#include <CGAL/OSM/Sparse_matrix.h>

Inherited by CGAL::OSM::Sub_sparse_matrix< CoefficientRing, StorageFormat >.

Definition

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

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

It provides standard linear algebra operators and fast iterators and block operations (set, get and nullify) which are required to implement efficiently HDVFs.

The implementation is based on mapped sparse matrices. Hence matrices of the Sparse_matrix class are either column of row major (the StorageFormat parameter determines this storage format). A column-major (resp. row-major) Sparse_matrix is a vector of Sparse_chain which encode columns (res. rows). Moreover, in order to efficiently iterate over non empty columns (resp. rows) the Bitboard data structure implements the concept SparseMatrix::NonZeroChainIndices. A bitboard is basically a bucket of bits recording the indices of non empty chains. However, this data structure has been designed in order to efficiently remove or add indices, as well as provide efficient iterators to visit non empty chains.

For instance, let us consider the \(5\times 4\) matrix:

\[ A = \left(\begin{array}{cccc} 1 & \cdot & \cdot & \cdot \\ -1 & \cdot & 2 & \cdot\\ \cdot & \cdot & 1 & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \end{array}\right) \]

where \(\cdot\) means \(0\).

Figures below shows the data structures are created according to the chosen representation (left: column-major, right: row-major):

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`).

Examples: HDVF/matrix_chain.cpp.

Public Types
typedef CoefficientRing	Coefficient_ring
	Type of coefficient ring.

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

Public Member Functions
	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 Member Functions
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)

Protected Attributes
std::vector< Sparse_chain< CoefficientRing, StorageFormat > >	_chains

Bitboard	_chainsStates

std::pair< size_t, size_t >	_size

Friends
template<typename _CT , int _CTF>
class	Sparse_matrix

Related Functions
(Note that these are not member functions.)
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

◆ Sparse_matrix() [1/3]

template<typename CoefficientRing , int StorageFormat>

CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::Sparse_matrix ( )

Default constructor (empty new Sparse_matrix object).

Create an empty matrix of type StorageFormat with coefficients of type CoefficientRing. The default matrix size is 0x0.

◆ Sparse_matrix() [2/3]

template<typename CoefficientRing , int StorageFormat>

CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::Sparse_matrix	(	const size_t	rowCount,
		const size_t	columnCount
	)

Constructor with given rows/columns sizes.

Create a new empty Sparse_matrix object of type StorageFormat with coefficients of type CoefficientRing and a given size along rows/columns.

Parameters

rowCount	The number of rows to preallocate.
columnCount	The number of columns to preallocate.

◆ Sparse_matrix() [3/3]

template<typename CoefficientRing , int StorageFormat>

template<int CTF>

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

Copy constructor.

Create a new SparseMatrix from another SparseMatrix object (with possibly a different StorageFormat). Initialize a SparseMatrix of same sizes, containing the same coefficients (but not necessarly of the same StorageFormat). If types are different, the constructor performs conversion.

Parameters

otherToCopy The matrix copied.

Member Function Documentation

◆ begin()

template<typename CoefficientRing , int StorageFormat>

Bitboard::iterator CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::begin ( ) const

noexcept

Iterator to the index of the first non null chain.

Return an iterator to the index of the first non null chain (the iterator visits indices of non null chains along the major dimension of the matrix).

Returns: The iterator to the index of the first non null chain.

◆ dimensions()

template<typename CoefficientRing , int StorageFormat>

std::pair< size_t, size_t > CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::dimensions ( ) const

Gets the matrix sizes.

Returns: The matrix size as a row/column pair.

◆ end()

template<typename CoefficientRing , int StorageFormat>

Bitboard::iterator CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::end ( ) const

noexcept

Iterator past-the-end of chain indices.

Returns: The iterator past-the-end of chain indices.

◆ is_null()

template<typename CoefficientRing , int StorageFormat>

bool CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::is_null ( )

Tests if a SparseMatrix is null.

The function return true is the SparseMatrix is null (that is, empty) and false otherwise.

◆ nullify()

template<typename CoefficientRing , int StorageFormat>

void CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::nullify ( )

Cleans a SparseMatrix (set all coefficients to zero).

Empty all structures of the sparse matrix.

◆ operator*()

template<typename CoefficientRing , int StorageFormat>

Sparse_matrix CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::operator* ( const CoefficientRing & lambda )

Applies factor on each coefficients into a new matrix.

This method creates a new matrix obtained by multiplying the matrix by a scalar factor lambda.

If lambda is zero, the function comes to nullify the matrix (when possible, prefer *= for efficiency).

Parameters

lambda The factor to apply.

Returns: A new matrix representing the result.

◆ operator*=()

template<typename CoefficientRing , int StorageFormat>

Sparse_matrix & CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::operator*= ( const CoefficientRing & lambda )

Applies factor on each coefficients and assign.

If lambda is 0, this comes to nullify the matrix.

Parameters

lambda The factor to apply.

Returns: The modified matrix representing the result.

◆ operator+()

template<typename CoefficientRing , int StorageFormat>

template<int _CTF>

Sparse_matrix CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::operator+ ( const Sparse_matrix< CoefficientRing, _CTF > & other )

Adds two matrices into a new matrix.

Adds each coefficient of the matrices and returns a new matrix (of the same type as this) representing the result (when possible, prefer += for efficiency).

Precondition: Matrices must have the same CoefficientRing but can have different StorageFormat.

Warning: Will raise an error if the other matrix is not the same CoefficientRing.

Parameters

other The second matrix.

Returns: A new matrix representing the result.

◆ operator-() [1/2]

template<typename CoefficientRing , int StorageFormat>

Sparse_matrix CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::operator- ( )

Computes the negative of a matrix (unary operator).

Returns: The resulting matrix.

◆ operator-() [2/2]

template<typename CoefficientRing , int StorageFormat>

template<int _CTF>

Sparse_matrix CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::operator- ( const Sparse_matrix< CoefficientRing, _CTF > & other )

Subtracts two matrices into a new matrix.

Subtracts each coefficient of the matrix other and returns a new matrix (of the same type as this) representing the result (when possible, prefer -= for efficiency).

Precondition: Matrices must have the same CoefficientRing but can have different StorageFormat.

Warning: Will raise an error if the other matrix is not the same CoefficientRing.

Parameters

other The second matrix.

Returns: A new matrix representing the result.

◆ operator=()

template<typename CoefficientRing , int StorageFormat>

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

Assigns to other matrix.

Assign to other matrix coefficient-wise, equivalent to copying it.

Precondition: The matrices must have the same type.

Parameters

otherToCopy The matrix we want to copy.

Returns: The reference to the modified matrix.

◆ operator[]()

template<typename CoefficientRing , int StorageFormat>

Matrix_chain CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::operator[] ( size_t index ) const

Gets the value of a chain from a const matrix.

Warning: The matrix will perform boundary check.

Parameters

index The chain index.

Returns: The chain stored at given index.

◆ reverse_begin()

template<typename CoefficientRing , int StorageFormat>

Bitboard::reverse_iterator CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::reverse_begin ( )

noexcept

Reverse iterator to the index of the last non null chain.

Return a reverse iiterator to the index of the last non null chain (the iterator visits indices of non null chains, in decreading order, along the major dimension of the matrix).

Returns: The reverse iterator to the index of the last non null chain.

◆ reverse_end()

template<typename CoefficientRing , int StorageFormat>

Bitboard::reverse_iterator CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::reverse_end ( )

noexcept

Reverse iterator past-the-end of chain indices.

Returns: The reverse iterator past-the-end of chain indices.

◆ transpose()

template<typename CoefficientRing , int StorageFormat>

Sparse_matrix< CoefficientRing, COLUMN+ROW - StorageFormat > CGAL::OSM::Sparse_matrix< CoefficientRing, StorageFormat >::transpose ( )

Transposes a matrix.

Returns: A new matrix where the StorageFormat has been swapped between COLUMN and ROW and data chains have been transposed.

Friends And Related Function Documentation

◆ cget_column

template<typename CoefficientRing , int StorageFormat>

template<typename _CT >

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

friend

Gets a const reference over a column from a column matrix.

Constant time get.

Warning: The matrix will perform boundary check.

Parameters

matrix	The matrix considered.
index	The column index.

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

◆ cget_row

template<typename CoefficientRing , int StorageFormat>

template<typename _CT >

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

friend

Gets a constant reference over a row from a row matrix.

Constant time get.

Warning: The matrix will perform boundary check.

Parameters

matrix	The matrix considered.
index	The row index.

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

◆ get_coefficient

template<typename CoefficientRing , int StorageFormat>

template<typename _CT , int _CTF>

_CT get_coefficient	(	const Sparse_matrix< _CT, _CTF > &	matrix,
		size_t	i,
		size_t	j
	)

friend

Gets a given coefficient.

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

Warning: The matrix will perform boundary check.

Parameters

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

Returns: The value of the given coefficient.

◆ operator*

template<typename CoefficientRing , int StorageFormat>

template<typename _CT , int _CTF>

Sparse_matrix operator*	(	const _CT &	lambda,
		const Sparse_matrix< _CT, _CTF > &	matrix
	)

friend

Applies factor on each coefficients into a new matrix.

This method creates a new matrix obtained by multiplying the matrix by a scalar factor lambda.

If lambda is zero, the function comes to nullify the matrix (when possible, prefer *= for efficiency).

Parameters

lambda	The factor to apply.
matrix	The matrix.

Returns: A new matrix representing the result.

◆ operator<<

template<typename CoefficientRing , int StorageFormat>

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

friend

Writes a sparse matrix in the output stream.

Parameters

stream	The output stream.
matrix	The matrix to display.

Returns: A reference to the modified stream.

◆ remove_coefficient

template<typename CoefficientRing , int StorageFormat>

template<typename _CT , int _CTF>

Sparse_matrix< _CT, _CTF > & remove_coefficient	(	Sparse_matrix< _CT, _CTF > &	matrix,
		size_t	i,
		size_t	j
	)

friend

Removes a coefficient from the matrix.

Removes coefficient at row i and column j.

Parameters

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

Returns: The modified matrix representing the result.

◆ remove_column

template<typename CoefficientRing , int StorageFormat>

template<typename _CT , int _CTF>

Sparse_matrix< _CT, _CTF > & remove_column	(	Sparse_matrix< _CT, _CTF > &	matrix,
		size_t	index
	)

friend

Removes a column from the matrix.

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

Parameters

matrix	Reference on the matrix to modify.
index	The index to remove.

Returns: The modified matrix representing the result.

◆ remove_row

template<typename CoefficientRing , int StorageFormat>

template<typename _CT , int _CTF>

Sparse_matrix< _CT, _CTF > & remove_row	(	Sparse_matrix< _CT, _CTF > &	matrix,
		size_t	index
	)

friend

Removes a row from the matrix.

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

Parameters

matrix	Reference on the matrix to modify.
index	The index to remove.

Returns: The modified matrix representing the result.

◆ set_coefficient

template<typename CoefficientRing , int StorageFormat>

template<typename _CT , int _CTF>

void set_coefficient	(	Sparse_matrix< _CT, _CTF > &	matrix,
		size_t	i,
		size_t	j,
		const _CT	d
	)

friend

Sets a given coefficient in matrix.

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

Warning: The matrix will perform boundary check.

Parameters

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

Definition

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Related Functions

Constructor & Destructor Documentation

◆ Sparse_matrix() [1/3]

◆ Sparse_matrix() [2/3]

◆ Sparse_matrix() [3/3]

Member Function Documentation

◆ begin()

◆ dimensions()

◆ end()

◆ is_null()

◆ nullify()

◆ operator*()

◆ operator*=()

◆ operator+()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator=()

◆ operator[]()

◆ reverse_begin()

◆ reverse_end()

◆ transpose()

Friends And Related Function Documentation

◆ cget_column

◆ cget_row

◆ get_coefficient

◆ operator*

◆ operator<<

◆ remove_coefficient

◆ remove_column

◆ remove_row

◆ set_coefficient