T_Morse_theory_based_analyzer< MorseSmaleWittenChainComplex > Class Template Reference

Analysis of a Morse Smale Witten chain complex. More...

#include <Morse_theory_based_analyzer.hpp>

Critical points and connexions
template<class OutputIterator>
OutputIterator	get_paths (OutputIterator out) const
	Returns the set of paths between pairs of 0-saddle points through a 1-saddle point.

Stable manifolds
template<class OutputIterator>
OutputIterator	get_stable_manifold_partition (OutputIterator out, bool skip_saddle_SM) const
	Returns the partition of stable manifolds for each critical vertex. The data type for stable manifolds is determined by the MorseSmaleWittenChainComplex data structure and is by default a list of points.

Disconnectivity Forest Methods
const Disconnectivity_forest &	get_disconnectivity_forest (void) const
	Returns the disconnectivity forest.
FT	get_Morse_function_value (Disconnectivity_vertex u) const
	Returns the value associated to a vertex in the disconnectivity forest.
const Point &	get_point (Disconnectivity_vertex u) const
	Returns the point associated to a vertex in the disconnectivity forest.
template<class OutputIterator>
OutputIterator	get_connected_component (Disconnectivity_vertex u, const FT &threshold, OutputIterator out) const
	Returns the set of points under the input threshold in the same component as the input vertex.
template<class OutputIterator>
OutputIterator	get_connected_component (Disconnectivity_vertex u, Disconnectivity_vertex v, const FT &threshold, OutputIterator out) const
	Returns the set of points in the component born with u and dead with v.
template<class OutputIterator>
OutputIterator	get_connected_component_before_death (Disconnectivity_vertex u, Disconnectivity_vertex v, OutputIterator out) const
	Same as before but the threshold is set to the upper bound of the stable manifold of u.

Persistence
template<class OutputIterator>
OutputIterator	get_infinite_persistent_critical_vertices (OutputIterator out) const
	Returns the set of 0-saddle vertices with an infinite persistence.
const Persistence_diagram &	get_persistence_diagram (void) const
template<class OutputIterator>
OutputIterator	get_persistence_diagram (OutputIterator out) const
	Same as before but copy it in an output container.
template<class OutputIterator>
OutputIterator	get_persistence_intervals (OutputIterator out)
	Returns the persistence intervals associated to the pairs of vertices in the persistence diagram.

Sublevelsets assignment
template<class OutputIterator>
OutputIterator	get_sublevelsets_connected_components (const FT &threshold, OutputIterator out) const
	Returns the all sub-level sets at a given threshold, that are the connected components of points having a value below the input threshold.

Simplifications
void	simplify (const FT &persistence)
	Eliminates the saddles with a persistence below the input threshold by removing them from the MSW chain complex (this operation requires recomputing the disconnectivity forest and the persistence diagram)

Detailed Description

template<class MorseSmaleWittenChainComplex>
class SBL::GT::T_Morse_theory_based_analyzer< MorseSmaleWittenChainComplex >

Analysis of a Morse Smale Witten chain complex.

Template Parameters

MorseSmaleWittenChainComplex

Hasse diagram representing the Morse Smale Witten chain complex.

Member Function Documentation

get_connected_component() [1/2]

template<class MorseSmaleWittenChainComplex>

template<class OutputIterator>

OutputIterator get_connected_component ( Disconnectivity_vertex u, const FT & threshold, OutputIterator out ) const

inline

Returns the set of points under the input threshold in the same component as the input vertex.

get_connected_component() [2/2]

template<class MorseSmaleWittenChainComplex>

template<class OutputIterator>

OutputIterator get_connected_component ( Disconnectivity_vertex u, Disconnectivity_vertex v, const FT & threshold, OutputIterator out ) const

inline

Returns the set of points in the component born with u and dead with v.

get_connected_component_before_death()

template<class MorseSmaleWittenChainComplex>

template<class OutputIterator>

OutputIterator get_connected_component_before_death ( Disconnectivity_vertex u, Disconnectivity_vertex v, OutputIterator out ) const

inline

Same as before but the threshold is set to the upper bound of the stable manifold of u.

get_disconnectivity_forest()

template<class MorseSmaleWittenChainComplex>

const T_Morse_theory_based_analyzer< MorseSmaleWittenChainComplex >::Disconnectivity_forest & get_disconnectivity_forest ( void ) const

inline

Returns the disconnectivity forest.

get_infinite_persistent_critical_vertices()

template<class MorseSmaleWittenChainComplex>

template<class OutputIterator>

OutputIterator get_infinite_persistent_critical_vertices ( OutputIterator out ) const

inline

Returns the set of 0-saddle vertices with an infinite persistence.

get_Morse_function_value()

template<class MorseSmaleWittenChainComplex>

T_Morse_theory_based_analyzer< MorseSmaleWittenChainComplex >::FT get_Morse_function_value ( Disconnectivity_vertex u ) const

inline

Returns the value associated to a vertex in the disconnectivity forest.

get_paths()

template<class MorseSmaleWittenChainComplex>

template<class OutputIterator>

OutputIterator get_paths ( OutputIterator out ) const

inline

Returns the set of paths between pairs of 0-saddle points through a 1-saddle point.

get_persistence_diagram() [1/2]

template<class MorseSmaleWittenChainComplex>

template<class OutputIterator>

OutputIterator get_persistence_diagram ( OutputIterator out ) const

inline

Same as before but copy it in an output container.

get_persistence_diagram() [2/2]

template<class MorseSmaleWittenChainComplex>

const T_Morse_theory_based_analyzer< MorseSmaleWittenChainComplex >::Persistence_diagram & get_persistence_diagram ( void ) const

inline

Returns the persistence diagram as a sorted set of pairs of vertices (0-saddle, 1-saddle) in the disconnectivity forest

get_persistence_intervals()

template<class MorseSmaleWittenChainComplex>

template<class OutputIterator>

OutputIterator get_persistence_intervals ( OutputIterator out )

inline

Returns the persistence intervals associated to the pairs of vertices in the persistence diagram.

get_point()

template<class MorseSmaleWittenChainComplex>

const T_Morse_theory_based_analyzer< MorseSmaleWittenChainComplex >::Point & get_point ( Disconnectivity_vertex u ) const

inline

Returns the point associated to a vertex in the disconnectivity forest.

get_stable_manifold_partition()

template<class MorseSmaleWittenChainComplex>

template<class OutputIterator>

OutputIterator get_stable_manifold_partition ( OutputIterator out, bool skip_saddle_SM ) const

inline

Returns the partition of stable manifolds for each critical vertex. The data type for stable manifolds is determined by the MorseSmaleWittenChainComplex data structure and is by default a list of points.

get_sublevelsets_connected_components()

template<class MorseSmaleWittenChainComplex>

template<class OutputIterator>

OutputIterator get_sublevelsets_connected_components ( const FT & threshold, OutputIterator out ) const

inline

Returns the all sub-level sets at a given threshold, that are the connected components of points having a value below the input threshold.

simplify()

template<class MorseSmaleWittenChainComplex>

void simplify ( const FT & persistence )

inline

Eliminates the saddles with a persistence below the input threshold by removing them from the MSW chain complex (this operation requires recomputing the disconnectivity forest and the persistence diagram)