Computes the persistent cohomology of a filtered complex. More...

Public Types
typedef FilteredComplex::Simplex_key	Simplex_key
	Data stored for each simplex.

typedef FilteredComplex::Simplex_handle	Simplex_handle
	Handle to specify a simplex.

typedef FilteredComplex::Filtration_value	Filtration_value
	Type for the value of the filtration function.

typedef CoefficientField::Element	Arith_element
	Type of element of the field.

typedef std::tuple< Simplex_handle, Simplex_handle, Arith_element >	Persistent_interval
	Type for birth and death FilteredComplex::Simplex_handle. The Arith_element field is used for the multi-field framework.

Public Types inherited from PersistentHomology
typedef unspecified	Filtered_complex
	Type of filtered cell complex on which persistent homology is computed. More...

typedef unspecified	Coefficient_field
	Type of coefficients to be used for computing persistent homology. More...

Public Member Functions
	Persistent_cohomology (FilteredComplex &cpx, bool persistence_dim_max=false)
	Initializes the Persistent_cohomology class. More...

void	init_coefficients (int charac)
	Initializes the coefficient field.

void	init_coefficients (int charac_min, int charac_max)
	Initializes the coefficient field for multi-field persistent homology.

void	compute_persistent_cohomology (Filtration_value min_interval_length=0)
	Compute the persistent homology of the filtered simplicial complex. More...

void	output_diagram (std::ostream &ostream=std::cout)
	Output the persistence diagram in ostream. More...

std::vector< int >	betti_numbers () const
	Returns Betti numbers. More...

int	betti_number (int dimension) const
	Returns the Betti number of the dimension passed by parameter. More...

std::vector< int >	persistent_betti_numbers (Filtration_value from, Filtration_value to) const
	Returns the persistent Betti numbers. More...

int	persistent_betti_number (int dimension, Filtration_value from, Filtration_value to) const
	Returns the persistent Betti number of the dimension passed by parameter. More...

const std::vector< Persistent_interval > &	get_persistent_pairs () const
	Returns a list of persistence birth and death FilteredComplex::Simplex_handle pairs. More...

std::vector< std::pair< Filtration_value, Filtration_value > >	intervals_in_dimension (int dimension)
	Returns persistence intervals for a given dimension. More...

Detailed Description

template<class FilteredComplex, class CoefficientField>
class Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >

Computes the persistent cohomology of a filtered complex.

The computation is implemented with a Compressed Annotation Matrix (CAM)[8], and is adapted to the computation of Multi-Field Persistent Homology (MF) [6] .

Examples: Random_bitmap_cubical_complex.cpp, alpha_complex_3d_persistence.cpp, alpha_complex_persistence.cpp, alpha_rips_persistence_bottleneck_distance.cpp, cech_persistence.cpp, cubical_complex_persistence.cpp, custom_persistence_sort.cpp, distance_matrix_edge_collapse_rips_persistence.cpp, edge_collapse_conserve_persistence.cpp, example_nearest_landmark_table.cpp, periodic_cubical_complex_persistence.cpp, persistence_from_file.cpp, persistence_from_simple_simplex_tree.cpp, plain_homology.cpp, point_cloud_edge_collapse_rips_persistence.cpp, rips_correlation_matrix_persistence.cpp, rips_distance_matrix_persistence.cpp, rips_multifield_persistence.cpp, rips_persistence.cpp, rips_persistence_step_by_step.cpp, rips_persistence_via_boundary_matrix.cpp, sparse_rips_persistence.cpp, strong_witness_persistence.cpp, and weak_witness_persistence.cpp.

Constructor & Destructor Documentation

◆ Persistent_cohomology()

template<class FilteredComplex , class CoefficientField >

Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >::Persistent_cohomology	(	FilteredComplex &	cpx,
		bool	persistence_dim_max = `false`
	)

inlineexplicit

Initializes the Persistent_cohomology class.

Parameters

[in]	cpx	Complex for which the persistent homology is computed. cpx is a model of FilteredComplex
[in]	persistence_dim_max	if true, the persistent homology for the maximal dimension in the complex is computed. If false, it is ignored. Default is false.

Exceptions

std::out_of_range In case the number of simplices is more than Simplex_key type numeric limit.

Member Function Documentation

◆ betti_number()

template<class FilteredComplex , class CoefficientField >

int Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >::betti_number ( int dimension ) const

inline

Returns the Betti number of the dimension passed by parameter.

Parameters

[in] dimension The Betti number dimension to get.

Returns: Betti number of the given dimension

◆ betti_numbers()

template<class FilteredComplex , class CoefficientField >

std::vector<int> Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >::betti_numbers ( ) const

inline

Returns Betti numbers.

Returns: A vector of Betti numbers.

◆ compute_persistent_cohomology()

template<class FilteredComplex , class CoefficientField >

void Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >::compute_persistent_cohomology ( Filtration_value min_interval_length = 0 )

inline

Compute the persistent homology of the filtered simplicial complex.

Parameters

[in] min_interval_length the computation discards all intervals of length less or equal than min_interval_length

Assumes that the filtration provided by the simplicial complex is valid. Undefined behavior otherwise.

Examples: cubical_complex_persistence.cpp, example_nearest_landmark_table.cpp, and periodic_cubical_complex_persistence.cpp.

◆ get_persistent_pairs()

template<class FilteredComplex , class CoefficientField >

const std::vector<Persistent_interval>& Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >::get_persistent_pairs ( ) const

inline

Returns a list of persistence birth and death FilteredComplex::Simplex_handle pairs.

Returns: A list of Persistent_cohomology::Persistent_interval

◆ intervals_in_dimension()

template<class FilteredComplex , class CoefficientField >

std::vector< std::pair< Filtration_value , Filtration_value > > Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >::intervals_in_dimension ( int dimension )

inline

Returns persistence intervals for a given dimension.

Parameters

[in] dimension Dimension to get the birth and death pairs from.

Returns: A vector of persistence intervals (birth and death) on a fixed dimension.

◆ output_diagram()

template<class FilteredComplex , class CoefficientField >

void Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >::output_diagram ( std::ostream & ostream = std::cout )

inline

Output the persistence diagram in ostream.

The file format is the following: p1*...*pr dim b d

where "dim" is the dimension of the homological feature, b and d are respectively the birth and death of the feature and p1*...*pr is the product of prime numbers pi such that the homology feature exists in homology with Z/piZ coefficients.

Examples: cubical_complex_persistence.cpp, example_nearest_landmark_table.cpp, and periodic_cubical_complex_persistence.cpp.

◆ persistent_betti_number()

template<class FilteredComplex , class CoefficientField >

int Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >::persistent_betti_number	(	int	dimension,
		Filtration_value	from,
		Filtration_value	to
	)		const

inline

Returns the persistent Betti number of the dimension passed by parameter.

Parameters

[in]	dimension	The Betti number dimension to get.
[in]	from	The persistence birth limit to be added in the number \((persistent birth \leq from)\).
[in]	to	The persistence death limit to be added in the number \((persistent death > to)\).

Returns: Persistent Betti number of the given dimension

◆ persistent_betti_numbers()

template<class FilteredComplex , class CoefficientField >

std::vector<int> Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >::persistent_betti_numbers	(	Filtration_value	from,
		Filtration_value	to
	)		const

inline

Returns the persistent Betti numbers.

Parameters

[in]	from	The persistence birth limit to be added in the number \((persistent birth \leq from)\).
[in]	to	The persistence death limit to be added in the number \((persistent death > to)\).

Returns: A vector of persistent Betti numbers.

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

include/gudhi/Persistent_cohomology.h

Public Types

Public Member Functions

Detailed Description

template<class FilteredComplex, class CoefficientField> class Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >

Constructor & Destructor Documentation

◆ Persistent_cohomology()

Member Function Documentation

◆ betti_number()

◆ betti_numbers()

◆ compute_persistent_cohomology()

◆ get_persistent_pairs()

◆ intervals_in_dimension()

◆ output_diagram()

◆ persistent_betti_number()

◆ persistent_betti_numbers()

template<class FilteredComplex, class CoefficientField>
class Gudhi::persistent_cohomology::Persistent_cohomology< FilteredComplex, CoefficientField >