Two-dimensional rectangular matrix with some algebraic operations. More...

#include <matrix.h>

Inheritance diagram for utl::matrix< T >:

Collaboration diagram for utl::matrix< T >:

Public Member Functions
	matrix ()
	Constructor creating an empty matrix.

	matrix (vector< T > &vec)
	Constructor using an external vector for matrix element storage.

	matrix (size_t r, size_t c)
	Constructor creating a matrix of dimension \(r \times c\).

	matrix (const matrix< T > &mat, bool transposed=false)
	Copy constructor, optionally creates the transpose of mat.

virtual	~matrix ()
	Empty destructor.

void	resize (size_t r, size_t c, bool forceClear=false)
	Resize the matrix to dimension \(r \times c\). More...

matrix< T > &	expandRows (int incRows)
	Increase or decrease the number of rows in the matrix.

bool	augmentRows (const matrix< T > &B)
	Increase the number of rows by augmenting the given matrix.

bool	augmentCols (const matrix< T > &B)
	Increase the number of columns by augmenting the given matrix.

size_t	rows () const
	Query number of matrix rows.

size_t	cols () const
	Query number of matrix columns.

matrix< T > &	operator= (const matrix< T > &A)
	Assignment operator.

matrix< T > &	operator= (const std::vector< T > &X)
	Overloaded assignment operator.

T &	operator() (size_t r, size_t c)
	Index-1 based element access. More...

const T &	operator() (size_t r, size_t c) const
	Index-1 based element reference. More...

vector< T >	getRow (size_t r) const
	Extract a row from the matrix.

std::vector< T >	getColumn (size_t c) const
	Extract a column from the matrix.

void	fill (const std::vector< T > &v, size_t n, size_t m=0)
	Fill the matrix with vector data.

void	fillColumn (size_t c, const std::vector< T > &data)
	Fill a column of the matrix.

void	fillColumn (size_t c, const T *data)
	Fill a column of the matrix.

void	fillRow (size_t r, const T *data)
	Fill a row of the matrix.

void	fillBlock (const matrix< T > &block, size_t r, size_t c, bool transposed=false)
	Fill a block of the matrix with another matrix.

void	addBlock (const matrix< T > &block, T s, size_t r, size_t c, bool transposed=false)
	Add a scalar multiple of another matrix to a block of the matrix.

void	extractBlock (matrix< T > &block, size_t r, size_t c, bool addTo=false, bool transposed=false) const
	Extract a block of the matrix to another matrix.

matrix< T > &	diag (T d, size_t dim=0)
	Create a diagonal matrix.

matrix< T > &	transpose ()
	Replace the current matrix by its transpose.

T	trace () const
	Return the trace of the matrix (sum of its diagonal elements).

T	rowsum (size_t r) const
	Return the sum of a matrix row.

T	colsum (size_t c) const
	Return the sum of a matrix column.

T	det () const
	Compute the determinant of a square matrix.

T	inverse (T tol=T(0))
	Compute the inverse of a square matrix. More...

bool	isSymmetric (T tol=T(0)) const
	Check for symmetry. More...

matrix< T > &	operator+= (const matrix< T > &A)
	Add the given matrix A to *this.

matrix< T > &	operator-= (const matrix< T > &A)
	Subtract the given matrix A from *this.

matrix< T > &	add (const matrix< T > &A, T alfa=T(1))
	Add the given matrix A scaled by alfa to *this.

matrix< T > &	operator*= (T c)
	Multiplication with a scalar.

matrix< T > &	operator/= (T d)
	Division by a scalar.

matrix< T > &	multiply (T c)
	Multiplication of this matrix by a scalar c.

matrix< T > &	multiply (const matrix< T > &A, const matrix< T > &B, bool transA=false, bool transB=false, bool addTo=false, const T &alpha=T(1))
	Matrix-matrix multiplication. More...

bool	multiplyMat (const matrix< T > &A, const std::vector< T > &B, bool transA=false, bool addTo=false)
	Matrix-matrix multiplication. More...

bool	multiplyMat (const std::vector< T > &A, const matrix< T > &B, bool transB=false, bool addTo=false)
	Matrix-matrix multiplication. More...

bool	multiply (const std::vector< T > &X, std::vector< T > &Y, bool transA=false, char addTo=0) const
	Matrix-vector multiplication. More...

bool	multiply (const std::vector< T > &X, std::vector< T > &Y, const T &alpha, const T &beta=T(0), bool transA=false, int stridex=1, int stridey=1, unsigned int ofsx=0, unsigned int ofsy=0) const
	Matrix-vector multiplication. More...

bool	outer_product (const std::vector< T > &X, const std::vector< T > &Y, bool addTo=false, T alpha=T(1))
	Outer product between two vectors.

T	normInf () const
	Return the infinite norm of the matrix.

Public Member Functions inherited from utl::matrixBase< T >
size_t	dim (short int d=1) const
	Query dimensions.

size_t	size () const
	Query total matrix size.

bool	empty () const
	Check if the matrix is empty.

bool	zero (T tol=T(0)) const
	Check if the matrix elements are all zero.

const vector< T > &	toVec () const
	Type casting to a one-dimensional utl::vector, for access.

	operator const std::vector< T > & () const
	Type casting to a one-dimensional std::vector, for access.

	operator std::vector< T > & ()
	Type casting to a one-dimensional vector, for update.

T *	ptr (size_t c=0)
	Access through pointer.

const T *	ptr (size_t c=0) const
	Reference through pointer.

std::vector< T >::iterator	begin ()
	Iterator to the start of the matrix elements.

std::vector< T >::iterator	end ()
	Iterator to the end of the matrix elements.

void	clear ()
	Clears the matrix and sets its dimension to zero.

void	fill (T s)
	Fill the matrix with a scalar value.

void	fill (const T *values, size_t n=0)
	Fill the matrix with data from an array.

matrixBase< T > &	add (const matrixBase< T > &A, const T &alfa)
	Add the given matrix A scaled by alfa to *this.

matrixBase< T > &	multiply (const T &c)
	Multiplication of this matrix by a scalar c.

T	norm2 (int inc=1) const
	Return the Euclidean norm of the matrix. More...

T	asum (int inc=1) const
	Return the sum of the absolute value of the matrix elements. More...

T	sum (int inc=1) const
	Return the sum of the matrix elements. More...

Protected Member Functions
void	clearIfNrowChanged (size_t n1, size_t, size_t) override
	Clears the content if the number of rows changed.

Protected Member Functions inherited from utl::matrixBase< T >
	matrixBase ()
	The constructor is protected to allow sub-class instances only.

	matrixBase (vector< T > &vec)
	Constructor using an external vector for matrix element storage.

	matrixBase (size_t n_1, size_t n_2, size_t n_3=1, size_t n_4=1)
	Constructor creating a matrix of dimension \(n_1 \times n_2 \times n_3 \times n_4\).

	matrixBase (const matrixBase< T > &mat, bool copyContent=true)
	Copy constructor. More...

void	redim (size_t n_1, size_t n_2, size_t n_3, size_t n_4, bool forceClear)
	Resize the matrix to dimension \(n_1 \times n_2 \times n_3 \times n_4\). More...

Private Member Functions
bool	compatible (const std::vector< T > &X, bool transA) const
	Check dimension compatibility for matrix-vector multiplication.

bool	compatible (const matrix< T > &A, const matrix< T > &B, bool transA, bool transB, size_t &M, size_t &N, size_t &K)
	Check dimension compatibility for matrix-matrix multiplication.

bool	compatible (const matrix< T > &A, const std::vector< T > &B, bool transA, size_t &M, size_t &N, size_t &K)
	Check dimension compatibility for matrix-matrix multiplication, when the matrix B is represented by a one-dimensional vector.

bool	compatible (const std::vector< T > &A, const matrix< T > &B, bool transB, size_t &M, size_t &N, size_t &K)
	Check dimension compatibility for matrix-matrix multiplication, when the matrix A is represented by a one-dimensional vector.

bool	compatible (const std::vector< T > &X, const std::vector< T > &Y)
	Check dimension compatibility for outer product multiplication.

Private Attributes
size_t &	nrow
	Number of matrix rows.

size_t &	ncol
	Number of matrix columns.

Additional Inherited Members
Protected Attributes inherited from utl::matrixBase< T >
size_t	n [4]
	Dimension of the matrix.

vector< T > &	elem
	Actual matrix elements, stored column by column.

Detailed Description

template<class T>
class utl::matrix< T >

Two-dimensional rectangular matrix with some algebraic operations.

This is a 2D equivalent to the vector class. The matrix elements are stored column-wise in a one-dimensional array, such that its pointer might be passed to Fortran subroutines requiring 2D arrays as arguments.

Member Function Documentation

◆ inverse()

template<class T >

T utl::matrix< T >::inverse ( T tol = T(0) )

inline

Compute the inverse of a square matrix.

Parameters

[in] tol Division by zero tolerance

Returns: Determinant of the matrix

References utl::matrix< T >::det().

Referenced by utl::invert(), and utl::Jacobian().

◆ isSymmetric()

template<class T >

bool utl::matrix< T >::isSymmetric ( T tol = T(0) ) const

inline

Check for symmetry.

Parameters

[in] tol Comparison tolerance

References utl::matrixBase< T >::elem, utl::matrix< T >::ncol, and utl::matrix< T >::nrow.

Referenced by utl::operator<<().

◆ multiply() [1/3]

template<class T >

matrix< T > & utl::matrix< T >::multiply	(	const matrix< T > &	A,
		const matrix< T > &	B,
		bool	transA = `false`,
		bool	transB = `false`,
		bool	addTo = `false`,
		const T &	alpha = `T(1)`
	)

inline

Matrix-matrix multiplication.

Performs one of the following operations (C = *this):

\( {\bf C} = {\bf A} {\bf B} \)
\( {\bf C} = {\bf A}^T {\bf B} \)
\( {\bf C} = {\bf A} {\bf B}^T \)
\( {\bf C} = {\bf A}^T {\bf B}^T \)
\( {\bf C} = {\bf C} + {\bf A} {\bf B} \)
\( {\bf C} = {\bf C} + {\bf A}^T {\bf B} \)
\( {\bf C} = {\bf C} + {\bf A} {\bf B}^T \)
\( {\bf C} = {\bf C} + {\bf A}^T {\bf B}^T \)

References K, and M.

◆ multiply() [2/3]

template<class T >

bool utl::matrix< T >::multiply	(	const std::vector< T > &	X,
		std::vector< T > &	Y,
		bool	transA = `false`,
		char	addTo = `0`
	)		const

inline

Matrix-vector multiplication.

Performs one of the following operations (A = *this):

\( {\bf Y} = {\bf A} {\bf X} \)
\( {\bf Y} = {\bf A}^T {\bf X} \)
\( {\bf Y} = {\bf Y} + {\bf A} {\bf X} \)
\( {\bf Y} = {\bf Y} + {\bf A}^T {\bf X} \)
\( {\bf Y} = {\bf Y} - {\bf A} {\bf X} \)
\( {\bf Y} = {\bf Y} - {\bf A}^T {\bf X} \)

◆ multiply() [3/3]

template<class T >

bool utl::matrix< T >::multiply	(	const std::vector< T > &	X,
		std::vector< T > &	Y,
		const T &	alpha,
		const T &	beta = `T(0)`,
		bool	transA = `false`,
		int	stridex = `1`,
		int	stridey = `1`,
		unsigned int	ofsx = `0`,
		unsigned int	ofsy = `0`
	)		const

inline

Matrix-vector multiplication.

Performs the following operations (A = *this):

\( {\bf Y} = {\alpha}{\bf A} {\bf X} + {\beta}{\bf Y}\)
\( {\bf Y} = {\alpha}{\bf A}^T {\bf X} + {\beta}{\bf Y}\)

◆ multiplyMat() [1/2]

template<class T >

bool utl::matrix< T >::multiplyMat	(	const matrix< T > &	A,
		const std::vector< T > &	B,
		bool	transA = `false`,
		bool	addTo = `false`
	)

inline

Matrix-matrix multiplication.

Performs one of the following operations (C = *this):

\( {\bf C} = {\bf A} {\bf B} \)
\( {\bf C} = {\bf A}^T {\bf B} \)
\( {\bf C} = {\bf C} + {\bf A} {\bf B} \)
\( {\bf C} = {\bf C} + {\bf A}^T {\bf B} \)

The matrix B is here represented by a one-dimensional vector, and its number of rows is assumed to match the number of columns in A (or its transpose) and its number of columns is then the total vector length divided by the number of rows.

References K, and M.

◆ multiplyMat() [2/2]

template<class T >

bool utl::matrix< T >::multiplyMat	(	const std::vector< T > &	A,
		const matrix< T > &	B,
		bool	transB = `false`,
		bool	addTo = `false`
	)

inline

Matrix-matrix multiplication.

Performs one of the following operations (C = *this):

\( {\bf C} = {\bf A} {\bf B} \)
\( {\bf C} = {\bf A} {\bf B}^T \)
\( {\bf C} = {\bf C} + {\bf A} {\bf B} \)
\( {\bf C} = {\bf C} + {\bf A} {\bf B}^T \)

The matrix A is here represented by a one-dimensional vector, and its number of columns is assumed to match the number of rows in B (or its transpose) and its number of rows is then the total vector length divided by the number of columns.

References K, and M.

◆ operator()() [1/2]

template<class T >

T& utl::matrix< T >::operator()	(	size_t	r,
		size_t	c
	)

inline

Index-1 based element access.

Assuming column-wise storage as in Fortran.

◆ operator()() [2/2]

template<class T >

const T& utl::matrix< T >::operator()	(	size_t	r,
		size_t	c
	)		const

inline

Index-1 based element reference.

Assuming column-wise storage as in Fortran.

◆ resize()

template<class T >

void utl::matrix< T >::resize	(	size_t	r,
		size_t	c,
		bool	forceClear = `false`
	)

inline

Resize the matrix to dimension \(r \times c\).

Will erase the previous content, but only if both the total matrix size and the number of rows in the matrix are changed. It is therefore possible to add or remove a given number of columns to the matrix without loosing the contents of the remaining columns. If forceClear is true, the old matrix content is always erased.

References utl::matrixBase< T >::redim().

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

src/LinAlg/matrix.h

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<class T> class utl::matrix< T >

Member Function Documentation

◆ inverse()

◆ isSymmetric()

◆ multiply() [1/3]

◆ multiply() [2/3]

◆ multiply() [3/3]

◆ multiplyMat() [1/2]

◆ multiplyMat() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ resize()

template<class T>
class utl::matrix< T >