Added the Euclidean files -_-

git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/relaxed-witness@1981 636b058d-ea47-450e-bf9e-a15bfbe3eedb

Former-commit-id: e7b06da298f5cf07658dc20302eb1da9a08b424c

2 files changed, 441 insertions, 0 deletions

diff --git a/src/Witness_complex/include/gudhi/Euclidean_strong_witness_complex.h b/src/Witness_complex/include/gudhi/Euclidean_strong_witness_complex.h
new file mode 100644
index 00000000..38fa5c22
--- /dev/null
+++ b/src/Witness_complex/include/gudhi/Euclidean_strong_witness_complex.h
@@ -0,0 +1,208 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA (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 EUCLIDEAN_STRONG_WITNESS_COMPLEX_H_
+#define EUCLIDEAN_STRONG_WITNESS_COMPLEX_H_
+
+#include <utility>
+#include <vector>
+#include <list>
+#include <limits>
+
+#include <gudhi/Active_witness/Active_witness.h>
+#include <gudhi/Kd_tree_search.h>
+
+namespace Gudhi {
+  
+namespace witness_complex {
+
+/**
+ *  \private
+ * \class Euclidean_strong_witness_complex
+ * \brief Constructs strong witness complex for given sets of witnesses and landmarks in Euclidean space.
+ * \ingroup witness_complex
+ *
+ * \tparam Kernel_ requires a <a target="_blank"
+ * href="http://doc.cgal.org/latest/Kernel_d/classCGAL_1_1Epick__d.html">CGAL::Epick_d</a> class.
+ */
+template< class Kernel_ >
+class Euclidean_strong_witness_complex {
+private:
+  typedef Kernel_                                                                      K;
+  typedef typename K::Point_d                                                          Point_d;
+  typedef typename K::FT                                                               FT;
+  typedef std::vector<Point_d>                                                         Point_range;
+  typedef Gudhi::spatial_searching::Kd_tree_search<Kernel_, Point_range>               Kd_tree;
+  typedef typename Kd_tree::INS_range                                                  Nearest_landmark_range;
+  typedef typename std::vector<Nearest_landmark_range>                                 Nearest_landmark_table;
+  typedef typename Nearest_landmark_range::iterator                                    Nearest_landmark_row_iterator;
+  
+  typedef FT Filtration_value;
+
+  
+  typedef std::size_t Witness_id;
+  typedef typename Nearest_landmark_range::Point_with_transformed_distance Id_distance_pair;
+  typedef typename Id_distance_pair::first_type Landmark_id;
+  typedef Active_witness<Id_distance_pair, Nearest_landmark_range> ActiveWitness;
+  typedef std::list< ActiveWitness > ActiveWitnessList;
+  typedef std::vector< Landmark_id > typeVectorVertex;
+  typedef std::pair< typeVectorVertex, Filtration_value> typeSimplex;
+
+  typedef Landmark_id Vertex_handle;
+  
+ private:
+  Point_range                         witnesses_, landmarks_;
+  Kd_tree                             landmark_tree_;
+  
+ public:
+  /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  /* @name Constructor
+   */
+
+  //@{
+
+  /**
+   *  \brief Initializes member variables before constructing simplicial complex.
+   *  \details Records landmarks from the range 'landmarks' into a 
+   *           table internally, as well as witnesses from the range 'witnesses'.
+   *           Both ranges should have value_type Kernel_::Point_d.
+   */
+  template< typename LandmarkRange,
+            typename WitnessRange >
+  Euclidean_strong_witness_complex(const LandmarkRange & landmarks,
+                         const WitnessRange &  witnesses)
+    : witnesses_(witnesses), landmarks_(landmarks), landmark_tree_(landmarks_)
+  {    
+  }
+
+  
+  /** \brief Returns the point corresponding to the given vertex.
+   */
+  template <typename Vertex_handle> 
+  Point_d get_point( Vertex_handle vertex ) const
+  {
+    return landmarks_[vertex];
+  }
+  
+  /** \brief Outputs the strong witness complex of relaxation 'max_alpha_square' 
+   *         in a simplicial complex data structure.
+   *  \details The function returns true if the construction is successful and false otherwise.
+   *  @param[out] complex Simplicial complex data structure, which is a model of
+   *              SimplicialComplexForWitness concept.
+   *  @param[in] max_alpha_square Maximal squared relaxation parameter.
+   *  @param[in] limit_dimension Represents the maximal dimension of the simplicial complex
+   *         (default value = no limit).
+   */
+  template < typename SimplicialComplexForWitness >
+  bool create_complex(SimplicialComplexForWitness& complex,
+                      FT  max_alpha_square,
+                      Landmark_id limit_dimension = std::numeric_limits<Landmark_id>::max()-1)       
+  {
+    Landmark_id complex_dim = 0;
+    if (complex.num_vertices() > 0) {
+      std::cerr << "Euclidean strong witness complex cannot create complex - complex is not empty.\n";
+      return false;
+    }
+    if (max_alpha_square < 0) {
+      std::cerr << "Euclidean strong witness complex cannot create complex - squared relaxation parameter must be non-negative.\n";
+      return false;
+    }
+    if (limit_dimension < 0) {
+      std::cerr << "Euclidean strong witness complex cannot create complex - limit dimension must be non-negative.\n";
+      return false;
+    }
+    for (auto w: witnesses_) {
+      ActiveWitness aw(landmark_tree_.query_incremental_nearest_neighbors(w));
+      typeVectorVertex simplex;
+      typename ActiveWitness::iterator aw_it = aw.begin();
+      float lim_dist2 = aw.begin()->second + max_alpha_square;
+      while ((Landmark_id)simplex.size() < limit_dimension + 1 && aw_it != aw.end() && aw_it->second < lim_dist2) {
+        simplex.push_back(aw_it->first);
+        complex.insert_simplex_and_subfaces(simplex, aw_it->second - aw.begin()->second);
+        aw_it++;
+      }
+      // continue inserting limD-faces of the following simplices
+      typeVectorVertex& vertices = simplex; //'simplex' now will be called vertices
+      while (aw_it != aw.end() && aw_it->second < lim_dist2) {
+        typeVectorVertex facet = {};
+        add_all_faces_of_dimension(limit_dimension, vertices, vertices.begin(), aw_it, aw_it->second - aw.begin()->second, facet, complex);
+        vertices.push_back(aw_it->first);
+        aw_it++;
+      }
+      if ((Landmark_id)simplex.size() - 1 > complex_dim)
+        complex_dim = simplex.size() - 1;
+    }
+    complex.set_dimension(complex_dim);
+    return true;
+  }
+
+private:
+
+    /* \brief Adds recursively all the faces of a certain dimension dim-1 witnessed by the same witness.
+   * Iterator is needed to know until how far we can take landmarks to form simplexes.
+   * simplex is the prefix of the simplexes to insert.
+   * The landmark pointed by aw_it is added to all formed simplices.
+   */
+  template < typename SimplicialComplexForWitness >
+  void add_all_faces_of_dimension(Landmark_id dim,
+                                  typeVectorVertex& vertices,
+                                  typename typeVectorVertex::iterator curr_it,
+                                  typename ActiveWitness::iterator aw_it,
+                                  FT filtration_value,
+                                  typeVectorVertex& simplex,
+                                  SimplicialComplexForWitness& sc) const
+  {
+    if (dim > 0)
+      while (curr_it != vertices.end()) {
+        simplex.push_back(*curr_it);
+        typename typeVectorVertex::iterator next_it = ++curr_it;        
+        add_all_faces_of_dimension(dim-1,
+                                   vertices,
+                                   next_it,
+                                   aw_it,
+                                   filtration_value,
+                                   simplex,
+                                   sc);
+        simplex.pop_back();
+        add_all_faces_of_dimension(dim,
+                                   vertices,
+                                   next_it,
+                                   aw_it,
+                                   filtration_value,
+                                   simplex,
+                                   sc);
+      } 
+    else if (dim == 0) {
+      simplex.push_back(aw_it->first);
+      sc.insert_simplex_and_subfaces(simplex, filtration_value);
+      simplex.pop_back();
+    } 
+  }      
+  
+  //@}
+};
+
+}  // namespace witness_complex
+
+}  // namespace Gudhi
+
+#endif // EUCLIDEAN_STRONG_WITNESS_COMPLEX_H_
diff --git a/src/Witness_complex/include/gudhi/Euclidean_witness_complex.h b/src/Witness_complex/include/gudhi/Euclidean_witness_complex.h
new file mode 100644
index 00000000..7045dc02
--- /dev/null
+++ b/src/Witness_complex/include/gudhi/Euclidean_witness_complex.h
@@ -0,0 +1,233 @@
+/*    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):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2015  INRIA (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 EUCLIDEAN_WITNESS_COMPLEX_H_
+#define EUCLIDEAN_WITNESS_COMPLEX_H_
+
+#include <gudhi/Active_witness/Active_witness.h>
+#include <gudhi/Kd_tree_search.h>
+#include <gudhi/Witness_complex/all_faces_in.h>
+
+#include <utility>
+#include <vector>
+#include <list>
+#include <limits>
+
+namespace Gudhi {
+  
+namespace witness_complex {
+
+/**
+ * \private
+ * \class Euclidean_witness_complex
+ * \brief Constructs (weak) witness complex for given sets of witnesses and landmarks in Euclidean space.
+ * \ingroup witness_complex
+ *
+ * \tparam Kernel_ requires a <a target="_blank"
+ * href="http://doc.cgal.org/latest/Kernel_d/classCGAL_1_1Epick__d.html">CGAL::Epick_d</a> class.
+*/
+template< class Kernel_ >
+class Euclidean_witness_complex {
+private:
+  typedef Kernel_                                                                      K;
+  typedef typename K::Point_d                                                          Point_d;
+  typedef typename K::FT                                                               FT;
+  typedef std::vector<Point_d>                                                         Point_range;
+  typedef Gudhi::spatial_searching::Kd_tree_search<Kernel_, Point_range>               Kd_tree;
+  typedef typename Kd_tree::INS_range                                                  Nearest_landmark_range;
+
+  typedef FT Filtration_value;
+
+  
+  typedef std::size_t Witness_id;
+  typedef typename Nearest_landmark_range::Point_with_transformed_distance Id_distance_pair;
+  typedef typename Id_distance_pair::first_type Landmark_id;
+  typedef Active_witness<Id_distance_pair, Nearest_landmark_range> ActiveWitness;
+  typedef std::list< ActiveWitness > ActiveWitnessList;
+  typedef std::vector< Landmark_id > typeVectorVertex;
+
+  typedef Landmark_id Vertex_handle;
+
+ private:
+  Point_range                         witnesses_, landmarks_;
+  Kd_tree                             landmark_tree_;
+  
+ public:
+  /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  /* @name Constructor
+   */
+
+  //@{
+
+  /**
+   *  \brief Initializes member variables before constructing simplicial complex.
+   *  \details Records landmarks from the range 'landmarks' into a 
+   *           table internally, as well as witnesses from the range 'witnesses'.
+   *           Both ranges should have value_type Kernel_::Point_d.
+   */
+  template< typename LandmarkRange,
+            typename WitnessRange >
+  Euclidean_witness_complex(const LandmarkRange & landmarks,
+                            const WitnessRange &  witnesses)
+    : witnesses_(witnesses), landmarks_(landmarks), landmark_tree_(landmarks_)
+  {    
+  }
+
+  /** \brief Returns the point corresponding to the given vertex.
+   *  @param[in] vertex Vertex handle of the point to retrieve.
+   */
+  Point_d get_point( Vertex_handle vertex ) const
+  {
+    return landmarks_[vertex];
+  }
+  
+  /** \brief Outputs the (weak) witness complex of relaxation 'max_alpha_square'
+   *         in a simplicial complex data structure.
+   *  \details The function returns true if the construction is successful and false otherwise.
+   *  @param[out] complex Simplicial complex data structure compatible which is a model of
+   *              SimplicialComplexForWitness concept.
+   *  @param[in] max_alpha_square Maximal squared relaxation parameter.
+   *  @param[in] limit_dimension Represents the maximal dimension of the simplicial complex
+   *         (default value = no limit).
+   */
+  template < typename SimplicialComplexForWitness >
+  bool create_complex(SimplicialComplexForWitness& complex,
+                      FT  max_alpha_square,
+                      Landmark_id limit_dimension = std::numeric_limits<Landmark_id>::max())      
+  {
+    if (complex.num_vertices() > 0) {
+      std::cerr << "Euclidean witness complex cannot create complex - complex is not empty.\n";
+      return false;
+    }
+    if (max_alpha_square < 0) {
+      std::cerr << "Euclidean witness complex cannot create complex - squared relaxation parameter must be non-negative.\n";
+      return false;
+    }
+    if (limit_dimension < 0) {
+      std::cerr << "Euclidean witness complex cannot create complex - limit dimension must be non-negative.\n";
+      return false;
+    }
+    typeVectorVertex vv;
+    ActiveWitnessList active_witnesses;
+    Landmark_id k = 0; /* current dimension in iterative construction */
+    for (auto w: witnesses_)
+      active_witnesses.push_back(ActiveWitness(landmark_tree_.query_incremental_nearest_neighbors(w)));
+    ActiveWitness aw_copy(active_witnesses.front());
+    while (!active_witnesses.empty() && k <= limit_dimension ) {
+      typename ActiveWitnessList::iterator aw_it = active_witnesses.begin();
+      std::vector<Landmark_id> simplex;
+      simplex.reserve(k+1);
+      while (aw_it != active_witnesses.end()) {
+        bool ok = add_all_faces_of_dimension(k,
+                                             max_alpha_square,
+                                             std::numeric_limits<double>::infinity(),
+                                             aw_it->begin(),
+                                             simplex,
+                                             complex,
+                                             aw_it->end());
+        assert(simplex.empty());
+        if (!ok)
+          active_witnesses.erase(aw_it++); //First increase the iterator and then erase the previous element
+        else
+          aw_it++;
+      } 
+      k++;
+    }
+    complex.set_dimension(k-1);
+    return true;
+  }
+
+  //@}
+
+ private:
+  /* \brief Adds recursively all the faces of a certain dimension dim witnessed by the same witness.
+   * Iterator is needed to know until how far we can take landmarks to form simplexes.
+   * simplex is the prefix of the simplexes to insert.
+   * The output value indicates if the witness rests active or not.
+   */
+  template < typename SimplicialComplexForWitness >
+  bool add_all_faces_of_dimension(int dim,
+                                  double alpha2,
+                                  double norelax_dist2,
+                                  typename ActiveWitness::iterator curr_l,
+                                  std::vector<Landmark_id>& simplex,
+                                  SimplicialComplexForWitness& sc,
+                                  typename ActiveWitness::iterator end) const
+  {
+    if (curr_l == end)
+      return false;
+    bool will_be_active = false;
+    typename ActiveWitness::iterator l_it = curr_l;
+    if (dim > 0)
+      for (; l_it->second - alpha2 <= norelax_dist2 && l_it != end; ++l_it) {
+        simplex.push_back(l_it->first);
+        if (sc.find(simplex) != sc.null_simplex()) {
+          typename ActiveWitness::iterator next_it = l_it;
+          will_be_active = add_all_faces_of_dimension(dim-1,
+                                                      alpha2,
+                                                      norelax_dist2,
+                                                      ++next_it,
+                                                      simplex,
+                                                      sc,
+                                                      end) || will_be_active;
+        }
+        assert(!simplex.empty());
+        simplex.pop_back();
+        // If norelax_dist is infinity, change to first omitted distance
+        if (l_it->second <= norelax_dist2)
+          norelax_dist2 = l_it->second;
+        typename ActiveWitness::iterator next_it = l_it;
+        will_be_active = add_all_faces_of_dimension(dim,
+                                                    alpha2,
+                                                    norelax_dist2,
+                                                    ++next_it,
+                                                    simplex,
+                                                    sc,
+                                                    end) || will_be_active;
+      } 
+    else if (dim == 0)
+      for (; l_it->second - alpha2 <= norelax_dist2 && l_it != end; ++l_it) {
+        simplex.push_back(l_it->first);
+        double filtration_value = 0;
+        // if norelax_dist is infinite, relaxation is 0.
+        if (l_it->second > norelax_dist2) 
+          filtration_value = l_it->second - norelax_dist2;
+        if (all_faces_in(simplex, &filtration_value, sc)) {
+          will_be_active = true;
+          sc.insert_simplex(simplex, filtration_value);
+        }
+        assert(!simplex.empty());
+        simplex.pop_back();
+        // If norelax_dist is infinity, change to first omitted distance
+        if (l_it->second < norelax_dist2)
+          norelax_dist2 = l_it->second;
+      } 
+    return will_be_active;
+  }
+
+};
+  
+}  // namespace witness_complex
+
+}  // namespace Gudhi
+
+#endif  // EUCLIDEAN_WITNESS_COMPLEX_H_