb_points=0, starting_point = ''):
+    """Subsample by a greedy strategy of iteratively adding the farthest point
+    from the current chosen point set to the subsampling.
+    The iteration starts with the landmark `starting point`.
+
+    :param points: The input point set.
+    :type points: vector[vector[double]].
+
+    Or
+
+    :param off_file: An OFF file style name.
+    :type off_file: string
+
+    :param nb_points: Number of points of the subsample.
+    :type nb_points: unsigned.
+    :param starting_point: The iteration starts with the landmark `starting \
+    point`,which is the index of the poit to start with. If not set, this \
+    index is choosen randomly.
+    :type starting_point: unsigned.
+    :returns:  The subsamplepoint set.
+    :rtype: vector[vector[double]]
+    """
+    if off_file is not '':
+        if os.path.isfile(off_file):
+            if starting_point is '':
+                return subsampling_n_farthest_points_from_file(off_file, nb_points)
+            else:
+                return subsampling_n_farthest_points_from_file(off_file, nb_points, starting_point)
+        else:
+            print("file " + off_file + " not found.")
+    else:
+        if starting_point is '':
+            return subsampling_n_farthest_points(points, nb_points)
+        else:
+            return subsampling_n_farthest_points(points, nb_points, starting_point)
diff --git a/src/cython/include/Subsampling_interface.h b/src/cython/include/Subsampling_interface.h
index bd37a015..12c48012 100644
--- a/src/cython/include/Subsampling_interface.h
+++ b/src/cython/include/Subsampling_interface.h
@@ -45,12 +45,32 @@ std::vector<std::vector<double>> subsampling_n_farthest_points(std::vector<std::
   std::vector<std::vector<double>> landmarks;
   Subsampling_dynamic_kernel k;
   choose_n_farthest_points(k, points, nb_points, std::back_inserter(landmarks));
-  std::cout << "output " << landmarks.size() << std::endl;
 
+  return landmarks;
+}
+
+std::vector<std::vector<double>> subsampling_n_farthest_points(std::vector<std::vector<double>>& points, unsigned nb_points, unsigned starting_point) {
+  std::vector<Subsampling_point_d> input, output;
+  for (auto point : points)
+      input.push_back(Subsampling_point_d(point.size(), point.begin(), point.end()));
+  std::vector<std::vector<double>> landmarks;
+  Subsampling_dynamic_kernel k;
+  choose_n_farthest_points(k, points, nb_points, starting_point, std::back_inserter(landmarks));
 
   return landmarks;
 }
 
+std::vector<std::vector<double>> subsampling_n_farthest_points_from_file(std::string& off_file, unsigned nb_points) {
+  Gudhi::Points_off_reader<std::vector<double>> off_reader(off_file);
+  std::vector<std::vector<double>> points = off_reader.get_point_cloud();
+  return subsampling_n_farthest_points(points, nb_points);
+}
+
+std::vector<std::vector<double>> subsampling_n_farthest_points_from_file(std::string& off_file, unsigned nb_points, unsigned starting_point) {
+    Gudhi::Points_off_reader<std::vector<double>> off_reader(off_file);
+    std::vector<std::vector<double>> points = off_reader.get_point_cloud();
+    return subsampling_n_farthest_points(points, nb_points, starting_point);
+}
 }  // namespace subsampling
 
 }  // namespace Gudhi
diff --git a/src/cython/test/test_subsampling.py b/src/cython/test/test_subsampling.py
new file mode 100755
index 00000000..e5f2d70a
--- /dev/null
+++ b/src/cython/test/test_subsampling.py
@@ -0,0 +1,94 @@
+import gudhi
+import os
+
+"""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) 2016 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/>.
+"""
+
+__author__ = "Vincent Rouvreau"
+__copyright__ = "Copyright (C) 2016 INRIA"
+__license__ = "GPL v3"
+
+
+def test_write_off_file_for_tests():
+    file = open("n_farthest.off", "w")
+    file.write("nOFF\n")
+    file.write("2 7 0 0\n")
+    file.write("1.0 1.0\n")
+    file.write("7.0 0.0\n")
+    file.write("4.0 6.0\n")
+    file.write("9.0 6.0\n")
+    file.write("0.0 14.0\n")
+    file.write("2.0 19.0\n")
+    file.write("9.0 17.0\n")
+    file.close()
+
+def test_simple_choose_n_farthest_points_with_a_starting_point():
+    point_set = [[0,1], [0,0], [1,0], [1,1]]
+    i = 0
+    for point in point_set:
+        # The iteration starts with the given starting point
+        sub_set = gudhi.choose_n_farthest_points(points = point_set, nb_points = 1, starting_point = i)
+        assert sub_set[0] == point_set[i]
+        i = i + 1
+
+    # The iteration finds then the farthest
+    sub_set = gudhi.choose_n_farthest_points(points = point_set, nb_points = 2, starting_point = 1)
+    assert sub_set[1] == point_set[3]
+    sub_set = gudhi.choose_n_farthest_points(points = point_set, nb_points = 2, starting_point = 3)
+    assert sub_set[1] == point_set[1]
+    sub_set = gudhi.choose_n_farthest_points(points = point_set, nb_points = 2, starting_point = 0)
+    assert sub_set[1] == point_set[2]
+    sub_set = gudhi.choose_n_farthest_points(points = point_set, nb_points = 2, starting_point = 2)
+    assert sub_set[1] == point_set[0]
+
+    # Test the limits
+    assert gudhi.choose_n_farthest_points(points = [], nb_points = 0, starting_point = 0) == []
+    assert gudhi.choose_n_farthest_points(points = [], nb_points = 1, starting_point = 0) == []
+    assert gudhi.choose_n_farthest_points(points = [], nb_points = 0, starting_point = 1) == []
+    assert gudhi.choose_n_farthest_points(points = [], nb_points = 1, starting_point = 1) == []
+
+    print(os.getcwd())
+    # From off file test
+    for i in range (0, 7):
+        assert len(gudhi.choose_n_farthest_points(off_file = 'n_farthest.off', nb_points = i, starting_point = i)) == i
+
+def test_simple_choose_n_farthest_points_randomed():
+    point_set = [[0,1], [0,0], [1,0], [1,1]]
+
+    # Test the limits
+    assert gudhi.choose_n_farthest_points(points = [], nb_points = 0) == []
+    assert gudhi.choose_n_farthest_points(points = [], nb_points = 1) == []
+    assert gudhi.choose_n_farthest_points(points = point_set, nb_points = 0) == []
+    # Go furter than point set on purpose
+    for iter in range(1,10):
+        sub_set = gudhi.choose_n_farthest_points(points = point_set, nb_points = iter)
+        for sub in sub_set:
+            found = False
+            for point in point_set:
+                if point == sub:
+                    found = True
+            assert found == True
+
+    print(os.getcwd())
+    # From off file test
+    for i in range (0, 7):
+        assert len(gudhi.choose_n_farthest_points(off_file = 'n_farthest.off', nb_points = i)) == i