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Diffstat (limited to 'trunk/src/Witness_complex/include/gudhi/Witness_complex.h')
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diff --git a/trunk/src/Witness_complex/include/gudhi/Witness_complex.h b/trunk/src/Witness_complex/include/gudhi/Witness_complex.h new file mode 100644 index 00000000..bcfe8484 --- /dev/null +++ b/trunk/src/Witness_complex/include/gudhi/Witness_complex.h @@ -0,0 +1,202 @@ +/* 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 WITNESS_COMPLEX_H_ +#define WITNESS_COMPLEX_H_ + +#include <gudhi/Active_witness/Active_witness.h> +#include <gudhi/Witness_complex/all_faces_in.h> + +#include <utility> +#include <vector> +#include <list> +#include <limits> + +namespace Gudhi { + +namespace witness_complex { + +/** + * \private + * \class Witness_complex + * \brief Constructs (weak) witness complex for a given table of nearest landmarks with respect to witnesses. + * \ingroup witness_complex + * + * \tparam Nearest_landmark_table_ needs to be a range of a range of pairs of nearest landmarks and distances. + * The class Nearest_landmark_table_::value_type must be a copiable range. + * The range of pairs must admit a member type 'iterator'. The dereference type + * of the pair range iterator needs to be 'std::pair<std::size_t, double>'. +*/ +template< class Nearest_landmark_table_ > +class Witness_complex { + private: + typedef typename Nearest_landmark_table_::value_type Nearest_landmark_range; + typedef std::size_t Witness_id; + typedef std::size_t Landmark_id; + typedef std::pair<Landmark_id, double> Id_distance_pair; + typedef Active_witness<Id_distance_pair, Nearest_landmark_range> ActiveWitness; + typedef std::list< ActiveWitness > ActiveWitnessList; + typedef std::vector< Landmark_id > typeVectorVertex; + typedef std::vector<Nearest_landmark_range> Nearest_landmark_table_internal; + typedef Landmark_id Vertex_handle; + + protected: + Nearest_landmark_table_internal nearest_landmark_table_; + + public: + ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////// + /* @name Constructor + */ + + //@{ + + Witness_complex() { + } + + /** + * \brief Initializes member variables before constructing simplicial complex. + * \details Records nearest landmark table. + * @param[in] nearest_landmark_table needs to be a range of a range of pairs of nearest landmarks and distances. + * The class Nearest_landmark_table_::value_type must be a copiable range. + * The range of pairs must admit a member type 'iterator'. The dereference type + * of the pair range iterator needs to be 'std::pair<std::size_t, double>'. + */ + + Witness_complex(Nearest_landmark_table_ const & nearest_landmark_table) + : nearest_landmark_table_(std::begin(nearest_landmark_table), std::end(nearest_landmark_table)) { + } + + /** \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, + double max_alpha_square, + std::size_t limit_dimension = std::numeric_limits<std::size_t>::max()) const { + if (complex.num_vertices() > 0) { + std::cerr << "Witness complex cannot create complex - complex is not empty.\n"; + return false; + } + if (max_alpha_square < 0) { + std::cerr << "Witness complex cannot create complex - squared relaxation parameter must be non-negative.\n"; + return false; + } + ActiveWitnessList active_witnesses; + Landmark_id k = 0; /* current dimension in iterative construction */ + for (auto w : nearest_landmark_table_) + active_witnesses.push_back(ActiveWitness(w)); + 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 != end && l_it->second - alpha2 <= norelax_dist2; ++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; + } + } else if (dim == 0) { + for (; l_it != end && l_it->second - alpha2 <= norelax_dist2; ++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 // WITNESS_COMPLEX_H_ |