#include <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)
VP_EXPLICIT	vpMatrix (const vpArray2D< double > &A)
	vpMatrix (const vpMatrix &A)
VP_EXPLICIT	vpMatrix (const vpHomogeneousMatrix &R)
VP_EXPLICIT	vpMatrix (const vpRotationMatrix &R)
VP_EXPLICIT	vpMatrix (const vpVelocityTwistMatrix &V)
VP_EXPLICIT	vpMatrix (const vpForceTwistMatrix &F)
VP_EXPLICIT	vpMatrix (const vpColVector &v)
VP_EXPLICIT	vpMatrix (const vpRowVector &v)
VP_EXPLICIT	vpMatrix (const vpTranslationVector &t)
	vpMatrix (vpMatrix &&A)
VP_EXPLICIT	vpMatrix (const std::initializer_list< double > &list)
VP_EXPLICIT	vpMatrix (unsigned int nrows, unsigned int ncols, const std::initializer_list< double > &list)
VP_EXPLICIT	vpMatrix (const std::initializer_list< std::initializer_list< double > > &lists)
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 *p)
vpMatrix &	operator<< (double val)
vpMatrix &	operator, (double val)
vpMatrix &	operator= (const vpArray2D< double > &A)
vpMatrix &	operator= (const vpMatrix &A)
vpMatrix &	operator= (const vpHomogeneousMatrix &M)
vpMatrix &	operator= (const vpRotationMatrix &R)
vpMatrix &	operator= (const vpVelocityTwistMatrix &V)
vpMatrix &	operator= (const vpForceTwistMatrix &F)
vpMatrix &	operator= (const vpColVector &v)
vpMatrix &	operator= (const vpRowVector &v)
vpMatrix &	operator= (const vpTranslationVector &t)
vpMatrix &	operator= (vpMatrix &&A)
vpMatrix &	operator= (const std::initializer_list< double > &list)
vpMatrix &	operator= (const std::initializer_list< std::initializer_list< double > > &lists)
vpMatrix &	operator= (double x)
Stacking
void	stack (const vpMatrix &A)
void	stack (const vpRowVector &r)
void	stack (const vpColVector &c)
void	stackColumns (vpColVector &out)
vpColVector	stackColumns ()
void	stackRows (vpRowVector &out)
vpRowVector	stackRows ()
Matrix insertion
void	insert (const vpMatrix &A, unsigned int r, 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 (unsigned int j) const
vpColVector	getCol (unsigned int j, unsigned int i_begin, unsigned int size) const
vpRowVector	getRow (unsigned int i) const
vpRowVector	getRow (unsigned int i, unsigned int j_begin, unsigned int size) const
vpColVector	getDiag () const
void	init (const vpMatrix &M, unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols)
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 &At) const
vpMatrix	AAt () const
void	AAt (vpMatrix &B) const
vpMatrix	AtA () const
void	AtA (vpMatrix &B) const
Matrix inversion
vpMatrix	inverseByLU () const
vpMatrix	inverseByLUEigen3 () const
vpMatrix	inverseByLULapack () const
vpMatrix	inverseByLUOpenCV () const
vpMatrix	inverseByCholesky () const
vpMatrix	inverseByCholeskyLapack () const
vpMatrix	inverseByCholeskyOpenCV () const
vpMatrix	inverseByQR () const
vpMatrix	inverseByQRLapack () const
vpMatrix	inverseTriangular (bool upper=true) const
vpMatrix	pseudoInverse (double svThreshold=1e-6) const
unsigned int	pseudoInverse (vpMatrix &Ap, double svThreshold=1e-6) const
unsigned int	pseudoInverse (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const
unsigned int	pseudoInverse (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt) const
unsigned int	pseudoInverse (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const
vpMatrix	pseudoInverse (int rank_in) const
int	pseudoInverse (vpMatrix &Ap, int rank_in) const
int	pseudoInverse (vpMatrix &Ap, vpColVector &sv, int rank_in) const
int	pseudoInverse (vpMatrix &Ap, vpColVector &sv, int rank_in, vpMatrix &imA, vpMatrix &imAt) const
int	pseudoInverse (vpMatrix &Ap, vpColVector &sv, int rank_in, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const
vpMatrix	pseudoInverseLapack (double svThreshold=1e-6) const
unsigned int	pseudoInverseLapack (vpMatrix &Ap, double svThreshold=1e-6) const
unsigned int	pseudoInverseLapack (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const
unsigned int	pseudoInverseLapack (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const
vpMatrix	pseudoInverseLapack (int rank_in) const
int	pseudoInverseLapack (vpMatrix &Ap, int rank_in) const
int	pseudoInverseLapack (vpMatrix &Ap, vpColVector &sv, int rank_in) const
int	pseudoInverseLapack (vpMatrix &Ap, vpColVector &sv, int rank_in, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const
vpMatrix	pseudoInverseEigen3 (double svThreshold=1e-6) const
unsigned int	pseudoInverseEigen3 (vpMatrix &Ap, double svThreshold=1e-6) const
unsigned int	pseudoInverseEigen3 (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const
unsigned int	pseudoInverseEigen3 (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const
vpMatrix	pseudoInverseEigen3 (int rank_in) const
int	pseudoInverseEigen3 (vpMatrix &Ap, int rank_in) const
int	pseudoInverseEigen3 (vpMatrix &Ap, vpColVector &sv, int rank_in) const
int	pseudoInverseEigen3 (vpMatrix &Ap, vpColVector &sv, int rank_in, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const
vpMatrix	pseudoInverseOpenCV (double svThreshold=1e-6) const
unsigned int	pseudoInverseOpenCV (vpMatrix &Ap, double svThreshold=1e-6) const
unsigned int	pseudoInverseOpenCV (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const
unsigned int	pseudoInverseOpenCV (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const
vpMatrix	pseudoInverseOpenCV (int rank_in) const
int	pseudoInverseOpenCV (vpMatrix &Ap, int rank_in) const
int	pseudoInverseOpenCV (vpMatrix &Ap, vpColVector &sv, int rank_in) const
int	pseudoInverseOpenCV (vpMatrix &Ap, vpColVector &sv, int rank_in, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const
vpMatrix	dampedInverse (const double &ratioOfMaxSvd=1e-4) const
SVD decomposition
double	cond (double svThreshold=1e-6) const
unsigned int	kernel (vpMatrix &kerAt, double svThreshold=1e-6) const
unsigned int	nullSpace (vpMatrix &kerA, double svThreshold=1e-6) const
unsigned int	nullSpace (vpMatrix &kerA, int dim) const
void	solveBySVD (const vpColVector &B, vpColVector &x) const
vpColVector	solveBySVD (const vpColVector &B) const
void	svd (vpColVector &w, vpMatrix &V)
void	svdEigen3 (vpColVector &w, vpMatrix &V)
void	svdLapack (vpColVector &w, vpMatrix &V)
void	svdOpenCV (vpColVector &w, vpMatrix &V)
QR decomposition
unsigned int	qr (vpMatrix &Q, vpMatrix &R, bool full=false, bool squareR=false, double tol=1e-6) const
unsigned int	qrPivot (vpMatrix &Q, vpMatrix &R, vpMatrix &P, bool full=false, bool squareR=false, double tol=1e-6) const
void	solveByQR (const vpColVector &b, vpColVector &x) const
vpColVector	solveByQR (const vpColVector &b) const
Eigen values
vpColVector	eigenValues () const
void	eigenValues (vpColVector &evalue, vpMatrix &evector) const
Norms
double	frobeniusNorm () const
double	inducedL2Norm () const
double	infinityNorm () const
Printing
std::ostream &	cppPrint (std::ostream &os, const std::string &matrixName="A", bool octet=false) const
std::ostream &	csvPrint (std::ostream &os) const
std::ostream &	maplePrint (std::ostream &os) const
std::ostream &	matlabPrint (std::ostream &os) const
int	print (std::ostream &s, unsigned int length, const std::string &intro="") const
void	printSize () const
Inherited functionalities from vpArray2D
unsigned int	getCols () const
double	getMaxValue () const
double	getMinValue () const
unsigned int	getRows () const
unsigned int	size () const
void	resize (unsigned int nrows, unsigned int ncols, bool flagNullify=true, bool recopy_=true)
void	reshape (unsigned int nrows, unsigned int ncols)
void	insert (const vpArray2D< double > &A, unsigned int r, unsigned int c)
bool	operator!= (const vpArray2D< double > &A) const
double *	operator[] (unsigned int i)
vpArray2D< double >	hadamard (const vpArray2D< double > &m) const

Static Public Member Functions
static vpMatrix	view (double *data, unsigned int rows, unsigned int cols)
static void	view (vpMatrix &v, double *data, unsigned int rows, unsigned int cols)
static vpArray2D< double >	view (const vpArray2D< double > &A)
Linear algebra optimization
static unsigned int	getLapackMatrixMinSize ()
static void	setLapackMatrixMinSize (unsigned int min_size)
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, unsigned int r, unsigned int c)
static void	insert (const vpMatrix &A, const vpMatrix &B, vpMatrix &C, unsigned int r, 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 vpMatrix	stack (const vpMatrix &A, const vpColVector &c)
static void	stack (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)
static void	stack (const vpMatrix &A, const vpRowVector &r, vpMatrix &C)
static void	stack (const vpMatrix &A, const vpColVector &c, vpMatrix &C)
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	mult2Matrices (const vpMatrix &A, const vpRotationMatrix &B, vpMatrix &C)
static void	mult2Matrices (const vpRotationMatrix &A, const vpMatrix &B, vpMatrix &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)

Public Attributes
double *	data

Related Symbols
(Note that these are not member symbols.)
vpMatrix	operator* (const double &x, const vpMatrix &B)
bool	operator== (const vpArray2D< double > &A) const
bool	operator== (const vpArray2D< float > &A) const
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)
enum	vpGEMMmethod

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 (unsigned int i)
VP_DEPRECATED vpColVector	column (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)

Matrix operations
double	det (vpDetMethod method=LU_DECOMPOSITION) const
double	detByLU () const
double	detByLUEigen3 () const
double	detByLULapack () const
double	detByLUOpenCV () const
vpMatrix	cholesky () const
vpMatrix	choleskyByEigen3 () const
vpMatrix	choleskyByLapack () const
vpMatrix	choleskyByOpenCV () 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 vpHomogeneousMatrix &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+= (double x)
vpMatrix &	operator-= (double x)
vpMatrix &	operator*= (double x)
vpMatrix &	operator/= (double x)
vpMatrix	operator* (double x) const
vpMatrix	operator/ (double x) const
double	sum () const
double	sumSquare () const
static vpMatrix	conv2 (const vpMatrix &M, const vpMatrix &kernel, const std::string &mode)
static void	conv2 (const vpMatrix &M, const vpMatrix &kernel, vpMatrix &res, const std::string &mode)

Matrix I/O with Static Public Member Functions
VP_DEPRECATED double	euclideanNorm () const
static bool	loadMatrix (const std::string &filename, vpArray2D< double > &M, bool binary=false, char *header=nullptr)
static bool	loadMatrixYAML (const std::string &filename, vpArray2D< double > &M, char *header=nullptr)
static bool	saveMatrix (const std::string &filename, const vpArray2D< double > &M, 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, bool binary=false, char *header=nullptr)
static bool	loadYAML (const std::string &filename, vpArray2D< double > &A, char *header=nullptr)
static bool	save (const std::string &filename, const vpArray2D< double > &A, bool binary=false, const char *header="")
static bool	saveYAML (const std::string &filename, const vpArray2D< double > &A, const char *header="")
static vpArray2D< double >	conv2 (const vpArray2D< double > &M, const vpArray2D< double > &kernel, const std::string &mode)
static bool	isFinite (const vpArray2D< double > &A)
unsigned int	rowNum
unsigned int	colNum
double **	rowPtrs
unsigned int	dsize
bool	isMemoryOwner
bool	isRowPtrsOwner

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;
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>.

The code below shows how to create a 2-by-3 matrix of doubles, set the element values and access them:

#include <visp3/code/vpMatrix.h
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  vpMatrix M(2, 3);
  M[0][0] = -1; M[0][1] =  -2; M[0][2] = -3;
  M[1][0] =  4; M[1][1] = 5.5; M[1][2] =  6.0f;
 
  std::cout << "M:" << std::endl;
  for (unsigned int i = 0; i < M.getRows(); ++i) {
    for (unsigned int j = 0; j < M.getCols(); ++j) {
      std::cout << M[i][j] << " ";
    }
    std::cout << std::endl;
  }
}

Once build, this previous code produces the following output:

M:
-1 -2 -3
4 5.5 6

If ViSP is build with c++11 enabled, you can do the same using:

#include <visp3/code/vpMatrix.h
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  vpMatrix M( {-1, -2, -3}, {4, 5.5, 6.0f} );
  std::cout << "M:\n" << M << std::endl;
}

You can also create and initialize a matrix this way:

#include <visp3/code/vpMatrix.h
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  vpMatrix M(2, 3, {-1, -2, -3, 4, 5.5, 6.0f} );
}

The Matrix could also be initialized using operator=(const std::initializer_list< std::initializer_list< double > > &)

#include <visp3/code/vpMatrix.h
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  vpMatrix M;
  M = { {-1, -2, -3}, {4, 5.5, 6.0f} };
}

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

Tutorials
If you are interested in linear algebra using vpMatrix, you may have a look at:

Tutorial: Basic linear algebra operations

Examples: catchEigenConversion.cpp, catchImageWarp.cpp, catchLuminanceMapping.cpp, catchMatrixCholesky.cpp, catchParticleFilter.cpp, catchRBT.cpp, catchRotation.cpp, manServo4PointsDisplay.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, perfImageWarp.cpp, perfMatrixMultiplication.cpp, perfMatrixTranspose.cpp, photometricMappingVisualServoing.cpp, photometricVisualServoingWithoutVpServo.cpp, quadprog.cpp, quadprog_eq.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6FourPoints2DCamVelocityLs_cur_integrator.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoFrankaIBVS-EyeToHand-Lcur_cVe_eJe.cpp, servoFrankaIBVS-EyeToHand-Lcur_cVf_fVe_eJe.cpp, servoFrankaIBVS-EyeToHand-Ldes_cVf_fVe_eJe.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPioneerPoint2DDepthWithoutVpServo.cpp, servoPixhawkDroneIBVS.cpp, servoPololuPtuPoint2DJointVelocity.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, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, servoViper850Point2DCamVelocityKalman.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testCameraParametersConversion.cpp, testColVector.cpp, testFeature.cpp, testFeatureMoment.cpp, testFrankaCartVelocity-2.cpp, testFrankaGetPose.cpp, testImageFilter.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixException.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testPoint.cpp, testPoseFeatures.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testRowVector.cpp, testSvd.cpp, testTranslationVector.cpp, tutorial-bridge-opencv-matrix.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-image-filter.cpp, tutorial-matlab.cpp, tutorial-pf.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, tutorial-simu-pioneer.cpp, tutorial-ukf.cpp, ukf-linear-example.cpp, ukf-nonlinear-complex-example.cpp, ukf-nonlinear-example.cpp, visp-compute-eye-in-hand-calibration.cpp, and visp-compute-eye-to-hand-calibration.cpp.

Definition at line 174 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 181 of file vpMatrix.h.

Constructor & Destructor Documentation

◆ vpMatrix() [1/17]

vpMatrix::vpMatrix ( )

inline

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

Definition at line 191 of file vpMatrix.h.

References vpArray2D< double >::vpArray2D().

Referenced by AAt(), AAt(), add2Matrices(), add2WeightedMatrices(), AtA(), AtA(), cholesky(), choleskyByEigen3(), choleskyByLapack(), choleskyByOpenCV(), computeCovarianceMatrix(), computeCovarianceMatrix(), computeCovarianceMatrixVVS(), computeCovarianceMatrixVVS(), computeHLM(), cond(), conv2(), conv2(), createDiagonalMatrix(), dampedInverse(), detByLULapack(), eigenValues(), eigenValues(), expm(), extract(), hadamard(), inducedL2Norm(), init(), vpSubMatrix::init(), insert(), insert(), insert(), inverseByCholesky(), inverseByCholeskyLapack(), inverseByCholeskyOpenCV(), inverseByLU(), inverseByLUEigen3(), inverseByLULapack(), inverseByLUOpenCV(), inverseByQR(), inverseByQRLapack(), inverseTriangular(), juxtaposeMatrices(), juxtaposeMatrices(), kernel(), kron(), kron(), kron(), kron(), mult2Matrices(), mult2Matrices(), mult2Matrices(), mult2Matrices(), mult2Matrices(), mult2Matrices(), multMatrixVector(), negateMatrix(), nullSpace(), nullSpace(), operator*(), operator*(), operator*(), operator*(), operator*(), operator*(), operator*(), operator*=(), operator+(), operator+=(), operator+=(), operator,(), operator-(), operator-(), operator-=(), operator-=(), operator/(), operator/=(), operator<<(), operator<<(), operator=(), operator=(), operator=(), operator=(), operator=(), operator=(), operator=(), operator=(), operator=(), operator=(), operator=(), operator=(), operator=(), vpSubMatrix::operator=(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverseEigen3(), pseudoInverseEigen3(), pseudoInverseEigen3(), pseudoInverseEigen3(), pseudoInverseEigen3(), pseudoInverseEigen3(), pseudoInverseEigen3(), pseudoInverseEigen3(), pseudoInverseLapack(), pseudoInverseLapack(), pseudoInverseLapack(), pseudoInverseLapack(), pseudoInverseLapack(), pseudoInverseLapack(), pseudoInverseLapack(), pseudoInverseLapack(), pseudoInverseOpenCV(), pseudoInverseOpenCV(), pseudoInverseOpenCV(), pseudoInverseOpenCV(), pseudoInverseOpenCV(), pseudoInverseOpenCV(), pseudoInverseOpenCV(), pseudoInverseOpenCV(), qr(), qrPivot(), solveByQR(), stack(), stack(), stack(), stack(), stack(), stack(), stack(), stack(), stackMatrices(), stackMatrices(), stackMatrices(), stackMatrices(), stackMatrices(), stackMatrices(), sub2Matrices(), svd(), svdEigen3(), svdLapack(), svdOpenCV(), t(), transpose(), transpose(), view(), view(), vpMatrix(), vpMatrix(), vpMatrix(), and vpSubMatrix::vpSubMatrix().

◆ vpMatrix() [2/17]

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 199 of file vpMatrix.h.

References vpArray2D< double >::vpArray2D().

◆ vpMatrix() [3/17]

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 208 of file vpMatrix.h.

References vpArray2D< double >::vpArray2D().

◆ vpMatrix() [4/17]

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 128 of file vpMatrix.cpp.

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

◆ vpMatrix() [5/17]

VP_EXPLICIT 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);

vpMatrix::vpMatrix

vpMatrix()

Definition vpMatrix.h:191

vpRotationMatrix

Implementation of a rotation matrix and operations on such kind of matrices.

Definition vpRotationMatrix.h:130

Definition at line 223 of file vpMatrix.h.

References vpArray2D< double >::vpArray2D().

◆ vpMatrix() [6/17]

vpMatrix::vpMatrix ( const vpMatrix & A )

inline

Definition at line 224 of file vpMatrix.h.

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

◆ vpMatrix() [7/17]

vpMatrix::vpMatrix ( const vpHomogeneousMatrix & M )

Create a matrix from a homogeneous matrix.

Parameters

M	: Homogeneous matrix.

Definition at line 146 of file vpMatrix.cpp.

◆ vpMatrix() [8/17]

vpMatrix::vpMatrix ( const vpRotationMatrix & R )

Create a matrix from a row vector.

Parameters

R	: Rotation matrix.

Definition at line 173 of file vpMatrix.cpp.

◆ vpMatrix() [9/17]

vpMatrix::vpMatrix ( const vpVelocityTwistMatrix & V )

Create a matrix from a velocity twist matrix.

Parameters

V	: Velocity twist matrix.

Definition at line 155 of file vpMatrix.cpp.

◆ vpMatrix() [10/17]

vpMatrix::vpMatrix ( const vpForceTwistMatrix & F )

Create a matrix from a force twist matrix.

Parameters

F	: Force twist matrix.

Definition at line 164 of file vpMatrix.cpp.

◆ vpMatrix() [11/17]

vpMatrix::vpMatrix ( const vpColVector & v )

Create a matrix from a column vector.

Parameters

v	: Column vector.

Definition at line 182 of file vpMatrix.cpp.

◆ vpMatrix() [12/17]

vpMatrix::vpMatrix ( const vpRowVector & v )

Create a matrix from a row vector.

Parameters

v	: Row vector.

Definition at line 191 of file vpMatrix.cpp.

◆ vpMatrix() [13/17]

vpMatrix::vpMatrix ( const vpTranslationVector & t )

Create a matrix from a row vector.

Parameters

t	: Translation vector.

Definition at line 200 of file vpMatrix.cpp.

References t().

◆ vpMatrix() [14/17]

vpMatrix::vpMatrix ( vpMatrix && A )

Definition at line 206 of file vpMatrix.cpp.

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

◆ vpMatrix() [15/17]

vpMatrix::vpMatrix ( const std::initializer_list< double > & list )

Construct a matrix from a list of double values.

Parameters

list	: List of double.

The following code shows how to use this constructor to initialize a 2-by-3 matrix using reshape() function:

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
vpMatrix M( {-1, -2, -3, 4, 5.5, 6.0f} );
M.reshape(2, 3);
std::cout << "M:\n" << M << std::endl;
}

It produces the following output:

M:
-1  -2  -3
4  5.5  6

Definition at line 236 of file vpMatrix.cpp.

References vpArray2D< double >::vpArray2D().

◆ vpMatrix() [16/17]

vpMatrix::vpMatrix	(	unsigned int	nrows,
		unsigned int	ncols,
		const std::initializer_list< double > &	list )

Construct a matrix from a list of double values.

Parameters

ncols	: Matrix number of columns.
nrows	: Matrix number of rows.
list	: List of double.

The following code shows how to use this constructor to initialize a 2-by-3 matrix:

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
vpMatrix M(2, 3, {-1, -2, -3, 4, 5.5, 6});
std::cout << "M:\n" << M << std::endl;
}

It produces the following output:

M:
-1  -2  -3
4  5.5  6

Definition at line 265 of file vpMatrix.cpp.

References vpArray2D< double >::vpArray2D().

◆ vpMatrix() [17/17]

vpMatrix::vpMatrix ( const std::initializer_list< std::initializer_list< double > > & lists )

Construct a matrix from a list of double values.

Parameters

lists

: List of double. The following code shows how to use this constructor to initialize a 2-by-3 matrix function:

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
vpMatrix M( { {-1, -2, -3}, {4, 5.5, 6} } );
std::cout << "M:\n" << M << std::endl;
}

It produces the following output:

M:
-1  -2  -3
4  5.5  6

Definition at line 293 of file vpMatrix.cpp.

References vpArray2D< double >::vpArray2D().

Member Function Documentation

◆ AAt() [1/2]

vpMatrix vpMatrix::AAt ( ) const

Computes the operation

Returns: The product .

See also: AAt(vpMatrix &) const

Examples: perfMatrixMultiplication.cpp.

Definition at line 644 of file vpMatrix_operations.cpp.

References AAt(), and vpMatrix().

Referenced by AAt(), vpServo::computeControlLaw(), vpServo::computeControlLaw(), vpServo::computeControlLaw(), and vpServo::computeProjectionOperators().

◆ AAt() [2/2]

void vpMatrix::AAt ( vpMatrix & B ) const

Compute the AAt operation such as .

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 664 of file vpMatrix_operations.cpp.

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

◆ add2Matrices() [1/2]

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 521 of file vpMatrix_operations.cpp.

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

◆ add2Matrices() [2/2]

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 487 of file vpMatrix_operations.cpp.

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

Referenced by operator+().

◆ 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 455 of file vpMatrix_operations.cpp.

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

◆ AtA() [1/2]

vpMatrix vpMatrix::AtA ( ) const

Compute the AtA operation such as .

Returns: The product .

See also: AtA(vpMatrix &) const

Examples: perfMatrixMultiplication.cpp, photometricVisualServoingWithoutVpServo.cpp, and testMatrixInverse.cpp.

Definition at line 785 of file vpMatrix_operations.cpp.

References AtA(), and vpMatrix().

Referenced by AtA(), vpServo::computeProjectionOperators(), vpMbTracker::computeVVSPoseEstimation(), vpTemplateTrackerWarpHomographySL3::findWarp(), and vpNurbs::globalCurveApprox().

◆ AtA() [2/2]

void vpMatrix::AtA ( vpMatrix & B ) const

Compute the AtA operation such as .

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 727 of file vpMatrix_operations.cpp.

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

◆ cholesky()

vpMatrix vpMatrix::cholesky ( ) const

Definition at line 1660 of file vpMatrix.cpp.

References choleskyByEigen3(), choleskyByLapack(), choleskyByOpenCV(), vpException::fatalError, and vpMatrix().

Referenced by choleskyByLapack(), vpUKSigmaDrawerMerwe::drawSigmaPoints(), and inverseByCholeskyLapack().

◆ choleskyByEigen3()

vpMatrix vpMatrix::choleskyByEigen3 ( ) const

Compute the Cholesky decomposition of a Hermitian positive-definite matrix using Eigen3 library.

Returns: vpMatrix The lower triangular matrix resulting from the Cholesky decomposition

Examples: catchMatrixCholesky.cpp.

Definition at line 372 of file vpMatrix_cholesky.cpp.

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

Referenced by cholesky().

◆ choleskyByLapack()

vpMatrix vpMatrix::choleskyByLapack ( ) const

Compute the Cholesky decomposition of a Hermitian positive-definite matrix using Lapack library.

Returns: vpMatrix The lower triangular matrix resulting from the Cholesky decomposition

Examples: catchMatrixCholesky.cpp.

Definition at line 228 of file vpMatrix_cholesky.cpp.

References cholesky(), vpArray2D< double >::colNum, vpMatrixException::forbiddenOperatorError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpMatrixException::matrixError, vpArray2D< double >::rowNum, and vpMatrix().

Referenced by cholesky().

◆ choleskyByOpenCV()

vpMatrix vpMatrix::choleskyByOpenCV ( ) const

Compute the Cholesky decomposition of a Hermitian positive-definite matrix using OpenCV library.

Returns: vpMatrix The lower triangular matrix resulting from the Cholesky decomposition

Examples: catchMatrixCholesky.cpp.

Definition at line 342 of file vpMatrix_cholesky.cpp.

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

Referenced by cholesky().

◆ clear()

void vpMatrix::clear ( )

inline

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

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

Definition at line 247 of file vpMatrix.h.

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

Referenced by check-tests.JavaParser::__init__(), gen2.PythonWrapperGenerator::__init__(), gen2.PythonWrapperGenerator::gen(), and gen_java.JavaWrapperGenerator::gen().

◆ column()

vpColVector vpMatrix::column ( unsigned int j )

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

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

should be replaced with:

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

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

Parameters

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

Definition at line 2055 of file vpMatrix.cpp.

References vpArray2D< double >::getRows().

◆ computeCovarianceMatrix() [1/2]

BEGIN_VISP_NAMESPACE 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 minimization 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 55 of file vpMatrix_covariance.cpp.

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

Referenced by computeCovarianceMatrixVVS(), computeCovarianceMatrixVVS(), 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 minimization 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 weights matrix from WAx = Wb.

Definition at line 84 of file vpMatrix_covariance.cpp.

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

◆ computeCovarianceMatrixVVS() [1/2]

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 119 of file vpMatrix_covariance.cpp.

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

◆ computeCovarianceMatrixVVS() [2/2]

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 144 of file vpMatrix_covariance.cpp.

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

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

◆ 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 1882 of file vpMatrix.cpp.

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

◆ cond()

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

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

Parameters

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

Examples: testMatrixConditionNumber.cpp.

Definition at line 1815 of file vpMatrix.cpp.

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

Referenced by pseudoInverseOpenCV().

◆ conv2() [1/3]

vpArray2D< double > vpArray2D< double >::conv2	(	const vpArray2D< double > &	M,
		const vpArray2D< double > &	kernel,
		const std::string &	mode )

staticinherited

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

Parameters

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

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

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

Definition at line 1142 of file vpArray2D.h.

References vpArray2D().

◆ conv2() [2/3]

vpMatrix vpMatrix::conv2	(	const vpMatrix &	M,
		const vpMatrix &	kernel,
		const std::string &	mode )

static

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

Parameters

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

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

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

Examples: testMatrixConvolution.cpp.

Definition at line 1047 of file vpMatrix_operations.cpp.

References conv2(), kernel(), and vpMatrix().

Referenced by conv2().

◆ conv2() [3/3]

void vpMatrix::conv2	(	const vpMatrix &	M,
		const vpMatrix &	kernel,
		vpMatrix &	res,
		const std::string &	mode )

static

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

Parameters

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

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

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

Definition at line 1054 of file vpMatrix_operations.cpp.

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

◆ 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 1112 of file vpMatrix.cpp.

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

Referenced by pseudoInverseOpenCV().

◆ 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 897 of file vpMatrix_operations.cpp.

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

◆ csvPrint()

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

Print/save a matrix in csv format.

The following code

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 1057 of file vpMatrix.cpp.

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

Referenced by pseudoInverseOpenCV().

◆ dampedInverse()

vpMatrix vpMatrix::dampedInverse ( const double & ratioOfMaxSvd = 1e-4 ) const

Permits to compute an approximated inverse of a matrix that is ill-conditionned. If the matrix is well-conditionned, the damped inverse is close to the Moore-Penrose pseudo-inverse.

The corresponding equation is the following, assuming that $\textbf{A}$ is the matrix we want to compute the damped inverse:

$\textbf{A} \approx ( \lambda \textbf{I} + \textbf{A}^T \textbf{A})^{-1} \textbf{A}^T$

Parameters

[in] ratioOfMaxSvd The ratio of the maximum singular value of we want to set $\lambda$ .

Returns: vpMatrix The damped inverse.

Definition at line 1029 of file vpMatrix_pseudo_inverse.cpp.

References vpArray2D< double >::colNum, inverseByLU(), svd(), transpose(), and vpMatrix().

Referenced by pseudoInverseOpenCV().

◆ 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 (Eigen3): " << A.detByLUEigen3() << std::endl;
}

Examples: testMatrixInverse.cpp.

Definition at line 1649 of file vpMatrix.cpp.

References det(), detByLU(), and LU_DECOMPOSITION.

Referenced by det(), detByLULapack(), detByLUOpenCV(), vpTemplateTrackerTriangle::init(), and inverseByLU().

◆ 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.

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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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()

Definition at line 236 of file vpMatrix_lu.cpp.

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

Referenced by det().

◆ detByLUEigen3()

double vpMatrix::detByLUEigen3 ( ) const

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

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

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

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

Definition at line 656 of file vpMatrix_lu.cpp.

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

Referenced by detByLU().

◆ detByLULapack()

double vpMatrix::detByLULapack ( ) const

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

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

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

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

Definition at line 404 of file vpMatrix_lu.cpp.

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

Referenced by detByLU().

◆ detByLUOpenCV()

double vpMatrix::detByLUOpenCV ( ) const

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

Returns: Determinant of the matrix.

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

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

Definition at line 558 of file vpMatrix_lu.cpp.

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

Referenced by detByLU().

◆ 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 878 of file vpMatrix_operations.cpp.

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

Referenced by vpMbTracker::computeCovarianceMatrixVVS(), getDiag(), and vpRBFeatureTracker::updateCovariance().

◆ 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 833 of file vpMatrix_operations.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 using Lapack 3rd party.

Returns: The eigenvalues of a n-by-n real symmetric matrix, sorted in ascending order.

Exceptions

vpException::dimensionError	If the matrix is not square.
vpException::fatalError	If the matrix is not symmetric.
vpException::functionNotImplementedError	If the Lapack 3rd party is not detected.

Here an example:

#include <iostream>
 
#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 1204 of file vpMatrix.cpp.

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

Referenced by vpQuadProg::fromCanonicalCost(), vpMath::lineFitting(), and pseudoInverseOpenCV().

◆ eigenValues() [2/2]

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

Compute the eigenvalues of a n-by-n real symmetric matrix using Lapack 3rd party.

Parameters

evalue	: Eigenvalues of the matrix, sorted in ascending order.
evector	: Corresponding eigenvectors of the matrix.

Exceptions

vpException::dimensionError	If the matrix is not square.
vpException::fatalError	If the matrix is not symmetric.
vpException::functionNotImplementedError	If Lapack 3rd party is not detected.

Here an example:

#include <iostream>
 
#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 1327 of file vpMatrix.cpp.

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

◆ euclideanNorm()

double vpMatrix::euclideanNorm ( ) const

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

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

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

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

Definition at line 2008 of file vpMatrix.cpp.

References frobeniusNorm().

◆ expm()

vpMatrix vpMatrix::expm ( ) const

Compute the exponential matrix of a square matrix.

Returns: Return the exponential matrix.

Definition at line 1681 of file vpMatrix.cpp.

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

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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 436 of file vpMatrix.cpp.

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

Referenced by vpLinProg::colReduction().

◆ eye() [1/3]

void vpMatrix::eye ( )

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

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

Definition at line 928 of file vpMatrix_operations.cpp.

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

Referenced by vpLinProg::colReduction(), vpMbDepthDenseTracker::computeVVS(), vpMbDepthNormalTracker::computeVVS(), vpMbGenericTracker::computeVVS(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbTracker::computeVVSPoseEstimation(), expm(), eye(), eye(), vpFeatureThetaU::interaction(), vpRBVisualOdometryUtils::levenbergMarquardtKeypoints2D(), vpRBVisualOdometryUtils::levenbergMarquardtKeypoints3D(), vpRobotKinova::setCartVelocity(), vpServo::setServo(), vpLinProg::solveLP(), and vpRBTracker::track().

◆ eye() [2/3]

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 917 of file vpMatrix_operations.cpp.

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

◆ eye() [3/3]

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 911 of file vpMatrix_operations.cpp.

References eye().

◆ frobeniusNorm()

double vpMatrix::frobeniusNorm ( ) const

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

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

See also: infinityNorm(), inducedL2Norm()

Examples: testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 1903 of file vpMatrix.cpp.

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

Referenced by euclideanNorm(), and pseudoInverseOpenCV().

◆ getCol() [1/2]

vpColVector vpMatrix::getCol ( 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  vpMatrix A(4,4);
 
  for (unsigned int i = 0; i < A.getRows(); i++)
    for (unsigned int j = 0; j < A.getCols(); j++)
      A[i][j] = i*A.getCols()+j;
 
  A.print(std::cout, 4);
 
  vpColVector cv = A.getCol(1);
  std::cout << "Column vector: \n" << cv << std::endl;
}

It produces the following output :

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

Examples: testMatrix.cpp.

Definition at line 560 of file vpMatrix.cpp.

References getCol(), and vpArray2D< double >::rowNum.

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

◆ getCol() [2/2]

vpColVector vpMatrix::getCol	(	unsigned int	j,
		unsigned int	i_begin,
		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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 504 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: catchLuminanceMapping.cpp, catchMatrixCholesky.cpp, catchPoseVector.cpp, perfMatrixMultiplication.cpp, perfMatrixTranspose.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 423 of file vpArray2D.h.

Referenced by vpMatrix::choleskyByEigen3(), vpMatrix::choleskyByLapack(), vpMatrix::choleskyByOpenCV(), vpMatrix::cond(), vpMatrix::cppPrint(), vpRowVector::cppPrint(), vpMatrix::csvPrint(), vpRowVector::csvPrint(), vpMatrix::detByLUEigen3(), vpMatrix::extract(), vpHomogeneousMatrix::getCol(), vpMatrix::getCol(), vpRotationMatrix::getCol(), vpMatrix::inducedL2Norm(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByQRLapack(), vpRotationMatrix::isARotationMatrix(), vpMatrix::kernel(), vpMatrix::maplePrint(), vpRowVector::maplePrint(), vpMatrix::matlabPrint(), vpRowVector::matlabPrint(), vpMatrix::nullSpace(), vpMatrix::nullSpace(), vpRowVector::operator*(), vpRowVector::operator+(), vpRowVector::operator+=(), vpRowVector::operator-(), vpRowVector::operator-=(), vpForceTwistMatrix::print(), vpMatrix::print(), vpRowVector::print(), vpVelocityTwistMatrix::print(), vpMatrix::row(), vpMatrix::svdEigen3(), vpMatrix::svdLapack(), vpMatrix::svdOpenCV(), vpRowVector::vpRowVector(), and vpRowVector::vpRowVector().

◆ getDiag()

vpColVector vpMatrix::getDiag ( ) const

Extract a diagonal vector from a matrix.

Returns: The diagonal of the matrix.

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

The following example shows how to use this function:

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

It produces the following output :

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

Definition at line 699 of file vpMatrix.cpp.

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

◆ getLapackMatrixMinSize()

unsigned int vpMatrix::getLapackMatrixMinSize ( )

inlinestatic

Return the minimum size of rows and columns required to enable Blas/Lapack usage on matrices and vectors.

To get more info see Tutorial: Basic linear algebra operations.

See also: setLapackMatrixMinSize()

Examples: perfMatrixMultiplication.cpp.

Definition at line 276 of file vpMatrix.h.

◆ getMaxValue()

double vpArray2D< double >::getMaxValue ( ) const

inherited

Return the array max value.

Examples: servoMomentImage.cpp.

Definition at line 425 of file vpArray2D.h.

◆ getMinValue()

double vpArray2D< double >::getMinValue ( ) const

inherited

Return the array min value.

Examples: servoMomentImage.cpp.

Definition at line 427 of file vpArray2D.h.

◆ getRow() [1/2]

vpRowVector vpMatrix::getRow ( 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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: catchLuminanceMapping.cpp, and testMatrix.cpp.

Definition at line 602 of file vpMatrix.cpp.

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

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

◆ getRow() [2/2]

vpRowVector vpMatrix::getRow	(	unsigned int	i,
		unsigned int	j_begin,
		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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 647 of file vpMatrix.cpp.

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

◆ getRows()

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

inlineinherited

Return the number of rows of the 2D array.

See also: getCols(), size()

Examples: catchLuminanceMapping.cpp, catchMatrixCholesky.cpp, catchParticleFilter.cpp, catchPoseVector.cpp, perfMatrixMultiplication.cpp, perfMatrixTranspose.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 433 of file vpArray2D.h.

◆ 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 : $m1 \circ m2 = (m1 \circ m2)_{i,j} = (m1)_{i,j} (m2)_{i,j}$

Definition at line 732 of file vpArray2D.h.

References vpArray2D().

◆ 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 948 of file vpMatrix_operations.cpp.

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

◆ inducedL2Norm()

double vpMatrix::inducedL2Norm ( ) const

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

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

See also: infinityNorm(), frobeniusNorm()

Examples: testMatrixConditionNumber.cpp.

Definition at line 1922 of file vpMatrix.cpp.

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

Referenced by pseudoInverseOpenCV().

◆ infinityNorm()

double vpMatrix::infinityNorm ( ) const

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

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

See also: frobeniusNorm(), inducedL2Norm()

Definition at line 1963 of file vpMatrix.cpp.

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

Referenced by vpLinProg::colReduction(), pseudoInverseOpenCV(), and vpLinProg::rowReduction().

◆ init() [1/2]

VP_DEPRECATED void vpMatrix::init ( )

inline

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

Definition at line 1094 of file vpMatrix.h.

Referenced by vpSubMatrix::vpSubMatrix().

◆ init() [2/2]

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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 369 of file vpMatrix.cpp.

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

Referenced by vpMatrix().

◆ insert() [1/4]

void vpArray2D< double >::insert	(	const vpArray2D< double > &	A,
		unsigned int	r,
		unsigned int	c )

inlineinherited

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

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

Parameters

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

Definition at line 586 of file vpArray2D.h.

◆ insert() [2/4]

vpMatrix vpMatrix::insert	(	const vpMatrix &	A,
		const vpMatrix &	B,
		unsigned int	r,
		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 727 of file vpMatrix.cpp.

References vpArray2D< Type >::insert(), vpArray2D< double >::vpArray2D(), and vpMatrix().

◆ insert() [3/4]

void insert	(	const vpMatrix &	A,
		const vpMatrix &	B,
		vpMatrix &	C,
		unsigned int	r,
		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 749 of file vpMatrix.cpp.

References vpArray2D< Type >::insert(), vpArray2D< double >::vpArray2D(), and vpMatrix().

◆ insert() [4/4]

void vpMatrix::insert	(	const vpMatrix &	A,
		unsigned int	r,
		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 1145 of file vpMatrix.cpp.

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

Referenced by cond(), conv2(), juxtaposeMatrices(), kernel(), nullSpace(), nullSpace(), vpRobotKinova::setCartVelocity(), and stack().

◆ inverseByCholesky()

BEGIN_VISP_NAMESPACE 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 112 of file vpMatrix_cholesky.cpp.

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

Referenced by vpUnscentedKalman::update().

◆ inverseByCholeskyLapack()

vpMatrix vpMatrix::inverseByCholeskyLapack ( ) const

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

Returns: The inverse matrix.

Here an example:

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

See also: inverseByCholesky(), inverseByCholeskyOpenCV()

Definition at line 164 of file vpMatrix_cholesky.cpp.

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

Referenced by inverseByCholesky().

◆ inverseByCholeskyOpenCV()

vpMatrix vpMatrix::inverseByCholeskyOpenCV ( ) const

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

Returns: The inverse matrix.

Here an example:

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

See also: inverseByCholesky(), inverseByCholeskyLapack()

Definition at line 320 of file vpMatrix_cholesky.cpp.

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

Referenced by inverseByCholesky().

◆ inverseByLU()

BEGIN_VISP_NAMESPACE 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

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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 defined(VISP_HAVE_OPENCV)
  std::cout << "(using OpenCV)";
#endif
  std::cout << ": \n" << A_1 << std::endl;
 
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

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

Examples: testMatrixConditionNumber.cpp.

Definition at line 130 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, det(), vpException::fatalError, inverseByLUEigen3(), inverseByLULapack(), inverseByLUOpenCV(), vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, and vpMatrix().

Referenced by dampedInverse(), expm(), vpTemplateTrackerWarpHomographySL3::findWarp(), vpTemplateTrackerTriangle::init(), vpTemplateTrackerSSDInverseCompositional::initCompInverse(), and vpImageTools::warpImage().

◆ inverseByLUEigen3()

vpMatrix vpMatrix::inverseByLUEigen3 ( ) const

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

Returns: The inverse matrix.

Here an example:

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

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

Definition at line 610 of file vpMatrix_lu.cpp.

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

Referenced by inverseByLU().

◆ inverseByLULapack()

vpMatrix vpMatrix::inverseByLULapack ( ) const

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

Returns: The inverse matrix.

Here an example:

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

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

Definition at line 303 of file vpMatrix_lu.cpp.

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

Referenced by inverseByLU().

◆ inverseByLUOpenCV()

vpMatrix vpMatrix::inverseByLUOpenCV ( ) const

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

Returns: The inverse matrix.

Here an example:

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

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

Definition at line 513 of file vpMatrix_lu.cpp.

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

Referenced by inverseByLU().

◆ 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 382 of file vpMatrix_qr.cpp.

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

Referenced by vpLinProg::simplex().

◆ inverseByQRLapack()

BEGIN_VISP_NAMESPACE vpMatrix vpMatrix::inverseByQRLapack ( ) const

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

Returns: The inverse matrix.

Here an example:

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

See also: inverseByQR()

Definition at line 148 of file vpMatrix_qr.cpp.

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

Referenced by inverseByQR().

◆ inverseTriangular()

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

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

Parameters

upper : if it is an upper triangular matrix

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

Returns: The inverse matrix

Definition at line 1172 of file vpMatrix_qr.cpp.

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

◆ isFinite()

bool vpArray2D< double >::isFinite ( const vpArray2D< double > & A )

inlinestaticinherited

Definition at line 1188 of file vpArray2D.h.

◆ 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 769 of file vpMatrix.cpp.

References juxtaposeMatrices(), and vpMatrix().

Referenced by vpLinProg::colReduction(), and juxtaposeMatrices().

◆ 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 790 of file vpMatrix.cpp.

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

◆ 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 of the matrix.

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

Definition at line 1424 of file vpMatrix.cpp.

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

Referenced by conv2(), conv2(), and pseudoInverseOpenCV().

◆ kron() [1/4]

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 1045 of file vpMatrix_operations.cpp.

References kron(), and vpMatrix().

◆ kron() [2/4]

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 1013 of file vpMatrix_operations.cpp.

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

◆ 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 974 of file vpMatrix_operations.cpp.

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

◆ kron() [4/4]

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 1005 of file vpMatrix_operations.cpp.

References kron(), and vpMatrix().

Referenced by kron(), and kron().

◆ load()

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

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 760 of file vpArray2D.h.

◆ loadMatrix()

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

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 data are considered as binary, otherwise as human readable (text) data. Using binary data allows to keep data precision.
header	: Header of the file is loaded in this parameter.

Returns: Returns true if success, false otherwise.

The following example shows how to use this function:

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  std::string filename("matrix.bin");
  bool binary_data = true;
  {
    vpMatrix M(2, 3);
    M[0][0] = -1; M[0][1] =  -2; M[0][2] = -3;
    M[1][0] =  4; M[1][1] = 5.5; M[1][2] =  6.0f;
 
    std::string header("My header");
 
    if (vpMatrix::saveMatrix(filename, M, binary_data, header.c_str())) {
      std::cout << "Matrix saved in " << filename << std::endl;
      M.print(std::cout, 10, header);
    } else {
      std::cout << "Cannot save matrix in " << filename << std::endl;
    }
  }
  {
    vpMatrix N;
    char header[FILENAME_MAX];
    if (vpMatrix::loadMatrix(filename, N, binary_data, header)) {
      std::cout << "Matrix loaded from " << filename << std::endl;
      N.print(std::cout, 10, header);
    } else {
      std::cout << "Cannot load matrix from " << filename << std::endl;
    }
  }
}

The output of this example is the following:

Matrix saved in matrix.bin
My header[2,3]=
  -1.0 -2.0 -3.0
   4.0  5.5  6.0
Matrix loaded from matrix.bin
My header[2,3]=
  -1.0 -2.0 -3.0
   4.0  5.5  6.0

And the content of matrix.bin file where data are saved as binary data is the following:

% cat matrix.bin
My header??@@@%

See also: saveMatrix(), saveMatrixYAML(), loadMatrixYAML()

Examples: testMatrix.cpp.

Definition at line 841 of file vpMatrix.h.

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

Referenced by vpDot2::defineDots(), and vpLuminancePCA::load().

◆ loadMatrixYAML()

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

inlinestatic

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

Parameters

filename	: Absolute YAML file name.
M	: Matrix to be loaded from the file.
header	: Header of the file is loaded in this parameter.

Returns: Returns true when success, false otherwise.

The following example shows how to use this function:

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  std::string filename("matrix.yaml");
  {
    vpMatrix M(2, 3);
    M[0][0] = -1; M[0][1] =  -2; M[0][2] = -3;
    M[1][0] =  4; M[1][1] = 5.5; M[1][2] =  6.0f;
 
    std::string header("My header");
 
    if (vpMatrix::saveMatrixYAML(filename, M, header.c_str())) {
      std::cout << "Matrix saved in " << filename << std::endl;
      M.print(std::cout, 10, header);
    } else {
      std::cout << "Cannot save matrix in " << filename << std::endl;
    }
  }
  {
    vpMatrix N;
    char header[FILENAME_MAX];
    if (vpMatrix::loadMatrixYAML(filename, N, header)) {
      std::cout << "Matrix loaded from " << filename << std::endl;
      N.print(std::cout, 10, header);
    } else {
      std::cout << "Cannot load matrix from " << filename << std::endl;
    }
  }
}

The output of this example is the following:

Matrix saved in matrix.yaml
My header[2,3]=
  -1.0 -2.0 -3.0
   4.0  5.5  6.0
Matrix loaded from matrix.yaml
My header[2,3]=
  -1.0 -2.0 -3.0
   4.0  5.5  6.0

And the content of matrix.yaml file is the following:

% cat matrix.yaml
My header
rows: 2
cols: 3
data:
  - [-1, -2, -3]
  - [4, 5.5, 6]

See also: saveMatrixYAML(), saveMatrix(), loadMatrix()

Examples: testMatrix.cpp.

Definition at line 920 of file vpMatrix.h.

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

◆ loadYAML()

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

inlinestaticinherited

Load an array from a YAML-formatted file.

Parameters

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

Returns: Returns true on success.

See also: saveYAML()

Examples: servoFlirPtuIBVS.cpp, servoFrankaIBVS-EyeToHand-Lcur_cVe_eJe.cpp, servoFrankaIBVS-EyeToHand-Lcur_cVf_fVe_eJe.cpp, servoFrankaIBVS-EyeToHand-Ldes_cVf_fVe_eJe.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, servoUniversalRobotsIBVS.cpp, servoUniversalRobotsPBVS.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-hsv-segmentation-pcl-viewer.cpp, tutorial-hsv-segmentation-pcl.cpp, tutorial-hsv-segmentation.cpp, visp-compute-eye-in-hand-calibration.cpp, and visp-compute-eye-to-hand-calibration.cpp.

Definition at line 874 of file vpArray2D.h.

◆ 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 1010 of file vpMatrix.cpp.

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

Referenced by pseudoInverseOpenCV().

◆ 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 959 of file vpMatrix.cpp.

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

Referenced by vpFeatureMoment::operator<<, vpFeatureMomentCentered::operator<<, and pseudoInverseOpenCV().

◆ mult2Matrices() [1/6]

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 440 of file vpMatrix_operations.cpp.

References multMatrixVector(), and vpMatrix().

◆ mult2Matrices() [2/6]

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 378 of file vpMatrix_operations.cpp.

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

◆ mult2Matrices() [3/6]

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*()

Examples: perfMatrixMultiplication.cpp.

Definition at line 158 of file vpMatrix_operations.cpp.

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

Referenced by vpPointMap::getVisiblePoints(), vpRBVisualOdometryUtils::levenbergMarquardtKeypoints2D(), vpRBVisualOdometryUtils::levenbergMarquardtKeypoints3D(), operator*(), vpPointMap::project(), vpPointMap::project(), and vpRBDenseDepthTracker::vpDepthPointSet::updateAndErrorAndInteractionMatrix().

◆ mult2Matrices() [4/6]

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 340 of file vpMatrix_operations.cpp.

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

◆ mult2Matrices() [5/6]

void vpMatrix::mult2Matrices	(	const vpMatrix &	A,
		const vpRotationMatrix &	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 218 of file vpMatrix_operations.cpp.

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

◆ mult2Matrices() [6/6]

void vpMatrix::mult2Matrices	(	const vpRotationMatrix &	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 277 of file vpMatrix_operations.cpp.

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

◆ 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 102 of file vpMatrix_operations.cpp.

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

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 623 of file vpMatrix_operations.cpp.

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

Referenced by operator-().

◆ nullSpace() [1/2]

unsigned int vpMatrix::nullSpace	(	vpMatrix &	kerA,
		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

kerA	: The matrix that contains the null space (kernel) of $\bf A$ . If matrix $\bf A$ is full rank, the dimension of `kerA` is (n, 0), otherwise its dimension is (n, n-r).
svThreshold	: Threshold used to test the singular values. The dimension of kerA corresponds to the number of singular values lower than this threshold

Returns: The dimension of the nullspace, that is .

Definition at line 1499 of file vpMatrix.cpp.

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

Referenced by vpMeEllipse::leastSquare(), vpMeLine::leastSquare(), vpMeEllipse::leastSquareRobustEllipse(), and pseudoInverseOpenCV().

◆ nullSpace() [2/2]

unsigned int vpMatrix::nullSpace	(	vpMatrix &	kerA,
		int	dim ) 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

kerA	: The matrix that contains the null space (kernel) of $\bf A$ . If matrix $\bf A$ is full rank, the dimension of `kerA` is (n, 0), otherwise its dimension is (n, n-r).
dim	: the dimension of the null space when it is known a priori

Returns: The estimated dimension of the nullspace, that is , by using 1e-6 as threshold for the sigular values.

Definition at line 1567 of file vpMatrix.cpp.

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

◆ operator!=()

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

inherited

Not equal to comparison operator of a 2D array.

Definition at line 612 of file vpArray2D.h.

References vpArray2D().

◆ operator*() [1/8]

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 403 of file vpMatrix_operators.cpp.

References multMatrixVector().

◆ operator*() [2/8]

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 548 of file vpMatrix_operators.cpp.

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

◆ operator*() [3/8]

vpMatrix vpMatrix::operator* ( const vpHomogeneousMatrix & M ) const

Operator that allow to multiply a matrix by a homogeneous matrix. The matrix should be of dimension m-by-4.

Definition at line 458 of file vpMatrix_operators.cpp.

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

◆ operator*() [4/8]

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 414 of file vpMatrix_operators.cpp.

References mult2Matrices(), and vpMatrix().

◆ operator*() [5/8]

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 427 of file vpMatrix_operators.cpp.

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

◆ operator*() [6/8]

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 376 of file vpMatrix_operators.cpp.

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

◆ operator*() [7/8]

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 490 of file vpMatrix_operators.cpp.

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

◆ operator*() [8/8]

vpMatrix vpMatrix::operator* ( double x ) const

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

Definition at line 689 of file vpMatrix_operators.cpp.

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

◆ operator*=()

vpMatrix & vpMatrix::operator*= ( 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 761 of file vpMatrix_operators.cpp.

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

◆ 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 606 of file vpMatrix_operators.cpp.

References add2Matrices(), and vpMatrix().

◆ operator+=() [1/2]

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

Operation A = A + B.

Definition at line 626 of file vpMatrix_operators.cpp.

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

◆ operator+=() [2/2]

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

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

Definition at line 734 of file vpMatrix_operators.cpp.

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

◆ operator,()

vpMatrix & vpMatrix::operator, ( double val )

Definition at line 365 of file vpMatrix_operators.cpp.

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

◆ operator-() [1/2]

vpMatrix vpMatrix::operator- ( void ) const

Operation C = -A (A is unchanged).

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

Definition at line 666 of file vpMatrix_operators.cpp.

References negateMatrix(), and vpMatrix().

◆ operator-() [2/2]

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 617 of file vpMatrix_operators.cpp.

References sub2Matrices(), and vpMatrix().

◆ operator-=() [1/2]

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

Operation A = A - B.

Definition at line 645 of file vpMatrix_operators.cpp.

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

◆ operator-=() [2/2]

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

subtract x to all the element of the matrix : Aij = Aij - x

Definition at line 746 of file vpMatrix_operators.cpp.

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

◆ operator/()

vpMatrix vpMatrix::operator/ ( double x ) const

Cij = Aij / x (A is unchanged).

Definition at line 709 of file vpMatrix_operators.cpp.

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

◆ operator/=()

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

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

Definition at line 777 of file vpMatrix_operators.cpp.

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

◆ operator<<() [1/2]

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

Assignment 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 348 of file vpMatrix_operators.cpp.

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

◆ operator<<() [2/2]

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

Definition at line 358 of file vpMatrix_operators.cpp.

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

◆ operator=() [1/13]

vpMatrix & vpMatrix::operator= ( const std::initializer_list< double > & list )

Set matrix elements from a list of values.

Parameters

list	: List of double. Matrix size (number of columns multiplied by number of columns) should match the number of elements.

Returns: The modified Matrix. The following example shows how to set each element of a 2-by-3 matrix.

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  vpMatrix M;
  M = { -1, -2, -3, -4, -5, -6 };
  M.reshape(2, 3);
  std::cout << "M:\n" << M << std::endl;
}

It produces the following printings:

M:
-1  -2  -3
-4  -5  -6

See also: operator<<()

Definition at line 279 of file vpMatrix_operators.cpp.

References vpArray2D< double >::data, vpArray2D< double >::dsize, vpArray2D< double >::resize(), and vpMatrix().

◆ operator=() [2/13]

vpMatrix & vpMatrix::operator= ( const std::initializer_list< std::initializer_list< double > > & lists )

Set matrix elements from a list of values.

Parameters

lists : List of double.

Returns: The modified Matrix. The following example shows how to set each element of a 2-by-3 matrix.
#include <visp3/core/vpMatrix.h>

#ifdef ENABLE_VISP_NAMESPACE

using namespace VISP_NAMESPACE_NAME;

#endif

int main()

{

vpMatrix M;

M = { {-1, -2, -3}, {-4, -5, -6} };

std::cout << "M:\n" << M << std::endl;

}

It produces the following printings:
M:

-1 -2 -3

-4 -5 -6

See also: operator<<()

Definition at line 317 of file vpMatrix_operators.cpp.

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

◆ operator=() [3/13]

BEGIN_VISP_NAMESPACE 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;
M = R;

Definition at line 59 of file vpMatrix_operators.cpp.

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

◆ operator=() [4/13]

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

Copy operator that allows to convert a column vector to a matrix.

Parameters

v	: Column vector.

The following example shows how to create a matrix from a column vector:

vpColVector v(3);
vpMatrix M;
M = v;

Definition at line 174 of file vpMatrix_operators.cpp.

References vpArray2D< double >::data, vpArray2D< double >::dsize, vpArray2D< double >::resize(), and vpMatrix().

◆ operator=() [5/13]

vpMatrix & vpMatrix::operator= ( const vpForceTwistMatrix & F )

Copy operator that allows to convert a force twist matrix to a matrix.

Parameters

F	: Force twist matrix.

The following example shows how to create a matrix from a force twist matrix:

vpForceTwistMatrix F;
vpMatrix M;
M = F;

Definition at line 151 of file vpMatrix_operators.cpp.

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

◆ operator=() [6/13]

vpMatrix & vpMatrix::operator= ( const vpHomogeneousMatrix & M )

Copy operator that allows to convert a homogenous matrix to a matrix.

Parameters

M	: Homogeneous matrix.

The following example shows how to create a matrix from a homogenous matrix:

vpHomogeneousMatrix H;
vpMatrix M;
M = H;

Definition at line 82 of file vpMatrix_operators.cpp.

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

◆ operator=() [7/13]

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

Definition at line 231 of file vpMatrix_operators.cpp.

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

◆ operator=() [8/13]

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

Copy operator that allows to convert a rotation matrix to a matrix.

Parameters

R	: Rotation matrix.

The following example shows how to create a matrix from a rotation matrix:

vpRotationMatrix R;
vpMatrix M;
M = R;

Definition at line 105 of file vpMatrix_operators.cpp.

References vpArray2D< double >::data, vpArray2D< double >::dsize, vpArray2D< double >::resize(), and vpMatrix().

◆ operator=() [9/13]

vpMatrix & vpMatrix::operator= ( const vpRowVector & v )

Copy operator that allows to convert a row vector to a matrix.

Parameters

v	: Column vector.

The following example shows how to create a matrix from a row vector:

vpRowVector v(3);
vpMatrix M;
M = v;

Definition at line 197 of file vpMatrix_operators.cpp.

References vpArray2D< double >::data, vpArray2D< double >::dsize, vpArray2D< double >::resize(), and vpMatrix().

◆ operator=() [10/13]

vpMatrix & vpMatrix::operator= ( const vpTranslationVector & t )

Copy operator that allows to convert a translation vector to a matrix.

Parameters

t	: Translation vector.

The following example shows how to create a matrix from a translation vector:

vpTranslationVector t;
vpMatrix M;
M = t;

Definition at line 220 of file vpMatrix_operators.cpp.

References vpArray2D< double >::data, vpArray2D< double >::dsize, vpArray2D< double >::resize(), t(), and vpMatrix().

◆ operator=() [11/13]

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

Copy operator that allows to convert a velocity twist matrix to a matrix.

Parameters

V	: Velocity twist matrix.

The following example shows how to create a matrix from a velocity twist matrix:

vpVelocityTwistMatrix V;
vpMatrix M;
M = V;

Definition at line 128 of file vpMatrix_operators.cpp.

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

◆ operator=() [12/13]

vpMatrix & vpMatrix::operator= ( double x )

Set all the element of the matrix A to x.

Definition at line 337 of file vpMatrix_operators.cpp.

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

◆ operator=() [13/13]

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

Definition at line 243 of file vpMatrix_operators.cpp.

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

◆ operator[]()

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

inlineinherited

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

Definition at line 696 of file vpArray2D.h.

◆ print()

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

Parameters

s	: Stream used for the printing.
length	: The suggested width of each matrix element. If needed, the used length grows in order to accommodate the whole integral part, and shrinks the decimal part to print only length digits.
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, testMatrixConditionNumber.cpp, visp-compute-eye-in-hand-calibration.cpp, and visp-compute-eye-to-hand-calibration.cpp.

Definition at line 836 of file vpMatrix.cpp.

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

Referenced by vpServo::computeControlLaw(), and pseudoInverseOpenCV().

◆ printSize()

void vpMatrix::printSize ( ) const

inline

Definition at line 670 of file vpMatrix.h.

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

◆ pseudoInverse() [1/10]

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

Compute and return the Moore-Penros pseudo inverse 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 or OpenCV).

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 that is rank 2.

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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: catchParticleFilter.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, testFrankaCartVelocity-2.cpp, testMatrixConditionNumber.cpp, testRobotViper650-frames.cpp, and testRobotViper850-frames.cpp.

Definition at line 336 of file vpMatrix_pseudo_inverse.cpp.

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

Referenced by vpSimulatorAfma6::computeArticularVelocity(), vpSimulatorViper850::computeArticularVelocity(), computeCovarianceMatrix(), computeCovarianceMatrix(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbTracker::computeVVSPoseEstimation(), vpRBTracker::getCovariance(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), vpHomography::inverse(), vpHomogeneousMatrix::mean(), vpRotationMatrix::mean(), vpRotationMatrix::mean(), vpPose::poseDementhonNonPlan(), vpPose::poseDementhonPlan(), vpPose::poseVirtualVS(), vpPose::poseVirtualVSWithDepth(), pseudoInverse(), pseudoInverse(), vpHomography::robust(), solveBySVD(), and vpQuadProg::solveQPi().

◆ pseudoInverse() [2/10]

vpMatrix vpMatrix::pseudoInverse ( int rank_in ) const

Compute and return the Moore-Penros pseudo inverse 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 or OpenCV).

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

[in] rank_in : Known rank of the matrix.

Returns: The Moore-Penros pseudo inverse .

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

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  vpMatrix A(2, 3);
 
  // This matrix rank is 2
  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: ");
 
  int rank_in = 2;
  vpMatrix A_p = A.pseudoInverseLapack(rank_in);
 
  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

Definition at line 405 of file vpMatrix_pseudo_inverse.cpp.

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

◆ pseudoInverse() [3/10]

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

Compute the Moore-Penros pseudo inverse of a m-by-n matrix $\bf A$ and return the rank 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 or OpenCV).

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 of the matrix.

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

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 186 of file vpMatrix_pseudo_inverse.cpp.

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

◆ pseudoInverse() [4/10]

int vpMatrix::pseudoInverse	(	vpMatrix &	Ap,
		int	rank_in ) const

Compute the Moore-Penros pseudo inverse of a m-by-n matrix $\bf A$ and return the rank 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 or OpenCV).

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 .
[in]	rank_in	: Known rank of the matrix.

Returns: The rank of the matrix.

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

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  vpMatrix A(2, 3);
 
  // This matrix rank is 2
  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;
  int rank_in = 2;
  int rank_out = A.pseudoInverse(A_p, rank_in);
  if (rank_out != rank_in) {
    std::cout << "There is a possibility that the pseudo-inverse in wrong." << std::endl;
    std::cout << "Are you sure that the matrix rank is " << rank_in << std::endl;
  }
 
  A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
  std::cout << "Rank in : " << rank_in << std::endl;
  std::cout << "Rank out: " << rank_out << 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 in : 2
Rank out: 2

Definition at line 266 of file vpMatrix_pseudo_inverse.cpp.

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

◆ pseudoInverse() [5/10]

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

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

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

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 666 of file vpMatrix_pseudo_inverse.cpp.

References pseudoInverse(), and vpMatrix().

◆ pseudoInverse() [6/10]

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

Compute the Moore-Penros pseudo inverse 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 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 or OpenCV).

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

Parameters

Ap	: The Moore-Penros pseudo inverse ${\bf A}^+$ .
sv	: Vector corresponding to matrix A 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 of the matrix $\bf A$ .

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

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 865 of file vpMatrix_pseudo_inverse.cpp.

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

◆ pseudoInverse() [7/10]

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

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

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 of the matrix $\bf A$ .

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

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 485 of file vpMatrix_pseudo_inverse.cpp.

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

◆ pseudoInverse() [8/10]

int vpMatrix::pseudoInverse	(	vpMatrix &	Ap,
		vpColVector &	sv,
		int	rank_in ) const

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

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).
[in]	rank_in	: Known rank of the matrix.

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

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

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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;
  int rank_in = 2;
  int rank_out = A.pseudoInverse(A_p, sv, rank_in);
  if (rank_out != rank_in) {
    std::cout << "There is a possibility that the pseudo-inverse in wrong." << std::endl;
    std::cout << "Are you sure that the matrix rank is " << rank_in << std::endl;
  }
 
  A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
 
  std::cout << "Rank in : " << rank_in << std::endl;
  std::cout << "Rank out: " << rank_out << 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 in : 2
Rank out: 2
Singular values: 6.874359351  4.443330227

Definition at line 572 of file vpMatrix_pseudo_inverse.cpp.

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

◆ pseudoInverse() [9/10]

int vpMatrix::pseudoInverse	(	vpMatrix &	Ap,
		vpColVector &	sv,
		int	rank_in,
		vpMatrix &	imA,
		vpMatrix &	imAt ) const

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

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

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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;
  int rank_in = 2;
  int rank_out = A.pseudoInverse(A_p, sv, rank_in, imA, imAt);
  if (rank_out != rank_in) {
    std::cout << "There is a possibility that the pseudo-inverse in wrong." << std::endl;
    std::cout << "Are you sure that the matrix rank is " << rank_in << std::endl;
  }
 
  A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
  std::cout << "Rank in : " << rank_in << std::endl;
  std::cout << "Rank out: " << rank_in << 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 754 of file vpMatrix_pseudo_inverse.cpp.

References pseudoInverse(), and vpMatrix().

◆ pseudoInverse() [10/10]

int vpMatrix::pseudoInverse	(	vpMatrix &	Ap,
		vpColVector &	sv,
		int	rank_in,
		vpMatrix &	imA,
		vpMatrix &	imAt,
		vpMatrix &	kerAt ) const

Compute the Moore-Penros pseudo inverse 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 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 or OpenCV).

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

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).
[in]	rank_in	: Known rank of the matrix.
	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 of the matrix $\bf A$ .

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

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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;
  int rank_in = 2;
  int rank_out = A.pseudoInverse(A_p, sv, rank_in, imA, imAt, kerAt);
  if (rank_out != rank_in) {
    std::cout << "There is a possibility that the pseudo-inverse in wrong." << std::endl;
    std::cout << "Are you sure that the matrix rank is " << rank_in << std::endl;
  }
 
  A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
  std::cout << "Rank in : " << rank_in << std::endl;
  std::cout << "Rank out: " << rank_out << 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_in; 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 in : 2
Rank out : 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 996 of file vpMatrix_pseudo_inverse.cpp.

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

◆ pseudoInverseEigen3() [1/8]

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

References vpMatrix().

Referenced by pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), and pseudoInverse().

◆ pseudoInverseEigen3() [2/8]

vpMatrix vpMatrix::pseudoInverseEigen3 ( int rank_in ) const

References vpMatrix().

◆ pseudoInverseEigen3() [3/8]

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

References vpMatrix().

◆ pseudoInverseEigen3() [4/8]

int vpMatrix::pseudoInverseEigen3	(	vpMatrix &	Ap,
		int	rank_in ) const

References vpMatrix().

◆ pseudoInverseEigen3() [5/8]

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

References vpMatrix().

◆ pseudoInverseEigen3() [6/8]

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

References vpMatrix().

◆ pseudoInverseEigen3() [7/8]

int vpMatrix::pseudoInverseEigen3	(	vpMatrix &	Ap,
		vpColVector &	sv,
		int	rank_in ) const

References vpMatrix().

◆ pseudoInverseEigen3() [8/8]

int vpMatrix::pseudoInverseEigen3	(	vpMatrix &	Ap,
		vpColVector &	sv,
		int	rank_in,
		vpMatrix &	imA,
		vpMatrix &	imAt,
		vpMatrix &	kerAt ) const

References vpMatrix().

◆ pseudoInverseLapack() [1/8]

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

References vpMatrix().

Referenced by pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), and pseudoInverse().

◆ pseudoInverseLapack() [2/8]

vpMatrix vpMatrix::pseudoInverseLapack ( int rank_in ) const

References vpMatrix().

◆ pseudoInverseLapack() [3/8]

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

References vpMatrix().

◆ pseudoInverseLapack() [4/8]

int vpMatrix::pseudoInverseLapack	(	vpMatrix &	Ap,
		int	rank_in ) const

References vpMatrix().

◆ pseudoInverseLapack() [5/8]

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

References vpMatrix().

◆ pseudoInverseLapack() [6/8]

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

References vpMatrix().

◆ pseudoInverseLapack() [7/8]

int vpMatrix::pseudoInverseLapack	(	vpMatrix &	Ap,
		vpColVector &	sv,
		int	rank_in ) const

References vpMatrix().

◆ pseudoInverseLapack() [8/8]

int vpMatrix::pseudoInverseLapack	(	vpMatrix &	Ap,
		vpColVector &	sv,
		int	rank_in,
		vpMatrix &	imA,
		vpMatrix &	imAt,
		vpMatrix &	kerAt ) const

References vpMatrix().

◆ pseudoInverseOpenCV() [1/8]

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

References vpMatrix().

Referenced by pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), pseudoInverse(), and pseudoInverse().

◆ pseudoInverseOpenCV() [2/8]

vpMatrix vpMatrix::pseudoInverseOpenCV ( int rank_in ) const

References vpMatrix().

◆ pseudoInverseOpenCV() [3/8]

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

References vpMatrix().

◆ pseudoInverseOpenCV() [4/8]

int vpMatrix::pseudoInverseOpenCV	(	vpMatrix &	Ap,
		int	rank_in ) const

References vpMatrix().

◆ pseudoInverseOpenCV() [5/8]

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

References vpMatrix().

◆ pseudoInverseOpenCV() [6/8]

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

References vpMatrix().

◆ pseudoInverseOpenCV() [7/8]

int vpMatrix::pseudoInverseOpenCV	(	vpMatrix &	Ap,
		vpColVector &	sv,
		int	rank_in ) const

References vpMatrix().

◆ pseudoInverseOpenCV() [8/8]

int vpMatrix::pseudoInverseOpenCV	(	vpMatrix &	Ap,
		vpColVector &	sv,
		int	rank_in,
		vpMatrix &	imA,
		vpMatrix &	imAt,
		vpMatrix &	kerAt ) const

◆ qr()

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

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

Parameters

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

Returns: The rank r of the matrix.

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

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

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

Here an example:

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

See also: qrPivot()

Definition at line 449 of file vpMatrix_qr.cpp.

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

Referenced by vpLinProg::colReduction(), and pseudoInverseOpenCV().

◆ qrPivot()

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

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

Parameters

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

Returns: The rank r of the matrix.

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

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

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

Here an example:

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

See also: qrPivot()

Definition at line 1142 of file vpMatrix_qr.cpp.

References vpException::fatalError, and vpMatrix().

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

◆ reshape()

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

inlineinherited

Examples: testMatrixInitialization.cpp.

Definition at line 545 of file vpArray2D.h.

◆ resize()

void vpArray2D< double >::resize	(	unsigned int	nrows,
		unsigned int	ncols,
		bool	flagNullify = true,
		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.

Examples: catchParticleFilter.cpp, perfMatrixMultiplication.cpp, perfMatrixTranspose.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixDeterminant.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 448 of file vpArray2D.h.

Referenced by vpMatrix::diag(), vpMatrix::eye(), vpMatrix::init(), vpMatrix::operator,(), vpMatrix::operator<<(), vpMatrix::operator=(), vpMatrix::operator=(), vpMatrix::operator=(), vpMatrix::operator=(), vpMatrix::operator=(), vpMatrix::operator=(), vpMatrix::operator=(), vpMatrix::operator=(), vpMatrix::operator=(), vpMatrix::operator=(), vpMatrix::operator=(), vpMatrix::stack(), vpMatrix::stack(), vpMatrix::stack(), vpMatrix::svdEigen3(), and vpMatrix::svdOpenCV().

◆ row()

vpRowVector vpMatrix::row ( unsigned int i )

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

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

should be replaced with:

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

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

Parameters

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

Definition at line 2028 of file vpMatrix.cpp.

References vpArray2D< double >::getCols().

◆ save()

bool vpArray2D< double >::save	(	const std::string &	filename,
		const vpArray2D< double > &	A,
		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 965 of file vpArray2D.h.

◆ saveMatrix()

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

inlinestatic

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

Parameters

filename	: Absolute file name.
M	: Matrix to be saved.
binary	: If true the matrix is save as a binary file, otherwise as a text file.
header	: Optional line that will be saved at the beginning of the file as a header.

Returns: Returns true if no problem appends.

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

The following example shows how to use this function:

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  std::string filename("matrix.bin");
  bool binary_data = true;
  {
    vpMatrix M(2, 3);
    M[0][0] = -1; M[0][1] =  -2; M[0][2] = -3;
    M[1][0] =  4; M[1][1] = 5.5; M[1][2] =  6.0f;
 
    std::string header("My header");
 
    if (vpMatrix::saveMatrix(filename, M, binary_data, header.c_str())) {
      std::cout << "Matrix saved in " << filename << std::endl;
      M.print(std::cout, 10, header);
    } else {
      std::cout << "Cannot save matrix in " << filename << std::endl;
    }
  }
  {
    vpMatrix N;
    char header[FILENAME_MAX];
    if (vpMatrix::loadMatrix(filename, N, binary_data, header)) {
      std::cout << "Matrix loaded from " << filename << std::endl;
      N.print(std::cout, 10, header);
    } else {
      std::cout << "Cannot load matrix from " << filename << std::endl;
    }
  }
}

The output of this example is the following:

Matrix saved in matrix.bin
My header[2,3]=
  -1.0 -2.0 -3.0
   4.0  5.5  6.0
Matrix loaded from matrix.bin
My header[2,3]=
  -1.0 -2.0 -3.0
   4.0  5.5  6.0

And the content of matrix.bin file where data are saved as binary data is the following:

% cat matrix.bin
My header??@@@%

See also: loadMatrix(), saveMatrixYAML(), loadMatrixYAML()

Examples: testMatrix.cpp.

Definition at line 997 of file vpMatrix.h.

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

Referenced by vpDot2::defineDots(), and vpLuminancePCA::save().

◆ saveMatrixYAML()

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 as a header.

Returns: Returns true if success.

The following example shows how to use this function:

#include <visp3/core/vpMatrix.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  std::string filename("matrix.yaml");
  {
    vpMatrix M(2, 3);
    M[0][0] = -1; M[0][1] =  -2; M[0][2] = -3;
    M[1][0] =  4; M[1][1] = 5.5; M[1][2] =  6.0f;
 
    std::string header("My header");
 
    if (vpMatrix::saveMatrixYAML(filename, M, header.c_str())) {
      std::cout << "Matrix saved in " << filename << std::endl;
      M.print(std::cout, 10, header);
    } else {
      std::cout << "Cannot save matrix in " << filename << std::endl;
    }
  }
  {
    vpMatrix N;
    char header[FILENAME_MAX];
    if (vpMatrix::loadMatrixYAML(filename, N, header)) {
      std::cout << "Matrix loaded from " << filename << std::endl;
      N.print(std::cout, 10, header);
    } else {
      std::cout << "Cannot load matrix from " << filename << std::endl;
    }
  }
}

The output of this example is the following:

Matrix saved in matrix.yaml
My header[2,3]=
  -1.0 -2.0 -3.0
   4.0  5.5  6.0
Matrix loaded from matrix.yaml
My header[2,3]=
  -1.0 -2.0 -3.0
   4.0  5.5  6.0

And the content of matrix.yaml file is the following:

% cat matrix.yaml
My header
rows: 2
cols: 3
data:
  - [-1, -2, -3]
  - [4, 5.5, 6]

See also: saveMatrix(), loadMatrix(), loadMatrixYAML()

Examples: testMatrix.cpp.

Definition at line 1077 of file vpMatrix.h.

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

◆ saveYAML()

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

inlinestaticinherited

Save an array in a YAML-formatted file.

Parameters

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

Returns: Returns true if success.

Here is an example of outputs.

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

Content of matrix.yml:

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

Content of matrixIndent.yml:

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

See also: loadYAML()

Examples: visp-acquire-franka-calib-data.cpp, and visp-acquire-universal-robots-calib-data.cpp.

Definition at line 1061 of file vpArray2D.h.

◆ 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 2071 of file vpMatrix.cpp.

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

◆ setLapackMatrixMinSize()

void vpMatrix::setLapackMatrixMinSize ( unsigned int min_size )

inlinestatic

Modify default size used to determine if Blas/Lapack basic linear algebra operations are enabled.

To get more info see Tutorial: Basic linear algebra operations.

Parameters

min_size : Minimum size of rows and columns required for a matrix or a vector to use Blas/Lapack third parties like MKL, OpenBLAS, Netlib or Atlas. When matrix or vector size is lower or equal to this parameter, Blas/Lapack is not used. In that case we prefer use naive code that runs faster for small matrices.

See also: getLapackMatrixMinSize()

Examples: perfMatrixMultiplication.cpp.

Definition at line 290 of file vpMatrix.h.

◆ size()

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

inlineinherited

Return the number of elements of the 2D array.

Examples: catchLuminanceMapping.cpp, catchParticleFilter.cpp, catchPoseVector.cpp, catchRotation.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixInitialization.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testTukeyEstimator.cpp, testUniversalRobotsGetData.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-pf.cpp, tutorial-ukf.cpp, ukf-nonlinear-complex-example.cpp, and ukf-nonlinear-example.cpp.

Definition at line 435 of file vpArray2D.h.

Referenced by vpHomogeneousMatrix::isValid(), vpColVector::operator*(), vpHomogeneousMatrix::operator,(), vpRotationMatrix::operator,(), vpRotationVector::operator,(), vpTranslationVector::operator,(), vpQuaternionVector::operator=(), vpRxyzVector::operator=(), vpRzyxVector::operator=(), vpRzyzVector::operator=(), vpThetaUVector::operator=(), vpThetaUVector::operator=(), vpTranslationVector::operator=(), vpForceTwistMatrix::print(), vpMatrix::print(), vpVelocityTwistMatrix::print(), vpMatrix::stack(), vpColVector::toStdVector(), vpPoseVector::toStdVector(), vpRotationVector::toStdVector(), vpRowVector::toStdVector(), vpColVector::vpColVector(), vpColVector::vpColVector(), vpColVector::vpColVector(), vpColVector::vpColVector(), vpColVector::vpColVector(), vpColVector::vpColVector(), vpRowVector::vpRowVector(), and vpRowVector::vpRowVector().

◆ solveByQR() [1/2]

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

Solve a linear system Ax = b using QR Decomposition.

Non destructive wrt. A and B.

Parameters

b	: Vector b

Returns: Vector x

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

Here an example:

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

See also: qrPivot()

Definition at line 1377 of file vpMatrix_qr.cpp.

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

◆ solveByQR() [2/2]

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

Solve a linear system Ax = b using QR Decomposition.

Non destructive wrt. A and b.

Parameters

b	: Vector b
x	: Vector x

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

Here an example:

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

See also: qrPivot()

Definition at line 1322 of file vpMatrix_qr.cpp.

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

Referenced by pseudoInverseOpenCV(), solveByQR(), and vpQuadProg::solveSVDorQR().

◆ solveBySVD() [1/2]

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

Solve a linear system 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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 184 of file vpMatrix_svd.cpp.

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

◆ solveBySVD() [2/2]

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

Solve a linear system 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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
vpMatrix A(3,3);
 
A[0][0] = 4.64;
A[0][1] = 0.288;
A[0][2] = -0.384;
 
A[1][0] = 0.288;
A[1][1] = 7.3296;
A[1][2] = 2.2272;
 
A[2][0] = -0.384;
A[2][1] = 2.2272;
A[2][2] = 6.0304;
 
vpColVector X(3), B(3);
B[0] = 1;
B[1] = 2;
B[2] = 3;
 
A.solveBySVD(B, X);
 
// Obtained values of X
// X[0] = 0.2468;
// X[1] = 0.120782;
// X[2] = 0.468587;
 
std::cout << "X:\n" << X << std::endl;
}

See also: solveBySVD(const vpColVector &)

Examples: quadprog.cpp, and quadprog_eq.cpp.

Definition at line 129 of file vpMatrix_svd.cpp.

References pseudoInverse().

Referenced by vpMeEllipse::leastSquare(), vpMeEllipse::leastSquareRobustCircle(), pseudoInverseOpenCV(), solveBySVD(), and vpQuadProg::solveSVDorQR().

◆ stack() [1/9]

void vpMatrix::stack ( const vpColVector & c )

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

Here an example for a robot velocity log matrix:

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

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

Definition at line 312 of file vpMatrix_stack.cpp.

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

◆ stack() [2/9]

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 239 of file vpMatrix_stack.cpp.

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

◆ stack() [3/9]

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

static

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

Parameters

A	: Left matrix.
c	: Right column vector.

Returns: Stacked matrix [ A c ]

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

Definition at line 205 of file vpMatrix_stack.cpp.

References stack(), and vpMatrix().

◆ stack() [4/9]

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

static

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

Parameters

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

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

Definition at line 224 of file vpMatrix_stack.cpp.

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

◆ stack() [5/9]

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 102 of file vpMatrix_stack.cpp.

References stack(), and vpMatrix().

◆ stack() [6/9]

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 122 of file vpMatrix_stack.cpp.

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

◆ stack() [7/9]

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 row vector.

Returns: Stacked matrix [ A r ]^T

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

Definition at line 166 of file vpMatrix_stack.cpp.

References stack(), and vpMatrix().

◆ stack() [8/9]

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

static

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

Parameters

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

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

Definition at line 185 of file vpMatrix_stack.cpp.

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

◆ stack() [9/9]

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.stack(v.t());
}

Definition at line 271 of file vpMatrix_stack.cpp.

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

◆ stackColumns() [1/2]

vpColVector vpMatrix::stackColumns ( )

Stacks columns of a matrix in a vector.

Returns: a vpColVector.

Definition at line 61 of file vpMatrix_stack.cpp.

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

Referenced by stackColumns().

◆ stackColumns() [2/2]

BEGIN_VISP_NAMESPACE void vpMatrix::stackColumns ( vpColVector & out )

Stacks columns of a matrix in a vector.

Parameters

out	: a vpColVector.

Definition at line 43 of file vpMatrix_stack.cpp.

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

◆ stackMatrices() [1/7]

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 342 of file vpMatrix_stack.cpp.

References vpColVector::stack(), and vpMatrix().

◆ stackMatrices() [2/7]

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 347 of file vpMatrix_stack.cpp.

References vpColVector::stack().

◆ stackMatrices() [3/7]

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

inline

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

Definition at line 1099 of file vpMatrix.h.

References stack(), and vpMatrix().

◆ stackMatrices() [4/7]

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 1104 of file vpMatrix.h.

References stack(), and vpMatrix().

◆ stackMatrices() [5/7]

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 1109 of file vpMatrix.h.

References stack(), and vpMatrix().

◆ stackMatrices() [6/7]

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 352 of file vpMatrix_stack.cpp.

References stack(), and vpMatrix().

◆ stackMatrices() [7/7]

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 354 of file vpMatrix_stack.cpp.

References stack(), and vpMatrix().

◆ stackRows() [1/2]

vpRowVector vpMatrix::stackRows ( )

Stacks rows of a matrix in a vector.

Returns: a vpRowVector.

Definition at line 85 of file vpMatrix_stack.cpp.

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

Referenced by stackRows().

◆ stackRows() [2/2]

void vpMatrix::stackRows ( vpRowVector & out )

Stacks rows of a matrix in a vector

Parameters

out	: a vpRowVector.

Definition at line 72 of file vpMatrix_stack.cpp.

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

◆ sub2Matrices() [1/2]

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 558 of file vpMatrix_operations.cpp.

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

◆ sub2Matrices() [2/2]

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 592 of file vpMatrix_operations.cpp.

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

Referenced by operator-().

◆ 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 673 of file vpMatrix_operators.cpp.

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

Referenced by expm().

◆ sumSquare()

double vpMatrix::sumSquare ( ) const

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

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

Definition at line 1984 of file vpMatrix.cpp.

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

◆ 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.

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

Given matrix , 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 .

The matrix object (*this) is updated with .

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>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
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()

Examples: servoMomentImage.cpp.

Definition at line 259 of file vpMatrix_svd.cpp.

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

Referenced by vpHomogeneousMatrix::compute3d3dTransformation(), cond(), dampedInverse(), vpHomography::DLT(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), inducedL2Norm(), kernel(), vpLuminancePCA::learn(), nullSpace(), nullSpace(), vpRotationMatrix::orthogonalize(), pseudoInverseOpenCV(), and svdEigen3().

◆ svdEigen3()

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

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

Given matrix , 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 .

The matrix object (*this) is updated with .

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

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

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

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

Definition at line 643 of file vpMatrix_svd.cpp.

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

Referenced by pseudoInverseOpenCV(), and svd().

◆ svdLapack()

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

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

Given matrix , 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 .

The matrix object (*this) is updated with .

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

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

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

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

Definition at line 436 of file vpMatrix_svd.cpp.

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

Referenced by pseudoInverseOpenCV(), and svd().

◆ svdOpenCV()

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

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

Given matrix , 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 .

The matrix object (*this) is updated with .

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

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

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

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

Definition at line 345 of file vpMatrix_svd.cpp.

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

Referenced by pseudoInverseOpenCV(), and svd().

◆ t()

BEGIN_VISP_NAMESPACE vpMatrix vpMatrix::t ( ) const

Compute and return the transpose of the matrix.

Examples: catchLuminanceMapping.cpp, perfMatrixTranspose.cpp, photometricMappingVisualServoing.cpp, photometricVisualServoingWithoutVpServo.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 46 of file vpMatrix_operations.cpp.

References transpose(), and vpMatrix().

Referenced by vpHomogeneousMatrix::compute3d3dTransformation(), computeCovarianceMatrix(), computeCovarianceMatrix(), vpRBFeatureTracker::computeCovarianceMatrix(), vpTemplateTracker::computeOptimalBrentGain(), eigenValues(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), vpTemplateTrackerWarpHomographySL3::findWarp(), vpLuminanceDCT::interaction(), vpLuminancePCA::learn(), vpRBVisualOdometryUtils::levenbergMarquardtKeypoints2D(), vpRBVisualOdometryUtils::levenbergMarquardtKeypoints3D(), vpHomogeneousMatrix::mean(), vpRotationMatrix::mean(), vpRotationMatrix::mean(), operator=(), vpRotationMatrix::orthogonalize(), vpLinProg::simplex(), solveByQR(), and vpMatrix().

◆ transpose() [1/2]

vpMatrix vpMatrix::transpose ( ) const

Compute and return the transpose of the matrix.

See also: t()

Examples: catchMatrixCholesky.cpp, testMatrixConditionNumber.cpp, and testMatrixPseudoInverse.cpp.

Definition at line 53 of file vpMatrix_operations.cpp.

References transpose(), and vpMatrix().

Referenced by vpLinProg::colReduction(), dampedInverse(), vpQuadProg::fromCanonicalCost(), vpLuminancePCA::learn(), vpLuminancePCA::learn(), vpLinProg::rowReduction(), vpLinProg::solveLP(), vpQuadProg::solveQPi(), svdLapack(), svdOpenCV(), t(), transpose(), and vpUnscentedKalman::update().

◆ 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 65 of file vpMatrix_operations.cpp.

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

◆ view() [1/3]

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

inlinestaticinherited

Creates a view of the Matrix A. A view shares the same underlying memory as the original array. It can be written into, modifying the original data. However, the array cannot be resized.

When you use this method, it is your responsibility to ensure that the lifespan of the view does not exceed the lifespan of the original array.

Parameters

A	the array to view

Returns: vpArray2D<T>

Definition at line 324 of file vpArray2D.h.

◆ view() [2/3]

vpMatrix vpMatrix::view	(	double *	raw_data,
		unsigned int	rows,
		unsigned int	cols )

static

Create a matrix view of a raw data array. The view can modify the contents of the raw data array, but may not resize it and does not own it: the memory is not released by the matrix and it should be freed by the user after the matrix view is released.

Parameters

[in]	raw_data	: The raw data.
[in]	rows	: Raw data number of rows.
[in]	cols	: Raw data number of columns.

Returns: vpMatrix

Examples: testMatrixInitialization.cpp.

Definition at line 307 of file vpMatrix.cpp.

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

Referenced by vpRBSilhouetteCCDTracker::buildGradientAndHessianStorageViews().

◆ view() [3/3]

void vpMatrix::view	(	vpMatrix &	v,
		double *	data,
		unsigned int	rows,
		unsigned int	cols )

static

Definition at line 314 of file vpMatrix.cpp.

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

◆ operator*()

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

Allow to multiply a scalar by a matrix.

Definition at line 802 of file vpMatrix_operators.cpp.

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

◆ operator==() [1/2]

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

Definition at line 1420 of file vpArray2D.h.

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

◆ operator==() [2/2]

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

Definition at line 1439 of file vpArray2D.h.

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

◆ 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 )

This function performs generalized matrix multiplication: D = alpha*op(A)*op(B) + beta*op(C), where op(X) is X or X^T. Operation on A, B and C matrices is described by enumeration vpGEMMmethod().

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);

vpArray2D< double >::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)

Definition vpGEMM.h:414

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 414 of file vpGEMM.h.

References vpException::functionNotImplementedError, and vpArray2D().

◆ vpGEMMmethod

enum vpGEMMmethod

Enumeration of the operations applied on matrices in vpGEMM() function.

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 53 of file vpGEMM.h.

Member Data Documentation

◆ colNum

unsigned int vpArray2D< double >::colNum

protectedinherited

Number of columns in the array.

Definition at line 1203 of file vpArray2D.h.

◆ data

double* vpArray2D< double >::data

inherited

Address of the first element of the data array.

Examples: catchQuaternion.cpp, catchRotation.cpp, perfMatrixMultiplication.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixInitialization.cpp, testUniversalRobotsGetData.cpp, and tutorial-bridge-opencv-matrix.cpp.

Definition at line 149 of file vpArray2D.h.

◆ dsize

unsigned int vpArray2D< double >::dsize

protectedinherited

Current array size (rowNum * colNum).

Definition at line 1207 of file vpArray2D.h.

◆ isMemoryOwner

bool vpArray2D< double >::isMemoryOwner

protectedinherited

Whether this array owns the memory it points to.

Definition at line 1209 of file vpArray2D.h.

Referenced by vpColVector::clear(), and vpRowVector::clear().

◆ isRowPtrsOwner

bool vpArray2D< double >::isRowPtrsOwner

protectedinherited

Whether this array owns the row pointers.

Definition at line 1211 of file vpArray2D.h.

◆ rowNum

unsigned int vpArray2D< double >::rowNum

protectedinherited

Number of rows in the array.

Definition at line 1201 of file vpArray2D.h.

◆ rowPtrs

double** vpArray2D< double >::rowPtrs

protectedinherited

Address of the first element of each rows.

Definition at line 1205 of file vpArray2D.h.

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Related Symbols

Deprecated functions

Matrix operations

Matrix I/O with Static Public Member Functions

Inherited I/O from vpArray2D with Static Public Member Functions

Detailed Description

Member Enumeration Documentation

◆ vpDetMethod

Constructor & Destructor Documentation

◆ vpMatrix() [1/17]

◆ vpMatrix() [2/17]

◆ vpMatrix() [3/17]

◆ vpMatrix() [4/17]

◆ vpMatrix() [5/17]

◆ vpMatrix() [6/17]

◆ vpMatrix() [7/17]

◆ vpMatrix() [8/17]

◆ vpMatrix() [9/17]

◆ vpMatrix() [10/17]

◆ vpMatrix() [11/17]

◆ vpMatrix() [12/17]

◆ vpMatrix() [13/17]

◆ vpMatrix() [14/17]

◆ vpMatrix() [15/17]

◆ vpMatrix() [16/17]

◆ vpMatrix() [17/17]

Member Function Documentation

◆ AAt() [1/2]

◆ AAt() [2/2]

◆ add2Matrices() [1/2]

◆ add2Matrices() [2/2]

◆ add2WeightedMatrices()

◆ AtA() [1/2]

◆ AtA() [2/2]

◆ cholesky()

◆ choleskyByEigen3()

◆ choleskyByLapack()

◆ choleskyByOpenCV()

◆ clear()

◆ column()

◆ computeCovarianceMatrix() [1/2]

◆ computeCovarianceMatrix() [2/2]

◆ computeCovarianceMatrixVVS() [1/2]

◆ computeCovarianceMatrixVVS() [2/2]

◆ computeHLM()

◆ cond()

◆ conv2() [1/3]

◆ conv2() [2/3]

◆ conv2() [3/3]

◆ cppPrint()

◆ createDiagonalMatrix()

◆ csvPrint()

◆ dampedInverse()

◆ det()

◆ detByLU()

◆ detByLUEigen3()

◆ detByLULapack()

◆ detByLUOpenCV()

◆ diag() [1/2]

◆ diag() [2/2]

◆ eigenValues() [1/2]

◆ eigenValues() [2/2]

◆ euclideanNorm()

◆ expm()

◆ extract()

◆ eye() [1/3]

◆ eye() [2/3]

◆ eye() [3/3]

◆ frobeniusNorm()

◆ getCol() [1/2]

◆ getCol() [2/2]

◆ getCols()

◆ getDiag()

◆ getLapackMatrixMinSize()

◆ getMaxValue()

◆ getMinValue()