#include <vpTranslationVector.h>

Inheritance diagram for vpTranslationVector:

Public Types
enum	vpDetMethod { LU_DECOMPOSITION }

Public Member Functions
	vpTranslationVector ()

	vpTranslationVector (const double tx, const double ty, const double tz)

	vpTranslationVector (const vpTranslationVector &t)

void	set (const double tx, const double ty, const double tz)

vpTranslationVector	operator+ (const vpTranslationVector &t) const

vpTranslationVector	operator- (const vpTranslationVector &t) const

vpTranslationVector	operator- () const

vpTranslationVector	operator* (const double x) const

vpTranslationVector &	operator= (const vpTranslationVector &t)

vpTranslationVector &	operator= (double x)

vpMatrix	skew () const

void	insert (unsigned int i, const vpColVector &v)

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

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

double &	operator[] (unsigned int n)

const double &	operator[] (unsigned int n) const

vpColVector &	operator<< (const vpColVector &v)

vpColVector &	operator<< (double *)

vpColVector	operator+ (const vpColVector &v) const

vpColVector	operator- (const vpColVector &v) const

double	operator* (const vpColVector &x) const

vpMatrix	operator* (const vpRowVector &x) const

vpColVector	rows (unsigned int first_row, unsigned int last_row)

void	reshape (vpMatrix &m, const unsigned int &nrows, const unsigned int &ncols)

vpMatrix	reshape (const unsigned int &nrows, const unsigned int &ncols)

void	stack (const double &b)

void	stack (const vpColVector &B)

vpRowVector	t () const

vpColVector &	normalize ()

void	rad2deg ()

void	deg2rad ()

unsigned int	size () const

void	kill ()

void	eye (unsigned int n)

void	eye (unsigned int m, unsigned int n)

void	setIdentity (const double &val=1.0)

void	stackMatrices (const vpMatrix &A)

Set/get Matrix size
void	resize (const unsigned int nrows, const unsigned int ncols, const bool nullify=true)

unsigned int	getRows () const

unsigned int	getCols () const

double	getMinValue () const

double	getMaxValue () const

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

vpMatrix	operator- (const vpMatrix &B) const

vpMatrix	operator* (const vpMatrix &B) const

vpMatrix	operator* (const vpHomography &H) const

vpTranslationVector	operator* (const vpTranslationVector &b) const

vpMatrix &	operator+= (const vpMatrix &B)

vpMatrix &	operator+= (const double x)

vpMatrix &	operator-= (const vpMatrix &B)

vpMatrix &	operator-= (const double x)

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 ()

Columns, Rows extraction, Submatrix
void	init (const vpMatrix &M, unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols)

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

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

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

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

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

std::ostream &	cppPrint (std::ostream &os, const char *matrixName=NULL, bool octet=false) const

void	printSize ()

Copy / assignment
void	diag (const vpColVector &A)

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

vpMatrix	kron (const vpMatrix &m1)

void	stackColumns (vpColVector &out)

vpColVector	stackColumns ()

void	stackRows (vpRowVector &out)

vpRowVector	stackRows ()

Transpose, Identity
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)

double	cond ()

Eigen values
vpColVector	eigenValues ()

void	eigenValues (vpColVector &evalue, vpMatrix &evector)

Norms
double	euclideanNorm () const

double	infinityNorm () const

Deprecated functions
vp_deprecated vpRowVector	row (const unsigned int i)

vp_deprecated vpColVector	column (const unsigned int j)

Static Public Member Functions
static vpMatrix	skew (const vpTranslationVector &t)

static void	skew (const vpTranslationVector &t, vpMatrix &M)

static vpTranslationVector	cross (const vpTranslationVector &a, const vpTranslationVector &b)

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)

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

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

static vpColVector	crossProd (const vpColVector &a, const vpColVector &b)

static vpColVector	cross (const vpColVector &a, const vpColVector &b)

static vpMatrix	skew (const vpColVector &v)

static double	dotProd (const vpColVector &a, const vpColVector &b)

static vpColVector	sort (const vpColVector &v)

static vpColVector	invSort (const vpColVector &v)

static double	median (const vpColVector &v)

static double	mean (const vpColVector &v)

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

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

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

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

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

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

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

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

static bool	loadMatrix (std::string filename, vpMatrix &M, const bool binary=false, char *Header=NULL)

static bool	loadMatrix (const char filename, vpMatrix &M, const bool binary=false, char Header=NULL)

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

static void	multMatrixVector (const vpMatrix &A, const vpColVector &b, vpColVector &c)

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

static bool	saveMatrix (std::string filename, const vpMatrix &M, const bool binary=false, const char *Header="")

static bool	saveMatrix (const char filename, const vpMatrix &M, const bool binary=false, const char Header="")

static bool	saveMatrixYAML (std::string filename, const vpMatrix &M, const char *header="")

static bool	saveMatrixYAML (const char filename, const vpMatrix &M, const char header="")

static bool	loadMatrixYAML (std::string filename, vpMatrix &M, char *header=NULL)

static bool	loadMatrixYAML (const char filename, vpMatrix &M, char header=NULL)

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

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

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

Public Attributes
double *	data

Protected Attributes
unsigned int	rowNum

unsigned int	colNum

double **	rowPtrs

unsigned int	dsize

unsigned int	trsize

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

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

enum	vpGEMMmethod

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

Detailed Description

Class that consider the case of a translation vector.

Let be $^{a}{\bf t}_{b} = [t_x,t_y,t_z]^\top$ be a translation from frame $ a $ to frame $ b $ . The representation of a translation is a column vector of dimension 3.

Translations are expressed in meters.

The code below shows how to use a translation vector to build an homogeneous matrix.

#include <visp/vpHomogeneousMatrix.h>
#include <visp/vpRotationMatrix.h>
#include <visp/vpTranslationVector.h>
int main()
{
  vpTranslationVector t; // Translation vector 
  // Initialization of the translation vector
  t[0] =  0.2; // tx = 0.2 meters
  t[1] = -0.1; // ty = -0.1 meters
  t[2] =  1.0; // tz = 1 meters
  // Construction of a rotation matrix
  vpRotationMatrix R; // Set to identity by default
  // Construction of an homogeneous matrix
  vpHomogeneousMatrix M(t, R);
}

Examples:: calibrateTsai.cpp, exponentialMap.cpp, HelloWorldOgre.cpp, homographyHartleyDLT2DObject.cpp, homographyHLM2DObject.cpp, homographyHLM3DObject.cpp, homographyRansac2DObject.cpp, manGeometricFeatures.cpp, servoAfma6FourPoints2DCamVelocityInteractionCurrent.cpp, servoAfma6FourPoints2DCamVelocityInteractionDesired.cpp, servoMomentImage.cpp, servoMomentPoints.cpp, servoMomentPolygon.cpp, servoSimu3D_cdMc_CamVelocityWithoutVpServo.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimuSphere.cpp, servoViper650FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper650FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPointsKinect.cpp, testDisplacement.cpp, testRobotAfma6Pose.cpp, testRobotViper850.cpp, testRobotViper850Pose.cpp, testTwistMatrix.cpp, testViper850.cpp, tutorial-homography-from-points.cpp, tutorial-ibvs-4pts-ogre-tracking.cpp, tutorial-ibvs-4pts-ogre.cpp, and tutorial-ibvs-4pts-wireframe-robot-viper.cpp.

Definition at line 95 of file vpTranslationVector.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 105 of file vpMatrix.h.

Constructor & Destructor Documentation

vpTranslationVector::vpTranslationVector ( )

inline

Default constructor. The translation vector is initialized to zero.

Definition at line 107 of file vpTranslationVector.h.

References vpMatrix::init().

vpTranslationVector::vpTranslationVector	(	const double	tx,
		const double	ty,
		const double	tz
	)

Contruct a translation vector $\bf t$ from 3 doubles.

Parameters

tx,ty,tz : Translation respectively along x, y and z axis.

Definition at line 72 of file vpTranslationVector.cpp.

vpTranslationVector::vpTranslationVector ( const vpTranslationVector & tv )

Copy constructor.

Parameters

tv	: Translation vector to copy.

vpTranslationVector t1(1,2,3); // Create and initialize a translation vector
vpTranslationVector t2(t1);    // t2 is now a copy of t1

Definition at line 94 of file vpTranslationVector.cpp.

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 1368 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 1388 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::resize(), vpMatrix::rowNum, vpMatrix::rowPtrs, vpCERROR, and vpERROR_TRACE.

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 602 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::resize(), vpMatrix::rowNum, vpMatrix::rowPtrs, and vpERROR_TRACE.

Referenced by vpMatrix::operator+().

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 563 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::resize(), vpMatrix::rowNum, vpMatrix::rowPtrs, and vpERROR_TRACE.

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 1479 of file vpMatrix.cpp.

Referenced by vpCalibration::calibrationTsai(), vpMbEdgeKltTracker::computeVVS(), vpMbKltTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), 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 1431 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::data, vpMatrix::resize(), vpMatrix::rowNum, vpCERROR, and vpERROR_TRACE.

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 2362 of file vpMatrix.cpp.

References vpMatrix::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 61 of file vpMatrix_covariance.cpp.

References vpException::divideByZeroError, vpMatrix::getCols(), vpMatrix::getRows(), vpMatrix::pseudoInverse(), and vpMatrix::t().

Referenced by vpMbTracker::computeCovarianceMatrix(), vpPose::poseVirtualVS(), 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 89 of file vpMatrix_covariance.cpp.

References vpException::divideByZeroError, vpMatrix::getCols(), and vpMatrix::t().

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 4320 of file vpMatrix.cpp.

References vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::resize(), and vpTRACE.

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

double vpMatrix::cond ( )

inherited

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

Definition at line 4295 of file vpMatrix.cpp.

References vpMatrix::getCols(), and vpMatrix::svd().

std::ostream & vpMatrix::cppPrint	(	std::ostream &	os,
		const char *	matrixName = `NULL`,
		bool	octet = `false`
	)		const

inherited

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

Print under the following form: vpMatrix A(6,4); A[0][0] = 1.4; A[0][1] = 0.6; ...

Parameters

os	the stream to be printed in.
matrixName	name of the matrix, "A" by default, to be used for the line vpMatrix A(6,7) (see example).
octet	if false, print using double, if true, print byte per byte each bytes of the double array.

Definition at line 3120 of file vpMatrix.cpp.

References vpMatrix::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 2869 of file vpMatrix.cpp.

References vpMatrix::getRows(), vpMatrix::resize(), vpCERROR, and vpERROR_TRACE.

vpTranslationVector vpTranslationVector::cross	(	const vpTranslationVector &	a,
		const vpTranslationVector &	b
	)

static

Return the cross product of two translation vectors $a \times b$ .

Parameters

a,b	: Translation vectors in input.

Returns: The cross product of two translation vectors $a \times b$ .

Definition at line 369 of file vpTranslationVector.cpp.

References skew().

static vpColVector vpColVector::cross	(	const vpColVector &	a,
		const vpColVector &	b
	)

inlinestaticinherited

Definition at line 158 of file vpColVector.h.

Referenced by vpMbtDistanceLine::buildFrom(), vpPlane::init(), and vpPose::poseDementhonNonPlan().

vpColVector vpColVector::crossProd	(	const vpColVector &	a,
		const vpColVector &	b
	)

staticinherited

Compute the cross product of two vectors C = a x b.

Parameters

a	: vpColVector
b	: vpColVector

Definition at line 747 of file vpColVector.cpp.

References vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpColVector::skew(), and vpERROR_TRACE.

Referenced by vpMbTracker::addPolygon(), vpPose::coplanar(), and vpImageSimulator::setCameraPosition().

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

inherited

Print matrix in csv format.

Print as comma separated values so that this output can be imported into any program which has a csv data import option: 0.939846, 0.0300754, 0.340272 0.0300788, 0.984961, -0.170136 -0.340272, 0.170136, 0.924807

Definition at line 3087 of file vpMatrix.cpp.

References vpMatrix::getCols(), and vpMatrix::getRows().

void vpColVector::deg2rad ( )

inlineinherited

Convert a column vector containing angles in degrees into radians.

Definition at line 192 of file vpColVector.h.

References vpMatrix::rowNum.

Referenced by vpRobotViper650::getPosition(), vpRobotViper850::getPosition(), vpRobotViper850::getVelocity(), vpRobotViper650::getVelocity(), vpRobotViper650::init(), vpRobotViper850::init(), vpSimulatorViper850::readPosFile(), vpRobotViper650::readPosFile(), vpRobotViper850::readPosFile(), vpRobotViper650::setPosition(), and vpRobotViper850::setPosition().

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 methos is faster than the method based on Gaussian elimination.

Returns: Determinant of the matrix.

#include <iostream>
#include <visp/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 3765 of file vpMatrix.cpp.

References vpMatrix::LU_DECOMPOSITION.

Referenced by vpTemplateTrackerTriangle::init().

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 <visp/vpColVector.h>
#include <visp/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;
// A is now equal to:
// 1 0 0
// 0 2 0
// 0 0 3
}

Definition at line 2841 of file vpMatrix.cpp.

References vpMatrix::getRows(), vpMatrix::resize(), vpCERROR, and vpERROR_TRACE.

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

double dotProd	(	const vpColVector &	a,
		const vpColVector &	b
	)

staticinherited

Dot Product.

compute the dot product of two vectors C = a.b

Definition at line 384 of file vpColVector.cpp.

References vpMatrix::data, vpMatrix::getRows(), vpMatrixException::notInitializedError, and vpERROR_TRACE.

Referenced by vpPose::calculArbreDementhon(), vpMbtPolygon::isVisible(), vpPose::poseDementhonPlan(), and vpImageSimulator::setCameraPosition().

vpColVector vpMatrix::eigenValues ( )

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

vpMatrixException::matrixError	If the matrix is not square or if the matrix is not symmetric.
vpMatrixException::notImplementedError	If the GSL library is not detected

Here an example:

#include <iostream>
#include <visp/vpColVector.h>
#include <visp/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 3348 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrixException::matrixError, vpMatrixException::notImplementedError, vpMatrix::rowNum, vpMatrix::t(), and vpERROR_TRACE.

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

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

vpMatrixException::matrixError	If the matrix is not square or if the matrix is not symmetric.
vpMatrixException::notImplementedError	If the GSL library is not detected

Here an example:

#include <iostream>
#include <visp/vpColVector.h>
#include <visp/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 3467 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::data, vpMatrixException::matrixError, vpMatrixException::notImplementedError, vpColVector::resize(), vpMatrix::resize(), vpMatrix::rowNum, vpMatrix::t(), and vpERROR_TRACE.

double vpMatrix::euclideanNorm ( ) const

inherited

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

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

See also: infinityNorm()

Definition at line 3168 of file vpMatrix.cpp.

References vpMatrix::data, and vpMatrix::dsize.

Referenced by vpSimulatorAfma6::setPosition().

vpMatrix vpMatrix::expm ( )

inherited

Compute the exponential matrix of a square matrix.

Returns: Return the exponential matrix.

Definition at line 4137 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::data, vpMatrixException::incorrectMatrixSizeError, vpMatrix::inverseByLU(), vpMatrix::rowNum, vpMatrix::setIdentity(), vpMatrix::sum(), and vpTRACE.

Referenced by vpTemplateTrackerWarpHomographySL3::computeCoeff().

void vpMatrix::eye ( unsigned int n )

inherited

Set an n-by-n matrix to identity.

eye(n) is an n-by-n matrix with ones on the diagonal and zeros else where.

Examples:: testMatrix.cpp.

Definition at line 1252 of file vpMatrix.cpp.

References vpCERROR, and vpERROR_TRACE.

Referenced by vpMbEdgeTracker::computeVVS(), and vpServo::setServo().

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

inherited

Set an m-by-n matrix to identity.

eye(m,n) is an m-by-n matrix with ones on the diagonal and zeros else where.

Definition at line 1272 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::resize(), vpMatrix::rowNum, vpCERROR, and vpERROR_TRACE.

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 <visp/vpColVector.h>
#include <visp/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 2463 of file vpMatrix.cpp.

References vpException::dimensionError, vpMatrix::getCols(), and vpMatrix::getRows().

Referenced by vpHomography::DLT(), vpPose::poseDementhonPlan(), and vpPose::poseFromRectangle().

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 <visp/vpColVector.h>
#include <visp/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 2413 of file vpMatrix.cpp.

References vpException::dimensionError, vpMatrix::getCols(), and vpMatrix::getRows().

unsigned int vpMatrix::getCols ( ) const

inlineinherited

Return the number of columns of the matrix.

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

Definition at line 163 of file vpMatrix.h.

Referenced by vpMatrix::add2Matrices(), vpMatrix::add2WeightedMatrices(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), vpMatrix::computeHLM(), vpServo::computeInteractionMatrix(), vpMbTracker::computeJTR(), vpMatrix::cond(), vpMatrix::csvPrint(), vpMatrix::getCol(), vpImageSimulator::getImage(), vpMatrix::getRow(), vpSubRowVector::init(), vpSubMatrix::init(), vpMatrix::init(), vpCameraParameters::initFromCalibrationMatrix(), vpMatrix::insert(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByQRLapack(), vpMatrix::juxtaposeMatrices(), vpMatrix::kernel(), vpMatrix::kron(), vpMatrix::maplePrint(), vpRowVector::operator*(), vpRotationMatrix::operator*(), vpVelocityTwistMatrix::operator*(), vpForceTwistMatrix::operator*(), vpMatrix::operator*(), vpRowVector::operator+(), vpMatrix::operator+=(), vpRowVector::operator-(), vpMatrix::operator-=(), vpSubRowVector::operator=(), vpSubColVector::operator=(), vpSubMatrix::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpRotationMatrix::operator=(), vpHomography::operator=(), vpPose::poseDementhonPlan(), vpMatrix::print(), vpMatrix::pseudoInverse(), vpIoTools::readConfigVar(), vpRowVector::reshape(), vpColVector::reshape(), vpMatrix::row(), vpMatrix::saveMatrix(), vpMatrix::saveMatrixYAML(), vpServo::secondaryTask(), vpRowVector::size(), vpMatrix::stackMatrices(), vpMatrix::sub2Matrices(), and vpMatrix::svd().

double vpMatrix::getMaxValue ( ) const

inherited

Examples:: servoMomentImage.cpp.

Definition at line 4238 of file vpMatrix.cpp.

References vpMatrix::data, and vpMatrix::dsize.

double vpMatrix::getMinValue ( ) const

inherited

Examples:: servoMomentImage.cpp.

Definition at line 4224 of file vpMatrix.cpp.

References vpMatrix::data, and vpMatrix::dsize.

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 <visp/vpMatrix.h>
#include <visp/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 2510 of file vpMatrix.cpp.

References vpException::dimensionError, vpMatrix::getCols(), and vpMatrix::getRows().

Referenced by vpMatrix::kernel(), and 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 <visp/vpMatrix.h>
#include <visp/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 2559 of file vpMatrix.cpp.

References vpException::dimensionError, vpMatrix::getCols(), and vpMatrix::getRows().

unsigned int vpMatrix::getRows ( ) const

inlineinherited

Return the number of rows of the matrix.

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

Definition at line 161 of file vpMatrix.h.

Referenced by vpMatrix::add2Matrices(), vpMatrix::add2WeightedMatrices(), vpLine::changeFrame(), vpSubColVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpMatrix::column(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), vpMbTracker::computeCovarianceMatrix(), vpServo::computeError(), vpMatrix::computeHLM(), vpServo::computeInteractionMatrix(), vpMbTracker::computeJTR(), vpPtu46::computeMGD(), vpPose::computeResidual(), vpMbEdgeKltTracker::computeVVS(), vpMbKltTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpMatrix::cppPrint(), vpMatrix::createDiagonalMatrix(), vpColVector::crossProd(), vpMatrix::csvPrint(), vpDot2::defineDots(), vpMatrix::diag(), vpProjectionDisplay::display(), vpColVector::dotProd(), vpGenericFeature::error(), vpImageFilter::filter(), vpPtu46::get_eJe(), vpBiclops::get_eJe(), vpPtu46::get_fJe(), vpBiclops::get_fJe(), vpBiclops::get_fMe(), vpGenericFeature::get_s(), vpMatrix::getCol(), vpBasicFeature::getDimension(), vpImageSimulator::getImage(), vpAfma6::getInverseKinematics(), vpViper::getInverseKinematicsWrist(), vpMatrix::getRow(), vpSubColVector::init(), vpSubMatrix::init(), vpMatrix::init(), vpCameraParameters::initFromCalibrationMatrix(), vpMatrix::insert(), vpFeatureLuminance::interaction(), vpGenericFeature::interaction(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByLU(), vpMatrix::inverseByQRLapack(), vpColVector::invSort(), vpMatrix::juxtaposeMatrices(), vpMatrix::kernel(), vpScale::KernelDensity(), vpScale::KernelDensityGradient(), vpMatrix::kron(), vpMatrix::maplePrint(), vpMatrix::matlabPrint(), vpColVector::mean(), vpScale::MeanShift(), vpColVector::median(), vpRobust::MEstimator(), vpMatrix::multMatrixVector(), vpRowVector::operator*(), vpRotationMatrix::operator*(), vpVelocityTwistMatrix::operator*(), vpForceTwistMatrix::operator*(), vpMatrix::operator*(), vpColVector::operator+(), vpMatrix::operator+=(), vpColVector::operator-(), vpMatrix::operator-=(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpSubMatrix::operator=(), vpColVector::operator=(), vpRotationMatrix::operator=(), vpRGBa::operator=(), vpHomography::operator=(), vpPlot::plot(), vpPose::poseDementhonPlan(), vpPose::poseVirtualVSrobust(), vpKalmanFilter::prediction(), vpMatrix::print(), vpLine::projection(), vpMatrix::pseudoInverse(), vpIoTools::readConfigVar(), vpRowVector::reshape(), vpColVector::reshape(), vpMatrix::saveMatrix(), vpMatrix::saveMatrixYAML(), vpGenericFeature::set_s(), vpGenericFeature::setError(), vpMbTracker::setEstimatedDoF(), vpGenericFeature::setInteractionMatrix(), vpSimulatorAfma6::setJointLimit(), vpSimulatorViper850::setJointLimit(), vpRobotBiclopsController::setPosition(), vpRobotAfma4::setPosition(), vpRobotBiclopsController::setVelocity(), vpRobotPtu46::setVelocity(), vpRobotBiclops::setVelocity(), vpSimulatorAfma6::setVelocity(), vpSimulatorViper850::setVelocity(), vpRobotAfma4::setVelocity(), vpLine::setWorldCoordinates(), vpRobust::simultMEstimator(), vpColVector::size(), vpColVector::skew(), vpColVector::sort(), vpColVector::stack(), vpMatrix::stackMatrices(), vpMatrix::sub2Matrices(), vpMatrix::svd(), and vpColVector::vpColVector().

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 3192 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::rowNum, and vpMatrix::rowPtrs.

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 <visp/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

Definition at line 331 of file vpMatrix.cpp.

References vpException::dimensionError, vpMatrix::getCols(), vpMatrix::getRows(), vpMatrix::resize(), and vpMatrix::rowPtrs.

void vpColVector::insert	(	unsigned int	i,
		const vpColVector &	v
	)

inherited

Insert a column vector.

Parameters

i	: Index of the first element to introduce. This index starts from 0.
v	: Column vector to insert.

The following example shows how to use this function:

#include <visp/vpColVector.h>
int main()
{
  vpColVector v(4);
  for (unsigned int i=0; i < v.size(); i++)
    v[i] = i;
  std::cout << "v:\n" << v << std::endl;
  vpColVector w(2);
  for (unsigned int i=0; i < w.size(); i++)
    w[i] = i+10;
  std::cout << "w:\n" << w << std::endl;
  v.insert(1, w);
  std::cout << "v:\n" << v << std::endl;
}

It produces the following output:

Definition at line 857 of file vpColVector.cpp.

References vpException::dimensionError, and vpColVector::size().

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 vpMatrixException::incorrectMatrixSizeError 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 3291 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, and vpMatrix::rowNum.

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

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 2666 of file vpMatrix.cpp.

References vpMatrix::insert(), and vpCERROR.

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 2697 of file vpMatrix.cpp.

References vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::resize(), vpCERROR, and vpERROR_TRACE.

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 <visp/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 122 of file vpMatrix_cholesky.cpp.

References vpMatrix::colNum, vpMatrix::inverseByCholeskyLapack(), vpMatrixException::matrixError, vpMatrix::rowNum, and vpERROR_TRACE.

vpMatrix vpMatrix::inverseByCholeskyLapack ( ) const

inherited

Definition at line 62 of file vpMatrix_cholesky.cpp.

References vpException::badValue, vpMatrix::data, vpMatrix::getCols(), and vpMatrix::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 <visp/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 236 of file vpMatrix_lu.cpp.

References vpMatrix::colNum, vpMatrix::getRows(), vpMatrixException::matrixError, vpMatrix::rowNum, and vpERROR_TRACE.

Referenced by vpMatrix::expm(), vpKalmanFilter::filtering(), vpTemplateTrackerWarpHomographySL3::findWarp(), vpTemplateTrackerWarpAffine::getParamInverse(), vpTemplateTrackerTriangle::init(), vpTemplateTrackerSSDInverseCompositional::initCompInverse(), vpTemplateTrackerZNCCForwardAdditional::initHessienDesired(), vpTemplateTrackerZNCCInverseCompositional::initHessienDesired(), vpTemplateTracker::setHDes(), vpTemplateTrackerSSDForwardCompositional::trackNoPyr(), and vpTemplateTrackerSSDForwardAdditional::trackNoPyr().

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 <visp/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 228 of file vpMatrix_qr.cpp.

References vpMatrix::colNum, vpMatrix::inverseByQRLapack(), vpMatrixException::matrixError, vpMatrix::rowNum, and vpERROR_TRACE.

vpMatrix vpMatrix::inverseByQRLapack ( ) const

inherited

Definition at line 76 of file vpMatrix_qr.cpp.

References vpException::badValue, vpMatrix::data, vpMatrix::getCols(), and vpMatrix::getRows().

Referenced by vpMatrix::inverseByQR().

vpColVector vpColVector::invSort ( const vpColVector & v )

staticinherited

reverse sorting of the elements of vector v

Definition at line 446 of file vpColVector.cpp.

References vpMatrix::data, vpMatrix::getRows(), vpMatrixException::notInitializedError, and vpERROR_TRACE.

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 2740 of file vpMatrix.cpp.

References vpCERROR.

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 column

Definition at line 2769 of file vpMatrix.cpp.

References vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::resize(), vpCERROR, and vpERROR_TRACE.

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

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(M) ={KerA : A*KerA =0}.

Parameters

kerA	: The matrix to contain the null space (kernel) of A (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 3569 of file vpMatrix.cpp.

References vpMatrix::getCols(), vpMatrix::getRow(), vpMatrix::getRows(), vpMatrix::resize(), vpMatrix::sumSquare(), and vpMatrix::svd().

void vpMatrix::kill ( )

inherited

Destruction of the matrix (Memory de-allocation)

Definition at line 355 of file vpMatrix.cpp.

References vpMatrix::data, and vpMatrix::rowPtrs.

Referenced by vpMatrix::~vpMatrix().

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 1563 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::rowNum, and vpERROR_TRACE.

Referenced by vpMatrix::kron().

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 1607 of file vpMatrix.cpp.

References vpMatrix::getCols(), and vpMatrix::getRows().

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

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 1597 of file vpMatrix.cpp.

References vpMatrix::kron().

vpMatrix vpMatrix::kron ( const vpMatrix & m )

inherited

Compute Kronecker product matrix.

Parameters

m	: vpMatrix;

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

Definition at line 1638 of file vpMatrix.cpp.

References vpMatrix::kron().

static bool vpMatrix::loadMatrix	(	std::string	filename,
		vpMatrix &	M,
		const bool	binary = `false`,
		char *	Header = `NULL`
	)

inlinestaticinherited

Load a matrix from a file.

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.

Definition at line 264 of file vpMatrix.h.

Referenced by vpDot2::defineDots().

bool vpMatrix::loadMatrix	(	const char *	filename,
		vpMatrix &	M,
		const bool	binary = `false`,
		char *	header = `NULL`
	)

staticinherited

Load a matrix from a file.

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 loaded in this parameter.

Returns: Returns true if no problem happened.

Definition at line 3963 of file vpMatrix.cpp.

References vpException::badValue, and vpMatrix::resize().

static bool vpMatrix::loadMatrixYAML	(	std::string	filename,
		vpMatrix &	M,
		char *	header = `NULL`
	)

inlinestaticinherited

Load a matrix from a YAML-formatted file.

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.

Definition at line 317 of file vpMatrix.h.

bool vpMatrix::loadMatrixYAML	(	const char *	filename,
		vpMatrix &	M,
		char *	header = `NULL`
	)

staticinherited

Load a matrix from a YAML-formatted file.

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 on success.

See also: saveMatrixYAML()

Definition at line 4060 of file vpMatrix.cpp.

References vpMatrix::resize().

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

inherited

Print using MAPLE matrix input format.

Print using the following way so that this output can be directly copied into MAPLE: ([ [0.939846, 0.0300754, 0.340272, ], [0.0300788, 0.984961, -0.170136, ], [-0.340272, 0.170136, 0.924807, ], ])

Definition at line 3061 of file vpMatrix.cpp.

References vpMatrix::getCols(), and vpMatrix::getRows().

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

inherited

Print using matlab syntax, to be put in matlab later.

Print using the following form: [ a,b,c; d,e,f; g,h,i]

Definition at line 3032 of file vpMatrix.cpp.

References vpMatrix::getRows().

double vpColVector::mean ( const vpColVector & v )

staticinherited

compute the mean

Compute the mean value of all the element of the vector.

Definition at line 626 of file vpColVector.cpp.

References vpMatrix::data, vpMatrix::getRows(), vpMatrixException::notInitializedError, and vpERROR_TRACE.

double vpColVector::median ( const vpColVector & v )

staticinherited

compute the median

Compute the median value of all the element of the vector

Definition at line 653 of file vpColVector.cpp.

References vpMatrix::data, vpMatrix::getRows(), vpMatrixException::notInitializedError, and vpERROR_TRACE.

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 480 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrixException::incorrectMatrixSizeError, vpMatrix::resize(), vpMatrix::rowNum, vpMatrix::rowPtrs, and vpERROR_TRACE.

Referenced by vpMatrix::operator*().

void vpMatrix::multMatrixVector	(	const vpMatrix &	A,
		const vpColVector &	b,
		vpColVector &	c
	)

staticinherited

Operation c = A * b (c and b are vectors).

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*(const vpColVector &b) const

Definition at line 931 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpColVector::resize(), vpMatrix::rowNum, vpMatrix::rowPtrs, and vpERROR_TRACE.

Referenced by vpRotationMatrix::operator*(), 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 818 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::resize(), vpMatrix::rowNum, vpMatrix::rowPtrs, and vpERROR_TRACE.

Referenced by vpMatrix::operator-().

vpColVector & normalize ( )

inherited

Normalise the vector.

normalise the vector

${\bf x}_i = \frac{{\bf x}_i}{\sqrt{\sum_{i=1}^{n}x^2_i}}$

normalise the vector

${\bf x}_i = \frac{{\bf x}_i}{\sqrt{\sum_{i=1}^{n}x^2_i}}$

Definition at line 430 of file vpColVector.cpp.

References vpMatrix::sumSquare().

Referenced by vpCameraParameters::computeFov(), vpMbtDistanceKltPoints::init(), vpMbtPolygon::isVisible(), vpPose::poseDementhonNonPlan(), and vpMbKltTracker::setPose().

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

Operator that allows to multiply a translation vector by a scalar.

Parameters

x	: The scalar.

Returns: The translation vector multiplied by the scalar. The current translation vector (*this) is unchanged.

vpTranslationVector t1(1,2,3); 
t2 = t1 * 3;
// t1 is unchanged 
// t2 is now equal to : 3, 6, 9 

Definition at line 209 of file vpTranslationVector.cpp.

References vpMatrix::data, and vpMatrix::dsize.

double vpColVector::operator* ( const vpColVector & x ) const

inherited

Dot product.

operator dot product

Definition at line 81 of file vpColVector.cpp.

References vpMatrix::rowNum.

vpMatrix vpColVector::operator* ( const vpRowVector & x ) const

inherited

Dot product.

operator dot product

Definition at line 91 of file vpColVector.cpp.

References vpMatrix::vpMatrix().

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 523 of file vpMatrix.cpp.

References vpMatrix::mult2Matrices().

vpMatrix vpMatrix::operator* ( const vpHomography & H ) const

inherited

Allows to multiply a matrix by an homography. Operation M = K * H (H is unchanged).

Definition at line 536 of file vpMatrix.cpp.

References vpMatrix::colNum, vpException::dimensionError, and vpMatrix::rowNum.

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

inherited

Operation c = A * b (A is unchanged, c and b are translation vectors).

Definition at line 975 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrixException::incorrectMatrixSizeError, vpMatrix::rowNum, vpMatrix::rowPtrs, and vpERROR_TRACE.

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

inherited

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

Definition at line 1178 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::rowNum, and vpMatrix::rowPtrs.

vpTranslationVector vpTranslationVector::operator+ ( const vpTranslationVector & tv ) const

Operator that allows to add two translation vectors.

Parameters

tv	: Translation vector to add.

Returns: The sum of the current translation vector (*this) and the one to add.
vpTranslationVector t1(1,2,3);

vpTranslationVector t2(4,5,6);

vpTranslationVector t3;

t3 = t2 + t1;

// t1 and t2 leave unchanged

// t3 is now equal to : 5, 7, 9

Definition at line 132 of file vpTranslationVector.cpp.

vpColVector vpColVector::operator+ ( const vpColVector & v ) const

inherited

Addition of two vectors V = A+v.

operator addition of two vectors

Definition at line 65 of file vpColVector.cpp.

References vpException::dimensionError, vpMatrix::getRows(), and vpMatrix::rowNum.

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 653 of file vpMatrix.cpp.

References vpMatrix::add2Matrices().

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

inherited

Operation A = A + B.

Definition at line 733 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::rowNum, vpMatrix::rowPtrs, and vpERROR_TRACE.

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

inherited

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

Definition at line 1130 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::rowNum, and vpMatrix::rowPtrs.

vpTranslationVector vpTranslationVector::operator- ( const vpTranslationVector & tv ) const

Operator that allows to substract two translation vectors.

Parameters

tv	: Translation vector to substract.

Returns: The substraction of the current translation vector (*this) and the one to substract.
vpTranslationVector t1(1,2,3);

vpTranslationVector t2(4,5,6);

vpTranslationVector t3;

t3 = t2 - t1;

// t1 and t2 leave unchanged

// t3 is now equal to : 3, 3, 3

Definition at line 159 of file vpTranslationVector.cpp.

vpTranslationVector vpTranslationVector::operator- ( void ) const

Operator that allows to negate a translation vector.

Returns: The negate translation. The current translation vector (*this) is unchanged.

vpTranslationVector t1(1,2,3); 
vpTranslationVector t2; 
t2 = -t1;
// t1 is unchanged 
// t2 is now equal to : -1, -2, -3 

Definition at line 183 of file vpTranslationVector.cpp.

References vpMatrix::data, and vpMatrix::dsize.

vpColVector vpColVector::operator- ( const vpColVector & v ) const

inherited

Substraction of two vectors V = A-v.

operator substraction of two vectors V = A-v

Definition at line 98 of file vpColVector.cpp.

References vpException::dimensionError, vpMatrix::getRows(), and vpMatrix::rowNum.

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 724 of file vpMatrix.cpp.

References vpMatrix::sub2Matrices().

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

inherited

Operation A = A - B.

Definition at line 773 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::rowNum, vpMatrix::rowPtrs, and vpERROR_TRACE.

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

inherited

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

Definition at line 1154 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::rowNum, and vpMatrix::rowPtrs.

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

inherited

Cij = Aij / x (A is unchanged)

Definition at line 1085 of file vpMatrix.cpp.

References vpMatrix::colNum, vpException::divideByZeroError, vpMatrix::resize(), vpMatrix::rowNum, vpMatrix::rowPtrs, vpCERROR, and vpERROR_TRACE.

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

inherited

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

Definition at line 1193 of file vpMatrix.cpp.

References vpMatrix::colNum, vpException::divideByZeroError, vpMatrix::rowNum, and vpMatrix::rowPtrs.

vpColVector & vpColVector::operator<< ( const vpColVector & v )

inherited

Copy operator. Allows operation such as A << v

#include <visp/vpColVector.h>
int main()
{
  vpColVector A, B(5);
  for (unsigned int i=0; i<B.size(); i++)
    B[i] = i;
  A << B;
  std::cout << "A: \n" << A << std::endl;
}

In column vector A we get:

Definition at line 265 of file vpColVector.cpp.

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

inherited

Assigment operator. Allow operation such as A = *v

The following example shows how to use this operator.

#include <visp/vpColVector.h>
int main()
{
  size_t n = 5;
  vpColVector A(n);
  double *B = new double [n];
  for (unsigned int i = 0; i < n; i++)
    B[i] = i;
  A << B;
  std::cout << "A: \n" << A << std::endl;
  delete [] B;
}

It produces the following output:

Definition at line 300 of file vpColVector.cpp.

References vpMatrix::colNum, vpMatrix::rowNum, and vpMatrix::rowPtrs.

vpTranslationVector & vpTranslationVector::operator= ( const vpTranslationVector & tv )

Copy operator.

Parameters

tv	: Translation vector to copy

Returns: A copy of t.

vpTranslationVector t1(1,2,3); 
vpTranslationVector t2; 
t2 = t1;
// t1 is unchanged 
// t2 is now equal to t1 : 1, 2, 3 

Definition at line 233 of file vpTranslationVector.cpp.

References vpMatrix::data, vpColVector::resize(), vpMatrix::rowNum, and vpERROR_TRACE.

vpTranslationVector & vpTranslationVector::operator= ( double x )

Initialize each element of a translation vector to the same value x.

Parameters

x	: Value to set for each element of the translation vector.

vpTranslationVector t;
t = 3;
// Here t is set to 3,3,3

Definition at line 264 of file vpTranslationVector.cpp.

References vpMatrix::data.

double& vpColVector::operator[] ( unsigned int n )

inlineinherited

Access V[i] = x.

Definition at line 104 of file vpColVector.h.

References vpMatrix::data.

const double& vpColVector::operator[] ( unsigned int n ) const

inlineinherited

Access x = V[i].

Definition at line 106 of file vpColVector.h.

References vpMatrix::data.

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

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 <<(ostream &s,const vpMatrix &m)

Examples:: servoSimu3D_cdMc_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocity.cpp, testMatrix.cpp, and testTwistMatrix.cpp.

Definition at line 2937 of file vpMatrix.cpp.

References vpMatrix::getCols(), vpMatrix::getRows(), and vpMath::maximum().

void vpMatrix::printSize ( )

inlineinherited

Definition at line 190 of file vpMatrix.h.

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 <visp/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()

Definition at line 1932 of file vpMatrix.cpp.

Referenced by vpCalibration::calibrationTsai(), vpSimulatorAfma6::computeArticularVelocity(), vpSimulatorViper850::computeArticularVelocity(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), vpMbEdgeKltTracker::computeVVS(), vpMbKltTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), 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 $Ap = A^+$ .

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

Parameters

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

Returns: Return the rank of the matrix A

Definition at line 1892 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 $Ap = A^+$ .

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

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 1948 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 $Ap = A^+$ along with Ker A, Ker $A^T$ , Im A and Im $A^T$ .

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

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 1987 of file vpMatrix.cpp.

References vpMatrix::getCols(), vpMatrix::getRows(), vpColVector::resize(), vpMatrix::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 $Ap = A^+$ along with Ker A, Ker $A^T$ , Im A and Im $A^T$ .

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

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 2165 of file vpMatrix.cpp.

References vpMatrix::getCols(), vpMatrix::getRow(), vpMatrix::getRows(), vpColVector::resize(), vpMatrix::resize(), vpMatrix::sumSquare(), vpMatrix::svd(), and vpMatrix::t().

void vpColVector::rad2deg ( )

inlineinherited

Convert a column vector containing angles in radians into degrees.

Definition at line 182 of file vpColVector.h.

References vpMatrix::rowNum.

Referenced by vpRobotViper650::setPosition(), vpRobotViper850::setPosition(), vpRobotViper650::setVelocity(), and vpRobotViper850::setVelocity().

void vpColVector::reshape	(	vpMatrix &	m,
		const unsigned int &	nrows,
		const unsigned int &	ncols
	)

inherited

Reshape methods.

reshape the colvector in a matrix

Parameters

m	: the reshaped Matrix
nrows	: number of rows of the matrix
ncols	: number of columns of the matrix

Definition at line 790 of file vpColVector.cpp.

References vpMatrix::data, vpMatrix::dsize, vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::resize(), and vpERROR_TRACE.

Referenced by vpColVector::reshape().

vpMatrix vpColVector::reshape	(	const unsigned int &	nrows,
		const unsigned int &	ncols
	)

inherited

reshape the colvector in a matrix

Parameters

nrows	: number of rows of the matrix
ncols	: number of columns of the matrix

Returns: a vpMatrix

Definition at line 778 of file vpColVector.cpp.

References vpColVector::reshape().

void vpColVector::resize	(	const unsigned int	i,
		const bool	flagNullify = `true`
	)

inlineinherited

Set the size of the column vector.

Parameters

i	: Column vector size.
flagNullify	: If true, set the data to zero.

Examples:: servoAfma4Point2DCamVelocityKalman.cpp, servoViper850Point2DCamVelocityKalman.cpp, and testSvd.cpp.

Definition at line 98 of file vpColVector.h.

References vpMatrix::resize().

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

inherited

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

Parameters

nrows	: number of rows
ncols	: number of column
flagNullify	: if true, then the matrix is re-initialized to 0 after resize. If false, the initial values from the common part of the matrix (common part between old and new version of the matrix) are kept. Default value is true.

Returns: OK or MEMORY_FAULT if memory cannot be allocated

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

Definition at line 199 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::data, vpMatrix::dsize, vpException::memoryAllocationError, vpMatrix::rowNum, vpMatrix::rowPtrs, vpMatrix::trsize, vpCDEBUG, vpDEBUG_TRACE, and vpERROR_TRACE.

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 2346 of file vpMatrix.cpp.

References vpMatrix::getCols().

vpColVector vpColVector::rows	(	unsigned int	first_row,
		unsigned int	last_row
	)

inlineinherited

Definition at line 131 of file vpColVector.h.

static bool vpMatrix::saveMatrix	(	std::string	filename,
		const vpMatrix &	M,
		const bool	binary = `false`,
		const char *	Header = `""`
	)

inlinestaticinherited

Save a matrix to a file.

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.

Definition at line 285 of file vpMatrix.h.

Referenced by vpDot2::defineDots().

bool vpMatrix::saveMatrix	(	const char *	filename,
		const vpMatrix &	M,
		const bool	binary = `false`,
		const char *	header = `""`
	)

staticinherited

Save a matrix to a file.

Parameters

filename	: Absolute file name.
M	: Matrix 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 no problem happened.

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

Definition at line 3792 of file vpMatrix.cpp.

References vpMatrix::getCols(), and vpMatrix::getRows().

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

inlinestaticinherited

Save a matrix in a YAML-formatted file.

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.

Definition at line 303 of file vpMatrix.h.

bool vpMatrix::saveMatrixYAML	(	const char *	filename,
		const vpMatrix &	M,
		const char *	header = `""`
	)

staticinherited

Save a matrix in a YAML-formatted file.

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.

Here is an example of outputs.

vpMatrix M(3,4);
vpMatrix::saveMatrixYAML("matrix.yml", M, "example: a YAML-formatted header");
vpMatrix::saveMatrixYAML("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: loadMatrixYAML()

Definition at line 3892 of file vpMatrix.cpp.

References vpMatrix::getCols(), and vpMatrix::getRows().

void vpTranslationVector::set	(	const double	tx,
		const double	ty,
		const double	tz
	)

Initialize a translation vector from 3 doubles.

Parameters

tx,ty,tz : Translation respectively along x, y and z axis.

Definition at line 105 of file vpTranslationVector.cpp.

Referenced by vpPioneerPan::set_mMp().

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

inherited

By default set the matrix to identity. More generally set M[i][i] = val.

Definition at line 1230 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrixException::matrixError, vpMatrix::rowNum, and vpERROR_TRACE.

Referenced by vpServo::computeControlLaw(), vpMbTracker::computeCovarianceMatrix(), vpMatrix::expm(), vpTemplateTrackerWarpHomographySL3::getdW0(), vpTemplateTrackerWarpHomographySL3::getdWdp0(), vpFeatureThetaU::interaction(), vpMeLine::leastSquare(), vpPose::poseFromRectangle(), vpServo::secondaryTask(), and vpMbTracker::vpMbTracker().

unsigned int vpColVector::size ( ) const

inlineinherited

Return the size of the vector in term of number of rows.

Examples:: tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, and tutorial-ibvs-4pts-wireframe-robot-viper.cpp.

Definition at line 204 of file vpColVector.h.

References vpMatrix::getRows().

Referenced by vpCalibration::calibrationTsai(), vpColVector::insert(), vpHomography::operator*(), vpRobot::saturateVelocities(), vpSimulatorPioneer::setVelocity(), vpRobotPioneer::setVelocity(), vpSimulatorPioneerPan::setVelocity(), and vpTemplateTrackerWarp::warpTriangle().

vpMatrix vpTranslationVector::skew ( ) const

Compute the skew symmetric matrix $M$ of the translation vector (matrice de pre-produit vectoriel), where

$M = \left( \begin{array}{ccc} 0 & -t_z & t_y \\ t_z & 0 & -t_x \\ -t_y & t_x & 0 \end{array}\right)$

and where $(t_x,t_y,t_z)$ are the coordinates of the translation vector.

Returns: Skew symmetric matrix of the translation vector.

Definition at line 351 of file vpTranslationVector.cpp.

Referenced by vpVelocityTwistMatrix::buildFrom(), vpForceTwistMatrix::buildFrom(), vpMbTracker::computeCovarianceMatrix(), cross(), vpViper::get_eJe(), and skew().

vpMatrix vpTranslationVector::skew ( const vpTranslationVector & t )

static

Compute the skew symmetric matrix $M$ of translation vector $t$ (matrice de pre-produit vectoriel).

$\mbox{if} \quad {\bf t} = \left( \begin{array}{c} t_x \\ t_y \\ t_z \end{array}\right), \quad \mbox{then} \qquad M = \left( \begin{array}{ccc} 0 & -t_z & t_y \\ t_z & 0 & -t_x \\ -t_y & t_x & 0 \end{array}\right)$

Parameters

t	: Translation vector in input.

Returns: Skew symmetric matrix of translation vector

Definition at line 325 of file vpTranslationVector.cpp.

References skew().

static void vpTranslationVector::skew	(	const vpTranslationVector &	t,
		vpMatrix &	M
	)

static

vpMatrix vpColVector::skew ( const vpColVector & v )

staticinherited

Compute the skew symmetric matrix $[{\bf v}]_\times$ of vector v.

$\mbox{if} \quad {\bf V} = \left( \begin{array}{c} x \\ y \\ z \end{array}\right), \quad \mbox{then} \qquad [{\bf v}]_\times = \left( \begin{array}{ccc} 0 & -z & y \\ z & 0 & -x \\ -y & x & 0 \end{array}\right)$

Parameters

v	: Input vector used to compute the skew symmetric matrix.

Examples:: servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp.

Definition at line 718 of file vpColVector.cpp.

References vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::resize(), and vpERROR_TRACE.

Referenced by vpCalibration::calibrationTsai(), vpMbTracker::computeCovarianceMatrix(), vpColVector::crossProd(), and vpFeatureThetaU::interaction().

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 <visp/vpColVector.h>
#include <visp/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 1693 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 <visp/vpColVector.h>
#include <visp/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 1748 of file vpMatrix.cpp.

References vpMatrix::colNum, and vpMatrix::solveBySVD().

vpColVector vpColVector::sort ( const vpColVector & v )

staticinherited

sort the elements of vector v

Examples:: testSvd.cpp.

Definition at line 477 of file vpColVector.cpp.

References vpMatrix::data, vpMatrix::getRows(), vpMatrixException::notInitializedError, and vpERROR_TRACE.

void vpColVector::stack ( const double & b )

inherited

Stack column vector with new element.

Parameters

b	: Element to stack to the existing one.

vpColVector A(3);
double b = 3;
A.stack(b); // A = [A b]T
// A is now an 4 dimension column vector

See also: stack(const vpColVector &, const vpColVector &); stack(const vpColVector &, const vpColVector &, vpColVector &)

Examples:: servoPioneerPoint2DDepthWithoutVpServo.cpp.

Definition at line 522 of file vpColVector.cpp.

References vpColVector::resize(), and vpMatrix::rowNum.

Referenced by vpColVector::stack().

void vpColVector::stack ( const vpColVector & B )

inherited

Stack column vectors.

Parameters

B	: Vector to stack to the existing one.

vpColVector A(3);
vpColVector B(5);
A.stack(B); // A = [A B]T
// A is now an 8 dimension column vector

See also: stack(const vpColVector &, const double &); stack(const vpColVector &, const vpColVector &); stack(const vpColVector &, const vpColVector &, vpColVector &)

Definition at line 545 of file vpColVector.cpp.

References vpColVector::stack().

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

staticinherited

Stack column vectors.

Parameters

A	: Initial vector.
B	: Vector to stack at the end of A.

Returns: Stacked vector .

vpColVector A(3);
vpColVector B(5);
vpColVector C;
C = vpColVector::stack(A, B); // C = [A B]T
// C is now an 8 dimension column vector

See also: stack(const vpColVector &); stack(const vpColVector &, const vpColVector &, vpColVector &)

Definition at line 568 of file vpColVector.cpp.

References vpColVector::stack().

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

staticinherited

Stack column vectors.

Parameters

A	: Initial vector.
B	: Vector to stack at the end of A.
C	: Resulting stacked vector .

vpColVector A(3);
vpColVector B(5);
vpColVector C;
vpColVector::stack(A, B, C); // C = [A B]T
// C is now an 8 dimension column vector

See also: stack(const vpColVector &); stack(const vpColVector &, const vpColVector &)

Definition at line 593 of file vpColVector.cpp.

References vpMatrix::getRows(), and vpColVector::resize().

void vpMatrix::stackColumns ( vpColVector & out )

inherited

Stacks columns of a matrix in a vector.

Parameters

out	: a vpColVector.

Definition at line 1493 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::data, vpColVector::resize(), vpMatrix::rowNum, vpMatrix::rowPtrs, vpCERROR, and vpERROR_TRACE.

vpColVector vpMatrix::stackColumns ( )

inherited

Stacks columns of a matrix in a vector.

Returns: a vpColVector.

Definition at line 1517 of file vpMatrix.cpp.

References vpMatrix::colNum, and vpMatrix::rowNum.

void vpMatrix::stackMatrices ( 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 Velocities;
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 3272 of file vpMatrix.cpp.

References vpMatrix::rowNum.

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

staticinherited

Stack two Matrices C = [ A B ]^T.

Stack matrices. "Stack" two matrices C = [ A B ]^T.

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

Parameters

A	: Upper matrix.
B	: Lower matrix.

Returns: Stacked matrix C = [ A B ]^T

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

Definition at line 2581 of file vpMatrix.cpp.

References vpMatrix::stackMatrices(), and vpCERROR.

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

staticinherited

Stack two Matrices C = [ A B ]^T.

stackMatrices. "stack" two matrices C = [ A B ]^T

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

Parameters

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

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

Definition at line 2610 of file vpMatrix.cpp.

References vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::resize(), vpCERROR, and vpERROR_TRACE.

void vpMatrix::stackRows ( vpRowVector & out )

inherited

Stacks rows of a matrix in a vector

Parameters

out	: a vpRowVector.

Definition at line 1528 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::data, vpMatrix::dsize, vpRowVector::resize(), vpMatrix::rowNum, vpCERROR, and vpERROR_TRACE.

vpRowVector vpMatrix::stackRows ( )

inherited

Stacks rows of a matrix in a vector.

Returns: a vpRowVector.

Definition at line 1550 of file vpMatrix.cpp.

References vpMatrix::colNum, and vpMatrix::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).

See also: operator-()

Definition at line 671 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::getCols(), vpMatrix::getRows(), vpMatrixException::incorrectMatrixSizeError, vpMatrix::resize(), vpMatrix::rowNum, vpMatrix::rowPtrs, and vpERROR_TRACE.

Referenced by vpMatrix::operator-().

double vpMatrix::sum ( ) const

inherited

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

Returns: $\sum a_{ij}$

Definition at line 903 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::rowNum, and vpMatrix::rowPtrs.

Referenced by vpMatrix::expm().

double vpMatrix::sumSquare ( ) const

inherited

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

Returns: $\sum a_{ij}^{2}$

Examples:: photometricVisualServoing.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoMomentImage.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 868 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::rowNum, and vpMatrix::rowPtrs.

Referenced by vpPose::calculArbreDementhon(), vpCalibration::calibrationTsai(), vpMbTracker::computeCovarianceMatrix(), vpPose::coplanar(), vpFeatureDepth::error(), vpFeatureThetaU::error(), vpFeatureTranslation::error(), vpMbTracker::extractCylinders(), vpFeatureThetaU::interaction(), vpMatrix::kernel(), vpRowVector::normalize(), vpColVector::normalize(), vpPose::poseDementhonNonPlan(), vpPose::poseDementhonPlan(), vpPose::poseFromRectangle(), vpPose::poseLagrangeNonPlan(), vpPose::poseLagrangePlan(), vpPose::poseVirtualVS(), vpPose::poseVirtualVSrobust(), vpMatrix::pseudoInverse(), vpServoData::save(), vpSimulatorAfma6::setPosition(), and vpSimulatorViper850::setPosition().

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 <visp/vpColVector.h>
#include <visp/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;
}

Examples:: servoMomentImage.cpp.

Definition at line 1822 of file vpMatrix.cpp.

References vpMatrix::getCols(), vpMatrix::getRows(), vpColVector::resize(), and vpMatrix::resize().

Referenced by vpHomography::computeDisplacement(), vpMatrix::cond(), vpHomography::DLT(), vpMatrix::kernel(), vpPose::poseDementhonPlan(), and vpMatrix::pseudoInverse().

vpRowVector vpColVector::t ( ) const

inherited

Transpose of a vector.

Examples:: movePtu46.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu3D_cdMc_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuPoint3DCamVelocity.cpp, servoSimuSphere2DCamVelocitySecondaryTask.cpp, testDisplacement.cpp, testFindMatch.cpp, testKalmanAcceleration.cpp, testPoseFeatures.cpp, testPoseRansac.cpp, testRobotViper850.cpp, testViper850.cpp, tutorial-homography-from-points.cpp, and tutorial-pioneer-robot.cpp.

Definition at line 333 of file vpColVector.cpp.

References vpMatrix::data, vpRowVector::resize(), vpMatrix::rowNum, and vpERROR_TRACE.

Referenced by vpPose::calculArbreDementhon(), vpRobotBiclopsController::getPosition(), vpRobotBiclops::getPosition(), vpRobotBiclops::getVelocity(), vpTemplateTrackerZNCCInverseCompositional::initHessienDesired(), vpSimulatorAfma6::initialiseCameraRelativeToObject(), vpSimulatorViper850::initialiseCameraRelativeToObject(), vpPose::poseDementhonPlan(), vpForwardProjection::print(), vpHomogeneousMatrix::print(), vpServo::print(), vpPose::printPoint(), vpServoData::save(), vpRobotBiclops::setVelocity(), vpRobotViper650::setVelocity(), vpRobotViper850::setVelocity(), and vpTemplateTrackerSSDForwardAdditional::trackNoPyr().

vpMatrix vpMatrix::transpose ( ) const

inherited

Compute and return the transpose of the matrix.

See also: t()

Definition at line 1326 of file vpMatrix.cpp.

Referenced by vpTemplateTrackerWarpSRT::getParamInverse().

void vpMatrix::transpose ( vpMatrix & At ) const

inherited

Compute At the transpose of the matrix.

Parameters

At	: Resulting transpose matrix.

See also: t()

Definition at line 1338 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::resize(), vpMatrix::rowNum, vpMatrix::rowPtrs, vpCERROR, and vpERROR_TRACE.

Friends And Related Function Documentation

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

Definition at line 363 of file vpColVector.cpp.

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

Definition at line 1006 of file vpMatrix.cpp.

References vpMatrix::getCols(), vpMatrix::getRows(), vpMatrix::resize(), and vpERROR_TRACE.

void vpGEMM	(	const vpMatrix &	A,
		const vpMatrix &	B,
		const double &	alpha,
		const vpMatrix &	C,
		const double &	beta,
		vpMatrix &	D,
		const unsigned int &	ops = `0`
	)

For example, to compute alpha*A^T*B^T+beta*C we need to call :

vpGEMM(A,B,alpha,C,beta, VP_GEMM_A_T + VP_GEMM_B_T);

If C is not used, vpGEMM must be called using an empty matrix null :

vpGEMM(A,B,alpha,C, null,0);

Exceptions

vpMatrixException::incorrectMatrixSizeError if the sizes of the matrices do not allow the operations.

Parameters

A	: a Matrix
B	: a Matrix
alpha	: a scalar
C	: a Matrix
beta	: a scalar
D	: a Matrix
ops	: a scalar describing operation applied on the matrices

Examples:: testMatrix.cpp.

Definition at line 331 of file vpGEMM.h.

References vpMatrixException::incorrectMatrixSizeError, and vpERROR_TRACE.

enum vpGEMMmethod

Operations are :

VP_GEMM_A_T to use the transpose matrix of A instead of the matrix A
VP_GEMM_B_T to use the transpose matrix of B instead of the matrix B
VP_GEMM_C_T to use the transpose matrix of C instead of the matrix C

Definition at line 63 of file vpGEMM.h.

Member Data Documentation

unsigned int vpMatrix::colNum

protectedinherited

number of columns

Definition at line 114 of file vpMatrix.h.

double* vpMatrix::data

inherited

address of the first element of the data array

Definition at line 118 of file vpMatrix.h.

Referenced by vpMatrix::AtA(), vpHomogeneousMatrix::buildFrom(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpPose::computeResidual(), vpPose::computeTransformation(), vpHomogeneousMatrix::convert(), vpColVector::dotProd(), vpMatrix::eigenValues(), vpMatrix::euclideanNorm(), vpMatrix::expm(), vpRobotViper650::getForceTorque(), vpRobotViper850::getForceTorque(), vpMatrix::getMaxValue(), vpMatrix::getMinValue(), vpRobotViper650::getPosition(), vpRobotViper850::getPosition(), vpRobotViper850::getVelocity(), vpRobotViper650::getVelocity(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpMatrix::init(), vpRobotViper650::init(), vpRobotViper850::init(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByQRLapack(), vpColVector::invSort(), vpMatrix::kill(), vpColVector::mean(), vpColVector::median(), vpRowVector::operator*(), operator*(), vpColVector::operator*(), operator-(), vpColVector::operator-(), vpRowVector::operator-(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), operator=(), vpMatrix::operator=(), vpRowVector::operator[](), vpColVector::operator[](), vpPose::ransac(), vpRowVector::reshape(), vpColVector::reshape(), vpMatrix::resize(), vpRobotAfma4::setPosition(), vpRobotViper650::setPosition(), vpRobotViper850::setPosition(), vpRobotAfma4::setVelocity(), vpRobotAfma6::setVelocity(), vpRobotViper650::setVelocity(), vpRobotViper850::setVelocity(), vpColVector::sort(), vpMatrix::stackColumns(), vpMatrix::stackRows(), vpRowVector::t(), vpColVector::t(), vpColVector::vpColVector(), vpMatrix::vpMatrix(), vpSubColVector::~vpSubColVector(), vpSubMatrix::~vpSubMatrix(), and vpSubRowVector::~vpSubRowVector().

unsigned int vpMatrix::dsize

protectedinherited

Current size (rowNum * colNum)

Definition at line 124 of file vpMatrix.h.

Referenced by vpMatrix::euclideanNorm(), vpMatrix::getMaxValue(), vpMatrix::getMinValue(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpMatrix::init(), operator*(), operator-(), vpMatrix::operator=(), vpRowVector::reshape(), vpColVector::reshape(), vpMatrix::resize(), and vpMatrix::stackRows().

unsigned int vpMatrix::rowNum

protectedinherited

number of rows

Definition at line 112 of file vpMatrix.h.

Referenced by vpMatrix::AAt(), vpMatrix::add2Matrices(), vpMatrix::add2WeightedMatrices(), vpMatrix::AtA(), vpColVector::deg2rad(), vpMatrix::eigenValues(), vpMatrix::expm(), vpMatrix::eye(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpMatrix::init(), vpMatrix::insert(), vpMatrix::inverseByCholesky(), vpMatrix::inverseByLU(), vpMatrix::inverseByQR(), vpMatrix::kron(), vpMatrix::mult2Matrices(), vpMatrix::multMatrixVector(), vpMatrix::negateMatrix(), vpColVector::operator*(), vpHomogeneousMatrix::operator*(), vpMatrix::operator*(), vpMatrix::operator*=(), vpColVector::operator+(), vpMatrix::operator+=(), vpColVector::operator-(), vpMatrix::operator-=(), vpMatrix::operator/(), vpMatrix::operator/=(), vpColVector::operator<<(), vpMatrix::operator<<(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpSubMatrix::operator=(), vpRowVector::operator=(), vpColVector::operator=(), operator=(), vpMatrix::operator=(), vpColVector::rad2deg(), vpMatrix::resize(), vpMatrix::setIdentity(), vpColVector::stack(), vpMatrix::stackColumns(), vpMatrix::stackMatrices(), vpMatrix::stackRows(), vpMatrix::sub2Matrices(), vpMatrix::sum(), vpMatrix::sumSquare(), vpColVector::t(), vpMatrix::t(), vpMatrix::transpose(), and vpMatrix::vpMatrix().

double** vpMatrix::rowPtrs

protectedinherited

address of the first element of each rows

Definition at line 121 of file vpMatrix.h.

unsigned int vpMatrix::trsize

protectedinherited

Total row space.

Definition at line 126 of file vpMatrix.h.

Referenced by vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpMatrix::init(), and vpMatrix::resize().

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