#include <base/math/Matrix.h>

Inherits Object.

Classes
class	ElementReference
	Reference to an element within a matrix. More...

class	IncompatibleMatrices
	Raised if an operation is given incompatible matrices to work on. More...

class	MatrixException
	Exception raised by the Matrix class. More...

class	NotSquare
	Raised by some operations if matrix is non-square. More...

class	Row

class	RowReference
	Reference to a row within a matrix. More...

class	Singular
	Raised by some operations if matrix is singular. More...

Public Member Functions
	Matrix () noexcept

	Matrix (const Dimension &dimension)

	Matrix (const TYPE elements[], const Dimension &dimension)

	Matrix (Enumerator< ReadEnumeratorTraits< TYPE > > &diagonal, const Dimension &dimension)

	Matrix (const Matrix &copy) noexcept

Matrix &	operator= (const Matrix &assign)

Dimension	getDimension () const noexcept

unsigned int	getRows () const noexcept

unsigned int	getColumns () const noexcept

bool	isEmpty () const noexcept

bool	isSquare () const noexcept

bool	isEqual (const Matrix &value) const noexcept

bool	isZero () const noexcept

bool	isDiagonal () const noexcept

bool	isLowerTriangular () const noexcept

bool	isUpperTriangular () const noexcept

bool	isSymmetric () const noexcept

TYPE	getNorm () const noexcept

TYPE	getDeterminant () const

Matrix	getMinor (unsigned int row, unsigned int column) const

TYPE	getCofactor (unsigned int row, unsigned int column) const

Matrix	getAdjoint () const

Matrix	solve (const Matrix< TYPE > &value) const

const TYPE &	getAt (unsigned int row, unsigned int colum) const

void	setAt (unsigned int row, unsigned int column, const TYPE &value)

const TYPE &	operator() (unsigned int row, unsigned int column) const

RowReference	operator[] (unsigned int row)

Matrix	plus () const noexcept

Matrix	minus () const noexcept

Matrix	invert () const

Matrix	transpose () const noexcept

Matrix &	clear ()

Matrix &	identity ()

Matrix &	zeroAdjust (const TYPE &zero)

Matrix &	rowEchelon ()

Matrix &	pivot (unsigned int row, unsigned int column)

Matrix &	clip (unsigned int rows, unsigned int columns)

Matrix &	negate ()

Matrix &	add (const Matrix &value)

Matrix &	subtract (const Matrix &value)

Matrix &	multiply (const TYPE &value)

Matrix &	divide (const TYPE &value)

Matrix &	negate (const Matrix &value)

Matrix &	add (const Matrix &left, const Matrix &right)

Matrix &	subtract (const Matrix &left, const Matrix &right)

Matrix &	multiply (const Matrix< TYPE > &left, const Matrix< TYPE > &right)

Matrix &	multiply (const Matrix &left, const TYPE &right)

Matrix &	multiply (const TYPE &left, const Matrix &right)

Matrix &	divide (const Matrix &left, const TYPE &right)

Matrix &	transpose (const Matrix &matrix)

bool	operator== (const Matrix &value) const noexcept

Matrix &	operator+= (const Matrix &value)

Matrix &	operator-= (const Matrix &value)

Matrix &	operator*= (const TYPE &value)

Matrix &	operator/= (const TYPE &value)

Matrix	operator+ () const

Matrix	operator- () const

Protected Member Functions
TYPE *	getMutableElements ()

TYPE *	getElements ()

const TYPE *	getReadOnlyElements () const noexcept

const TYPE *	getElements () const noexcept

bool	isCompatible (const Matrix &value) const noexcept

void	setSize (unsigned int rows, unsigned int columns)

void	setDimension (const Matrix &value)

MemorySize	getSize () const noexcept

void	validateElement (unsigned int row, unsigned int column) const

void	validateRow (unsigned int row) const

void	validateColumn (unsigned int column) const

unsigned int	getIndexOfElement (unsigned int row, unsigned int column) const noexcept

Protected Attributes
Reference< ReferenceCountedAllocator< TYPE > >	elements

unsigned int	rows = 0

unsigned int	columns = 0

Related Functions
(Note that these are not member functions.)
template<class TYPE >
bool	operator== (const Matrix< TYPE > &left, const Matrix< TYPE > &right) noexcept

template<class TYPE >
Matrix< TYPE >	operator+ (const Matrix< TYPE > &left, const Matrix< TYPE > &right)

template<class TYPE >
Matrix< TYPE >	operator- (const Matrix< TYPE > &left, const Matrix< TYPE > &right)

template<class TYPE >
Matrix< TYPE >	operator* (const Matrix< TYPE > &left, const Matrix< TYPE > &right)

template<class TYPE >
Matrix< TYPE >	operator* (const Matrix< TYPE > &left, const TYPE &right)

template<class TYPE >
Matrix< TYPE >	operator* (const TYPE &left, const Matrix< TYPE > &right)

template<class TYPE >
Matrix< TYPE >	operator/ (const Matrix< TYPE > &left, const Matrix< TYPE > &right)

template<class TYPE >
Matrix< TYPE >	operator/ (const Matrix< TYPE > &left, const TYPE &right)

template<class TYPE >
Matrix< TYPE >	operator/ (const TYPE &left, const Matrix< TYPE > &right)

Detailed Description

template<class TYPE>
class Matrix< TYPE >

Matrix.

Matrix implementation.

Version: 1.10

Constructor & Destructor Documentation

◆ Matrix() [1/5]

template<class TYPE >

Matrix< TYPE >::Matrix ( )

inlinenoexcept

Initializes a matrix with no elements.

◆ Matrix() [2/5]

template<class TYPE >

Matrix< TYPE >::Matrix ( const Dimension & dimension )

explicit

Initializes matrix with the specified dimension.

Parameters

dimension The desired dimension of the matrix.

◆ Matrix() [3/5]

template<class TYPE >

Matrix< TYPE >::Matrix	(	const TYPE	elements[],
		const Dimension &	dimension
	)

Initializes matrix using the elements of an array. The elements are expected to be ordered from left to right and top to bottom.

Parameters

elements	The desired elements of the matrix.
dimension	The desired dimension of the matrix.

◆ Matrix() [4/5]

template<class TYPE >

Matrix< TYPE >::Matrix	(	Enumerator< ReadEnumeratorTraits< TYPE > > &	diagonal,
		const Dimension &	dimension
	)

Initializes matrix as a diagonal matrix with the diagonal elements provided by the specified enumerator. Raises OutOfDomain if enumeration is empty.

Parameters

diagonal	The enumerator containing the desired diagonal elements.
dimension	The desired dimension of the matrix.

◆ Matrix() [5/5]

template<class TYPE >

Matrix< TYPE >::Matrix ( const Matrix< TYPE > & copy )

inlinenoexcept

Initializes matrix from other matrix.

Parameters

matrix The matrix to be copied.

Member Function Documentation

◆ add() [1/2]

template<class TYPE >

Matrix& Matrix< TYPE >::add	(	const Matrix< TYPE > &	left,
		const Matrix< TYPE > &	right
	)

Sets this matrix to the sum of the specified matrices.

Parameters

left	Matrix.
right	Matrix.

◆ add() [2/2]

template<class TYPE >

Matrix& Matrix< TYPE >::add ( const Matrix< TYPE > & value )

Adds the specified matrix to this matrix.

Parameters

value The matrix to be added.

◆ clear()

template<class TYPE >

Matrix& Matrix< TYPE >::clear ( )

Sets this matrix to the zero matrix.

◆ clip()

template<class TYPE >

Matrix& Matrix< TYPE >::clip	(	unsigned int	rows,
		unsigned int	columns
	)

Throws away any elements that exceed the specified dimension.

Parameters

rows	The desired number of row.
columns	The desired number of columns.

◆ divide() [1/2]

template<class TYPE >

Matrix& Matrix< TYPE >::divide	(	const Matrix< TYPE > &	left,
		const TYPE &	right
	)

Sets this matrix to the result of the division of the left by right operand.

Parameters

left	The left operand.
right	The right operand.

◆ divide() [2/2]

template<class TYPE >

Matrix& Matrix< TYPE >::divide ( const TYPE & value )

Divides this matrix with the specified value.

Parameters

value The divisor.

◆ getAdjoint()

template<class TYPE >

Matrix Matrix< TYPE >::getAdjoint ( ) const

Returns the adjoint of this matrix.

◆ getAt()

template<class TYPE >

const TYPE& Matrix< TYPE >::getAt	(	unsigned int	row,
		unsigned int	colum
	)		const

Returns an enumeration of all the elements in the specified row.

Parameters

row	The desired row to enumerate. Returns a read-only enumeration of all the elements in the specified row.
row	The desired row to enumerate. Returns an enumeration of all the elements in the specified column.
column	The desired column to enumerate. Returns a read-only enumeration of all the elements in the specified column.
column	The desired column to enumerate. Returns an enumeration of all the elements of the diagonal. Returns a read-only enumeration of all the elements of the diagonal. Returns the element at the specified position.
row	The row of the element.
column	The column of the element.

◆ getCofactor()

template<class TYPE >

TYPE Matrix< TYPE >::getCofactor	(	unsigned int	row,
		unsigned int	column
	)		const

Returns the cofactor of this matrix for the specified element.

Parameters

row	The row of the element.
column	The column of the element.

◆ getColumns()

template<class TYPE >

unsigned int Matrix< TYPE >::getColumns ( ) const

inlinenoexcept

Returns the number of columns of this matrix.

◆ getDeterminant()

template<class TYPE >

TYPE Matrix< TYPE >::getDeterminant ( ) const

Returns the determinant of this matrix.

◆ getDimension()

template<class TYPE >

Dimension Matrix< TYPE >::getDimension ( ) const

inlinenoexcept

Returns the dimension of the matrix.

◆ getIndexOfElement()

template<class TYPE >

unsigned int Matrix< TYPE >::getIndexOfElement	(	unsigned int	row,
		unsigned int	column
	)		const

inlineprotectednoexcept

Converts 2D index to 1D index in the element array. Does NOT check boundaries.

◆ getMinor()

template<class TYPE >

Matrix Matrix< TYPE >::getMinor	(	unsigned int	row,
		unsigned int	column
	)		const

Returns the minor of this matrix.

Parameters

row	The row to be discarded.
column	The column to be discarded.

◆ getMutableElements()

template<class TYPE >

TYPE* Matrix< TYPE >::getMutableElements ( )

inlineprotected

Returns the elements of the matrix for modification. May copy all elements of the matrix.

◆ getNorm()

template<class TYPE >

TYPE Matrix< TYPE >::getNorm ( ) const

noexcept

Returns the Hilbert-Schmidt norm of the matrix.

◆ getReadOnlyElements()

template<class TYPE >

const TYPE* Matrix< TYPE >::getReadOnlyElements ( ) const

inlineprotectednoexcept

Returns the elements of the matrix for read-only.

◆ getRows()

template<class TYPE >

unsigned int Matrix< TYPE >::getRows ( ) const

inlinenoexcept

Returns the number of rows of this matrix.

◆ getSize()

template<class TYPE >

MemorySize Matrix< TYPE >::getSize ( ) const

inlineprotectednoexcept

Gets the number of elements in the matrix.

◆ identity()

template<class TYPE >

Matrix& Matrix< TYPE >::identity ( )

Sets this matrix to the identity matrix.

◆ invert()

template<class TYPE >

Matrix Matrix< TYPE >::invert ( ) const

Unary inversion.

◆ isCompatible()

template<class TYPE >

bool Matrix< TYPE >::isCompatible ( const Matrix< TYPE > & value ) const

inlineprotectednoexcept

Returns true if this matrix and the specified matrix have identical dimensions.

◆ isDiagonal()

template<class TYPE >

bool Matrix< TYPE >::isDiagonal ( ) const

noexcept

Returns true if this matrix is a diagonal matrix.

Returns: false if matrix is not square or contains no elements.

◆ isEmpty()

template<class TYPE >

bool Matrix< TYPE >::isEmpty ( ) const

inlinenoexcept

Returns true if the matrix is empty (i.e. has no elements).

◆ isEqual()

template<class TYPE >

bool Matrix< TYPE >::isEqual ( const Matrix< TYPE > & value ) const

noexcept

Returns true if the matrices are equal.

◆ isLowerTriangular()

template<class TYPE >

bool Matrix< TYPE >::isLowerTriangular ( ) const

noexcept

Returns true if this matrix is lower triangular (i.e. the matrix has no non-zero values above the diagonal line).

Returns: false if matrix is not square or contains no elements.

◆ isSquare()

template<class TYPE >

bool Matrix< TYPE >::isSquare ( ) const

inlinenoexcept

Returns true if the matrix is a square matrix.

◆ isSymmetric()

template<class TYPE >

bool Matrix< TYPE >::isSymmetric ( ) const

noexcept

Returns true if this matrix is symmetric.

Returns: false if matrix is not square or contains no elements.

◆ isUpperTriangular()

template<class TYPE >

bool Matrix< TYPE >::isUpperTriangular ( ) const

noexcept

Returns true if this matrix is upper triangular (i.e. the matrix has no non-zero values below the diagonal line).

Returns: false if matrix is not square or contains no elements.

◆ isZero()

template<class TYPE >

bool Matrix< TYPE >::isZero ( ) const

noexcept

Returns true if the matrix is the zero matrix.

Returns: false if matrix contains no elements.

◆ minus()

template<class TYPE >

Matrix Matrix< TYPE >::minus ( ) const

noexcept

Unary minus.

◆ multiply() [1/4]

template<class TYPE >

Matrix& Matrix< TYPE >::multiply	(	const Matrix< TYPE > &	left,
		const TYPE &	right
	)

Sets this matrix to the product of the operands.

Parameters

left	The left operand.
right	The right operand.

◆ multiply() [2/4]

template<class TYPE >

Matrix& Matrix< TYPE >::multiply	(	const Matrix< TYPE > &	left,
		const Matrix< TYPE > &	right
	)

Sets this matrix to the product of the specified matrices.

Parameters

left	Matrix.
right	Matrix.

◆ multiply() [3/4]

template<class TYPE >

Matrix& Matrix< TYPE >::multiply	(	const TYPE &	left,
		const Matrix< TYPE > &	right
	)

Sets this matrix to the product of the operands.

Parameters

left	The left operand.
right	The right operand.

◆ multiply() [4/4]

template<class TYPE >

Matrix& Matrix< TYPE >::multiply ( const TYPE & value )

Multiplies this matrix with the specified value.

Parameters

value The multiplicator.

◆ negate() [1/2]

template<class TYPE >

Matrix& Matrix< TYPE >::negate ( )

Negates this matrix.

◆ negate() [2/2]

template<class TYPE >

Matrix& Matrix< TYPE >::negate ( const Matrix< TYPE > & value )

Negates the specified matrix and stores the result in this matrix.

◆ operator()()

template<class TYPE >

const TYPE& Matrix< TYPE >::operator()	(	unsigned int	row,
		unsigned int	column
	)		const

inline

Returns the element at the specified position.

◆ operator*=()

template<class TYPE >

Matrix& Matrix< TYPE >::operator*= ( const TYPE & value )

inline

Multiplies this matrix with the specified value.

Parameters

value The multiplicator.

◆ operator+()

template<class TYPE >

Matrix Matrix< TYPE >::operator+ ( ) const

inline

Unary plus.

◆ operator+=()

template<class TYPE >

Matrix& Matrix< TYPE >::operator+= ( const Matrix< TYPE > & value )

inline

Adds the specified matrix from this matrix.

Parameters

value The value to be added.

◆ operator-()

template<class TYPE >

Matrix Matrix< TYPE >::operator- ( ) const

inline

Unary minus.

◆ operator-=()

template<class TYPE >

Matrix& Matrix< TYPE >::operator-= ( const Matrix< TYPE > & value )

inline

Subtracts the specified matrix from this matrix.

Parameters

value The value to be subtracted.

◆ operator/=()

template<class TYPE >

Matrix& Matrix< TYPE >::operator/= ( const TYPE & value )

inline

Divides this matrix with the specified value.

Parameters

value The divisor.

◆ operator=()

template<class TYPE >

Matrix& Matrix< TYPE >::operator= ( const Matrix< TYPE > & assign )

inline

Assigns matrix to this matrix.

Parameters

eq	The matrix containing the desired elements.

◆ operator==()

template<class TYPE >

bool Matrix< TYPE >::operator== ( const Matrix< TYPE > & value ) const

inlinenoexcept

Returns true if the matrices are equal element by element. This member should only be used for integer types.

Parameters

value Matrix to be compared.

◆ operator[]()

template<class TYPE >

RowReference Matrix< TYPE >::operator[] ( unsigned int row )

inline

Returns a reference to the specified row.

◆ pivot()

template<class TYPE >

Matrix& Matrix< TYPE >::pivot	(	unsigned int	row,
		unsigned int	column
	)

Does a reduced row echelon transformation of this matrix for the specified element. The element value is transformed to 1 and the other values of the column are transformed to 0.

Parameters

row	The row of the element.
column	The column of the element.

◆ plus()

template<class TYPE >

Matrix Matrix< TYPE >::plus ( ) const

noexcept

Unary plus.

◆ rowEchelon()

template<class TYPE >

Matrix& Matrix< TYPE >::rowEchelon ( )

Does a row echelon transformation of this matrix.

◆ setAt()

template<class TYPE >

void Matrix< TYPE >::setAt	(	unsigned int	row,
		unsigned int	column,
		const TYPE &	value
	)

Sets the element at the specified position.

Parameters

row	The row of the element.
column	The column of the element.
value	The desired value.

◆ setDimension()

template<class TYPE >

void Matrix< TYPE >::setDimension ( const Matrix< TYPE > & value )

inlineprotected

Sets the dimension of this matrix to the dimension of the specified matrix.

◆ setSize()

template<class TYPE >

void Matrix< TYPE >::setSize	(	unsigned int	rows,
		unsigned int	columns
	)

inlineprotected

Sets the size of the matrix. Only invocated by constructors.

◆ solve()

template<class TYPE >

Matrix Matrix< TYPE >::solve ( const Matrix< TYPE > & value ) const

Returns the solution(s) for the linear system(s).

Parameters

value The constant column vector(s).

◆ subtract() [1/2]

template<class TYPE >

Matrix& Matrix< TYPE >::subtract	(	const Matrix< TYPE > &	left,
		const Matrix< TYPE > &	right
	)

Sets this matrix to the difference of the specified matrices.

Parameters

left	Matrix.
right	Matrix.

◆ subtract() [2/2]

template<class TYPE >

Matrix& Matrix< TYPE >::subtract ( const Matrix< TYPE > & value )

Subtracts the specified matrix from this matrix.

Parameters

value The matrix to be subtracted.

◆ transpose() [1/2]

template<class TYPE >

Matrix Matrix< TYPE >::transpose ( ) const

noexcept

Returns a new matrix that is the transpose of this matrix.

◆ transpose() [2/2]

template<class TYPE >

Matrix& Matrix< TYPE >::transpose ( const Matrix< TYPE > & matrix )

Sets this matrix to the transpose of the specified matrix.

Parameters

matrix The matrix to be transposed.

◆ validateColumn()

template<class TYPE >

void Matrix< TYPE >::validateColumn ( unsigned int column ) const

inlineprotected

Raises OutOfRange if column is invalid.

◆ validateElement()

template<class TYPE >

void Matrix< TYPE >::validateElement	(	unsigned int	row,
		unsigned int	column
	)		const

inlineprotected

Raises OutOfRange if element coordinate (row, column) is invalid.

◆ validateRow()

template<class TYPE >

void Matrix< TYPE >::validateRow ( unsigned int row ) const

inlineprotected

Raises OutOfRange if row is invalid.

◆ zeroAdjust()

template<class TYPE >

Matrix& Matrix< TYPE >::zeroAdjust ( const TYPE & zero )

Pivot transformation of this matrix. Solves the equations. Sets the values of this matrix that exceed the specified value to zero (0).

Parameters

zero	Specifies the zero limit.

Member Data Documentation

◆ columns

template<class TYPE >

unsigned int Matrix< TYPE >::columns = 0

protected

The number of columns in the matrix.

◆ elements

template<class TYPE >

Reference<ReferenceCountedAllocator<TYPE> > Matrix< TYPE >::elements

protected

The elements of the matrix stored in an array. The array is guarantied to be non-empty when the matrix object has been initialized.

◆ rows

template<class TYPE >

unsigned int Matrix< TYPE >::rows = 0

protected

The number of rows in the matrix.

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Related Functions

Detailed Description

template<class TYPE> class Matrix< TYPE >

Constructor & Destructor Documentation

◆ Matrix() [1/5]

◆ Matrix() [2/5]

◆ Matrix() [3/5]

◆ Matrix() [4/5]

◆ Matrix() [5/5]

Member Function Documentation

◆ add() [1/2]

◆ add() [2/2]

◆ clear()

◆ clip()

◆ divide() [1/2]

◆ divide() [2/2]

◆ getAdjoint()

◆ getAt()

◆ getCofactor()

◆ getColumns()

◆ getDeterminant()

◆ getDimension()

◆ getIndexOfElement()

◆ getMinor()

◆ getMutableElements()

◆ getNorm()

◆ getReadOnlyElements()

◆ getRows()

◆ getSize()

◆ identity()

◆ invert()

◆ isCompatible()

◆ isDiagonal()

◆ isEmpty()

◆ isEqual()

◆ isLowerTriangular()

◆ isSquare()

◆ isSymmetric()

◆ isUpperTriangular()

◆ isZero()

◆ minus()

◆ multiply() [1/4]

◆ multiply() [2/4]

◆ multiply() [3/4]

◆ multiply() [4/4]

◆ negate() [1/2]

◆ negate() [2/2]

◆ operator()()

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator/=()

◆ operator=()

◆ operator==()

◆ operator[]()

◆ pivot()

◆ plus()

◆ rowEchelon()

◆ setAt()

◆ setDimension()

◆ setSize()

◆ solve()

◆ subtract() [1/2]

◆ subtract() [2/2]

◆ transpose() [1/2]

◆ transpose() [2/2]

◆ validateColumn()

◆ validateElement()

◆ validateRow()

◆ zeroAdjust()

Member Data Documentation

◆ columns

◆ elements

◆ rows

template<class TYPE>
class Matrix< TYPE >