Gudhi::rips_complex::Rips_complex< Filtration_value > Class Template Reference

Rips complex data structure. More...

Public Types
typedef boost::adjacency_list< boost::vecS, boost::vecS, boost::directedS, boost::property< vertex_filtration_t, Filtration_value >, boost::property< edge_filtration_t, Filtration_value > >	OneSkeletonGraph
	Type of the one skeleton graph stored inside the Rips complex structure.

Public Member Functions
template<typename ForwardPointRange , typename Distance >
	Rips_complex (const ForwardPointRange &points, Filtration_value threshold, Distance distance)
	Rips_complex constructor from a list of points. More...
template<typename DistanceMatrix >
	Rips_complex (const DistanceMatrix &distance_matrix, Filtration_value threshold)
	Rips_complex constructor from a distance matrix. More...
template<typename SimplicialComplexForRips >
void	create_complex (SimplicialComplexForRips &complex, int dim_max)
	Initializes the simplicial complex from the Rips graph and expands it until a given maximal dimension. More...

Detailed Description

template<typename Filtration_value>
class Gudhi::rips_complex::Rips_complex< Filtration_value >

Rips complex data structure.

The data structure is a one skeleton graph, or Rips graph, containing edges when the edge length is less or equal to a given threshold. Edge length is computed from a user given point cloud with a given distance function, or a distance matrix.

Template Parameters

Filtration_value

is the type used to store the filtration values of the simplicial complex.

Examples:

Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp, Persistent_cohomology/rips_multifield_persistence.cpp, Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp, Rips_complex/example_one_skeleton_rips_from_distance_matrix.cpp, Rips_complex/example_one_skeleton_rips_from_points.cpp, Rips_complex/example_rips_complex_from_csv_distance_matrix_file.cpp, Rips_complex/example_rips_complex_from_off_file.cpp, Rips_complex/rips_distance_matrix_persistence.cpp, and Rips_complex/rips_persistence.cpp.

Constructor & Destructor Documentation

Rips_complex() [1/2]

template<typename Filtration_value >

template<typename ForwardPointRange , typename Distance >

Gudhi::rips_complex::Rips_complex< Filtration_value >::Rips_complex ( const ForwardPointRange &  points, Filtration_value  threshold, Distance  distance  )

inline

Rips_complex constructor from a list of points.

Parameters

[in]	points	Range of points.
[in]	threshold	Rips value.
[in]	distance	distance function that returns a Filtration_value from 2 given points.

Template Parameters

ForwardPointRange	must be a range for which std::begin and std::end return input iterators on a point.
Distance	furnishes operator()(const Point& p1, const Point& p2), where Point is a point from the ForwardPointRange, and that returns a Filtration_value.

Rips_complex() [2/2]

template<typename Filtration_value >

template<typename DistanceMatrix >

Gudhi::rips_complex::Rips_complex< Filtration_value >::Rips_complex ( const DistanceMatrix &  distance_matrix, Filtration_value  threshold  )

inline

Rips_complex constructor from a distance matrix.

Parameters

[in]	distance_matrix	Range of distances.
[in]	threshold	Rips value.

Template Parameters

DistanceMatrix

must have a size() method and on which distance_matrix[i][j] returns the distance between points \(i\) and \(j\) as long as \( 0 \leqslant j < i \leqslant distance\_matrix.size().\)

Member Function Documentation

create_complex()

template<typename Filtration_value >

template<typename SimplicialComplexForRips >

void Gudhi::rips_complex::Rips_complex< Filtration_value >::create_complex ( SimplicialComplexForRips &  complex, int  dim_max  )

inline

Initializes the simplicial complex from the Rips graph and expands it until a given maximal dimension.

Template Parameters

SimplicialComplexForRips

must meet SimplicialComplexForRips concept.

Parameters

[in]	complex	SimplicialComplexForRips to be created.
[in]	dim_max	graph expansion for Rips until this given maximal dimension.

Exceptions

std::invalid_argument

In debug mode, if complex.num_vertices() does not return 0.

Examples:

Rips_complex/example_one_skeleton_rips_from_distance_matrix.cpp, and Rips_complex/example_one_skeleton_rips_from_points.cpp.

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The documentation for this class was generated from the following file:

• include/gudhi/Rips_complex.h