Ocean::MatrixT< T > Class Template Reference

This class implements a matrix with arbitrary size. More...

Inheritance diagram for Ocean::MatrixT< T >:

Public Types
enum	MatrixProperty { MP_UNKNOWN , MP_SYMMETRIC }
	Definition of specific properties of matrices. More...
typedef T	Type
	Definition of the used data type. More...

Public Member Functions
	MatrixT ()=default
	Creates a new matrix with no size. More...
	MatrixT (const size_t rows, const size_t columns)
	Creates a new matrix with defined rows and columns. More...
	MatrixT (const size_t rows, const size_t columns, bool toIdentity)
	Creates a new matrix with defined rows and columns. More...
	MatrixT (const size_t rows, const size_t columns, const T value)
	Creates a new matrix with defined rows and columns. More...
	MatrixT (const size_t rows, const size_t columns, const T *source)
	Creates a new matrix with defined rows and columns. More...
	MatrixT (const size_t rows, const size_t columns, const T *source, const bool valuesRowAligned)
	Creates a new matrix with defined rows and columns. More...
	MatrixT (const size_t rows, const size_t columns, const MatrixT< T > &diagonal)
	Creates a new matrix with defined rows and columns and initializes the diagonal with small sub matrices. More...
	MatrixT (const size_t rows, const size_t columns, const MatrixT< T > &subMatrix, const size_t row, const size_t column, const T value=T(0.0))
	Creates a new matrix with defined rows and columns and a given sub-matrix. More...
	MatrixT (const MatrixT< T > &matrix)
	Copies a matrix. More...
	MatrixT (MatrixT< T > &&matrix) noexcept
	Move constructor. More...
	~MatrixT ()
	Destructs a matrix and releases the elements. More...
size_t	rows () const
	Returns the count of rows. More...
size_t	columns () const
	Returns the count of columns. More...
size_t	elements () const
	Returns the number of entire elements, which is the product of rows and columns. More...
MatrixT< T >	inverted () const
	Returns the inverted of this matrix. More...
bool	invert ()
	Inverts this matrix. More...
MatrixT< T >	transposed () const
	Returns the transposed of this matrix. More...
void	transpose ()
	Transposes this matrix. More...
MatrixT< T >	selfSquareMatrix () const
	Returns the matrix product of this matrix and the transposed matrix of this matrix. More...
MatrixT< T >	selfTransposedSquareMatrix () const
	Returns the matrix product of transposed matrix of this matrix and this matrix. More...
void	selfTransposedSquareMatrix (MatrixT< T > &result) const
	Returns the matrix product of transposed matrix of this matrix and this matrix. More...
void	weightedSelfTransposedSquareMatrix (const MatrixT< T > &weightDiagonal, MatrixT< T > &result) const
	Returns the matrix product of transposed matrix of this matrix and this matrix and applies a further squared diagonal weighting matrix. More...
bool	selfSquareDiagonalMatrixMultiply (const MatrixT< T > &right, MatrixT< T > &result) const
	Interprets this matrix as diagonal matrix and multiplies a second matrix on the right of the interpreted diagonal matrix. More...
bool	selfSquareDiagonalMatrixMultiply (const MatrixT< T > &weightDiagonal, const MatrixT< T > &right, MatrixT< T > &result) const
	Interprets this matrix as diagonal matrix and multiplies a second matrix on the right of the interpreted diagonal matrix. More...
MatrixT< T >	transposedMultiply (const MatrixT< T > &right) const
	Multiplies this transposed matrix with a second matrix. More...
void	transposedMultiply (const MatrixT< T > &right, MatrixT< T > &result) const
	Multiplies this transposed matrix with a second matrix. More...
bool	solve (const MatrixT< T > &b, MatrixT< T > &x, const MatrixProperty matrixProperty=MP_UNKNOWN) const
	Solves the given linear system. More...
template<MatrixProperty tMatrixProperty>
bool	solve (const MatrixT< T > &b, MatrixT< T > &x) const
	Solves the given linear system. More...
bool	solve (const T *b, T *x, const MatrixProperty matrixProperty=MP_UNKNOWN) const
	Solves the given linear system. More...
template<MatrixProperty tMatrixProperty>
bool	solve (const T *b, T *x) const
	Solves the given linear system. More...
bool	nonNegativeMatrixFactorization (MatrixT< T > &subcomponents, MatrixT< T > &weights, const size_t 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...
bool	eigenSystem (MatrixT< T > &values, MatrixT< T > &vectors) const
	Computes the eigen system of this matrix. More...
bool	singularValueDecomposition (MatrixT< T > &u, MatrixT< T > &w, MatrixT< T > &v) const
	Computes the singular value decomposition for this matrix. More...
bool	qrDecomposition (MatrixT< T > &qMatrix, MatrixT< T > *rMatrix=nullptr) const
	Computes the QR decomposition for this matrix [m x n] while m >= n must hold. More...
bool	choleskyDecomposition (MatrixT< T > &lMatrix) const
	Computes the Cholesky decomposition for this square matrix [m x m]. More...
MatrixT< T >	pseudoInverted (const T epsilon=NumericT< T >::eps()) const
	Returns the pseudo inverse of this matrix by application of the singular value decomposition. More...
size_t	rank () const
	Computes the rank of this matrix. More...
MatrixT< T >	row (const size_t index) const
	Returns a row of the matrix. More...
MatrixT< T >	vector (const size_t column) const
	Returns a column vector of the matrix. More...
MatrixT< T >	diagonal () const
	Returns a vector containing the values of the diagonal. More...
T	norm () const
	Determines the L1 norm (sum of absolute elements) of this matrix. More...
T	sum () const
	Determines the sum of all elements of this matrix. More...
MatrixT< T >	subMatrix (const size_t row, const size_t column, const size_t rows, const size_t columns)
	Returns a sub matrix of this one. More...
void	multiplyRow (const size_t row, const T scalar)
	Multiplies a row with a scalar. More...
void	multiplyColumn (const size_t column, const T scalar)
	Multiplies a column with a scalar. More...
void	resize (const size_t rows, const size_t columns)
	Resizes this matrix. More...
bool	isEqual (const MatrixT< T > &matrix, const T eps=NumericT< T >::eps()) const
	Returns whether two matrices are almost identical up to a specified epsilon. More...
bool	isSymmetric (const T eps=NumericT< T >::eps()) const
	Returns whether this matrix is symmetric (and whether this matrix is a square matrix). More...
const T *	data () const
	Returns a pointer to the internal values. More...
T *	data ()
	Returns a pointer to the internal values. More...
MatrixT< T > &	operator= (const MatrixT< T > &matrix)
	Assigns a matrix to this one. More...
MatrixT< T > &	operator= (MatrixT< T > &&matrix) noexcept
	Move assign operator. More...
bool	operator== (const MatrixT< T > &right) const
	Returns whether two matrices are identical up to a small epsilon. More...
bool	operator!= (const MatrixT< T > &right) const
	Returns whether two matrices are not identical up to a small epsilon. More...
MatrixT< T >	operator+ (const MatrixT< T > &right) const
	Adds two matrices. More...
MatrixT< T > &	operator+= (const MatrixT< T > &right)
	Adds and assigns two matrices. More...
MatrixT< T >	operator- (const MatrixT< T > &right) const
	Subtracts two matrices. More...
MatrixT< T > &	operator-= (const MatrixT< T > &right)
	Subtracts and assigns two matrices. More...
MatrixT< T >	operator* (const MatrixT< T > &right) const
	Multiplies two matrices. More...
MatrixT< T >	operator* (const T scalar) const
	Multiplies the matrix with a scalar. More...
MatrixT< T > &	operator*= (const MatrixT< T > &right)
	Multiplies and assigns two matrices. More...
MatrixT< T > &	operator*= (const T scalar)
	Multiplies this matrix by a scalar. More...
const T *	operator[] (const size_t row) const
	Returns the pointer to the elements of a specified row. More...
T *	operator[] (const size_t row)
	Element operator for the row aligned elements. More...
T	operator() (const size_t row, const size_t column) const
	Element operator allowing to access a specific elements of this matrix. More...
T &	operator() (const size_t row, const size_t column)
	Element operator allowing to access a specific elements of this matrix. More...
T	operator() (const size_t index) const
	Element operator for the row aligned elements. More...
T &	operator() (const size_t index)
	Element operator for the row aligned elements. More...
	operator bool () const
	Returns whether the matrix holds at least one element. More...

Static Public Member Functions
static size_t	rank (const T *data, const size_t rows, const size_t columns)
	Computes the rank of given matrix data. More...

Protected Member Functions
void	swapRows (const size_t row0, const size_t row1)
	Swaps two rows. More...
void	swapColumns (const size_t column0, const size_t column1)
	Swaps two columns. More...
void	addRows (const size_t targetRow, const size_t sourceRow, const T scalar)
	Adds a multiple of a row to another one. More...
void	elementwiseMultiplication (const MatrixT< T > &multiplier)
	Performs an element-wise matrix multiplication meaning that each element of this matrix will be multiplied by a corresponding element from 'multiplier'. More...
void	elementwiseDivision (const MatrixT< T > &denominator)
	Performs an element-wise matrix division meaning that each element of this matrix will be divided by a corresponding element from 'denominator'. More...

Protected Attributes
size_t	rows_ = 0
	Number of rows. More...
size_t	columns_ = 0
	Number of columns. More...
T *	values_ = nullptr
	Elements of the matrix. More...

Detailed Description

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

This class implements a matrix with arbitrary size.

The elements of this matrix are stored in a row aligned order.
That means that elements are stored in the following pattern:

|  0  1   2   3   4  ...  c-1 |
|  c c+1 c+2 c+3 c+4 ...      |
| ...                         |

Template Parameters

T	Data type of matrix elements

See also

Matrix, MatrixF, MatrixD, StaticMatrix, SparseMatrix, SquareMatrix2, SquareMatrix3, SquareMatrix4.

Member Typedef Documentation

Type

template<typename T >

typedef T Ocean::MatrixT< T >::Type

Definition of the used data type.

Member Enumeration Documentation

MatrixProperty

template<typename T >

enum Ocean::MatrixT::MatrixProperty

Definition of specific properties of matrices.

Enumerator
MP_UNKNOWN	No specific property known.
MP_SYMMETRIC	The matrix is symmetric.

Constructor & Destructor Documentation

MatrixT() [1/10]

template<typename T >

Ocean::MatrixT< T >::MatrixT ( )

default

Creates a new matrix with no size.

MatrixT() [2/10]

template<typename T >

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

Creates a new matrix with defined rows and columns.

Parameters

rows	The rows of the new matrix
columns	The columns of the new matrix

MatrixT() [3/10]

template<typename T >

Ocean::MatrixT< T >::MatrixT	(	const size_t	rows,
		const size_t	columns,
		bool	toIdentity
	)

Creates a new matrix with defined rows and columns.

Parameters

rows	The rows of the new matrix
columns	The columns of the new matrix
toIdentity	Determines whether the matrix will be initialized with as entity matrix or zero matrix.

MatrixT() [4/10]

template<typename T >

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

Creates a new matrix with defined rows and columns.

Parameters

rows	The rows of the new matrix
columns	The columns of the new matrix
value	The value that every matrix element will be set to

MatrixT() [5/10]

template<typename T >

Ocean::MatrixT< T >::MatrixT	(	const size_t	rows,
		const size_t	columns,
		const T *	source
	)

Creates a new matrix with defined rows and columns.

Parameters

rows	The rows of the new matrix
columns	The columns of the new matrix
source	Elements to be copied into this matrix

MatrixT() [6/10]

template<typename T >

Ocean::MatrixT< T >::MatrixT	(	const size_t	rows,
		const size_t	columns,
		const T *	source,
		const bool	valuesRowAligned
	)

Creates a new matrix with defined rows and columns.

Parameters

rows	The rows of the new matrix
columns	The columns of the new matrix
source	Elements to be copied into this matrix
valuesRowAligned	True, if the given values are stored in a row aligned order (which is the default case for this matrix); False, if the values are stored in a column aligned order

MatrixT() [7/10]

template<typename T >

Ocean::MatrixT< T >::MatrixT	(	const size_t	rows,
		const size_t	columns,
		const MatrixT< T > &	diagonal
	)

Creates a new 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	The rows of the new matrix
columns	The columns of the new matrix
diagonal	The diagonal vector matrix holding the new diagonal sub matrices

MatrixT() [8/10]

template<typename T >

Ocean::MatrixT< T >::MatrixT	(	const size_t	rows,
		const size_t	columns,
		const MatrixT< T > &	subMatrix,
		const size_t	row,
		const size_t	column,
		const T	value = T(0.0)
	)

Creates a new matrix with defined rows and columns and a given sub-matrix.

The given sub-matrix can be larger than the new matrix as elements not fitting into the new matrix will be skipped.
All remaining elements of the matrix will be set to the specified value.

Parameters

rows	The number of rows the new matrix will have, with range [1, infinity)
columns	The number of columns the new matrix will have, with range [1, infinity)
subMatrix	The sub-matrix from which the elements will be copied into the new matrix
row	The row at which the sub-matrix will be placed in the new matrix, with range [0, rows - 1]
column	The column at which the sub-matrix will be placed in the new matrix, with range [0, columns - 1]
value	The value which will be used to fill the remaining matrix elements, with range (-infinity, infinity)

MatrixT() [9/10]

template<typename T >

Ocean::MatrixT< T >::MatrixT

(

const MatrixT< T > &

matrix

)

Copies a matrix.

Parameters

matrix

The matrix to copy

MatrixT() [10/10]

template<typename T >

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

noexcept

Move constructor.

Parameters

matrix

The matrix to be moved

~MatrixT()

template<typename T >

Ocean::MatrixT< T >::~MatrixT

(

)

Destructs a matrix and releases the elements.

Member Function Documentation

addRows()

template<typename T >

void Ocean::MatrixT< T >::addRows ( const size_t  targetRow, const size_t  sourceRow, const T  scalar  )

protected

Adds a multiple of a row to another one.

Parameters

targetRow	The index of the target row to which the multiple of the source row will be added, with range [0, rows())
sourceRow	The index of the source row, with range [0, rows())
scalar	The scalar to multiply the source elements with

choleskyDecomposition()

template<typename T >

bool Ocean::MatrixT< T >::choleskyDecomposition

(

MatrixT< T > &

lMatrix

)

const

Computes the Cholesky decomposition for this square matrix [m x m].

This matrix is decomposed into M = L * L^T, where L is a lower triangular matrix [m x m].

Parameters

lMatrix

Resulting L matrix, the lower triangle matrix

Returns

True, if succeeded

columns()

template<typename T >

size_t Ocean::MatrixT< T >::columns

inline

Returns the count of columns.

Returns

Columns of the matrix, with range [0, infinity)

data() [1/2]

template<typename T >

T * Ocean::MatrixT< T >::data

inline

Returns a pointer to the internal values.

Returns

Pointer to the internal values

data() [2/2]

template<typename T >

const T * Ocean::MatrixT< T >::data

inline

Returns a pointer to the internal values.

Returns

Pointer to the internal values

diagonal()

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::diagonal

(

)

const

Returns a vector containing the values of the diagonal.

Returns

Vector with diagonal values

eigenSystem()

template<typename T >

bool Ocean::MatrixT< T >::eigenSystem	(	MatrixT< T > &	values,
		MatrixT< T > &	vectors
	)		const

Computes the eigen system of this matrix.

The function determines values and vectors that: matrix * vectors = vectors * diagonal(values).
Beware: The eigen values are not ordered!

Parameters

values	Vector with resulting eigen values
vectors	Matrix with resulting eigen vectors as columns

Returns

True, if succeeded

elements()

template<typename T >

size_t Ocean::MatrixT< T >::elements

inline

Returns the number of entire elements, which is the product of rows and columns.

Returns

Number of elements, with range [0, infinity)

elementwiseDivision()

template<typename T >

void Ocean::MatrixT< T >::elementwiseDivision ( const MatrixT< T > &  denominator )

protected

Performs an element-wise matrix division meaning that each element of this matrix will be divided by a corresponding element from 'denominator'.

Parameters

denominator

The matrix providing the denominator elements, with same size as this matrix

elementwiseMultiplication()

template<typename T >

void Ocean::MatrixT< T >::elementwiseMultiplication ( const MatrixT< T > &  multiplier )

protected

Performs an element-wise matrix multiplication meaning that each element of this matrix will be multiplied by a corresponding element from 'multiplier'.

Parameters

multiplier

The matrix providing the multiplication elements, with same size as this matrix, all elements must not be zero

invert()

template<typename T >

bool Ocean::MatrixT< T >::invert

(

)

Inverts this matrix.

Returns

True, if the matrix is not singular.

See also

inverted().

inverted()

template<typename T >

MatrixT< T > Ocean::MatrixT< T >::inverted

inline

Returns the inverted of this matrix.

Beware: This function does not throw an exception if the matrix cannot be inverted.
Thus, ensure that the matrix is invertible before calling this function.
This matrix is invertible e.g., if the matrix is square and has full rank (rank() == rows() && rank() == columns()).
Even better: avoid the usage of this function and call invert() instead.
In case, this matrix is not invertible, this matrix will be returned instead.

Returns

Inverted matrix

See also

invert(), rank().

isEqual()

template<typename T >

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

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

Parameters

matrix	Second matrix that will be checked
eps	The epsilon threshold to be used, with range [0, infinity)

Returns

True, if so

isSymmetric()

template<typename T >

bool Ocean::MatrixT< T >::isSymmetric

(

const T

eps = NumericT< T >::eps()

)

const

Returns whether this matrix is symmetric (and whether this matrix is a square matrix).

Beware: An empty matrix (without any rows or columns) is symmetric.

Parameters

eps	The epsilon threshold to be used, with range [0, infinity)

Returns

True, if so

multiplyColumn()

template<typename T >

void Ocean::MatrixT< T >::multiplyColumn	(	const size_t	column,
		const T	scalar
	)

Multiplies a column with a scalar.

Beware: No range check will be done!

Parameters

column	The column to multiply, with range [0, columns() - 1]
scalar	The scalar to multiply, with range (-infinity, infinity)

multiplyRow()

template<typename T >

void Ocean::MatrixT< T >::multiplyRow	(	const size_t	row,
		const T	scalar
	)

Multiplies a row with a scalar.

Beware: No range check will be done!

Parameters

row	The row to multiply, with range [0, rows() - 1]
scalar	The scalar to multiply, with range (-infinity, infinity)

nonNegativeMatrixFactorization()

template<typename T >

bool Ocean::MatrixT< T >::nonNegativeMatrixFactorization	(	MatrixT< T > &	subcomponents,
		MatrixT< T > &	weights,
		const size_t	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 usually 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 aborting the calculation (0, infinity)

Returns

True, if succeeded

norm()

template<typename T >

T Ocean::MatrixT< T >::norm

inline

Determines the L1 norm (sum of absolute elements) of this matrix.

Returns

Matrix norm

operator bool()

template<typename T >

Ocean::MatrixT< T >::operator bool

inlineexplicit

Returns whether the matrix holds at least one element.

Returns

True, if so

operator!=()

template<typename T >

bool Ocean::MatrixT< T >::operator!= ( const MatrixT< T > &  right ) const

inline

Returns whether two matrices are not identical up to a small epsilon.

Parameters

right

The right matrix

Returns

True, if so

operator()() [1/4]

template<typename T >

T & Ocean::MatrixT< T >::operator() ( const size_t  index )

inline

Element operator for the row aligned elements.

Parameters

index

The index of the element to return, with range [0, elements())

Returns

Specified element

operator()() [2/4]

template<typename T >

T Ocean::MatrixT< T >::operator() ( const size_t  index ) const

inline

Element operator for the row aligned elements.

Parameters

index

The index of the element to return, with range [0, elements())

Returns

Specified element

operator()() [3/4]

template<typename T >

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

inline

Element operator allowing to access a specific elements of this matrix.

Parameters

row	The row of the element to return, with range [0, rows())
column	The column of the element to return, with range [0, columns())

Returns

Specified element

operator()() [4/4]

template<typename T >

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

inline

Element operator allowing to access a specific elements of this matrix.

Parameters

row	The row of the element to return, with range [0, rows())
column	The column of the element to return, with range [0, columns())

Returns

Specified element

operator*() [1/2]

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::operator*

(

const MatrixT< T > &

right

)

const

Multiplies two matrices.

Parameters

right

The right matrix

Returns

Resulting matrix

operator*() [2/2]

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::operator*

(

const T

scalar

)

const

Multiplies the matrix with a scalar.

Parameters

scalar

The scalar to multiply

Returns

Resulting matrix

operator*=() [1/2]

template<typename T >

MatrixT< T > & Ocean::MatrixT< T >::operator*= ( const MatrixT< T > &  right )

inline

Multiplies and assigns two matrices.

Parameters

right

The right matrix

Returns

Reference to this matrix

operator*=() [2/2]

template<typename T >

MatrixT<T>& Ocean::MatrixT< T >::operator*=

(

const T

scalar

)

Multiplies this matrix by a scalar.

Parameters

scalar

The scalar to multiply

Returns

Reference to this matrix

operator+()

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::operator+

(

const MatrixT< T > &

right

)

const

Adds two matrices.

Parameters

right

The right matrix

Returns

Sum matrix

operator+=()

template<typename T >

MatrixT<T>& Ocean::MatrixT< T >::operator+=

(

const MatrixT< T > &

right

)

Adds and assigns two matrices.

Parameters

right

The right matrix

Returns

Reference to this matrix

operator-()

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::operator-

(

const MatrixT< T > &

right

)

const

Subtracts two matrices.

Parameters

right

The right matrix

Returns

Subtracted matrix

operator-=()

template<typename T >

MatrixT<T>& Ocean::MatrixT< T >::operator-=

(

const MatrixT< T > &

right

)

Subtracts and assigns two matrices.

Parameters

right

The right matrix

Returns

Reference to this matrix

operator=() [1/2]

template<typename T >

MatrixT<T>& Ocean::MatrixT< T >::operator=

(

const MatrixT< T > &

matrix

)

Assigns a matrix to this one.

Parameters

matrix

The matrix to assign

Returns

Reference to this matrix

operator=() [2/2]

template<typename T >

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

noexcept

Move assign operator.

Parameters

matrix

The matrix to moved

Returns

Reference to this matrix

operator==()

template<typename T >

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

inline

Returns whether two matrices are identical up to a small epsilon.

Parameters

right

The right matrix

Returns

True, if so

operator[]() [1/2]

template<typename T >

T * Ocean::MatrixT< T >::operator[] ( const size_t  row )

inline

Element operator for the row aligned elements.

Parameters

row	Index of the element to return, with range [0, rows())

Returns

Specified element

operator[]() [2/2]

template<typename T >

const T * Ocean::MatrixT< T >::operator[] ( const size_t  row ) const

inline

Returns the pointer to the elements of a specified row.

Parameters

row	Index of the row to return, with range [0, rows())

Returns

Specified row

pseudoInverted()

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::pseudoInverted

(

const T

epsilon = NumericT< T >::eps()

)

const

Returns the pseudo inverse of this matrix by application of the singular value decomposition.

Parameters

epsilon

The tolerance value, with range [0, infinity)

Returns

The resulting pseudo inverted matrix

qrDecomposition()

template<typename T >

bool Ocean::MatrixT< T >::qrDecomposition	(	MatrixT< T > &	qMatrix,
		MatrixT< T > *	rMatrix = nullptr
	)		const

Computes the QR decomposition for this matrix [m x n] while m >= n must hold.

This matrix is decomposed into two matrices as follows: q * r, where q is a orthogonal [m x m] matrix (m * m^T = I), and r is a upper triangular matrix [m x n].

Parameters

qMatrix	Resulting q matrix, containing the null space in the last (m - rank) columns, the size of the matrix will be adjusted internally
rMatrix	Optional resulting r matrix, upper triangle matrix, the size of the matrix will be adjusted internally, nullptr if the matrix is not needed

Returns

True, if succeeded

rank() [1/2]

template<typename T >

size_t Ocean::MatrixT< T >::rank

inline

Computes the rank of this matrix.

The matrix must be valid.

Returns

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

rank() [2/2]

template<typename T >

static size_t Ocean::MatrixT< T >::rank ( const T *  data, const size_t  rows, const size_t  columns  )

static

Computes the rank of given matrix data.

Parameters

data	The elements of the matrix for which the rank will be calculated, provided in a row aligned order, must be valid
rows	The number of rows of the provided matrix, with range [1, infinity)
columns	The number of columns of the provided matrix, with range [1, infinity)

Returns

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

resize()

template<typename T >

void Ocean::MatrixT< T >::resize	(	const size_t	rows,
		const size_t	columns
	)

Resizes this matrix.

Parameters

rows	Number of rows of the resized matrix
columns	Number of columns of the resized matrix

row()

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::row

(

const size_t

index

)

const

Returns a row of the matrix.

Parameters

index

The index of the row to receive, with range [0, rows())

Returns

Entire row

rows()

template<typename T >

size_t Ocean::MatrixT< T >::rows

inline

Returns the count of rows.

Returns

Rows of the matrix, with range [0, infinity)

selfSquareDiagonalMatrixMultiply() [1/2]

template<typename T >

bool Ocean::MatrixT< T >::selfSquareDiagonalMatrixMultiply	(	const MatrixT< T > &	right,
		MatrixT< T > &	result
	)		const

Interprets this matrix as diagonal matrix and multiplies a second matrix on the right of the interpreted diagonal matrix.

The square sub matrices size is defined by the number of columns of this matrix.
Thus the number of rows must be a multiple of the number of columns of this matrix.
Actually, the following matrix will be returned: result = diag(*this) * right.

Parameters

right	The right matrix to be multiplied with the interpreted diagonal matrix
result	Resulting matrix

Returns

True, if succeeded

selfSquareDiagonalMatrixMultiply() [2/2]

template<typename T >

bool Ocean::MatrixT< T >::selfSquareDiagonalMatrixMultiply	(	const MatrixT< T > &	weightDiagonal,
		const MatrixT< T > &	right,
		MatrixT< T > &	result
	)		const

Interprets this matrix as diagonal matrix and multiplies a second matrix on the right of the interpreted diagonal matrix.

Further, a diagonal weighting vector is applied.
The square sub matrices size is defined by the number of columns of this matrix.
Thus the number of rows must be a multiple of the number of columns of this matrix.
Actually, the following matrix will be returned: result = diag(*this) * diag(weightDiagonal) * right.

Parameters

right	The right matrix to be multiplied with the interpreted diagonal matrix
weightDiagonal	Weight vector defining the diagonal of the weighting matrix, with one column
result	Resulting matrix

Returns

True, if succeeded

selfSquareMatrix()

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::selfSquareMatrix

(

)

const

Returns the matrix product of this matrix and the transposed matrix of this matrix.

The result will be a square matrix with size: rows() x rows().
Actually, the following matrix will be returned: (*this) * (*this).transposed().

Returns

Resulting matrix

selfTransposedSquareMatrix() [1/2]

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::selfTransposedSquareMatrix

(

)

const

Returns the matrix product of transposed matrix of this matrix and this matrix.

The result will be a square matrix with size: columns() x columns().
Actually, the following matrix will be returned: (*this).transposed() * (*this).

Returns

Resulting matrix

selfTransposedSquareMatrix() [2/2]

template<typename T >

void Ocean::MatrixT< T >::selfTransposedSquareMatrix

(

MatrixT< T > &

result

)

const

Returns the matrix product of transposed matrix of this matrix and this matrix.

The result will be a square matrix with size: columns() x columns().
Actually, the following matrix will be returned: (*this).transposed() * (*this).

Parameters

result

Resulting matrix

singularValueDecomposition()

template<typename T >

bool Ocean::MatrixT< T >::singularValueDecomposition	(	MatrixT< T > &	u,
		MatrixT< T > &	w,
		MatrixT< T > &	v
	)		const

Computes the singular value decomposition for this matrix.

This matrix is decomposed into three matrices as follows: u * w * v.transposed().
The diagonal values of w are ordered in descending order already.

Parameters

u	Resulting u matrix
w	Resulting w vector holding the values of the diagonal matrix
v	Resulting v matrix

Returns

True, if succeeded

solve() [1/4]

template<typename T >

template<typename MatrixT< T >::MatrixProperty tMatrixProperty>

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

inline

Solves the given linear system.

M * x = b, with M and b known and M is a square matrix
This matrix is M, the given vector is b and the result will be x.
Note: If a non-square matrix should be solved, use: (M.transposed() * M) * x = M.transposed() * b

Parameters

b	Vector defining the linear system, with size columns() x 1
x	Solution vector receiving the solution if existing, with size columns() x 1

Returns

True, if succeeded

Template Parameters

tMatrixProperty

The property of the matrix allowing to improve the solving performance and stability, MP_UNKNOWN to apply a standard solving

solve() [2/4]

template<typename T >

bool Ocean::MatrixT< T >::solve ( const MatrixT< T > &  b, MatrixT< T > &  x, const MatrixProperty  matrixProperty = MP_UNKNOWN  ) const

inline

Solves the given linear system.

M * x = b, with M and b known and M is a square matrix
This matrix is M, the given vector is b and the result will be x.
Note: If a non-square matrix should be solved, use: (M.transposed() * M) * x = M.transposed() * b

Parameters

b	Vector defining the linear system, with size columns() x 1
x	Solution vector receiving the solution if existing, with size columns() x 1
matrixProperty	The property of the matrix allowing to improve the solving performance and stability, MP_UNKNOWN to apply a standard solving

Returns

True, if succeeded

solve() [3/4]

template<typename T >

template<MatrixProperty tMatrixProperty>

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

Solves the given linear system.

M * x = b, with M and b known and M is a square matrix
This matrix is M, the given vector is b and the result will be x..
Note: If a non-square matrix should be solved, use: (M.transposed() * M) * x = M.transposed() * b

Parameters

b	Pointer to the vector defining the linear system, ensure that the number of provided values is equal to columns()
x	Pointer to the solution vector receiving the solution if existing, ensure that the number of elements is equal to columns()

Returns

True, if succeeded

Template Parameters

tMatrixProperty

The property of the matrix allowing to improve the solving performance and stability, MP_UNKNOWN to apply a standard solving

solve() [4/4]

template<typename T >

bool Ocean::MatrixT< T >::solve ( const T *  b, T *  x, const MatrixProperty  matrixProperty = MP_UNKNOWN  ) const

inline

Solves the given linear system.

M * x = b, with M and b known and M is a square matrix
This matrix is M, the given vector is b and the result will be x..
Note: If a non-square matrix should be solved, use: (M.transposed() * M) * x = M.transposed() * b

Parameters

b	Pointer to the vector defining the linear system, ensure that the number of provided values is equal to columns()
x	Pointer to the solution vector receiving the solution if existing, ensure that the number of elements is equal to columns()
matrixProperty	The property of the matrix allowing to improve the solving performance and stability, MP_UNKNOWN to apply a standard solving

Returns

True, if succeeded

subMatrix()

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::subMatrix	(	const size_t	row,
		const size_t	column,
		const size_t	rows,
		const size_t	columns
	)

Returns a sub matrix of this one.

Parameters

row	The start row at which the sub matrix will start, with range [0, row() - 1]
column	The start column at which the sub matrix will start, with range [0, columns() - 1]
rows	The number of rows in the sub matrix, with range [1, rows() - row]
columns	The number of columns in the sub matrix, with range [1, columns() - row]

Returns

The resulting sub matrix

sum()

template<typename T >

T Ocean::MatrixT< T >::sum

inline

Determines the sum of all elements of this matrix.

Returns

Matrix sum

swapColumns()

template<typename T >

void Ocean::MatrixT< T >::swapColumns ( const size_t  column0, const size_t  column1  )

protected

Swaps two columns.

Parameters

column0	The index of the first column to be swapped, with range [0, columns())
column1	The index of the second column to be swapped, with range [0, columns())

swapRows()

template<typename T >

void Ocean::MatrixT< T >::swapRows ( const size_t  row0, const size_t  row1  )

protected

Swaps two rows.

Parameters

row0	The index of the first row to be swapped, with range [0, rows())
row1	The index of the second row to be swapped, with range [0, rows())

transpose()

template<typename T >

void Ocean::MatrixT< T >::transpose

inline

Transposes this matrix.

transposed()

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::transposed

(

)

const

Returns the transposed of this matrix.

Returns

Transposed matrix

transposedMultiply() [1/2]

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::transposedMultiply

(

const MatrixT< T > &

right

)

const

Multiplies this transposed matrix with a second matrix.

Actually, the following matrix will be returned: (*this).transposed() * right.
The resulting matrix will have the size: columns() x right.columns().

Parameters

right

Matrix to multiply

Returns

Matrix product

transposedMultiply() [2/2]

template<typename T >

void Ocean::MatrixT< T >::transposedMultiply	(	const MatrixT< T > &	right,
		MatrixT< T > &	result
	)		const

Multiplies this transposed matrix with a second matrix.

Actually, the following matrix will be returned: (*this).transposed() * right.
The resulting matrix will have the size: columns() x right.columns().

Parameters

right	Matrix to multiply
result	Resulting matrix product

vector()

template<typename T >

MatrixT<T> Ocean::MatrixT< T >::vector

(

const size_t

column

)

const

Returns a column vector of the matrix.

Parameters

column

The column to receive the vector from, with range [0, columns())

Returns

Column vector

weightedSelfTransposedSquareMatrix()

template<typename T >

void Ocean::MatrixT< T >::weightedSelfTransposedSquareMatrix	(	const MatrixT< T > &	weightDiagonal,
		MatrixT< T > &	result
	)		const

Returns the matrix product of transposed matrix of this matrix and this matrix and applies a further squared diagonal weighting matrix.

The result will be a square matrix with size: columns() x columns().
Actually, the following matrix will be returned: (*this).transposed() * diag(weightDiagonal) * (*this).

Parameters

weightDiagonal	Weight vector defining the diagonal of the weighting matrix, with one column
result	Resulting matrix

Field Documentation

columns_

template<typename T >

size_t Ocean::MatrixT< T >::columns_ = 0

protected

Number of columns.

rows_

template<typename T >

size_t Ocean::MatrixT< T >::rows_ = 0

protected

Number of rows.

values_

template<typename T >

T* Ocean::MatrixT< T >::values_ = nullptr

protected

Elements of the matrix.

---

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

• Matrix.h