Classes
class	Error

Public Member Functions
	Matrix (void)

	Matrix (const Matrix &m)

	Matrix (double *data, size_t r, size_t c)

	Matrix (size_t r, size_t c)

	Matrix (size_t r, size_t c, double v)

	Matrix (size_t n)

	Matrix (double *diag, size_t n)

	~Matrix (void)

int	rows (void) const

int	columns (void) const

int	size (void) const

bool	isZeroSized (void) const

void	fill (double value)

void	fill (size_t r, size_t c, const double *data=0)

void	identity (void)

void	maxLimitValues (double max)

void	minLimitValues (double min)

void	trimValues (double min, double max)

Matrix	get (size_t i1, size_t i2, size_t j1, size_t j2) const

Matrix &	set (size_t i1, size_t i2, size_t j1, size_t j2, const Matrix &m_in)

Matrix &	blkDiag (const Matrix &m_in)

Matrix &	vertCat (const Matrix &m_in)

Matrix &	horzCat (const Matrix &m_in)

Matrix &	pow (unsigned int n)

void	toFile (const char *path)

void	fromFile (const char *path)

void	readFromLines (const std::vector< std::string > &clines)

void	readFromConfig (DUNE::Parsers::Config &cfg, const std::string &section, const std::string &param)

Matrix	row (size_t i) const

Matrix	column (size_t j) const

void	swapColumns (size_t i, size_t j)

void	swapRows (size_t i, size_t j)

void	resize (const Matrix &m)

void	resize (size_t r, size_t c)

void	resizeAndKeep (size_t r, size_t c)

void	resizeAndFill (size_t r, size_t c, double value)

double &	operator() (size_t i, size_t j)

double	operator() (size_t i, size_t j) const

double &	operator() (size_t i)

double	operator() (size_t i) const

double	element (size_t i, size_t j) const

double	element (size_t i)

void	to_row (void)

void	to_column (void)

Matrix	multiply (const Matrix &m)

bool	operator== (const Matrix &m) const

Matrix &	operator= (const Matrix &m)

Matrix &	operator+= (const Matrix &m)

Matrix &	operator-= (const Matrix &m)

Matrix &	operator&= (const Matrix &m)

Matrix &	operator/= (const Matrix &m)

Matrix	operator- (void)

Matrix &	operator*= (double x)

Matrix &	operator/= (double x)

void	put (size_t i, size_t j, const Matrix &a)

Matrix	mminor (size_t i, size_t j) const

unsigned int	lup (Matrix &L, Matrix &U, Matrix &P) const

void	lu (Matrix &L, Matrix &U) const

double	detr (void) const

double	det (void) const

bool	Sylvester (void) const

Matrix	toDCM (void) const

Matrix	toQuaternion (void) const

Matrix	toEulerAngles (void) const

Matrix	expmts (double tol=1e-05) const

double	norm_p (double p) const

double	norm_2 (void) const

double	norm_inf (void) const

double	median (void) const

double	trace (void) const

bool	isInvertible (void) const

bool	isSquare (void) const

bool	isVector (void) const

bool	isColumnVector (void) const

bool	isColumnVector (size_t rows) const

bool	isRowVector (void) const

bool	isRowVector (size_t columns) const

Static Public Member Functions
static void	set_precision (double p)

static double	get_precision (void)

static double	dot (const Matrix &a, const Matrix &b)

static Matrix	cross (const Matrix &a, const Matrix &b)

static int	upper_triangular_pp (double *M, int n, int m, double tolerance)

static int	upper_triangular_tp (double M, int index, int n, int m, double tolerance)

Friends
DUNE_DLL_SYM Matrix	operator+ (const Matrix &m1, const Matrix &m2)

DUNE_DLL_SYM Matrix	operator- (const Matrix &m1, const Matrix &m2)

DUNE_DLL_SYM Matrix	operator* (const Matrix &m1, const Matrix &m2)

DUNE_DLL_SYM Matrix	operator& (const Matrix &m1, const Matrix &m2)

DUNE_DLL_SYM Matrix	operator/ (const Matrix &a, const Matrix &b)

DUNE_DLL_SYM Matrix	operator* (double x, const Matrix &a)

DUNE_DLL_SYM Matrix	operator* (const Matrix &a, double x)

DUNE_DLL_SYM Matrix	operator/ (const Matrix &a, double x)

DUNE_DLL_SYM std::ostream &	operator<< (std::ostream &os, const Matrix &a)

DUNE_DLL_SYM std::istream &	operator>> (std::istream &is, Matrix &a)

DUNE_DLL_SYM Matrix	transpose (const Matrix &a)

DUNE_DLL_SYM Matrix	inverse (const Matrix &a)

DUNE_DLL_SYM Matrix	inverse (const Matrix &a, const Matrix &b)

Matrix	skew (double data[3])

Matrix	skew (const Matrix &a)

Matrix	inverse_pp (const Matrix &a)

Matrix	inverse_pp (const Matrix &, const Matrix &)

Matrix	inverse_lup (const Matrix &a)

Matrix	abs (const Matrix &a)

double	max (const Matrix &a)

double	min (const Matrix &a)

double	sum (const Matrix &a)

double	squaresum (const Matrix &a)

Constructor & Destructor Documentation

DUNE::Math::Matrix::Matrix ( void )

Constructor.

Construct a zero sized matrix.

Referenced by DUNE::Math::operator>>(), toDCM(), toEulerAngles(), and toQuaternion().

DUNE::Math::Matrix::Matrix ( const Matrix & m )

Constructor.

Create a Matrix of the same dimension of another Matrix. It simply sets the new data pointer to the old data and increases the copy counter.

Parameters

[in] m reference to matrix

DUNE::Math::Matrix::Matrix	(	double *	data,
		size_t	r,
		size_t	c
	)

Constructor.

Create a Matrix of dimension (rows * columns) and fills it with the data pointed by 'data'.

Parameters

[in]	data	pointer to data to be copied to new matrix
[in]	r	number of rows of new matrix
[in]	c	number of columns of new matrix

DUNE::Math::Matrix::Matrix	(	size_t	r,
		size_t	c
	)

Constructor.

Construct a matrix of size rows*columns.

Parameters

[in]	r	number of rows of new matrix
[in]	c	number of columns of new matrix

DUNE::Math::Matrix::Matrix	(	size_t	r,
		size_t	c,
		double	v
	)

Constructor.

Construct a matrix of size rows * columns filled with constant value.

Parameters

[in]	r	number of rows of new matrix
[in]	c	number of rows of new matrix
[in]	v	value used to initialize cells.

References fill().

DUNE::Math::Matrix::Matrix ( size_t n )

Constructor.

Construct a square identity matrix of size n param[in] n size of new matrix (n * n)

References identity().

DUNE::Math::Matrix::Matrix	(	double *	diag,
		size_t	n
	)

Constructor.

Construct a diagonal matrix using the values in data param[in] diag pointer to data to be copied to diagonal matrix param[in] n size of new matrix (n * n)

References fill().

DUNE::Math::Matrix::~Matrix ( void )

Destructor.

Decrement the number of copies of a Matrix and frees the allocated memory if this number reaches zero.

Member Function Documentation

Matrix & DUNE::Math::Matrix::blkDiag ( const Matrix & m_in )

Returns the diagonal concatenation of a matrix Return a matrix of size (nrows + rows(m_in)) x (ncolumns +columns(m_in)) and fills the remaining elements with zeros.

Parameters

[in] m_in reference to matrix

Returns: reference to diagonal concatenation of matrix

References columns(), resizeAndFill(), rows(), and set().

Referenced by DUNE::Control::LinearSystem::append().

Matrix DUNE::Math::Matrix::column ( size_t j ) const

This method returns a column of the Matrix.

Parameters

[in] j column to be retrieved

Returns: matrix of the returned column

Referenced by swapColumns().

int DUNE::Math::Matrix::columns ( void ) const

Retrieve the number of columns of the matrix.

Returns: number of columns of the matrix.

Matrix DUNE::Math::Matrix::cross	(	const Matrix &	a,
		const Matrix &	b
	)

static

Calculate cross product.

Arguments must be 3D column or row vectors.

Parameters

[in]	a	matrix.
[in]	b	matrix.

Returns: resultant matrix of cross product

References columns(), isVector(), resizeAndFill(), rows(), and size().

double DUNE::Math::Matrix::det ( void ) const

Matrix determinant through LUP decomposition Iterative technique O(n^3).

Returns: matrix determinant

References element(), and lup().

Referenced by Sylvester().

double DUNE::Math::Matrix::detr ( void ) const

Matrix determinant through Laplace expansion Recursive technique O(n!).

Returns: matrix determinant

References element(), and mminor().

double DUNE::Math::Matrix::dot	(	const Matrix &	a,
		const Matrix &	b
	)

static

Calculate dot product.

Arguments must be equally sized column or row vectors.

Parameters

[in]	a	matrix.
[in]	b	matrix.

Returns: resultant matrix of dot product

References isVector().

Referenced by DUNE::Math::QPSolver::solve().

double DUNE::Math::Matrix::element	(	size_t	i,
		size_t	j
	)		const

This method returns the value of an entry of a Matrix.

As this is a reading method it does not care if the data is shared by other matrices.

Parameters

[in]	i	row index
[in]	j	column index

Returns: value of matrix

Referenced by det(), detr(), set(), toDCM(), toEulerAngles(), and toQuaternion().

double DUNE::Math::Matrix::element ( size_t i )

This method returns the value of an entry of a Matrix.

As this is a reading method it does not care if the data is shared by other matrices.

Parameters

[in] i matrix index

Returns: value of matrix

Matrix DUNE::Math::Matrix::expmts ( double tol = 1e-05 ) const

Compute matrix exponential of a square matrix through Taylor series expansion technique.

Revised according to: "Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later" SIAM Review, 2003 (pages 12-13 - "Scale and squaring method").

Parameters

[in] tol tolerance value

Returns: resultant matrix

References DUNE::Math::computeNextPowerOfTwo(), expmts(), and norm_p().

Referenced by DUNE::Control::LinearSystem::c2d(), and expmts().

void DUNE::Math::Matrix::fill ( double value )

Fill the Matrix with a constant value.

Parameters

[in] value constant value to fill matrix with

Referenced by identity(), Matrix(), Control::ROV::RemoteOperation::Task::onActivation(), Control::ROV::RemoteOperation::Task::onConnectionTimeout(), Control::ROV::RemoteOperation::Task::onDeactivation(), Sensors::IFOG::Task::onUpdateParameters(), Navigation::General::ROV::Task::resetMatrixA(), Navigation::AUV::SGNavigation::Task::resetMatrixA(), DUNE::Navigation::KalmanFilter::resetOutputs(), DUNE::Navigation::KalmanFilter::resetState(), resizeAndFill(), and resizeAndKeep().

void DUNE::Math::Matrix::fill	(	size_t	r,
		size_t	c,
		const double *	data = `0`
	)

Resize matrix and fill with new values.

Parameters

[in]	r	number of rows of resized matrix
[in]	c	number of columns of resized matrix
[in]	data	pointer to data to be copied to resized matrix

References resize().

void DUNE::Math::Matrix::fromFile ( const char * path )

Loads a matrix from text file (must initialize matrix dimensions first).

Parameters

[in] path file path string (eg: "E:\dir/x.txt").

Matrix DUNE::Math::Matrix::get	(	size_t	i1,
		size_t	i2,
		size_t	j1,
		size_t	j2
	)		const

Retrieve a submatrix.

Parameters

[in]	i1	initial row
[in]	i2	final row
[in]	j1	initial column
[in]	j2	final column

Returns: submatrix

Referenced by DUNE::Navigation::KalmanFilter::getCovariance(), DUNE::Navigation::KalmanFilter::getObservation(), DUNE::Navigation::AAKR::normalize(), and Control::ROV::RemoteOperation::Task::onRemoteActions().

double DUNE::Math::Matrix::get_precision ( void )

static

This method returns the precision currently in use.

Returns: value of the precision in use

Matrix & DUNE::Math::Matrix::horzCat ( const Matrix & m_in )

Returns the horizontal concatenation of a matrix Return a matrix of size (nrows x (ncolumns + columns(m_in)) ) and fills the remaining elements with zeros.

Parameters

[in] m_in reference to matrix

Returns: reference to vertical concatenation of matrix

References columns(), resizeAndFill(), rows(), and set().

Referenced by Simulators::AUV::Task::matrixJ(), and Simulators::UAV::Task::matrixJ().

void DUNE::Math::Matrix::identity ( void )

Turns the Matrix into an identity matrix if it is squared.

References fill().

Referenced by Matrix().

bool DUNE::Math::Matrix::isColumnVector ( void ) const

This routine checks if matrix is a column vector.

Returns: true if it is a column vector, false otherwise

Referenced by DUNE::Math::QPSolver::solve().

bool DUNE::Math::Matrix::isColumnVector ( size_t rows ) const

This routine checks if matrix is a column vector with certain size.

Parameters

[in] rows size of the vector

Returns: true if it is a column vector, false otherwise

bool DUNE::Math::Matrix::isInvertible ( void ) const

This routine checks if matrix is invertible.

Returns: true if it is invertible, false otherwise

References upper_triangular_pp().

bool DUNE::Math::Matrix::isRowVector ( void ) const

This routine checks if matrix is a row vector.

Returns: true if it is a row vector, false otherwise

bool DUNE::Math::Matrix::isRowVector ( size_t columns ) const

This routine checks if matrix is a row vector with certain size.

Parameters

[in] columns size of the vector

Returns: true if it is a row vector, false otherwise

bool DUNE::Math::Matrix::isSquare ( void ) const

This routine checks if matrix is square.

Returns: true if it is squared, false otherwise

Referenced by DUNE::Math::QPSolver::solve(), and trace().

bool DUNE::Math::Matrix::isVector ( void ) const

This routine checks if matrix is a vector.

Returns: true if it is a vector, false otherwise

Referenced by cross(), and dot().

bool DUNE::Math::Matrix::isZeroSized ( void ) const

Return true for zero sized matrices.

Returns: return true for zero sized matrices, false otherwise.

Referenced by put(), and readFromLines().

void DUNE::Math::Matrix::lu	(	Matrix &	L,
		Matrix &	U
	)		const

Parameters

[in]	L	lower triangular matrix
[in]	U	upper triangular matrix

unsigned int DUNE::Math::Matrix::lup	(	Matrix &	L,
		Matrix &	U,
		Matrix &	P
	)		const

LUP decomposition (P * A = L * U).

This method returns the number of permutations.

Parameters

[in]	L	lower triangular matrix
[in]	U	upper triangular matrix
[in]	P	permutation matrix

Returns: number of permutations

References multiply(), and swapRows().

Referenced by det(), and DUNE::Math::inverse_lup().

void DUNE::Math::Matrix::maxLimitValues ( double max )

Limit the maximum Matrix elements values.

Parameters

[in] max maximum value

References max.

Referenced by trimValues().

double DUNE::Math::Matrix::median ( void ) const

Compute the median value of the ordered data of the matrix.

(does not assume the data is already ordered)

Returns: median of the matrix

References DUNE::Math::median().

void DUNE::Math::Matrix::minLimitValues ( double min )

Limit the minimum Matrix elements values.

Parameters

[in] min minimum value

References min.

Referenced by trimValues().

Matrix DUNE::Math::Matrix::mminor	(	size_t	i,
		size_t	j
	)		const

This routine returns the (i, j) minor Matrix.

Parameters

[in]	i	row index
[in]	j	row index

Returns: matrix

References put(), and resizeAndFill().

Referenced by detr(), and Sylvester().

Matrix DUNE::Math::Matrix::multiply ( const Matrix & m )

Right-multiply a matrix with given matrix.

Parameters

[in] m matrix to be multiplied

Returns: multiplied matrix

Referenced by lup().

double DUNE::Math::Matrix::norm_2 ( void ) const

This implements the (element-wise) 2-norm, corresponding to the Euclidean norm for vectors and Froebnius norm for matrices.

Returns: resultant norm

Referenced by Navigation::General::Alignment::Task::calibrate().

double DUNE::Math::Matrix::norm_inf ( void ) const

This implements the infinity-norm.

Returns: resultant norm

double DUNE::Math::Matrix::norm_p ( double p ) const

This method implements the p-norm for both matrices and vectors.

The following values of p yield particular cases: Vectors: p = 1: Manhattan/taxicab norm; p = 2: Euclidean norm; very large values of p: infinity/maximum norm; Matrices: p = 2: Froebnius norm; very large values of p: maximum norm;

Parameters

[in] p norm value

Returns: resultant norm

Referenced by expmts().

Matrix & DUNE::Math::Matrix::operator&= ( const Matrix & m )

This methods multiplies each entry of a Matrix by the corresponding entry of another Matrix.

Parameters

[in] m reference to matrix to be multiplied

Returns: reference to resultant matrix

double & DUNE::Math::Matrix::operator()	(	size_t	i,
		size_t	j
	)

This operator returns a reference to a given entry of a Matrix.

As this methods makes possible to change the entries of a Matrix a spliting is necessary to avoid corrupting other matrices sharing the same data.

Note: As this method returns a reference it is very powerful, and it can be used to gain access to the pointer to the Matrix entries. This use can be dangerous because the data of a given matrix can move from place to place due to splitting.

Parameters

[in]	i	row index
[in]	j	column index

Returns: reference to entry of a matrix

double DUNE::Math::Matrix::operator()	(	size_t	i,
		size_t	j
	)		const

This routine returns a value of the matrix.

Parameters

[in]	i	row index
[in]	j	column index

Returns: value of matrix

double & DUNE::Math::Matrix::operator() ( size_t i )

This operator returns a reference to a given entry of a Matrix.

As this methods makes possible to change the entries of a Matrix a spliting is necessary to avoid corrupting other matrices sharing the same data.

Note: As this method returns a reference it is very powerful, and it can be used to gain access to the pointer to the Matrix entries. This use can be dangerous because the data of a given matrix can move from place to place due to splitting.

Parameters

[in] i matrix index

Returns: reference to entry of a matrix

double DUNE::Math::Matrix::operator() ( size_t i ) const

This routine returns a value of the matrix.

Parameters

[in] i matrix index

Returns: value of matrix

Matrix & DUNE::Math::Matrix::operator*= ( double x )

This method multiplies a Matrix by a real number.

Parameters

[in] x real number

Returns: reference to resultant matrix

Matrix & DUNE::Math::Matrix::operator+= ( const Matrix & m )

This methods adds to a Matrix the contents of another Matrix.

Parameters

[in] m reference to matrix to be added

Returns: reference to resultant matrix

Matrix DUNE::Math::Matrix::operator- ( void )

This method implements the unary minus operator.

Returns: resultant matrix

Matrix & DUNE::Math::Matrix::operator-= ( const Matrix & m )

This methods subtracts from a Matrix the contents of another Matrix.

Parameters

[in] m reference to matrix to be subtracted

Returns: reference to resultant matrix

Matrix & DUNE::Math::Matrix::operator/= ( const Matrix & m )

This methods divides each entry of Matrix by the correspondig entry of another Matrix.

Parameters

[in] m reference to matrix to be divided

Returns: reference to resultant matrix

Matrix & DUNE::Math::Matrix::operator/= ( double x )

This method divides a Matrix by a real number.

Care must be taken to avoid divisions by zero.

Parameters

[in] x real number

Returns: reference to resultant matrix

Matrix & DUNE::Math::Matrix::operator= ( const Matrix & m )

This method assigns a Matrix with another Matrix.

The silly assignement 'a = a' is handled correctly (nothing is done!).

Parameters

[in] m reference to matrix to be assigned

Returns: reference to resultant matrix

bool DUNE::Math::Matrix::operator== ( const Matrix & m ) const

Compare matrices for equality.

Parameters

[in] m matrix to compare.

Returns: true if matrices are equal, false otherwise.

Matrix & DUNE::Math::Matrix::pow ( unsigned int n )

Returns the power matrix X^n.

Parameters

[in] n positive integer exponent to raise the matrix to

Returns: reference to the power of the matrix

void DUNE::Math::Matrix::put	(	size_t	i,
		size_t	j,
		const Matrix &	a
	)

This method fills a submatrix of a given Matrix.

Parameters

[in]	i	row index
[in]	j	row index
[in]	a	submatrix

References isZeroSized().

Referenced by mminor(), swapColumns(), and swapRows().

void DUNE::Math::Matrix::readFromConfig	(	DUNE::Parsers::Config &	cfg,
		const std::string &	section,
		const std::string &	param
	)

Read a matrix from a configuration file.

The matrix dimensions must be defined a priori.

Parameters

[in]	cfg	configuration parser
[in]	section	configuration section
[in]	param	configuration parameter

References DUNE::Parsers::Config::get(), and readFromLines().

Referenced by DUNE::Parsers::PlanConfigParser::parse().

void DUNE::Math::Matrix::readFromLines ( const std::vector< std::string > & clines )

Read a matrix from a vector of strings The matrix dimensions must be defined a priori.

Parameters

[in] clines vector of strings containing the matrix data

References isZeroSized(), DUNE::Utils::String::split(), and DUNE::Utils::String::str().

Referenced by readFromConfig().

void DUNE::Math::Matrix::resize ( const Matrix & m )

This method resizes a Matrix to the same dimensions of other matrix.

Note that no data copy is performed.

Parameters

[in] m reference to matrix

Referenced by DUNE::Navigation::AAKR::add(), fill(), resizeAndFill(), DUNE::Math::QPSolver::solve(), and Sensors::IFOG::Task::Task().

void DUNE::Math::Matrix::resize	(	size_t	r,
		size_t	c
	)

This method resizes a Matrix to the dimensions of (r * c).

Parameters

[in]	r	number of rows
[in]	c	number of columns

void DUNE::Math::Matrix::resizeAndFill	(	size_t	r,
		size_t	c,
		double	value
	)

This method resizes a Matrix to the dimensions of (r * c) and fills the matrix with constant value.

Parameters

[in]	r	number of rows
[in]	c	number of columns
[in]	value	constant value to fill matrix with

References fill(), and resize().

Referenced by blkDiag(), Navigation::General::Alignment::Task::calibrate(), DUNE::Navigation::CompassCalibration::clear(), DUNE::Navigation::BeamFilter::clear(), cross(), horzCat(), DUNE::Navigation::KalmanFilter::KalmanFilter(), DUNE::Control::LinearSystem::LinearSystem(), mminor(), DUNE::Navigation::AAKR::normalize(), DUNE::Navigation::KalmanFilter::reset(), DUNE::Navigation::AAKR::resize(), and vertCat().

void DUNE::Math::Matrix::resizeAndKeep	(	size_t	r,
		size_t	c
	)

This method resizes a Matrix to the dimensions of (r * c) and keeps previous matrix values if/when possible.

Parameters

[in]	r	number of rows
[in]	c	number of columns

References fill().

Referenced by DUNE::Navigation::KalmanFilter::resize().

Matrix DUNE::Math::Matrix::row ( size_t i ) const

This method returns a row of the Matrix.

Parameters

[in] i row to be retrieved

Returns: matrix of the returned row

Referenced by swapRows().

int DUNE::Math::Matrix::rows ( void ) const

Retrieve the number of rows of the matrix.

Returns: number of rows of the matrix.

Matrix & DUNE::Math::Matrix::set	(	size_t	i1,
		size_t	i2,
		size_t	j1,
		size_t	j2,
		const Matrix &	m_in
	)

Set a submatrix.

Parameters

[in]	i1	initial row
[in]	i2	final row
[in]	j1	initial column
[in]	j2	final column
[in]	m_in	reference to matrix to be copied into submatrix

Returns: reference matrix

References element().

Referenced by DUNE::Navigation::AAKR::add(), blkDiag(), Navigation::General::Alignment::Task::calibrate(), horzCat(), and vertCat().

void DUNE::Math::Matrix::set_precision ( double p )

static

This method sets the precision used when inverting a Matrix.

Parameters

[in] p value of the precision to be used when inverting

int DUNE::Math::Matrix::size ( void ) const

Retrieve the size of the matrix.

Returns: size of the matrix.

Referenced by cross(), DUNE::Math::max(), DUNE::Math::min(), DUNE::Math::operator&(), DUNE::Math::operator+(), DUNE::Math::operator-(), DUNE::Math::operator/(), DUNE::Math::squaresum(), and DUNE::Math::sum().

void DUNE::Math::Matrix::swapColumns	(	size_t	i,
		size_t	j
	)

This method swaps two columns.

Parameters

[in]	i	index of column
[in]	j	index of column

References column(), and put().

void DUNE::Math::Matrix::swapRows	(	size_t	i,
		size_t	j
	)

This method swaps two rows.

Parameters

[in]	i	index of row
[in]	j	index of row

References put(), and row().

Referenced by lup().

bool DUNE::Math::Matrix::Sylvester ( void ) const

Sylvester's criterion implementation.

Returns: true if success, false otherwise

References det(), and mminor().

void DUNE::Math::Matrix::to_column ( void )

This method changes the dimensions of a Matrix to a one column Matrix.

The elements are not changed.

void DUNE::Math::Matrix::to_row ( void )

This method changes the dimensions of a Matrix to a one row Matrix.

The elements are not changed.

Matrix DUNE::Math::Matrix::toDCM ( void ) const

Convert from Euler angles or quaternions to Direction Cosines Matrix attitude representation.

Returns: DCM matrix

References element(), Matrix(), and transpose.

Referenced by Control::PTU::Task::consume(), Simulators::UAV::Task::matrixJ(), and DUNE::Navigation::CompassCalibration::updateField().

Matrix DUNE::Math::Matrix::toEulerAngles ( void ) const

Convert from DCM or Quaternion to Euler angles attitude representation.

Returns: Euler Angles representation

References element(), and Matrix().

Referenced by Navigation::General::Alignment::Task::calibrate().

void DUNE::Math::Matrix::toFile ( const char * path )

Saves matrix to text file.

Parameters

[in] path file path string (eg: "E:\dir/x.txt").

Matrix DUNE::Math::Matrix::toQuaternion ( void ) const

Convert from DCM or Euler angles to Quaternion attitude representation.

Returns: Quaternion representation

References element(), and Matrix().

double DUNE::Math::Matrix::trace ( void ) const

Compute matrix trace (sum of diagonal elements for a square matrix).

Returns: trace of matrix

References isSquare().

void DUNE::Math::Matrix::trimValues	(	double	min,
		double	max
	)

Limit the minimum and maximum Matrix elements values.

Parameters

[in]	min	minimum value
[in]	max	maximum value

References maxLimitValues(), and minLimitValues().

int DUNE::Math::Matrix::upper_triangular_pp	(	double *	M,
		int	n,
		int	m,
		double	tolerance
	)

static

This function tranforms a Matrix 'M' (n*m) into an upper triangular Matrix using Gauss elimination with partial pivoting.

'm' should be >= 'n'.

Parameters

[out]	M	matrix to be transformed
[in]	m	number of columns
[in]	n	number of rows
[in]	tolerance	small positive constant used to test for zero entries in 'M'

Returns: 0 if elimination done successfully, -1 if Matrix M is not full rank (elimination impossible)

Referenced by DUNE::Math::inverse_pp(), and isInvertible().

int DUNE::Math::Matrix::upper_triangular_tp	(	double *	M,
		int *	index,
		int	n,
		int	m,
		double	tolerance
	)

static

This function tranforms a Matrix 'M' (n*m) into an upper triangular Matrix using Gauss elimination with total pivoting.

'm' should be >= 'n'.

The parameter 'index' is a pointer to an array of 'n' integers that indicates the permutations that are done during total pivotation. When this function is called the 'index' array must be properly initialized, i.e. ind[0]=0, ind[1]=1, ..., ind[n-1]=n-1.

Parameters

[out]	M	matrix to be transformed
[out]	index	pointer to array that indicates permutations
[in]	m	number of columns
[in]	n	number of rows
[in]	tolerance	small positive constant used to test for zero entries in 'M'

Returns: 0 if elimination done successfully, -1 if matrix is not full rank (elimination impossible)

Referenced by DUNE::Math::inverse().

Matrix & DUNE::Math::Matrix::vertCat ( const Matrix & m_in )

Returns the vertical concatenation of a matrix Return a matrix of size (nrows + rows(m_in)) x (ncolumns) and fills the remaining elements with zeros.

Parameters

[in] m_in reference to matrix

Returns: reference to vertical concatenation of matrix

References columns(), resizeAndFill(), rows(), and set().

Referenced by DUNE::Control::LinearSystem::append(), Simulators::AUV::Task::matrixJ(), Simulators::UAV::Task::matrixJ(), and DUNE::Math::operator>>().

Friends And Related Function Documentation

Matrix abs ( const Matrix & a )

friend

This function returns a Matrix with the absolute values of the entries of a given Matrix.

Parameters

[in] a matrix

Returns: matrix with absolute values

DUNE_DLL_SYM Matrix inverse ( const Matrix & a )

friend

This methods calculates the inverse of a Matrix.

The inverse is calculated using Gauss elimination with total pivoting.

If Matrix 'a' is singular (with current precision) a zero Matrix with the same dimension of 'a' is returned and the variable 'dMatrix::inversionerror' is set to 1. Otherwise it is set to 0.

Parameters

[in] a matrix to be inverted.

Returns: inverted matrix

DUNE_DLL_SYM Matrix inverse	(	const Matrix &	a,
		const Matrix &	b
	)

friend

This methods calculates the Matrix 'x' that solves the linear system of equations 'a.x=b'.

The system is solved using Gauss elimination with total pivoting.

If Matrix 'a' is singular (with current precision) a zero Matrix with the same dimension of 'b' is returned and the variable 'dMatrix::inversionerror' is set to 1. Otherwise it is set to 0.

Parameters

[in]	a	matrix
[in]	b	matrix

Returns: resultant matrix

Matrix inverse_lup ( const Matrix & a )

friend

This function computes the Matrix inverse using LU or LUP decomposition.

Parameters

[in] a reference to matrix to be inverted

Returns: inverted matrix

Matrix inverse_pp ( const Matrix & a )

friend

This methods calculates the inverse of a Matrix.

The inverse is calculated using Gauss elimination with partial pivoting.

If Matrix is singular (with current precision) a zero Matrix with the same dimension is returned and the variable. 'dMatrix::inversionerror' is set to 1. Otherwise is is set to 0.

Parameters

[in] a reference to matrix to be inverted

Returns: inverted matrix

Matrix inverse_pp	(	const Matrix &	a,
		const Matrix &	b
	)

friend

This methods calculates the Matrix 'x' that solves the linear system of equations 'a.x=b'.

The system is solved using Gauss elimination with partial pivoting.

If Matrix 'a' is singular (with current precision) a zero Matrix with the same dimension of 'b' is returned and the variable. 'dMatrix::inversionerror' is set to 1. Otherwise it is set to 0.

Parameters

[in]	a	matrix
[in]	b	matrix

Returns: resultant matrix

double max ( const Matrix & a )

friend

This function returns the maximum value of a Matrix.

Parameters

[in] a matrix

Returns: maximum value of matrix

Referenced by maxLimitValues().

double min ( const Matrix & a )

friend

This function returns the minimum value of a Matrix.

Parameters

[in] a matrix

Returns: minimum value of matrix

Referenced by minLimitValues().

DUNE_DLL_SYM Matrix operator&	(	const Matrix &	m1,
		const Matrix &	m2
	)

friend

This method returns the element-element product of two matrices.

Parameters

[in]	m1	matrix to be multiplied (element-element).
[in]	m2	matrix to be multiplied (element-element).

Returns: resultant matrix.

DUNE_DLL_SYM Matrix operator*	(	const Matrix &	m1,
		const Matrix &	m2
	)

friend

This method returns the product of two matrices.

Note on optimization by Eduardo Marques - Sep 8 2010

Applied loop interchange to achieve memory stride 1 (better data locality) in iterations of the innermost loop, This makes for better cache behavior (i.e. less cache misses), particularly as matrix dimensions increase. For those interested, see papers or books by M J Wolfe.

Parameters

[in]	m1	matrix to be summed.
[in]	m2	matrix to be summed.

Returns: resultant matrix.

DUNE_DLL_SYM Matrix operator*	(	double	x,
		const Matrix &	a
	)

friend

This function multiplies a Matrix by a real number.

Parameters

[in]	x	real number.
[in]	a	matrix to be multiplied.

Returns: resultant matrix.

DUNE_DLL_SYM Matrix operator*	(	const Matrix &	a,
		double	x
	)

friend

This function multiplies a Matrix by a real number.

Parameters

[in]	a	matrix to be multiplied.
[in]	x	real number.

Returns: resultant matrix.

DUNE_DLL_SYM Matrix operator+	(	const Matrix &	m1,
		const Matrix &	m2
	)

friend

This method returns the sum of two matrices.

Parameters

[in]	m1	matrix to be summed.
[in]	m2	matrix to be summed.

Returns: resultant matrix.

DUNE_DLL_SYM Matrix operator-	(	const Matrix &	m1,
		const Matrix &	m2
	)

friend

This method returns the difference of two matrices.

Parameters

[in]	m1	matrix to be subtracted.
[in]	m2	matrix to subtract.

Returns: resultant matrix.

DUNE_DLL_SYM Matrix operator/	(	const Matrix &	a,
		const Matrix &	b
	)

friend

This method returns the element-element quocient of two matrices.

Parameters

[in]	a	matrix for element-element quocient.
[in]	b	matrix for element-element quocient.

Returns: resultant matrix.

DUNE_DLL_SYM Matrix operator/	(	const Matrix &	a,
		double	x
	)

friend

This function divides a Matrix by a real number.

Parameters

[in]	a	matrix to be divided.
[in]	x	real number.

Returns: resultant matrix.

DUNE_DLL_SYM std::ostream& operator<<	(	std::ostream &	os,
		const Matrix &	a
	)

friend

This method sends a Matrix to an 'ostream'.

Each row of the Matrix is put on a different line.

Parameters

[in]	os	output stream.
[in]	a	matrix to be outputted.

DUNE_DLL_SYM std::istream& operator>>	(	std::istream &	is,
		Matrix &	a
	)

friend

This method reads a Matrix from an 'istream'.

The Matrix is filled row by row.

Parameters

[in]	is	input stream.
[in]	a	matrix to be filled.

Returns: resultant matrix.

Matrix skew ( double data[3] )

friend

This function returns a 3x3 skew symmetrical matrix using an array with 3 elements.

Parameters

[in] data array with 3 elements

Returns: skewed matrix

Referenced by DUNE::Math::skew().

Matrix skew ( const Matrix & a )

friend

This function returns a 3x3 skew symmetrical matrix using a matrix (3x1 or 1x3)

Parameters

[in] a row or column vector with 3 elements

Returns: skewed matrix

double squaresum ( const Matrix & a )

friend

This function returns the sum of the squares of the elements of a given Matrix.

Parameters

[in] a matrix

Returns: squared sum of the elements of matrix

double sum ( const Matrix & a )

friend

This function returns the sum of the elements of a given Matrix.

Parameters

[in] a matrix

Returns: sum of the elements of matrix

DUNE_DLL_SYM Matrix transpose ( const Matrix & a )

friend

This method returns the transpose of a Matrix.

Parameters

[in] a to be transposed.

Returns: transposed matrix.

Referenced by toDCM().

Collaboration diagram for DUNE::Math::Matrix:

Classes

Public Member Functions

Static Public Member Functions

Friends

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Note on optimization by Eduardo Marques - Sep 8 2010