Representation of the complex of the same name. More...

#include <Morse_Smale_Witten_chain_complex.hpp>

Public Types
typedef StableManifoldTraits	Stable_manifold_traits
	Simple representation of a stable manifold as a list of points.

Manipulation
Critical_vertex	add_critical_vertex (const Point &p, Morse_index_type k)
	Adds a critical vertex of index k associated to the input point p.
Critical_vertex	add_abstract_critical_vertex (const FT &lower_bound, Morse_index_type k)
	Adds a critical vertex of index k that has no critical point, and a lower bound for its Morse function value.
Critical_vertex	add_abstract_critical_vertex (Morse_index_type k)
	Adds a critical vertex of index k that has no critical point, and no defined lower bound for its Morse function value.
void	connect_critical_vertices (Critical_vertex u, Critical_vertex v)
	Connects u and v such that u is one index higher than v. If u is purely abstract, its lower bound is updated from the value of v.
void	remove_connected_component (Critical_vertex u)
	Removes all critical vertices in the complex that are in the same connected component as u.
void	cancel_pair (Critical_vertex u, Critical_vertex v)
	Simplifies the chain complex by cancelling the pair (u, v), where u is a face of v.

Traversal
Critical_vertices_iterator	critical_vertices_begin (void) const
	Starts the set of all critical vertices.
Critical_vertices_iterator	critical_vertices_end (void) const
	Ends the set of all critical vertices.
Critical_vertices_of_same_index_iterator	critical_vertices_begin (Morse_index_type k) const
	Starts the set of critical vertices of index k.
Critical_vertices_of_same_index_iterator	critical_vertices_end (Morse_index_type k) const
	Ends the set of critical vertices of index k.
Faces_iterator	faces_begin (Critical_vertex u) const
	Starts the set of faces of u, that are incident critical vertices of higher index.
Faces_iterator	faces_end (Critical_vertex u) const
	Ends the set of faces of u, that are incident critical vertices of higher index.
Cofaces_iterator	cofaces_begin (Critical_vertex u) const
	Starts the set of cofaces of u, that are incident critical vertices of lower index.
Cofaces_iterator	cofaces_end (Critical_vertex u) const
	Ends the set of cofaces of u, that are incident critical vertices of lower index.
template<class OutputIterator>
OutputIterator	get_common_cofaces (Critical_vertex u, Critical_vertex v, OutputIterator out) const
	Returns the common cofaces of u and v, sharing the same index.
template<class InputIterator, class OutputIterator>
OutputIterator	get_common_cofaces (InputIterator begin, InputIterator end, OutputIterator out) const
	Returns the common cofaces of the input critical vertices, sharing the same index.

Combinatorial
const Directed_acyclic_graph &	get_directed_acyclic_graph (void) const
	Returns the data structure ofthe chain complex, that is a directed acyclic graph.
const Point &	get_critical_point (Critical_vertex u)
	Returns the point associated to u, a non-abstract vertex.
Morse_index_type	get_Morse_index (Critical_vertex u) const
	Returns the index of a critical vertex.
bool	is_abstract_critical_vertex (Critical_vertex u) const
	Returns true iff there is no associated point to u.
bool	is_pure_abstract_critical_vertex (Critical_vertex u) const
	Returns true iff there is no associated point to u and no lower bound.
unsigned	get_number_of_critical_vertices (void) const
	Returns the number of vertices.
unsigned	get_number_of_critical_vertices (Morse_index_type k) const
	Returns the number of vertices wof index k.
bool	is_face_of (Critical_vertex u, Critical_vertex v) const
	Checks that u and v are incident, and that the index of v is higher than the index u.
unsigned	get_number_of_faces (Critical_vertex u) const
	Returns the number of incident vertices of u with a higher index.
unsigned	get_number_of_cofaces (Critical_vertex u) const
	Returns the number of incident vertices of u with a lower index.

Stable Manifolds
void	add_point_to_stable_manifold (const Point &p, Critical_vertex u)
	Adds p to the stable manifold of u.
Stable_manifold &	get_stable_manifold (Critical_vertex u)
	Returns the stable manifold of u.
FT	get_lower_bound_of_stable_manifold (Critical_vertex u)
	Returns the lower bound of the stable manifold of u. When u is purely abstract and has no point in its stable manifold, its lower bound is estimated from its faces.
FT	get_upper_bound_of_stable_manifold (Critical_vertex u)
	Returns the upper bound of the stable manifold of u when u is not purely abstract or its stable manifold has at least one point; returns its lower bound otherwise.

Morse Function
Morse_function &	get_Morse_function (void)
	Returns the associated function as a functor.
void	set_Morse_function (Morse_function &function)
	Sets the Morse function of the complex.
FT	get_Morse_function_value (const Point &p)
	Returns the value of a point.
FT	get_Morse_function_value (Critical_vertex u)
	Returns the value of a vertex.

Detailed Description

template<class MorseFunction, class StableManifoldTraits = T_Stable_manifold_as_list_traits<typename MorseFunction::Point>>
class SBL::GT::T_Morse_Smale_Witten_chain_complex< MorseFunction, StableManifoldTraits >

Representation of the complex of the same name.

Template Parameters

MorseFunction	is a functor that return the height of a sample and the gradient of two samples. Note that it has to define the number type FT it uses for returning a value, and the type Point it uses as input.
StableManifoldTraits	Traits class defining types and static methods on a stable manifold.

Member Typedef Documentation

◆ Stable_manifold_traits

template<class MorseFunction, class StableManifoldTraits = T_Stable_manifold_as_list_traits<typename MorseFunction::Point>>

typedef StableManifoldTraits Stable_manifold_traits

Simple representation of a stable manifold as a list of points.

Template Parameters

Point Type of points in the stable manifold.