This class implements a sparse matrix using a float type for its elements that is specified by T. More...

Data Structures
class	Entry
	This class implements a triple object for matrix entries. More...

Public Types
typedef std::vector< Entry >	Entries
	Definition of a vector holding entries. More...

Public Member Functions
	SparseMatrixT ()
	Creates an empty sparse matrix object. More...

	SparseMatrixT (const SparseMatrixT< T > &matrix)
	Copy constructor. More...

	SparseMatrixT (SparseMatrixT< T > &&matrix) noexcept
	Move constructor. More...

	SparseMatrixT (const size_t rows, const size_t columns)
	Creates a new spare matrix with given dimensions. More...

	SparseMatrixT (const size_t rows, const size_t columns, const size_t nonZeroElements)
	Creates a new spare matrix with given dimensions. More...

	SparseMatrixT (const size_t rows, const size_t columns, const Entries &entries)
	Creates a new spare matrix with given dimensions. More...

	SparseMatrixT (const size_t rows, const size_t columns, const MatrixT< T > &diagonal, const bool forceNonZeros=false)
	Creates a new sparse matrix with defined rows and columns and initializes the diagonal with small sub matrices. More...

	SparseMatrixT (const MatrixT< T > &denseMatrix)
	Creates a new sparse matrix with defined rows and columns and copies all non-zero values from a dense matrix. More...

	~SparseMatrixT ()
	Destructs a sparse matrix object. More...

size_t	rows () const
	Returns the number of rows this matrix has. More...

size_t	columns () const
	Returns the number of columns this matrix has. More...

size_t	nonZeroElements () const
	Returns the number of non zero elements stored in this matrix. More...

MatrixT< T >	diagonal () const
	Returns a vector containing the values of the diagonal. More...

void	reserve (const size_t elements)
	Reserves memory for a specified number of non zero elements. More...

bool	isZero (const size_t row, const size_t column) const
	Returns whether a specified elements is zero. More...

bool	isEqual (const SparseMatrixT< T > &matrix, const T eps) const
	Returns whether two matrices are almost identical up to a specified epsilon. More...

bool	isEqual (const MatrixT< T > &matrix, const T eps) const
	Returns whether two matrices are almost identical up to a specified epsilon. More...

void	setEntries (const Entries &entries)
	(Re-)sets the non-zero entries of this sparse matrix. More...

SparseMatrixT< T >	submatrix (const size_t row, const size_t column, const size_t rows, const size_t columns) const
	Returns a submatrix of this matrix. More...

SparseMatrixT< T >	transposed () const
	Returns the transposes matrix of this matrix. More...

void	transpose ()
	Transposes this matrix. More...

bool	solve (const MatrixT< T > &b, MatrixT< T > &x) const
	Solves the given linear system. More...

size_t	rank () const
	Computes the rank of this matrix. More...

T	sum () const
	Determines the sum of all elements of this matrix. More...

bool	invertDiagonal ()
	Inverts this square diagonal matrix. More...

bool	invertBlockDiagonal3 ()
	Inverts this square block diagonal matrix with 3x3 block size. More...

bool	invertBlockDiagonal (const size_t size)
	Inverts this square block diagonal matrix with size x size block size. More...

MatrixT< T >	denseMatrix () const
	Returns the dense matrix of this matrix. More...

bool	nonNegativeMatrixFactorization (MatrixT< T > &subcomponents, MatrixT< T > &weights, const unsigned int components=0u, const unsigned int iterations=100u, const T convergenceThreshold=T(0.0001)) const
	Performs a non-negative matrix factorization with multiplicative update rules V = W * H, V is a matrix containing non-negative values This matrix is V, and will be factorized into two matrices W (weights) and H (subcomponents). More...

SparseMatrixT< T > &	operator= (const SparseMatrixT< T > &matrix)
	Assign operator. More...

SparseMatrixT< T > &	operator= (SparseMatrixT< T > &&matrix) noexcept
	Move operator. More...

SparseMatrixT< T >	operator* (const SparseMatrixT< T > &matrix) const
	Multiplies two sparse matrix objects and returns the matrix result. More...

SparseMatrixT< T > &	operator*= (const SparseMatrixT< T > &matrix)
	Multiplies a second sparse matrix object to this matrix object. More...

SparseMatrixT< T >	operator+ (const SparseMatrixT< T > &matrix) const
	Adds two sparse matrix objects and returns the matrix result. More...

SparseMatrixT< T > &	operator+= (const SparseMatrixT< T > &matrix)
	Adds a second sparse matrix object to this matrix. More...

SparseMatrixT< T >	operator- (const SparseMatrixT< T > &matrix) const
	Subtracts two sparse matrix objects and returns the matrix result. More...

SparseMatrixT< T > &	operator-= (const SparseMatrixT< T > &matrix)
	Subtracts a second sparse matrix object from this matrix. More...

MatrixT< T >	operator* (const MatrixT< T > &matrix) const
	Multiplies a dense matrix object on this sparse matrix object and returns the dense matrix result. More...

bool	operator== (const SparseMatrixT< T > &matrix) const
	Returns whether this matrix is equal to an other one up to an epsilon value. More...

bool	operator== (const MatrixT< T > &matrix) const
	Returns whether this matrix is equal to an other one up to an epsilon value. More...

T	operator() (const size_t row, const size_t column) const
	Returns a specific element of the sparse matrix. More...

T &	operator() (const size_t row, const size_t column)
	Returns the reference to a specific element of the sparse matrix. More...

Private Member Functions
	SparseMatrixT (void *matrix)
	Creates a new sparse matrix object by the internal matrix object data directly. More...

Private Attributes
void *	internalMatrix
	Abstract pointer to the internal matrix object. More...

Detailed Description

template<typename T>
class Ocean::SparseMatrixT< T >

This class implements a sparse matrix using a float type for its elements that is specified by T.

Template Parameters

T	Data type of matrix elements

See also: SparseMatrix, SparseMatrixF, SparseMatrixD, Matrix.

Member Typedef Documentation

◆ Entries

template<typename T >

typedef std::vector<Entry> Ocean::SparseMatrixT< T >::Entries

Definition of a vector holding entries.

Constructor & Destructor Documentation

◆ SparseMatrixT() [1/9]

template<typename T >

Ocean::SparseMatrixT< T >::SparseMatrixT ( )

Creates an empty sparse matrix object.

◆ SparseMatrixT() [2/9]

template<typename T >

Ocean::SparseMatrixT< T >::SparseMatrixT ( const SparseMatrixT< T > & matrix )

Copy constructor.

Parameters

matrix Sparse matrix to be copied

◆ SparseMatrixT() [3/9]

template<typename T >

Ocean::SparseMatrixT< T >::SparseMatrixT ( SparseMatrixT< T > && matrix )

noexcept

Move constructor.

Parameters

matrix Sparse matrix to be movied

◆ SparseMatrixT() [4/9]

template<typename T >

Ocean::SparseMatrixT< T >::SparseMatrixT	(	const size_t	rows,
		const size_t	columns
	)

Creates a new spare matrix with given dimensions.

Parameters

rows	Number of rows to create a sparse matrix for
columns	Number of columns to create a sparse matrix for

◆ SparseMatrixT() [5/9]

template<typename T >

Ocean::SparseMatrixT< T >::SparseMatrixT	(	const size_t	rows,
		const size_t	columns,
		const size_t	nonZeroElements
	)

Creates a new spare matrix with given dimensions.

Parameters

rows	Number of rows to create a sparse matrix for
columns	Number of columns to create a sparse matrix for
nonZeroElements	Number of expected non zero elements to reserve memory for

◆ SparseMatrixT() [6/9]

template<typename T >

Ocean::SparseMatrixT< T >::SparseMatrixT	(	const size_t	rows,
		const size_t	columns,
		const Entries &	entries
	)

Creates a new spare matrix with given dimensions.

Parameters

rows	Number of rows to create a sparse matrix for
columns	Number of columns to create a sparse matrix for
entries	All non-zero entries of the new matrix

◆ SparseMatrixT() [7/9]

template<typename T >

Ocean::SparseMatrixT< T >::SparseMatrixT	(	const size_t	rows,
		const size_t	columns,
		const MatrixT< T > &	diagonal,
		const bool	forceNonZeros = `false`
	)

Creates a new sparse matrix with defined rows and columns and initializes the diagonal with small sub matrices.

The number of columns of the given diagonal vector matrix defines the size of the small sub matrices.
The number of rows of the diagonal vector matrix must be a multiple of the number of rows.

Parameters

rows	Rows of the new matrix
columns	Columns of the new matrix
diagonal	Diagonal vector matrix holding the new diagonal sub matrices
forceNonZeros	True, to force all diagonal elements to be an epsilon larger than zero (if the given element is zero)

◆ SparseMatrixT() [8/9]

template<typename T >

Ocean::SparseMatrixT< T >::SparseMatrixT ( const MatrixT< T > & denseMatrix )

explicit

Creates a new sparse matrix with defined rows and columns and copies all non-zero values from a dense matrix.

Parameters

denseMatrix Dense matrix from that the non-zero values are copied

◆ ~SparseMatrixT()

template<typename T >

Ocean::SparseMatrixT< T >::~SparseMatrixT ( )

Destructs a sparse matrix object.

◆ SparseMatrixT() [9/9]

template<typename T >

Ocean::SparseMatrixT< T >::SparseMatrixT ( void * matrix )

explicitprivate

Creates a new sparse matrix object by the internal matrix object data directly.

Parameters

matrix Internal matrix object

Member Function Documentation

◆ columns()

template<typename T >

size_t Ocean::SparseMatrixT< T >::columns ( ) const

Returns the number of columns this matrix has.

Returns: Number of columns

◆ denseMatrix()

template<typename T >

MatrixT<T> Ocean::SparseMatrixT< T >::denseMatrix ( ) const

Returns the dense matrix of this matrix.

Returns: Dense matrix

◆ diagonal()

template<typename T >

MatrixT<T> Ocean::SparseMatrixT< T >::diagonal ( ) const

Returns a vector containing the values of the diagonal.

Returns: Vector with diagonal values with dimension n x 1

◆ invertBlockDiagonal()

template<typename T >

bool Ocean::SparseMatrixT< T >::invertBlockDiagonal ( const size_t size )

Inverts this square block diagonal matrix with size x size block size.

The size of the matrix must be a multiple of size.
Each of the size x size block is inverted individually.

Parameters

size	The size of the block (size x size) with range (2, infinity)

Returns: True, if succeeded

◆ invertBlockDiagonal3()

template<typename T >

bool Ocean::SparseMatrixT< T >::invertBlockDiagonal3 ( )

Inverts this square block diagonal matrix with 3x3 block size.

The size of the matrix must be a multiple of three.
Each of the 3x3 block is inverted individually.

Returns: True, if succeeded

◆ invertDiagonal()

template<typename T >

bool Ocean::SparseMatrixT< T >::invertDiagonal ( )

Inverts this square diagonal matrix.

Returns: True, if succeeded

◆ isEqual() [1/2]

template<typename T >

bool Ocean::SparseMatrixT< T >::isEqual	(	const MatrixT< T > &	matrix,
		const T	eps
	)		const

Returns whether two matrices are almost identical up to a specified epsilon.

Parameters

matrix	Second matrix that will be checked
eps	Epsilon to be used

Returns: True, if so

◆ isEqual() [2/2]

template<typename T >

bool Ocean::SparseMatrixT< T >::isEqual	(	const SparseMatrixT< T > &	matrix,
		const T	eps
	)		const

Returns whether two matrices are almost identical up to a specified epsilon.

Parameters

matrix	Second matrix that will be checked
eps	Epsilon to be used

Returns: True, if so

◆ isZero()

template<typename T >

bool Ocean::SparseMatrixT< T >::isZero	(	const size_t	row,
		const size_t	column
	)		const

Returns whether a specified elements is zero.

Parameters

row	The row of the element to be checked
column	The column of the element to be checked

Returns: True, if so

◆ nonNegativeMatrixFactorization()

template<typename T >

bool Ocean::SparseMatrixT< T >::nonNegativeMatrixFactorization	(	MatrixT< T > &	subcomponents,
		MatrixT< T > &	weights,
		const unsigned int	components = `0u`,
		const unsigned int	iterations = `100u`,
		const T	convergenceThreshold = `T(0.0001)`
	)		const

Performs a non-negative matrix factorization with multiplicative update rules V = W * H, V is a matrix containing non-negative values
This matrix is V, and will be factorized into two matrices W (weights) and H (subcomponents).

Parameters

subcomponents	Solution matrix containing base component vectors
weights	Solution matrix containing weights to the component vectors
components	Number of base component vectors (Number of components is usally much smaller than its rank). If set to 0, the rank of matrix is used [0, rank]
iterations	Number of iterations maximal performed [1, infinity)
convergenceThreshold	Differential threshold as convergence criterion (0, infinity)

Returns: True, if succeeded

◆ nonZeroElements()

template<typename T >

size_t Ocean::SparseMatrixT< T >::nonZeroElements ( ) const

Returns the number of non zero elements stored in this matrix.

Returns: Number of non zero elements

◆ operator()() [1/2]

template<typename T >

T& Ocean::SparseMatrixT< T >::operator()	(	const size_t	row,
		const size_t	column
	)

Returns the reference to a specific element of the sparse matrix.

Beware: The element must be non zero, thus the element must have been inserted before!

Parameters

row	Element row to be returned
column	Element column to be returned

Returns: Matrix element

See also: insert().

◆ operator()() [2/2]

template<typename T >

T Ocean::SparseMatrixT< T >::operator()	(	const size_t	row,
		const size_t	column
	)		const

Returns a specific element of the sparse matrix.

Parameters

row	Element row to be returned
column	Element column to be returned

Returns: Matrix element

◆ operator*() [1/2]

template<typename T >

MatrixT<T> Ocean::SparseMatrixT< T >::operator* ( const MatrixT< T > & matrix ) const

Multiplies a dense matrix object on this sparse matrix object and returns the dense matrix result.

Parameters

matrix Right matrix to multiply

Returns: Matrix product result

◆ operator*() [2/2]

template<typename T >

SparseMatrixT<T> Ocean::SparseMatrixT< T >::operator* ( const SparseMatrixT< T > & matrix ) const

Multiplies two sparse matrix objects and returns the matrix result.

Parameters

matrix Right sparse matrix to multiply

Returns: Matrix product result

◆ operator*=()

template<typename T >

SparseMatrixT< T > & Ocean::SparseMatrixT< T >::operator*= ( const SparseMatrixT< T > & matrix )

inline

Multiplies a second sparse matrix object to this matrix object.

Parameters

matrix Right sparse matrix to multiply

Returns: Reference to this (modified) sparse matrix

◆ operator+()

template<typename T >

SparseMatrixT<T> Ocean::SparseMatrixT< T >::operator+ ( const SparseMatrixT< T > & matrix ) const

Adds two sparse matrix objects and returns the matrix result.

Parameters

matrix Right sparse matrix to add

Returns: Matrix result

◆ operator+=()

template<typename T >

SparseMatrixT<T>& Ocean::SparseMatrixT< T >::operator+= ( const SparseMatrixT< T > & matrix )

Adds a second sparse matrix object to this matrix.

Parameters

matrix Right sparse matrix to add

Returns: Reference to this (modified) matrix

◆ operator-()

template<typename T >

SparseMatrixT<T> Ocean::SparseMatrixT< T >::operator- ( const SparseMatrixT< T > & matrix ) const

Subtracts two sparse matrix objects and returns the matrix result.

Parameters

matrix Right sparse matrix to subtract

Returns: Matrix result

◆ operator-=()

template<typename T >

SparseMatrixT<T>& Ocean::SparseMatrixT< T >::operator-= ( const SparseMatrixT< T > & matrix )

Subtracts a second sparse matrix object from this matrix.

Parameters

matrix Right sparse matrix to subtract

Returns: Reference to this (modified) matrix

◆ operator=() [1/2]

template<typename T >

SparseMatrixT<T>& Ocean::SparseMatrixT< T >::operator= ( const SparseMatrixT< T > & matrix )

Assign operator.

Parameters

matrix Sparse matrix to be assigned to this matrix

Returns: Reference to this matrix

◆ operator=() [2/2]

template<typename T >

SparseMatrixT<T>& Ocean::SparseMatrixT< T >::operator= ( SparseMatrixT< T > && matrix )

noexcept

Move operator.

Parameters

matrix Sparse matrix to be move to this matrix

Returns: Reference to this matrix

◆ operator==() [1/2]

template<typename T >

bool Ocean::SparseMatrixT< T >::operator== ( const MatrixT< T > & matrix ) const

inline

Returns whether this matrix is equal to an other one up to an epsilon value.

Parameters

matrix Second matrix to compare

Returns: True, if succeeded

◆ operator==() [2/2]

template<typename T >

bool Ocean::SparseMatrixT< T >::operator== ( const SparseMatrixT< T > & matrix ) const

inline

Returns whether this matrix is equal to an other one up to an epsilon value.

Parameters

matrix Second matrix to compare

Returns: True, if succeeded

◆ rank()

template<typename T >

size_t Ocean::SparseMatrixT< T >::rank ( ) const

Computes the rank of this matrix.

The matrix must be valid.

Returns: The matrix's rank with range [0, min(rows(), columns())]

◆ reserve()

template<typename T >

void Ocean::SparseMatrixT< T >::reserve ( const size_t elements )

Reserves memory for a specified number of non zero elements.

Parameters

elements Number of non zero elements.

◆ rows()

template<typename T >

size_t Ocean::SparseMatrixT< T >::rows ( ) const

Returns the number of rows this matrix has.

Returns: Number of rows

◆ setEntries()

template<typename T >

void Ocean::SparseMatrixT< T >::setEntries ( const Entries & entries )

(Re-)sets the non-zero entries of this sparse matrix.

All previous non-zero entries will be removed.
If the given set of entries contains zero-values these zero values will be skipped.

Parameters

entries The entries to set

◆ solve()

template<typename T >

bool Ocean::SparseMatrixT< T >::solve	(	const MatrixT< T > &	b,
		MatrixT< T > &	x
	)		const

Solves the given linear system.

M * x = b, with M and b known.
This matrix is M, the given vector is b and the result will be x.

Parameters

b	Vector defining the linear system
x	Solution vector receiving the solution if existing

Returns: True, if succeeded

◆ submatrix()

template<typename T >

SparseMatrixT<T> Ocean::SparseMatrixT< T >::submatrix	(	const size_t	row,
		const size_t	column,
		const size_t	rows,
		const size_t	columns
	)		const

Returns a submatrix of this matrix.

Parameters

row	The index of the row which will be the first row of the new submatrix, with range [0, rows())
column	The index of the column which will be the first column of the new sub-matrix, with range [0, colums())
rows	The number of rows of the new sub-matrix, with range [1, rows() - row]
columns	The number of columns of the new sub-matrix, with range [1, columns() - column]

Returns: The specified submatrix of this matrix

◆ sum()

template<typename T >

T Ocean::SparseMatrixT< T >::sum ( ) const

inline

Determines the sum of all elements of this matrix.

Returns: Matrix sum

◆ transpose()

template<typename T >

void Ocean::SparseMatrixT< T >::transpose ( )

Transposes this matrix.

◆ transposed()

template<typename T >

SparseMatrixT<T> Ocean::SparseMatrixT< T >::transposed ( ) const

Returns the transposes matrix of this matrix.

Returns: Transposes matrix of this matrix

Field Documentation

◆ internalMatrix

template<typename T >

void* Ocean::SparseMatrixT< T >::internalMatrix

private

Abstract pointer to the internal matrix object.

The documentation for this class was generated from the following file:

SparseMatrix.h

Data Structures

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<typename T> class Ocean::SparseMatrixT< T >

Member Typedef Documentation

◆ Entries

Constructor & Destructor Documentation

◆ SparseMatrixT() [1/9]

◆ SparseMatrixT() [2/9]

◆ SparseMatrixT() [3/9]

◆ SparseMatrixT() [4/9]

◆ SparseMatrixT() [5/9]

◆ SparseMatrixT() [6/9]

◆ SparseMatrixT() [7/9]

◆ SparseMatrixT() [8/9]

◆ ~SparseMatrixT()

◆ SparseMatrixT() [9/9]

Member Function Documentation

◆ columns()

◆ denseMatrix()

◆ diagonal()

◆ invertBlockDiagonal()

◆ invertBlockDiagonal3()

◆ invertDiagonal()

◆ isEqual() [1/2]

◆ isEqual() [2/2]

◆ isZero()

◆ nonNegativeMatrixFactorization()

◆ nonZeroElements()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ rank()

◆ reserve()

◆ rows()

◆ setEntries()

◆ solve()

◆ submatrix()

◆ sum()

◆ transpose()

◆ transposed()

Field Documentation

◆ internalMatrix

template<typename T>
class Ocean::SparseMatrixT< T >