#include <CGAL/HDVF/Sub_sparse_matrix.h>

Inherits from

CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >.

Definition

template<typename CoefficientRing, int StorageFormat>
class CGAL::OSM::Sub_sparse_matrix< CoefficientRing, StorageFormat >

The class Sub_sparse_matrix is a technical class implementing the concept SparseMatrix together with a system of masks to partially screen matrices (and restrict computations to a subset of indices along their major direction).

This class is used to compute reduced homology (and thus to compute persistent homology and Alexander duality).

Sub_sparse_matrix inherits Sparse_matrix structure and basically adds two bitboards:

one describing indices of cells belonging to the subset of indices considered (let us denote it by \(A\))
the second providing indices of non-empty chains in \(A\)

The class does not modify linear algebra operators, but focuses on adapted iterators, output operators and methods to adjust the "mask".

Is model of: SparseMatrix

Template Parameters

CoefficientRing	a model of the `IntegralDomainWithoutDivision` concept, providing the ring used to compute homology.
StorageFormat	an integer constant encoding the storage format of matrices (`OSM::COLUMN` or `OSM::ROW`).

Public Member Functions
	Sub_sparse_matrix (size_t rowCount=0, size_t columnCount=0)
	Default constructor of a new `Sub_sparse_matrix` (with given rows/columns sizes and mask set to `full`).

	Sub_sparse_matrix (size_t rowCount, size_t columnCount, const Bitboard &subChain)
	Constructor with given rows/columns sizes and a mask.

	Sub_sparse_matrix (const Sub_sparse_matrix &otherToCopy)
	Copy constructor from another `Sub_sparse_matrix`.

	Sub_sparse_matrix (const Sparse_matrix< CoefficientRing, StorageFormat > &otherToCopy)
	Copy constructor from `Sparse_matrix`.

Bitboard::iterator	begin () const noexcept
	Iterator to the beginning of the indices of non empty chains inside the mask.

Bitboard::iterator	end () const noexcept
	Iterator past-the-end of the indices of non empty chains inside the mask.

void	set_sub (const Bitboard &new_subChains)
	Changes the indices subset mask.

void	set_bit_on (size_t index)
	Adds an index to the mask.

void	set_bit_off (size_t index)
	Removes an index from the mask.

void	complement ()
	Changes the mask to its complement.

Sub_sparse_matrix &	operator= (const Sub_sparse_matrix &otherToCopy)
	Assigns to other `Sub_sparse_matrix`.

Public Member Functions inherited from CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >
	Sparse_matrix ()
	Default constructor (empty new `Sparse_matrix` object).

	Sparse_matrix (const size_t rowCount, const size_t columnCount)
	Constructor with given rows/columns sizes.

template<int CTF>
	Sparse_matrix (const Sparse_matrix< CoefficientRing, CTF > &otherToCopy)
	Copy constructor.

Sparse_matrix &	operator= (const Sparse_matrix &otherToCopy)
	Assigns to other matrix.

void	nullify ()
	Cleans a SparseMatrix (set all coefficients to zero).

bool	is_null ()
	Tests if a SparseMatrix is null.

template<int _CTF>
Sparse_matrix	operator+ (const Sparse_matrix< CoefficientRing, _CTF > &other)
	Adds two matrices into a new matrix.

template<int _CTF>
Sparse_matrix	operator- (const Sparse_matrix< CoefficientRing, _CTF > &other)
	Subtracts two matrices into a new matrix.

Sparse_matrix	operator* (const CoefficientRing &lambda)
	Applies factor on each coefficients into a new matrix.

Sparse_matrix &	operator*= (const CoefficientRing &lambda)
	Applies factor on each coefficients and assign.

Sparse_matrix	operator- ()
	Computes the negative of a matrix (unary operator).

Matrix_chain	operator[] (size_t index) const
	Gets the value of a chain from a const matrix.

Sparse_matrix	operator/ (const std::vector< size_t > &_indices)
	Removes a set of chains from a copy of the matrix.

Sparse_matrix	operator/ (size_t index)
	Removes the chain at a given `index` from a copy of the matrix.

Sparse_matrix &	operator/= (const std::vector< size_t > &indices)
	Removes a set of chains from a matrix.

Sparse_matrix &	operator/= (const size_t index)
	Removes the chain at a given `index` from a matrix.

Bitboard::iterator	begin () const noexcept
	Iterator to the index of the first non null chain.

Bitboard::iterator	end () const noexcept
	Iterator past-the-end of chain indices.

Bitboard::reverse_iterator	reverse_begin () noexcept
	Reverse iterator to the index of the last non null chain.

Bitboard::reverse_iterator	reverse_begin (size_t index) noexcept

Bitboard::reverse_iterator	reverse_end () noexcept
	Reverse iterator past-the-end of chain indices.

Sparse_matrix< CoefficientRing, COLUMN+ROW - StorageFormat >	transpose ()
	Transposes a matrix.

std::pair< size_t, size_t >	dimensions () const
	Gets the matrix sizes.

Protected Attributes
Bitboard	_subChains
	A bitboard describing subchains restriction.

Bitboard	_subChainsStates
	A bitboard containing state of each chain (restricted to subchains).

Protected Attributes inherited from CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >
std::vector< Sparse_chain< CoefficientRing, StorageFormat > >	_chains

Bitboard	_chainsStates

std::pair< size_t, size_t >	_size

Friends
std::ostream &	operator<< (std::ostream &stream, const Sub_sparse_matrix &matrix)
	Displays a `Sub_sparse_matrix` in the output stream.

Additional Inherited Members
Public Types inherited from CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >
typedef CoefficientRing	Coefficient_ring
	Type of coefficient ring.

typedef Sparse_chain< CoefficientRing, StorageFormat >	Matrix_chain
	Type of chains associated to the matrix.

Protected Member Functions inherited from CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >
Matrix_chain &	operator[] (const size_t _index)

void	set_coefficient (const size_t i, const size_t j, const Coefficient_ring d)

Coefficient_ring	get_coefficient (const size_t i, const size_t j) const

Sparse_matrix &	remove_column (size_t index)

Sparse_matrix &	remove_row (size_t index)

Sparse_matrix &	remove_coefficient (size_t i, size_t j)

Related Functions inherited from CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >
template<typename _CT >
bool	operator== (const Sparse_matrix< _CT, OSM::COLUMN > &matrix, const Sparse_matrix< _CT, OSM::COLUMN > &other)
	Comparison of two COLUMN matrices.

template<typename _CT >
bool	operator== (const Sparse_matrix< _CT, OSM::COLUMN > &matrix, const Sparse_matrix< _CT, OSM::ROW > &other)
	Comparison of a COLUMN and a ROW matrix.

template<typename _CT >
bool	operator== (const Sparse_matrix< _CT, OSM::ROW > &matrix, const Sparse_matrix< _CT, OSM::COLUMN > &other)
	Comparison of a ROW and a COLUMN matrix.

template<typename _CT >
bool	operator== (const Sparse_matrix< _CT, OSM::ROW > &matrix, const Sparse_matrix< _CT, OSM::ROW > &other)
	Comparison of two ROW matrices.

std::ostream &	operator<< (std::ostream &stream, const Sparse_matrix &matrix)
	Writes a sparse matrix in the output stream.

template<typename _CT >
std::ostream &	write_matrix (const Sparse_matrix< _CT, OSM::COLUMN > &M, std::ostream &out)
	Writes a sparse COLUMN matrix to a stream.

template<typename _CT >
std::ostream &	write_matrix (const Sparse_matrix< _CT, OSM::ROW > &M, std::ostream &out)
	Writes a sparse ROW matrix to a stream.

template<typename _CT >
void	write_matrix (const Sparse_matrix< _CT, OSM::COLUMN > &M, std::string filename)
	Writes a sparse COLUMN matrix to a file.

template<typename _CT >
void	write_matrix (const Sparse_matrix< _CT, OSM::ROW > &M, std::string filename)
	Writes a sparse ROW matrix to a file.

template<typename _CT >
std::istream &	read_matrix (Sparse_matrix< _CT, OSM::COLUMN > &M, std::istream &in)
	Reads a sparse COLUMN matrix from a stream.

template<typename _CT >
std::istream &	read_matrix (Sparse_matrix< _CT, OSM::ROW > &M, std::istream &in)
	Reads a sparse ROW matrix from a stream.

template<typename _CT >
void	read_matrix (Sparse_matrix< _CT, OSM::COLUMN > &M, std::string filename)
	Reads a sparse COLUMN matrix from a file.

template<typename _CT >
void	read_matrix (Sparse_matrix< _CT, OSM::ROW > &M, std::string filename)
	Reads a sparse ROW matrix from a file.

template<typename _CT , int _CTF>
Sparse_matrix	operator* (const _CT &lambda, const Sparse_matrix< _CT, _CTF > &matrix)
	Applies factor on each coefficients into a new matrix.

template<typename _CT >
Sparse_matrix< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, COLUMN > &first, const Sparse_matrix< _CT, COLUMN > &second)
	Matrix multiplication: COLUMN x COLUMN -> COLUMN.

template<typename _CT >
Sparse_matrix< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, ROW > &first, const Sparse_matrix< _CT, COLUMN > &second)
	Matrix multiplication: ROW x COLUMN -> COLUMN.

template<typename _CT >
Sparse_matrix< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, COLUMN > &first, const Sparse_matrix< _CT, ROW > &second)
	Matrix multiplication: COLUMN x ROW -> COLUMN.

template<typename _CT >
Sparse_matrix< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, ROW > &first, const Sparse_matrix< _CT, ROW > &second)
	Matrix multiplication: ROW x ROW -> COLUMN.

template<typename _CT >
Sparse_chain< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, COLUMN > &_matrix, const Sparse_chain< _CT, COLUMN > &_column)
	Matrix/column chain multiplication: COLUMN matrix x COLUMN chain -> COLUMN chain.

template<typename _CT >
Sparse_chain< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, ROW > &_matrix, const Sparse_chain< _CT, COLUMN > &_column)
	Matrix/column chain multiplication: ROW matrix x COLUMN chain -> COLUMN chain.

template<typename _CT >
Sparse_chain< _CT, ROW >	operator* (const Sparse_chain< _CT, ROW > &_row, const Sparse_matrix< _CT, ROW > &_matrix)
	Row chain/matrix multiplication: ROW chain x COLUMN matrix -> ROW chain.

template<typename _CT >
Sparse_chain< _CT, ROW >	operator* (const Sparse_chain< _CT, ROW > &_row, const Sparse_matrix< _CT, COLUMN > &_matrix)
	Row chain/matrix multiplication: ROW chain x ROW matrix -> ROW chain.

template<typename _CT >
Sparse_matrix< _CT, ROW >	operator% (const Sparse_matrix< _CT, COLUMN > &_first, const Sparse_matrix< _CT, COLUMN > &_second)
	matrix multiplication: COLUMN x COLUMN -> ROW

template<typename _CT >
Sparse_matrix< _CT, ROW >	operator% (const Sparse_matrix< _CT, ROW > &_first, const Sparse_matrix< _CT, COLUMN > &_second)
	matrix multiplication: ROW x COLUMN -> ROW

template<typename _CT >
Sparse_matrix< _CT, ROW >	operator% (const Sparse_matrix< _CT, COLUMN > &_first, const Sparse_matrix< _CT, ROW > &_second)
	matrix multiplication: COLUMN x ROW -> ROW

template<typename _CT >
Sparse_matrix< _CT, ROW >	operator% (const Sparse_matrix< _CT, ROW > &_first, const Sparse_matrix< _CT, ROW > &_second)
	matrix multiplication: ROW x ROW -> ROW

Sparse_matrix &	operator+= (const Sparse_matrix &other)
	Matrices sum and assign: COLUMN += COLUMN or ROW += ROW.

template<typename _CT >
Sparse_matrix< _CT, COLUMN > &	operator+= (Sparse_matrix< _CT, COLUMN > &matrix, const Sparse_matrix< _CT, ROW > &other)
	Matrices sum and assign: COLUMN += ROW.

template<typename _CT >
Sparse_matrix< _CT, ROW > &	operator+= (Sparse_matrix< _CT, ROW > &matrix, const Sparse_matrix< _CT, COLUMN > &other)
	Matrices sum and assign: ROW += COLUMN.

Sparse_matrix &	operator-= (const Sparse_matrix &other)
	Matrices subtraction and assign: COLUMN -= COLUMN or ROW -= ROW.

template<typename _CT >
Sparse_matrix< _CT, COLUMN > &	operator-= (Sparse_matrix< _CT, COLUMN > &matrix, const Sparse_matrix< _CT, ROW > &other)
	Matrices subtraction and assign: COLUMN -= ROW.

template<typename _CT >
Sparse_matrix< _CT, ROW > &	operator-= (Sparse_matrix< _CT, ROW > &matrix, const Sparse_matrix< _CT, COLUMN > &other)
	Matrices subtraction and assign: ROW -= COLUMN.

template<typename _CT >
Sparse_matrix< _CT, COLUMN > &	*operator=** (Sparse_matrix< _CT, COLUMN > &matrix, const Sparse_matrix< _CT, COLUMN > &other)
	Matrix multiplication and assign: COLUMN *= COLUMN.

template<typename _CT >
Sparse_matrix< _CT, ROW > &	*operator=** (Sparse_matrix< _CT, ROW > &matrix, const Sparse_matrix< _CT, ROW > &other)
	Matrix multiplication and assign: ROW *= ROW.

template<typename _CT >
Sparse_matrix< _CT, COLUMN > &	*operator=** (Sparse_matrix< _CT, COLUMN > &matrix, const Sparse_matrix< _CT, ROW > &other)
	Matrix multiplication and assign: COLUMN *= ROW.

template<typename _CT >
Sparse_matrix< _CT, ROW > &	*operator=** (Sparse_matrix< _CT, ROW > &matrix, const Sparse_matrix< _CT, COLUMN > &other)
	Matrix multiplication and assign: ROW *= COLUMN.

template<typename _CT , int _CTF>
void	set_coefficient (Sparse_matrix< _CT, _CTF > &matrix, size_t i, size_t j, const _CT d)
	Sets a given coefficient in `matrix`.

template<typename _CT , int _CTF>
_CT	get_coefficient (const Sparse_matrix< _CT, _CTF > &matrix, size_t i, size_t j)
	Gets a given coefficient.

template<typename _CT >
Sparse_chain< _CT, COLUMN >	get_column (const Sparse_matrix< _CT, COLUMN > &matrix, size_t index)
	Gets a column from a COLUMN matrix.

template<typename _CT >
Sparse_chain< _CT, COLUMN >	get_column (const Sparse_matrix< _CT, ROW > &matrix, size_t index)
	Gets a column from a ROW matrix.

template<typename _CT >
Sparse_chain< _CT, ROW >	get_row (const Sparse_matrix< _CT, COLUMN > &matrix, size_t index)
	Gets a row from a COLUMN matrix.

template<typename _CT >
Sparse_chain< _CT, ROW >	get_row (const Sparse_matrix< _CT, ROW > &matrix, size_t index)
	Gets a row from a ROW matrix.

template<typename _CT >
const Sparse_chain< _CT, COLUMN > &	cget_column (const Sparse_matrix< _CT, COLUMN > &matrix, size_t index)
	Gets a const reference over a column from a column matrix.

template<typename _CT >
const Sparse_chain< _CT, ROW > &	cget_row (const Sparse_matrix< _CT, ROW > &matrix, const size_t index)
	Gets a constant reference over a row from a row matrix.

template<typename _CT >
void	set_column (Sparse_matrix< _CT, COLUMN > &matrix, size_t index, const Sparse_chain< _CT, COLUMN > &column)
	Sets a column in a COLUMN matrix.

template<typename _CT >
void	set_column (Sparse_matrix< _CT, ROW > &matrix, size_t index, const Sparse_chain< _CT, COLUMN > &column)
	Sets a column in a ROW matrix.

template<typename _CT >
void	set_row (Sparse_matrix< _CT, COLUMN > &matrix, size_t index, const Sparse_chain< _CT, ROW > &row)
	Sets a row in a COLUMN matrix.

template<typename _CT >
void	set_row (Sparse_matrix< _CT, ROW > &matrix, size_t index, const Sparse_chain< _CT, ROW > &row)
	Sets a row in a ROW matrix.

template<typename _CT , int _CTF>
Sparse_matrix< _CT, _CTF > &	remove_column (Sparse_matrix< _CT, _CTF > &matrix, size_t index)
	Removes a column from the matrix.

template<typename _CT , int _CTF>
Sparse_matrix< _CT, _CTF > &	remove_row (Sparse_matrix< _CT, _CTF > &matrix, size_t index)
	Removes a row from the matrix.

template<typename _CT , int _CTF>
Sparse_matrix< _CT, _CTF > &	remove_coefficient (Sparse_matrix< _CT, _CTF > &matrix, size_t i, size_t j)
	Removes a coefficient from the matrix.

Constructor & Destructor Documentation

◆ Sub_sparse_matrix() [1/4]

template<typename CoefficientRing , int StorageFormat>

CGAL::OSM::Sub_sparse_matrix< CoefficientRing, StorageFormat >::Sub_sparse_matrix	(	size_t	rowCount = `0`,
		size_t	columnCount = `0`
	)

Default constructor of a new Sub_sparse_matrix (with given rows/columns sizes and mask set to full).

Default constructor. Constructor with sizes, initialize an empty Sub_sparse_matrix of type StorageFormat with coefficients of type CoefficientRing, a given size along rows/columns. The constructor sets the mask to full.

Parameters

rowCount	The number of rows to preallocate (default 0).
columnCount	The number of columns to preallocate (default 0).

◆ Sub_sparse_matrix() [2/4]

template<typename CoefficientRing , int StorageFormat>

CGAL::OSM::Sub_sparse_matrix< CoefficientRing, StorageFormat >::Sub_sparse_matrix	(	size_t	rowCount,
		size_t	columnCount,
		const Bitboard &	subChain
	)

Constructor with given rows/columns sizes and a mask.

Create a new empty Sub_sparse_matrix of type StorageFormat with coefficients of type CoefficientRing, a given size along rows/columns and a given mask.

Parameters

rowCount	The number of rows to preallocate.
columnCount	The number of columns to preallocate.
subChain	Bitboard describing the subset of indices considered as a mask.

◆ Sub_sparse_matrix() [3/4]

template<typename CoefficientRing , int StorageFormat>

CGAL::OSM::Sub_sparse_matrix< CoefficientRing, StorageFormat >::Sub_sparse_matrix ( const Sub_sparse_matrix< CoefficientRing, StorageFormat > & otherToCopy )

Copy constructor from another Sub_sparse_matrix.

Create a new empty Sub_sparse_matrix from another of type StorageFormat with coefficients of type CoefficientRing, a given size along rows/columns and a given mask.

Parameters

otherToCopy Sub_sparse_matrix copied into this.

◆ Sub_sparse_matrix() [4/4]

template<typename CoefficientRing , int StorageFormat>

CGAL::OSM::Sub_sparse_matrix< CoefficientRing, StorageFormat >::Sub_sparse_matrix ( const Sparse_matrix< CoefficientRing, StorageFormat > & otherToCopy )

Copy constructor from Sparse_matrix.

Create a new Sub_sparse_matrix from a Sparse_matrix object (with the same StorageFormat). Create a "full" mask.

Parameters

otherToCopy The matrix copied.

Member Function Documentation

◆ operator=()

template<typename CoefficientRing , int StorageFormat>

Sub_sparse_matrix & CGAL::OSM::Sub_sparse_matrix< CoefficientRing, StorageFormat >::operator= ( const Sub_sparse_matrix< CoefficientRing, StorageFormat > & otherToCopy )

Assigns to other Sub_sparse_matrix.

Assign to other matrix coefficient-wise, and copy the bitboard.

Precondition: The matrices must have the same type.

Parameters

otherToCopy The matrix we want to copy.

Returns: The reference to the modified matrix.

◆ set_bit_off()

template<typename CoefficientRing , int StorageFormat>

void CGAL::OSM::Sub_sparse_matrix< CoefficientRing, StorageFormat >::set_bit_off ( size_t index )

Removes an index from the mask.

Set the bit encoding a given index to 0 (ie. remove the index from the mask).

Parameters

index Index to turn off in the mask.

◆ set_bit_on()

template<typename CoefficientRing , int StorageFormat>

void CGAL::OSM::Sub_sparse_matrix< CoefficientRing, StorageFormat >::set_bit_on ( size_t index )

Adds an index to the mask.

Set the bit encoding a given index to 1 (ie. add the index in the mask).

Parameters

index Index to turn on in the mask.

◆ set_sub()

template<typename CoefficientRing , int StorageFormat>

void CGAL::OSM::Sub_sparse_matrix< CoefficientRing, StorageFormat >::set_sub ( const Bitboard & new_subChains )

Changes the indices subset mask.

Set a new mask encoding a new subset of indices along the major dimension.

Friends And Related Function Documentation

◆ operator<<

template<typename CoefficientRing , int StorageFormat>

std::ostream & operator<<	(	std::ostream &	stream,
		const Sub_sparse_matrix< CoefficientRing, StorageFormat > &	matrix
	)

friend

Displays a Sub_sparse_matrix in the output stream.

Displays the sparse matrix as well as its mask.

Parameters

stream	The output stream.
matrix	The matrix to display.

Returns: A reference to the modified stream.

Inherits from

Definition

Public Member Functions

Protected Attributes

Friends

Additional Inherited Members

Constructor & Destructor Documentation

◆ Sub_sparse_matrix() [1/4]

◆ Sub_sparse_matrix() [2/4]

◆ Sub_sparse_matrix() [3/4]

◆ Sub_sparse_matrix() [4/4]

Member Function Documentation

◆ operator=()

◆ set_bit_off()

◆ set_bit_on()

◆ set_sub()

Friends And Related Function Documentation

◆ operator<<