#include <vpHomography.h>

Inheritance diagram for vpHomography:

Public Types
enum	vpDetMethod { LU_DECOMPOSITION }

Public Member Functions
	vpHomography ()

	vpHomography (const vpHomography &aMb)

	vpHomography (const vpHomogeneousMatrix &aMb, const vpPlane &bP)

	vpHomography (const vpRotationMatrix &aRb, const vpTranslationVector &atb, const vpPlane &bP)

	vpHomography (const vpThetaUVector &tu, const vpTranslationVector &atb, const vpPlane &bP)

	vpHomography (const vpPoseVector &arb, const vpPlane &bP)

virtual	~vpHomography ()

void	buildFrom (const vpRotationMatrix &aRb, const vpTranslationVector &atb, const vpPlane &bP)

void	buildFrom (const vpThetaUVector &tu, const vpTranslationVector &atb, const vpPlane &bP)

void	buildFrom (const vpPoseVector &arb, const vpPlane &bP)

void	buildFrom (const vpHomogeneousMatrix &aMb, const vpPlane &bP)

void	build ()

void	computeDisplacement (vpRotationMatrix &aRb, vpTranslationVector &atb, vpColVector &n)

void	computeDisplacement (const vpColVector &nd, vpRotationMatrix &aRb, vpTranslationVector &atb, vpColVector &n)

void	load (std::ifstream &f)

void	print ()

void	save (std::ofstream &f) const

vpHomography	inverse () const

void	inverse (vpHomography &Hi) const

vpHomography	operator* (const vpHomography &H) const

vpHomography	operator* (const double &v) const

vpHomography	operator/ (const double &v) 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)

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

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

vpRowVector	row (const unsigned int i)

vpColVector	column (const unsigned int j)

Set/get Matrix size
unsigned int	getRows () const

unsigned int	getCols () const

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

double	getMinValue () const

double	getMaxValue () const

Copy / assignment
vpMatrix &	operator<< (double *)

void	diag (const vpColVector &A)

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

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

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

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

void	printSize ()

Access/modification operators
double *	operator[] (unsigned int n)

double *	operator[] (unsigned int n) const

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

vpMatrix &	operator+= (const double x)

vpMatrix &	operator-= (const vpMatrix &B)

vpMatrix &	operator-= (const double x)

vpMatrix	operator* (const vpMatrix &B) const

vpColVector	operator* (const vpColVector &b) const

vpTranslationVector	operator* (const vpTranslationVector &b) const

vpMatrix	operator* (const double x) const

vpMatrix	operator+ (const vpMatrix &B) const

vpMatrix	operator- (const vpMatrix &B) const

vpMatrix	operator- () const

vpMatrix &	operator*= (const double x)

vpMatrix &	operator/= (double x)

vpMatrix	operator/ (const double x) const

double	sumSquare () const

double	det (vpDetMethod method=LU_DECOMPOSITION) const

vpMatrix	expm ()

Transpose, Identity
vpMatrix	t () const

vpMatrix	transpose () const

void	transpose (vpMatrix &C) const

vpMatrix	AAt () const

void	AAt (vpMatrix &B) const

vpMatrix	AtA () const

void	AtA (vpMatrix &B) const

Kronecker product
void	stackColumns (vpColVector &out)

vpColVector	stackColumns ()

void	stackRows (vpRowVector &out)

vpRowVector	stackRows ()

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

vpMatrix	kron (const vpMatrix &m1)

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)

Eigen values
vpColVector	eigenValues ()

void	eigenValues (vpColVector &evalue, vpMatrix &evector)

Norms
double	euclideanNorm () const

double	infinityNorm () const

Static Public Member Functions
static void	HartleyNormalization (unsigned int n, double x, double y, double xn, double yn, double &xg, double &yg, double &coef)

static void	HartleyDenormalization (vpHomography &aHbn, vpHomography &aHb, double xg1, double yg1, double coef1, double xg2, double yg2, double coef2)

static void	build (vpHomography &aHb, const vpHomogeneousMatrix &aMb, const vpPlane &bP)

static void	DLT (unsigned int n, double xb, double yb, double xa, double ya, vpHomography &aHb)

static void	HartleyDLT (unsigned int n, double xb, double yb, double xa, double ya, vpHomography &aHb)

static void	HLM (unsigned int n, double xb, double yb, double xa, double ya, bool isplan, vpHomography &aHb)

static void	computeDisplacement (const vpHomography &aHb, const vpColVector &nd, vpRotationMatrix &aRb, vpTranslationVector &atb, vpColVector &n)

static void	computeDisplacement (const vpHomography &aHb, vpRotationMatrix &aRb, vpTranslationVector &atb, vpColVector &n)

static void	computeDisplacement (const vpMatrix &H, const double x, const double y, std::list< vpRotationMatrix > &vR, std::list< vpTranslationVector > &vT, std::list< vpColVector > &vN)

static double	computeDisplacement (unsigned int nbpoint, vpPoint c1P, vpPoint c2P, vpPlane &oN, vpHomogeneousMatrix &c2Mc1, vpHomogeneousMatrix &c1Mo, int userobust)

static double	computeDisplacement (unsigned int nbpoint, vpPoint c1P, vpPoint c2P, vpPlane *oN, vpHomogeneousMatrix &c2Mc1, vpHomogeneousMatrix &c1Mo, int userobust)

static double	computeResidual (vpColVector &x, vpColVector &M, vpColVector &d)

static double	computeRotation (unsigned int nbpoint, vpPoint c1P, vpPoint c2P, vpHomogeneousMatrix &c2Mc1, int userobust)

static void	computeTransformation (vpColVector &x, unsigned int *ind, vpColVector &M)

static bool	degenerateConfiguration (vpColVector &x, unsigned int *ind)

static bool	degenerateConfiguration (vpColVector &x, unsigned int *ind, double threshold_area)

static bool	ransac (unsigned int n, double xb, double yb, double xa, double ya, vpHomography &aHb, int consensus=1000, double threshold=1e-6)

static bool	ransac (unsigned int n, double xb, double yb, double xa, double ya, vpHomography &aHb, vpColVector &inliers, double &residual, int consensus=1000, double epsilon=1e-6, double areaThreshold=0.0)

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

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

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

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

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

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

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

static void	multMatrixVector (const vpMatrix &A, const vpColVector &b, vpColVector &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	kron (const vpMatrix &m1, const vpMatrix &m2, vpMatrix &out)

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

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

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

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

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

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

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)

Deprecated functions
static vp_deprecated void	computeDisplacement (const vpMatrix H, const double x, const double y, vpList< vpRotationMatrix > &vR, vpList< vpTranslationVector > &vT, vpList< vpColVector > &vN)

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.)
enum	vpGEMMmethod

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

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

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

Detailed Description

This class aims to compute the homography wrt.two images.

These two images are both described by a set of points. The 2 sets (one per image) are sets of corresponding points : for a point in a image, there is the corresponding point (image of the same 3D point) in the other image points set. These 2 sets are the only data needed to compute the homography. One method used is the one introduced by Ezio Malis during his PhD [9]. A normalization is carried out on this points in order to improve the conditioning of the problem, what leads to improve the stability of the result.

Store and compute the homography such that

$^a{\bf p} = ^a{\bf H}_b\; ^b{\bf p}$

with

$^a{\bf H}_b = ^a{\bf R}_b + \frac{^a{\bf t}_b}{^bd} { ^b{\bf n}^T}$

The example below shows how to manipulate this class to first compute a ground truth homography from camera poses, project pixel coordinates points using an homography and lastly estimate an homography from a subset of 4 matched points in frame a and frame b respectively.

#include <visp/vpHomogeneousMatrix.h>
#include <visp/vpHomography.h>
#include <visp/vpMath.h>
#include <visp/vpMeterPixelConversion.h>
int main()
{
  // Initialize in the object frame the coordinates in meters of 4 points that
  // belong to a planar object
  vpPoint Po[4];
  Po[0].setWorldCoordinates(-0.1, -0.1, 0);
  Po[1].setWorldCoordinates( 0.2, -0.1, 0);
  Po[2].setWorldCoordinates( 0.1,  0.1, 0);
  Po[3].setWorldCoordinates(-0.1,  0.3, 0);
  // Initialize the pose between camera frame a and object frame o
  vpHomogeneousMatrix aMo(0, 0, 1, 0, 0, 0); // Camera is 1 meter far
  // Initialize the pose between camera frame a and camera frame
  // b. These two frames correspond for example to two successive
  // camera positions
  vpHomogeneousMatrix aMb(0.2, 0.1, 0, 0, 0, vpMath::rad(2));
  // Compute the pose between camera frame b and object frame
  vpHomogeneousMatrix bMo = aMb.inverse() * aMo;
  // Initialize camera intrinsic parameters
  vpCameraParameters cam;
  // Compute the coordinates in pixels of the 4 object points in the
  // camera frame a
  vpPoint Pa[4];
  double xa[4], ya[4]; // Coordinates in pixels of the points in frame a
  for(int i=0 ; i < 4 ; i++) {
    Pa[i] = Po[i];
    Pa[i].project(aMo); // Project the points from object frame to
            // camera frame a
    vpMeterPixelConversion::convertPoint(cam, 
                     Pa[i].get_x(), Pa[i].get_y(),
                     xa[i], ya[i]);
  }
  // Compute the coordinates in pixels of the 4 object points in the
  // camera frame b
  vpPoint Pb[4];
  double xb[4], yb[4]; // Coordinates in pixels of the points in frame b
  for(int i=0 ; i < 4 ; i++) {
    Pb[i] = Po[i];
    Pb[i].project(bMo); // Project the points from object frame to
                // camera frame a
  }
  // Compute equation of the 3D plane containing the points in camera frame b
  vpPlane bP(Pb[0], Pb[1], Pb[2]);
  // Compute the corresponding ground truth homography
  vpHomography aHb(aMb, bP);
  std::cout << "Ground truth homography aHb: \n" << aHb<< std::endl;
  // Compute the coordinates of the points in frame b using the ground
  // truth homography and the coordinates of the points in frame a
  vpHomography bHa = aHb.inverse();
  for(int i = 0; i < 4 ; i++){
    double inv_z = 1. / (bHa[2][0] * xa[i] + bHa[2][1] * ya[i] + bHa[2][2]);
    
    xb[i] = (bHa[0][0] * xa[i] + bHa[0][1] * ya[i] + bHa[0][2]) * inv_z;
    yb[i] = (bHa[1][0] * xa[i] + bHa[1][1] * ya[i] + bHa[1][2]) * inv_z;
  }
  // Estimate the homography from 4 points coordinates expressed in pixels
  vpHomography::HartleyDLT(4, xb, yb, xa, ya, aHb);
  aHb /= aHb[2][2]; // Apply a scale factor to have aHb[2][2] = 1
  std::cout << "Estimated homography aHb: \n" << aHb<< std::endl;
}

Examples:: homographyHartleyDLT2DObject.cpp, homographyHLM2DObject.cpp, homographyHLM3DObject.cpp, homographyRansac2DObject.cpp, planarObjectDetector.cpp, and testDisplacement.cpp.

Definition at line 173 of file vpHomography.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 103 of file vpMatrix.h.

Constructor & Destructor Documentation

vpHomography::vpHomography ( )

initialize an homography as Identity

Definition at line 96 of file vpHomography.cpp.

vpHomography::vpHomography ( const vpHomography & aMb )

copy constructor

initialize an homography from another homography

Definition at line 106 of file vpHomography.cpp.

vpHomography::vpHomography	(	const vpHomogeneousMatrix &	aMb,
		const vpPlane &	bP
	)

Construction from Translation and rotation and a plane.

initialize an homography from another homography

Definition at line 116 of file vpHomography.cpp.

References buildFrom().

vpHomography::vpHomography	(	const vpRotationMatrix &	aRb,
		const vpTranslationVector &	atb,
		const vpPlane &	bP
	)

Construction from Translation and rotation and a plane.

Definition at line 136 of file vpHomography.cpp.

References buildFrom().

vpHomography::vpHomography	(	const vpThetaUVector &	tu,
		const vpTranslationVector &	atb,
		const vpPlane &	bP
	)

Construction from Translation and rotation and a plane.

Definition at line 128 of file vpHomography.cpp.

References buildFrom().

vpHomography::vpHomography	(	const vpPoseVector &	arb,
		const vpPlane &	bP
	)

Construction from Translation and rotation and a plane.

Definition at line 144 of file vpHomography.cpp.

References buildFrom().

virtual vpHomography::~vpHomography ( )

inlinevirtual

Definition at line 233 of file vpHomography.h.

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 1248 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 1268 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 493 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 454 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 1359 of file vpMatrix.cpp.

Referenced by vpCalibration::calibrationTsai(), vpMbEdgeKltTracker::computeVVS(), vpMbKltTracker::computeVVS(), 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 1311 of file vpMatrix.cpp.

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

void vpHomography::build ( )

build the homography from aMb and Rb

Compute aHb such that.

$^a{\bf H}_b = ^a{\bf R}_b + \frac{^a{\bf t}_b}{^bd} { ^b{\bf n}^T}$

Definition at line 429 of file vpHomography.cpp.

References vpPlane::getD(), vpPlane::getNormal(), and vpColVector::t().

Referenced by buildFrom().

void vpHomography::build	(	vpHomography &	aHb,
		const vpHomogeneousMatrix &	aMb,
		const vpPlane &	bP
	)

static

build the homography from aMb and Rb

Compute aHb such that.

$^a{\bf H}_b = ^a{\bf R}_b + \frac{^a{\bf t}_b}{^bd} { ^b{\bf n}^T}$

note d => -d verifier

Definition at line 459 of file vpHomography.cpp.

References vpPlane::getD(), vpPlane::getNormal(), and vpColVector::t().

void vpHomography::buildFrom	(	const vpRotationMatrix &	aRb,
		const vpTranslationVector &	atb,
		const vpPlane &	bP
	)

Construction from Translation and rotation and a plane.

Definition at line 180 of file vpHomography.cpp.

References build().

Referenced by vpHomography().

void vpHomography::buildFrom	(	const vpThetaUVector &	tu,
		const vpTranslationVector &	atb,
		const vpPlane &	bP
	)

Construction from Translation and rotation and a plane.

Definition at line 168 of file vpHomography.cpp.

References build().

void vpHomography::buildFrom	(	const vpPoseVector &	arb,
		const vpPlane &	bP
	)

Construction from Translation and rotation and a plane.

Definition at line 192 of file vpHomography.cpp.

References build(), and vpHomogeneousMatrix::buildFrom().

void vpHomography::buildFrom	(	const vpHomogeneousMatrix &	aMb,
		const vpPlane &	bP
	)

Construction from homogeneous matrix and a plane.

Definition at line 155 of file vpHomography.cpp.

References build().

vpColVector vpMatrix::column ( const unsigned int j )

inherited

Column extraction.

Return the ith columns of the matrix.

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

Definition at line 2240 of file vpMatrix.cpp.

References vpMatrix::getRows().

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

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 56 of file vpMatrix_covariance.cpp.

References vpMatrix::pseudoInverse(), vpColVector::t(), and vpMatrix::t().

Referenced by vpMbEdgeKltTracker::computeVVS(), vpMbKltTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), 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 74 of file vpMatrix_covariance.cpp.

References vpMatrix::pseudoInverse(), and vpMatrix::t().

void vpHomography::computeDisplacement	(	vpRotationMatrix &	aRb,
		vpTranslationVector &	atb,
		vpColVector &	n
	)

Compute the camera displacement between two images from the homography ${^a}{\bf H}_b$ which is here an implicit parameter (*this).

Parameters

aRb	: Rotation matrix as an output ${^a}{\bf R}_b$ .
atb	: Translation vector as an output $^a{\bf t}_b$ .
n	: Normal vector to the plane as an output.

See also: computeDisplacement(const vpHomography &, vpRotationMatrix &, vpTranslationVector &, vpColVector &)

Examples:: homographyHartleyDLT2DObject.cpp, homographyHLM2DObject.cpp, and homographyHLM3DObject.cpp.

Definition at line 671 of file vpHomographyExtract.cpp.

Referenced by computeDisplacement().

void vpHomography::computeDisplacement	(	const vpColVector &	nd,
		vpRotationMatrix &	aRb,
		vpTranslationVector &	atb,
		vpColVector &	n
	)

Compute the camera displacement between two images from the homography ${^a}{\bf H}_b$ which is here an implicit parameter (*this).

Camera displacement between ${^a}{\bf p}$ and ${^a}{\bf p}$ is represented as a rotation matrix ${^a}{\bf R}_b$ and a translation vector $^a{\bf t}_b$ from which an homogenous matrix can be build (vpHomogeneousMatrix).

Parameters

nd	: Input normal vector to the plane used to compar with the normal vector n extracted from the homography.
aRb	: Rotation matrix as an output ${^a}{\bf R}_b$ .
atb	: Translation vector as an output $^a{\bf t}_b$ .
n	: Normal vector to the plane as an output.

See also: computeDisplacement(const vpHomography &, const vpColVector &, vpRotationMatrix &, vpTranslationVector &, vpColVector &)

Definition at line 366 of file vpHomographyExtract.cpp.

References computeDisplacement().

void vpHomography::computeDisplacement	(	const vpHomography &	aHb,
		const vpColVector &	nd,
		vpRotationMatrix &	aRb,
		vpTranslationVector &	atb,
		vpColVector &	n
	)

static

Compute the camera displacement between two images from the homography ${^a}{\bf H}_b$ .

Camera displacement between ${^a}{\bf p}$ and ${^a}{\bf p}$ is represented as a rotation matrix ${^a}{\bf R}_b$ and a translation vector $^a{\bf t}_b$ from which an homogenous matrix can be build (vpHomogeneousMatrix).

Parameters

aHb	: Input homography ${^a}{\bf H}_b$ .
nd	: Input normal vector to the plane used to compar with the normal vector n extracted from the homography.
aRb	: Rotation matrix as an output ${^a}{\bf R}_b$ .
atb	: Translation vector as an output $^a{\bf t}_b$ .
n	: Normal vector to the plane as an output.

Definition at line 76 of file vpHomographyExtract.cpp.

References vpMatrix::det(), vpRotationMatrix::isARotationMatrix(), vpColVector::resize(), vpMatrix::svd(), and vpColVector::t().

void vpHomography::computeDisplacement	(	const vpHomography &	aHb,
		vpRotationMatrix &	aRb,
		vpTranslationVector &	atb,
		vpColVector &	n
	)

static

Compute the camera displacement between two images from the homography ${^a}{\bf H}_b$ .

Camera displacement between ${^a}{\bf p}$ and ${^a}{\bf p}$ is represented as a rotation matrix ${^a}{\bf R}_b$ and a translation vector $^a{\bf t}_b$ from which an homogenous matrix can be build (vpHomogeneousMatrix).

Parameters

aHb	: Input homography ${^a}{\bf H}_b$ .
aRb	: Rotation matrix as an output ${^a}{\bf R}_b$ .
atb	: Translation vector as an output $^a{\bf t}_b$ .
n	: Normal vector to the plane as an output.

Definition at line 392 of file vpHomographyExtract.cpp.

References vpMatrix::det(), vpRotationMatrix::isARotationMatrix(), vpColVector::resize(), vpMatrix::svd(), and vpColVector::t().

void vpHomography::computeDisplacement	(	const vpMatrix &	H,
		const double	x,
		const double	y,
		std::list< vpRotationMatrix > &	vR,
		std::list< vpTranslationVector > &	vT,
		std::list< vpColVector > &	vN
	)

static

Definition at line 684 of file vpHomographyExtract.cpp.

References vpRotationMatrix::setIdentity(), vpMath::sqr(), vpMatrix::svd(), and vpRotationMatrix::t().

double vpHomography::computeDisplacement	(	unsigned int	nbpoint,
		vpPoint *	c1P,
		vpPoint *	c2P,
		vpPlane &	oN,
		vpHomogeneousMatrix &	c2Mc1,
		vpHomogeneousMatrix &	c1Mo,
		int	userobust
	)

static

Definition at line 301 of file vpHomographyVVS.cpp.

References vpExponentialMap::direct(), vpMath::equal(), vpHomogeneousMatrix::extract(), vpPoint::get_x(), vpPoint::get_y(), vpHomogeneousMatrix::inverse(), vpRobust::MEstimator(), vpMatrix::pseudoInverse(), vpRobust::setIteration(), vpRobust::setThreshold(), vpTranslationVector::skew(), vpMath::sqr(), vpMatrix::stackMatrices(), vpMatrix::sumSquare(), vpColVector::t(), vpRobust::TUKEY, and vpMatrix::vpMatrix().

double vpHomography::computeDisplacement	(	unsigned int	nbpoint,
		vpPoint *	c1P,
		vpPoint *	c2P,
		vpPlane *	oN,
		vpHomogeneousMatrix &	c2Mc1,
		vpHomogeneousMatrix &	c1Mo,
		int	userobust
	)

static

Definition at line 521 of file vpHomographyVVS.cpp.

References vpExponentialMap::direct(), vpMath::equal(), vpHomogeneousMatrix::extract(), vpPoint::get_x(), vpPoint::get_y(), vpHomogeneousMatrix::inverse(), vpRobust::MEstimator(), vpMatrix::pseudoInverse(), vpRobust::setIteration(), vpRobust::setThreshold(), vpTranslationVector::skew(), vpMath::sqr(), vpMatrix::stackMatrices(), vpMatrix::sumSquare(), vpColVector::t(), vpRobust::TUKEY, and vpMatrix::vpMatrix().

void vpHomography::computeDisplacement	(	const vpMatrix	H,
		const double	x,
		const double	y,
		vpList< vpRotationMatrix > &	vR,
		vpList< vpTranslationVector > &	vT,
		vpList< vpColVector > &	vN
	)

static

Deprecated:: This method is deprecated. You should use computeDisplacement(const vpMatrix &, const double, const double, std::list<vpRotationMatrix> &, std::list<vpTranslationVector> &, std::list<vpColVector> &) instead.

Definition at line 1342 of file vpHomographyExtract.cpp.

References vpList< type >::addRight(), vpList< type >::kill(), vpRotationMatrix::setIdentity(), vpMath::sqr(), vpMatrix::svd(), and vpRotationMatrix::t().

double vpHomography::computeResidual	(	vpColVector &	x,
		vpColVector &	M,
		vpColVector &	d
	)

static

Definition at line 193 of file vpHomographyRansac.cpp.

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

double vpHomography::computeRotation	(	unsigned int	nbpoint,
		vpPoint *	c1P,
		vpPoint *	c2P,
		vpHomogeneousMatrix &	c2Mc1,
		int	userobust
	)

static

Definition at line 102 of file vpHomographyVVS.cpp.

References vpMath::equal(), vpPoint::get_x(), vpPoint::get_y(), vpMath::maximum(), vpRobust::MEstimator(), vpMatrix::pseudoInverse(), vpRobust::setIteration(), vpRobust::setThreshold(), vpMath::sqr(), vpMatrix::stackMatrices(), vpMatrix::sumSquare(), vpMatrix::t(), and vpRobust::TUKEY.

void vpHomography::computeTransformation	(	vpColVector &	x,
		unsigned int *	ind,
		vpColVector &	M
	)

static

Definition at line 154 of file vpHomographyRansac.cpp.

References vpMatrix::data, vpMatrix::getRows(), HLM(), vpColVector::resize(), and vpMatrix::setIdentity().

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

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 2768 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 2551 of file vpMatrix.cpp.

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

bool vpHomography::degenerateConfiguration	(	vpColVector &	x,
		unsigned int *	ind
	)

static

Definition at line 121 of file vpHomographyRansac.cpp.

References vpMatrix::getRows().

bool vpHomography::degenerateConfiguration	(	vpColVector &	x,
		unsigned int *	ind,
		double	threshold_area
	)

static

Definition at line 48 of file vpHomographyRansac.cpp.

References vpMatrix::getRows().

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

inherited

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

Parameters

method : Method used to compute the determinant. Default LU decomposition 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 3413 of file vpMatrix.cpp.

References vpMatrix::LU_DECOMPOSITION.

Referenced by computeDisplacement().

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 2523 of file vpMatrix.cpp.

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

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

void vpHomography::DLT	(	unsigned int	n,
		double *	xb,
		double *	yb,
		double *	xa,
		double *	ya,
		vpHomography &	aHb
	)

static

Computes the homography matrix wrt. the data using the DLT (Direct Linear Transform) algorithm.

Computes H such as

$^a{\bf p} = ^a{\bf H}_b\; ^b{\bf p}$

To do so, we use the DLT algorithm on the data, ie we resolve the linear system by SDV : $\bf{Ah} =0$ . $\bf{h}$ is the vector with the terms of $\mathbf{H}$ ,

$\mathbf{A}$ depends on the points coordinates.

At least 4 correspondant points couples are needed.

For each point, in homogeneous coordinates we have:

$\mathbf{p}_{a}= \mathbf{H}\mathbf{p}_{b}$

which is equivalent to:

$\mathbf{p}_{a} \times \mathbf{H}\mathbf{p}_{b} =0$

If we note $\mathbf{h}_j^T$ the $j^{\textrm{th}}$ line of $\mathbf{H}$ , we can write:

$\mathbf{H}\mathbf{p}_{b} = \left( \begin{array}{c}\mathbf{h}_1^T\mathbf{p}_{b} \\\mathbf{h}_2^T\mathbf{p}_{b} \\\mathbf{h}_3^T \mathbf{p}_{b} \end{array}\right)$

Setting $\mathbf{p}_{a}=(x_{a},y_{a},w_{a})$ , the cross product can be rewritten by:

$\mathbf{p}_{a} \times \mathbf{H}\mathbf{p}_{b} =\left( \begin{array}{c}y_{a}\mathbf{h}_3^T\mathbf{p}_{b}-w_{a}\mathbf{h}_2^T\mathbf{p}_{b} \\w_{a}\mathbf{h}_1^T\mathbf{p}_{b} -x_{a}\mathbf{h}_3^T \mathbf{p}_{b} \\x_{a}\mathbf{h}_2^T \mathbf{p}_{b}- y_{a}\mathbf{h}_1^T\mathbf{p}_{b}\end{array}\right)$

$\underbrace{\left( \begin{array}{ccc}\mathbf{0}^T & -w_{a} \mathbf{p}_{b}^T & y_{a} \mathbf{p}_{b}^T \\ w_{a} \mathbf{p}_{b}^T&\mathbf{0}^T & -x_{a} \mathbf{p}_{b}^T \\ -y_{a} \mathbf{p}_{b}^T & x_{a} \mathbf{p}_{b}^T & \mathbf{0}^T\end{array}\right)}_{\mathbf{A}_i (3\times 9)} \underbrace{\left( \begin{array}{c}\mathbf{h}_{1}^{T} \\ \mathbf{h}_{2}^{T}\\\mathbf{h}_{3}^{T}\end{array}\right)}_{\mathbf{h} (9\times 1)}=0$

leading to an homogeneous system to be solve: $\mathbf{A}\mathbf{h}=0$ with $\mathbf{A}=\left(\mathbf{A}_1^T, ..., \mathbf{A}_i^T, ..., \mathbf{A}_n^T \right)^T$ .

It can be solved using an SVD decomposition:

$\bf A = UDV^T$

h is the column of V associated with the smalest singular value of A

Exceptions

vpMatrixException::rankDeficient : When the rank of the matrix that should be 8 is deficient.

Definition at line 269 of file vpHomographyDLT.cpp.

References vpMatrix::column(), vpMatrixException::rankDeficient, vpMatrix::resize(), vpMatrix::svd(), vpERROR_TRACE, and vpTRACE.

Referenced by HartleyDLT().

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 2996 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 3115 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 2816 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 3600 of file vpMatrix.cpp.

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

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 1132 of file vpMatrix.cpp.

References vpCERROR, and vpERROR_TRACE.

Referenced by 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 1152 of file vpMatrix.cpp.

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

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 159 of file vpMatrix.h.

Referenced by vpMatrix::add2Matrices(), vpMatrix::add2WeightedMatrices(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpServo::computeControlLaw(), vpServo::computeInteractionMatrix(), vpMbTracker::computeJTR(), vpImageSimulator::getImage(), vpSubRowVector::init(), vpSubMatrix::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*(), vpMatrix::operator+=(), vpMatrix::operator-=(), vpSubRowVector::operator=(), vpRowVector::operator=(), vpSubColVector::operator=(), vpSubMatrix::operator=(), vpRotationMatrix::operator=(), vpColVector::operator=(), vpPose::poseDementhonPlan(), vpMatrix::print(), vpMatrix::pseudoInverse(), vpIoTools::readConfigVar(), vpRowVector::reshape(), vpColVector::reshape(), vpMatrix::row(), vpMatrix::saveMatrix(), vpServo::secondaryTask(), vpRowVector::size(), vpMatrix::stackMatrices(), vpMatrix::sub2Matrices(), and vpMatrix::svd().

double vpMatrix::getMaxValue ( ) const

inherited

Examples:: servoMomentImage.cpp.

Definition at line 3685 of file vpMatrix.cpp.

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

double vpMatrix::getMinValue ( ) const

inherited

Examples:: servoMomentImage.cpp.

Definition at line 3671 of file vpMatrix.cpp.

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

unsigned int vpMatrix::getRows ( ) const

inlineinherited

Return the number of rows of the matrix.

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

Definition at line 157 of file vpMatrix.h.

Referenced by vpMatrix::add2Matrices(), vpMatrix::add2WeightedMatrices(), vpLine::changeFrame(), vpSubColVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpMatrix::column(), vpServo::computeError(), vpServo::computeInteractionMatrix(), vpMbTracker::computeJTR(), vpPtu46::computeMGD(), vpPose::computeResidual(), computeResidual(), computeTransformation(), vpMbEdgeKltTracker::computeVVS(), vpMbKltTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpMatrix::cppPrint(), vpMatrix::createDiagonalMatrix(), vpColVector::crossProd(), vpDot2::defineDots(), degenerateConfiguration(), 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(), vpBasicFeature::getDimension(), vpImageSimulator::getImage(), vpAfma6::getInverseKinematics(), vpViper::getInverseKinematicsWrist(), vpSubColVector::init(), vpSubMatrix::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*(), vpMatrix::operator+=(), vpMatrix::operator-=(), vpColVector::operator<<(), vpSubColVector::operator=(), vpSubMatrix::operator=(), vpSubRowVector::operator=(), vpRotationMatrix::operator=(), vpColVector::operator=(), vpRGBa::operator=(), vpPlot::plot(), vpPose::poseDementhonPlan(), vpPose::poseVirtualVSrobust(), vpKalmanFilter::prediction(), vpMatrix::print(), vpLine::projection(), vpMatrix::pseudoInverse(), vpIoTools::readConfigVar(), vpRowVector::reshape(), vpColVector::reshape(), vpMatrix::saveMatrix(), vpGenericFeature::set_s(), vpGenericFeature::setError(), 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().

void vpHomography::HartleyDenormalization	(	vpHomography &	aHbn,
		vpHomography &	aHb,
		double	xg1,
		double	yg1,
		double	coef1,
		double	xg2,
		double	yg2,
		double	coef2
	)

static

Definition at line 107 of file vpHomographyDLT.cpp.

References vpMatrix::pseudoInverse(), vpMatrix::setIdentity(), and vpMatrix::vpMatrix().

Referenced by HartleyDLT().

void vpHomography::HartleyDLT	(	unsigned int	n,
		double *	xb,
		double *	yb,
		double *	xa,
		double *	ya,
		vpHomography &	aHb
	)

static

Computes the homography matrix using the DLT (Direct Linear Transform) algorithm on normalized data.

Normalizes data, computes H wrt. these normalized data and denormalizes the result. The normalization carried out is the one preconized by Hartley . At least 4 correspondant points couples are needed.

See also: DLT()

Exceptions

vpMatrixException::rankDeficient : When the rank of the matrix that should be 8 is deficient.

Examples:: homographyHartleyDLT2DObject.cpp.

Definition at line 159 of file vpHomographyDLT.cpp.

References DLT(), HartleyDenormalization(), HartleyNormalization(), and vpTRACE.

void vpHomography::HartleyNormalization	(	unsigned int	n,
		double *	x,
		double *	y,
		double *	xn,
		double *	yn,
		double &	xg,
		double &	yg,
		double &	coef
	)

static

Definition at line 57 of file vpHomographyDLT.cpp.

References vpMath::sqr().

Referenced by HartleyDLT().

void vpHomography::HLM	(	unsigned int	n,
		double *	xb,
		double *	yb,
		double *	xa,
		double *	ya,
		bool	isplanar,
		vpHomography &	aHb
	)

static

Computes the homography matrix from planar [9] or non planar points using Ezio Malis linear method (HLM) [8].

Computes H such as

$^a{\bf p} = ^a{\bf H}_b\; ^b{\bf p}$

The algorithm for 2D scene implemented in this file is described in Ezio Malis PhD thesis.

If the boolean isplanar is true the point is assumed to be in a plane otherwise there are assumed to be planar.

The reference planar is the plane build from the 3 first points.

Examples:: homographyHLM2DObject.cpp, and homographyHLM3DObject.cpp.

Definition at line 714 of file vpHomographyMalis.cpp.

References vpMatrix::setIdentity().

Referenced by computeTransformation(), and vpPose::poseFromRectangle().

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 2840 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

subvpMatrix extraction

Definition at line 263 of file vpMatrix.cpp.

References vpMatrix::resize(), and vpERROR_TRACE.

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 2939 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 2348 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 2379 of file vpMatrix.cpp.

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

vpHomography vpHomography::inverse ( ) const

invert the homography

Returns: [H]^-1

Definition at line 274 of file vpHomography.cpp.

References vpMatrix::pseudoInverse().

Referenced by inverse().

void vpHomography::inverse ( vpHomography & bHa ) const

invert the homography

Parameters

bHa : [H]^-1

Definition at line 291 of file vpHomography.cpp.

References inverse().

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);
  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.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 124 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(), vpMatrix::getRows(), and vpMatrix::rowNum.

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(), and vpKalmanFilter::filtering().

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 226 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 73 of file vpMatrix_qr.cpp.

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

Referenced by vpMatrix::inverseByQR().

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

staticinherited

Juxtapose to matrices C = [ A B ].

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

Parameters

A	: Left matrix.
B	: Right matrix.

Returns: Juxtaposed matrix C = [ A B ]

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

Definition at line 2422 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 2451 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 3217 of file vpMatrix.cpp.

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

void vpMatrix::kill ( )

inherited

Destruction of the matrix (Memory de-allocation)

Definition at line 286 of file vpMatrix.cpp.

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

Referenced by vpMatrix::~vpMatrix().

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 1477 of file vpMatrix.cpp.

Referenced by 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 1518 of file vpMatrix.cpp.

References vpMatrix::kron().

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

staticinherited

Compute Kronecker product matrix.

Parameters

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

Definition at line 1443 of file vpMatrix.cpp.

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

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

staticinherited

Compute Kronecker product matrix.

Parameters

m1	: vpMatrix;
m2	: vpMatrix;

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

Definition at line 1487 of file vpMatrix.cpp.

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

void vpHomography::load ( std::ifstream & f )

Load an homography from a file.

Read an homography in a file, verify if it is really an homogeneous matrix.

Parameters

f	: the file.

Definition at line 395 of file vpHomography.cpp.

References vpException::ioError, and vpERROR_TRACE.

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

staticinherited

Load a matrix to 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 3513 of file vpMatrix.cpp.

References vpMatrix::resize().

Referenced by vpDot2::defineDots(), and vpMatrix::loadMatrix().

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

inlinestaticinherited

Load a matrix to a file.

Parameters

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

Returns: Returns true if no problem appends.

Definition at line 218 of file vpMatrix.h.

References vpMatrix::loadMatrix().

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

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 2735 of file vpMatrix.cpp.

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

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

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 2706 of file vpMatrix.cpp.

References vpMatrix::getRows().

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

staticinherited

Operation C = A * B.

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

See also: operator*()

Definition at line 393 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 811 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 709 of file vpMatrix.cpp.

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

Referenced by vpMatrix::operator-().

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

Multiplication by an homography.

Parameters

H	: Homography to multiply with.

vpHomography aHb, bHc; 
// Initialize aHb and bHc homographies
vpHomography aHc = aHb * bHc;  

Definition at line 324 of file vpHomography.cpp.

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 436 of file vpMatrix.cpp.

References vpMatrix::mult2Matrices().

vpHomography vpHomography::operator* ( const double & v ) const

Multiply an homography by a scalar.

Parameters

v	: Value of the scalar.

double v = 1.1;
vpHomography aHb; 
// Initialize aHb
vpHomography H = aHb * v;  

Definition at line 353 of file vpHomography.cpp.

References vpMatrix::data.

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

inherited

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

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

Definition at line 846 of file vpMatrix.cpp.

References vpMatrix::multMatrixVector().

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

inherited

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

Definition at line 855 of file vpMatrix.cpp.

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

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

inherited

Cij = Aij * x (A is unchanged)

Definition at line 930 of file vpMatrix.cpp.

References vpMatrix::colNum, vpMatrix::resize(), 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 1058 of file vpMatrix.cpp.

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

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

inherited

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

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

Definition at line 544 of file vpMatrix.cpp.

References vpMatrix::add2Matrices().

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

inherited

Operation A = A + B.

Definition at line 624 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 1010 of file vpMatrix.cpp.

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

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

inherited

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

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

Definition at line 615 of file vpMatrix.cpp.

References vpMatrix::sub2Matrices().

vpMatrix vpMatrix::operator- ( void ) const

inherited

Operation C = -A (A is unchanged).

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

Definition at line 751 of file vpMatrix.cpp.

References vpMatrix::negateMatrix().

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

inherited

Operation A = A - B.

Definition at line 664 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 1034 of file vpMatrix.cpp.

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

vpHomography vpHomography::operator/ ( const double & v ) const

Divide an homography by a scalar.

Parameters

v	: Value of the scalar.

vpHomography aHb; 
// Initialize aHb
vpHomography H = aHb / aHb[2][2];  

Definition at line 377 of file vpHomography.cpp.

References vpMatrix::data.

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

inherited

Cij = Aij / x (A is unchanged)

Definition at line 965 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 1073 of file vpMatrix.cpp.

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

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

inherited

Assigment from an array of double.

Definition at line 368 of file vpMatrix.cpp.

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

double* vpMatrix::operator[] ( unsigned int n )

inlineinherited

write elements Aij (usage : A[i][j] = x )

Definition at line 248 of file vpMatrix.h.

double* vpMatrix::operator[] ( unsigned int n ) const

inlineinherited

read elements Aij (usage : x = A[i][j] )

Definition at line 250 of file vpMatrix.h.

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 2615 of file vpMatrix.cpp.

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

void vpHomography::print ( )

Print the matrix.

Print the matrix as a vector [T thetaU].

Definition at line 416 of file vpHomography.cpp.

void vpMatrix::printSize ( )

inlineinherited

Definition at line 183 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 1812 of file vpMatrix.cpp.

Referenced by vpCalibration::calibrationTsai(), vpSimulatorAfma6::computeArticularVelocity(), vpSimulatorViper850::computeArticularVelocity(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), computeDisplacement(), computeRotation(), vpMbEdgeKltTracker::computeVVS(), vpMbKltTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), HartleyDenormalization(), vpMeEllipse::initTracking(), inverse(), vpMeLine::leastSquare(), vpPose::poseDementhonNonPlan(), vpPose::poseFromRectangle(), vpPose::poseVirtualVS(), vpMatrix::pseudoInverse(), 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 1772 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 1828 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 1867 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 2045 of file vpMatrix.cpp.

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

bool vpHomography::ransac	(	unsigned int	n,
		double *	xb,
		double *	yb,
		double *	xa,
		double *	ya,
		vpHomography &	aHb,
		int	consensus = `1000`,
		double	threshold = `1e-6`
	)

static

Examples:: homographyRansac2DObject.cpp.

Definition at line 265 of file vpHomographyRansac.cpp.

References vpMatrix::data, and vpRansac< vpTransformation >::ransac().

bool vpHomography::ransac	(	unsigned int	n,
		double *	xb,
		double *	yb,
		double *	xa,
		double *	ya,
		vpHomography &	bHa,
		vpColVector &	inliers,
		double &	residual,
		int	consensus = `1000`,
		double	threshold = `1e-6`,
		double	areaThreshold = `0.0`
	)

static

Computes homography matrix $ b^H_a $ such as $X_b = b^H_a X_a $ with $ X_a = (xa, ya)^t $ and $ X_b = (xb, yb)^t $ .

Parameters

n	: Number of points.
xb,yb	: Coordinates of the points in vector.
xa,ya	: Coordinates of the points in vector.
bHa	: Homography matrix computed from and vectors.
inliers	: n dimention vector indicating if a point is an inlier (value 1.0) or an outlier (value 0). Matches are stocked in inliers vector column.
residual	: Residual. Not used.
consensus	: Minimal number of points (less than n) fitting the model.
threshold	: Threshold for outlier removing.
areaThreshold	: Ensure that the area formed by every 3 points within the 4 points used to compute the homography is greater than this threshold. If the area is smaller, we are in a degenerate case.

Returns: true if the homography could be computed from 4 non-degenerated points.

Definition at line 323 of file vpHomographyRansac.cpp.

References vpMatrix::data, and vpRansac< vpTransformation >::ransac().

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 174 of file vpMatrix.cpp.

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

vpRowVector vpMatrix::row ( const unsigned int j )

inherited

Row extraction.

Return the ith rows of the matrix.

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

Definition at line 2225 of file vpMatrix.cpp.

References vpMatrix::getCols().

Referenced by vpMatrix::kernel(), vpMatrix::pseudoInverse(), and vpMatrix::transpose().

void vpHomography::save ( std::ofstream & f ) const

Save an homography in a file.

Definition at line 298 of file vpHomography.cpp.

References vpException::ioError, and vpERROR_TRACE.

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 3440 of file vpMatrix.cpp.

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

Referenced by vpDot2::defineDots(), and vpMatrix::saveMatrix().

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 201 of file vpMatrix.h.

References vpMatrix::saveMatrix().

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 1110 of file vpMatrix.cpp.

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

Referenced by vpServo::computeControlLaw(), computeTransformation(), vpMatrix::expm(), HartleyDenormalization(), HLM(), vpFeatureThetaU::interaction(), vpMeLine::leastSquare(), vpPose::poseFromRectangle(), and vpServo::secondaryTask().

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 1573 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 1628 of file vpMatrix.cpp.

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

void vpMatrix::stackColumns ( vpColVector & out )

inherited

Stacks columns of a matrix in a vector.

Parameters

out	: a vpColVector.

Definition at line 1373 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 1397 of file vpMatrix.cpp.

References vpMatrix::colNum, and 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.

Examples:: servoPioneerPoint2DDepthWithoutVpServo.cpp.

Definition at line 2263 of file vpMatrix.cpp.

References 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 2292 of file vpMatrix.cpp.

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

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());
}

Definition at line 2920 of file vpMatrix.cpp.

References vpMatrix::rowNum, and vpMatrix::stackMatrices().

void vpMatrix::stackRows ( vpRowVector & out )

inherited

Stacks rows of a matrix in a vector

Parameters

out	: a vpRowVector.

Definition at line 1408 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 1430 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 562 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::sumSquare ( ) const

inherited

return sum of the Aij^2 (for all i, for all j)

Examples:: photometricVisualServoing.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoMomentImage.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 760 of file vpMatrix.cpp.

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

Referenced by vpPose::calculArbreDementhon(), vpCalibration::calibrationTsai(), computeDisplacement(), computeResidual(), computeRotation(), 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 1702 of file vpMatrix.cpp.

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

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

vpMatrix vpMatrix::t ( ) const

inherited

Compute and return the transpose of the matrix.

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

Definition at line 1176 of file vpMatrix.cpp.

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

Referenced by vpVelocityTwistMatrix::buildFrom(), vpForceTwistMatrix::buildFrom(), vpHomogeneousMatrix::buildFrom(), vpCalibration::calibrationTsai(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), computeRotation(), vpMatrix::eigenValues(), vpKalmanFilter::filtering(), vpPose::poseDementhonNonPlan(), vpPose::poseDementhonPlan(), vpKalmanFilter::prediction(), vpMatrix::pseudoInverse(), and vpMatrix::resize().

vpMatrix vpMatrix::transpose ( ) const

inherited

Compute and return the transpose of the matrix.

See also: t()

Definition at line 1206 of file vpMatrix.cpp.

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 1218 of file vpMatrix.cpp.

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

Friends And Related Function Documentation

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

Definition at line 886 of file vpMatrix.cpp.

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

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

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

Parameters

t	: Translation vector in input used to compute the skew symmetric matrix M.
M	: Skew symmetric matrix of translation vector .

Examples:: servoSimuSphere.cpp.

Definition at line 296 of file vpTranslationVector.cpp.

References vpMatrix::resize().

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 112 of file vpMatrix.h.

Referenced by vpMatrix::AAt(), vpMatrix::add2Matrices(), vpMatrix::add2WeightedMatrices(), vpMatrix::AtA(), 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::inverseByQRLapack(), vpMatrix::kron(), vpMatrix::mult2Matrices(), vpMatrix::multMatrixVector(), vpMatrix::negateMatrix(), vpRowVector::operator*(), vpMatrix::operator*(), vpMatrix::operator*=(), vpMatrix::operator+=(), vpMatrix::operator-=(), vpMatrix::operator/(), vpMatrix::operator/=(), vpColVector::operator<<(), vpMatrix::operator<<(), vpSubRowVector::operator=(), vpRowVector::operator=(), vpSubMatrix::operator=(), vpMatrix::operator=(), vpMatrix::resize(), vpMatrix::setIdentity(), vpMatrix::solveBySVD(), vpMatrix::stackColumns(), vpMatrix::stackRows(), vpMatrix::sub2Matrices(), vpMatrix::sumSquare(), vpRowVector::t(), vpMatrix::t(), vpMatrix::transpose(), vpMatrix::vpMatrix(), vpSubColVector::vpSubColVector(), vpSubMatrix::vpSubMatrix(), and vpSubRowVector::vpSubRowVector().

double* vpMatrix::data

inherited

address of the first element of the data array

Definition at line 116 of file vpMatrix.h.

Referenced by vpMatrix::AtA(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpPose::computeResidual(), computeResidual(), vpPose::computeTransformation(), computeTransformation(), vpColVector::dotProd(), vpMatrix::eigenValues(), vpMatrix::euclideanNorm(), 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*(), vpColVector::operator*(), vpTranslationVector::operator*(), operator*(), vpColVector::operator+(), vpTranslationVector::operator-(), vpColVector::operator-(), operator/(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpTranslationVector::operator=(), vpMatrix::operator=(), vpRowVector::operator[](), vpColVector::operator[](), vpPose::ransac(), 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(), vpSubRowVector::vpSubRowVector(), vpSubColVector::~vpSubColVector(), vpSubMatrix::~vpSubMatrix(), and vpSubRowVector::~vpSubRowVector().

unsigned int vpMatrix::dsize

protectedinherited

Current size (rowNum * colNum)

Definition at line 122 of file vpMatrix.h.

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

unsigned int vpMatrix::rowNum

protectedinherited

number of rows

Definition at line 110 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::inverseByCholeskyLapack(), vpMatrix::inverseByLU(), vpMatrix::inverseByQR(), vpMatrix::inverseByQRLapack(), 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=(), vpRowVector::operator=(), vpSubMatrix::operator=(), vpColVector::operator=(), vpTranslationVector::operator=(), vpMatrix::operator=(), vpColVector::rad2deg(), vpMatrix::resize(), vpMatrix::setIdentity(), vpColVector::stack(), vpMatrix::stackColumns(), vpMatrix::stackMatrices(), vpMatrix::stackRows(), vpMatrix::sub2Matrices(), vpMatrix::sumSquare(), vpColVector::t(), vpMatrix::t(), vpMatrix::transpose(), vpMatrix::vpMatrix(), vpSubColVector::vpSubColVector(), vpSubMatrix::vpSubMatrix(), and vpSubRowVector::vpSubRowVector().

double** vpMatrix::rowPtrs

protectedinherited

address of the first element of each rows

Definition at line 119 of file vpMatrix.h.

unsigned int vpMatrix::trsize

protectedinherited

Total row space.

Definition at line 124 of file vpMatrix.h.

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

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