#include <visp3/core/vpSubMatrix.h>

Inheritance diagram for vpSubMatrix:

Public Types
enum	vpDetMethod { LU_DECOMPOSITION }

Public Member Functions
	vpSubMatrix ()

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

	~vpSubMatrix ()

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

void	checkParentStatus () const

vpSubMatrix &	operator= (const vpSubMatrix &B)

vpSubMatrix &	operator= (const vpMatrix &B)

vpSubMatrix &	operator= (const double &x)

void	clear ()

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

void	diag (const vpColVector &A)

void	eye ()

Assignment operators
vpMatrix &	operator<< (double *)

Stacking
void	stack (const vpMatrix &A)

void	stack (const vpRowVector &r)

void	stackColumns (vpColVector &out)

vpColVector	stackColumns ()

void	stackRows (vpRowVector &out)

vpRowVector	stackRows ()

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

Columns, rows, sub-matrices extraction
vpRowVector	getRow (const unsigned int i) const

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

vpColVector	getCol (const unsigned int j) const

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

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

Matrix operations
vpMatrix &	operator+= (const vpMatrix &B)

vpMatrix &	operator+= (const double x)

vpMatrix &	operator-= (const vpMatrix &B)

vpMatrix &	operator-= (const double x)

vpMatrix	operator* (const vpMatrix &B) const

vpMatrix	operator* (const vpRotationMatrix &R) const

vpMatrix	operator* (const vpVelocityTwistMatrix &V) const

vpMatrix	operator* (const vpForceTwistMatrix &V) const

vpTranslationVector	operator* (const vpTranslationVector &tv) const

vpColVector	operator* (const vpColVector &v) const

vpMatrix	operator* (const double x) const

vpMatrix	operator+ (const vpMatrix &B) const

vpMatrix	operator- (const vpMatrix &B) const

vpMatrix	operator- () const

vpMatrix &	operator*= (const double x)

vpMatrix &	operator/= (double x)

vpMatrix	operator/ (const double x) const

double	sum () const

double	sumSquare () const

double	det (vpDetMethod method=LU_DECOMPOSITION) const

vpMatrix	expm () const

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

vpMatrix	kron (const vpMatrix &m1) const

Transpose
vpMatrix	t () const

vpMatrix	transpose () const

void	transpose (vpMatrix &C) const

vpMatrix	AAt () const

void	AAt (vpMatrix &B) const

vpMatrix	AtA () const

void	AtA (vpMatrix &B) const

Matrix inversion
vpMatrix	inverseByLU () const

vpMatrix	inverseByCholesky () const

vpMatrix	inverseByCholeskyLapack () const

vpMatrix	inverseByQR () const

vpMatrix	inverseByQRLapack () 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 &kerA) const

SVD decomposition
void	svd (vpColVector &w, vpMatrix &v)

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

vpColVector	solveBySVD (const vpColVector &B) const

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

double	cond () const

Eigen values
vpColVector	eigenValues () const

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

Norms
double	euclideanNorm () const

double	infinityNorm () const

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

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

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

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

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

void	printSize () const

Inherited functionalities from vpArray2D
double	getMinValue () const

double	getMaxValue () const

unsigned int	getRows () const

unsigned int	getCols () const

unsigned int	size () const

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

double *	operator[] (unsigned int i)

double *	operator[] (unsigned int i) const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Public Attributes
double *	data

Protected Attributes
unsigned int	pRowNum

unsigned int	pColNum

vpMatrix *	parent

unsigned int	rowNum

unsigned int	colNum

double **	rowPtrs

unsigned int	dsize

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

enum	vpGEMMmethod

Deprecated functions
vp_deprecated void	init ()

vp_deprecated void	stackMatrices (const vpMatrix &A)

vp_deprecated void	setIdentity (const double &val=1.0)

vp_deprecated vpRowVector	row (const unsigned int i)

vp_deprecated vpColVector	column (const unsigned int j)

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

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

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

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

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

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

Detailed Description

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

Author: Jean Laneurit (IRISA - INRIA Rennes)

See Also: vpMatrix vpColvector vpRowVector

Definition at line 62 of file vpSubMatrix.h.

Member Enumeration Documentation

enum vpMatrix::vpDetMethod

inherited

Method used to compute the determinant of a square matrix.

See Also: det()

Enumerator
LU_DECOMPOSITION	LU decomposition method.

Definition at line 104 of file vpMatrix.h.

Constructor & Destructor Documentation

vpSubMatrix::vpSubMatrix ( )

Default constructor.

Definition at line 44 of file vpSubMatrix.cpp.

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

Constructor.

Parameters

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

Definition at line 57 of file vpSubMatrix.cpp.

References vpMatrix::init().

vpSubMatrix::~vpSubMatrix ( )

Destructor.

Definition at line 175 of file vpSubMatrix.cpp.

References vpArray2D< double >::data.

Member Function Documentation

vpMatrix vpMatrix::AAt ( ) const

inherited

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

Returns

See Also: AAt(vpMatrix &) const

Definition at line 272 of file vpMatrix.cpp.

void vpMatrix::AAt ( vpMatrix & B ) const

inherited

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

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

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

See Also: AAt()

Definition at line 292 of file vpMatrix.cpp.

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

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

staticinherited

Operation C = A + B.

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

See Also: operator+()

Definition at line 915 of file vpMatrix.cpp.

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

Referenced by vpMatrix::operator+().

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

staticinherited

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

Operation C = A + B.

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

See Also: vpColVector::operator+()

Definition at line 953 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
	)

staticinherited

Operation C = A*wA + B*wB

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

See Also: operator+()

Definition at line 882 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

inherited

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

Returns

See Also: AtA(vpMatrix &) const

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

Definition at line 376 of file vpMatrix.cpp.

Referenced by vpCalibration::calibrationTsai(), vpMbEdgeKltTracker::computeVVS(), vpMbEdgeKltMultiTracker::computeVVS(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbKltTracker::computeVVSPoseEstimation(), vpMbEdgeTracker::computeVVSSecondPhasePoseEstimation(), vpTemplateTrackerWarpHomographySL3::findWarp(), and vpNurbs::globalCurveApprox().

void vpMatrix::AtA ( vpMatrix & B ) const

inherited

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

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

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

See Also: AtA()

Definition at line 331 of file vpMatrix.cpp.

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

void vpSubMatrix::checkParentStatus ( ) const

Check is parent vpRowVector has changed since initialization.

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

Definition at line 106 of file vpSubMatrix.cpp.

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

void vpMatrix::clear ( )

inlineinherited

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

Definition at line 150 of file vpMatrix.h.

vpColVector vpMatrix::column ( const unsigned int j )

inherited

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

Return the j-th columns of the matrix.

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

Parameters

j	: Index of the column to extract.

Definition at line 3652 of file vpMatrix.cpp.

References vpArray2D< double >::getRows().

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

staticinherited

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

Parameters

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

Definition at line 59 of file vpMatrix_covariance.cpp.

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

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

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

staticinherited

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

Parameters

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

Definition at line 87 of file vpMatrix_covariance.cpp.

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

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

staticinherited

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

Parameters

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

Definition at line 139 of file vpMatrix_covariance.cpp.

References vpMatrix::computeCovarianceMatrix().

Referenced by vpMatrix::computeCovarianceMatrixVVS(), vpMbEdgeMultiTracker::computeVVS(), vpMbEdgeKltTracker::computeVVS(), vpMbEdgeKltMultiTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpMbKltTracker::computeVVSCovariance(), and vpPose::poseVirtualVS().

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

staticinherited

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

Parameters

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

Definition at line 117 of file vpMatrix_covariance.cpp.

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

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

staticinherited

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

Parameters

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

Definition at line 3525 of file vpMatrix.cpp.

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

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

double vpMatrix::cond ( ) const

inherited

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

Definition at line 3500 of file vpMatrix.cpp.

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

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

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

inherited

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

Parameters

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

The following code shows how to use this function:

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

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

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

Definition at line 2888 of file vpMatrix.cpp.

References vpArray2D< double >::getRows().

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

staticinherited

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

Parameters

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

See Also: diag()

Definition at line 545 of file vpMatrix.cpp.

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

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

inherited

Print/save a matrix in csv format.

The following code

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

produces log.csv file that contains:

0, 1, 2

3, 4, 5

Definition at line 2838 of file vpMatrix.cpp.

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

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

inherited

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

Parameters

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

Returns: Determinant of the matrix.

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

Examples:: testMatrixInverse.cpp.

Definition at line 3352 of file vpMatrix.cpp.

References vpMatrix::LU_DECOMPOSITION.

Referenced by vpTemplateTrackerTriangle::init().

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

inherited

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

Parameters

val	: Value to set.

See Also: eye()

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

Matrix A is now equal to:

0 0 0
2 0 0
0 2 0

Definition at line 524 of file vpMatrix.cpp.

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

Referenced by vpMbEdgeMultiTracker::computeVVS(), vpMbEdgeKltTracker::computeVVS(), vpMbEdgeKltMultiTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), and vpMbKltTracker::computeVVSCovariance().

void vpMatrix::diag ( const vpColVector & A )

inherited

Create a diagonal matrix with the element of a vector.

Parameters

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

See Also: createDiagonalMatrix()

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

Matrix A is now equal to:

0 0
2 0
0 3

Definition at line 478 of file vpMatrix.cpp.

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

vpColVector vpMatrix::eigenValues ( ) const

inherited

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

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

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

Exceptions

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

Here an example:

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

See Also: eigenValues(vpColVector &, vpMatrix &)

Definition at line 3067 of file vpMatrix.cpp.

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

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

inherited

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

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

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

Parameters

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

Exceptions

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

Here an example:

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

See Also: eigenValues()

Definition at line 3179 of file vpMatrix.cpp.

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

double vpMatrix::euclideanNorm ( ) const

inherited

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

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

See Also: infinityNorm()

Definition at line 3552 of file vpMatrix.cpp.

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

vpMatrix vpMatrix::expm ( ) const

inherited

Compute the exponential matrix of a square matrix.

Returns: Return the exponential matrix.

Definition at line 3372 of file vpMatrix.cpp.

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

Referenced by vpTemplateTrackerWarpHomographySL3::computeCoeff().

void vpMatrix::eye ( )

inherited

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

Examples:: testMatrix.cpp.

Definition at line 194 of file vpMatrix.cpp.

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

Referenced by vpServo::computeControlLaw(), vpServo::computeProjectionOperators(), vpMbEdgeKltTracker::computeVVS(), vpMbEdgeKltMultiTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbKltTracker::computeVVSPoseEstimation(), vpMbEdgeTracker::computeVVSSecondPhasePoseEstimation(), vpMatrix::expm(), vpMatrix::eye(), vpTemplateTrackerWarpHomographySL3::getdW0(), vpTemplateTrackerWarpHomographySL3::getdWdp0(), vpFeatureThetaU::interaction(), vpMeLine::leastSquare(), vpPose::poseFromRectangle(), vpServo::setServo(), vpMbTracker::vpMbTracker(), and vpServo::vpServo().

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

inherited

Extract a column vector from a matrix.

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

Parameters

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

Returns: The extracted column vector.

The following example shows how to use this function:

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

It produces the following output:

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

Definition at line 2235 of file vpMatrix.cpp.

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

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

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

inherited

Extract a column vector from a matrix.

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

Parameters

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

Returns: The extracted column vector.

The following example shows how to use this function:

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

It produces the following output:

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

Definition at line 2185 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.

Examples:: servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, testColVector.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, and testTranslationVector.cpp.

Definition at line 154 of file vpArray2D.h.

References vpArray2D< Type >::colNum.

Referenced by vpRowVector::csvPrint(), vpMatrix::csvPrint(), vpRotationMatrix::getCol(), vpHomogeneousMatrix::getCol(), vpMatrix::getCol(), vpMatrix::getRow(), vpMatrix::inverseByQRLapack(), vpMatrix::kernel(), vpRowVector::maplePrint(), vpMatrix::maplePrint(), vpRowVector::operator*(), vpRowVector::operator+(), vpRowVector::operator+=(), vpRowVector::operator-(), vpRowVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpRowVector::print(), vpMatrix::print(), vpMatrix::pseudoInverse(), vpMatrix::row(), and vpMatrix::svd().

double vpArray2D< double >::getMaxValue ( ) const

inherited

Return the array max value.

Examples:: servoMomentImage.cpp.

double vpArray2D< double >::getMinValue ( ) const

inherited

Return the array min value.

Examples:: servoMomentImage.cpp.

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

inherited

Extract a row vector from a matrix.

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

Parameters

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

Returns: The extracted row vector.

The following example shows how to use this function:

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

It produces the following output:

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

Definition at line 2282 of file vpMatrix.cpp.

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

Referenced by vpMatrix::pseudoInverse().

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

inherited

Extract a row vector from a matrix.

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

Parameters

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

Returns: The extracted row vector.

The following example shows how to use this function:

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

It produces the following output:

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

Definition at line 2331 of file vpMatrix.cpp.

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

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

inlineinherited

Return the number of rows of the 2D array.

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

Definition at line 152 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

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

double vpMatrix::infinityNorm ( ) const

inherited

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

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

See Also: euclideanNorm()

Definition at line 3573 of file vpMatrix.cpp.

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

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

Initialisation of vpMatrix.

Initialisation of a sub matrix.

Parameters

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

Definition at line 72 of file vpSubMatrix.cpp.

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

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

inherited

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

Parameters

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

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

The following code shows how to use this function:

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

It produces the following output:

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

Examples:: testMatrix.cpp.

Definition at line 137 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 ( )

inlineinherited

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

Definition at line 587 of file vpMatrix.h.

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

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

inherited

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

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

Parameters

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

Definition at line 3011 of file vpMatrix.cpp.

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

Referenced by vpNurbs::curveKnotIns(), and vpMatrix::insert().

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

staticinherited

Insert matrix B in matrix A at the given position.

Parameters

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

Returns: Matrix with B insert in A.

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

Definition at line 2482 of file vpMatrix.cpp.

References vpMatrix::insert().

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

staticinherited

Insert matrix B in matrix A at the given position.

Parameters

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

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

Definition at line 2511 of file vpMatrix.cpp.

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

vpMatrix vpMatrix::inverseByCholesky ( ) const

inherited

Compute the inverse of a n-by-n matrix using the Cholesky decomposition. The matrix must be real and symmetric. Only available if lapack is installed.

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 113 of file vpMatrix_cholesky.cpp.

References vpArray2D< double >::colNum, vpMatrix::inverseByCholeskyLapack(), vpMatrixException::matrixError, vpArray2D< double >::rowNum, and vpERROR_TRACE.

vpMatrix vpMatrix::inverseByCholeskyLapack ( ) const

inherited

Definition at line 55 of file vpMatrix_cholesky.cpp.

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

Referenced by vpMatrix::inverseByCholesky().

vpMatrix vpMatrix::inverseByLU ( ) const

inherited

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

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.inverseByLU();
  std::cout << "Inverse by LU: \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See Also: pseudoInverse()

Examples:: photometricVisualServoing.cpp.

Definition at line 231 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::getRows(), vpMatrixException::matrixError, vpArray2D< double >::rowNum, and vpERROR_TRACE.

vpMatrix vpMatrix::inverseByQR ( ) const

inherited

Compute the inverse of a n-by-n matrix using the QR decomposition. Only available if lapack is installed.

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.inverseByQR();
  std::cout << "Inverse by QR: \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See Also: pseudoInverse()

Definition at line 224 of file vpMatrix_qr.cpp.

References vpArray2D< double >::colNum, vpMatrix::inverseByQRLapack(), vpMatrixException::matrixError, vpArray2D< double >::rowNum, and vpERROR_TRACE.

vpMatrix vpMatrix::inverseByQRLapack ( ) const

inherited

Definition at line 72 of file vpMatrix_qr.cpp.

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

Referenced by vpMatrix::inverseByQR().

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

staticinherited

Juxtapose to matrices C = [ A B ].

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

Parameters

A	: Left matrix.
B	: Right matrix.

Returns: Juxtaposed matrix C = [ A B ]

Warning: A and B must have the same number of column

Definition at line 2552 of file vpMatrix.cpp.

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

staticinherited

Juxtapose to matrices C = [ A B ].

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

Parameters

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

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

Definition at line 2579 of file vpMatrix.cpp.

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

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

inherited

Function to compute the null space (the kernel) of the interaction matrix A which is not full rank. The null space ( the kernel ) of a matrix A is defined as Null(A) = Ker(A) = {X : A*X =0}.

Parameters

kerA	: The matrix to contain the null space (kernel) of A defined by the row vectors (A*KerA.t()=0)
svThreshold	: Specify the used threshold in the svd(...) function (a function to compute the singular value decomposition)

Returns: the rank of the matrix.

Examples:: servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp.

Definition at line 3260 of file vpMatrix.cpp.

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

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

inherited

Compute Kronecker product matrix.

Parameters

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

Definition at line 1404 of file vpMatrix.cpp.

Referenced by vpMatrix::kron().

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

inherited

Compute Kronecker product matrix.

Parameters

m	: vpMatrix;

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

Definition at line 1446 of file vpMatrix.cpp.

References vpMatrix::kron().

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

staticinherited

Compute Kronecker product matrix.

Parameters

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

Definition at line 1369 of file vpMatrix.cpp.

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

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

staticinherited

Compute Kronecker product matrix.

Parameters

m1	: vpMatrix;
m2	: vpMatrix;

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

Definition at line 1415 of file vpMatrix.cpp.

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

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

inlinestaticinherited

Load a matrix from a file.

Parameters

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

Returns: Returns true if success.

See Also: save()

Definition at line 308 of file vpArray2D.h.

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

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

inlinestaticinherited

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

Parameters

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

Returns: Returns true if no problem appends.

Examples:: testMatrix.cpp.

Definition at line 523 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`
	)

inlinestaticinherited

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

Parameters

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

Returns: Returns true if no problem appends.

Examples:: testMatrix.cpp.

Definition at line 538 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()

Definition at line 417 of file vpArray2D.h.

References vpArray2D< Type >::resize().

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

inherited

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

The following code

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

produces this output:

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

that could be copy/paste in Maple.

Definition at line 2797 of file vpMatrix.cpp.

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

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

inherited

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

The following code

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

produces this output:

M = [ 0, 1, 2, ;

3, 4, 5, ]

that could be copy/paste in Matlab:

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

Definition at line 2756 of file vpMatrix.cpp.

References vpArray2D< double >::getRows().

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

staticinherited

Operation C = A * B.

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

See Also: operator*()

Definition at line 643 of file vpMatrix.cpp.

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

Referenced by vpMatrix::operator*().

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

staticinherited

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

Operation C = A * B.

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

Exceptions

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

Definition at line 689 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
	)

staticinherited

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

Operation C = A * B.

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

Exceptions

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

Definition at line 728 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 vpColVector &	B,
		vpColVector &	C
	)

staticinherited

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

Operation C = A * B.

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

See Also: multMatrixVector()

Definition at line 766 of file vpMatrix.cpp.

References vpMatrix::multMatrixVector().

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

staticinherited

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

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

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

Definition at line 606 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.

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

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

staticinherited

Operation C = -A.

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

See Also: operator-(void)

Definition at line 1124 of file vpMatrix.cpp.

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

Referenced by vpMatrix::operator-().

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

inherited

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

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

Definition at line 775 of file vpMatrix.cpp.

References vpMatrix::mult2Matrices().

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

inherited

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

Definition at line 788 of file vpMatrix.cpp.

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

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

inherited

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

Definition at line 817 of file vpMatrix.cpp.

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

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

inherited

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

Definition at line 846 of file vpMatrix.cpp.

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

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

inherited

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

Definition at line 565 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

inherited

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

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

Definition at line 591 of file vpMatrix.cpp.

References vpMatrix::multMatrixVector().

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

inherited

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

Definition at line 1203 of file vpMatrix.cpp.

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

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

inherited

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

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

Definition at line 1266 of file vpMatrix.cpp.

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

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

inherited

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

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

Definition at line 983 of file vpMatrix.cpp.

References vpMatrix::add2Matrices().

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

inherited

Operation A = A + B.

Definition at line 1081 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.

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

inherited

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

Definition at line 1242 of file vpMatrix.cpp.

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

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

inherited

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

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

Definition at line 1072 of file vpMatrix.cpp.

References vpMatrix::sub2Matrices().

vpMatrix vpMatrix::operator- ( void ) const

inherited

Operation C = -A (A is unchanged).

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

Definition at line 1146 of file vpMatrix.cpp.

References vpMatrix::negateMatrix().

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

inherited

Operation A = A - B.

Definition at line 1099 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.

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

inherited

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

Definition at line 1253 of file vpMatrix.cpp.

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

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

inherited

Cij = Aij / x (A is unchanged)

Definition at line 1215 of file vpMatrix.cpp.

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

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

inherited

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

Definition at line 1276 of file vpMatrix.cpp.

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

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

inherited

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

Definition at line 431 of file vpMatrix.cpp.

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

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

Operation such as subA = subB.

Operation A = B.

Parameters

B	: a subMatrix

Definition at line 143 of file vpSubMatrix.cpp.

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

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

Operation such as subA = B.

Operation A = B.

Parameters

B	: a matrix

Definition at line 123 of file vpSubMatrix.cpp.

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

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

Operation such as subA = x.

Operation A = x.

Parameters

x	: a scalar

Definition at line 166 of file vpSubMatrix.cpp.

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

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

inlineinherited

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

Definition at line 259 of file vpArray2D.h.

References vpArray2D< Type >::rowPtrs.

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

inlineinherited

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

Definition at line 261 of file vpArray2D.h.

References vpArray2D< Type >::rowPtrs.

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

inherited

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

Parameters

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

Returns: Returns the common total width for all matrix elements

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

Examples:: testMatrix.cpp.

Definition at line 2634 of file vpMatrix.cpp.

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

void vpMatrix::printSize ( ) const

inlineinherited

Definition at line 422 of file vpMatrix.h.

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

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

inherited

Compute the pseudo inverse of the matrix using the SVD.

Compute and return the pseudo inverse of a n-by-m matrix : $ A^+ $

Parameters

svThreshold : Threshold used to test the singular values.

Returns: Pseudo inverse of the matrix.

Here an example to compute the inverse of a n-by-n matrix. If the matrix is n-by-n it is also possible to use inverseByLU().

#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.pseudoInverse();
  std::cout << "Inverse by pseudo inverse: \n" << A_1 << std::endl;
  std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}

See Also: inverseByLU()

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

Definition at line 1741 of file vpMatrix.cpp.

Referenced by vpCalibration::calibrationTsai(), vpSimulatorAfma6::computeArticularVelocity(), vpSimulatorViper850::computeArticularVelocity(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), vpMbEdgeKltTracker::computeVVS(), vpMbEdgeKltMultiTracker::computeVVS(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbKltTracker::computeVVSPoseEstimation(), vpMbEdgeTracker::computeVVSSecondPhasePoseEstimation(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), vpMeEllipse::initTracking(), vpHomography::inverse(), vpMeLine::leastSquare(), vpPose::poseDementhonNonPlan(), vpPose::poseFromRectangle(), vpPose::poseVirtualVS(), vpMatrix::pseudoInverse(), vpHomography::robust(), and vpMatrix::solveBySVD().

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

inherited

Compute the pseudo inverse of the matrix using the SVD. return the rank

Compute the pseudo inverse of the matrix $Ap = A^+$

Parameters

Ap	: The pseudo inverse .
svThreshold	: Threshold used to test the singular values.

Returns: Return the rank of the matrix A

Definition at line 1701 of file vpMatrix.cpp.

References vpMatrix::pseudoInverse().

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

inherited

Compute the pseudo inverse of the matrix using the SVD. return the rank and the singular value

Compute the pseudo inverse of the matrix $Ap = A^+$

Parameters

Ap	: The pseudo inverse .
sv	: Singular values.
svThreshold	: Threshold used to test the singular values.

Returns: Return the rank of the matrix A

Definition at line 1757 of file vpMatrix.cpp.

References vpMatrix::pseudoInverse().

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

inherited

Compute the pseudo inverse of the matrix using the SVD. return the rank and the singular value, image

Compute the pseudo inverse of the matrix $Ap = A^+$ along with Ker A, Ker $A^T$ , Im A and Im $A^T$

Pseudo inverse, kernel and image are computed using the SVD decomposition.

A is an m x n matrix, if m >=n the svd works on A other wise it works on $A^T$ .

Therefore if m>=n we have

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

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

where Im(A) is an m x r matrix (r is the rank of A) and Im(A^T) is an r x n matrix

Parameters

Ap	: The pseudo inverse .
sv	: Singular values.
svThreshold	: Threshold used to test the singular values.
imAt	: Image A^T
imA	Image A

Returns: Return the rank of the matrix A

Definition at line 1795 of file vpMatrix.cpp.

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

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

inherited

Compute the pseudo inverse of the matrix using the SVD. return the rank and the singular value, image, kernel.

Compute the pseudo inverse of the matrix $Ap = A^+$ along with Ker A, Ker $A^T$ , Im A and Im $A^T$

Pseudo inverse, kernel and image are computed using the SVD decomposition.

A is an m x n matrix, if m >=n the svd works on A other wise it works on $A^T$ .

Therefore if m>=n we have

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

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

where Im(A) is an m x r matrix (r is the rank of A) and Im(A^T) is an r x n matrix

Parameters

Ap	: The pseudo inverse .
sv	: Singular values.
svThreshold	: Threshold used to test the singular values.
imA	Image A
imAt	: Image A^T
kerA	: null space of A

Returns: Return the rank of the matrix A

Definition at line 1971 of file vpMatrix.cpp.

References vpArray2D< double >::getCols(), vpArray2D< Type >::getCols(), vpMatrix::getRow(), vpArray2D< double >::getRows(), vpArray2D< Type >::resize(), vpColVector::resize(), vpRowVector::sumSquare(), vpMatrix::svd(), and vpMatrix::t().

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

Examples:: testArray2D.cpp, testMatrix.cpp, testMatrixInverse.cpp, and testSvd.cpp.

Definition at line 167 of file vpArray2D.h.

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

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

vpRowVector vpMatrix::row ( const unsigned int i )

inherited

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

Return the i-th row of the matrix.

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

Definition at line 3636 of file vpMatrix.cpp.

References vpArray2D< double >::getCols().

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

inlinestaticinherited

Save a matrix to a file.

Parameters

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

Returns: Returns true if success.

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

See Also: load()

Definition at line 499 of file vpArray2D.h.

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

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

inlinestaticinherited

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

Parameters

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

Returns: Returns true if no problem appends.

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

Examples:: testMatrix.cpp.

Definition at line 555 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 = `""`
	)

inlinestaticinherited

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

Parameters

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

Returns: Returns true if success.

Examples:: testMatrix.cpp.

Definition at line 572 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()

Definition at line 588 of file vpArray2D.h.

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

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

inherited

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

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

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

Definition at line 3667 of file vpMatrix.cpp.

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

Referenced by vpServo::secondaryTask().

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

inlineinherited

Return the number of elements of the 2D array.

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

Definition at line 156 of file vpArray2D.h.

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

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

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

inherited

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

Non destructive wrt. A and B.

Parameters

b	: Vector .
x	: Vector .

Here an example:

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

See Also: solveBySVD(const vpColVector &)

Definition at line 1502 of file vpMatrix.cpp.

References vpMatrix::pseudoInverse().

Referenced by vpMatrix::solveBySVD().

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

inherited

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

Non destructive wrt. A and B.

Parameters

B	: Vector .

Returns: Vector .

Here an example:

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

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

Definition at line 1557 of file vpMatrix.cpp.

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

void vpMatrix::stack ( const vpMatrix & A )

inherited

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

Here an example for a robot velocity log :

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

Examples:: servoPioneerPoint2DDepthWithoutVpServo.cpp.

Definition at line 2981 of file vpMatrix.cpp.

References vpArray2D< double >::rowNum.

void vpMatrix::stack ( const vpRowVector & r )

inherited

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

Definition at line 2992 of file vpMatrix.cpp.

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

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

staticinherited

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

Parameters

A	: Upper matrix.
B	: Lower matrix.

Returns: Stacked matrix [ A B ]^T

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

Definition at line 2351 of file vpMatrix.cpp.

References vpMatrix::stack().

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

staticinherited

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

Parameters

A	: Upper matrix.
r	: Lower matrix.

Returns: Stacked matrix [ A r ]^T

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

Definition at line 2375 of file vpMatrix.cpp.

References vpMatrix::stack().

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

staticinherited

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

Parameters

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

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

Definition at line 2399 of file vpMatrix.cpp.

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

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

staticinherited

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

Parameters

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

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

Definition at line 2441 of file vpMatrix.cpp.

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

void vpMatrix::stackColumns ( vpColVector & out )

inherited

Stacks columns of a matrix in a vector.

Parameters

out	: a vpColVector.

Definition at line 1305 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 ( )

inherited

Stacks columns of a matrix in a vector.

Returns: a vpColVector.

Definition at line 1326 of file vpMatrix.cpp.

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

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

inlineinherited

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

Definition at line 591 of file vpMatrix.h.

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

inlinestaticinherited

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

Definition at line 595 of file vpMatrix.h.

References vpMatrix::stack().

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

inlinestaticinherited

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

Definition at line 599 of file vpMatrix.h.

References vpMatrix::stack().

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

staticinherited

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

Definition at line 3619 of file vpMatrix.cpp.

References vpMatrix::stack().

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

staticinherited

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

Definition at line 3624 of file vpMatrix.cpp.

References vpMatrix::stack().

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

staticinherited

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

Definition at line 3609 of file vpMatrix.cpp.

References vpColVector::stack().

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

staticinherited

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

Definition at line 3614 of file vpMatrix.cpp.

References vpColVector::stack().

void vpMatrix::stackRows ( vpRowVector & out )

inherited

Stacks rows of a matrix in a vector

Parameters

out	: a vpRowVector.

Definition at line 1337 of file vpMatrix.cpp.

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

vpRowVector vpMatrix::stackRows ( )

inherited

Stacks rows of a matrix in a vector.

Returns: a vpRowVector.

Definition at line 1356 of file vpMatrix.cpp.

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

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

staticinherited

Operation C = A - B.

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

Exceptions

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

See Also: operator-()

Definition at line 1042 of file vpMatrix.cpp.

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

Referenced by vpMatrix::operator-().

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

staticinherited

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

Operation C = A - B on column vectors.

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

Exceptions

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

See Also: vpColVector::operator-()

Definition at line 1005 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

inherited

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

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

Definition at line 1155 of file vpMatrix.cpp.

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

Referenced by vpMatrix::expm().

double vpMatrix::sumSquare ( ) const

inherited

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

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

Definition at line 3593 of file vpMatrix.cpp.

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

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

inherited

Singular value decomposition (SVD).

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

Warning: Destructive method wrt. to the matrix to decompose. You should make a COPY of that matrix if needed not to CHANGE.

Parameters

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

Returns: Matrix .

Warning: If the GNU Scientific Library (GSL) third party library is used to compute the SVD decomposition, the singular values $\Sigma_{i,i}$ are ordered in decreasing fashion in w. This is not the case, if the GSL is not detected by ViSP.

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.svd(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;
}