Classes
class	Bitboard
	The class `Bitboard` implements an accelerating structure, derived from the chess community. More...

class	Sparse_chain
	The class `Sparse_chain` implements the concept `SparseChain`, that is, sparse vectors (encoding homological chains) optimized for topological computations. More...

class	Sparse_matrix
	The class `Sparse_matrix` implements the concept `SparseMatrix`, that is, sparse matrices optimized for topological computations. More...

class	Sub_sparse_matrix
	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). More...

Typedefs
typedef int	ZCoefficient
	The default type for signed integers.

Functions
template<typename _CT >
Sparse_matrix< _CT, COLUMN >	operator* (const Sparse_chain< _CT, COLUMN > &column, const Sparse_chain< _CT, ROW > &row)

template<typename _CT >
Sparse_matrix< _CT, ROW >	operator% (const Sparse_chain< _CT, COLUMN > &column, const Sparse_chain< _CT, ROW > &row)

template<typename CoefficientType >
CoefficientType	operator* (const Sparse_chain< CoefficientType, ROW > &row, const Sparse_chain< CoefficientType, COLUMN > &column)

template<typename _CT , int _CTF>
Sparse_chain< _CT, _CTF >	operator/ (const Sparse_chain< _CT, _CTF > &chain, const std::vector< size_t > &indices)

template<typename _CT , int _CTF>
Sparse_chain< _CT, _CTF >	operator/ (const Sparse_chain< _CT, _CTF > &chain, size_t index)

template<typename _CT >
bool	operator== (const Sparse_chain< _CT, OSM::COLUMN > &chain, const Sparse_chain< _CT, OSM::COLUMN > &other)

template<typename _CT >
bool	operator== (const Sparse_chain< _CT, OSM::ROW > &chain, const Sparse_chain< _CT, OSM::ROW > &other)

template<typename _CT >
bool	operator== (const Sparse_chain< _CT, OSM::COLUMN > &chain, const Sparse_chain< _CT, OSM::ROW > &other)

template<typename _CT >
bool	operator== (const Sparse_chain< _CT, OSM::ROW > &chain, const Sparse_chain< _CT, OSM::COLUMN > &other)

template<typename _CT >
Sparse_matrix< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, COLUMN > &first, const Sparse_matrix< _CT, COLUMN > &second)

template<typename _CT >
Sparse_matrix< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, ROW > &first, const Sparse_matrix< _CT, COLUMN > &second)

template<typename _CT >
Sparse_matrix< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, COLUMN > &first, const Sparse_matrix< _CT, ROW > &second)

template<typename _CT >
Sparse_matrix< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, ROW > &first, const Sparse_matrix< _CT, ROW > &second)

template<typename _CT >
Sparse_chain< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, COLUMN > &first, const Sparse_chain< _CT, COLUMN > &second)

template<typename _CT >
Sparse_chain< _CT, COLUMN >	operator* (const Sparse_matrix< _CT, ROW > &first, const Sparse_chain< _CT, COLUMN > &second)

template<typename _CT >
Sparse_chain< _CT, ROW >	operator* (const Sparse_chain< _CT, ROW > &first, const Sparse_matrix< _CT, ROW > &second)

template<typename _CT >
Sparse_chain< _CT, ROW >	operator* (const Sparse_chain< _CT, ROW > &first, const Sparse_matrix< _CT, COLUMN > &second)

template<typename _CT >
Sparse_matrix< _CT, ROW >	operator% (const Sparse_matrix< _CT, COLUMN > &first, const Sparse_matrix< _CT, COLUMN > &second)

template<typename _CT >
Sparse_matrix< _CT, ROW >	operator% (const Sparse_matrix< _CT, ROW > &first, const Sparse_matrix< _CT, COLUMN > &second)

template<typename _CT >
Sparse_matrix< _CT, ROW >	operator% (const Sparse_matrix< _CT, COLUMN > &first, const Sparse_matrix< _CT, ROW > &second)

template<typename _CT >
Sparse_matrix< _CT, ROW >	operator% (const Sparse_matrix< _CT, ROW > &first, const Sparse_matrix< _CT, ROW > &second)

template<typename _CT >
Sparse_matrix< _CT, COLUMN > &	operator+= (Sparse_matrix< _CT, COLUMN > &matrix, const Sparse_matrix< _CT, ROW > &other)

template<typename _CT >
Sparse_matrix< _CT, ROW > &	operator+= (Sparse_matrix< _CT, ROW > &matrix, const Sparse_matrix< _CT, COLUMN > &other)

template<typename _CT >
Sparse_matrix< _CT, COLUMN > &	operator-= (Sparse_matrix< _CT, COLUMN > &matrix, const Sparse_matrix< _CT, ROW > &other)

template<typename _CT >
Sparse_matrix< _CT, ROW > &	operator-= (Sparse_matrix< _CT, ROW > &matrix, const Sparse_matrix< _CT, COLUMN > &other)

template<typename _CT >
Sparse_matrix< _CT, COLUMN > &	*operator=** (Sparse_matrix< _CT, COLUMN > &matrix, const Sparse_matrix< _CT, COLUMN > &other)

template<typename _CT >
Sparse_matrix< _CT, ROW > &	*operator=** (Sparse_matrix< _CT, ROW > &matrix, const Sparse_matrix< _CT, ROW > &other)

template<typename _CT >
Sparse_matrix< _CT, COLUMN > &	*operator=** (Sparse_matrix< _CT, COLUMN > &matrix, const Sparse_matrix< _CT, ROW > &other)

template<typename _CT >
Sparse_matrix< _CT, ROW > &	*operator=** (Sparse_matrix< _CT, ROW > &matrix, const Sparse_matrix< _CT, COLUMN > &other)

template<typename _CT >
Sparse_chain< _CT, COLUMN >	get_column (const Sparse_matrix< _CT, COLUMN > &matrix, size_t index)

template<typename _CT >
Sparse_chain< _CT, COLUMN >	get_column (const Sparse_matrix< _CT, ROW > &matrix, size_t index)

template<typename _CT >
Sparse_chain< _CT, ROW >	get_row (const Sparse_matrix< _CT, COLUMN > &matrix, size_t index)

template<typename _CT >
Sparse_chain< _CT, ROW >	get_row (const Sparse_matrix< _CT, ROW > &matrix, size_t index)

template<typename _CT >
const Sparse_chain< _CT, COLUMN > &	cget_column (const Sparse_matrix< _CT, COLUMN > &matrix, size_t index)

template<typename _CT >
const Sparse_chain< _CT, ROW > &	cget_row (const Sparse_matrix< _CT, ROW > &matrix, const size_t index)

template<typename _CT >
void	set_column (Sparse_matrix< _CT, COLUMN > &matrix, size_t index, const Sparse_chain< _CT, COLUMN > &chain)

template<typename _CT >
void	set_column (Sparse_matrix< _CT, ROW > &matrix, size_t index, const Sparse_chain< _CT, COLUMN > &chain)

template<typename _CT >
void	set_row (Sparse_matrix< _CT, COLUMN > &matrix, size_t index, const Sparse_chain< _CT, ROW > &chain)

template<typename _CT >
void	set_row (Sparse_matrix< _CT, ROW > &matrix, size_t index, const Sparse_chain< _CT, ROW > &chain)

template<typename _CT , int _CTF>
void	set_coef (Sparse_matrix< _CT, _CTF > &matrix, size_t i, size_t j, const _CT d)

template<typename _CT , int _CTF>
_CT	get_coef (const Sparse_matrix< _CT, _CTF > &matrix, size_t i, size_t j)

template<typename _CT , int _CTF>
Sparse_matrix< _CT, _CTF > &	del_column (Sparse_matrix< _CT, _CTF > &matrix, size_t index)

template<typename _CT , int _CTF>
Sparse_matrix< _CT, _CTF > &	del_row (Sparse_matrix< _CT, _CTF > &matrix, size_t index)

template<typename _CT , int _CTF>
Sparse_matrix< _CT, _CTF > &	del_coef (Sparse_matrix< _CT, _CTF > &matrix, size_t i, size_t j)

template<typename _CT >
std::ostream &	write_matrix (const Sparse_matrix< _CT, OSM::COLUMN > &M, std::ostream &out)

template<typename _CT >
std::ostream &	write_matrix (const Sparse_matrix< _CT, OSM::ROW > &M, std::ostream &out)

template<typename _CT >
std::istream &	read_matrix (Sparse_matrix< _CT, OSM::COLUMN > &M, std::istream &in)

template<typename _CT >
std::istream &	read_matrix (Sparse_matrix< _CT, OSM::ROW > &M, std::istream &in)

template<typename _CT >
bool	operator== (const Sparse_matrix< _CT, OSM::COLUMN > &matrix, const Sparse_matrix< _CT, OSM::COLUMN > &other)

template<typename _CT >
bool	operator== (const Sparse_matrix< _CT, OSM::ROW > &matrix, const Sparse_matrix< _CT, OSM::ROW > &other)

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

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

Variables
const int	COLUMN = 0b01
	Chain type flag for column chain.

const int	ROW = 0b10
	Chain type flag for row chain.

const size_t	size_t_maxvalue = std::numeric_limits<size_t>::max()

const int	tab64 [64]

const int	index64 [64]

Function Documentation

◆ cget_column()

template<typename _CT >

const Sparse_chain< _CT, COLUMN > & CGAL::OSM::cget_column	(	const Sparse_matrix< _CT, COLUMN > &	matrix,
		size_t	index
	)

Constant time get.

Warning: The matrix will perform boundary check.

Parameters

[in]	matrix	The matrix considered.
[in]	index	The column index.

Returns: A constant reference over the column stored at given index.

Examples: HDVF/example_matrix_chain.cpp.

◆ cget_row()

template<typename _CT >

const Sparse_chain< _CT, ROW > & CGAL::OSM::cget_row	(	const Sparse_matrix< _CT, ROW > &	matrix,
		const size_t	index
	)

Constant time get.

Warning: The matrix will perform boundary check.

Parameters

[in]	matrix	The matrix considered.
[in]	index	The row index.

Returns: A const reference over the row stored at given index.

◆ del_coef()

template<typename _CT , int _CTF>

Sparse_matrix< _CT, _CTF > & CGAL::OSM::del_coef	(	Sparse_matrix< _CT, _CTF > &	matrix,
		size_t	i,
		size_t	j
	)

Removes coefficient at row i and column j.

Parameters

[in]	matrix	Reference on the matrix to modify.
[in]	i	Index of the row
[in]	j	Index of the column

Returns: The modified matrix representing the result.

◆ del_column()

template<typename _CT , int _CTF>

Sparse_matrix< _CT, _CTF > & CGAL::OSM::del_column	(	Sparse_matrix< _CT, _CTF > &	matrix,
		size_t	index
	)

Removes column of index index whatever the ChainTypeFlag of the matrix. For column matrices, it just comes to the \= operator and for row matrices, it entails a traversal of the matrix.

Parameters

[in]	matrix	Reference on the matrix to modify.
[in]	index	The index to remove.

Returns: The modified matrix representing the result.

◆ del_row()

template<typename _CT , int _CTF>

Sparse_matrix< _CT, _CTF > & CGAL::OSM::del_row	(	Sparse_matrix< _CT, _CTF > &	matrix,
		size_t	index
	)

Removes row of index index whatever the ChainTypeFlag of the matrix. For row matrices, it just comes to the \= operator and for column matrices, it entails a traversal of the matrix.

Parameters

[in]	matrix	Reference on the matrix to modify.
[in]	index	The index to remove.

Returns: The modified matrix representing the result.

◆ get_coef()

template<typename _CT , int _CTF>

_CT CGAL::OSM::get_coef	(	const Sparse_matrix< _CT, _CTF > &	matrix,
		size_t	i,
		size_t	j
	)

Returns the coefficient on row i and column j of the matrix.

Warning: The matrix will perform boundary check.

Parameters

[in]	matrix	Constant reference on the matrix.
[in]	i	The row index.
[in]	j	The column index.

Returns: The value of the given coefficient.

◆ operator%()

template<typename _CT >

Sparse_matrix< _CT, ROW > CGAL::OSM::operator%	(	const Sparse_chain< _CT, COLUMN > &	column,
		const Sparse_chain< _CT, ROW > &	row
	)

Generate a row-based matrix from the matrix multiplication and return it.

Precondition: Chains must have the same CoefficientType.

Warning: Will raise an error if chains do not have the same CoefficientType.

Parameters

[in]	column	The column chain.
[in]	row	The row chain.

Returns: The result of the matrix multiplication, row-based.

◆ operator*()

template<typename _CT >

Sparse_matrix< _CT, COLUMN > CGAL::OSM::operator*	(	const Sparse_chain< _CT, COLUMN > &	column,
		const Sparse_chain< _CT, ROW > &	row
	)

Generate a column-based matrix from the matrix multiplication and return it.

Precondition: Chains must have the same CoefficientType.

Warning: Will raise an error if chains do not have the same CoefficientType.

Parameters

[in]	column	The column chain.
[in]	row	The row chain.

Returns: The result of the matrix multiplication, column-based.

◆ operator/() [1/2]

template<typename _CT , int _CTF>

Sparse_chain< _CT, _CTF > CGAL::OSM::operator/	(	const Sparse_chain< _CT, _CTF > &	chain,
		const std::vector< size_t > &	indices
	)

Return a new chain where all coefficients of indices provided in the vector are removed.

Note: Will return a copy of the chain if indices is empty.

Parameters

[in]	chain	The chain to process.
[in]	indices	The indexes to remove.

Returns: A new chain representing the result.

◆ operator/() [2/2]

template<typename _CT , int _CTF>

Sparse_chain< _CT, _CTF > CGAL::OSM::operator/	(	const Sparse_chain< _CT, _CTF > &	chain,
		size_t	index
	)

Return a new chain where the coefficients at a given index is removed.

Parameters

[in]	chain	The chain to process.
[in]	index	The index to remove.

◆ set_coef()

template<typename _CT , int _CTF>

void CGAL::OSM::set_coef	(	Sparse_matrix< _CT, _CTF > &	matrix,
		size_t	i,
		size_t	j,
		const _CT	d
	)

Assign the scalar d to the coefficient on row i and column j.

Warning: The matrix will perform boundary check.

Parameters

[in]	matrix	Reference on the matrix to modify.
[in]	i	The row index.
[in]	j	The column index.
[in]	d	The value.

Examples: HDVF/example_matrix_chain.cpp.

Variable Documentation

◆ index64

const int CGAL::OSM::index64[64]

Initial value:

= {
    0, 47,  1, 56, 48, 27,  2, 60,
   57, 49, 41, 37, 28, 16,  3, 61,
   54, 58, 35, 52, 50, 42, 21, 44,
   38, 32, 29, 23, 17, 11,  4, 62,
   46, 55, 26, 59, 40, 36, 15, 53,
   34, 51, 20, 43, 31, 22, 10, 45,
   25, 39, 14, 33, 19, 30,  9, 24,
   13, 18,  8, 12,  7,  6,  5, 63
}

◆ tab64

const int CGAL::OSM::tab64[64]

Initial value:

= {
    63,  0, 58,  1, 59, 47, 53,  2,
    60, 39, 48, 27, 54, 33, 42,  3,
    61, 51, 37, 40, 49, 18, 28, 20,
    55, 30, 34, 11, 43, 14, 22,  4,
    62, 57, 46, 52, 38, 26, 32, 41,
    50, 36, 17, 19, 29, 10, 13, 21,
    56, 45, 25, 31, 35, 16,  9, 12,
    44, 24, 15,  8, 23,  7,  6,  5
}

Classes

Typedefs

Functions

Variables

Function Documentation

◆ cget_column()

◆ cget_row()

◆ del_coef()

◆ del_column()

◆ del_row()

◆ get_coef()

◆ operator%()

◆ operator*()

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ set_coef()

Variable Documentation

◆ index64

◆ tab64