#include <CGAL/HDVF/Sub_chain_complex_mask.h>

Definition

template<typename CoefficientType, typename ComplexType>
class CGAL::HDVF::Sub_chain_complex_mask< CoefficientType, ComplexType >

The class Sub_chain_complex_mask is a technical class implementing a sub chain complex.

A sub chain complex \(A\) of a chain complex \(K\) is a subset \(A\subseteq K\) such that the restricted boundary operator \(\partial_A = \partial_K|_A\) still satisfies \(\partial_A^2 = 0\).

The Sub_chain_complex_mask class is used to compute reduced homology. This class is based on a set of bitboard masks (one in each dimension) used to define sub chain complexes and their associated reduction encoded in sub-sparse matrices (OSM::Sub_sparse_matrix class). Technically, Sub_chain_complex_mask are used to partially screen chain complexes and chains in associated boundary matrices, and hence compute homology "locally".

Warning: For efficiency reasons, when a Sub_chain_complex_mask is used to screen sparse matrices (with the screen_matrices method), screening is only performed on the major direction of matrices (thus column-major matrices are restricted over columns and row-major matrices are restricted over rows). Iterators are restricted accordingly. But chains themselves are not restricted.
However, if A is a proper sub-complex of K (that is, closed with respect to faces), chains automatically comply with the screening. Indeed, for any \(q\)-cell \(\sigma\in A\) (thus the corresponding bit is on in the mask), all the faces of \(\sigma\) also belong to \(A\). Thus for any \(q-1\)-cell \(\tau\) in the boundary of \(\sigma\) (that is, such that \(\langle\partial_k(\sigma),\tau\rangle\neq 0\)), \(\tau\) belongs to \(A\) (and thus the corresponding bit in the mask is also on).

Template Parameters

CoefficientType	a model of the `Ring` concept.
ComplexType	a model of the `AbstractChainComplex` concept (type of the chain complex screened by `Sub_chain_complex_mask`).

Examples: HDVF/main_dual_hdvf.cpp.

Public Member Functions
	Sub_chain_complex_mask (const ComplexType &K, bool full=true)
	Constructor from a complex.

	Sub_chain_complex_mask (const ComplexType &K, const std::vector< std::vector< int > > &cells, bool close=true)
	Constructor from an enumeration of cells.

	Sub_chain_complex_mask (const Sub_chain_complex_mask &otherToCopy)
	Constructor by copy.

Sub_chain_complex_mask &	operator= (const Sub_chain_complex_mask &otherToCopy)
	Assignment operator.

Sub_chain_complex_mask	complement ()
	Returns the complement of the mask.

bool	get_bit (int q, int i) const
	Gets a bit of the mask (bit i in dimension q).

void	set_bit_on (int q, int i)
	Sets a bit to 1 (bit i in dimension q).

void	set_bit_off (int q, int i)
	Sets a bit to 0 (bit i in dimension q).

const std::vector< OSM::Bitboard > &	get_bitboard () const
	Gets the bitboards of the sub chain complex.

const OSM::Bitboard &	get_bitboard (int q) const
	Gets the bitboard of the sub chain complex in dimension q.

template<typename CT , int CTF>
void	screen_matrices (std::vector< OSM::Sub_sparse_matrix< CT, CTF > > &matrices)
	Screens a sequence of Sub_sparse_matrix (in each dimension).

template<typename CT , int CTF>
void	screen_chain (OSM::Sparse_chain< CT, CTF > &chain, int q)
	Restricts a chain in a given dimension to the sub chain complex maks.

Protected Attributes
int	_dim
	Dimension of the underlying complex.

std::vector< OSM::Bitboard >	_sub
	Vector of bitboards coding masks in each dimension.

std::vector< int >	_nb_cells
	Number of cells in the mask in each dimension.

const ComplexType &	_K
	Constant reference to the underlying complex.

bool	_full
	Is full sub_complex.

Friends
std::ostream &	operator<< (std::ostream &out, const Sub_chain_complex_mask &sub)
	Overload of the `<<`operator for `Sub_chain_complex_mask`.

Constructor & Destructor Documentation

◆ Sub_chain_complex_mask() [1/3]

template<typename CoefficientType , typename ComplexType >

CGAL::HDVF::Sub_chain_complex_mask< CoefficientType, ComplexType >::Sub_chain_complex_mask	(	const ComplexType &	K,
		bool	full = `true`
	)

Constructor from a complex.

Build a Sub_chain_complex_mask associated to K with all bits set to 1 in the masks if full is true, and all bits set to 0 otherwise.

Parameters

[in]	K	A constant reference to the underlying complex.
[in]	full	Build full / empty masks (default: full).

◆ Sub_chain_complex_mask() [2/3]

template<typename CoefficientType , typename ComplexType >

CGAL::HDVF::Sub_chain_complex_mask< CoefficientType, ComplexType >::Sub_chain_complex_mask	(	const ComplexType &	K,
		const std::vector< std::vector< int > > &	cells,
		bool	close = `true`
	)

Constructor from an enumeration of cells.

Build masks associated to the underlying complex K with all bits corresponding to cells (and their faces if close is true) set to 1.

Parameters

[in]	K	A constant reference to the underlying complex.
[in]	cells	A vector containing, in each dimension, a vector of cells indexes.
[in]	close	If this boolean is true, the faces of `cells` are also set to 1.

◆ Sub_chain_complex_mask() [3/3]

template<typename CoefficientType , typename ComplexType >

CGAL::HDVF::Sub_chain_complex_mask< CoefficientType, ComplexType >::Sub_chain_complex_mask ( const Sub_chain_complex_mask< CoefficientType, ComplexType > & otherToCopy )

Constructor by copy.

Builds a Sub_chain_complex_mask by copy from another.

Parameters

[in] otherToCopy An initial Sub_chain_complex_mask.

Member Function Documentation

◆ complement()

template<typename CoefficientType , typename ComplexType >

Sub_chain_complex_mask CGAL::HDVF::Sub_chain_complex_mask< CoefficientType, ComplexType >::complement ( )

Returns the complement of the mask.

The method return a new Sub_chain_complex_mask containing the complement of the current mask (0 and 1 bits in the mask are exchanged).

◆ get_bitboard()

template<typename CoefficientType , typename ComplexType >

const std::vector< OSM::Bitboard > & CGAL::HDVF::Sub_chain_complex_mask< CoefficientType, ComplexType >::get_bitboard ( ) const

Gets the bitboards of the sub chain complex.

Returns a constant reference to the vector of bitboards in each dimension.

◆ operator=()

template<typename CoefficientType , typename ComplexType >

Sub_chain_complex_mask & CGAL::HDVF::Sub_chain_complex_mask< CoefficientType, ComplexType >::operator= ( const Sub_chain_complex_mask< CoefficientType, ComplexType > & otherToCopy )

Assignment operator.

Warning: The operator argument must provide a sub chain complex mask over the same underlying chain complex. It not so, the assignment will throw an exception.

Parameters

[in] otherToCopy A Sub_chain_complex_mask copied into this (otherToCopy and this must have the same underlying chain complex).

◆ screen_chain()

template<typename CoefficientType , typename ComplexType >

template<typename CT , int CTF>

void CGAL::HDVF::Sub_chain_complex_mask< CoefficientType, ComplexType >::screen_chain	(	OSM::Sparse_chain< CT, CTF > &	chain,
		int	q
	)

Restricts a chain in a given dimension to the sub chain complex maks.

Nullify all coefficients out of the mask.

Parameters

[in]	chain	The chain restricted.
[in]	q	Dimension of the chain.

◆ screen_matrices()

template<typename CoefficientType , typename ComplexType >

template<typename CT , int CTF>

void CGAL::HDVF::Sub_chain_complex_mask< CoefficientType, ComplexType >::screen_matrices ( std::vector< OSM::Sub_sparse_matrix< CT, CTF > > & matrices )

Screens a sequence of Sub_sparse_matrix (in each dimension).

Given a sequence of matrices (vector of Sub_sparse_matrices) sets the masks of Sub_sparse_matrices in each dimension to the current Sub_chain_complex_mask.

Warning: For efficiency, screening is performed on the major direction of matrices (so along columns for column-major matrices and along row for row-major matrices).

Parameters

[in] matrices A vector of Sub_sparse_matrix (in each dimension).

Member Data Documentation

◆ _full

template<typename CoefficientType , typename ComplexType >

bool CGAL::HDVF::Sub_chain_complex_mask< CoefficientType, ComplexType >::_full

protected

Is full sub_complex.

This boolean flag is true is all bits in the bitboards are on.

Definition

Public Member Functions

Protected Attributes

Friends

Constructor & Destructor Documentation

◆ Sub_chain_complex_mask() [1/3]

◆ Sub_chain_complex_mask() [2/3]

◆ Sub_chain_complex_mask() [3/3]

Member Function Documentation

◆ complement()

◆ get_bitboard()

◆ operator=()

◆ screen_chain()

◆ screen_matrices()

Member Data Documentation

◆ _full