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Diffstat (limited to 'src')
-rw-r--r-- | src/Witness_complex/include/gudhi/Euclidean_strong_witness_complex.h | 208 | ||||
-rw-r--r-- | src/Witness_complex/include/gudhi/Euclidean_witness_complex.h | 233 |
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_ |