#include <visp3/core/vpMatrix.h>

Inheritance diagram for vpMatrix:

Public Types
enum	vpDetMethod { LU_DECOMPOSITION }

Public Member Functions
	vpMatrix ()

	vpMatrix (unsigned int r, unsigned int c)

	vpMatrix (unsigned int r, unsigned int c, double val)

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

	vpMatrix (const vpArray2D< double > &A)

	vpMatrix (const vpMatrix &A)

	vpMatrix (vpMatrix &&A)

virtual	~vpMatrix ()

void	clear ()

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

void	diag (const vpColVector &A)

void	eye ()

void	eye (unsigned int n)

void	eye (unsigned int m, unsigned int n)

Assignment operators
vpMatrix &	operator<< (double *)

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

vpMatrix &	operator= (const vpMatrix &A)

vpMatrix &	operator= (vpMatrix &&A)

vpMatrix &	operator= (const double x)

Stacking
void	stack (const vpMatrix &A)

void	stack (const vpRowVector &r)

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

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

vpMatrix	expm () const

vpMatrix &	operator+= (const vpMatrix &B)

vpMatrix &	operator-= (const vpMatrix &B)

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 vpMatrix &B) const

vpMatrix	operator- (const vpMatrix &B) const

vpMatrix	operator- () const

vpMatrix &	operator+= (const double x)

vpMatrix &	operator-= (const double x)

vpMatrix &	operator*= (const double x)

vpMatrix &	operator/= (double x)

vpMatrix	operator* (const double x) const

vpMatrix	operator/ (const double x) const

double	sum () const

double	sumSquare () const

Hadamard product
vpMatrix	hadamard (const vpMatrix &m) 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 &C) const

vpMatrix	AAt () const

void	AAt (vpMatrix &B) const

vpMatrix	AtA () const

void	AtA (vpMatrix &B) const

Matrix inversion
vpMatrix	inverseByLU () const

vpMatrix	inverseByCholesky () const

vpMatrix	inverseByQR () 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

SVD decomposition
double	cond () 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)

Eigen values
vpColVector	eigenValues () const

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

Norms
double	euclideanNorm () 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, char const *intro=0) const

void	printSize () const

Inherited functionalities from vpArray2D
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)

double *	operator[] (unsigned int i)

double *	operator[] (unsigned int i) const

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

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

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)

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

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

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

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

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

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

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)

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)

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	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

Implementation of a matrix and operations on matrices.

This class needs one of the following third-party to compute matrix inverse, pseudo-inverse, singular value decomposition, determinant:

If Lapack is installed and detected by ViSP, this 3rd party is used by vpMatrix. Installation instructions are provided here https://visp.inria.fr/3rd_lapack;
else if Eigen3 is installed and detected by ViSP, this 3rd party is used by vpMatrix. Installation instructions are provided here https://visp.inria.fr/3rd_eigen;
else if OpenCV is installed and detected by ViSP, this 3rd party is used, Installation instructions are provided here https://visp.inria.fr/3rd_opencv;
else if GSL is installed and detected by ViSP, we use this other 3rd party. Installation instructions are provided here https://visp.inria.fr/3rd_gsl.
If none of these previous 3rd parties is installed, we use by default a Lapack built-in version.

vpMatrix class provides a data structure for the matrices as well as a set of operations on these matrices.

The vpMatrix class is derived from vpArray2D<double>.

See also: vpArray2D, vpRowVector, vpColVector, vpHomogeneousMatrix, vpRotationMatrix, vpVelocityTwistMatrix, vpForceTwistMatrix, vpHomography

Examples:: manServo4PointsDisplay.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, photometricVisualServoing.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocityKalman.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoMomentImage.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPioneerPoint2DDepthWithoutVpServo.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimu4Points.cpp, servoSimuCylinder.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuSphere.cpp, servoViper650FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DArtVelocityInteractionDesired.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, servoViper850Point2DCamVelocityKalman.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testColVector.cpp, testFeature.cpp, testImageFilter.cpp, testMatrix.cpp, testMatrixDeterminant.cpp, testMatrixException.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testPoseFeatures.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testRowVector.cpp, testSvd.cpp, testTranslationVector.cpp, tutorial-image-filter.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 104 of file vpMatrix.h.

Member Enumeration Documentation

◆ vpDetMethod

enum vpMatrix::vpDetMethod

Method used to compute the determinant of a square matrix.

See also: det()

Enumerator
LU_DECOMPOSITION	LU decomposition method.

Definition at line 111 of file vpMatrix.h.

Constructor & Destructor Documentation

◆ vpMatrix() [1/7]

vpMatrix::vpMatrix ( )

inline

Basic constructor of a matrix of double. Number of columns and rows are zero.

Definition at line 120 of file vpMatrix.h.

◆ vpMatrix() [2/7]

vpMatrix::vpMatrix	(	unsigned int	r,
		unsigned int	c
	)

inline

Constructor that initialize a matrix of double with 0.

Parameters

r	: Matrix number of rows.
c	: Matrix number of columns.

Definition at line 127 of file vpMatrix.h.

◆ vpMatrix() [3/7]

vpMatrix::vpMatrix	(	unsigned int	r,
		unsigned int	c,
		double	val
	)

inline

Constructor that initialize a matrix of double with val.

Parameters

r	: Matrix number of rows.
c	: Matrix number of columns.
val	: Each element of the matrix is set to val.

Definition at line 135 of file vpMatrix.h.

◆ vpMatrix() [4/7]

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

Construct a matrix as a sub-matrix of the input matrix M.

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

Definition at line 181 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, init(), and vpArray2D< Type >::rowNum.

◆ vpMatrix() [5/7]

vpMatrix::vpMatrix ( const vpArray2D< double > & A )

inline

Create a matrix from a 2D array that could be one of the following container that inherit from vpArray2D such as vpMatrix, vpRotationMatrix, vpHomogeneousMatrix, vpPoseVector, vpColVector, vpRowVector...

The following example shows how to create a matrix from an homogeneous matrix:

vpRotationMatrix R;

vpMatrix M(R);

Definition at line 149 of file vpMatrix.h.

◆ vpMatrix() [6/7]

vpMatrix::vpMatrix ( const vpMatrix & A )

inline

Definition at line 152 of file vpMatrix.h.

◆ vpMatrix() [7/7]

vpMatrix::vpMatrix ( vpMatrix && A )

Definition at line 196 of file vpMatrix.cpp.

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

◆ ~vpMatrix()

virtual vpMatrix::~vpMatrix ( )

inlinevirtual

Destructor (Memory de-allocation)

Definition at line 158 of file vpMatrix.h.

Member Function Documentation

◆ AAt() [1/2]

vpMatrix vpMatrix::AAt ( ) const

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

Returns

See also: AAt(vpMatrix &) const

Definition at line 426 of file vpMatrix.cpp.

◆ AAt() [2/2]

void vpMatrix::AAt ( vpMatrix & B ) const

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 446 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
	)

static

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 1112 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 operator+().

◆ add2Matrices() [2/2]

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

static

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 1145 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
	)

static

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 1083 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

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

Returns

See also: AtA(vpMatrix &) const

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

Definition at line 524 of file vpMatrix.cpp.

Referenced by vpCalibration::calibrationTsai(), 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

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 480 of file vpMatrix.cpp.

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

◆ clear()

void vpMatrix::clear ( )

inline

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

Definition at line 164 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 )

Deprecated:: This method is deprecated. You should use getCol().

Return the j-th columns of the matrix.

Warning: notice column(1) is the 0-th column.

Parameters

j	: Index of the column to extract.

Definition at line 5132 of file vpMatrix.cpp.

References vpArray2D< double >::getRows().

◆ computeCovarianceMatrix() [1/2]

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

static

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(), pseudoInverse(), and t().

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

◆ computeCovarianceMatrix() [2/2]

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

static

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 t().

◆ computeCovarianceMatrixVVS() [1/2]

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

static

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

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

◆ computeCovarianceMatrixVVS() [2/2]

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

static

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 computeCovarianceMatrix(), and computeCovarianceMatrixVVS().

◆ computeHLM()

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

static

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 5013 of file vpMatrix.cpp.

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

Referenced by vpTemplateTrackerWarpHomographySL3::findWarp(), vpTemplateTrackerSSDESM::initCompInverse(), vpTemplateTrackerSSDInverseCompositional::initCompInverse(), vpTemplateTrackerZNCCForwardAdditional::initHessienDesired(), vpTemplateTrackerMIForwardCompositional::initHessienDesired(), vpTemplateTrackerZNCCInverseCompositional::initHessienDesired(), vpTemplateTrackerMIESM::initHessienDesired(), vpTemplateTrackerMIForwardAdditional::initHessienDesired(), vpTemplateTrackerMIInverseCompositional::initHessienDesired(), vpTemplateTracker::setHDes(), vpTemplateTrackerSSDForwardCompositional::trackNoPyr(), vpTemplateTrackerMIForwardCompositional::trackNoPyr(), vpTemplateTrackerSSDESM::trackNoPyr(), vpTemplateTrackerSSDForwardAdditional::trackNoPyr(), vpTemplateTrackerMIESM::trackNoPyr(), vpTemplateTrackerMIForwardAdditional::trackNoPyr(), vpTemplateTrackerMIInverseCompositional::trackNoPyr(), and vpTemplateTrackerWarp::warp().

◆ cond()

double vpMatrix::cond ( ) const

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

Definition at line 4987 of file vpMatrix.cpp.

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

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

◆ cppPrint()

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

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 4423 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
	)

static

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 711 of file vpMatrix.cpp.

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

◆ csvPrint()

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

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 4374 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

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 4848 of file vpMatrix.cpp.

References detByLU(), and LU_DECOMPOSITION.

Referenced by vpTriangle::buildFrom(), vpHomography::computeDisplacement(), detByLU(), and vpTemplateTrackerTriangle::init().

◆ detByLU()

double vpMatrix::detByLU ( ) const

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 180 of file vpMatrix_lu.cpp.

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

Referenced by det().

◆ diag() [1/2]

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

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 692 of file vpMatrix.cpp.

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

Referenced by vpMbTracker::computeCovarianceMatrixVVS().

◆ diag() [2/2]

void vpMatrix::diag ( const vpColVector & A )

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 652 of file vpMatrix.cpp.

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

◆ eigenValues() [1/2]

vpColVector vpMatrix::eigenValues ( ) const

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 4566 of file vpMatrix.cpp.

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

◆ eigenValues() [2/2]

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

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 4677 of file vpMatrix.cpp.

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

◆ euclideanNorm()

double vpMatrix::euclideanNorm ( ) const

Compute and return the Euclidean norm $||x|| = \sqrt{ \sum{A_{ij}^2}}$ .

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

See also: infinityNorm()

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

Definition at line 5038 of file vpMatrix.cpp.

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

Referenced by vpColVector::deg2rad().

◆ expm()

vpMatrix vpMatrix::expm ( ) const

Compute the exponential matrix of a square matrix.

Returns: Return the exponential matrix.

Definition at line 4866 of file vpMatrix.cpp.

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

Referenced by vpTemplateTrackerWarpHomographySL3::computeCoeff().

◆ extract()

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

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 319 of file vpMatrix.cpp.

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

Referenced by vpVelocityTwistMatrix::~vpVelocityTwistMatrix().

◆ eye() [1/3]

void vpMatrix::eye ( )

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

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

Definition at line 360 of file vpMatrix.cpp.

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

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

◆ eye() [2/3]

void vpMatrix::eye ( unsigned int n )

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

Definition at line 343 of file vpMatrix.cpp.

References eye().

◆ eye() [3/3]

void vpMatrix::eye	(	unsigned int	m,
		unsigned int	n
	)

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

Definition at line 349 of file vpMatrix.cpp.

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

◆ getCol() [1/2]

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

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

Definition at line 3797 of file vpMatrix.cpp.

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

Referenced by vpHomography::DLT(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), kernel(), vpPose::poseDementhonPlan(), vpPose::poseFromRectangle(), and vpServo::secondaryTaskJointLimitAvoidance().

◆ getCol() [2/2]

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

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 3748 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, testMatrixDeterminant.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, and testTranslationVector.cpp.

Definition at line 146 of file vpArray2D.h.

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

Referenced by vpRowVector::cppPrint(), cppPrint(), vpRowVector::csvPrint(), csvPrint(), detByLU(), extract(), vpRotationMatrix::getCol(), vpHomogeneousMatrix::getCol(), getCol(), getRow(), kernel(), vpRowVector::maplePrint(), maplePrint(), vpRowVector::matlabPrint(), matlabPrint(), vpRowVector::operator*(), vpRowVector::operator+(), vpRowVector::operator+=(), vpRowVector::operator-(), vpRowVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpRowVector::print(), print(), pseudoInverse(), and row().

◆ getMaxValue()

double vpArray2D< double >::getMaxValue ( ) const

inherited

Return the array max value.

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

Definition at line 671 of file vpArray2D.h.

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

◆ getMinValue()

double vpArray2D< double >::getMinValue ( ) const

inherited

Return the array min value.

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

Definition at line 655 of file vpArray2D.h.

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

◆ getRow() [1/2]

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

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 3843 of file vpMatrix.cpp.

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

◆ getRow() [2/2]

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

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 3895 of file vpMatrix.cpp.

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

◆ getRows()

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

inlineinherited

Return the number of rows of the 2D array.

See also: getCols(), size()

Examples:: testColVector.cpp, testDisplacement.cpp, testImageFilter.cpp, testMatrix.cpp, testMatrixDeterminant.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, and testTranslationVector.cpp.

Definition at line 156 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

Referenced by column(), vpColVector::cppPrint(), cppPrint(), vpColVector::csvPrint(), csvPrint(), detByLU(), extract(), vpRotationMatrix::getCol(), vpHomogeneousMatrix::getCol(), getCol(), getRow(), inverseByCholesky(), kernel(), vpColVector::maplePrint(), maplePrint(), vpColVector::matlabPrint(), matlabPrint(), vpColVector::operator+(), vpColVector::operator+=(), vpColVector::operator-(), vpColVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpPoseVector::print(), vpColVector::print(), print(), and pseudoInverse().

◆ hadamard() [1/2]

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 690 of file vpArray2D.h.

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

◆ hadamard() [2/2]

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

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 1512 of file vpMatrix.cpp.

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

◆ infinityNorm()

double vpMatrix::infinityNorm ( ) const

Compute and return the infinity norm ${||x||}_{\infty} = max\left(\sum_{j=0}^{n}{\mid x_{ij} \mid}\right)$ 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: euclideanNorm()

Definition at line 5059 of file vpMatrix.cpp.

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

Referenced by vpColVector::extract().

◆ init() [1/2]

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

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 258 of file vpMatrix.cpp.

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

◆ init() [2/2]

vp_deprecated void vpMatrix::init ( )

inline

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

Definition at line 673 of file vpMatrix.h.

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

◆ insert() [1/3]

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

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 4512 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::colNum, vpArray2D< double >::data, vpArray2D< Type >::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(), vpMbGenericTracker::computeVVSInteractionMatrixAndResidu(), vpMbKltMultiTracker::computeVVSInteractionMatrixAndResidu(), vpMbEdgeMultiTracker::computeVVSInteractionMatrixAndResidu(), vpMbEdgeKltMultiTracker::computeVVSInteractionMatrixAndResidu(), vpNurbs::curveKnotIns(), vpColVector::extract(), insert(), juxtaposeMatrices(), kernel(), pseudoInverse(), 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
	)

static

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 4046 of file vpMatrix.cpp.

References insert().

◆ insert() [3/3]

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

static

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 4068 of file vpMatrix.cpp.

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

◆ inverseByCholesky()

vpMatrix vpMatrix::inverseByCholesky ( ) const

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 105 of file vpMatrix_cholesky.cpp.

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

◆ inverseByLU()

vpMatrix vpMatrix::inverseByLU ( ) const

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.

Definition at line 130 of file vpMatrix_lu.cpp.

References vpException::fatalError.

◆ inverseByQR()

vpMatrix vpMatrix::inverseByQR ( ) const

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 271 of file vpMatrix_qr.cpp.

References vpException::fatalError.

◆ juxtaposeMatrices() [1/2]

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

static

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 4099 of file vpMatrix.cpp.

◆ juxtaposeMatrices() [2/2]

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

static

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 4120 of file vpMatrix.cpp.

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

◆ kernel()

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

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.

Definition at line 4763 of file vpMatrix.cpp.

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

◆ kron() [1/4]

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

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 1578 of file vpMatrix.cpp.

Referenced by kron().

◆ kron() [2/4]

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

Compute Kronecker product matrix.

Parameters

m	: vpMatrix;

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

Definition at line 1616 of file vpMatrix.cpp.

References kron().

◆ kron() [3/4]

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

static

Compute Kronecker product matrix.

Parameters

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

Definition at line 1545 of file vpMatrix.cpp.

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

◆ kron() [4/4]

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

static

Compute Kronecker product matrix.

Parameters

m1	: vpMatrix;
m2	: vpMatrix;

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

Definition at line 1586 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 318 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`
	)

inlinestatic

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 605 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`
	)

inlinestatic

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 621 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()

Definition at line 426 of file vpArray2D.h.

References vpArray2D< Type >::resize().

◆ maplePrint()

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

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 4333 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

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 4289 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
	)

static

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 805 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 operator*().

◆ mult2Matrices() [2/4]

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

static

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 854 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
	)

static

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 893 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
	)

static

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 931 of file vpMatrix.cpp.

References multMatrixVector().

◆ multMatrixVector()

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

static

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 764 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 mult2Matrices(), and operator*().

◆ negateMatrix()

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

static

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 1300 of file vpMatrix.cpp.

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

Referenced by operator-().

◆ operator*() [1/7]

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

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

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

Definition at line 940 of file vpMatrix.cpp.

References mult2Matrices().

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

◆ operator*() [2/7]

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

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

Definition at line 953 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

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

Definition at line 980 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

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 1049 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

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

Definition at line 724 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

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 749 of file vpMatrix.cpp.

References multMatrixVector().

◆ operator*() [7/7]

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

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

Definition at line 1367 of file vpMatrix.cpp.

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

◆ operator*=()

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

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 1423 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

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

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

Definition at line 1170 of file vpMatrix.cpp.

References add2Matrices().

Referenced by vpColVector::operator[]().

◆ operator+=() [1/2]

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

Operation A = A + B.

Definition at line 1259 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 )

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

Definition at line 1400 of file vpMatrix.cpp.

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

◆ operator-() [1/2]

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

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

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

Definition at line 1250 of file vpMatrix.cpp.

References sub2Matrices().

◆ operator-() [2/2]

vpMatrix vpMatrix::operator- ( void ) const

Operation C = -A (A is unchanged).

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

Definition at line 1318 of file vpMatrix.cpp.

References negateMatrix().

Referenced by vpColVector::operator[]().

◆ operator-=() [1/2]

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

Operation A = A - B.

Definition at line 1276 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 )

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

Definition at line 1410 of file vpMatrix.cpp.

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

◆ operator/()

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

Cij = Aij / x (A is unchanged)

Definition at line 1379 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 )

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

Definition at line 1433 of file vpMatrix.cpp.

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

Referenced by vpColVector::operator[]().

◆ operator<<()

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

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 606 of file vpMatrix.cpp.

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

◆ operator=() [1/4]

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

Copy operator that allows to convert on of the following container that inherit from vpArray2D such as vpMatrix, vpRotationMatrix, vpHomogeneousMatrix, vpPoseVector, vpColVector, vpRowVector... into a vpMatrix.

Parameters

A	: 2D array to be copied.

The following example shows how to create a matrix from an homogeneous matrix:

vpRotationMatrix R;

vpMatrix M = R;

Definition at line 549 of file vpMatrix.cpp.

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

◆ operator=() [2/4]

vpMatrix & vpMatrix::operator= ( const vpMatrix & A )

Definition at line 559 of file vpMatrix.cpp.

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

◆ operator=() [3/4]

vpMatrix & vpMatrix::operator= ( vpMatrix && A )

Definition at line 568 of file vpMatrix.cpp.

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

◆ operator=() [4/4]

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

Set all the element of the matrix A to x.

Definition at line 592 of file vpMatrix.cpp.

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

◆ operator[]() [1/2]

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

inlineinherited

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

Definition at line 264 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 266 of file vpArray2D.h.

◆ print()

int vpMatrix::print	(	std::ostream &	s,
		unsigned int	length,
		char const *	intro = `0`
	)		const

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.

Definition at line 4166 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

inline

Definition at line 498 of file vpMatrix.h.

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

◆ pseudoInverse() [1/5]

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

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:: testRobotViper650-frames.cpp, and testRobotViper850-frames.cpp.

Definition at line 1931 of file vpMatrix.cpp.

References vpException::fatalError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), insert(), vpArray2D< Type >::resize(), vpColVector::resize(), vpArray2D< Type >::size(), and t().

Referenced by vpCalibration::calibrationTsai(), vpSimulatorAfma6::computeArticularVelocity(), vpSimulatorViper850::computeArticularVelocity(), vpServo::computeControlLaw(), computeCovarianceMatrix(), computeCovarianceMatrixVVS(), vpPoseFeatures::computePose(), vpMbEdgeMultiTracker::computeVVSFirstPhasePoseEstimation(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbTracker::computeVVSPoseEstimation(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), vpMeEllipse::initTracking(), vpHomography::inverse(), vpMeLine::leastSquare(), vpPose::poseDementhonNonPlan(), vpPose::poseFromRectangle(), vpPose::poseVirtualVS(), vpMeEllipse::printParameters(), pseudoInverse(), vpHomography::robust(), and solveBySVD().

◆ pseudoInverse() [2/5]

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

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 1862 of file vpMatrix.cpp.

References vpException::fatalError.

◆ pseudoInverse() [3/5]

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

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 3449 of file vpMatrix.cpp.

References vpException::fatalError.

◆ pseudoInverse() [4/5]

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

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 3543 of file vpMatrix.cpp.

References pseudoInverse().

◆ pseudoInverse() [5/5]

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

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 3684 of file vpMatrix.cpp.

References vpException::fatalError.

◆ 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, testMatrixDeterminant.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 171 of file vpArray2D.h.

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

Referenced by diag(), eye(), init(), operator=(), and stack().

◆ row()

vpRowVector vpMatrix::row ( const unsigned int i )

Deprecated:: This method is deprecated. You should use getRow().

Return the i-th row of the matrix.

Warning: notice row(1) is the 0th row.

Definition at line 5116 of file vpMatrix.cpp.

References vpArray2D< double >::getCols().

Referenced by 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 508 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 = `""`
	)

inlinestatic

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 640 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 = `""`
	)

inlinestatic

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 658 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()

Definition at line 597 of file vpArray2D.h.

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

◆ setIdentity()

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

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 5147 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, testMatrix.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 158 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

Referenced by vpRowVector::insert(), vpColVector::insert(), vpColVector::operator*(), and stack().

◆ solveBySVD() [1/2]

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

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 &)

Definition at line 1668 of file vpMatrix.cpp.

References pseudoInverse().

Referenced by solveBySVD().

◆ solveBySVD() [2/2]

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

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 1719 of file vpMatrix.cpp.

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

◆ stack() [1/6]

void vpMatrix::stack ( const vpMatrix & A )

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 4447 of file vpMatrix.cpp.

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

◆ stack() [2/6]

void vpMatrix::stack ( const vpRowVector & r )

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.stackMatrices(v.t());
}

Definition at line 4478 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() [3/6]

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

static

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 3915 of file vpMatrix.cpp.

References stack().

◆ stack() [4/6]

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

static

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

Parameters

A	: Upper matrix.
r	: Lower matrix.

Returns: Stacked matrix [ A r ]^T

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

Definition at line 3934 of file vpMatrix.cpp.

References stack().

◆ stack() [5/6]

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

static

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 3954 of file vpMatrix.cpp.

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

◆ stack() [6/6]

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

static

Stack row vector v 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 4000 of file vpMatrix.cpp.

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

◆ stackColumns() [1/2]

void vpMatrix::stackColumns ( vpColVector & out )

Stacks columns of a matrix in a vector.

Parameters

out	: a vpColVector.

Definition at line 1456 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 ( )

Stacks columns of a matrix in a vector.

Returns: a vpColVector.

Definition at line 1473 of file vpMatrix.cpp.

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

◆ stackMatrices() [1/7]

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

inline

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

Definition at line 678 of file vpMatrix.h.

◆ stackMatrices() [2/7]

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

inlinestatic

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

Definition at line 683 of file vpMatrix.h.

◆ stackMatrices() [3/7]

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

inlinestatic

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

Definition at line 688 of file vpMatrix.h.

References operator*().

◆ stackMatrices() [4/7]

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

static

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

Definition at line 5106 of file vpMatrix.cpp.

References stack().

◆ stackMatrices() [5/7]

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

static

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

Definition at line 5108 of file vpMatrix.cpp.

References stack().

◆ stackMatrices() [6/7]

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

static

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

Definition at line 5096 of file vpMatrix.cpp.

References vpColVector::stack().

◆ stackMatrices() [7/7]

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

static

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

Definition at line 5101 of file vpMatrix.cpp.

References vpColVector::stack().

◆ stackRows() [1/2]

void vpMatrix::stackRows ( vpRowVector & out )

Stacks rows of a matrix in a vector

Parameters

out	: a vpRowVector.

Definition at line 1484 of file vpMatrix.cpp.

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

◆ stackRows() [2/2]

vpRowVector vpMatrix::stackRows ( )

Stacks rows of a matrix in a vector.

Returns: a vpRowVector.

Definition at line 1499 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
	)

static

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 1225 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 operator-().

◆ sub2Matrices() [2/2]

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

static

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 1192 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

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

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

Definition at line 1325 of file vpMatrix.cpp.

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

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

◆ sumSquare()

double vpMatrix::sumSquare ( ) const

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 5080 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
	)

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 1791 of file vpMatrix.cpp.

References vpException::fatalError.

Referenced by vpHomography::computeDisplacement(), cond(), vpHomography::DLT(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), kernel(), and vpPose::poseDementhonPlan().

◆ t()

vpMatrix vpMatrix::t ( ) const

Compute and return the transpose of the matrix.

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

Definition at line 375 of file vpMatrix.cpp.

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

Referenced by vpCalibration::calibrationTsai(), vpServo::computeControlLaw(), computeCovarianceMatrix(), vpTemplateTracker::computeOptimalBrentGain(), eigenValues(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), vpKalmanFilter::filtering(), vpTemplateTrackerWarpHomographySL3::findWarp(), vpPose::poseDementhonNonPlan(), vpPose::poseDementhonPlan(), vpKalmanFilter::prediction(), pseudoInverse(), vpColVector::resize(), vpColVector::vpColVector(), vpTemplateTrackerWarp::warp(), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().

◆ transpose() [1/2]

vpMatrix vpMatrix::transpose ( ) const

Compute and return the transpose of the matrix.

See also: t()

Definition at line 394 of file vpMatrix.cpp.

Referenced by vpServo::computeProjectionOperators(), vpTemplateTrackerWarpRT::getParamInverse(), vpTemplateTrackerWarpSRT::getParamInverse(), and vpColVector::resize().

◆ transpose() [2/2]

void vpMatrix::transpose ( vpMatrix & At ) const

Compute At the transpose of the matrix.

Parameters

At	(output) : Resulting transpose matrix.

See also: t()

Definition at line 406 of file vpMatrix.cpp.

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

Friends And Related Function Documentation

◆ operator*()

vpMatrix operator*	(	const double &	x,
		const vpMatrix &	B
	)

Definition at line 1349 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 76 of file vpArray2D.h.

◆ data

double * vpArray2D< double >::data

inherited

Address of the first element of the data array.

Examples:: testArray2D.cpp, testDisplacement.cpp, testMatrix.cpp, testPoseVector.cpp, and testTranslationVector.cpp.

Definition at line 84 of file vpArray2D.h.

Referenced by AtA(), vpHomogeneousMatrix::buildFrom(), vpThetaUVector::buildFrom(), vpRzyzVector::buildFrom(), vpRxyzVector::buildFrom(), vpRzyxVector::buildFrom(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpColVector::clear(), vpHomogeneousMatrix::convert(), detByLU(), vpTranslationVector::euclideanNorm(), vpRowVector::euclideanNorm(), euclideanNorm(), expm(), vpThetaUVector::extract(), getRow(), vpThetaUVector::getTheta(), vpThetaUVector::getU(), vpColVector::hadamard(), hadamard(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpColVector::insert(), insert(), inverseByCholesky(), vpTranslationVector::operator*(), vpRowVector::operator*(), vpColVector::operator*(), vpHomography::operator*(), operator*(), vpTranslationVector::operator-(), vpRowVector::operator-(), vpColVector::operator-(), vpTranslationVector::operator/(), vpRowVector::operator/(), vpColVector::operator/(), vpHomography::operator/(), vpHomography::operator/=(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpQuaternionVector::operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpRzyzVector::operator=(), vpRxyzVector::operator=(), vpRzyxVector::operator=(), vpColVector::operator=(), vpThetaUVector::operator=(), operator=(), vpColVector::operator[](), vpRowVector::reshape(), vpColVector::reshape(), vpQuaternionVector::set(), stack(), stackRows(), vpColVector::sum(), vpColVector::sumSquare(), vpRotationVector::t(), vpTranslationVector::t(), vpPoseVector::t(), vpRowVector::t(), vpColVector::t(), vpColVector::vpColVector(), vpMatrix(), vpQuaternionVector::vpQuaternionVector(), vpRxyzVector::vpRxyzVector(), vpRzyxVector::vpRzyxVector(), vpRzyzVector::vpRzyzVector(), vpThetaUVector::vpThetaUVector(), vpQuaternionVector::w(), vpQuaternionVector::x(), vpQuaternionVector::y(), vpQuaternionVector::z(), vpSubColVector::~vpSubColVector(), vpSubMatrix::~vpSubMatrix(), and vpSubRowVector::~vpSubRowVector().

◆ dsize

unsigned int vpArray2D< double >::dsize

protectedinherited

◆ rowNum

unsigned int vpArray2D< double >::rowNum

protectedinherited

Number of rows in the array.

Definition at line 74 of file vpArray2D.h.

◆ rowPtrs

double ** vpArray2D< double >::rowPtrs

protectedinherited

Address of the first element of each rows.

Definition at line 78 of file vpArray2D.h.

Referenced by AAt(), vpColVector::clear(), infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpRowVector::init(), vpColVector::init(), init(), vpRotationMatrix::operator*(), vpForceTwistMatrix::operator*(), vpVelocityTwistMatrix::operator*(), vpHomogeneousMatrix::operator*(), operator*(), vpRotationMatrix::operator*=(), operator*=(), operator+=(), operator-=(), operator/(), operator/=(), operator<<(), vpColVector::operator<<(), vpSubMatrix::operator=(), vpRotationMatrix::operator=(), vpHomogeneousMatrix::operator=(), vpForceTwistMatrix::operator=(), vpVelocityTwistMatrix::operator=(), vpRowVector::operator=(), vpColVector::operator=(), operator=(), stackColumns(), vpRowVector::sum(), sum(), vpRotationVector::sumSquare(), vpTranslationVector::sumSquare(), vpRowVector::sumSquare(), sumSquare(), transpose(), vpColVector::vpColVector(), and vpMatrix().

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

◆ vpMatrix() [1/7]

◆ vpMatrix() [2/7]

◆ vpMatrix() [3/7]

◆ vpMatrix() [4/7]

◆ vpMatrix() [5/7]

◆ vpMatrix() [6/7]

◆ vpMatrix() [7/7]

◆ ~vpMatrix()

Member Function Documentation

◆ AAt() [1/2]

◆ AAt() [2/2]

◆ add2Matrices() [1/2]

◆ add2Matrices() [2/2]

◆ add2WeightedMatrices()

◆ AtA() [1/2]

◆ AtA() [2/2]

◆ clear()

◆ column()

◆ computeCovarianceMatrix() [1/2]

◆ computeCovarianceMatrix() [2/2]

◆ computeCovarianceMatrixVVS() [1/2]

◆ computeCovarianceMatrixVVS() [2/2]

◆ computeHLM()

◆ cond()

◆ cppPrint()

◆ createDiagonalMatrix()

◆ csvPrint()

◆ det()

◆ detByLU()

◆ diag() [1/2]

◆ diag() [2/2]

◆ eigenValues() [1/2]

◆ eigenValues() [2/2]

◆ euclideanNorm()

◆ expm()

◆ extract()

◆ eye() [1/3]

◆ eye() [2/3]

◆ eye() [3/3]

◆ getCol() [1/2]

◆ getCol() [2/2]

◆ getCols()

◆ getMaxValue()

◆ getMinValue()

◆ getRow() [1/2]

◆ getRow() [2/2]

◆ getRows()

◆ hadamard() [1/2]

◆ hadamard() [2/2]

◆ infinityNorm()

◆ init() [1/2]

◆ init() [2/2]

◆ insert() [1/3]

◆ insert() [2/3]

◆ insert() [3/3]

◆ inverseByCholesky()

◆ inverseByLU()

◆ inverseByQR()

◆ juxtaposeMatrices() [1/2]

◆ juxtaposeMatrices() [2/2]

◆ kernel()

◆ kron() [1/4]

◆ kron() [2/4]

◆ kron() [3/4]

◆ kron() [4/4]

◆ load()

◆ loadMatrix()

◆ loadMatrixYAML()

◆ loadYAML()