#include <visp3/core/vpSubMatrix.h>

Inheritance diagram for vpSubMatrix:

Public Types
enum	vpDetMethod { LU_DECOMPOSITION }

Public Member Functions
	vpSubMatrix ()

	vpSubMatrix (vpMatrix &m, const unsigned int &row, const unsigned int &col, const unsigned int &nrows, const unsigned int &ncols)

virtual	~vpSubMatrix ()

void	init (vpMatrix &m, const unsigned int &row, const unsigned int &col, const unsigned int &nrows, const unsigned int &ncols)

void	checkParentStatus () const

vpSubMatrix &	operator= (const vpSubMatrix &B)

vpSubMatrix &	operator= (const vpMatrix &B)

vpSubMatrix &	operator= (const double &x)

void	clear ()

bool	operator== (const vpArray2D< float > &A) const

Setting a diagonal matrix
void	diag (const double &val=1.0)

void	diag (const vpColVector &A)

void	eye ()

Assignment operators
vpMatrix &	operator<< (double *)

vpMatrix &	operator<< (double val)

vpMatrix &	operator, (double val)

Stacking
void	stack (const vpMatrix &A)

void	stack (const vpRowVector &r)

void	stack (const vpColVector &c)

void	stackColumns (vpColVector &out)

vpColVector	stackColumns ()

void	stackRows (vpRowVector &out)

vpRowVector	stackRows ()

Matrix insertion
void	insert (const vpMatrix &A, const unsigned int r, const unsigned int c)

Columns, rows, sub-matrices extraction
vpMatrix	extract (unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols) const

vpColVector	getCol (const unsigned int j) const

vpColVector	getCol (const unsigned int j, const unsigned int i_begin, const unsigned int size) const

vpRowVector	getRow (const unsigned int i) const

vpRowVector	getRow (const unsigned int i, const unsigned int j_begin, const unsigned int size) const

vpColVector	getDiag () const

void	init (const vpMatrix &M, unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols)

Matrix operations
double	det (vpDetMethod method=LU_DECOMPOSITION) const

double	detByLU () const

double	detByLUEigen3 () const

double	detByLUGsl () const

double	detByLULapack () const

double	detByLUOpenCV () const

vpMatrix	expm () const

vpMatrix &	operator+= (const vpMatrix &B)

vpMatrix &	operator+= (const double x)

vpMatrix &	operator-= (const vpMatrix &B)

vpMatrix &	operator-= (const double x)

vpMatrix	operator* (const vpMatrix &B) const

vpMatrix	operator* (const vpRotationMatrix &R) const

vpMatrix	operator* (const vpVelocityTwistMatrix &V) const

vpMatrix	operator* (const vpForceTwistMatrix &V) const

vpTranslationVector	operator* (const vpTranslationVector &tv) const

vpColVector	operator* (const vpColVector &v) const

vpMatrix	operator* (const double x) const

vpMatrix	operator+ (const vpMatrix &B) const

vpMatrix	operator- (const vpMatrix &B) const

vpMatrix	operator- () const

vpMatrix &	operator*= (const double x)

vpMatrix &	operator/= (double x)

vpMatrix	operator/ (const double x) const

double	sum () const

double	sumSquare () const

Hadamard product
vpMatrix	hadamard (const vpMatrix &m) const

Inherited functionalities from vpArray2D
vpArray2D< double >	hadamard (const vpArray2D< double > &m) const

unsigned int	getCols () const

double	getMaxValue () const

double	getMinValue () const

unsigned int	getRows () const

unsigned int	size () const

void	resize (const unsigned int nrows, const unsigned int ncols, const bool flagNullify=true, const bool recopy_=true)

void	reshape (unsigned int nrows, unsigned int ncols)

bool	operator== (const vpArray2D< double > &A) const

bool	operator!= (const vpArray2D< double > &A) const

double *	operator[] (unsigned int i)

double *	operator[] (unsigned int i) const

Kronecker product
void	kron (const vpMatrix &m1, vpMatrix &out) const

vpMatrix	kron (const vpMatrix &m1) const

Transpose
vpMatrix	t () const

vpMatrix	transpose () const

void	transpose (vpMatrix &At) const

vpMatrix	AAt () const

void	AAt (vpMatrix &B) const

vpMatrix	AtA () const

void	AtA (vpMatrix &B) const

Matrix inversion
vpMatrix	inverseByLU () const

vpMatrix	inverseByLUEigen3 () const

vpMatrix	inverseByLUGsl () const

vpMatrix	inverseByLULapack () const

vpMatrix	inverseByLUOpenCV () const

vpMatrix	inverseByCholesky () const

vpMatrix	inverseByCholeskyLapack () const

vpMatrix	inverseByCholeskyOpenCV () const

vpMatrix	inverseByQR () const

vpMatrix	inverseByQRLapack () const

vpMatrix	inverseTriangular (bool upper=true) const

vpMatrix	pseudoInverse (double svThreshold=1e-6) const

unsigned int	pseudoInverse (vpMatrix &Ap, double svThreshold=1e-6) const

unsigned int	pseudoInverse (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const

unsigned int	pseudoInverse (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt) const

unsigned int	pseudoInverse (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const

vpMatrix	pseudoInverseLapack (double svThreshold=1e-6) const

unsigned int	pseudoInverseLapack (vpMatrix &Ap, double svThreshold=1e-6) const

unsigned int	pseudoInverseLapack (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const

unsigned int	pseudoInverseLapack (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const

vpMatrix	pseudoInverseEigen3 (double svThreshold=1e-6) const

unsigned int	pseudoInverseEigen3 (vpMatrix &Ap, double svThreshold=1e-6) const

unsigned int	pseudoInverseEigen3 (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const

unsigned int	pseudoInverseEigen3 (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const

vpMatrix	pseudoInverseOpenCV (double svThreshold=1e-6) const

unsigned int	pseudoInverseOpenCV (vpMatrix &Ap, double svThreshold=1e-6) const

unsigned int	pseudoInverseOpenCV (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const

unsigned int	pseudoInverseOpenCV (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const

vpMatrix	pseudoInverseGsl (double svThreshold=1e-6) const

unsigned int	pseudoInverseGsl (vpMatrix &Ap, double svThreshold=1e-6) const

unsigned int	pseudoInverseGsl (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const

unsigned int	pseudoInverseGsl (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const

SVD decomposition
double	cond (double svThreshold=1e-6) const

unsigned int	kernel (vpMatrix &kerAt, double svThreshold=1e-6) const

void	solveBySVD (const vpColVector &B, vpColVector &x) const

vpColVector	solveBySVD (const vpColVector &B) const

void	svd (vpColVector &w, vpMatrix &V)

void	svdEigen3 (vpColVector &w, vpMatrix &V)

void	svdGsl (vpColVector &w, vpMatrix &V)

void	svdLapack (vpColVector &w, vpMatrix &V)

void	svdOpenCV (vpColVector &w, vpMatrix &V)

QR decomposition
unsigned int	qr (vpMatrix &Q, vpMatrix &R, bool full=false, bool squareR=false, double tol=1e-6) const

unsigned int	qrPivot (vpMatrix &Q, vpMatrix &R, vpMatrix &P, bool full=false, bool squareR=false, double tol=1e-6) const

void	solveByQR (const vpColVector &b, vpColVector &x) const

vpColVector	solveByQR (const vpColVector &b) const

Eigen values
vpColVector	eigenValues () const

void	eigenValues (vpColVector &evalue, vpMatrix &evector) const

Norms
double	euclideanNorm () const

double	frobeniusNorm () const

double	inducedL2Norm () const

double	infinityNorm () const

Printing
std::ostream &	cppPrint (std::ostream &os, const std::string &matrixName="A", bool octet=false) const

std::ostream &	csvPrint (std::ostream &os) const

std::ostream &	maplePrint (std::ostream &os) const

std::ostream &	matlabPrint (std::ostream &os) const

int	print (std::ostream &s, unsigned int length, const std::string &intro="") const

void	printSize () const

Static Public Member Functions
Stacking with Static Public Member Functions
static vpMatrix	stack (const vpMatrix &A, const vpMatrix &B)

static vpMatrix	stack (const vpMatrix &A, const vpRowVector &r)

static vpMatrix	stack (const vpMatrix &A, const vpColVector &c)

static void	stack (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)

static void	stack (const vpMatrix &A, const vpRowVector &r, vpMatrix &C)

static void	stack (const vpMatrix &A, const vpColVector &c, vpMatrix &C)

static vpMatrix	juxtaposeMatrices (const vpMatrix &A, const vpMatrix &B)

static void	juxtaposeMatrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)

Matrix insertion with Static Public Member Functions
static vpMatrix	insert (const vpMatrix &A, const vpMatrix &B, const unsigned int r, const unsigned int c)

static void	insert (const vpMatrix &A, const vpMatrix &B, vpMatrix &C, const unsigned int r, const unsigned int c)

Kronecker product with Static Public Member Functions
static void	kron (const vpMatrix &m1, const vpMatrix &m2, vpMatrix &out)

static vpMatrix	kron (const vpMatrix &m1, const vpMatrix &m2)

Setting a diagonal matrix with Static Public Member Functions
static void	createDiagonalMatrix (const vpColVector &A, vpMatrix &DA)

Matrix operations with Static Public Member Functions
static void	add2Matrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)

static void	add2Matrices (const vpColVector &A, const vpColVector &B, vpColVector &C)

static void	add2WeightedMatrices (const vpMatrix &A, const double &wA, const vpMatrix &B, const double &wB, vpMatrix &C)

static void	computeHLM (const vpMatrix &H, const double &alpha, vpMatrix &HLM)

static void	mult2Matrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)

static void	mult2Matrices (const vpMatrix &A, const vpMatrix &B, vpRotationMatrix &C)

static void	mult2Matrices (const vpMatrix &A, const vpMatrix &B, vpHomogeneousMatrix &C)

static void	mult2Matrices (const vpMatrix &A, const vpColVector &B, vpColVector &C)

static void	multMatrixVector (const vpMatrix &A, const vpColVector &v, vpColVector &w)

static void	negateMatrix (const vpMatrix &A, vpMatrix &C)

static void	sub2Matrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)

static void	sub2Matrices (const vpColVector &A, const vpColVector &B, vpColVector &C)

2D Convolution with Static Public Member Functions
static vpMatrix	conv2 (const vpMatrix &M, const vpMatrix &kernel, const std::string &mode="full")

static void	conv2 (const vpMatrix &M, const vpMatrix &kernel, vpMatrix &res, const std::string &mode="full")

Covariance computation with Static Public Member Functions
static vpMatrix	computeCovarianceMatrix (const vpMatrix &A, const vpColVector &x, const vpColVector &b)

static vpMatrix	computeCovarianceMatrix (const vpMatrix &A, const vpColVector &x, const vpColVector &b, const vpMatrix &w)

static vpMatrix	computeCovarianceMatrixVVS (const vpHomogeneousMatrix &cMo, const vpColVector &deltaS, const vpMatrix &Ls, const vpMatrix &W)

static vpMatrix	computeCovarianceMatrixVVS (const vpHomogeneousMatrix &cMo, const vpColVector &deltaS, const vpMatrix &Ls)

Matrix I/O with Static Public Member Functions
static bool	loadMatrix (const std::string &filename, vpArray2D< double > &M, const bool binary=false, char *header=NULL)

static bool	loadMatrixYAML (const std::string &filename, vpArray2D< double > &M, char *header=NULL)

static bool	saveMatrix (const std::string &filename, const vpArray2D< double > &M, const bool binary=false, const char *header="")

static bool	saveMatrixYAML (const std::string &filename, const vpArray2D< double > &M, const char *header="")

Inherited I/O from vpArray2D with Static Public Member Functions
static bool	load (const std::string &filename, vpArray2D< double > &A, const bool binary=false, char *header=NULL)

static bool	loadYAML (const std::string &filename, vpArray2D< double > &A, char *header=NULL)

static bool	save (const std::string &filename, const vpArray2D< double > &A, const bool binary=false, const char *header="")

static bool	saveYAML (const std::string &filename, const vpArray2D< double > &A, const char *header="")

Public Attributes
double *	data

Protected Attributes
unsigned int	pRowNum

unsigned int	pColNum

vpMatrix *	parent

unsigned int	rowNum

unsigned int	colNum

double **	rowPtrs

unsigned int	dsize

Related Functions
(Note that these are not member functions.)
vpMatrix	operator* (const double &x, const vpMatrix &B)

enum	vpGEMMmethod

void	vpGEMM (const vpArray2D< double > &A, const vpArray2D< double > &B, const double &alpha, const vpArray2D< double > &C, const double &beta, vpArray2D< double > &D, const unsigned int &ops=0)

Deprecated functions
vp_deprecated void	init ()

vp_deprecated void	stackMatrices (const vpMatrix &A)

vp_deprecated void	setIdentity (const double &val=1.0)

vp_deprecated vpRowVector	row (const unsigned int i)

vp_deprecated vpColVector	column (const unsigned int j)

static vp_deprecated vpMatrix	stackMatrices (const vpMatrix &A, const vpMatrix &B)

static vp_deprecated void	stackMatrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)

static vp_deprecated vpMatrix	stackMatrices (const vpMatrix &A, const vpRowVector &B)

static vp_deprecated void	stackMatrices (const vpMatrix &A, const vpRowVector &B, vpMatrix &C)

static vp_deprecated vpMatrix	stackMatrices (const vpColVector &A, const vpColVector &B)

static vp_deprecated void	stackMatrices (const vpColVector &A, const vpColVector &B, vpColVector &C)

Detailed Description

Definition of the vpSubMatrix vpSubMatrix class provides a mask on a vpMatrix all properties of vpMatrix are available with a vpSubMatrix.

Author: Jean Laneurit (IRISA - INRIA Rennes)

See also: vpMatrix vpColvector vpRowVector

Definition at line 62 of file vpSubMatrix.h.

Member Enumeration Documentation

◆ vpDetMethod

enum vpMatrix::vpDetMethod

inherited

Method used to compute the determinant of a square matrix.

See also: det()

Enumerator
LU_DECOMPOSITION	LU decomposition method.

Definition at line 171 of file vpMatrix.h.

Constructor & Destructor Documentation

◆ vpSubMatrix() [1/2]

vpSubMatrix::vpSubMatrix ( )

Default constructor.

Definition at line 45 of file vpSubMatrix.cpp.

◆ vpSubMatrix() [2/2]

vpSubMatrix::vpSubMatrix	(	vpMatrix &	m,
		const unsigned int &	row_offset,
		const unsigned int &	col_offset,
		const unsigned int &	nrows,
		const unsigned int &	ncols
	)

Constructor.

Parameters

m	: parent matrix
row_offset	: row offset
col_offset	: col offset
nrows	: number of rows of the sub matrix
ncols	: number of columns of the sub matrix

Definition at line 55 of file vpSubMatrix.cpp.

References vpMatrix::init().

◆ ~vpSubMatrix()

vpSubMatrix::~vpSubMatrix ( )

virtual

Destructor.

Definition at line 176 of file vpSubMatrix.cpp.

References vpArray2D< double >::data.

Member Function Documentation

◆ AAt() [1/2]

vpMatrix vpMatrix::AAt ( ) const

inherited

Computes the $AA^T$ operation $B = A*A^T$

Returns

See also: AAt(vpMatrix &) const

Definition at line 493 of file vpMatrix.cpp.

◆ AAt() [2/2]

void vpMatrix::AAt ( vpMatrix & B ) const

inherited

Compute the AAt operation such as $B = A*A^T$ .

The result is placed in the parameter B and not returned.

A new matrix won't be allocated for every use of the function. This results in a speed gain if used many times with the same result matrix size.

See also: AAt()

Definition at line 513 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpArray2D< double >::colNum, vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, vpArray2D< Type >::rowNum, and vpArray2D< double >::rowPtrs.

◆ add2Matrices() [1/2]

void vpMatrix::add2Matrices	(	const vpMatrix &	A,
		const vpMatrix &	B,
		vpMatrix &	C
	)

staticinherited

Operation C = A + B.

The result is placed in the third parameter C and not returned. A new matrix won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).

See also: operator+()

Definition at line 1269 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

Referenced by vpMatrix::operator+().

◆ add2Matrices() [2/2]

void vpMatrix::add2Matrices	(	const vpColVector &	A,
		const vpColVector &	B,
		vpColVector &	C
	)

staticinherited

Warning: This function is provided for compat with previous releases. You should rather use the functionalities provided in vpColVector class.

Operation C = A + B.

The result is placed in the third parameter C and not returned. A new vector won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).

See also: vpColVector::operator+()

Definition at line 1302 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpColVector::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

◆ add2WeightedMatrices()

void vpMatrix::add2WeightedMatrices	(	const vpMatrix &	A,
		const double &	wA,
		const vpMatrix &	B,
		const double &	wB,
		vpMatrix &	C
	)

staticinherited

Operation C = A*wA + B*wB

The result is placed in the third parameter C and not returned. A new matrix won't be allocated for every use of the function (Speed gain if used many times with the same result matrix size).

See also: operator+()

Definition at line 1240 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

◆ AtA() [1/2]

vpMatrix vpMatrix::AtA ( ) const

inherited

Compute the AtA operation such as $B = A^T*A$

Returns

See also: AtA(vpMatrix &) const

Examples:: photometricVisualServoing.cpp, and testMatrixInverse.cpp.

Definition at line 591 of file vpMatrix.cpp.

Referenced by vpMbDepthDenseTracker::computeVVS(), vpMbDepthNormalTracker::computeVVS(), vpMbGenericTracker::computeVVS(), vpMbEdgeMultiTracker::computeVVSFirstPhasePoseEstimation(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbTracker::computeVVSPoseEstimation(), vpTemplateTrackerWarpHomographySL3::findWarp(), vpNurbs::globalCurveApprox(), vpMbGenericTracker::track(), and vpTemplateTrackerWarp::warp().

◆ AtA() [2/2]

void vpMatrix::AtA ( vpMatrix & B ) const

inherited

Compute the AtA operation such as $B = A^T*A$ .

The result is placed in the parameter B and not returned.

A new matrix won't be allocated for every use of the function. This results in a speed gain if used many times with the same result matrix size.

See also: AtA()

Definition at line 547 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, and vpArray2D< Type >::rowNum.

◆ checkParentStatus()

void vpSubMatrix::checkParentStatus ( ) const

Check is parent vpRowVector has changed since initialization.

This method can be used to detect if the parent matrix always exits or its size have not changed and throw an exception is not.

Definition at line 104 of file vpSubMatrix.cpp.

References vpArray2D< double >::data, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrixException::incorrectMatrixSizeError, parent, pColNum, and pRowNum.

◆ clear()

void vpMatrix::clear ( )

inlineinherited

Removes all elements from the matrix (which are destroyed), leaving the container with a size of 0.

Definition at line 230 of file vpMatrix.h.

References vpArray2D< Type >::hadamard(), operator*(), vpArray2D< Type >::operator<<, and vpArray2D< Type >::operator=().

Referenced by vpPose::init().

◆ column()

vpColVector vpMatrix::column ( const unsigned int j )

inherited

Deprecated:: This method is deprecated. You should rather use getCol(). More precisely, the following code:

vpMatrix L;
unsigned int column_index = ...;
... = L.column(column_index);

should be replaced with:

... = L.getCol(column_index - 1);

Warning: Notice column(1) is the 0-th column. This function returns the j-th columns of the matrix.

Parameters

j	: Index of the column to extract noting that column index start at 1 to get the first column.

Definition at line 5583 of file vpMatrix.cpp.

References vpArray2D< double >::getRows().

◆ computeCovarianceMatrix() [1/2]

vpMatrix vpMatrix::computeCovarianceMatrix	(	const vpMatrix &	A,
		const vpColVector &	x,
		const vpColVector &	b
	)

staticinherited

Compute the covariance matrix of the parameters x from a least squares minimisation defined as: Ax = b

Parameters

A	: Matrix A from Ax = b.
x	: Vector x from Ax = b corresponding to the parameters to estimate.
b	: Vector b from Ax = b.

Definition at line 59 of file vpMatrix_covariance.cpp.

References vpException::divideByZeroError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrix::pseudoInverse(), and vpMatrix::t().

Referenced by vpMatrix::computeCovarianceMatrixVVS(), vpPoseFeatures::computePose(), and vpPose::poseVirtualVSrobust().

◆ computeCovarianceMatrix() [2/2]

vpMatrix vpMatrix::computeCovarianceMatrix	(	const vpMatrix &	A,
		const vpColVector &	x,
		const vpColVector &	b,
		const vpMatrix &	W
	)

staticinherited

Compute the covariance matrix of the parameters x from a least squares minimisation defined as: WAx = Wb

Parameters

A	: Matrix A from WAx = Wb.
x	: Vector x from WAx = Wb corresponding to the parameters to estimate.
b	: Vector b from WAx = Wb.
W	: Diagonal weigths matrix from WAx = Wb.

Definition at line 91 of file vpMatrix_covariance.cpp.

References vpException::divideByZeroError, vpArray2D< Type >::getCols(), and vpMatrix::t().

◆ computeCovarianceMatrixVVS() [1/2]

vpMatrix vpMatrix::computeCovarianceMatrixVVS	(	const vpHomogeneousMatrix &	cMo,
		const vpColVector &	deltaS,
		const vpMatrix &	Ls,
		const vpMatrix &	W
	)

staticinherited

Compute the covariance matrix of an image-based virtual visual servoing. This assumes the optimization has been done via v = (W * Ls).pseudoInverse() W * DeltaS.

Parameters

cMo	: Pose matrix that has been computed with the v.
deltaS	: Error vector used in v = (W * Ls).pseudoInverse() * W * DeltaS.
Ls	: interaction matrix used in v = (W * Ls).pseudoInverse() * W * DeltaS.
W	: Weight matrix used in v = (W * Ls).pseudoInverse() * W * DeltaS.

Definition at line 149 of file vpMatrix_covariance.cpp.

References vpMatrix::computeCovarianceMatrix(), vpHomogeneousMatrix::extract(), vpMatrix::eye(), vpArray2D< Type >::getRows(), vpMatrix::pseudoInverse(), vpMath::sinc(), vpTranslationVector::skew(), vpColVector::skew(), vpMath::sqr(), and vpColVector::sumSquare().

Referenced by vpMatrix::computeCovarianceMatrixVVS(), vpMbTracker::computeCovarianceMatrixVVS(), and vpPose::poseVirtualVS().

◆ computeCovarianceMatrixVVS() [2/2]

vpMatrix vpMatrix::computeCovarianceMatrixVVS	(	const vpHomogeneousMatrix &	cMo,
		const vpColVector &	deltaS,
		const vpMatrix &	Ls
	)

staticinherited

Compute the covariance matrix of an image-based virtual visual servoing. This assumes the optimization has been done via v = Ls.pseudoInverse() * DeltaS.

Parameters

cMo	: Pose matrix that has been computed with the v.
deltaS	: Error vector used in v = Ls.pseudoInverse() * DeltaS
Ls	: interaction matrix used in v = Ls.pseudoInverse() * DeltaS

Definition at line 124 of file vpMatrix_covariance.cpp.

References vpMatrix::computeCovarianceMatrix(), and vpMatrix::computeCovarianceMatrixVVS().

◆ computeHLM()

void vpMatrix::computeHLM	(	const vpMatrix &	H,
		const double &	alpha,
		vpMatrix &	HLM
	)

staticinherited

Compute ${\bf H} + \alpha * diag({\bf H})$

Parameters

H	: input Matrix ${\bf H}$ . This matrix should be square.
alpha	: Scalar $\alpha$
HLM	: Resulting operation.

Definition at line 5300 of file vpMatrix.cpp.

References vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), and vpArray2D< Type >::resize().

◆ cond()

double vpMatrix::cond ( double svThreshold = 1e-6 ) const

inherited

Returns: The condition number, the ratio of the largest singular value of the matrix to the smallest.

Parameters

svThreshold Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.

Examples:: testMatrixConditionNumber.cpp.

Definition at line 5240 of file vpMatrix.cpp.

References vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpMatrix::insert(), vpArray2D< Type >::resize(), and vpMatrix::svd().

Referenced by vpTemplateTrackerMIForwardCompositional::trackNoPyr(), vpTemplateTrackerMIForwardAdditional::trackNoPyr(), vpTemplateTrackerMIESM::trackNoPyr(), and vpTemplateTrackerMIInverseCompositional::trackNoPyr().

◆ conv2() [1/2]

vpMatrix vpMatrix::conv2	(	const vpMatrix &	M,
		const vpMatrix &	kernel,
		const std::string &	mode = `"full"`
	)

staticinherited

Perform a 2D convolution similar to Matlab conv2 function: $M \star kernel$ .

Parameters

M	: First matrix.
kernel	: Second matrix.
mode	: Convolution mode: "full" (default), "same", "valid".

Convolution mode: full, same, valid (image credit: Theano doc).

Note: This is a very basic implementation that does not use FFT.

Examples:: testMatrixConvolution.cpp.

Definition at line 5445 of file vpMatrix.cpp.

Referenced by vpImageFilter::getSobelKernelY().

◆ conv2() [2/2]

void vpMatrix::conv2	(	const vpMatrix &	M,
		const vpMatrix &	kernel,
		vpMatrix &	res,
		const std::string &	mode = `"full"`
	)

staticinherited

Perform a 2D convolution similar to Matlab conv2 function: $M \star kernel$ .

Parameters

M	: First matrix.
kernel	: Second matrix.
res	: Result.
mode	: Convolution mode: "full" (default), "same", "valid".

Convolution mode: full, same, valid (image credit: Theano doc).

Note: This is a very basic implementation that does not use FFT.

Definition at line 5464 of file vpMatrix.cpp.

References vpArray2D< Type >::data, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrix::insert(), and vpArray2D< Type >::resize().

◆ cppPrint()

std::ostream & vpMatrix::cppPrint	(	std::ostream &	os,
		const std::string &	matrixName = `"A"`,
		bool	octet = `false`
	)		const

inherited

Print to be used as part of a C++ code later.

Parameters

os	: the stream to be printed in.
matrixName	: name of the matrix, "A" by default.
octet	: if false, print using double, if true, print byte per byte each bytes of the double array.

The following code shows how to use this function:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix M(2,3);
  int cpt = 0;
  for (unsigned int i=0; i<M.getRows(); i++)
    for (unsigned int j=0; j<M.getCols(); j++)
      M[i][j] = cpt++;
  M.cppPrint(std::cout, "M");
}

It produces the following output that could be copy/paste in a C++ code:

vpMatrix M (2, 3);
M[0][0] = 0;
M[0][1] = 1;
M[0][2] = 2;
M[1][0] = 3;
M[1][1] = 4;
M[1][2] = 5;

Definition at line 4627 of file vpMatrix.cpp.

References vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().

Referenced by vpColVector::clear().

◆ createDiagonalMatrix()

void vpMatrix::createDiagonalMatrix	(	const vpColVector &	A,
		vpMatrix &	DA
	)

staticinherited

Create a diagonal matrix with the element of a vector $DA_{ii} = A_i$ .

Parameters

A	: Vector which element will be put in the diagonal.
DA	: Diagonal matrix DA[i][i] = A[i]

See also: diag()

Definition at line 868 of file vpMatrix.cpp.

References vpArray2D< Type >::getRows(), and vpArray2D< Type >::resize().

◆ csvPrint()

std::ostream & vpMatrix::csvPrint ( std::ostream & os ) const

inherited

Print/save a matrix in csv format.

The following code

#include <visp3/core/vpMatrix.h>
int main()
{
  std::ofstream ofs("log.csv", std::ofstream::out);
  vpMatrix M(2,3);
  int cpt = 0;
  for (unsigned int i=0; i<M.getRows(); i++)
    for (unsigned int j=0; j<M.getCols(); j++)
      M[i][j] = cpt++;
  M.csvPrint(ofs);
  ofs.close();
}

produces log.csv file that contains:

0, 1, 2

3, 4, 5

Definition at line 4578 of file vpMatrix.cpp.

References vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().

Referenced by vpColVector::clear().

◆ det()

double vpMatrix::det ( vpDetMethod method = LU_DECOMPOSITION ) const

inherited

Compute the determinant of a n-by-n matrix.

Parameters

method : Method used to compute the determinant. Default LU decomposition method is faster than the method based on Gaussian elimination.

Returns: Determinant of the matrix.

#include <iostream>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(3,3);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.;
  A[1][0] = 1/3.; A[1][1] = 1/4.; A[1][2] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/7.; A[2][2] = 1/8.;
  std::cout << "Initial matrix: \n" << A << std::endl;
  // Compute the determinant
  std:: cout << "Determinant by default method           : " << A.det() << std::endl;
  std:: cout << "Determinant by LU decomposition         : " << A.detByLU() << std::endl;
  std:: cout << "Determinant by LU decomposition (Lapack): " << A.detByLULapack() << std::endl;
  std:: cout << "Determinant by LU decomposition (OpenCV): " << A.detByLUOpenCV() << std::endl;
  std:: cout << "Determinant by LU decomposition (GSL)   : " << A.detByLUGsl() << std::endl;
}

Examples:: testMatrixInverse.cpp.

Definition at line 5096 of file vpMatrix.cpp.

References vpMatrix::detByLU(), and vpMatrix::LU_DECOMPOSITION.

Referenced by vpTriangle::buildFrom(), vpHomography::computeDisplacement(), vpMatrix::detByLUGsl(), vpMatrix::detByLULapack(), vpMatrix::detByLUOpenCV(), and vpTemplateTrackerTriangle::init().

◆ detByLU()

double vpMatrix::detByLU ( ) const

inherited

Compute the determinant of a square matrix using the LU decomposition.

This function calls the first following function that is available:

detByLULapack() if Lapack 3rd party is installed
detByLUEigen3() if Eigen3 3rd party is installed
detByLUOpenCV() if OpenCV 3rd party is installed
detByLUGsl() if GSL 3rd party is installed.

If none of these previous 3rd parties is installed, we use by default detByLULapack() with a Lapack built-in version.

Returns: The determinant of the matrix if the matrix is square.

#include <iostream>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(3,3);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.;
  A[1][0] = 1/3.; A[1][1] = 1/4.; A[1][2] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/7.; A[2][2] = 1/8.;
  std::cout << "Initial matrix: \n" << A << std::endl;
  // Compute the determinant
  std:: cout << "Determinant by default method           : " << A.det() << std::endl;
  std:: cout << "Determinant by LU decomposition         : " << A.detByLU() << std::endl;
}

See also: detByLULapack(), detByLUEigen3(), detByLUOpenCV(), detByLUGsl()

Definition at line 184 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, vpMatrix::detByLUEigen3(), vpMatrix::detByLUGsl(), vpMatrix::detByLULapack(), vpMatrix::detByLUOpenCV(), vpException::fatalError, and vpArray2D< double >::rowNum.

Referenced by vpMatrix::det().

◆ detByLUEigen3()

double vpMatrix::detByLUEigen3 ( ) const

inherited

Compute the determinant of a square matrix using the LU decomposition with Eigen3 3rd party.

Returns: The determinant of the matrix if the matrix is square.

#include <iostream>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(3,3);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.;
  A[1][0] = 1/3.; A[1][1] = 1/4.; A[1][2] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/7.; A[2][2] = 1/8.;
  std::cout << "Initial matrix: \n" << A << std::endl;
  // Compute the determinant
  std:: cout << "Determinant by LU decomposition (Eigen3): " << A.detByLUEigen3() << std::endl;
}

See also: detByLU(), detByLUOpenCV(), detByLULapack()

Definition at line 628 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::data, vpException::fatalError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), and vpArray2D< double >::rowNum.

Referenced by vpMatrix::detByLU().

◆ detByLUGsl()

double vpMatrix::detByLUGsl ( ) const

inherited

Compute the determinant of a square matrix using the LU decomposition with GSL 3rd party.

Returns: The determinant of the matrix if the matrix is square.

#include <iostream>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(3,3);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.;
  A[1][0] = 1/3.; A[1][1] = 1/4.; A[1][2] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/7.; A[2][2] = 1/8.;
  std::cout << "Initial matrix: \n" << A << std::endl;
  // Compute the determinant
  std:: cout << "Determinant by LU decomposition (GSL): " << A.detByLUGsl() << std::endl;
}

See also: detByLU(), detByLUEigen3(), detByLUOpenCV(), detByLULapack()

Definition at line 305 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, vpMatrix::det(), vpException::fatalError, and vpArray2D< double >::rowNum.

Referenced by vpMatrix::detByLU().

◆ detByLULapack()

double vpMatrix::detByLULapack ( ) const

inherited

Compute the determinant of a square matrix using the LU decomposition with GSL 3rd party.

Returns: The determinant of the matrix if the matrix is square.

#include <iostream>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(3,3);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.;
  A[1][0] = 1/3.; A[1][1] = 1/4.; A[1][2] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/7.; A[2][2] = 1/8.;
  std::cout << "Initial matrix: \n" << A << std::endl;
  // Compute the determinant
  std:: cout << "Determinant by LU decomposition (Lapack): " << A.detByLULapack() << std::endl;
}

See also: detByLU(), detByLUEigen3(), detByLUGsl(), detByLUOpenCV()

Definition at line 425 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpMatrix::det(), vpException::fatalError, and vpArray2D< double >::rowNum.

Referenced by vpMatrix::detByLU().

◆ detByLUOpenCV()

double vpMatrix::detByLUOpenCV ( ) const

inherited

Compute the determinant of a n-by-n matrix using the LU decomposition with OpenCV 3rd party.

Returns: Determinant of the matrix.

#include <iostream>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(3,3);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.;
  A[1][0] = 1/3.; A[1][1] = 1/4.; A[1][2] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/7.; A[2][2] = 1/8.;
  std::cout << "Initial matrix: \n" << A << std::endl;
  // Compute the determinant
  std:: cout << "Determinant by LU decomposition (OpenCV): " << A.detByLUOpenCV() << std::endl;
}

See also: detByLU(), detByLUEigen3(), detByLUGsl(), detByLULapack()

Definition at line 537 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::data, vpMatrix::det(), vpException::fatalError, and vpArray2D< double >::rowNum.

Referenced by vpMatrix::detByLU().

◆ diag() [1/2]

void vpMatrix::diag ( const double & val = 1.0 )

inherited

Set the matrix as a diagonal matrix where each element on the diagonal is set to val. Elements that are not on the diagonal are set to 0.

Parameters

val	: Value to set.

See also: eye()

#include <iostream>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(3, 4);
  A.diag(2);
  std::cout << "A:\n" << A << std::endl;
}

Matrix A is now equal to:

0 0 0
2 0 0
0 2 0

Examples:: testSvd.cpp.

Definition at line 849 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, and vpArray2D< double >::rowNum.

Referenced by vpMbTracker::computeCovarianceMatrixVVS(), vpQuadProg::fromCanonicalCost(), and vpMatrix::getDiag().

◆ diag() [2/2]

void vpMatrix::diag ( const vpColVector & A )

inherited

Create a diagonal matrix with the element of a vector.

Parameters

A	: Vector which element will be put in the diagonal.

See also: createDiagonalMatrix()

#include <iostream>
#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A;
  vpColVector v(3);
  v[0] = 1;
  v[1] = 2;
  v[2] = 3;
  A.diag(v);
  std::cout << "A:\n" << A << std::endl;
}

Matrix A is now equal to:

0 0
2 0
0 3

Definition at line 809 of file vpMatrix.cpp.

References vpArray2D< Type >::getRows(), and vpArray2D< double >::resize().

◆ eigenValues() [1/2]

vpColVector vpMatrix::eigenValues ( ) const

inherited

Compute the eigenvalues of a n-by-n real symmetric matrix.

Returns: The eigenvalues of a n-by-n real symmetric matrix.

Warning: This method is only available if the Gnu Scientific Library (GSL) is detected as a third party library.

Exceptions

vpException::dimensionError	If the matrix is not square.
vpException::fatalError	If the matrix is not symmetric.
vpException::functionNotImplementedError	If the GSL library is not detected.

Here an example:

#include <iostream>
#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(3,3); // A is a symmetric matrix
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.;
  A[1][0] = 1/2.; A[1][1] = 1/3.; A[1][2] = 1/4.;
  A[2][0] = 1/3.; A[2][1] = 1/4.; A[2][2] = 1/5.;
  std::cout << "Initial symmetric matrix: \n" << A << std::endl;
  // Compute the eigen values
  vpColVector evalue; // Eigenvalues
  evalue = A.eigenValues();
  std::cout << "Eigen values: \n" << evalue << std::endl;
}

See also: eigenValues(vpColVector &, vpMatrix &)

Definition at line 4814 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::dimensionError, vpException::fatalError, vpException::functionNotImplementedError, vpArray2D< double >::rowNum, and vpMatrix::t().

Referenced by vpQuadProg::fromCanonicalCost().

◆ eigenValues() [2/2]

void vpMatrix::eigenValues	(	vpColVector &	evalue,
		vpMatrix &	evector
	)		const

inherited

Compute the eigenvalues of a n-by-n real symmetric matrix.

Returns: The eigenvalues of a n-by-n real symmetric matrix.

Warning: This method is only available if the Gnu Scientific Library (GSL) is detected as a third party library.

Parameters

evalue	: Eigenvalues of the matrix.
evector	: Eigenvector of the matrix.

Exceptions

vpException::dimensionError	If the matrix is not square.
vpException::fatalError	If the matrix is not symmetric.
vpException::functionNotImplementedError	If the GSL library is not detected.

Here an example:

#include <iostream>
#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(4,4); // A is a symmetric matrix
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.; A[0][3] = 1/4.;
  A[1][0] = 1/2.; A[1][1] = 1/3.; A[1][2] = 1/4.; A[1][3] = 1/5.;
  A[2][0] = 1/3.; A[2][1] = 1/4.; A[2][2] = 1/5.; A[2][3] = 1/6.;
  A[3][0] = 1/4.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  std::cout << "Initial symmetric matrix: \n" << A << std::endl;
  vpColVector d; // Eigenvalues
  vpMatrix    V; // Eigenvectors
  // Compute the eigenvalues and eigenvectors
  A.eigenValues(d, V);
  std::cout << "Eigen values: \n" << d << std::endl;
  std::cout << "Eigen vectors: \n" << V << std::endl;
  vpMatrix D;
  D.diag(d); // Eigenvalues are on the diagonal
  std::cout << "D: " << D << std::endl;
  // Verification: A * V = V * D
  std::cout << "AV-VD = 0 ? \n" << (A*V) - (V*D) << std::endl;
}

See also: eigenValues()

Definition at line 4925 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::dimensionError, vpException::fatalError, vpException::functionNotImplementedError, vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, and vpMatrix::t().

◆ euclideanNorm()

vp_deprecated double vpMatrix::euclideanNorm ( ) const

inherited

Deprecated:: This function is deprecated. You should rather use frobeniusNorm().

Compute and return the Euclidean norm (also called Frobenius norm) $||A|| = \sqrt{ \sum{A_{ij}^2}}$ .

Returns: The Euclidean norm (also called Frobenius norm) if the matrix is initialized, 0 otherwise.

See also: frobeniusNorm(), infinityNorm(), inducedL2Norm()

Definition at line 5326 of file vpMatrix.cpp.

References vpMatrix::frobeniusNorm().

Referenced by vpColVector::deg2rad().

◆ expm()

vpMatrix vpMatrix::expm ( ) const

inherited

Compute the exponential matrix of a square matrix.

Returns: Return the exponential matrix.

Definition at line 5114 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::data, vpArray2D< Type >::data, vpException::dimensionError, vpMatrix::eye(), vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrix::inverseByLU(), vpMatrix::row(), vpArray2D< double >::rowNum, and vpMatrix::sum().

Referenced by vpTemplateTrackerWarpHomographySL3::computeCoeff().

◆ extract()

vpMatrix vpMatrix::extract	(	unsigned int	r,
		unsigned int	c,
		unsigned int	nrows,
		unsigned int	ncols
	)		const

inherited

Extract a sub matrix from a matrix M.

Parameters

r	: row index in matrix M.
c	: column index in matrix M.
nrows	: Number of rows of the matrix that should be extracted.
ncols	: Number of columns of the matrix that should be extracted.

The following code shows how to use this function:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix M(4,5);
  int val = 0;
  for(size_t i=0; i<M.getRows(); i++) {
    for(size_t j=0; j<M.getCols(); j++) {
      M[i][j] = val++;
    }
  }
  M.print (std::cout, 4, "M ");
  vpMatrix N = M.extract(0, 1, 2, 3);
  N.print (std::cout, 4, "N ");
}

It produces the following output:

M [4,5]=
1  2  3  4
6  7  8  9
11 12 13 14
16 17 18 19
N [2,3]=
2 3
7 8

See also: init(const vpMatrix &, unsigned int, unsigned int, unsigned int, unsigned int)

Definition at line 399 of file vpMatrix.cpp.

References vpException::dimensionError, vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().

Referenced by vpLinProg::colReduction(), vpLinProg::rowReduction(), vpMatrix::solveByQR(), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().

◆ eye()

void vpMatrix::eye ( )

inherited

Set an m-by-n matrix to identity with ones on the diagonal and zeros else where.

Examples:: testMatrix.cpp, testMatrixConditionNumber.cpp, and testMatrixInverse.cpp.

Definition at line 440 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, and vpArray2D< double >::rowNum.

Referenced by vpLinProg::colReduction(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrixVVS(), vpServo::computeProjectionOperators(), vpMbDepthDenseTracker::computeVVS(), vpMbDepthNormalTracker::computeVVS(), vpMbGenericTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpMbEdgeMultiTracker::computeVVSFirstPhasePoseEstimation(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbTracker::computeVVSPoseEstimation(), vpMatrix::expm(), vpMatrix::eye(), vpTemplateTrackerWarpHomographySL3::getdW0(), vpTemplateTrackerWarpHomographySL3::getdWdp0(), vpFeatureThetaU::interaction(), vpMeLine::leastSquare(), vpPose::poseFromRectangle(), vpMeEllipse::printParameters(), vpServo::setServo(), vpLinProg::solveLP(), vpMbGenericTracker::track(), vpMbTracker::vpMbTracker(), vpRobotCamera::vpRobotCamera(), vpServo::vpServo(), vpSimulatorCamera::vpSimulatorCamera(), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().

◆ frobeniusNorm()

double vpMatrix::frobeniusNorm ( ) const

inherited

Compute and return the Frobenius norm (also called Euclidean norm) $||A|| = \sqrt{ \sum{A_{ij}^2}}$ .

Returns: The Frobenius norm (also called Euclidean norm) if the matrix is initialized, 0 otherwise.

See also: infinityNorm(), inducedL2Norm()

Examples:: testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 5338 of file vpMatrix.cpp.

References vpArray2D< double >::data, and vpArray2D< double >::dsize.

Referenced by vpMatrix::euclideanNorm(), and vpColVector::extract().

◆ getCol() [1/2]

vpColVector vpMatrix::getCol ( const unsigned int j ) const

inherited

Extract a column vector from a matrix.

Warning: All the indexes start from 0 in this function.

Parameters

j	: Index of the column to extract. If j=0, the first column is extracted.

Returns: The extracted column vector.

The following example shows how to use this function:

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(4,4);
  for(unsigned int i=0; i < A.getRows(); i++)
    for(unsigned int j=0; j < A.getCols(); j++)
      A[i][j] = i*A.getCols()+j;
  A.print(std::cout, 4);
  vpColVector cv = A.getCol(1);
  std::cout << "Column vector: \n" << cv << std::endl;
}

It produces the following output:

[4,4]=
   0  1  2  3
   4  5  6  7
   8  9 10 11
  12 13 14 15
column vector:
1
5
9
13

Examples:: testMatrix.cpp.

Definition at line 3947 of file vpMatrix.cpp.

References vpArray2D< double >::rowNum.

Referenced by vpLinProg::colReduction(), vpHomography::DLT(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), vpMatrix::kernel(), vpPose::poseFromRectangle(), vpServo::secondaryTaskJointLimitAvoidance(), and vpLinProg::simplex().

◆ getCol() [2/2]

vpColVector vpMatrix::getCol	(	const unsigned int	j,
		const unsigned int	i_begin,
		const unsigned int	column_size
	)		const

inherited

Extract a column vector from a matrix.

Warning: All the indexes start from 0 in this function.

Parameters

j	: Index of the column to extract. If col=0, the first column is extracted.
i_begin	: Index of the row that gives the location of the first element of the column vector to extract.
column_size	: Size of the column vector to extract.

Returns: The extracted column vector.

The following example shows how to use this function:

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(4,4);
  for(unsigned int i=0; i < A.getRows(); i++)
    for(unsigned int j=0; j < A.getCols(); j++)
      A[i][j] = i*A.getCols()+j;
  A.print(std::cout, 4);
  vpColVector cv = A.getCol(1, 1, 3);
  std::cout << "Column vector: \n" << cv << std::endl;
}

It produces the following output:

[4,4]=
   0  1  2  3
   4  5  6  7
   8  9 10 11
  12 13 14 15
column vector:
5
9
13

Definition at line 3898 of file vpMatrix.cpp.

References vpException::dimensionError, vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().

◆ getCols()

unsigned int vpArray2D< double >::getCols ( ) const

inlineinherited

Return the number of columns of the 2D array.

See also: getRows(), size()

Examples:: servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, testColVector.cpp, testDisplacement.cpp, testImageFilter.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, testTranslationVector.cpp, and tutorial-matlab.cpp.

Definition at line 279 of file vpArray2D.h.

References vpArray2D< Type >::colNum, vpArray2D< Type >::getMaxValue(), and vpArray2D< Type >::getMinValue().

Referenced by vpMatrix::cond(), vpRowVector::cppPrint(), vpMatrix::cppPrint(), vpRowVector::csvPrint(), vpMatrix::csvPrint(), vpMatrix::detByLUEigen3(), vpMatrix::extract(), vpRotationMatrix::getCol(), vpHomogeneousMatrix::getCol(), vpMatrix::getCol(), vpMatrix::inducedL2Norm(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByQRLapack(), vpRotationMatrix::isARotationMatrix(), vpMatrix::kernel(), vpRowVector::maplePrint(), vpMatrix::maplePrint(), vpRowVector::matlabPrint(), vpMatrix::matlabPrint(), vpRowVector::operator*(), vpRowVector::operator+(), vpRowVector::operator+=(), vpRowVector::operator-(), vpRowVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpRowVector::print(), vpMatrix::print(), vpMatrix::pseudoInverse(), vpMatrix::row(), vpMatrix::svdEigen3(), vpMatrix::svdGsl(), vpMatrix::svdLapack(), and vpMatrix::svdOpenCV().

◆ getDiag()

vpColVector vpMatrix::getDiag ( ) const

inherited

Extract a diagonal vector from a matrix.

Returns: The diagonal of the matrix.

Warning: An empty vector is returned if the matrix is empty.

The following example shows how to use this function:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(3,4);
  for(unsigned int i=0; i < A.getRows(); i++)
    for(unsigned int j=0; j < A.getCols(); j++)
      A[i][j] = i*A.getCols()+j;
  A.print(std::cout, 4);
  vpColVector diag = A.getDiag();
  std::cout << "Diag vector: \n" << diag.t() << std::endl;
}

It produces the following output:

[3,4]=
   0  1  2  3
   4  5  6  7
   8  9 10 11
Diag vector:
0  5  10

Examples:: testMatrix.cpp.

Definition at line 4079 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpMatrix::diag(), vpColVector::resize(), and vpArray2D< double >::rowNum.

◆ getMaxValue()

double vpArray2D< double >::getMaxValue ( ) const

inherited

Return the array max value.

Examples:: servoMomentImage.cpp, and testArray2D.cpp.

Definition at line 914 of file vpArray2D.h.

References vpArray2D< Type >::data.

◆ getMinValue()

double vpArray2D< double >::getMinValue ( ) const

inherited

Return the array min value.

Examples:: servoMomentImage.cpp, and testArray2D.cpp.

Definition at line 897 of file vpArray2D.h.

References vpArray2D< Type >::data.

◆ getRow() [1/2]

vpRowVector vpMatrix::getRow ( const unsigned int i ) const

inherited

Extract a row vector from a matrix.

Warning: All the indexes start from 0 in this function.

Parameters

i	: Index of the row to extract. If i=0, the first row is extracted.

Returns: The extracted row vector.

The following example shows how to use this function:

#include <visp3/core/vpMatrix.h>
#include <visp3/core/vpRowVector.h>
int main()
{
  vpMatrix A(4,4);
  for(unsigned int i=0; i < A.getRows(); i++)
    for(unsigned int j=0; j < A.getCols(); j++)
      A[i][j] = i*A.getCols()+j;
  A.print(std::cout, 4);
  vpRowVector rv = A.getRow(1);
  std::cout << "Row vector: \n" << rv << std::endl;
}  

It produces the following output:

[4,4]=
1  2  3
5  6  7
9 10 11
13 14 15
Row vector:
5  6  7

Examples:: testMatrix.cpp.

Definition at line 3987 of file vpMatrix.cpp.

References vpArray2D< double >::colNum.

Referenced by vpLinProg::allClose(), vpLinProg::allLesser(), vpLinProg::solveLP(), and vpQuadProg::solveQPi().

◆ getRow() [2/2]

vpRowVector vpMatrix::getRow	(	const unsigned int	i,
		const unsigned int	j_begin,
		const unsigned int	row_size
	)		const

inherited

Extract a row vector from a matrix.

Warning: All the indexes start from 0 in this function.

Parameters

i	: Index of the row to extract. If i=0, the first row is extracted.
j_begin	: Index of the column that gives the location of the first element of the row vector to extract.
row_size	: Size of the row vector to extract.

Returns: The extracted row vector.

The following example shows how to use this function:

#include <visp3/core/vpMatrix.h>
#include <visp3/core/vpRowVector.h>
int main()
{
  vpMatrix A(4,4);
  for(unsigned int i=0; i < A.getRows(); i++)
    for(unsigned int j=0; j < A.getCols(); j++)
      A[i][j] = i*A.getCols()+j;
  A.print(std::cout, 4);
  vpRowVector rv = A.getRow(1, 1, 3);
  std::cout << "Row vector: \n" << rv << std::endl;
}

It produces the following output:

[4,4]=
1  2  3
5  6  7
9 10 11
13 14 15
Row vector:
6  7

Definition at line 4031 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::data, vpArray2D< Type >::data, vpException::dimensionError, and vpArray2D< double >::rowNum.

◆ getRows()

unsigned int vpArray2D< double >::getRows ( ) const

inlineinherited

Return the number of rows of the 2D array.

See also: getCols(), size()

Examples:: mbtGenericTrackingDepth.cpp, mbtGenericTrackingDepthOnly.cpp, testColVector.cpp, testDisplacement.cpp, testGenericTracker.cpp, testGenericTrackerDepth.cpp, testImageFilter.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, testTranslationVector.cpp, tutorial-matlab.cpp, tutorial-mb-generic-tracker-rgbd-blender.cpp, and tutorial-mb-generic-tracker-rgbd-realsense.cpp.

Definition at line 289 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

Referenced by vpMatrix::column(), vpMatrix::cond(), vpColVector::cppPrint(), vpMatrix::cppPrint(), vpColVector::csvPrint(), vpMatrix::csvPrint(), vpMatrix::detByLUEigen3(), vpMatrix::extract(), vpRotationMatrix::getCol(), vpHomogeneousMatrix::getCol(), vpMatrix::getCol(), vpMatrix::inducedL2Norm(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByQRLapack(), vpRotationMatrix::isARotationMatrix(), vpMatrix::kernel(), vpColVector::maplePrint(), vpMatrix::maplePrint(), vpColVector::matlabPrint(), vpMatrix::matlabPrint(), vpColVector::operator+(), vpColVector::operator+=(), vpColVector::operator-(), vpColVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpPoseVector::print(), vpColVector::print(), vpMatrix::print(), vpMatrix::pseudoInverse(), vpMatrix::svdEigen3(), vpMatrix::svdGsl(), vpMatrix::svdLapack(), and vpMatrix::svdOpenCV().

◆ hadamard() [1/2]

vpMatrix vpMatrix::hadamard ( const vpMatrix & m ) const

inherited

Compute the Hadamard product (element wise matrix multiplication).

Parameters

m	: Second matrix;

Returns: m1.hadamard(m2) The Hadamard product : $m1 \circ m2 = (m1 \circ m2)_{i,j} = (m1)_{i,j} (m2)_{i,j}$

Examples:: testMatrix.cpp.

Definition at line 1665 of file vpMatrix.cpp.

References vpCPUFeatures::checkSSE2(), vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::dimensionError, vpArray2D< double >::dsize, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::resize(), and vpArray2D< double >::rowNum.

◆ hadamard() [2/2]

vpArray2D< double > vpArray2D< double >::hadamard ( const vpArray2D< double > & m ) const

inherited

Compute the Hadamard product (element wise matrix multiplication).

Parameters

m	: Second matrix;

Returns: m1.hadamard(m2) The Hadamard product : $m1 \circ m2 = (m1 \circ m2)_{i,j} = (m1)_{i,j} (m2)_{i,j}$

Examples:: testArray2D.cpp.

Definition at line 934 of file vpArray2D.h.

References vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpException::dimensionError, vpArray2D< Type >::dsize, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), and vpArray2D< Type >::resize().

◆ inducedL2Norm()

double vpMatrix::inducedL2Norm ( ) const

inherited

Compute and return the induced L2 norm $||A|| = \Sigma_{max}(A)$ which is equal to the maximum singular value of the matrix.

Returns: The induced L2 norm if the matrix is initialized, 0 otherwise.

See also: infinityNorm(), frobeniusNorm()

Examples:: testMatrixConditionNumber.cpp.

Definition at line 5357 of file vpMatrix.cpp.

References vpArray2D< double >::dsize, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpArray2D< Type >::size(), and vpMatrix::svd().

◆ infinityNorm()

double vpMatrix::infinityNorm ( ) const

inherited

Compute and return the infinity norm ${||A||}_{\infty} = max\left(\sum_{j=0}^{n}{\mid A_{ij} \mid}\right)$ with $i \in \{0, ..., m\}$ where $(m,n)$ is the matrix size.

Returns: The infinity norm if the matrix is initialized, 0 otherwise.

See also: frobeniusNorm(), inducedL2Norm()

Definition at line 5398 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

Referenced by vpLinProg::colReduction(), and vpColVector::extract().

◆ init() [1/3]

void vpSubMatrix::init	(	vpMatrix &	m,
		const unsigned int &	row_offset,
		const unsigned int &	col_offset,
		const unsigned int &	nrows,
		const unsigned int &	ncols
	)

Initialisation of vpMatrix.

Initialisation of a sub matrix.

Parameters

m	: parent matrix
row_offset	: row offset
col_offset	: col offset
nrows	: number of rows of the sub matrix
ncols	: number of columns of the sub matrix

Definition at line 70 of file vpSubMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpArray2D< double >::dsize, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrixException::incorrectMatrixSizeError, parent, pColNum, pRowNum, vpArray2D< double >::rowNum, vpArray2D< double >::rowPtrs, and vpMatrixException::subMatrixError.

◆ init() [2/3]

void vpMatrix::init	(	const vpMatrix &	M,
		unsigned int	r,
		unsigned int	c,
		unsigned int	nrows,
		unsigned int	ncols
	)

inherited

Initialize the matrix from a part of an input matrix M.

Parameters

M	: Input matrix used for initialization.
r	: row index in matrix M.
c	: column index in matrix M.
nrows	: Number of rows of the matrix that should be initialized.
ncols	: Number of columns of the matrix that should be initialized.

The sub-matrix starting from M[r][c] element and ending on M[r+nrows-1][c+ncols-1] element is used to initialize the matrix.

The following code shows how to use this function:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix M(4,5);
  int val = 0;
  for(size_t i=0; i<M.getRows(); i++) {
    for(size_t j=0; j<M.getCols(); j++) {
      M[i][j] = val++;
    }
  }
  M.print (std::cout, 4, "M ");
  vpMatrix N;
  N.init(M, 0, 1, 2, 3);
  N.print (std::cout, 4, "N ");
}

It produces the following output:

M [4,5]=
1  2  3  4
6  7  8  9
11 12 13 14
16 17 18 19
N [2,3]=
2 3
7 8

See also: extract()

Examples:: testMatrix.cpp.

Definition at line 338 of file vpMatrix.cpp.

References vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::resize(), and vpArray2D< double >::rowPtrs.

◆ init() [3/3]

vp_deprecated void vpMatrix::init ( )

inlineinherited

Deprecated:: Only provided for compatibilty with ViSP previous releases. This function does nothing.

Definition at line 760 of file vpMatrix.h.

Referenced by vpColVector::extract(), vpMatrix::vpMatrix(), and vpSubMatrix().

◆ insert() [1/3]

void vpMatrix::insert	(	const vpMatrix &	A,
		const unsigned int	r,
		const unsigned int	c
	)

inherited

Insert matrix A at the given position in the current matrix.

Warning: Throw vpException::dimensionError if the dimensions of the matrices do not allow the operation.

Parameters

A	: The matrix to insert.
r	: The index of the row to begin to insert data.
c	: The index of the column to begin to insert data.

Examples:: testMatrix.cpp, and testMatrixPseudoInverse.cpp.

Definition at line 4760 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::rowNum, and vpArray2D< Type >::size().

Referenced by vpMbEdgeKltTracker::computeVVS(), vpMbEdgeMultiTracker::computeVVS(), vpMbDepthDenseTracker::computeVVSInteractionMatrixAndResidu(), vpMbDepthNormalTracker::computeVVSInteractionMatrixAndResidu(), vpMbKltMultiTracker::computeVVSInteractionMatrixAndResidu(), vpMbEdgeMultiTracker::computeVVSInteractionMatrixAndResidu(), vpMbEdgeKltMultiTracker::computeVVSInteractionMatrixAndResidu(), vpMbGenericTracker::computeVVSInteractionMatrixAndResidu(), vpMatrix::cond(), vpMatrix::conv2(), vpNurbs::curveKnotIns(), vpColVector::extract(), vpMatrix::insert(), vpMatrix::juxtaposeMatrices(), vpMatrix::kernel(), vpMatrix::pseudoInverse(), vpMatrix::stack(), vpColVector::stackMatrices(), and vpMbGenericTracker::track().

◆ insert() [2/3]

vpMatrix vpMatrix::insert	(	const vpMatrix &	A,
		const vpMatrix &	B,
		const unsigned int	r,
		const unsigned int	c
	)

staticinherited

Insert matrix B in matrix A at the given position.

Parameters

A	: Main matrix.
B	: Matrix to insert.
r	: Index of the row where to add the matrix.
c	: Index of the column where to add the matrix.

Returns: Matrix with B insert in A.

Warning: Throw exception if the sizes of the matrices do not allow the insertion.

Definition at line 4250 of file vpMatrix.cpp.

References vpMatrix::insert().

◆ insert() [3/3]

void insert	(	const vpMatrix &	A,
		const vpMatrix &	B,
		vpMatrix &	C,
		const unsigned int	r,
		const unsigned int	c
	)

staticinherited

Insert matrix B in matrix A at the given position.

Parameters

A	: Main matrix.
B	: Matrix to insert.
C	: Result matrix.
r	: Index of the row where to insert matrix B.
c	: Index of the column where to insert matrix B.

Warning: Throw exception if the sizes of the matrices do not allow the insertion.

Definition at line 4272 of file vpMatrix.cpp.

References vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), and vpArray2D< Type >::resize().

◆ inverseByCholesky()

vpMatrix vpMatrix::inverseByCholesky ( ) const

inherited

Compute the inverse of a n-by-n matrix using the Cholesky decomposition. The matrix must be real symmetric positive defined.

This function calls the first following function that is available:

inverseByCholeskyLapack() if Lapack 3rd party is installed
inverseByLUOpenCV() if OpenCV 3rd party is installed.

If none of these 3rd parties is installed we use a Lapack built-in version.

Returns: The inverse matrix.

Here an example:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(4,4);
  // Symmetric matrix
  A[0][0] = 1/1.; A[0][1] = 1/5.; A[0][2] = 1/6.; A[0][3] = 1/7.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/3.; A[2][2] = 1/2.; A[2][3] = 1/6.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  // Compute the inverse
  vpMatrix A_1; // A^-1
  A_1 = A.inverseByCholesky();
  std::cout << "Inverse by Cholesky: \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See also: pseudoInverse()

Definition at line 109 of file vpMatrix_cholesky.cpp.

References vpException::fatalError, vpMatrix::inverseByCholeskyLapack(), and vpMatrix::inverseByCholeskyOpenCV().

◆ inverseByCholeskyLapack()

vpMatrix vpMatrix::inverseByCholeskyLapack ( ) const

inherited

Compute the inverse of a n-by-n matrix using the Cholesky decomposition with Lapack 3rd party. The matrix must be real symmetric positive defined.

Returns: The inverse matrix.

Here an example:

#include <visp3/core/vpMatrix.h>
int main()
{
  unsigned int n = 4;
  vpMatrix A(n, n);
  vpMatrix I;
  I.eye(4);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.; A[0][3] = 1/4.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.; A[2][3] = 1/6.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  // Make matrix symmetric positive
  A = 0.5*(A+A.t());
  A = A + n*I;
  // Compute the inverse
  vpMatrix A_1 = A.inverseByCholeskyLapack();
  std::cout << "Inverse by Cholesky (Lapack): \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See also: inverseByCholesky(), inverseByCholeskyOpenCV()

Definition at line 159 of file vpMatrix_cholesky.cpp.

References vpException::badValue, vpArray2D< double >::colNum, vpArray2D< Type >::data, vpException::fatalError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::getRows(), vpMatrixException::matrixError, and vpArray2D< double >::rowNum.

Referenced by vpMatrix::inverseByCholesky().

◆ inverseByCholeskyOpenCV()

vpMatrix vpMatrix::inverseByCholeskyOpenCV ( ) const

inherited

Compute the inverse of a n-by-n matrix using the Cholesky decomposition with OpenCV 3rd party. The matrix must be real symmetric positive defined.

Returns: The inverse matrix.

Here an example:

#include <visp3/core/vpMatrix.h>
int main()
{
  unsigned int n = 4;
  vpMatrix A(n, n);
  vpMatrix I;
  I.eye(4);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.; A[0][3] = 1/4.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.; A[2][3] = 1/6.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  // Make matrix symmetric positive
  A = 0.5*(A+A.t());
  A = A + n*I;
  // Compute the inverse
  vpMatrix A_1 = A.inverseByCholeskyOpenCV();
  std::cout << "Inverse by Cholesky (OpenCV): \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See also: inverseByCholesky(), inverseByCholeskyLapack()

Definition at line 228 of file vpMatrix_cholesky.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::fatalError, and vpArray2D< double >::rowNum.

Referenced by vpMatrix::inverseByCholesky().

◆ inverseByLU()

vpMatrix vpMatrix::inverseByLU ( ) const

inherited

Compute the inverse of a n-by-n matrix using the LU decomposition.

This function calls the first following function that is available:

inverseByLULapack() if Lapack 3rd party is installed
inverseByLUEigen3() if Eigen3 3rd party is installed
inverseByLUOpenCV() if OpenCV 3rd party is installed
inverseByLUGsl() if GSL 3rd party is installed.

If none of these previous 3rd parties is installed, we use by default inverseByLULapack() with a Lapack built-in version.

Returns: The inverse matrix.

Here an example:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(4,4);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.; A[0][3] = 1/4.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.; A[2][3] = 1/6.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  // Compute the inverse
  vpMatrix A_1 = A.inverseByLU();
  std::cout << "Inverse by LU ";
#if defined(VISP_HAVE_LAPACK)
  std::cout << "(using Lapack)";
#elif defined(VISP_HAVE_EIGEN3)
  std::cout << "(using Eigen3)";
#elif (VISP_HAVE_OPENCV_VERSION >= 0x020101)
  std::cout << "(using OpenCV)";
#elif defined (VISP_HAVE_GSL)
  std::cout << "(using GSL)";
#endif
  std::cout << ": \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See also: inverseByLULapack(), inverseByLUEigen3(), inverseByLUOpenCV(), inverseByLUGsl(), pseudoInverse()

Examples:: photometricVisualServoing.cpp, and testMatrixConditionNumber.cpp.

Definition at line 134 of file vpMatrix_lu.cpp.

References vpException::fatalError, vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByLUGsl(), vpMatrix::inverseByLULapack(), and vpMatrix::inverseByLUOpenCV().

◆ inverseByLUEigen3()

vpMatrix vpMatrix::inverseByLUEigen3 ( ) const

inherited

Compute the inverse of a n-by-n matrix using the LU decomposition with Eigen3 3rd party.

Returns: The inverse matrix.

Here an example:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(4,4);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.; A[0][3] = 1/4.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.; A[2][3] = 1/6.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  // Compute the inverse
  vpMatrix A_1; // A^-1
  A_1 = A.inverseByLUEigen3();
  std::cout << "Inverse by LU (Eigen3): \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See also: inverseByLU(), inverseByLULapack(), inverseByLUOpenCV(), inverseByLUGsl()

Definition at line 586 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::fatalError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), and vpArray2D< double >::rowNum.

Referenced by vpMatrix::inverseByLU().

◆ inverseByLUGsl()

vpMatrix vpMatrix::inverseByLUGsl ( ) const

inherited

Compute the inverse of a n-by-n matrix using the LU decomposition with GSL 3rd party.

Returns: The inverse matrix.

Here an example:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(4,4);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.; A[0][3] = 1/4.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.; A[2][3] = 1/6.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  // Compute the inverse
  vpMatrix A_1; // A^-1
  A_1 = A.inverseByLUGsl();
  std::cout << "Inverse by LU (GSL): \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See also: inverseByLU(), inverseByLUEigen3(), inverseByLULapack(), inverseByLUOpenCV()

Definition at line 241 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpException::fatalError, and vpArray2D< double >::rowNum.

Referenced by vpMatrix::inverseByLU().

◆ inverseByLULapack()

vpMatrix vpMatrix::inverseByLULapack ( ) const

inherited

Compute the inverse of a n-by-n matrix using the LU decomposition with Lapack 3rd party.

Returns: The inverse matrix.

Here an example:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(4,4);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.; A[0][3] = 1/4.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.; A[2][3] = 1/6.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  // Compute the inverse
  vpMatrix A_1; // A^-1
  A_1 = A.inverseByLULapack();
  std::cout << "Inverse by LU (Lapack): \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See also: inverseByLU(), inverseByLUEigen3(), inverseByLUGsl(), inverseByLUOpenCV()

Definition at line 370 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpException::fatalError, and vpArray2D< double >::rowNum.

Referenced by vpMatrix::inverseByLU().

◆ inverseByLUOpenCV()

vpMatrix vpMatrix::inverseByLUOpenCV ( ) const

inherited

Compute the inverse of a n-by-n matrix using the LU decomposition with OpenCV 3rd party.

Returns: The inverse matrix.

Here an example:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(4,4);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.; A[0][3] = 1/4.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.; A[2][3] = 1/6.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  // Compute the inverse
  vpMatrix A_1; // A^-1
  A_1 = A.inverseByLUOpenCV();
  std::cout << "Inverse by LU (OpenCV): \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See also: inverseByLU(), inverseByLUEigen3(), inverseByLUGsl(), inverseByLULapack()

Definition at line 496 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::fatalError, and vpArray2D< double >::rowNum.

Referenced by vpMatrix::inverseByLU().

◆ inverseByQR()

vpMatrix vpMatrix::inverseByQR ( ) const

inherited

Compute the inverse of a n-by-n matrix using the QR decomposition. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.

Returns: The inverse matrix.

Here an example:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(4,4);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.; A[0][3] = 1/4.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.; A[2][3] = 1/6.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  // Compute the inverse
  vpMatrix A_1 = A.inverseByQR();
  std::cout << "Inverse by QR: \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See also: inverseByLU(), inverseByCholesky()

Definition at line 285 of file vpMatrix_qr.cpp.

References vpException::fatalError, and vpMatrix::inverseByQRLapack().

Referenced by vpLinProg::simplex().

◆ inverseByQRLapack()

vpMatrix vpMatrix::inverseByQRLapack ( ) const

inherited

Compute the inverse of a n-by-n matrix using the QR decomposition with Lapack 3rd party.

Returns: The inverse matrix.

Here an example:

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(4,4);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.; A[0][3] = 1/4.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.; A[2][3] = 1/6.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  // Compute the inverse
  vpMatrix A_1 = A.inverseByQRLapack();
  std::cout << "Inverse by QR: \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See also: inverseByQR()

Definition at line 124 of file vpMatrix_qr.cpp.

References vpException::badValue, vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpArray2D< Type >::getRows(), vpMatrixException::matrixError, and vpArray2D< double >::rowNum.

Referenced by vpMatrix::inverseByQR().

◆ inverseTriangular()

vpMatrix vpMatrix::inverseTriangular ( bool upper = true ) const

inherited

Compute the inverse of a full-rank n-by-n triangular matrix. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.

Parameters

upper : if it is an upper triangular matrix

The function does not check if the matrix is actually upper or lower triangular.

Returns: The inverse matrix

Definition at line 725 of file vpMatrix_qr.cpp.

References vpException::badValue, vpArray2D< double >::colNum, vpArray2D< Type >::data, vpException::dimensionError, vpException::fatalError, vpMatrixException::rankDeficient, and vpArray2D< double >::rowNum.

Referenced by vpLinProg::colReduction(), vpLinProg::rowReduction(), and vpMatrix::solveByQR().

◆ juxtaposeMatrices() [1/2]

vpMatrix vpMatrix::juxtaposeMatrices	(	const vpMatrix &	A,
		const vpMatrix &	B
	)

staticinherited

Juxtapose to matrices C = [ A B ].

$C = \left( \begin{array}{cc} A & B \end{array}\right)$

Parameters

A	: Left matrix.
B	: Right matrix.

Returns: Juxtaposed matrix C = [ A B ]

Warning: A and B must have the same number of rows.

Examples:: testMatrix.cpp.

Definition at line 4303 of file vpMatrix.cpp.

Referenced by vpLinProg::colReduction().

◆ juxtaposeMatrices() [2/2]

void juxtaposeMatrices	(	const vpMatrix &	A,
		const vpMatrix &	B,
		vpMatrix &	C
	)

staticinherited

Juxtapose to matrices C = [ A B ].

$C = \left( \begin{array}{cc} A & B \end{array}\right)$

Parameters

A	: Left matrix.
B	: Right matrix.
C	: Juxtaposed matrix C = [ A B ]

Warning: A and B must have the same number of rows.

Definition at line 4324 of file vpMatrix.cpp.

References vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrix::insert(), and vpArray2D< Type >::resize().

◆ kernel()

unsigned int vpMatrix::kernel	(	vpMatrix &	kerAt,
		double	svThreshold = `1e-6`
	)		const

inherited

Function to compute the null space (the kernel) of a m-by-n matrix $\bf A$ .

The null space of a matrix $\bf A$ is defined as $\mbox{Ker}({\bf A}) = { {\bf X} : {\bf A}*{\bf X} = {\bf 0}}$ .

Parameters

kerAt	The matrix that contains the null space (kernel) of $\bf A$ defined by the matrix ${\bf X}^T$ . If matrix $\bf A$ is full rank, the dimension of `kerAt` is (0, n), otherwise the dimension is (n-r, n). This matrix is thus the transpose of $\mbox{Ker}({\bf A})$ .
svThreshold	Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.

Returns: The rank r of the matrix.

Examples:: servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, and testMatrixConditionNumber.cpp.

Definition at line 5011 of file vpMatrix.cpp.

References vpMatrix::getCol(), vpArray2D< double >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::getRows(), vpMatrix::insert(), vpArray2D< Type >::resize(), vpColVector::sumSquare(), and vpMatrix::svd().

◆ kron() [1/4]

void vpMatrix::kron	(	const vpMatrix &	m,
		vpMatrix &	out
	)		const

inherited

Compute Kronecker product matrix.

Parameters

m	: vpMatrix.
out	: If m1.kron(m2) out contains the kronecker product's result : $m1 \otimes m2$ .

Definition at line 1728 of file vpMatrix.cpp.

Referenced by vpMatrix::kron().

◆ kron() [2/4]

vpMatrix vpMatrix::kron ( const vpMatrix & m ) const

inherited

Compute Kronecker product matrix.

Parameters

m	: vpMatrix;

Returns: m1.kron(m2) The kronecker product : $m1 \otimes m2$

Definition at line 1766 of file vpMatrix.cpp.

References vpMatrix::kron().

◆ kron() [3/4]

void vpMatrix::kron	(	const vpMatrix &	m1,
		const vpMatrix &	m2,
		vpMatrix &	out
	)

staticinherited

Compute Kronecker product matrix.

Parameters

m1	: vpMatrix;
m2	: vpMatrix;
out	: The kronecker product : $m1 \otimes m2$

Definition at line 1698 of file vpMatrix.cpp.

References vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), and vpArray2D< Type >::resize().

◆ kron() [4/4]

vpMatrix vpMatrix::kron	(	const vpMatrix &	m1,
		const vpMatrix &	m2
	)

staticinherited

Compute Kronecker product matrix.

Parameters

m1	: vpMatrix;
m2	: vpMatrix;

Returns: The kronecker product : $m1 \otimes m2$

Definition at line 1736 of file vpMatrix.cpp.

References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().

◆ load()

static bool vpArray2D< double >::load	(	const std::string &	filename,
		vpArray2D< double > &	A,
		const bool	binary = `false`,
		char *	header = `NULL`
	)

inlinestaticinherited

Load a matrix from a file.

Parameters

filename	: Absolute file name.
A	: Array to be loaded
binary	: If true the matrix is loaded from a binary file, else from a text file.
header	: Header of the file is loaded in this parameter.

Returns: Returns true if success.

See also: save()

Definition at line 542 of file vpArray2D.h.

References vpException::badValue, and vpArray2D< Type >::resize().

◆ loadMatrix()

static bool vpMatrix::loadMatrix	(	const std::string &	filename,
		vpArray2D< double > &	M,
		const bool	binary = `false`,
		char *	header = `NULL`
	)

inlinestaticinherited

Load a matrix from a file. This function overloads vpArray2D::load().

Parameters

filename	: absolute file name.
M	: matrix to be loaded.
binary	:If true the matrix is loaded from a binary file, else from a text file.
header	: Header of the file is loaded in this parameter

Returns: Returns true if no problem appends.

Examples:: testMatrix.cpp.

Definition at line 692 of file vpMatrix.h.

References vpArray2D< Type >::load().

Referenced by vpDot2::defineDots().

◆ loadMatrixYAML()

static bool vpMatrix::loadMatrixYAML	(	const std::string &	filename,
		vpArray2D< double > &	M,
		char *	header = `NULL`
	)

inlinestaticinherited

Load a matrix from a YAML-formatted file. This function overloads vpArray2D::loadYAML().

Parameters

filename	: absolute file name.
M	: matrix to be loaded from the file.
header	: Header of the file is loaded in this parameter.

Returns: Returns true if no problem appends.

Examples:: testMatrix.cpp.

Definition at line 708 of file vpMatrix.h.

References vpArray2D< Type >::loadYAML().

◆ loadYAML()

static bool vpArray2D< double >::loadYAML	(	const std::string &	filename,
		vpArray2D< double > &	A,
		char *	header = `NULL`
	)

inlinestaticinherited

Load an array from a YAML-formatted file.

Parameters

filename	: absolute file name.
A	: array to be loaded from the file.
header	: header of the file is loaded in this parameter.

Returns: Returns true on success.

See also: saveYAML()

Examples:: servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, and tutorial-hand-eye-calibration.cpp.

Definition at line 654 of file vpArray2D.h.

References vpArray2D< Type >::resize().

◆ maplePrint()

std::ostream & vpMatrix::maplePrint ( std::ostream & os ) const

inherited

Print using Maple syntax, to copy/paste in Maple later.

The following code

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix M(2,3);
  int cpt = 0;
  for (unsigned int i=0; i<M.getRows(); i++)
    for (unsigned int j=0; j<M.getCols(); j++)
      M[i][j] = cpt++;
  std::cout << "M = "; M.maplePrint(std::cout);
}

produces this output:

M = ([
[0, 1, 2, ],
[3, 4, 5, ],
])

that could be copy/paste in Maple.

Definition at line 4537 of file vpMatrix.cpp.

References vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().

Referenced by vpColVector::extract().

◆ matlabPrint()

std::ostream & vpMatrix::matlabPrint ( std::ostream & os ) const

inherited

Print using Matlab syntax, to copy/paste in Matlab later.

The following code

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix M(2,3);
  int cpt = 0;
  for (unsigned int i=0; i<M.getRows(); i++)
    for (unsigned int j=0; j<M.getCols(); j++)
      M[i][j] = cpt++;
  std::cout << "M = "; M.matlabPrint(std::cout);
}

produces this output:

M = [ 0, 1, 2, ;

3, 4, 5, ]

that could be copy/paste in Matlab:

>> M = [ 0, 1, 2, ;
3, 4, 5, ]
M =
    0    1    2
    3    4    5
>>

Definition at line 4493 of file vpMatrix.cpp.

References vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().

Referenced by vpColVector::extract().

◆ mult2Matrices() [1/4]

void vpMatrix::mult2Matrices	(	const vpMatrix &	A,
		const vpMatrix &	B,
		vpMatrix &	C
	)

staticinherited

Operation C = A * B.

The result is placed in the third parameter C and not returned. A new matrix won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).

See also: operator*()

Definition at line 962 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

Referenced by vpMatrix::operator*().

◆ mult2Matrices() [2/4]

void vpMatrix::mult2Matrices	(	const vpMatrix &	A,
		const vpMatrix &	B,
		vpRotationMatrix &	C
	)

staticinherited

Warning: This function is provided for compat with previous releases. You should rather use the functionalities provided in vpRotationMatrix class.

Operation C = A * B.

The result is placed in the third parameter C and not returned. A new matrix won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).

Exceptions

vpException::dimensionError If matrices are not 3-by-3 dimension.

Definition at line 1011 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

◆ mult2Matrices() [3/4]

void vpMatrix::mult2Matrices	(	const vpMatrix &	A,
		const vpMatrix &	B,
		vpHomogeneousMatrix &	C
	)

staticinherited

Warning: This function is provided for compat with previous releases. You should rather use the functionalities provided in vpHomogeneousMatrix class.

Operation C = A * B.

The result is placed in the third parameter C and not returned. A new matrix won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).

Exceptions

vpException::dimensionError If matrices are not 4-by-4 dimension.

Definition at line 1050 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

◆ mult2Matrices() [4/4]

void vpMatrix::mult2Matrices	(	const vpMatrix &	A,
		const vpColVector &	B,
		vpColVector &	C
	)

staticinherited

Warning: This function is provided for compat with previous releases. You should rather use multMatrixVector() that is more explicit.

Operation C = A * B.

The result is placed in the third parameter C and not returned. A new matrix won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).

See also: multMatrixVector()

Definition at line 1088 of file vpMatrix.cpp.

References vpMatrix::multMatrixVector().

◆ multMatrixVector()

void vpMatrix::multMatrixVector	(	const vpMatrix &	A,
		const vpColVector &	v,
		vpColVector &	w
	)

staticinherited

Operation w = A * v (v and w are vectors).

A new matrix won't be allocated for every use of the function (Speed gain if used many times with the same result matrix size).

See also: operator*(const vpColVector &v) const

Definition at line 921 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpColVector::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

Referenced by vpMatrix::mult2Matrices(), and vpMatrix::operator*().

◆ negateMatrix()

void vpMatrix::negateMatrix	(	const vpMatrix &	A,
		vpMatrix &	C
	)

staticinherited

Operation C = -A.

The result is placed in the second parameter C and not returned. A new matrix won't be allocated for every use of the function (Speed gain if used many times with the same result matrix size).

See also: operator-(void)

Definition at line 1457 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpArray2D< Type >::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

Referenced by vpMatrix::operator-().

◆ operator!=()

bool vpArray2D< double >::operator!= ( const vpArray2D< double > & A ) const

inherited

Not equal to comparison operator of a 2D array.

Definition at line 995 of file vpArray2D.h.

◆ operator*() [1/7]

vpMatrix vpMatrix::operator* ( const vpMatrix & B ) const

inherited

Operation C = A * B (A is unchanged).

See also: mult2Matrices() to avoid matrix allocation for each use.

Definition at line 1097 of file vpMatrix.cpp.

References vpMatrix::mult2Matrices().

Referenced by vpColVector::operator[](), vpColVector::stackMatrices(), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().

◆ operator*() [2/7]

vpMatrix vpMatrix::operator* ( const vpRotationMatrix & R ) const

inherited

Operator that allow to multiply a matrix by a rotation matrix. The matrix should be of dimension m-by-3.

Definition at line 1110 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

◆ operator*() [3/7]

vpMatrix vpMatrix::operator* ( const vpVelocityTwistMatrix & V ) const

inherited

Operator that allow to multiply a matrix by a velocity twist matrix. The matrix should be of dimension m-by-6.

Definition at line 1137 of file vpMatrix.cpp.

References vpCPUFeatures::checkSSE2(), vpArray2D< double >::colNum, vpArray2D< Type >::colNum, vpArray2D< double >::data, vpArray2D< Type >::data, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

◆ operator*() [4/7]

vpMatrix vpMatrix::operator* ( const vpForceTwistMatrix & V ) const

inherited

Operator that allow to multiply a matrix by a force/torque twist matrix. The matrix should be of dimension m-by-6.

Definition at line 1206 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

◆ operator*() [5/7]

vpTranslationVector vpMatrix::operator* ( const vpTranslationVector & tv ) const

inherited

Operator that allows to multiply a matrix by a translation vector. The matrix should be of dimension (3x3)

Definition at line 881 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

◆ operator*() [6/7]

vpColVector vpMatrix::operator* ( const vpColVector & v ) const

inherited

Operation w = A * v (matrix A is unchanged, v and w are column vectors).

See also: multMatrixVector() to avoid matrix allocation for each use.

Definition at line 906 of file vpMatrix.cpp.

References vpMatrix::multMatrixVector().

◆ operator*() [7/7]

vpMatrix vpMatrix::operator* ( const double x ) const

inherited

Operator that allows to multiply all the elements of a matrix by a scalar.

Definition at line 1524 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

◆ operator*=()

vpMatrix & vpMatrix::operator*= ( const double x )

inherited

Multiply all the element of the matrix by x : Aij = Aij * x.

Operator that allows to multiply all the elements of a matrix by a scalar.

Definition at line 1580 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

Referenced by vpColVector::operator[]().

◆ operator+()

vpMatrix vpMatrix::operator+ ( const vpMatrix & B ) const

inherited

Operation C = A + B (A is unchanged).

See also: add2Matrices() to avoid matrix allocation for each use.

Definition at line 1327 of file vpMatrix.cpp.

References vpMatrix::add2Matrices().

Referenced by vpColVector::operator[]().

◆ operator+=() [1/2]

vpMatrix & vpMatrix::operator+= ( const vpMatrix & B )

inherited

Operation A = A + B.

Definition at line 1416 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::rowNum, vpArray2D< Type >::rowPtrs, and vpArray2D< double >::rowPtrs.

Referenced by vpColVector::operator[]().

◆ operator+=() [2/2]

vpMatrix & vpMatrix::operator+= ( const double x )

inherited

Add x to all the element of the matrix : Aij = Aij + x.

Definition at line 1557 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

◆ operator,()

vpMatrix & vpMatrix::operator, ( double val )

inherited

Definition at line 767 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::resize(), and vpArray2D< double >::rowPtrs.

Referenced by vpColVector::operator[]().

◆ operator-() [1/2]

vpMatrix vpMatrix::operator- ( const vpMatrix & B ) const

inherited

Operation C = A - B (A is unchanged).

See also: sub2Matrices() to avoid matrix allocation for each use.

Definition at line 1407 of file vpMatrix.cpp.

References vpMatrix::sub2Matrices().

◆ operator-() [2/2]

vpMatrix vpMatrix::operator- ( void ) const

inherited

Operation C = -A (A is unchanged).

See also: negateMatrix() to avoid matrix allocation for each use.

Definition at line 1475 of file vpMatrix.cpp.

References vpMatrix::negateMatrix().

Referenced by vpColVector::operator[]().

◆ operator-=() [1/2]

vpMatrix & vpMatrix::operator-= ( const vpMatrix & B )

inherited

Operation A = A - B.

Definition at line 1433 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::rowNum, vpArray2D< Type >::rowPtrs, and vpArray2D< double >::rowPtrs.

Referenced by vpColVector::operator[]().

◆ operator-=() [2/2]

vpMatrix & vpMatrix::operator-= ( const double x )

inherited

Substract x to all the element of the matrix : Aij = Aij - x.

Definition at line 1567 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

◆ operator/()

vpMatrix vpMatrix::operator/ ( const double x ) const

inherited

Cij = Aij / x (A is unchanged)

Definition at line 1536 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::divideByZeroError, vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

Referenced by vpColVector::operator[]().

◆ operator/=()

vpMatrix & vpMatrix::operator/= ( double x )

inherited

Divide all the element of the matrix by x : Aij = Aij / x.

Definition at line 1590 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::divideByZeroError, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

Referenced by vpColVector::operator[]().

◆ operator<<() [1/2]

vpMatrix & vpMatrix::operator<< ( double * x )

inherited

Assigment from an array of double. This method has to be used carefully since the array allocated behind x pointer should have the same dimension than the matrix.

Definition at line 750 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

◆ operator<<() [2/2]

vpMatrix & vpMatrix::operator<< ( double val )

inherited

Definition at line 760 of file vpMatrix.cpp.

References vpArray2D< double >::resize(), and vpArray2D< double >::rowPtrs.

◆ operator=() [1/3]

vpSubMatrix & vpSubMatrix::operator= ( const vpSubMatrix & B )

Operation such as subA = subB.

Operation A = B.

Parameters

B	: a subMatrix

Definition at line 140 of file vpSubMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrixException::incorrectMatrixSizeError, parent, pColNum, pRowNum, vpArray2D< double >::rowNum, vpArray2D< double >::rowPtrs, and vpArray2D< Type >::rowPtrs.

◆ operator=() [2/3]

vpSubMatrix & vpSubMatrix::operator= ( const vpMatrix & B )

Operation such as subA = B.

Operation A = B.

Parameters

B	: a matrix

Definition at line 120 of file vpSubMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrixException::incorrectMatrixSizeError, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

◆ operator=() [3/3]

vpSubMatrix & vpSubMatrix::operator= ( const double & x )

Operation such as subA = x.

Operation A = x.

Parameters

x	: a scalar

Definition at line 166 of file vpSubMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

◆ operator==() [1/2]

bool vpArray2D< double >::operator== ( const vpArray2D< double > & A ) const

inherited

Equal to comparison operator of a 2D array.

Definition at line 950 of file vpArray2D.h.

References vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpArray2D< Type >::operator==(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::size().

◆ operator==() [2/2]

bool vpArray2D< float >::operator== ( const vpArray2D< float > & A ) const

inlineinherited

Definition at line 980 of file vpArray2D.h.

References vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpArray2D< Type >::rowNum, and vpArray2D< Type >::size().

◆ operator[]() [1/2]

double * vpArray2D< double >::operator[] ( unsigned int i )

inlineinherited

Set element $A_{ij} = x$ using A[i][j] = x.

Definition at line 486 of file vpArray2D.h.

◆ operator[]() [2/2]

double * vpArray2D< double >::operator[] ( unsigned int i ) const

inlineinherited

Get element $x = A_{ij}$ using x = A[i][j].

Definition at line 488 of file vpArray2D.h.

◆ print()

int vpMatrix::print	(	std::ostream &	s,
		unsigned int	length,
		const std::string &	intro = `""`
	)		const

inherited

Pretty print a matrix. The data are tabulated. The common widths before and after the decimal point are set with respect to the parameter maxlen.

Parameters

s	Stream used for the printing.
length	The suggested width of each matrix element. The actual width grows in order to accomodate the whole integral part, and shrinks if the whole extent is not needed for all the numbers.
intro	The introduction which is printed before the matrix. Can be set to zero (or omitted), in which case the introduction is not printed.

Returns: Returns the common total width for all matrix elements

See also: std::ostream &operator<<(std::ostream &s, const vpArray2D<Type> &A)

Examples:: testMatrix.cpp, and testMatrixConditionNumber.cpp.

Definition at line 4370 of file vpMatrix.cpp.

References vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), and vpMath::maximum().

Referenced by vpServo::computeControlLaw(), vpColVector::operator[](), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().

◆ printSize()

void vpMatrix::printSize ( ) const

inlineinherited

Definition at line 576 of file vpMatrix.h.

References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().

◆ pseudoInverse() [1/5]

vpMatrix vpMatrix::pseudoInverse ( double svThreshold = 1e-6 ) const

inherited

Compute and return the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ .

Note: By default, this function uses Lapack 3rd party. It is also possible to use a specific 3rd party suffixing this function name with one of the following 3rd party names (Lapack, Eigen3, OpenCV or Gsl).

Warning: To inverse a square n-by-n matrix, you have to use rather one of the following functions inverseByLU(), inverseByQR(), inverseByCholesky() that are kwown as faster.

Parameters

svThreshold : Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.

Returns: The Moore-Penros pseudo inverse .

Here an example to compute the pseudo-inverse of a 2-by-3 matrix.

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(2, 3);
  A[0][0] = 2; A[0][1] = 3; A[0][2] = 5;
  A[1][0] = -4; A[1][1] = 2; A[1][2] = 3;
  A.print(std::cout, 10, "A: ");
  vpMatrix A_p = A.pseudoInverse();
  A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
}

Once build, the previous example produces the following output:

A: [2,3]=
   2  3  5
  -4  2  3
A^+ (pseudo-inverse): [3,2]=
   0.117899 -0.190782
   0.065380  0.039657
   0.113612  0.052518

Examples:: testFrankaCartVelocity-2.cpp, testMatrixConditionNumber.cpp, testRobotViper650-frames.cpp, and testRobotViper850-frames.cpp.

Definition at line 2081 of file vpMatrix.cpp.

References vpException::fatalError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpMatrix::insert(), vpMatrix::pseudoInverseEigen3(), vpMatrix::pseudoInverseGsl(), vpMatrix::pseudoInverseLapack(), vpMatrix::pseudoInverseOpenCV(), vpArray2D< Type >::resize(), vpColVector::resize(), vpArray2D< Type >::size(), vpMatrix::svdEigen3(), vpMatrix::svdGsl(), vpMatrix::svdLapack(), vpMatrix::svdOpenCV(), and vpMatrix::t().

Referenced by vpSimulatorAfma6::computeArticularVelocity(), vpSimulatorViper850::computeArticularVelocity(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), vpMatrix::computeCovarianceMatrixVVS(), vpPoseFeatures::computePose(), vpMbEdgeMultiTracker::computeVVSFirstPhasePoseEstimation(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbTracker::computeVVSPoseEstimation(), vpQuadProg::fromCanonicalCost(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), vpMeEllipse::initTracking(), vpHomography::inverse(), vpMeLine::leastSquare(), vpRotationMatrix::mean(), vpHomogeneousMatrix::mean(), vpPose::poseDementhonNonPlan(), vpPose::poseDementhonPlan(), vpPose::poseFromRectangle(), vpPose::poseVirtualVS(), vpMeEllipse::printParameters(), vpMatrix::pseudoInverse(), vpHomography::robust(), vpMatrix::solveBySVD(), and vpQuadProg::solveQPi().

◆ pseudoInverse() [2/5]

unsigned int vpMatrix::pseudoInverse	(	vpMatrix &	Ap,
		double	svThreshold = `1e-6`
	)		const

inherited

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ and return the rank r of the matrix.

Note: By default, this function uses Lapack 3rd party. It is also possible to use a specific 3rd party suffixing this function name with one of the following 3rd party names (Lapack, Eigen3, OpenCV or Gsl).

Warning: To inverse a square n-by-n matrix, you have to use rather one of the following functions inverseByLU(), inverseByQR(), inverseByCholesky() that are kwown as faster.

Parameters

Ap	: The Moore-Penros pseudo inverse .
svThreshold	: Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.

Returns: The rank r of the matrix.

Here an example to compute the pseudo-inverse of a 2-by-3 matrix.

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(2, 3);
  A[0][0] = 2; A[0][1] = 3; A[0][2] = 5;
  A[1][0] = -4; A[1][1] = 2; A[1][2] = 3;
  A.print(std::cout, 10, "A: ");
  vpMatrix A_p;
  unsigned int rank = A.pseudoInverse(A_p);
  A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
  std::cout << "Rank: " << rank << std::endl;
}

Once build, the previous example produces the following output:

A: [2,3]=
   2  3  5
  -4  2  3
A^+ (pseudo-inverse): [3,2]=
   0.117899 -0.190782
   0.065380  0.039657
   0.113612  0.052518
Rank: 2

Definition at line 2012 of file vpMatrix.cpp.

References vpException::fatalError, vpMatrix::pseudoInverseEigen3(), vpMatrix::pseudoInverseGsl(), vpMatrix::pseudoInverseLapack(), and vpMatrix::pseudoInverseOpenCV().

◆ pseudoInverse() [3/5]

unsigned int vpMatrix::pseudoInverse	(	vpMatrix &	Ap,
		vpColVector &	sv,
		double	svThreshold = `1e-6`
	)		const

inherited

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ along with singular values and return the rank r of the matrix.

Note: By default, this function uses Lapack 3rd party. It is also possible to use a specific 3rd party suffixing this function name with one of the following 3rd party names (Lapack, Eigen3, OpenCV or Gsl).

Warning: To inverse a square n-by-n matrix, you have to use rather one of the following functions inverseByLU(), inverseByQR(), inverseByCholesky() that are kwown as faster.

Parameters

Ap	: The Moore-Penros pseudo inverse .
sv	Vector corresponding to matrix singular values. The size of this vector is equal to min(m, n).
svThreshold	: Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.

Returns: The rank r of the matrix $\bf A$ .

Here an example to compute the pseudo-inverse of a 2-by-3 matrix.

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(2, 3);
  A[0][0] = 2; A[0][1] = 3; A[0][2] = 5;
  A[1][0] = -4; A[1][1] = 2; A[1][2] = 3;
  A.print(std::cout, 10, "A: ");
  vpMatrix A_p;
  vpColVector sv;
  unsigned int rank = A.pseudoInverse(A_p, sv);
  A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
  std::cout << "Rank: " << rank << std::endl;
  std::cout << "Singular values: " << sv.t() << std::endl;
}

Once build, the previous example produces the following output:

A: [2,3]=
   2  3  5
  -4  2  3
A^+ (pseudo-inverse): [3,2]=
   0.117899 -0.190782
   0.065380  0.039657
   0.113612  0.052518
Rank: 2
Singular values: 6.874359351  4.443330227

Definition at line 3598 of file vpMatrix.cpp.

References vpException::fatalError, vpMatrix::pseudoInverseEigen3(), vpMatrix::pseudoInverseGsl(), vpMatrix::pseudoInverseLapack(), and vpMatrix::pseudoInverseOpenCV().

◆ pseudoInverse() [4/5]

unsigned int vpMatrix::pseudoInverse	(	vpMatrix &	Ap,
		vpColVector &	sv,
		double	svThreshold,
		vpMatrix &	imA,
		vpMatrix &	imAt
	)		const

inherited

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ along with singular values, $\mbox{Im}(A)$ and $\mbox{Im}(A^T)$ and return the rank r of the matrix.

See pseudoInverse(vpMatrix &, vpColVector &, double, vpMatrix &, vpMatrix &, vpMatrix &) const for a complete description of this function.

Warning: To inverse a square n-by-n matrix, you have to use rather one of the following functions inverseByLU(), inverseByQR(), inverseByCholesky() that are kwown as faster.

Parameters

Ap	: The Moore-Penros pseudo inverse .
sv	Vector corresponding to matrix singular values. The size of this vector is equal to min(m, n).
svThreshold	: Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.
imA	$\mbox{Im}({\bf A})$ that is a m-by-r matrix.
imAt	$\mbox{Im}({\bf A}^T)$ that is n-by-r matrix.

Returns: The rank r of the matrix $\bf A$ .

Here an example to compute the pseudo-inverse of a 2-by-3 matrix.

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(2, 3);
  A[0][0] = 2; A[0][1] = 3; A[0][2] = 5;
  A[1][0] = -4; A[1][1] = 2; A[1][2] = 3;
  A.print(std::cout, 10, "A: ");
  vpMatrix A_p;
  vpColVector sv;
  vpMatrix imA, imAt;
  unsigned int rank = A.pseudoInverse(A_p, sv, 1e-6, imA, imAt);
  A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
  std::cout << "Rank: " << rank << std::endl;
  std::cout << "Singular values: " << sv.t() << std::endl;
  imA.print(std::cout, 10, "Im(A): ");
  imAt.print(std::cout, 10, "Im(A^T): ");
}

Once build, the previous example produces the following output:

A: [2,3]=
   2  3  5
  -4  2  3
A^+ (pseudo-inverse): [3,2]=
   0.117899 -0.190782
   0.065380  0.039657
   0.113612  0.052518
Rank: 2
Singular values: 6.874359351  4.443330227
Im(A): [2,2]=
   0.81458 -0.58003
   0.58003  0.81458
Im(A^T): [3,2]=
  -0.100515 -0.994397
   0.524244 -0.024967
   0.845615 -0.102722

Definition at line 3692 of file vpMatrix.cpp.

References vpMatrix::pseudoInverse().

◆ pseudoInverse() [5/5]

unsigned int vpMatrix::pseudoInverse	(	vpMatrix &	Ap,
		vpColVector &	sv,
		double	svThreshold,
		vpMatrix &	imA,
		vpMatrix &	imAt,
		vpMatrix &	kerAt
	)		const

inherited

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ along with singular values, $\mbox{Im}(A)$ , $\mbox{Im}(A^T)$ and $\mbox{Ker}(A)$ and return the rank r of the matrix.

Note: By default, this function uses Lapack 3rd party. It is also possible to use a specific 3rd party suffixing this function name with one of the following 3rd party names (Lapack, Eigen3, OpenCV or Gsl).

Warning: To inverse a square n-by-n matrix, you have to use rather inverseByLU(), inverseByCholesky(), or inverseByQR() that are kwown as faster.

Using singular value decomposition, we have:

${\bf A}_{m\times n} = {\bf U}_{m\times m} \; {\bf S}_{m\times n} \; {\bf V^\top}_{n\times n}$

${\bf A}_{m\times n} = \left[\begin{array}{ccc}\mbox{Im} ({\bf A}) & | & \mbox{Ker} ({\bf A}^\top) \end{array} \right] {\bf S}_{m\times n} \left[ \begin{array}{c} \left[\mbox{Im} ({\bf A}^\top)\right]^\top \\ \\ \hline \\ \left[\mbox{Ker}({\bf A})\right]^\top \end{array}\right]$

where the diagonal of ${\bf S}_{m\times n}$ corresponds to the matrix $A$ singular values.

This equation could be reformulated in a minimal way:

${\bf A}_{m\times n} = \mbox{Im} ({\bf A}) \; {\bf S}_{r\times n} \left[ \begin{array}{c} \left[\mbox{Im} ({\bf A}^\top)\right]^\top \\ \\ \hline \\ \left[\mbox{Ker}({\bf A})\right]^\top \end{array}\right]$

where the diagonal of ${\bf S}_{r\times n}$ corresponds to the matrix $A$ first r singular values.

The null space of a matrix $\bf A$ is defined as $\mbox{Ker}({\bf A}) = { {\bf X} : {\bf A}*{\bf X} = {\bf 0}}$ .

Parameters

Ap	The Moore-Penros pseudo inverse ${\bf A}^+$ .
sv	Vector corresponding to matrix singular values. The size of this vector is equal to min(m, n).
svThreshold	Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.
imA	$\mbox{Im}({\bf A})$ that is a m-by-r matrix.
imAt	$\mbox{Im}({\bf A}^T)$ that is n-by-r matrix.
kerAt	The matrix that contains the null space (kernel) of $\bf A$ defined by the matrix ${\bf X}^T$ . If matrix $\bf A$ is full rank, the dimension of `kerAt` is (0, n), otherwise the dimension is (n-r, n). This matrix is thus the transpose of $\mbox{Ker}({\bf A})$ .

Returns: The rank r of the matrix $\bf A$ .

Here an example to compute the pseudo-inverse of a 2-by-3 matrix.

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(2, 3);
  A[0][0] = 2; A[0][1] = 3; A[0][2] = 5;
  A[1][0] = -4; A[1][1] = 2; A[1][2] = 3;
  A.print(std::cout, 10, "A: ");
  vpColVector sv;
  vpMatrix A_p, imA, imAt, kerAt;
  unsigned int rank = A.pseudoInverse(A_p, sv, 1e-6, imA, imAt, kerAt);
  A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
  std::cout << "Rank: " << rank << std::endl;
  std::cout << "Singular values: " << sv.t() << std::endl;
  imA.print(std::cout, 10, "Im(A): ");
  imAt.print(std::cout, 10, "Im(A^T): ");
  if (kerAt.size()) {
    kerAt.t().print(std::cout, 10, "Ker(A): ");
  }
  else {
    std::cout << "Ker(A) empty " << std::endl;
  }
  // Reconstruct matrix A from ImA, ImAt, KerAt
  vpMatrix S(rank, A.getCols());
  for(unsigned int i = 0; i< rank; i++)
    S[i][i] = sv[i];
  vpMatrix Vt(A.getCols(), A.getCols());
  Vt.insert(imAt.t(), 0, 0);
  Vt.insert(kerAt, rank, 0);
  (imA * S * Vt).print(std::cout, 10, "Im(A) * S * [Im(A^T) | Ker(A)]^T:");
}

Once build, the previous example produces the following output:

A: [2,3]=
   2  3  5
  -4  2  3
A^+ (pseudo-inverse): [3,2]=
   0.117899 -0.190782
   0.065380  0.039657
   0.113612  0.052518
Rank: 2
Singular values: 6.874359351  4.443330227
Im(A): [2,2]=
   0.81458 -0.58003
   0.58003  0.81458
Im(A^T): [3,2]=
  -0.100515 -0.994397
   0.524244 -0.024967
   0.845615 -0.102722
Ker(A): [3,1]=
  -0.032738
  -0.851202
   0.523816
Im(A) * S * [Im(A^T) | Ker(A)]^T:[2,3]=
   2  3  5
  -4  2  3

Definition at line 3833 of file vpMatrix.cpp.

References vpException::fatalError, vpMatrix::pseudoInverseEigen3(), vpMatrix::pseudoInverseGsl(), vpMatrix::pseudoInverseLapack(), and vpMatrix::pseudoInverseOpenCV().

◆ pseudoInverseEigen3() [1/4]

vpMatrix vpMatrix::pseudoInverseEigen3 ( double svThreshold = 1e-6 ) const

inherited

Referenced by vpMatrix::pseudoInverse().

◆ pseudoInverseEigen3() [2/4]

unsigned int vpMatrix::pseudoInverseEigen3	(	vpMatrix &	Ap,
		double	svThreshold = `1e-6`
	)		const

inherited

◆ pseudoInverseEigen3() [3/4]

unsigned int vpMatrix::pseudoInverseEigen3	(	vpMatrix &	Ap,
		vpColVector &	sv,
		double	svThreshold = `1e-6`
	)		const

inherited

◆ pseudoInverseEigen3() [4/4]

unsigned int vpMatrix::pseudoInverseEigen3	(	vpMatrix &	Ap,
		vpColVector &	sv,
		double	svThreshold,
		vpMatrix &	imA,
		vpMatrix &	imAt,
		vpMatrix &	kerAt
	)		const

inherited

◆ pseudoInverseGsl() [1/4]

vpMatrix vpMatrix::pseudoInverseGsl ( double svThreshold = 1e-6 ) const

inherited

Referenced by vpMatrix::pseudoInverse().

◆ pseudoInverseGsl() [2/4]

unsigned int vpMatrix::pseudoInverseGsl	(	vpMatrix &	Ap,
		double	svThreshold = `1e-6`
	)		const

inherited

◆ pseudoInverseGsl() [3/4]

unsigned int vpMatrix::pseudoInverseGsl	(	vpMatrix &	Ap,
		vpColVector &	sv,
		double	svThreshold = `1e-6`
	)		const

inherited

◆ pseudoInverseGsl() [4/4]

unsigned int vpMatrix::pseudoInverseGsl	(	vpMatrix &	Ap,
		vpColVector &	sv,
		double	svThreshold,
		vpMatrix &	imA,
		vpMatrix &	imAt,
		vpMatrix &	kerAt
	)		const

inherited

◆ pseudoInverseLapack() [1/4]

vpMatrix vpMatrix::pseudoInverseLapack ( double svThreshold = 1e-6 ) const

inherited

Referenced by vpMatrix::pseudoInverse().

◆ pseudoInverseLapack() [2/4]

unsigned int vpMatrix::pseudoInverseLapack	(	vpMatrix &	Ap,
		double	svThreshold = `1e-6`
	)		const

inherited

◆ pseudoInverseLapack() [3/4]

unsigned int vpMatrix::pseudoInverseLapack	(	vpMatrix &	Ap,
		vpColVector &	sv,
		double	svThreshold = `1e-6`
	)		const

inherited

◆ pseudoInverseLapack() [4/4]

unsigned int vpMatrix::pseudoInverseLapack	(	vpMatrix &	Ap,
		vpColVector &	sv,
		double	svThreshold,
		vpMatrix &	imA,
		vpMatrix &	imAt,
		vpMatrix &	kerAt
	)		const

inherited

◆ pseudoInverseOpenCV() [1/4]

vpMatrix vpMatrix::pseudoInverseOpenCV ( double svThreshold = 1e-6 ) const

inherited

Referenced by vpMatrix::pseudoInverse().

◆ pseudoInverseOpenCV() [2/4]

unsigned int vpMatrix::pseudoInverseOpenCV	(	vpMatrix &	Ap,
		double	svThreshold = `1e-6`
	)		const

inherited

◆ pseudoInverseOpenCV() [3/4]

unsigned int vpMatrix::pseudoInverseOpenCV	(	vpMatrix &	Ap,
		vpColVector &	sv,
		double	svThreshold = `1e-6`
	)		const

inherited

◆ pseudoInverseOpenCV() [4/4]

unsigned int vpMatrix::pseudoInverseOpenCV	(	vpMatrix &	Ap,
		vpColVector &	sv,
		double	svThreshold,
		vpMatrix &	imA,
		vpMatrix &	imAt,
		vpMatrix &	kerAt
	)		const

inherited

◆ qr()

unsigned int vpMatrix::qr	(	vpMatrix &	Q,
		vpMatrix &	R,
		bool	full = `false`,
		bool	squareR = `false`,
		double	tol = `1e-6`
	)		const

inherited

Compute the QR decomposition of a (m x n) matrix of rank r. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.

Parameters

Q	: orthogonal matrix (will be modified).
R	: upper-triangular matrix (will be modified).
full	: whether or not we want full decomposition.
squareR	: will return only the square (min(m,n) x min(m,n)) part of R.
tol	: tolerance to test the rank of R.

Returns: The rank r of the matrix.

If full is false (default) then Q is (m x min(n,m)) and R is (min(n,m) x n). We then have this = QR.

If full is true and m > n then Q is (m x m) and R is (n x n). In this case this = Q (R, 0)^T

If squareR is true and n > m then R is (m x m). If r = m then R is invertible.

Here an example:

#include <visp3/core/vpMatrix.h>
double residual(vpMatrix M1, vpMatrix M2)
{
    return (M1 - M2).frobeniusNorm();
}
int main()
{
  vpMatrix A(4,3);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.;
  // Economic QR (Q 4x3, R 3x3)
  vpMatrix Q, R;
  int r = A.qr(A, R);
  std::cout << "QR Residual: "
            << residual(A, Q*R) << std::endl;
  // Full QR (Q 4x4, R 3x3)
  r = A.qr(Q, R, true);
  std::cout << "Full QR Residual: "
            << residual(A, Q.extract(0, 0, 4, 3)*R) << std::endl;
}

See also: qrPivot()

Definition at line 349 of file vpMatrix_qr.cpp.

References vpException::badValue, vpArray2D< double >::colNum, vpArray2D< double >::data, vpException::fatalError, vpArray2D< Type >::resize(), and vpArray2D< double >::rowNum.

Referenced by vpLinProg::colReduction().

◆ qrPivot()

unsigned int vpMatrix::qrPivot	(	vpMatrix &	Q,
		vpMatrix &	R,
		vpMatrix &	P,
		bool	full = `false`,
		bool	squareR = `false`,
		double	tol = `1e-6`
	)		const

inherited

Compute the QR pivot decomposition of a (m x n) matrix of rank r. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.

Parameters

Q	: orthogonal matrix (will be modified).
R	: upper-triangular matrix (will be modified).
P	: the (n x n) permutation matrix.
full	: whether or not we want full decomposition.
squareR	: will return only the (r x r) part of R and the (r x n) part of P.
tol	: tolerance to test the rank of R.

Returns: The rank r of the matrix.

If full is false (default) then Q is (m x min(n,m)) and R is (min(n,m) x n). We then have this.P = Q.R.

If full is true and m > n then Q is (m x m) and R is (n x n). In this case this.P = Q (R, 0)^T

If squareR is true then R is (r x r) invertible.

Here an example:

#include <visp3/core/vpMatrix.h>
double residual(vpMatrix M1, vpMatrix M2)
{
    return (M1 - M2).frobeniusNorm();
}
int main()
{
  vpMatrix A(4,3);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/2.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/4.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/5.;
  // A is rank (4x3) but rank 2
  // Economic QR (Q 4x3, R 3x3)
  vpMatrix Q, R, P;
  int r = A.qrPivot(Q, R, P);
  std::cout << "A rank: " << r << std::endl;
  std::cout << "Residual: " << residual(A*P, Q*R) << std::endl;
  // Full QR (Q 4x4, R 3x3)
  r = A.qrPivot(Q, R, P, true);
  std::cout << "QRPivot Residual: " <<
  residual(A*P, Q.extract(0, 0, 4, 3)*R) << std::endl;
  // Using permutation matrix: keep only non-null part of R
  Q.resize(4, r, false);            // Q is 4 x 2
  R = R.extract(0, 0, r, 3)*P.t();  // R is 2 x 3
  std::cout << "Full QRPivot Residual: " <<
  residual(A, Q*R) << std::endl;
}

See also: qrPivot()

Definition at line 549 of file vpMatrix_qr.cpp.

References vpException::badValue, vpArray2D< double >::colNum, vpArray2D< double >::data, vpException::fatalError, vpArray2D< Type >::resize(), and vpArray2D< double >::rowNum.

Referenced by vpLinProg::colReduction(), vpLinProg::rowReduction(), and vpMatrix::solveByQR().

◆ reshape()

void vpArray2D< double >::reshape	(	unsigned int	nrows,
		unsigned int	ncols
	)

inlineinherited

Examples:: testMatrixInitialization.cpp.

Definition at line 381 of file vpArray2D.h.

References vpException::dimensionError, vpArray2D< Type >::dsize, vpArray2D< Type >::operator!=(), vpArray2D< Type >::operator==(), vpArray2D< Type >::resize(), and vpArray2D< Type >::rowPtrs.

◆ resize()

void vpArray2D< double >::resize	(	const unsigned int	nrows,
		const unsigned int	ncols,
		const bool	flagNullify = `true`,
		const bool	recopy_ = `true`
	)

inlineinherited

Set the size of the array and initialize all the values to zero.

Parameters

nrows	: number of rows.
ncols	: number of column.
flagNullify	: if true, then the array is re-initialized to 0 after resize. If false, the initial values from the common part of the array (common part between old and new version of the array) are kept. Default value is true.
recopy_	: if true, will perform an explicit recopy of the old data if needed and if flagNullify is set to false.

Examples:: testArray2D.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixDeterminant.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 305 of file vpArray2D.h.

References vpArray2D< Type >::colNum, vpArray2D< Type >::dsize, vpException::memoryAllocationError, vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

Referenced by vpMatrix::diag(), vpMatrix::eye(), vpMatrix::init(), vpMatrix::operator,(), vpMatrix::operator<<(), vpMatrix::operator=(), vpMatrix::stack(), and vpMatrix::svdOpenCV().

◆ row()

vpRowVector vpMatrix::row ( const unsigned int i )

inherited

Deprecated:: This method is deprecated. You should rather use getRow(). More precisely, the following code:

vpMatrix L;
unsigned int row_index = ...;
... = L.row(row_index);

should be replaced with:

... = L.getRow(row_index - 1);

Warning: Notice row(1) is the 0th row. This function returns the i-th row of the matrix.

Parameters

i	: Index of the row to extract noting that row index start at 1 to get the first row.

Definition at line 5557 of file vpMatrix.cpp.

References vpArray2D< double >::getCols().

Referenced by vpMatrix::expm().

◆ save()

static bool vpArray2D< double >::save	(	const std::string &	filename,
		const vpArray2D< double > &	A,
		const bool	binary = `false`,
		const char *	header = `""`
	)

inlinestaticinherited

Save a matrix to a file.

Parameters

filename	: Absolute file name.
A	: Array to be saved.
binary	: If true the matrix is saved in a binary file, else a text file.
header	: Optional line that will be saved at the beginning of the file.

Returns: Returns true if success.

Warning : If you save the matrix as in a text file the precision is less than if you save it in a binary file.

See also: load()

Definition at line 739 of file vpArray2D.h.

References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().

◆ saveMatrix()

static bool vpMatrix::saveMatrix	(	const std::string &	filename,
		const vpArray2D< double > &	M,
		const bool	binary = `false`,
		const char *	header = `""`
	)

inlinestaticinherited

Save a matrix to a file. This function overloads vpArray2D::load().

Parameters

filename	: absolute file name.
M	: matrix to be saved.
binary	: If true the matrix is save in a binary file, else a text file.
header	: optional line that will be saved at the beginning of the file.

Returns: Returns true if no problem appends.

Warning : If you save the matrix as in a text file the precision is less than if you save it in a binary file.

Examples:: testMatrix.cpp.

Definition at line 727 of file vpMatrix.h.

References vpArray2D< Type >::save().

Referenced by vpDot2::defineDots().

◆ saveMatrixYAML()

static bool vpMatrix::saveMatrixYAML	(	const std::string &	filename,
		const vpArray2D< double > &	M,
		const char *	header = `""`
	)

inlinestaticinherited

Save a matrix in a YAML-formatted file. This function overloads vpArray2D::saveYAML().

Parameters

filename	: absolute file name.
M	: matrix to be saved in the file.
header	: optional lines that will be saved at the beginning of the file. Should be YAML-formatted and will adapt to the indentation if any.

Returns: Returns true if success.

Examples:: testMatrix.cpp.

Definition at line 745 of file vpMatrix.h.

References vpArray2D< Type >::saveYAML().

◆ saveYAML()

static bool vpArray2D< double >::saveYAML	(	const std::string &	filename,
		const vpArray2D< double > &	A,
		const char *	header = `""`
	)

inlinestaticinherited

Save an array in a YAML-formatted file.

Parameters

filename	: absolute file name.
A	: array to be saved in the file.
header	: optional lines that will be saved at the beginning of the file. Should be YAML-formatted and will adapt to the indentation if any.

Returns: Returns true if success.

Here is an example of outputs.

vpArray2D<double> M(3,4);
vpArray2D::saveYAML("matrix.yml", M, "example: a YAML-formatted header");
vpArray2D::saveYAML("matrixIndent.yml", M, "example:\n    - a YAML-formatted
header\n    - with inner indentation"); 

Content of matrix.yml:

example: a YAML-formatted header
rows: 3
cols: 4
data:
  - [0, 0, 0, 0]
  - [0, 0, 0, 0]
  - [0, 0, 0, 0]

Content of matrixIndent.yml:

example:
    - a YAML-formatted header
    - with inner indentation
rows: 3
cols: 4
data:
    - [0, 0, 0, 0]
    - [0, 0, 0, 0]
    - [0, 0, 0, 0]

See also: loadYAML()

Examples:: tutorial-chessboard-pose.cpp, tutorial-franka-acquire-calib-data.cpp, and tutorial-hand-eye-calibration.cpp.

Definition at line 832 of file vpArray2D.h.

References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().

◆ setIdentity()

void vpMatrix::setIdentity ( const double & val = 1.0 )

inherited

Deprecated:: You should rather use diag(const double &)

Deprecated:: You should rather use diag(const double &)

Set the matrix diagonal elements to val. More generally set M[i][i] = val.

Definition at line 5598 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, and vpArray2D< double >::rowNum.

Referenced by vpVelocityTwistMatrix::init(), vpColVector::rows(), and vpServo::secondaryTask().

◆ size()

unsigned int vpArray2D< double >::size ( ) const

inlineinherited

Return the number of elements of the 2D array.

Examples:: testColVector.cpp, testDisplacement.cpp, testEigenConversion.cpp, testMatrix.cpp, testMatrixInitialization.cpp, testPoseVector.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testRowVector.cpp, testThread2.cpp, testTranslationVector.cpp, testTukeyEstimator.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, and tutorial-ibvs-4pts-wireframe-robot-viper.cpp.

Definition at line 291 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

Referenced by vpRowVector::insert(), vpColVector::insert(), vpColVector::operator*(), vpRotationVector::operator,(), vpTranslationVector::operator,(), vpRotationMatrix::operator,(), vpQuaternionVector::operator=(), vpTranslationVector::operator=(), vpRxyzVector::operator=(), vpRzyzVector::operator=(), vpRzyxVector::operator=(), vpThetaUVector::operator=(), vpMatrix::stack(), vpRotationVector::toStdVector(), vpRowVector::toStdVector(), and vpColVector::toStdVector().

◆ solveByQR() [1/2]

void vpMatrix::solveByQR	(	const vpColVector &	b,
		vpColVector &	x
	)		const

inherited

Solve a linear system Ax = b using QR Decomposition.

Non destructive wrt. A and b.

Parameters

b	: Vector b
x	: Vector x

Warning: If Ax = b does not have a solution, this method does not return the least-square minimizer. Use solveBySVD() to get this vector.

Here an example:

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(3,3);
  A[0][0] = 4.64;
  A[0][1] = 0.288;
  A[0][2] = -0.384;
  A[1][0] = 0.288;
  A[1][1] = 7.3296;
  A[1][2] = 2.2272;
  A[2][0] = -0.384;
  A[2][1] = 2.2272;
  A[2][2] = 6.0304;
  vpColVector X(3), B(3);
  B[0] = 1;
  B[1] = 2;
  B[2] = 3;
  A.solveByQR(B, X);
  // Obtained values of X
  // X[0] = 0.2468;
  // X[1] = 0.120782;
  // X[2] = 0.468587;
  std::cout << "X:\n" << X << std::endl;
}

See also: qrPivot()

Definition at line 804 of file vpMatrix_qr.cpp.

References vpArray2D< double >::colNum, vpMatrix::extract(), vpMatrix::inverseTriangular(), vpMatrix::qrPivot(), and vpMatrix::t().

Referenced by vpMatrix::solveByQR().

◆ solveByQR() [2/2]

vpColVector vpMatrix::solveByQR ( const vpColVector & b ) const

inherited

Solve a linear system Ax = b using QR Decomposition.

Non destructive wrt. A and B.

Parameters

b	: Vector b

Returns: Vector x

Warning: If Ax = b does not have a solution, this method does not return the least-square minimizer. Use solveBySVD() to get this vector.

Here an example:

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix A(3,3);
  A[0][0] = 4.64;
  A[0][1] = 0.288;
  A[0][2] = -0.384;
  A[1][0] = 0.288;
  A[1][1] = 7.3296;
  A[1][2] = 2.2272;
  A[2][0] = -0.384;
  A[2][1] = 2.2272;
  A[2][2] = 6.0304;
  vpColVector X(3), B(3);
  B[0] = 1;
  B[1] = 2;
  B[2] = 3;
  X = A.solveByQR(B);
  // Obtained values of X
  // X[0] = 0.2468;
  // X[1] = 0.120782;
  // X[2] = 0.468587;
  std::cout << "X:\n" << X << std::endl;
}

See also: qrPivot()

Definition at line 856 of file vpMatrix_qr.cpp.

References vpArray2D< double >::colNum, and vpMatrix::solveByQR().

◆ solveBySVD() [1/2]

void vpMatrix::solveBySVD	(	const vpColVector &	b,
		vpColVector &	x
	)		const

inherited

Solve a linear system $ A X = B $ using Singular Value Decomposition (SVD).

Non destructive wrt. A and B.

Parameters

b	: Vector .
x	: Vector .

Here an example:

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix A(3,3);
A[0][0] = 4.64;
A[0][1] = 0.288;
A[0][2] = -0.384;
A[1][0] = 0.288;
A[1][1] = 7.3296;
A[1][2] = 2.2272;
A[2][0] = -0.384;
A[2][1] = 2.2272;
A[2][2] = 6.0304;
vpColVector X(3), B(3);
B[0] = 1;
B[1] = 2;
B[2] = 3;
A.solveBySVD(B, X);
// Obtained values of X
// X[0] = 0.2468;
// X[1] = 0.120782;
// X[2] = 0.468587;
std::cout << "X:\n" << X << std::endl;
}

See also: solveBySVD(const vpColVector &)

Examples:: quadprog.cpp, and quadprog_eq.cpp.

Definition at line 1818 of file vpMatrix.cpp.

References vpMatrix::pseudoInverse().

Referenced by vpQuadProg::solveByProjection(), vpMatrix::solveBySVD(), and vpQuadProg::solveQPe().

◆ solveBySVD() [2/2]

vpColVector vpMatrix::solveBySVD ( const vpColVector & B ) const

inherited

Solve a linear system $ A X = B $ using Singular Value Decomposition (SVD).

Non destructive wrt. A and B.

Parameters

B	: Vector .

Returns: Vector .

Here an example:

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix A(3,3);
A[0][0] = 4.64;
A[0][1] = 0.288;
A[0][2] = -0.384;
A[1][0] = 0.288;
A[1][1] = 7.3296;
A[1][2] = 2.2272;
A[2][0] = -0.384;
A[2][1] = 2.2272;
A[2][2] = 6.0304;
vpColVector X(3), B(3);
B[0] = 1;
B[1] = 2;
B[2] = 3;
X = A.solveBySVD(B);
// Obtained values of X
// X[0] = 0.2468;
// X[1] = 0.120782;
// X[2] = 0.468587;
std::cout << "X:\n" << X << std::endl;
}

See also: solveBySVD(const vpColVector &, vpColVector &)

Definition at line 1869 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, and vpMatrix::solveBySVD().

◆ stack() [1/9]

void vpMatrix::stack ( const vpMatrix & A )

inherited

Stack A at the end of the current matrix, or copy if the matrix has no dimensions : this = [ this A ]^T.

Examples:: servoPioneerPoint2DDepthWithoutVpServo.cpp, and testMatrix.cpp.

Definition at line 4651 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrix::insert(), vpArray2D< double >::resize(), and vpArray2D< double >::rowNum.

◆ stack() [2/9]

void vpMatrix::stack ( const vpRowVector & r )

inherited

Stack row vector r at the end of the current matrix, or copy if the matrix has no dimensions: this = [ this r ]^T.

Here an example for a robot velocity log :

vpMatrix A;
vpColVector v(6);
for(unsigned int i = 0;i<100;i++)
{
  robot.getVelocity(vpRobot::ARTICULAR_FRAME, v);
  Velocities.stack(v.t());
}

Definition at line 4682 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::data, vpArray2D< Type >::data, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< double >::resize(), vpArray2D< double >::rowNum, vpArray2D< double >::size(), and vpArray2D< Type >::size().

◆ stack() [3/9]

void vpMatrix::stack ( const vpColVector & c )

inherited

Stack column vector c at the right of the current matrix, or copy if the matrix has no dimensions: this = [ this c ].

Here an example for a robot velocity log matrix:

vpMatrix log;
vpColVector v(6);
for(unsigned int i = 0; i<100;i++)
{
  robot.getVelocity(vpRobot::ARTICULAR_FRAME, v);
  log.stack(v);
}

Here the log matrix has size 6 rows by 100 columns.

Definition at line 4722 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::dimensionError, vpArray2D< Type >::getRows(), vpArray2D< double >::resize(), vpArray2D< double >::rowNum, vpArray2D< double >::rowPtrs, and vpArray2D< Type >::size().

◆ stack() [4/9]

vpMatrix vpMatrix::stack	(	const vpMatrix &	A,
		const vpMatrix &	B
	)

staticinherited

Stack matrix B to the end of matrix A and return the resulting matrix [ A B ]^T

Parameters

A	: Upper matrix.
B	: Lower matrix.

Returns: Stacked matrix [ A B ]^T

Warning: A and B must have the same number of columns.

Definition at line 4105 of file vpMatrix.cpp.

References vpMatrix::stack().

◆ stack() [5/9]

vpMatrix vpMatrix::stack	(	const vpMatrix &	A,
		const vpRowVector &	r
	)

staticinherited

Stack row vector r to matrix A and return the resulting matrix [ A r ]^T

Parameters

A	: Upper matrix.
r	: Lower row vector.

Returns: Stacked matrix [ A r ]^T

Warning: A and r must have the same number of columns.

Definition at line 4169 of file vpMatrix.cpp.

References vpMatrix::stack().

◆ stack() [6/9]

vpMatrix vpMatrix::stack	(	const vpMatrix &	A,
		const vpColVector &	c
	)

staticinherited

Stack column vector c to matrix A and return the resulting matrix [ A c ]

Parameters

A	: Left matrix.
c	: Right column vector.

Returns: Stacked matrix [ A c ]

Warning: A and c must have the same number of rows.

Definition at line 4208 of file vpMatrix.cpp.

References vpMatrix::stack().

◆ stack() [7/9]

void vpMatrix::stack	(	const vpMatrix &	A,
		const vpMatrix &	B,
		vpMatrix &	C
	)

staticinherited

Stack matrix B to the end of matrix A and return the resulting matrix in C.

Parameters

A	: Upper matrix.
B	: Lower matrix.
C	: Stacked matrix C = [ A B ]^T

Warning: A and B must have the same number of columns. A and C, B and C must be two different objects.

Definition at line 4125 of file vpMatrix.cpp.

References vpArray2D< Type >::data, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::resize(), and vpArray2D< Type >::size().

◆ stack() [8/9]

void vpMatrix::stack	(	const vpMatrix &	A,
		const vpRowVector &	r,
		vpMatrix &	C
	)

staticinherited

Stack row vector r to the end of matrix A and return the resulting matrix in C.

Parameters

A	: Upper matrix.
r	: Lower row vector.
C	: Stacked matrix C = [ A r ]^T

Warning: A and r must have the same number of columns. A and C must be two different objects.

Definition at line 4188 of file vpMatrix.cpp.

References vpArray2D< Type >::data, and vpMatrix::stack().

◆ stack() [9/9]

void vpMatrix::stack	(	const vpMatrix &	A,
		const vpColVector &	c,
		vpMatrix &	C
	)

staticinherited

Stack column vector c to the end of matrix A and return the resulting matrix in C.

Parameters

A	: Left matrix.
c	: Right column vector.
C	: Stacked matrix C = [ A c ]

Warning: A and c must have the same number of rows. A and C must be two different objects.

Definition at line 4227 of file vpMatrix.cpp.

References vpArray2D< Type >::data, and vpMatrix::stack().

◆ stackColumns() [1/2]

void vpMatrix::stackColumns ( vpColVector & out )

inherited

Stacks columns of a matrix in a vector.

Parameters

out	: a vpColVector.

Examples:: testMatrix.cpp.

Definition at line 1613 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpColVector::resize(), vpArray2D< Type >::rowNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

◆ stackColumns() [2/2]

vpColVector vpMatrix::stackColumns ( )

inherited

Stacks columns of a matrix in a vector.

Returns: a vpColVector.

Definition at line 1630 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, and vpArray2D< double >::rowNum.

◆ stackMatrices() [1/7]

vp_deprecated void vpMatrix::stackMatrices ( const vpMatrix & A )

inlineinherited

Deprecated:: You should rather use stack(const vpMatrix &A)

Definition at line 765 of file vpMatrix.h.

◆ stackMatrices() [2/7]

static vp_deprecated vpMatrix vpMatrix::stackMatrices	(	const vpMatrix &	A,
		const vpMatrix &	B
	)

inlinestaticinherited

Deprecated:: You should rather use stack(const vpMatrix &A, const vpMatrix &B)

Definition at line 770 of file vpMatrix.h.

◆ stackMatrices() [3/7]

static vp_deprecated void vpMatrix::stackMatrices	(	const vpMatrix &	A,
		const vpMatrix &	B,
		vpMatrix &	C
	)

inlinestaticinherited

Deprecated:: You should rather use stack(const vpMatrix &A, const vpMatrix &B, vpMatrix &C)

Definition at line 775 of file vpMatrix.h.

References operator*().

◆ stackMatrices() [4/7]

vpMatrix vpMatrix::stackMatrices	(	const vpMatrix &	A,
		const vpRowVector &	B
	)

staticinherited

Deprecated:: You should rather use stack(const vpMatrix &A, const vpMatrix &B)

Definition at line 5535 of file vpMatrix.cpp.

References vpMatrix::stack().

◆ stackMatrices() [5/7]

void vpMatrix::stackMatrices	(	const vpMatrix &	A,
		const vpRowVector &	B,
		vpMatrix &	C
	)

staticinherited

Deprecated:: You should rather use stack(const vpMatrix &A, const vpRowVector &B, vpMatrix &C)

Definition at line 5537 of file vpMatrix.cpp.

References vpMatrix::stack().

◆ stackMatrices() [6/7]

vpMatrix vpMatrix::stackMatrices	(	const vpColVector &	A,
		const vpColVector &	B
	)

staticinherited

Deprecated:: You should rather use vpColVector::stack(const vpColVector &A, const vpColVector &B)

Definition at line 5525 of file vpMatrix.cpp.

References vpColVector::stack().

◆ stackMatrices() [7/7]

void vpMatrix::stackMatrices	(	const vpColVector &	A,
		const vpColVector &	B,
		vpColVector &	C
	)

staticinherited

Deprecated:: You should rather use vpColVector::stack(const vpColVector &A, const vpColVector &B, vpColVector &C)

Definition at line 5530 of file vpMatrix.cpp.

References vpColVector::stack().

◆ stackRows() [1/2]

void vpMatrix::stackRows ( vpRowVector & out )

inherited

Stacks rows of a matrix in a vector

Parameters

out	: a vpRowVector.

Examples:: testMatrix.cpp.

Definition at line 1641 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::data, vpArray2D< Type >::data, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpRowVector::resize(), and vpArray2D< double >::rowNum.

◆ stackRows() [2/2]

vpRowVector vpMatrix::stackRows ( )

inherited

Stacks rows of a matrix in a vector.

Returns: a vpRowVector.

Definition at line 1652 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, and vpArray2D< double >::rowNum.

◆ sub2Matrices() [1/2]

void vpMatrix::sub2Matrices	(	const vpMatrix &	A,
		const vpMatrix &	B,
		vpMatrix &	C
	)

staticinherited

Operation C = A - B.

The result is placed in the third parameter C and not returned. A new matrix won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).

Exceptions

vpException::dimensionError If A and B matrices have not the same size.

See also: operator-()

Definition at line 1382 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

Referenced by vpMatrix::operator-().

◆ sub2Matrices() [2/2]

void vpMatrix::sub2Matrices	(	const vpColVector &	A,
		const vpColVector &	B,
		vpColVector &	C
	)

staticinherited

Warning: This function is provided for compat with previous releases. You should rather use the functionalities provided in vpColVector class.

Operation C = A - B on column vectors.

The result is placed in the third parameter C and not returned. A new vector won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).

Exceptions

vpException::dimensionError If A and B vectors have not the same size.

See also: vpColVector::operator-()

Definition at line 1349 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpColVector::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

◆ sum()

double vpMatrix::sum ( ) const

inherited

Return the sum of all the $a_{ij}$ elements of the matrix.

Returns: Value of $\sum a_{ij}$

Definition at line 1482 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

Referenced by vpMatrix::expm(), and vpColVector::resize().

◆ sumSquare()

double vpMatrix::sumSquare ( ) const

inherited

Return the sum square of all the $A_{ij}$ elements of the matrix $A(m, n)$ .

Returns: The value $\sum A_{ij}^{2}$ .

Definition at line 5419 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

Referenced by vpColVector::resize().

◆ svd()

void vpMatrix::svd	(	vpColVector &	w,
		vpMatrix &	V
	)

inherited

Matrix singular value decomposition (SVD).

This function calls the first following function that is available:

svdLapack() if Lapack 3rd party is installed
svdEigen3() if Eigen3 3rd party is installed
svdOpenCV() if OpenCV 3rd party is installed
svdGsl() if GSL 3rd party is installed.

If none of these previous 3rd parties is installed, we use by default svdLapack() with a Lapack built-in version.

Given matrix $M$ , this function computes it singular value decomposition such as

$M = U \Sigma V^{\top}$

Warning: This method is destructive wrt. to the matrix to decompose. You should make a COPY of that matrix if needed.

Parameters

w	: Vector of singular values: $\Sigma = diag(w)$ .
V	: Matrix .

Returns: Matrix .

Note: The singular values are ordered in decreasing fashion in w. It means that the highest singular value is in w[0].

Here an example of SVD decomposition of a non square Matrix M.

#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix M(3,2);
  M[0][0] = 1;   M[0][1] = 6;
  M[1][0] = 2;   M[1][1] = 8;
  M[2][0] = 0.5; M[2][1] = 9;
  vpColVector w;
  vpMatrix V, Sigma, U = M;
  U.svd(w, V);
  // Construct the diagonal matrix from the singular values
  Sigma.diag(w);
  // Reconstruct the initial matrix using the decomposition
  vpMatrix Mrec =  U * Sigma * V.t();
  // Here, Mrec is obtained equal to the initial value of M
  // Mrec[0][0] = 1;   Mrec[0][1] = 6;
  // Mrec[1][0] = 2;   Mrec[1][1] = 8;
  // Mrec[2][0] = 0.5; Mrec[2][1] = 9;
  std::cout << "Reconstructed M matrix: \n" << Mrec << std::endl;
}

See also: svdLapack(), svdEigen3(), svdOpenCV(), svdGsl()

Examples:: servoMomentImage.cpp.

Definition at line 1941 of file vpMatrix.cpp.

References vpException::fatalError, vpMatrix::svdEigen3(), vpMatrix::svdGsl(), vpMatrix::svdLapack(), and vpMatrix::svdOpenCV().

Referenced by vpHomography::computeDisplacement(), vpMatrix::cond(), vpHomography::DLT(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), vpMatrix::inducedL2Norm(), vpMatrix::kernel(), and vpMatrix::svdEigen3().

◆ svdEigen3()

void vpMatrix::svdEigen3	(	vpColVector &	w,
		vpMatrix &	V
	)

inherited

Singular value decomposition (SVD) using Eigen3 3rd party.

Given matrix $M$ , this function computes it singular value decomposition such as

$M = U \Sigma V^{\top}$

Warning: This method is destructive wrt. to the matrix to decompose. You should make a COPY of that matrix if needed.

Parameters

w	: Vector of singular values: $\Sigma = diag(w)$ .
V	: Matrix .

Returns: Matrix .

Note: The singular values are ordered in decreasing fashion in w. It means that the highest singular value is in w[0].

Here an example of SVD decomposition of a non square Matrix M.

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix M(3,2);
  M[0][0] = 1;
  M[1][0] = 2;
  M[2][0] = 0.5;
  M[0][1] = 6;
  M[1][1] = 8 ;
  M[2][1] = 9 ;
  vpMatrix V;
  vpColVector w;
  vpMatrix Mrec;
  vpMatrix Sigma;
  M.svdEigen3(w, V);
  // Here M is modified and is now equal to U
  // Construct the diagonal matrix from the singular values
  Sigma.diag(w);
  // Reconstruct the initial matrix M using the decomposition
  Mrec =  M * Sigma * V.t();
  // Here, Mrec is obtained equal to the initial value of M
  // Mrec[0][0] = 1;
  // Mrec[1][0] = 2;
  // Mrec[2][0] = 0.5;
  // Mrec[0][1] = 6;
  // Mrec[1][1] = 8 ;
  // Mrec[2][1] = 9 ;
  std::cout << "Reconstructed M matrix: \n" << Mrec << std::endl;
}

See also: svd(), svdLapack(), svdOpenCV(), svdGsl()

Definition at line 455 of file vpMatrix_svd.cpp.

References vpArray2D< double >::data, vpArray2D< Type >::data, vpArray2D< Type >::getCols(), vpArray2D< double >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::getRows(), vpArray2D< Type >::resize(), vpColVector::resize(), vpArray2D< Type >::size(), and vpMatrix::svd().

Referenced by vpMatrix::pseudoInverse(), and vpMatrix::svd().

◆ svdGsl()

void vpMatrix::svdGsl	(	vpColVector &	w,
		vpMatrix &	V
	)

inherited

Singular value decomposition (SVD) using GSL 3rd party.

Given matrix $M$ , this function computes it singular value decomposition such as

$M = U \Sigma V^{\top}$

Warning: This method is destructive wrt. to the matrix to decompose. You should make a COPY of that matrix if needed.

Parameters

w	: Vector of singular values: $\Sigma = diag(w)$ .
V	: Matrix .

Returns: Matrix .

Note: The singular values are ordered in decreasing fashion in w. It means that the highest singular value is in w[0].

Here an example of SVD decomposition of a non square Matrix M.

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix M(3,2);
  M[0][0] = 1;
  M[1][0] = 2;
  M[2][0] = 0.5;
  M[0][1] = 6;
  M[1][1] = 8 ;
  M[2][1] = 9 ;
  vpMatrix V;
  vpColVector w;
  vpMatrix Mrec;
  vpMatrix Sigma;
  M.svdGsl(w, V);
  // Here M is modified and is now equal to U
  // Construct the diagonal matrix from the singular values
  Sigma.diag(w);
  // Reconstruct the initial matrix M using the decomposition
  Mrec =  M * Sigma * V.t();
  // Here, Mrec is obtained equal to the initial value of M
  // Mrec[0][0] = 1;
  // Mrec[1][0] = 2;
  // Mrec[2][0] = 0.5;
  // Mrec[0][1] = 6;
  // Mrec[1][1] = 8 ;
  // Mrec[2][1] = 9 ;
  std::cout << "Reconstructed M matrix: \n" << Mrec << std::endl;
}

See also: svd(), svdEigen3(), svdOpenCV(), svdLapack()

Definition at line 350 of file vpMatrix_svd.cpp.

References vpArray2D< double >::data, vpArray2D< Type >::data, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpArray2D< Type >::resize(), and vpColVector::resize().

Referenced by vpMatrix::pseudoInverse(), and vpMatrix::svd().

◆ svdLapack()

void vpMatrix::svdLapack	(	vpColVector &	w,
		vpMatrix &	V
	)

inherited

Singular value decomposition (SVD) using Lapack 3rd party.

Given matrix $M$ , this function computes it singular value decomposition such as

$M = U \Sigma V^{\top}$

Warning: This method is destructive wrt. to the matrix to decompose. You should make a COPY of that matrix if needed.

Parameters

w	: Vector of singular values: $\Sigma = diag(w)$ .
V	: Matrix .

Returns: Matrix .

Note: The singular values are ordered in decreasing fashion in w. It means that the highest singular value is in w[0].

Here an example of SVD decomposition of a non square Matrix M.

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix M(3,2);
  M[0][0] = 1;
  M[1][0] = 2;
  M[2][0] = 0.5;
  M[0][1] = 6;
  M[1][1] = 8 ;
  M[2][1] = 9 ;
  vpMatrix V;
  vpColVector w;
  vpMatrix Mrec;
  vpMatrix Sigma;
  M.svdLapack(w, V);
  // Here M is modified and is now equal to U
  // Construct the diagonal matrix from the singular values
  Sigma.diag(w);
  // Reconstruct the initial matrix M using the decomposition
  Mrec =  M * Sigma * V.t();
  // Here, Mrec is obtained equal to the initial value of M
  // Mrec[0][0] = 1;
  // Mrec[1][0] = 2;
  // Mrec[2][0] = 0.5;
  // Mrec[0][1] = 6;
  // Mrec[1][1] = 8 ;
  // Mrec[2][1] = 9 ;
  std::cout << "Reconstructed M matrix: \n" << Mrec << std::endl;
}

See also: svd(), svdEigen3(), svdOpenCV(), svdGsl()

Definition at line 241 of file vpMatrix_svd.cpp.

References vpArray2D< Type >::data, vpArray2D< double >::data, vpException::fatalError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpArray2D< Type >::resize(), vpColVector::resize(), and vpMatrix::transpose().

Referenced by vpMatrix::pseudoInverse(), and vpMatrix::svd().

◆ svdOpenCV()

void vpMatrix::svdOpenCV	(	vpColVector &	w,
		vpMatrix &	V
	)

inherited

Singular value decomposition (SVD) using OpenCV 3rd party.

Given matrix $M$ , this function computes it singular value decomposition such as

$M = U \Sigma V^{\top}$

Warning: This method is destructive wrt. to the matrix to decompose. You should make a COPY of that matrix if needed.

Parameters

w	: Vector of singular values: $\Sigma = diag(w)$ .
V	: Matrix .

Returns: Matrix .

Note: The singular values are ordered in decreasing fashion in w. It means that the highest singular value is in w[0].

Here an example of SVD decomposition of a non square Matrix M.

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
  vpMatrix M(3,2);
  M[0][0] = 1;
  M[1][0] = 2;
  M[2][0] = 0.5;
  M[0][1] = 6;
  M[1][1] = 8 ;
  M[2][1] = 9 ;
  vpMatrix V;
  vpColVector w;
  vpMatrix Mrec;
  vpMatrix Sigma;
  M.svdOpenCV(w, V);
  // Here M is modified and is now equal to U
  // Construct the diagonal matrix from the singular values
  Sigma.diag(w);
  // Reconstruct the initial matrix M using the decomposition
  Mrec =  M * Sigma * V.t();
  // Here, Mrec is obtained equal to the initial value of M
  // Mrec[0][0] = 1;
  // Mrec[1][0] = 2;
  // Mrec[2][0] = 0.5;
  // Mrec[0][1] = 6;
  // Mrec[1][1] = 8 ;
  // Mrec[2][1] = 9 ;
  std::cout << "Reconstructed M matrix: \n" << Mrec << std::endl;
}

See also: svd(), svdEigen3(), svdLapack(), svdGsl()

Definition at line 154 of file vpMatrix_svd.cpp.

References vpArray2D< double >::data, vpArray2D< Type >::data, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpArray2D< Type >::resize(), vpArray2D< double >::resize(), vpColVector::resize(), and vpMatrix::transpose().

Referenced by vpMatrix::pseudoInverse(), and vpMatrix::svd().

◆ t()

vpMatrix vpMatrix::t ( ) const

inherited

Compute and return the transpose of the matrix.

Examples:: photometricVisualServoing.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 455 of file vpMatrix.cpp.

References vpMatrix::transpose().

Referenced by vpLinProg::colReduction(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), vpTemplateTracker::computeOptimalBrentGain(), vpMatrix::eigenValues(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), vpKalmanFilter::filtering(), vpTemplateTrackerWarpHomographySL3::findWarp(), vpQuadProg::fromCanonicalCost(), vpImageFilter::getSobelKernelX(), vpRotationMatrix::mean(), vpHomogeneousMatrix::mean(), vpKalmanFilter::prediction(), vpMatrix::pseudoInverse(), vpColVector::resize(), vpLinProg::simplex(), vpMatrix::solveByQR(), vpColVector::vpColVector(), vpTemplateTrackerWarp::warp(), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().

◆ transpose() [1/2]

vpMatrix vpMatrix::transpose ( ) const

inherited

Compute and return the transpose of the matrix.

See also: t()

Examples:: testMatrixConditionNumber.cpp.

Definition at line 465 of file vpMatrix.cpp.

Referenced by vpLinProg::colReduction(), vpServo::computeProjectionOperators(), vpQuadProg::fromCanonicalCost(), vpTemplateTrackerWarpSRT::getParamInverse(), vpTemplateTrackerWarpRT::getParamInverse(), vpColVector::resize(), vpLinProg::rowReduction(), vpLinProg::solveLP(), vpQuadProg::solveQPi(), vpMatrix::svdLapack(), vpMatrix::svdOpenCV(), and vpMatrix::t().

◆ transpose() [2/2]

void vpMatrix::transpose ( vpMatrix & At ) const

inherited

Compute At the transpose of the matrix.

Parameters

At	(output) : Resulting transpose matrix.

See also: t()

Definition at line 477 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::resize(), and vpArray2D< double >::rowNum.

Friends And Related Function Documentation

◆ operator*()

vpMatrix operator*	(	const double &	x,
		const vpMatrix &	B
	)

Definition at line 1506 of file vpMatrix.cpp.

References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().

◆ vpGEMM()

void vpGEMM	(	const vpArray2D< double > &	A,
		const vpArray2D< double > &	B,
		const double &	alpha,
		const vpArray2D< double > &	C,
		const double &	beta,
		vpArray2D< double > &	D,
		const unsigned int &	ops = `0`
	)

For example, to compute D = alpha*A^T*B^T+beta*C we need to call :

vpGEMM(A, B, alpha, C, beta, D, VP_GEMM_A_T + VP_GEMM_B_T);

If C is not used, vpGEMM must be called using an empty array null. Thus to compute D = alpha*A^T*B, we have to call:

vpGEMM(A, B, alpha, null, 0, D, VP_GEMM_B_T);

Exceptions

vpException::incorrectMatrixSizeError if the sizes of the matrices do not allow the operations.

Parameters

A	: An array that could be a vpMatrix.
B	: An array that could be a vpMatrix.
alpha	: A scalar.
C	: An array that could be a vpMatrix.
beta	: A scalar.
D	: The resulting array that could be a vpMatrix.
ops	: A scalar describing operation applied on the matrices. Possible values are the one defined in vpGEMMmethod(): VP_GEMM_A_T, VP_GEMM_B_T, VP_GEMM_C_T.

Definition at line 393 of file vpGEMM.h.

References vpException::functionNotImplementedError.

◆ vpGEMMmethod

enum vpGEMMmethod

Operations are :

VP_GEMM_A_T to use the transpose matrix of A instead of the matrix A
VP_GEMM_B_T to use the transpose matrix of B instead of the matrix B
VP_GEMM_C_T to use the transpose matrix of C instead of the matrix C

Definition at line 57 of file vpGEMM.h.

Member Data Documentation

◆ colNum

unsigned int vpArray2D< double >::colNum

protectedinherited

Number of columns in the array.

Definition at line 137 of file vpArray2D.h.

◆ data

double * vpArray2D< double >::data

inherited

Address of the first element of the data array.

Examples:: testArray2D.cpp, testDisplacement.cpp, testEigenConversion.cpp, testImageFilter.cpp, testMatrix.cpp, testTranslationVector.cpp, and tutorial-matlab.cpp.

Definition at line 145 of file vpArray2D.h.

Referenced by vpMatrix::AtA(), vpQuaternionVector::buildFrom(), vpHomogeneousMatrix::buildFrom(), vpThetaUVector::buildFrom(), vpRzyzVector::buildFrom(), vpRxyzVector::buildFrom(), vpRzyxVector::buildFrom(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), checkParentStatus(), vpColVector::clear(), vpHomogeneousMatrix::convert(), vpMatrix::detByLUEigen3(), vpMatrix::detByLUOpenCV(), vpMatrix::expm(), vpThetaUVector::extract(), vpMatrix::frobeniusNorm(), vpMatrix::getRow(), vpThetaUVector::getTheta(), vpThetaUVector::getU(), vpColVector::hadamard(), vpMatrix::hadamard(), vpSubColVector::init(), vpSubRowVector::init(), init(), vpColVector::insert(), vpMatrix::insert(), vpMatrix::inverseByCholeskyOpenCV(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByLUOpenCV(), vpTranslationVector::operator*(), vpRowVector::operator*(), vpHomography::operator*(), vpColVector::operator*(), vpMatrix::operator*(), vpRotationVector::operator,(), vpTranslationVector::operator,(), vpRotationMatrix::operator,(), vpRowVector::operator,(), vpColVector::operator,(), vpTranslationVector::operator-(), vpRowVector::operator-(), vpColVector::operator-(), vpTranslationVector::operator/(), vpRowVector::operator/(), vpHomography::operator/(), vpColVector::operator/(), vpHomography::operator/=(), vpRotationVector::operator<<(), vpTranslationVector::operator<<(), vpRotationMatrix::operator<<(), vpRowVector::operator<<(), vpColVector::operator<<(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpQuaternionVector::operator=(), vpTranslationVector::operator=(), vpRotationMatrix::operator=(), vpRxyzVector::operator=(), vpRzyzVector::operator=(), vpRzyxVector::operator=(), vpRowVector::operator=(), vpThetaUVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpRowVector::operator==(), vpColVector::operator==(), vpColVector::operator[](), vpMatrix::qr(), vpMatrix::qrPivot(), vpRowVector::reshape(), vpColVector::reshape(), vpQuaternionVector::set(), vpMatrix::stack(), vpMatrix::stackRows(), vpColVector::sum(), vpColVector::sumSquare(), vpMatrix::svdEigen3(), vpMatrix::svdGsl(), vpMatrix::svdLapack(), vpMatrix::svdOpenCV(), vpRotationVector::t(), vpTranslationVector::t(), vpPoseVector::t(), vpRowVector::t(), vpColVector::t(), vpRotationVector::toStdVector(), vpRowVector::toStdVector(), vpColVector::toStdVector(), vpColVector::vpColVector(), vpMatrix::vpMatrix(), vpRowVector::vpRowVector(), vpQuaternionVector::w(), vpQuaternionVector::x(), vpQuaternionVector::y(), vpQuaternionVector::z(), vpSubColVector::~vpSubColVector(), ~vpSubMatrix(), and vpSubRowVector::~vpSubRowVector().

◆ dsize

unsigned int vpArray2D< double >::dsize

protectedinherited

◆ parent

vpMatrix* vpSubMatrix::parent

protected

Definition at line 76 of file vpSubMatrix.h.

Referenced by checkParentStatus(), init(), and operator=().

◆ pColNum

unsigned int vpSubMatrix::pColNum

protected

Definition at line 75 of file vpSubMatrix.h.

Referenced by checkParentStatus(), init(), and operator=().

◆ pRowNum

unsigned int vpSubMatrix::pRowNum

protected

Definition at line 74 of file vpSubMatrix.h.

Referenced by checkParentStatus(), init(), and operator=().

◆ rowNum

unsigned int vpArray2D< double >::rowNum

protectedinherited

Number of rows in the array.

Definition at line 135 of file vpArray2D.h.

◆ rowPtrs

double ** vpArray2D< double >::rowPtrs

protectedinherited

Address of the first element of each rows.

Definition at line 139 of file vpArray2D.h.

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Attributes

Related Functions

Deprecated functions

Detailed Description

Member Enumeration Documentation

◆ vpDetMethod

Constructor & Destructor Documentation

◆ vpSubMatrix() [1/2]

◆ vpSubMatrix() [2/2]

◆ ~vpSubMatrix()

Member Function Documentation

◆ AAt() [1/2]

◆ AAt() [2/2]

◆ add2Matrices() [1/2]

◆ add2Matrices() [2/2]

◆ add2WeightedMatrices()

◆ AtA() [1/2]

◆ AtA() [2/2]

◆ checkParentStatus()

◆ clear()

◆ column()

◆ computeCovarianceMatrix() [1/2]

◆ computeCovarianceMatrix() [2/2]

◆ computeCovarianceMatrixVVS() [1/2]

◆ computeCovarianceMatrixVVS() [2/2]

◆ computeHLM()

◆ cond()

◆ conv2() [1/2]

◆ conv2() [2/2]

◆ cppPrint()

◆ createDiagonalMatrix()

◆ csvPrint()

◆ det()

◆ detByLU()

◆ detByLUEigen3()

◆ detByLUGsl()

◆ detByLULapack()

◆ detByLUOpenCV()

◆ diag() [1/2]

◆ diag() [2/2]

◆ eigenValues() [1/2]

◆ eigenValues() [2/2]

◆ euclideanNorm()

◆ expm()

◆ extract()

◆ eye()

◆ frobeniusNorm()

◆ getCol() [1/2]

◆ getCol() [2/2]

◆ getCols()

◆ getDiag()

◆ getMaxValue()

◆ getMinValue()

◆ getRow() [1/2]

◆ getRow() [2/2]

◆ getRows()

◆ hadamard() [1/2]

◆ hadamard() [2/2]

◆ inducedL2Norm()

◆ infinityNorm()

◆ init() [1/3]

◆ init() [2/3]

◆ init() [3/3]

◆ insert() [1/3]

◆ insert() [2/3]

◆ insert() [3/3]

◆ inverseByCholesky()

◆ inverseByCholeskyLapack()

◆ inverseByCholeskyOpenCV()

◆ inverseByLU()

◆ inverseByLUEigen3()

◆ inverseByLUGsl()

◆ inverseByLULapack()

◆ inverseByLUOpenCV()

◆ inverseByQR()

◆ inverseByQRLapack()