#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)

	vpMatrix (const vpArray2D< double > &A)

	vpMatrix (const vpMatrix &A)

	vpMatrix (vpMatrix &&A)

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

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

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

virtual	~vpMatrix ()

void	clear ()

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

void	diag (const vpColVector &A)

void	eye ()

void	eye (unsigned int n)

void	eye (unsigned int m, unsigned int n)

Assignment operators
vpMatrix &	operator<< (double *)

vpMatrix &	operator<< (double val)

vpMatrix &	operator, (double val)

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

vpMatrix &	operator= (const vpMatrix &A)

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)

Matrix operations
double	det (vpDetMethod method=LU_DECOMPOSITION) const

double	detByLU () const

double	detByLUEigen3 () const

double	detByLULapack () const

double	detByLUOpenCV () 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

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

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	euclideanNorm () const

double	frobeniusNorm () const

double	inducedL2Norm () const

double	infinityNorm () const

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

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

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

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

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

void	printSize () const

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)

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

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

double *	operator[] (unsigned int i)

double *	operator[] (unsigned int i) const

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

Static Public Member Functions
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	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)

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

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

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

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

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

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

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

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

static bool	saveMatrix (const std::string &filename, const vpArray2D< double > &M, 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=NULL)

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

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

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

Public Attributes
double *	data

Protected Attributes
unsigned int	rowNum

unsigned int	colNum

double **	rowPtrs

unsigned int	dsize

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

enum	vpGEMMmethod

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)

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
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
int main()
{
#if (VISP_CXX_STANDARD >= VISP_CXX_STANDARD_11)
  vpMatrix M( {-1, -2, -3}, {4, 5.5, 6.0f} );
  std::cout << "M:\n" << M << std::endl;
#endif
}

You can also create and initialize a matrix this way:

#include <visp3/code/vpMatrix.h
int main()
{
#if (VISP_CXX_STANDARD >= VISP_CXX_STANDARD_11)
  vpMatrix M(2, 3, {-1, -2, -3, 4, 5.5, 6.0f} );
#endif
}

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

int main()
{
#if (VISP_CXX_STANDARD >= VISP_CXX_STANDARD_11)
  vpMatrix M;
  M = { {-1, -2, -3}, {4, 5.5, 6.0f} };
#endif
}

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

Examples:: manServo4PointsDisplay.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, photometricVisualServoingWithoutVpServo.cpp, quadprog.cpp, quadprog_eq.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocityKalman.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoMomentImage.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPioneerPoint2DDepthWithoutVpServo.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimu4Points.cpp, servoSimuCylinder.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuSphere.cpp, 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, testColVector.cpp, testEigenConversion.cpp, testFeature.cpp, testFrankaCartVelocity-2.cpp, testFrankaGetPose.cpp, testImageFilter.cpp, testImageWarp.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixException.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testPoseFeatures.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testRowVector.cpp, testSvd.cpp, testTranslationVector.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-image-filter.cpp, tutorial-matlab.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 153 of file vpMatrix.h.

Member Enumeration Documentation

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 160 of file vpMatrix.h.

Constructor & Destructor Documentation

vpMatrix::vpMatrix ( )

inline

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

Definition at line 169 of file vpMatrix.h.

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 177 of file vpMatrix.h.

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 186 of file vpMatrix.h.

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 189 of file vpMatrix.cpp.

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

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

inline

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

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

vpRotationMatrix R;

vpMatrix M(R);

Definition at line 201 of file vpMatrix.h.

vpMatrix::vpMatrix ( const vpMatrix & A )

inline

Definition at line 203 of file vpMatrix.h.

vpMatrix::vpMatrix ( vpMatrix && A )

Definition at line 204 of file vpMatrix.cpp.

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

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

explicit

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>
int main()
{
#if (VISP_CXX_STANDARD >= VISP_CXX_STANDARD_11)
vpMatrix M( {-1, -2, -3, 4, 5.5, 6.0f} );
M.reshape(2, 3);
std::cout << "M:\n" << M << std::endl;
#endif
}

It produces the following output:

M:
-1  -2  -3
4  5.5  6

Definition at line 244 of file vpMatrix.cpp.

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

explicit

Construct a matrix from a list of double values.

Parameters

ncols,nrows	: Matrix size.
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>
int main()
{
#if (VISP_CXX_STANDARD >= VISP_CXX_STANDARD_11)
vpMatrix M(2, 3, {-1, -2, -3, 4, 5.5, 6});
std::cout << "M:\n" << M << std::endl;
#endif
}

It produces the following output:

M:
-1  -2  -3
4  5.5  6

Definition at line 271 of file vpMatrix.cpp.

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

explicit

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>
int main()
{
#if (VISP_CXX_STANDARD >= VISP_CXX_STANDARD_11)
vpMatrix M( { {-1, -2, -3}, {4, 5.5, 6} } );
std::cout << "M:\n" << M << std::endl;
#endif
}

It produces the following output:

M:
-1  -2  -3
4  5.5  6

Definition at line 296 of file vpMatrix.cpp.

virtual vpMatrix::~vpMatrix ( )

inlinevirtual

Destructor (Memory de-allocation)

Definition at line 213 of file vpMatrix.h.

Member Function Documentation

vpMatrix vpMatrix::AAt ( ) const

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

Returns

See also: AAt(vpMatrix &) const

Definition at line 507 of file vpMatrix.cpp.

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

void vpMatrix::AAt ( vpMatrix & B ) const

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

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

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

See also: AAt()

Definition at line 527 of file vpMatrix.cpp.

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

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 1352 of file vpMatrix.cpp.

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

Referenced by operator+().

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 1385 of file vpMatrix.cpp.

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

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 1323 of file vpMatrix.cpp.

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

vpMatrix vpMatrix::AtA ( ) const

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

Returns

See also: AtA(vpMatrix &) const

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

Definition at line 629 of file vpMatrix.cpp.

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

void vpMatrix::AtA ( vpMatrix & B ) const

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

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

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

See also: AtA()

Definition at line 579 of file vpMatrix.cpp.

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

void vpMatrix::clear ( )

inline

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

Definition at line 219 of file vpMatrix.h.

Referenced by vpPose::init().

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 6963 of file vpMatrix.cpp.

References vpArray2D< double >::getRows().

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

static

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

Parameters

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

Definition at line 59 of file vpMatrix_covariance.cpp.

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

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

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

static

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

Parameters

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

Definition at line 91 of file vpMatrix_covariance.cpp.

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

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

static

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

Parameters

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

Definition at line 149 of file vpMatrix_covariance.cpp.

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

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

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

static

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

Parameters

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

Definition at line 124 of file vpMatrix_covariance.cpp.

References computeCovarianceMatrix(), and computeCovarianceMatrixVVS().

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 6684 of file vpMatrix.cpp.

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

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 6623 of file vpMatrix.cpp.

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

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

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

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 6811 of file vpMatrix.cpp.

Referenced by vpImageFilter::getSobelKernelY().

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

static

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

Parameters

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

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

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

Definition at line 6830 of file vpMatrix.cpp.

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

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

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

Parameters

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

The following code shows how to use this function:

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

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

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

Definition at line 5855 of file vpMatrix.cpp.

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

Referenced by vpColVector::clear().

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 906 of file vpMatrix.cpp.

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

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

Print/save a matrix in csv format.

The following code

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

produces log.csv file that contains:

0, 1, 2

3, 4, 5

Definition at line 5806 of file vpMatrix.cpp.

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

Referenced by vpColVector::clear().

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

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

Parameters

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

Returns: Determinant of the matrix.

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

Examples:: testMatrixInverse.cpp.

Definition at line 6477 of file vpMatrix.cpp.

References detByLU(), and LU_DECOMPOSITION.

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

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>
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 224 of file vpMatrix_lu.cpp.

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

Referenced by det().

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>
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 614 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().

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>
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 378 of file vpMatrix_lu.cpp.

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

Referenced by detByLU().

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>
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 524 of file vpMatrix_lu.cpp.

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

Referenced by detByLU().

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

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

Parameters

val	: Value to set.

See also: eye()

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

Matrix A is now equal to:

0 0 0
2 0 0
0 2 0

Examples:: testSvd.cpp.

Definition at line 887 of file vpMatrix.cpp.

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

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

void vpMatrix::diag ( const vpColVector & A )

Create a diagonal matrix with the element of a vector.

Parameters

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

See also: createDiagonalMatrix()

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

Matrix A is now equal to:

0 0
2 0
0 3

Definition at line 847 of file vpMatrix.cpp.

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

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>
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 6040 of file vpMatrix.cpp.

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

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

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

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>
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 6164 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, and t().

vp_deprecated 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 6900 of file vpMatrix.cpp.

References frobeniusNorm().

Referenced by vpColVector::deg2rad().

vpMatrix vpMatrix::expm ( ) const

Compute the exponential matrix of a square matrix.

Returns: Return the exponential matrix.

Definition at line 6495 of file vpMatrix.cpp.

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

Referenced by vpTemplateTrackerWarpHomographySL3::computeCoeff().

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

Extract a sub matrix from a matrix M.

Parameters

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

The following code shows how to use this function:

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

It produces the following output:

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

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

Definition at line 407 of file vpMatrix.cpp.

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

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

void vpMatrix::eye ( )

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

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

Definition at line 449 of file vpMatrix.cpp.

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

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

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 432 of file vpMatrix.cpp.

References eye().

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 438 of file vpMatrix.cpp.

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

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

Definition at line 6704 of file vpMatrix.cpp.

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

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

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>
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 5175 of file vpMatrix.cpp.

References vpArray2D< double >::rowNum.

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

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>
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 5126 of file vpMatrix.cpp.

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

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

inlineinherited

Return the number of columns of the 2D array.

See also: getRows(), size()

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

Definition at line 279 of file vpArray2D.h.

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

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

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

It produces the following output:

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

Examples:: testMatrix.cpp.

Definition at line 5307 of file vpMatrix.cpp.

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

static 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()

Definition at line 246 of file vpMatrix.h.

double vpArray2D< double >::getMaxValue ( ) const

inherited

Return the array max value.

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

double vpArray2D< double >::getMinValue ( ) const

inherited

Return the array min value.

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

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

It produces the following output:

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

Examples:: testMatrix.cpp.

Definition at line 5215 of file vpMatrix.cpp.

References vpArray2D< double >::colNum.

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

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>
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 5259 of file vpMatrix.cpp.

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

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

inlineinherited

Return the number of rows of the 2D array.

See also: getCols(), size()

Examples:: mbtGenericTrackingDepth.cpp, mbtGenericTrackingDepthOnly.cpp, testAprilTag.cpp, testColVector.cpp, testDisplacement.cpp, testGenericTracker.cpp, testGenericTrackerDepth.cpp, testImageFilter.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, testTranslationVector.cpp, and tutorial-matlab.cpp.

Definition at line 289 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

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

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 1767 of file vpMatrix.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(), and vpArray2D< double >::rowNum.

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

inherited

Compute the Hadamard product (element wise matrix multiplication).

Parameters

m	: Second matrix;

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

Examples:: testArray2D.cpp.

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 6723 of file vpMatrix.cpp.

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

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 $(m,n)$ is the matrix size.

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

See also: frobeniusNorm(), inducedL2Norm()

Definition at line 6764 of file vpMatrix.cpp.

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

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

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

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

Parameters

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

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

The following code shows how to use this function:

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

It produces the following output:

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

See also: extract()

Examples:: testMatrix.cpp.

Definition at line 346 of file vpMatrix.cpp.

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

vp_deprecated void vpMatrix::init ( )

inline

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

Definition at line 781 of file vpMatrix.h.

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

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 5988 of file vpMatrix.cpp.

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

Referenced by vpMbEdgeKltTracker::computeVVS(), vpMbDepthDenseTracker::computeVVSInteractionMatrixAndResidu(), vpMbDepthNormalTracker::computeVVSInteractionMatrixAndResidu(), vpMbGenericTracker::computeVVSInteractionMatrixAndResidu(), cond(), conv2(), vpNurbs::curveKnotIns(), vpColVector::extract(), insert(), juxtaposeMatrices(), kernel(), nullSpace(), pseudoInverse(), vpRobotKinova::setCartVelocity(), stack(), vpColVector::stackMatrices(), and vpMbGenericTracker::track().

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 5478 of file vpMatrix.cpp.

References insert().

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 5500 of file vpMatrix.cpp.

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

vpMatrix vpMatrix::inverseByCholesky ( ) const

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

This function calls the first following function that is available:

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

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

Returns: The inverse matrix.

Here an example:

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

See also: pseudoInverse()

Definition at line 112 of file vpMatrix_cholesky.cpp.

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

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>
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 162 of file vpMatrix_cholesky.cpp.

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

Referenced by inverseByCholesky().

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>
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 255 of file vpMatrix_cholesky.cpp.

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

Referenced by inverseByCholesky().

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>
int main()
{
  vpMatrix A(4,4);
  A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.; A[0][3] = 1/4.;
  A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
  A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.; A[2][3] = 1/6.;
  A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
  // Compute the inverse
  vpMatrix A_1 = A.inverseByLU();
  std::cout << "Inverse by LU ";
#if defined(VISP_HAVE_LAPACK)
  std::cout << "(using Lapack)";
#elif defined(VISP_HAVE_EIGEN3)
  std::cout << "(using Eigen3)";
#elif (VISP_HAVE_OPENCV_VERSION >= 0x020101)
  std::cout << "(using OpenCV)";
#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:: photometricVisualServoingWithoutVpServo.cpp, and testMatrixConditionNumber.cpp.

Definition at line 130 of file vpMatrix_lu.cpp.

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

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>
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 572 of file vpMatrix_lu.cpp.

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

Referenced by inverseByLU().

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>
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 281 of file vpMatrix_lu.cpp.

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

Referenced by inverseByLU().

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>
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 483 of file vpMatrix_lu.cpp.

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

Referenced by inverseByLU().

vpMatrix vpMatrix::inverseByQR ( ) const

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

Returns: The inverse matrix.

Here an example:

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

See also: inverseByLU(), inverseByCholesky()

Definition at line 381 of file vpMatrix_qr.cpp.

References vpException::fatalError, and inverseByQRLapack().

Referenced by vpLinProg::simplex().

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>
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 152 of file vpMatrix_qr.cpp.

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

Referenced by inverseByQR().

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 1024 of file vpMatrix_qr.cpp.

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

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

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 5531 of file vpMatrix.cpp.

Referenced by vpLinProg::colReduction().

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 5552 of file vpMatrix.cpp.

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

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 6265 of file vpMatrix.cpp.

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

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 1817 of file vpMatrix.cpp.

Referenced by kron().

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 1856 of file vpMatrix.cpp.

References kron().

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 1787 of file vpMatrix.cpp.

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

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 1825 of file vpMatrix.cpp.

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

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

inlinestaticinherited

Load a matrix from a file.

Parameters

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

Returns: Returns true if success.

See also: save()

Definition at line 540 of file vpArray2D.h.

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

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

inlinestatic

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

Parameters

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

Returns: Returns true if no problem appends.

Examples:: testMatrix.cpp.

Definition at line 713 of file vpMatrix.h.

References vpArray2D< Type >::load().

Referenced by vpDot2::defineDots().

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

inlinestatic

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

Parameters

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

Returns: Returns true if no problem appends.

Examples:: testMatrix.cpp.

Definition at line 729 of file vpMatrix.h.

References vpArray2D< Type >::loadYAML().

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

inlinestaticinherited

Load an array from a YAML-formatted file.

Parameters

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

Returns: Returns true on success.

See also: saveYAML()

Examples:: servoFlirPtuIBVS.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, tutorial-flir-ptu-ibvs.cpp, and tutorial-hand-eye-calibration.cpp.

Definition at line 652 of file vpArray2D.h.

References vpArray2D< Type >::resize().

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

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

The following code

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

produces this output:

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

that could be copy/paste in Maple.

Definition at line 5765 of file vpMatrix.cpp.

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

Referenced by vpColVector::extract().

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

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

The following code

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

produces this output:

M = [ 0, 1, 2, ;

3, 4, 5, ]

that could be copy/paste in Matlab:

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

Definition at line 5721 of file vpMatrix.cpp.

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

Referenced by vpColVector::extract().

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

static

Operation C = A * B.

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

See also: operator*()

Definition at line 1009 of file vpMatrix.cpp.

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

Referenced by operator*().

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 1065 of file vpMatrix.cpp.

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

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 1102 of file vpMatrix.cpp.

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

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 1159 of file vpMatrix.cpp.

References 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 959 of file vpMatrix.cpp.

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

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

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 1540 of file vpMatrix.cpp.

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

Referenced by operator-().

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 6336 of file vpMatrix.cpp.

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

Referenced by vpMeEllipse::leastSquare(), and vpMeEllipse::leastSquareRobust().

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 6401 of file vpMatrix.cpp.

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

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

inherited

Not equal to comparison operator of a 2D array.

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 1168 of file vpMatrix.cpp.

References mult2Matrices().

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

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 1181 of file vpMatrix.cpp.

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

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 1210 of file vpMatrix.cpp.

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

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 1239 of file vpMatrix.cpp.

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

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 1278 of file vpMatrix.cpp.

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

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 919 of file vpMatrix.cpp.

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

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 944 of file vpMatrix.cpp.

References multMatrixVector().

vpMatrix vpMatrix::operator* ( double x ) const

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

Definition at line 1612 of file vpMatrix.cpp.

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

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 1675 of file vpMatrix.cpp.

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

Referenced by vpColVector::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 1410 of file vpMatrix.cpp.

References add2Matrices().

Referenced by vpColVector::operator[]().

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

Operation A = A + B.

Definition at line 1499 of file vpMatrix.cpp.

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

Referenced by vpColVector::operator[]().

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

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

Definition at line 1652 of file vpMatrix.cpp.

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

vpMatrix & vpMatrix::operator, ( double val )

Definition at line 805 of file vpMatrix.cpp.

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

Referenced by vpColVector::operator[]().

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 1490 of file vpMatrix.cpp.

References sub2Matrices().

vpMatrix vpMatrix::operator- ( void ) const

Operation C = -A (A is unchanged).

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

Definition at line 1558 of file vpMatrix.cpp.

References negateMatrix().

Referenced by vpColVector::operator[]().

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

Operation A = A - B.

Definition at line 1516 of file vpMatrix.cpp.

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

Referenced by vpColVector::operator[]().

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

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

Definition at line 1662 of file vpMatrix.cpp.

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

vpMatrix vpMatrix::operator/ ( double x ) const

Cij = Aij / x (A is unchanged)

Definition at line 1629 of file vpMatrix.cpp.

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

Referenced by vpColVector::operator[]().

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

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

Definition at line 1689 of file vpMatrix.cpp.

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

Referenced by vpColVector::operator[]().

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

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

Definition at line 788 of file vpMatrix.cpp.

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

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

Definition at line 798 of file vpMatrix.cpp.

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

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

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

Parameters

A	: 2D array to be copied.

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

vpRotationMatrix R;

vpMatrix M = R;

Definition at line 654 of file vpMatrix.cpp.

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

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

Definition at line 666 of file vpMatrix.cpp.

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

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

Definition at line 677 of file vpMatrix.cpp.

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

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>
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 723 of file vpMatrix.cpp.

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

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>
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 757 of file vpMatrix.cpp.

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

vpMatrix & vpMatrix::operator= ( double x )

Set all the element of the matrix A to x.

Definition at line 777 of file vpMatrix.cpp.

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

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

inherited

Equal to comparison operator of a 2D array.

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

inlineinherited

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

Definition at line 484 of file vpArray2D.h.

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

inlineinherited

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

Definition at line 486 of file vpArray2D.h.

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 maxlen.

Parameters

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

Returns: Returns the common total width for all matrix elements

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

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

Definition at line 5598 of file vpMatrix.cpp.

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

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

void vpMatrix::printSize ( ) const

inline

Definition at line 597 of file vpMatrix.h.

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

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

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

Note: By default, this function uses Lapack 3rd party. It is also possible to use a specific 3rd party suffixing this function name with one of the following 3rd party names (Lapack, Eigen3 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>
int main()
{
  vpMatrix A(2, 3);
  A[0][0] = 2; A[0][1] = 3; A[0][2] = 5;
  A[1][0] = -4; A[1][1] = 2; A[1][2] = 3;
  A.print(std::cout, 10, "A: ");
  vpMatrix A_p = A.pseudoInverse();
  A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
}

Once build, the previous example produces the following output:

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

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

Definition at line 2241 of file vpMatrix.cpp.

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

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

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

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ and return the rank 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>
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 2099 of file vpMatrix.cpp.

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

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

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ along with singular values and return the rank 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>
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 4509 of file vpMatrix.cpp.

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

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

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ along with singular values, $\mbox{Im}(A)$ and $\mbox{Im}(A^T)$ and return the rank 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>
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 4682 of file vpMatrix.cpp.

References pseudoInverse().

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

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

Using singular value decomposition, we have:

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

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

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

This equation could be reformulated in a minimal way:

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

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

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

Parameters

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

Returns: The rank 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>
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 4906 of file vpMatrix.cpp.

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

vpMatrix vpMatrix::pseudoInverse ( int rank_in ) const

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

Note: By default, this function uses Lapack 3rd party. It is also possible to use a specific 3rd party suffixing this function name with one of the following 3rd party names (Lapack, Eigen3 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>
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 2306 of file vpMatrix.cpp.

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

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

Compute the Moore-Penros pseudo inverse $A^+$ 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>
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 2175 of file vpMatrix.cpp.

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

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

Compute the Moore-Penros pseudo inverse $A^+$ 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>
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 4592 of file vpMatrix.cpp.

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

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

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ along with singular values, $\mbox{Im}(A)$ and $\mbox{Im}(A^T)$ and return the rank 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>
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 4766 of file vpMatrix.cpp.

References pseudoInverse().

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

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

Using singular value decomposition, we have:

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

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

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

This equation could be reformulated in a minimal way:

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

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

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

Parameters

	Ap	The Moore-Penros pseudo inverse ${\bf A}^+$ .
	sv	Vector corresponding to matrix singular values. The size of this vector is equal to min(m, n).
[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>
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 5065 of file vpMatrix.cpp.

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

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

Referenced by pseudoInverse().

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

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

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

vpMatrix vpMatrix::pseudoInverseEigen3 ( int rank_in ) const

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

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

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

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

Referenced by pseudoInverse().

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

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

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

vpMatrix vpMatrix::pseudoInverseLapack ( int rank_in ) const

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

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

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

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

Referenced by pseudoInverse().

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

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

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

vpMatrix vpMatrix::pseudoInverseOpenCV ( int rank_in ) const

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

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

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

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>
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 444 of file vpMatrix_qr.cpp.

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

Referenced by vpLinProg::colReduction().

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>
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 737 of file vpMatrix_qr.cpp.

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

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

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

inlineinherited

Examples:: testMatrixInitialization.cpp.

Definition at line 379 of file vpArray2D.h.

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

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

Definition at line 304 of file vpArray2D.h.

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

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

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 6937 of file vpMatrix.cpp.

References vpArray2D< double >::getCols().

Referenced by expm().

static 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 737 of file vpArray2D.h.

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

static 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::load().

Parameters

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

Returns: Returns true if no problem appends.

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

Examples:: testMatrix.cpp.

Definition at line 748 of file vpMatrix.h.

References vpArray2D< Type >::save().

Referenced by vpDot2::defineDots().

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

inlinestatic

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

Parameters

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

Returns: Returns true if success.

Examples:: testMatrix.cpp.

Definition at line 766 of file vpMatrix.h.

References vpArray2D< Type >::saveYAML().

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

inlinestaticinherited

Save an array in a YAML-formatted file.

Parameters

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

Returns: Returns true if success.

Here is an example of outputs.

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

Content of matrix.yml:

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

Content of matrixIndent.yml:

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

See also: loadYAML()

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

Definition at line 830 of file vpArray2D.h.

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

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 6978 of file vpMatrix.cpp.

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

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

static 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()

Definition at line 262 of file vpMatrix.h.

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

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

inlineinherited

Return the number of elements of the 2D array.

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

Definition at line 291 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

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

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>
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 1170 of file vpMatrix_qr.cpp.

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

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

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>
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 1222 of file vpMatrix_qr.cpp.

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

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

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

Non destructive wrt. A and B.

Parameters

b	: Vector .
x	: Vector .

Here an example:

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

See also: solveBySVD(const vpColVector &)

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

Definition at line 1908 of file vpMatrix.cpp.

References pseudoInverse().

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

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

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

Non destructive wrt. A and B.

Parameters

B	: Vector .

Returns: Vector .

Here an example:

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

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

Definition at line 1959 of file vpMatrix.cpp.

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

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 5879 of file vpMatrix.cpp.

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

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 5910 of file vpMatrix.cpp.

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

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 5950 of file vpMatrix.cpp.

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

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 5333 of file vpMatrix.cpp.

References stack().

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 5397 of file vpMatrix.cpp.

References stack().

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 5436 of file vpMatrix.cpp.

References stack().

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 5353 of file vpMatrix.cpp.

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

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 5416 of file vpMatrix.cpp.

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

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 5455 of file vpMatrix.cpp.

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

void vpMatrix::stackColumns ( vpColVector & out )

Stacks columns of a matrix in a vector.

Parameters

out	: a vpColVector.

Examples:: testMatrix.cpp.

Definition at line 1715 of file vpMatrix.cpp.

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

vpColVector vpMatrix::stackColumns ( )

Stacks columns of a matrix in a vector.

Returns: a vpColVector.

Definition at line 1732 of file vpMatrix.cpp.

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

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

inline

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

Definition at line 786 of file vpMatrix.h.

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

inlinestatic

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

Definition at line 791 of file vpMatrix.h.

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

inlinestatic

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

Definition at line 796 of file vpMatrix.h.

References vpException::fatalError, and operator*().

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 6915 of file vpMatrix.cpp.

References stack().

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 6917 of file vpMatrix.cpp.

References stack().

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 6905 of file vpMatrix.cpp.

References vpColVector::stack().

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 6910 of file vpMatrix.cpp.

References vpColVector::stack().

void vpMatrix::stackRows ( vpRowVector & out )

Stacks rows of a matrix in a vector

Parameters

out	: a vpRowVector.

Examples:: testMatrix.cpp.

Definition at line 1743 of file vpMatrix.cpp.

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

vpRowVector vpMatrix::stackRows ( )

Stacks rows of a matrix in a vector.

Returns: a vpRowVector.

Definition at line 1754 of file vpMatrix.cpp.

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

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 1465 of file vpMatrix.cpp.

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

Referenced by operator-().

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 1432 of file vpMatrix.cpp.

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

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 1565 of file vpMatrix.cpp.

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

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

double vpMatrix::sumSquare ( ) const

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

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

Definition at line 6785 of file vpMatrix.cpp.

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

Referenced by vpColVector::resize().

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

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

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

Parameters

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

Returns: Matrix .

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

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

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

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

Examples:: servoMomentImage.cpp.

Definition at line 2030 of file vpMatrix.cpp.

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

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

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

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

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

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

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

Parameters

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

Returns: Matrix .

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

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

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

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

Definition at line 411 of file vpMatrix_svd.cpp.

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

Referenced by pseudoInverse(), and svd().

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

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

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

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

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

Parameters

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

Returns: Matrix .

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

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

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

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

Definition at line 240 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(), vpColVector::resize(), vpArray2D< double >::rowNum, and transpose().

Referenced by pseudoInverse(), and svd().

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

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

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

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

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

Parameters

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

Returns: Matrix .

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

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

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