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Diffstat (limited to 'src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation/Cell_complex/Cell_complex.h')
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diff --git a/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation/Cell_complex/Cell_complex.h b/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation/Cell_complex/Cell_complex.h new file mode 100644 index 00000000..de342ecc --- /dev/null +++ b/src/Coxeter_triangulation/include/gudhi/Coxeter_triangulation/Cell_complex/Cell_complex.h @@ -0,0 +1,340 @@ +/* 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): Siargey Kachanovich + * + * Copyright (C) 2019 Inria + * + * Modification(s): + * - YYYY/MM Author: Description of the modification + */ + +#ifndef CELL_COMPLEX_H_ +#define CELL_COMPLEX_H_ + +#include <Eigen/Dense> + +#include <vector> +#include <map> +#include <utility> // for std::make_pair + +#include <gudhi/IO/output_debug_traces_to_html.h> // for DEBUG_TRACES +#include <gudhi/Permutahedral_representation/Simplex_comparator.h> +#include <gudhi/Coxeter_triangulation/Cell_complex/Hasse_diagram_cell.h> // for Hasse_cell + +namespace Gudhi { + +namespace coxeter_triangulation { + +/** \class Cell_complex + * \brief A class that constructs the cell complex from the output provided by the class + * \ref Gudhi::coxeter_triangulation::Manifold_tracing. + * + * The use and interfaces of this cell complex is limited to the \ref coxeter_triangulation implementation. + * + * \tparam Out_simplex_map_ The type of a map from a simplex type that is a + * model of SimplexInCoxeterTriangulation to Eigen::VectorXd. + */ +template <class Out_simplex_map_> +class Cell_complex { + public: + /** \brief Type of a simplex in the ambient triangulation. + * Is a model of the concept SimplexInCoxeterTriangulation. + */ + using Simplex_handle = typename Out_simplex_map_::key_type; + /** \brief Type of a cell in the cell complex. + * Always is Gudhi::Hasse_cell from the Hasse diagram module. + * The additional information is the boolean that is true if and only if the cell lies + * on the boundary. + */ + using Hasse_cell = Gudhi::Hasse_diagram::Hasse_diagram_cell<int, double, bool>; + /** \brief Type of a map from permutahedral representations of simplices in the + * ambient triangulation to the corresponding cells in the cell complex of some + * specific dimension. + */ + using Simplex_cell_map = std::map<Simplex_handle, Hasse_cell*, Simplex_comparator<Simplex_handle> >; + /** \brief Type of a vector of maps from permutahedral representations of simplices in the + * ambient triangulation to the corresponding cells in the cell complex of various dimensions. + */ + using Simplex_cell_maps = std::vector<Simplex_cell_map>; + + /** \brief Type of a map from cells in the cell complex to the permutahedral representations + * of the corresponding simplices in the ambient triangulation. + */ + using Cell_simplex_map = std::map<Hasse_cell*, Simplex_handle>; + + /** \brief Type of a map from vertex cells in the cell complex to the permutahedral representations + * of their Cartesian coordinates. + */ + using Cell_point_map = std::map<Hasse_cell*, Eigen::VectorXd>; + + private: + Hasse_cell* insert_cell(const Simplex_handle& simplex, std::size_t cell_d, bool is_boundary) { + Simplex_cell_maps& simplex_cell_maps = (is_boundary ? boundary_simplex_cell_maps_ : interior_simplex_cell_maps_); +#ifdef DEBUG_TRACES + CC_detail_list& cc_detail_list = + (is_boundary ? cc_boundary_detail_lists[cell_d] : cc_interior_detail_lists[cell_d]); + cc_detail_list.emplace_back(simplex); +#endif + Simplex_cell_map& simplex_cell_map = simplex_cell_maps[cell_d]; + auto map_it = simplex_cell_map.find(simplex); + if (map_it == simplex_cell_map.end()) { + hasse_cells_.push_back(new Hasse_cell(is_boundary, cell_d)); + Hasse_cell* new_cell = hasse_cells_.back(); + simplex_cell_map.emplace(simplex, new_cell); + cell_simplex_map_.emplace(new_cell, simplex); +#ifdef DEBUG_TRACES + cc_detail_list.back().status_ = CC_detail_info::Result_type::inserted; +#endif + return new_cell; + } +#ifdef DEBUG_TRACES + CC_detail_info& cc_info = cc_detail_list.back(); + cc_info.trigger_ = to_string(map_it->first); + cc_info.status_ = CC_detail_info::Result_type::self; +#endif + return map_it->second; + } + + void expand_level(std::size_t cell_d) { + bool is_manifold_with_boundary = boundary_simplex_cell_maps_.size() > 0; + for (auto& sc_pair : interior_simplex_cell_maps_[cell_d - 1]) { + const Simplex_handle& simplex = sc_pair.first; + Hasse_cell* cell = sc_pair.second; + for (Simplex_handle coface : simplex.coface_range(cod_d_ + cell_d)) { + Hasse_cell* new_cell = insert_cell(coface, cell_d, false); + new_cell->get_boundary().emplace_back(cell, 1); + } + } + + if (is_manifold_with_boundary) { + for (auto& sc_pair : boundary_simplex_cell_maps_[cell_d - 1]) { + const Simplex_handle& simplex = sc_pair.first; + Hasse_cell* cell = sc_pair.second; + if (cell_d != intr_d_) + for (Simplex_handle coface : simplex.coface_range(cod_d_ + cell_d + 1)) { + Hasse_cell* new_cell = insert_cell(coface, cell_d, true); + new_cell->get_boundary().emplace_back(cell, 1); + } + auto map_it = interior_simplex_cell_maps_[cell_d].find(simplex); + if (map_it == interior_simplex_cell_maps_[cell_d].end()) + std::cerr << "Cell_complex::expand_level error: A boundary cell does not have an interior counterpart.\n"; + else { + Hasse_cell* i_cell = map_it->second; + i_cell->get_boundary().emplace_back(cell, 1); + } + } + } + } + + void construct_complex_(const Out_simplex_map_& out_simplex_map) { +#ifdef DEBUG_TRACES + cc_interior_summary_lists.resize(interior_simplex_cell_maps_.size()); + cc_interior_prejoin_lists.resize(interior_simplex_cell_maps_.size()); + cc_interior_detail_lists.resize(interior_simplex_cell_maps_.size()); +#endif + for (auto& os_pair : out_simplex_map) { + const Simplex_handle& simplex = os_pair.first; + const Eigen::VectorXd& point = os_pair.second; + Hasse_cell* new_cell = insert_cell(simplex, 0, false); + cell_point_map_.emplace(new_cell, point); + } + for (std::size_t cell_d = 1; + cell_d < interior_simplex_cell_maps_.size() && !interior_simplex_cell_maps_[cell_d - 1].empty(); ++cell_d) { + expand_level(cell_d); + } + } + + void construct_complex_(const Out_simplex_map_& interior_simplex_map, const Out_simplex_map_& boundary_simplex_map) { +#ifdef DEBUG_TRACES + cc_interior_summary_lists.resize(interior_simplex_cell_maps_.size()); + cc_interior_prejoin_lists.resize(interior_simplex_cell_maps_.size()); + cc_interior_detail_lists.resize(interior_simplex_cell_maps_.size()); + cc_boundary_summary_lists.resize(boundary_simplex_cell_maps_.size()); + cc_boundary_prejoin_lists.resize(boundary_simplex_cell_maps_.size()); + cc_boundary_detail_lists.resize(boundary_simplex_cell_maps_.size()); +#endif + for (auto& os_pair : boundary_simplex_map) { + const Simplex_handle& simplex = os_pair.first; + const Eigen::VectorXd& point = os_pair.second; + Hasse_cell* new_cell = insert_cell(simplex, 0, true); + cell_point_map_.emplace(new_cell, point); + } + for (auto& os_pair : interior_simplex_map) { + const Simplex_handle& simplex = os_pair.first; + const Eigen::VectorXd& point = os_pair.second; + Hasse_cell* new_cell = insert_cell(simplex, 0, false); + cell_point_map_.emplace(new_cell, point); + } +#ifdef DEBUG_TRACES + for (const auto& sc_pair : interior_simplex_cell_maps_[0]) + cc_interior_summary_lists[0].push_back(CC_summary_info(sc_pair)); + for (const auto& sc_pair : boundary_simplex_cell_maps_[0]) + cc_boundary_summary_lists[0].push_back(CC_summary_info(sc_pair)); +#endif + + for (std::size_t cell_d = 1; + cell_d < interior_simplex_cell_maps_.size() && !interior_simplex_cell_maps_[cell_d - 1].empty(); ++cell_d) { + expand_level(cell_d); + +#ifdef DEBUG_TRACES + for (const auto& sc_pair : interior_simplex_cell_maps_[cell_d]) + cc_interior_summary_lists[cell_d].push_back(CC_summary_info(sc_pair)); + if (cell_d < boundary_simplex_cell_maps_.size()) + for (const auto& sc_pair : boundary_simplex_cell_maps_[cell_d]) + cc_boundary_summary_lists[cell_d].push_back(CC_summary_info(sc_pair)); +#endif + } + } + + public: + /** + * \brief Constructs the the cell complex that approximates an \f$m\f$-dimensional manifold + * without boundary embedded in the \f$ d \f$-dimensional Euclidean space + * from the output of the class Gudhi::Manifold_tracing. + * + * \param[in] out_simplex_map A map from simplices of dimension \f$(d-m)\f$ + * in the ambient triangulation that intersect the relative interior of the manifold + * to the intersection points. + */ + void construct_complex(const Out_simplex_map_& out_simplex_map) { + interior_simplex_cell_maps_.resize(intr_d_ + 1); + if (!out_simplex_map.empty()) cod_d_ = out_simplex_map.begin()->first.dimension(); + construct_complex_(out_simplex_map); + } + + /** + * \brief Constructs the skeleton of the cell complex that approximates + * an \f$m\f$-dimensional manifold without boundary embedded + * in the \f$d\f$-dimensional Euclidean space + * up to a limit dimension from the output of the class Gudhi::Manifold_tracing. + * + * \param[in] out_simplex_map A map from simplices of dimension \f$(d-m)\f$ + * in the ambient triangulation that intersect the relative interior of the manifold + * to the intersection points. + * \param[in] limit_dimension The dimension of the constructed skeleton. + */ + void construct_complex(const Out_simplex_map_& out_simplex_map, std::size_t limit_dimension) { + interior_simplex_cell_maps_.resize(limit_dimension + 1); + if (!out_simplex_map.empty()) cod_d_ = out_simplex_map.begin()->first.dimension(); + construct_complex_(out_simplex_map); + } + + /** + * \brief Constructs the the cell complex that approximates an \f$m\f$-dimensional manifold + * with boundary embedded in the \f$ d \f$-dimensional Euclidean space + * from the output of the class Gudhi::Manifold_tracing. + * + * \param[in] interior_simplex_map A map from simplices of dimension \f$(d-m)\f$ + * in the ambient triangulation that intersect the relative interior of the manifold + * to the intersection points. + * \param[in] boundary_simplex_map A map from simplices of dimension \f$(d-m+1)\f$ + * in the ambient triangulation that intersect the boundary of the manifold + * to the intersection points. + */ + void construct_complex(const Out_simplex_map_& interior_simplex_map, const Out_simplex_map_& boundary_simplex_map) { + interior_simplex_cell_maps_.resize(intr_d_ + 1); + boundary_simplex_cell_maps_.resize(intr_d_); + if (!interior_simplex_map.empty()) cod_d_ = interior_simplex_map.begin()->first.dimension(); + construct_complex_(interior_simplex_map, boundary_simplex_map); + } + + /** + * \brief Constructs the skeleton of the cell complex that approximates + * an \f$m\f$-dimensional manifold with boundary embedded + * in the \f$d\f$-dimensional Euclidean space + * up to a limit dimension from the output of the class Gudhi::Manifold_tracing. + * + * \param[in] interior_simplex_map A map from simplices of dimension \f$(d-m)\f$ + * in the ambient triangulation that intersect the relative interior of the manifold + * to the intersection points. + * \param[in] boundary_simplex_map A map from simplices of dimension \f$(d-m+1)\f$ + * in the ambient triangulation that intersect the boundary of the manifold + * to the intersection points. + * \param[in] limit_dimension The dimension of the constructed skeleton. + */ + void construct_complex(const Out_simplex_map_& interior_simplex_map, const Out_simplex_map_& boundary_simplex_map, + std::size_t limit_dimension) { + interior_simplex_cell_maps_.resize(limit_dimension + 1); + boundary_simplex_cell_maps_.resize(limit_dimension); + if (!interior_simplex_map.empty()) cod_d_ = interior_simplex_map.begin()->first.dimension(); + construct_complex_(interior_simplex_map, boundary_simplex_map); + } + + /** + * \brief Returns the dimension of the cell complex. + */ + std::size_t intrinsic_dimension() const { return intr_d_; } + + /** + * \brief Returns a vector of maps from the cells of various dimensions in the interior + * of the cell complex of type Gudhi::Hasse_cell to the permutahedral representations + * of the corresponding simplices in the ambient triangulation. + */ + const Simplex_cell_maps& interior_simplex_cell_maps() const { return interior_simplex_cell_maps_; } + + /** + * \brief Returns a vector of maps from the cells of various dimensions on the boundary + * of the cell complex of type Gudhi::Hasse_cell to the permutahedral representations + * of the corresponding simplices in the ambient triangulation. + */ + const Simplex_cell_maps& boundary_simplex_cell_maps() const { return boundary_simplex_cell_maps_; } + + /** + * \brief Returns a map from the cells of a given dimension in the interior + * of the cell complex of type Gudhi::Hasse_cell to the permutahedral representations + * of the corresponding simplices in the ambient triangulation. + * + * \param[in] cell_d The dimension of the cells. + */ + const Simplex_cell_map& interior_simplex_cell_map(std::size_t cell_d) const { + return interior_simplex_cell_maps_[cell_d]; + } + + /** + * \brief Returns a map from the cells of a given dimension on the boundary + * of the cell complex of type Gudhi::Hasse_cell to the permutahedral representations + * of the corresponding simplices in the ambient triangulation. + * + * \param[in] cell_d The dimension of the cells. + */ + const Simplex_cell_map& boundary_simplex_cell_map(std::size_t cell_d) const { + return boundary_simplex_cell_maps_[cell_d]; + } + + /** + * \brief Returns a map from the cells in the cell complex of type Gudhi::Hasse_cell + * to the permutahedral representations of the corresponding simplices in the + * ambient triangulation. + */ + const Cell_simplex_map& cell_simplex_map() const { return cell_simplex_map_; } + + /** + * \brief Returns a map from the vertex cells in the cell complex of type Gudhi::Hasse_cell + * to their Cartesian coordinates. + */ + const Cell_point_map& cell_point_map() const { return cell_point_map_; } + + /** + * \brief Constructor for the class Cell_complex. + * + * \param[in] intrinsic_dimension The dimension of the cell complex. + */ + Cell_complex(std::size_t intrinsic_dimension) : intr_d_(intrinsic_dimension) {} + + ~Cell_complex() { + for (Hasse_cell* hs_ptr : hasse_cells_) delete hs_ptr; + } + + private: + std::size_t intr_d_, cod_d_; + Simplex_cell_maps interior_simplex_cell_maps_, boundary_simplex_cell_maps_; + Cell_simplex_map cell_simplex_map_; + Cell_point_map cell_point_map_; + std::vector<Hasse_cell*> hasse_cells_; +}; + +} // namespace coxeter_triangulation + +} // namespace Gudhi + +#endif |