diff options
| -rw-r--r-- | biblio/bibliography.bib | 4 | ||||
| -rw-r--r-- | src/cython/CMakeLists.txt | 4 | ||||
| -rw-r--r-- | src/cython/cython/witness_complex.pyx | 285 | ||||
| -rw-r--r-- | src/cython/doc/euclidean_strong_witness_complex_ref.rst | 10 | ||||
| -rw-r--r-- | src/cython/doc/euclidean_witness_complex_ref.rst | 10 | ||||
| -rw-r--r-- | src/cython/doc/strong_witness_complex_ref.rst | 10 | ||||
| -rw-r--r-- | src/cython/doc/witness_complex_sum.rst | 20 | ||||
| -rw-r--r-- | src/cython/doc/witness_complex_user.rst | 86 | ||||
| -rw-r--r-- | src/cython/include/Witness_complex_interface.h | 150 |
9 files changed, 149 insertions, 430 deletions
diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index 8e202d32..9d53a628 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -976,6 +976,6 @@ language={English} title={Topological estimation using witness complexes}, author={De Silva, Vin and Carlsson, Gunnar}, journal={Proc. Sympos. Point-Based Graphics}, - pages={157--166}, + pages={157-166}, year={2004} -}
\ No newline at end of file +} diff --git a/src/cython/CMakeLists.txt b/src/cython/CMakeLists.txt index e1d71c75..bcc1e929 100644 --- a/src/cython/CMakeLists.txt +++ b/src/cython/CMakeLists.txt @@ -50,9 +50,13 @@ if(PYTHON_PATH AND CYTHON_PATH) # Developper version for doc images file(GLOB GUDHI_DEV_DOC_IMAGES "${CMAKE_SOURCE_DIR}/src/*/doc/*.png") file(COPY ${GUDHI_DEV_DOC_IMAGES} DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/doc/img") + file(GLOB GUDHI_DEV_DOC_IMAGES "${CMAKE_SOURCE_DIR}/src/*/doc/*.svg") + file(COPY ${GUDHI_DEV_DOC_IMAGES} DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/doc/img") # User version for doc images file(GLOB GUDHI_USER_DOC_IMAGES "${CMAKE_SOURCE_DIR}/doc/*/*.png") file(COPY ${GUDHI_USER_DOC_IMAGES} DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/doc/img") + file(GLOB GUDHI_USER_DOC_IMAGES "${CMAKE_SOURCE_DIR}/doc/*/*.svg") + file(COPY ${GUDHI_USER_DOC_IMAGES} DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/doc/img") # Biblio file(GLOB GUDHI_BIB_FILES "${CMAKE_SOURCE_DIR}/biblio/*.bib") file(COPY ${GUDHI_BIB_FILES} DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/doc/") diff --git a/src/cython/cython/witness_complex.pyx b/src/cython/cython/witness_complex.pyx index b2ad4e68..e0d8b1e3 100644 --- a/src/cython/cython/witness_complex.pyx +++ b/src/cython/cython/witness_complex.pyx @@ -30,28 +30,10 @@ __license__ = "GPL v3" cdef extern from "Witness_complex_interface.h" namespace "Gudhi": cdef cppclass Witness_complex_interface "Gudhi::witness_complex::Witness_complex_interface": - Witness_complex_interface(vector[vector[double]] points, int number_of_landmarks) - double filtration() - double simplex_filtration(vector[int] simplex) - void set_filtration(double filtration) - void initialize_filtration() - int num_vertices() - int num_simplices() - void set_dimension(int dimension) - int dimension() - bint find_simplex(vector[int] simplex) - bint insert_simplex_and_subfaces(vector[int] simplex, - double filtration) - vector[pair[vector[int], double]] get_filtered_tree() - vector[pair[vector[int], double]] get_skeleton_tree(int dimension) - vector[pair[vector[int], double]] get_star_tree(vector[int] simplex) - vector[pair[vector[int], double]] get_coface_tree(vector[int] simplex, - int dimension) - void remove_maximal_simplex(vector[int] simplex) - vector[double] get_point(int vertex) - vector[pair[int, pair[double, double]]] get_persistence(int homology_coeff_field, double min_persistence) - vector[int] get_betti_numbers() - vector[int] get_persistent_betti_numbers(double from_value, double to_value) + Witness_complex_interface(vector[vector[pair[size_t, double]]] nearest_landmark_table) + void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square) + void create_simplex_tree(Simplex_tree_interface_full_featured* simplex_tree, double max_alpha_square, + unsigned limit_dimension) # WitnessComplex python interface cdef class WitnessComplex: @@ -65,258 +47,35 @@ cdef class WitnessComplex: def __init__(self, points=None, number_of_landmarks=5): """WitnessComplex constructor. - :param points: A list of points in d-Dimension. - :type points: list of list of double - :param number_of_landmarks: Number of landmarks to build the - WitnessComplex. - :type number_of_landmarks: int + :param nearest_landmark_table: A list of nearest landmark. + :type nearest_landmark_table: list of list of pair of unsigned and double """ # The real cython constructor - def __cinit__(self, points=None, number_of_landmarks=5): - if points is not None: - self.thisptr = new Witness_complex_interface(points, - number_of_landmarks) + def __cinit__(self, nearest_landmark_table=None): + if nearest_landmark_table is not None: + self.thisptr = new Witness_complex_interface(nearest_landmark_table) def __dealloc__(self): if self.thisptr != NULL: del self.thisptr def __is_defined(self): - """Returns true if AlphaComplex pointer is not NULL. + """Returns true if WitnessComplex pointer is not NULL. """ return self.thisptr != NULL - def get_filtration(self): - """This function returns the main simplicial complex filtration value. - - :returns: float -- the simplicial complex filtration value. - """ - return self.thisptr.filtration() - - def filtration(self, simplex): - """This function returns the simplicial complex filtration value for a - given N-simplex. - - :param simplex: The N-simplex, represented by a list of vertex. - :type simplex: list of int. - :returns: float -- the simplicial complex filtration value. - """ - return self.thisptr.simplex_filtration(simplex) - - def set_filtration(self, filtration): - """This function sets the main simplicial complex filtration value. - - :param filtration: The filtration value. - :type filtration: float. - """ - self.thisptr.set_filtration(<double> filtration) - - def initialize_filtration(self): - """This function initializes and sorts the simplicial complex - filtration vector. - - .. note:: - - This function must be launched before persistence, betti_numbers, - persistent_betti_numbers or get_filtered_tree after inserting or - removing simplices. - """ - self.thisptr.initialize_filtration() - - def num_vertices(self): - """This function returns the number of vertices of the simplicial - complex. - - :returns: int -- the simplicial complex number of vertices. + def create_simplex_tree(self, max_alpha_square, limit_dimension = -1): """ - return self.thisptr.num_vertices() - - def num_simplices(self): - """This function returns the number of simplices of the simplicial - complex. - - :returns: int -- the simplicial complex number of simplices. - """ - return self.thisptr.num_simplices() - - def dimension(self): - """This function returns the dimension of the simplicial complex. - - :returns: int -- the simplicial complex dimension. - """ - return self.thisptr.dimension() - - def set_dimension(self, dimension): - """This function sets the dimension of the simplicial complex. - - :param dimension: The new dimension value. - :type dimension: int. - """ - self.thisptr.set_dimension(<int>dimension) - - def find(self, simplex): - """This function returns if the N-simplex was found in the simplicial - complex or not. - - :param simplex: The N-simplex to find, represented by a list of vertex. - :type simplex: list of int. - :returns: bool -- true if the simplex was found, false otherwise. - """ - cdef vector[int] complex - for i in simplex: - complex.push_back(i) - return self.thisptr.find_simplex(complex) - - def insert(self, simplex, filtration=0.0): - """This function inserts the given N-simplex with the given filtration - value (default value is '0.0'). - - :param simplex: The N-simplex to insert, represented by a list of - vertex. - :type simplex: list of int. - :param filtration: The filtration value of the simplex. - :type filtration: float. - :returns: bool -- true if the simplex was found, false otherwise. - """ - cdef vector[int] complex - for i in simplex: - complex.push_back(i) - return self.thisptr.insert_simplex_and_subfaces(complex, - <double>filtration) - - def get_filtered_tree(self): - """This function returns the tree sorted by increasing filtration - values. - - :returns: list of tuples(simplex, filtration) -- the tree sorted by - increasing filtration values. - """ - cdef vector[pair[vector[int], double]] coface_tree \ - = self.thisptr.get_filtered_tree() - ct = [] - for filtered_complex in coface_tree: - v = [] - for vertex in filtered_complex.first: - v.append(vertex) - ct.append((v, filtered_complex.second)) - return ct - - def get_skeleton_tree(self, dimension): - """This function returns the tree skeleton of a maximum given - dimension. - - :param dimension: The skeleton dimension value. - :type dimension: int. - :returns: list of tuples(simplex, filtration) -- the skeleton tree - of a maximum dimension. - """ - cdef vector[pair[vector[int], double]] coface_tree \ - = self.thisptr.get_skeleton_tree(<int>dimension) - ct = [] - for filtered_complex in coface_tree: - v = [] - for vertex in filtered_complex.first: - v.append(vertex) - ct.append((v, filtered_complex.second)) - return ct - - def get_star_tree(self, simplex): - """This function returns the star tree of a given N-simplex. - - :param simplex: The N-simplex, represented by a list of vertex. - :type simplex: list of int. - :returns: list of tuples(simplex, filtration) -- the star tree of a - simplex. - """ - cdef vector[int] complex - for i in simplex: - complex.push_back(i) - cdef vector[pair[vector[int], double]] coface_tree \ - = self.thisptr.get_star_tree(complex) - ct = [] - for filtered_complex in coface_tree: - v = [] - for vertex in filtered_complex.first: - v.append(vertex) - ct.append((v, filtered_complex.second)) - return ct - - def get_coface_tree(self, simplex, codimension): - """This function returns the coface tree of a given N-simplex with a - given codimension. - - :param simplex: The N-simplex, represented by a list of vertex. - :type simplex: list of int. - :param codimension: The codimension. If codimension = 0, all cofaces - are returned (equivalent of get_star_tree function) - :type codimension: int. - :returns: list of tuples(simplex, filtration) -- the coface tree of a - simplex. - """ - cdef vector[int] complex - for i in simplex: - complex.push_back(i) - cdef vector[pair[vector[int], double]] coface_tree \ - = self.thisptr.get_coface_tree(complex, <int>codimension) - ct = [] - for filtered_complex in coface_tree: - v = [] - for vertex in filtered_complex.first: - v.append(vertex) - ct.append((v, filtered_complex.second)) - return ct - - def remove_maximal_simplex(self, simplex): - """This function removes a given maximal N-simplex from the simplicial - complex. - - :param simplex: The N-simplex, represented by a list of vertex. - :type simplex: list of int. - """ - self.thisptr.remove_maximal_simplex(simplex) - - def persistence(self, homology_coeff_field=11, min_persistence=0): - """This function returns the persistence of the simplicial complex. - - :param homology_coeff_field: The homology coefficient field. Must be a - prime number - :type homology_coeff_field: int. - :param min_persistence: The minimum persistence value to take into - account (strictly greater than min_persistence). Default value is - 0.0. - Sets min_persistence to -1.0 to see all values. - :type min_persistence: float. - :note: list of pairs(dimension, pair(birth, death)) -- the - persistence of the simplicial complex. - """ - return self.thisptr.get_persistence(homology_coeff_field, min_persistence) - - def betti_numbers(self): - """This function returns the Betti numbers of the simplicial complex. - - :returns: list of int -- The Betti numbers ([B0, B1, ..., Bn]). - - :note: betti_numbers function requires persistence function to be - launched first. - """ - return self.thisptr.get_betti_numbers() - - def persistent_betti_numbers(self, from_value, to_value): - """This function returns the persistent Betti numbers of the - simplicial complex. - - :param from_value: The persistence birth limit to be added in the - numbers (persistent birth <= from_value). - :type from_value: float. - :param to_value: The persistence death limit to be added in the - numbers (persistent death > to_value). - :type to_value: float. - - :returns: list of int -- The persistent Betti numbers ([B0, B1, ..., - Bn]). - - :note: persistent_betti_numbers function requires persistence - function to be launched first. + :param max_alpha_square: The maximum alpha square threshold the + simplices shall not exceed. Default is set to infinity. + :type max_alpha_square: float + :returns: A simplex tree created from the Delaunay Triangulation. + :rtype: SimplexTree """ - return self.thisptr.get_persistent_betti_numbers(from_value, to_value) + simplex_tree = SimplexTree() + if limit_dimension is not -1: + self.thisptr.create_simplex_tree(simplex_tree.thisptr, max_alpha_square, limit_dimension) + else: + self.thisptr.create_simplex_tree(simplex_tree.thisptr, max_alpha_square) + return simplex_tree diff --git a/src/cython/doc/euclidean_strong_witness_complex_ref.rst b/src/cython/doc/euclidean_strong_witness_complex_ref.rst new file mode 100644 index 00000000..bebf0f9a --- /dev/null +++ b/src/cython/doc/euclidean_strong_witness_complex_ref.rst @@ -0,0 +1,10 @@ +================================================= +Euclidean strong witness complex reference manual +================================================= + +.. autoclass:: gudhi.EuclideanStrongWitnessComplex + :members: + :undoc-members: + :show-inheritance: + + .. automethod:: gudhi.EuclideanStrongWitnessComplex.__init__ diff --git a/src/cython/doc/euclidean_witness_complex_ref.rst b/src/cython/doc/euclidean_witness_complex_ref.rst new file mode 100644 index 00000000..29b8806f --- /dev/null +++ b/src/cython/doc/euclidean_witness_complex_ref.rst @@ -0,0 +1,10 @@ +========================================== +Euclidean witness complex reference manual +========================================== + +.. autoclass:: gudhi.EuclideanWitnessComplex + :members: + :undoc-members: + :show-inheritance: + + .. automethod:: gudhi.EuclideanWitnessComplex.__init__ diff --git a/src/cython/doc/strong_witness_complex_ref.rst b/src/cython/doc/strong_witness_complex_ref.rst new file mode 100644 index 00000000..4ed4fe46 --- /dev/null +++ b/src/cython/doc/strong_witness_complex_ref.rst @@ -0,0 +1,10 @@ +======================================= +Strong witness complex reference manual +======================================= + +.. autoclass:: gudhi.StrongWitnessComplex + :members: + :undoc-members: + :show-inheritance: + + .. automethod:: gudhi.StrongWitnessComplex.__init__ diff --git a/src/cython/doc/witness_complex_sum.rst b/src/cython/doc/witness_complex_sum.rst index 1b20d4bc..b65522ba 100644 --- a/src/cython/doc/witness_complex_sum.rst +++ b/src/cython/doc/witness_complex_sum.rst @@ -1,25 +1,17 @@ ================================================================= =================================== =================================== :Author: Siargey Kachanovich :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3 +:Euclidean version requires: CGAL :math:`\geq` 4.6.0 Eigen3 ================================================================= =================================== =================================== +-----------------------------------------------------------------+----------------------------------------------------------------------+ | .. image:: | Witness complex :math:`Wit(W,L)` is a simplicial complex defined on | -| img/Witness_complex_representation.png | two sets of points in :math:`\mathbb{R}^D`:Wit(W,L)` is a simplicial | -| | complex defined on two sets of points in :math:`\mathbb{R}^D`: | -| | | -| | * :math:`W` set of **witnesses** and | -| | * :math:`L \subseteq W` set of **landmarks**. | -| | | -| | The simplices are based on landmarks and a simplex belongs to the | -| | witness complex if and only if it is witnessed, that is: | -| | | -| | :math:`\sigma \subset L` is witnessed if there exists a point | -| | :math:`w \in W` such that w is closer to the vertices of | -| | :math:`\sigma` than other points in :math:`L` and all of its faces | -| | are witnessed as well. | +| img/Witness_complex_representation.png | two sets of points in :math:`\mathbb{R}^D`. | | | | | | The data structure is described in | | | :cite:`boissonnatmariasimplextreealgorithmica`. | +-----------------------------------------------------------------+----------------------------------------------------------------------+ -| :doc:`witness_complex_user` | :doc:`witness_complex_ref` | +| :doc:`witness_complex_user` | * :doc:`witness_complex_ref` | +| | * :doc:`strong_witness_complex_ref` | +| | * :doc:`euclidean_witness_complex_ref` | +| | * :doc:`euclidean_strong_witness_complex_ref` | +-----------------------------------------------------------------+----------------------------------------------------------------------+ diff --git a/src/cython/doc/witness_complex_user.rst b/src/cython/doc/witness_complex_user.rst index 604c7357..071d8ef5 100644 --- a/src/cython/doc/witness_complex_user.rst +++ b/src/cython/doc/witness_complex_user.rst @@ -6,26 +6,80 @@ Definition .. include:: witness_complex_sum.rst + +Definitions +----------- + +Witness complex is a simplicial complex defined on two sets of points in :math:`\mathbb{R}^D`: + +- :math:`W` set of **witnesses** and +- :math:`L` set of **landmarks**. + +Even though often the set of landmarks :math:`L` is a subset of the set of witnesses :math:`W`, it is not a requirement +for the current implementation. + +Landmarks are the vertices of the simplicial complex and witnesses help to decide on which simplices are inserted via a +predicate "is witnessed". + +De Silva and Carlsson in their paper :cite:`de2004topological` differentiate **weak witnessing** and +**strong witnessing**: + +- *weak*: :math:`\sigma \subset L` is witnessed by :math:`w \in W` if :math:`\forall l \in \sigma,\ \forall l' \in \mathbf{L \setminus \sigma},\ d(w,l) \leq d(w,l')` +- *strong*: :math:`\sigma \subset L` is witnessed by :math:`w \in W` if :math:`\forall l \in \sigma,\ \forall l' \in \mathbf{L},\ d(w,l) \leq d(w,l')` + +where :math:`d(.,.)` is a distance function. + +Both definitions can be relaxed by a real value :math:`\alpha`: + +- *weak*: :math:`\sigma \subset L` is :math:`\alpha`-witnessed by :math:`w \in W` if :math:`\forall l \in \sigma,\ \forall l' \in \mathbf{L \setminus \sigma},\ d(w,l)^2 \leq d(w,l')^2 + \alpha^2` +- *strong*: :math:`\sigma \subset L` is :math:`\alpha`-witnessed by :math:`w \in W` if :math:`\forall l \in \sigma,\ \forall l' \in \mathbf{L},\ d(w,l)^2 \leq d(w,l')^2 + \alpha^2` + +which leads to definitions of **weak relaxed witness complex** (or just relaxed witness complex for short) and +**strong relaxed witness complex** respectively. + +.. figure:: img/swit.svg + :alt: Strongly witnessed simplex + :figclass: align-center + + Strongly witnessed simplex + + +In particular case of 0-relaxation, weak complex corresponds to **witness complex** introduced in +:cite:`de2004topological`, whereas 0-relaxed strong witness complex consists of just vertices and is not very +interesting. Hence for small relaxation weak version is preferable. +However, to capture the homotopy type (for example using Gudhi::persistent_cohomology::Persistent_cohomology) it is +often necessary to work with higher filtration values. In this case strong relaxed witness complex is faster to compute +and offers similar results. + Implementation -------------- -The principal class of this module is Gudhi::Witness_complex. +The two complexes described above are implemented in the corresponding classes + +- :doc:`witness_complex_ref` +- :doc:`strong_witness_complex_ref` +- :doc:`euclidean_witness_complex_ref` +- :doc:`euclidean_strong_witness_complex_ref` + +The construction of the Euclidean versions of complexes follow the same scheme: + +1. Construct a search tree on landmarks. +2. Construct lists of nearest landmarks for each witness. +3. Construct the witness complex for nearest landmark lists. + +In the non-Euclidean classes, the lists of nearest landmarks are supposed to be given as input. + +The constructors take on the steps 1 and 2, while the function 'create_complex' executes the step 3. + +Constructing weak relaxed witness complex from an off file +---------------------------------------------------------- + +Let's start with a simple example, which reads an off point file and computes a weak witness complex. -In both cases, the constructor for this class takes a {witness}x{closest_landmarks} table, where each row represents a -witness and consists of landmarks sorted by distance to this witness. +Example2: Computing persistence using strong relaxed witness complex +-------------------------------------------------------------------- -.. todo:: - This table can be constructed by two additional classes Landmark_choice_by_furthest_point and - Landmark_choice_by_random_point also included in the module. +Here is an example of constructing a strong witness complex filtration and computing persistence on it: -.. figure:: - img/bench_Cy8.png - :align: center - - Running time as function on number of landmarks. +.. include:: biblio.rst -.. figure:: - img/bench_sphere.png - :align: center - - Running time as function on number of witnesses for |L|=300. diff --git a/src/cython/include/Witness_complex_interface.h b/src/cython/include/Witness_complex_interface.h index a753bc1d..38661cb6 100644 --- a/src/cython/include/Witness_complex_interface.h +++ b/src/cython/include/Witness_complex_interface.h @@ -25,161 +25,41 @@ #include <gudhi/Simplex_tree.h> #include <gudhi/Witness_complex.h> -#include <gudhi/Construct_closest_landmark_table.h> -#include <gudhi/pick_n_random_points.h> -#include "Persistent_cohomology_interface.h" +#include "Simplex_tree_interface.h" #include <vector> #include <utility> // std::pair #include <iostream> +#include <cstddef> namespace Gudhi { namespace witness_complex { class Witness_complex_interface { - typedef typename Simplex_tree<>::Simplex_handle Simplex_handle; - typedef typename Simplex_tree<>::Filtration_value Filtration_value; - typedef typename Simplex_tree<>::Vertex_handle Vertex_handle; - typedef typename std::pair<Simplex_handle, bool> Insertion_result; - using Simplex = std::vector<Vertex_handle>; - using Filtered_complex = std::pair<Simplex, Filtration_value>; - using Complex_tree = std::vector<Filtered_complex>; + using Nearest_landmark_range = std::vector<std::pair<std::size_t, double>>; + using Nearest_landmark_table = std::vector<Nearest_landmark_range>; public: - Witness_complex_interface(std::vector<std::vector<double>>&points, int number_of_landmarks) - : pcoh_(nullptr) { - std::vector<std::vector< int > > knn; - std::vector<std::vector<double>> landmarks; - Gudhi::subsampling::pick_n_random_points(points, number_of_landmarks, std::back_inserter(landmarks)); - Gudhi::witness_complex::construct_closest_landmark_table<Filtration_value>(points, landmarks, knn); - - Gudhi::witness_complex::witness_complex(knn, number_of_landmarks, points[0].size(), simplex_tree_); + Witness_complex_interface(Nearest_landmark_table& nlt) { + witness_complex_ = new Witness_complex<Nearest_landmark_table>(nlt); } - bool find_simplex(const Simplex& vh) { - return (simplex_tree_.find(vh) != simplex_tree_.null_simplex()); + void create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square, + std::size_t limit_dimension) { + witness_complex_->create_complex(*simplex_tree, max_alpha_square, limit_dimension); + simplex_tree->initialize_filtration(); } - bool insert_simplex_and_subfaces(const Simplex& complex, Filtration_value filtration = 0) { - Insertion_result result = simplex_tree_.insert_simplex_and_subfaces(complex, filtration); - return (result.second); + void create_simplex_tree(Simplex_tree_interface<>* simplex_tree, + double max_alpha_square) { + witness_complex_->create_complex(*simplex_tree, max_alpha_square, std::numeric_limits<std::size_t>::max()); + simplex_tree->initialize_filtration(); } - Filtration_value simplex_filtration(const Simplex& complex) { - return simplex_tree_.filtration(simplex_tree_.find(complex)); - } - - void remove_maximal_simplex(const Simplex& complex) { - return simplex_tree_.remove_maximal_simplex(simplex_tree_.find(complex)); - } - - Complex_tree get_filtered_tree() { - Complex_tree filtered_tree; - for (auto f_simplex : simplex_tree_.filtration_simplex_range()) { - Simplex simplex; - for (auto vertex : simplex_tree_.simplex_vertex_range(f_simplex)) { - simplex.insert(simplex.begin(), vertex); - } - filtered_tree.push_back(std::make_pair(simplex, simplex_tree_.filtration(f_simplex))); - } - return filtered_tree; - - } - - Complex_tree get_skeleton_tree(int dimension) { - Complex_tree skeleton_tree; - for (auto f_simplex : simplex_tree_.skeleton_simplex_range(dimension)) { - Simplex simplex; - for (auto vertex : simplex_tree_.simplex_vertex_range(f_simplex)) { - simplex.insert(simplex.begin(), vertex); - } - skeleton_tree.push_back(std::make_pair(simplex, simplex_tree_.filtration(f_simplex))); - } - return skeleton_tree; - } - - Complex_tree get_star_tree(const Simplex& complex) { - Complex_tree star_tree; - for (auto f_simplex : simplex_tree_.star_simplex_range(simplex_tree_.find(complex))) { - Simplex simplex; - for (auto vertex : simplex_tree_.simplex_vertex_range(f_simplex)) { - simplex.insert(simplex.begin(), vertex); - } - star_tree.push_back(std::make_pair(simplex, simplex_tree_.filtration(f_simplex))); - } - return star_tree; - } - - Complex_tree get_coface_tree(const Simplex& complex, int dimension) { - Complex_tree coface_tree; - for (auto f_simplex : simplex_tree_.cofaces_simplex_range(simplex_tree_.find(complex), dimension)) { - Simplex simplex; - for (auto vertex : simplex_tree_.simplex_vertex_range(f_simplex)) { - simplex.insert(simplex.begin(), vertex); - } - coface_tree.push_back(std::make_pair(simplex, simplex_tree_.filtration(f_simplex))); - } - return coface_tree; - } - - // Specific to Witness complex because no inheritance - Filtration_value filtration() const { - return simplex_tree_.filtration(); - } - - void set_filtration(Filtration_value fil) { - simplex_tree_.set_filtration(fil); - } - - void initialize_filtration() { - simplex_tree_.initialize_filtration(); - } - - size_t num_vertices() const { - return simplex_tree_.num_vertices(); - } - - size_t num_simplices() { - return simplex_tree_.num_simplices(); - } - - int dimension() const { - return simplex_tree_.dimension(); - } - - void set_dimension(int dimension) { - simplex_tree_.set_dimension(dimension); - } - - std::vector<std::pair<int, std::pair<double, double>>> get_persistence(int homology_coeff_field, double min_persistence) { - if (pcoh_ != nullptr) { - delete pcoh_; - } - pcoh_ = new Persistent_cohomology_interface<Simplex_tree<>>(&simplex_tree_); - return pcoh_->get_persistence(homology_coeff_field, min_persistence); - } - - std::vector<int> get_betti_numbers() const { - if (pcoh_ != nullptr) { - return pcoh_->betti_numbers(); - } - std::vector<int> betti_numbers; - return betti_numbers; - } - - std::vector<int> get_persistent_betti_numbers(Filtration_value from, Filtration_value to) const { - if (pcoh_ != nullptr) { - return pcoh_->persistent_betti_numbers(from, to); - } - std::vector<int> persistent_betti_numbers; - return persistent_betti_numbers; - } - private: - Simplex_tree<> simplex_tree_; - Persistent_cohomology_interface<Simplex_tree<>>* pcoh_; + Witness_complex<Nearest_landmark_table>* witness_complex_; }; |