#include <CGAL/HDVF/Filtration_core.h>

Inherited by CGAL::HDVF::Filtration_lower_star< CoefficientType, ComplexType, DegreeType >.

Definition

template<typename CoefficientType, typename ComplexType, typename DegreeType>
class CGAL::HDVF::Filtration_core< CoefficientType, ComplexType, DegreeType >

The class Filtration_core implements data structures and methods required by the Filtration concept.

By definition, a filtration over a chain complex K is a sequence of sub complexes \(\{K_t\,;\, t\in[d_1, \ldots, d_N]\}\), where \(d_i\) are scalars, such that:

\(\forall d\leqslant d'\), \(K_d\subseteq K_{d'}\).
\(|K_{d_{i+1}}| = |K_{d_{i}}|+1\).
- As a consequence, any cell \(\sigma\in K\), is "added" at a given time \(i\) and the corresponding \(d_i\) is called its degree (denoted by \(\mathrm{deg}(\sigma)\)).
\(K_{d_1}\) is an empty complex.
\(K_{d_N} = K\).
For any cell \(\sigma\in K\), if \(\tau\) is a proper face of \(\sigma\), then \(\mathrm{deg}(\tau)\leqslant \mathrm{deg}(\sigma)\).

In consequence, a filtration associated to a complex K:

maps each cell to a scalar called its degree
orders the cells of K (each cell has a unique index along the filtration called time along the filtration) such that:
- the index of a cell is larger that the indices of its faces,
- the degree map is increasing along the filtration.

The class Filtration_core provides elementary constructors and methods used in derived filtrations.

Is model of: Filtration

Template Parameters

CoefficientType	a model of the `Ring` concept (ring used for homology computation).
ComplexType	a model of the `AbstractChainComplex` concept (type of the underlying chain complex).
DegreeType	the scalar type of degrees.

Classes
struct	FiltrationIterValue
	Type of value returned by the iterator. More...

struct	iterator
	Iterator over a filtration. More...

Public Types
typedef std::pair< std::size_t, int >	CellDim
	Type for indexing uniquely a cell.

Public Member Functions
	Filtration_core (const ComplexType &K)
	Filtration_core default constructor.

	Filtration_core (const ComplexType &K, const std::vector< CellDim > &filtration, const std::vector< DegreeType > &deg)
	Constructor from a vector of cells (ordering of cells) and an associated vector of degrees.

	Filtration_core (const Filtration_core &f)
	Constructor by copy.

iterator	begin ()
	Iterator to the beginning of the filtration.

iterator	end ()
	Iterator to the ending of the filtration.

std::size_t	get_filtration_size () const
	Gets the filtration size.

CellDim	get_cell_dim (std::size_t i) const
	Gets the cell (that is cell index and dimension) at the index `i` of the filtration.

DegreeType	get_degree (std::size_t i) const
	Gets the degree of the `i`th element of the filtration.

vector< vector< std::size_t > >	export_filtration () const
	Exports the filtration time indices.

bool	is_valid_filtration () const
	Checks if a filtration is valid.

Protected Types
typedef OSM::Sparse_matrix< CoefficientType, OSM::COLUMN >	CMatrix
	Type of column-major sparse matrices.

typedef OSM::Sparse_matrix< CoefficientType, OSM::ROW >	RMatrix
	Type of row-major sparse matrices.

typedef OSM::Sparse_chain< CoefficientType, OSM::COLUMN >	CChain
	Type of column-major chains.

typedef OSM::Sparse_chain< CoefficientType, OSM::ROW >	RChain
	Type of row-major chains.

Protected Member Functions
void	build_filtration_structure ()

Protected Attributes
const ComplexType &	_K
	Constant reference to the underlying chain complex.

std::vector< CellDim >	_filtration
	Vector of cells of the filtration (full ordering of cells).

std::vector< DegreeType >	_deg
	Vector of degrees of cells along the filtration.

std::map< CellDim, std::size_t >	_cell_to_t
	Map from cells to their index in the filtration.

Friends
template<typename CoefT , typename ComplexT , typename DegT , typename FiltrT >
class	Hdvf_persistence

std::ostream &	operator<< (std::ostream &out, const Filtration_core &f)
	Overload of the `<<`operator for filtrations.

Member Typedef Documentation

◆ CellDim

template<typename CoefficientType , typename ComplexType , typename DegreeType >

typedef std::pair<std::size_t, int> CGAL::HDVF::Filtration_core< CoefficientType, ComplexType, DegreeType >::CellDim

Type for indexing uniquely a cell.

First element of the pair: index of the cell.
Second element of the pair: dimension of the cell.

Constructor & Destructor Documentation

◆ Filtration_core() [1/3]

template<typename CoefficientType , typename ComplexType , typename DegreeType >

CGAL::HDVF::Filtration_core< CoefficientType, ComplexType, DegreeType >::Filtration_core ( const ComplexType & K )

Filtration_core default constructor.

Builds an "empty" filtration with K as underlying chain complex.

Parameters

[in] K A chain complex (a model of AbstractChainComplex), the underlying chain complex of the filtration.

◆ Filtration_core() [2/3]

template<typename CoefficientType , typename ComplexType , typename DegreeType >

CGAL::HDVF::Filtration_core< CoefficientType, ComplexType, DegreeType >::Filtration_core	(	const ComplexType &	K,
		const std::vector< CellDim > &	filtration,
		const std::vector< DegreeType > &	deg
	)

Constructor from a vector of cells (ordering of cells) and an associated vector of degrees.

The constructor check that the filtration is valid (a cell is introduced in the filtration after its faces and the degree vector is increasing) and throw an exception if not.

Parameters

[in]	K	A chain complex (a model of `AbstractChainComplex`), the underlying chain complex of the filtration.
[in]	filtration	An ordering of the cells of `K` encoded as a vector of its cells.
[in]	deg	The (increasing) vector of cells degrees.

◆ Filtration_core() [3/3]

template<typename CoefficientType , typename ComplexType , typename DegreeType >

CGAL::HDVF::Filtration_core< CoefficientType, ComplexType, DegreeType >::Filtration_core ( const Filtration_core< CoefficientType, ComplexType, DegreeType > & f )

Constructor by copy.

Builds a Filtration_core by copy from another.

Parameters

[in] f An initial Filtration_core.

Member Function Documentation

◆ begin()

template<typename CoefficientType , typename ComplexType , typename DegreeType >

iterator CGAL::HDVF::Filtration_core< CoefficientType, ComplexType, DegreeType >::begin ( )

Iterator to the beginning of the filtration.

Returns: The iterator to the beginning of the filtration.

◆ end()

template<typename CoefficientType , typename ComplexType , typename DegreeType >

iterator CGAL::HDVF::Filtration_core< CoefficientType, ComplexType, DegreeType >::end ( )

Iterator to the ending of the filtration.

Returns: The iterator to the ending of the filtration.

◆ export_filtration()

template<typename CoefficientType , typename ComplexType , typename DegreeType >

vector< vector< std::size_t > > CGAL::HDVF::Filtration_core< CoefficientType, ComplexType, DegreeType >::export_filtration ( ) const

Exports the filtration time indices.

The method exports the time index of every cells in each dimension.

Returns: A vector containing, for each dimension, the vector of labels by cell index.

◆ is_valid_filtration()

template<typename CoefficientType , typename ComplexType , typename DegreeType >

bool CGAL::HDVF::Filtration_core< CoefficientType, ComplexType, DegreeType >::is_valid_filtration

Checks if a filtration is valid.

Checks that cells are ordered in increasing degrees and all cells have indices larger than their faces.

Returns: true if the filtration is valid, false otherwise

Definition

Classes

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Friends

Member Typedef Documentation

◆ CellDim

Constructor & Destructor Documentation

◆ Filtration_core() [1/3]

◆ Filtration_core() [2/3]

◆ Filtration_core() [3/3]

Member Function Documentation

◆ begin()

◆ end()

◆ export_filtration()

◆ is_valid_filtration()