ViSP  2.6.2
Public Types | Public Member Functions | Static Public Member Functions | Public Attributes | Protected Attributes | Related Functions | List of all members
vpHomogeneousMatrix Class Reference
Mathematics » Transformations » 3D transformations » Pose

#include <vpHomogeneousMatrix.h>

+ Inheritance diagram for vpHomogeneousMatrix:

Public Types

enum  vpDetMethod { LU_DECOMPOSITION }
 

Public Member Functions

 vpHomogeneousMatrix ()
 
 vpHomogeneousMatrix (const vpHomogeneousMatrix &M)
 
 vpHomogeneousMatrix (const vpTranslationVector &t, const vpRotationMatrix &R)
 
 vpHomogeneousMatrix (const vpTranslationVector &t, const vpThetaUVector &tu)
 
 vpHomogeneousMatrix (const vpTranslationVector &t, const vpQuaternionVector &q)
 
 vpHomogeneousMatrix (const vpPoseVector &p)
 
 vpHomogeneousMatrix (const double tx, const double ty, const double tz, const double tux, const double tuy, const double tuz)
 
void buildFrom (const vpTranslationVector &t, const vpRotationMatrix &R)
 
void buildFrom (const vpTranslationVector &t, const vpThetaUVector &tu)
 
void buildFrom (const vpTranslationVector &t, const vpQuaternionVector &q)
 
void buildFrom (const vpPoseVector &p)
 
void buildFrom (const double tx, const double ty, const double tz, const double tux, const double tuy, const double tuz)
 
vpHomogeneousMatrix & operator= (const vpHomogeneousMatrix &M)
 
vpHomogeneousMatrix operator* (const vpHomogeneousMatrix &M) const
 
vpColVector operator* (vpColVector &v) const
 
vpHomogeneousMatrix inverse () const
 
void inverse (vpHomogeneousMatrix &Mi) const
 
bool isAnHomogeneousMatrix () const
 
void insert (const vpRotationMatrix &R)
 
void insert (const vpThetaUVector &tu)
 
void insert (const vpTranslationVector &t)
 
void insert (const vpQuaternionVector &t)
 
void extract (vpRotationMatrix &R) const
 
void extract (vpTranslationVector &t) const
 
void extract (vpThetaUVector &tu) const
 
void extract (vpQuaternionVector &q) const
 
void load (std::ifstream &f)
 
void save (std::ofstream &f) const
 
void eye ()
 
void init ()
 
void setIdentity ()
 
void print ()
 
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 & 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)
 
LU decomposition
vpMatrix inverseByLU () const
 
SVD decomposition
void svd (vpColVector &w, vpMatrix &v)
 
void solveBySVD (const vpColVector &B, vpColVector &x) const
 
vpColVector solveBySVD (const vpColVector &B) 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
 
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 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)
 

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

The class provides a data structure for the homogeneous matrices as well as a set of operations on these matrices.

The vpHomogeneousMatrix is derived from vpMatrix.

Author
Eric Marchand (Eric..nosp@m.Marc.nosp@m.hand@.nosp@m.iris.nosp@m.a.fr) Irisa / Inria Rennes

An homogeneous matrix is 4x4 matrix defines as

\[ ^a{\bf M}_b = \left(\begin{array}{cc} ^a{\bf R}_b & ^a{\bf t}_b \\ {\bf 0}_{1\times 3} & 1 \end{array} \right) \]

that defines the position of frame b in frame a

$ ^a{\bf R}_b $ is a rotation matrix and $ ^a{\bf t}_b $ is a translation vector.

Examples:
AROgre.cpp, AROgreBasic.cpp, calibrate2dGrid.cpp, calibrateTsai.cpp, exponentialMap.cpp, HelloWorldOgre.cpp, HelloWorldOgreAdvanced.cpp, homographyHartleyDLT2DObject.cpp, homographyHLM2DObject.cpp, homographyHLM3DObject.cpp, homographyRansac2DObject.cpp, manGeometricFeatures.cpp, manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbtTracking.cpp, photometricVisualServoing.cpp, poseVirtualVS.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6FourPoints2DCamVelocityInteractionCurrent.cpp, servoAfma6FourPoints2DCamVelocityInteractionDesired.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoMomentImage.cpp, servoMomentPoints.cpp, servoMomentPolygon.cpp, servoPioneerPanSegment3D.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu3D_cdMc_CamVelocity.cpp, servoSimu3D_cdMc_CamVelocityWithoutVpServo.cpp, servoSimu3D_cMcd_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity1.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuPoint3DCamVelocity.cpp, servoSimuSphere.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocitySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper850FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPointsKinect.cpp, servoViper850Point2DArtVelocity.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testDisplacement.cpp, testFeatureSegment.cpp, testFindMatch.cpp, testPose.cpp, testPoseFeatures.cpp, testPoseRansac.cpp, testRobotAfma6Pose.cpp, testRobotViper850.cpp, testRobotViper850Pose.cpp, testViper850.cpp, and wireframeSimulator.cpp.

Definition at line 102 of file vpHomogeneousMatrix.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

vpHomogeneousMatrix::vpHomogeneousMatrix ( )

Basic constructor.

Initialize an homogeneous matrix as identity.

Definition at line 99 of file vpHomogeneousMatrix.cpp.

References init().

vpHomogeneousMatrix::vpHomogeneousMatrix ( const vpHomogeneousMatrix &  M)

Copy constructor.

Initialize an homogeneous matrix from another homogeneous matrix.

Definition at line 108 of file vpHomogeneousMatrix.cpp.

References init().

vpHomogeneousMatrix::vpHomogeneousMatrix ( const vpTranslationVector &  t,
const vpRotationMatrix &  R 
)

Construction from translation vector and rotation matrix.

Definition at line 121 of file vpHomogeneousMatrix.cpp.

References init(), and insert().

vpHomogeneousMatrix::vpHomogeneousMatrix ( const vpTranslationVector &  t,
const vpThetaUVector &  tu 
)

Construction from translation vector and theta u rotation vector.

Definition at line 114 of file vpHomogeneousMatrix.cpp.

References buildFrom(), and init().

vpHomogeneousMatrix::vpHomogeneousMatrix ( const vpTranslationVector &  t,
const vpQuaternionVector &  q 
)

Construction from translation vector and quaternion rotation vector.

Definition at line 89 of file vpHomogeneousMatrix.cpp.

References buildFrom(), and init().

vpHomogeneousMatrix::vpHomogeneousMatrix ( const vpPoseVector &  p)

Construction from translation vector and theta u rotation vector defined as a pose vector.

Definition at line 129 of file vpHomogeneousMatrix.cpp.

References buildFrom(), and init().

vpHomogeneousMatrix::vpHomogeneousMatrix ( const double  tx,
const double  ty,
const double  tz,
const double  tux,
const double  tuy,
const double  tuz 
)

Construction from translation and rotation defined as a theta u vector.

Definition at line 136 of file vpHomogeneousMatrix.cpp.

References buildFrom(), and init().

Member Function Documentation

vpMatrix vpMatrix::AAt ( ) const
inherited

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

Returns
$A*A^T$
See also
AAt(vpMatrix &) const

Definition at line 1246 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 1266 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 491 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 452 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
$A^T*A$
See also
AtA(vpMatrix &) const
Examples:
photometricVisualServoing.cpp.

Definition at line 1357 of file vpMatrix.cpp.

Referenced by vpCalibration::calibrationTsai(), 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 1309 of file vpMatrix.cpp.

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

void vpHomogeneousMatrix::buildFrom ( const vpTranslationVector &  t,
const vpRotationMatrix &  R 
)

Construction from translation vector and rotation matrix.

Examples:
calibrateTsai.cpp, photometricVisualServoing.cpp, servoAfma6FourPoints2DCamVelocityInteractionCurrent.cpp, servoAfma6FourPoints2DCamVelocityInteractionDesired.cpp, servoSimu3D_cdMc_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocity.cpp, servoSimu4Points.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuSphere.cpp, servoSimuThetaUCamVelocity.cpp, servoViper850FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPointsKinect.cpp, testRobotAfma6Pose.cpp, and testRobotViper850Pose.cpp.

Definition at line 156 of file vpHomogeneousMatrix.cpp.

References init(), and insert().

Referenced by vpHomography::buildFrom(), vpViper850::init(), vpAfma6::init(), vpSimulatorAfma6::init(), vpSimulatorViper850::init(), vpMbTracker::initClick(), vpMbTracker::initFromPose(), vpWireFrameSimulator::navigation(), vpViper850::parseConfigFile(), vpAfma6::parseConfigFile(), vpWireFrameSimulator::setExternalCameraPosition(), vpAfma4::vpAfma4(), vpHomogeneousMatrix(), vpKinect::vpKinect(), and vpWireFrameSimulator::vpWireFrameSimulator().

void vpHomogeneousMatrix::buildFrom ( const vpTranslationVector &  t,
const vpThetaUVector &  tu 
)

Construction from translation vector and theta u rotation vector.

Definition at line 148 of file vpHomogeneousMatrix.cpp.

References insert().

void vpHomogeneousMatrix::buildFrom ( const vpTranslationVector &  t,
const vpQuaternionVector &  q 
)

Construction from translation vector and quaternion rotation vector.

Definition at line 176 of file vpHomogeneousMatrix.cpp.

References insert().

void vpHomogeneousMatrix::buildFrom ( const vpPoseVector &  p)

Construction from translation vector and theta u rotation vector defined as a pose vector.

Definition at line 166 of file vpHomogeneousMatrix.cpp.

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

void vpHomogeneousMatrix::buildFrom ( const double  tx,
const double  ty,
const double  tz,
const double  tux,
const double  tuy,
const double  tuz 
)

Construction from translation and rotation defined as a theta u vector.

Definition at line 184 of file vpHomogeneousMatrix.cpp.

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

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 2238 of file vpMatrix.cpp.

References vpMatrix::getRows().

Referenced by vpHomography::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 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().

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

Definition at line 2737 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 2549 of file vpMatrix.cpp.

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

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;
}

Definition at line 3382 of file vpMatrix.cpp.

References vpMatrix::LU_DECOMPOSITION.

Referenced by vpHomography::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 2521 of file vpMatrix.cpp.

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

Referenced by vpMbEdgeTracker::computeVVS().

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::matrixErrorIf the matrix is not square or if the matrix is not symmetric.
vpMatrixException::notImplementedErrorIf 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 2965 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::matrixErrorIf the matrix is not square or if the matrix is not symmetric.
vpMatrixException::notImplementedErrorIf 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 3084 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 2785 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 3569 of file vpMatrix.cpp.

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

void vpHomogeneousMatrix::extract ( vpRotationMatrix &  R) const

Extract the rotational matrix from the homogeneous matrix.

Parameters
R: rotational component as a rotation matrix.
Examples:
calibrateTsai.cpp, exponentialMap.cpp, servoAfma6FourPoints2DCamVelocityInteractionCurrent.cpp, servoMomentImage.cpp, servoMomentPoints.cpp, servoMomentPolygon.cpp, servoSimu3D_cdMc_CamVelocityWithoutVpServo.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoViper850FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPointsKinect.cpp, testPose.cpp, testRobotAfma6Pose.cpp, testRobotViper850.cpp, testRobotViper850Pose.cpp, and testViper850.cpp.

Definition at line 298 of file vpHomogeneousMatrix.cpp.

Referenced by vpPoseVector::buildFrom(), vpVelocityTwistMatrix::buildFrom(), vpForceTwistMatrix::buildFrom(), vpThetaUVector::buildFrom(), vpFeatureThetaU::buildFrom(), vpCalibration::calibrationTsai(), vpHomography::computeDisplacement(), vpViper::get_eJe(), vpViper::get_fJe(), vpRobotAfma6::getDisplacement(), vpSimulatorAfma6::getPosition(), vpRobotAfma4::getPosition(), vpSimulatorViper850::getPosition(), vpRobotAfma6::getPosition(), vpRobotAfma6::getVelocity(), vpRobotViper850::getVelocity(), vpExponentialMap::inverse(), inverse(), isAnHomogeneousMatrix(), operator*(), vpPose::poseLowe(), vpImageSimulator::setCameraPosition(), vpAROgre::setPosition(), vpSimulatorAfma6::setPosition(), vpRobotAfma4::setVelocity(), and vpFeatureThetaU::vpFeatureThetaU().

void vpHomogeneousMatrix::extract ( vpTranslationVector &  t) const

Extract the translation vector from the homogeneous matrix.

Definition at line 311 of file vpHomogeneousMatrix.cpp.

void vpHomogeneousMatrix::extract ( vpThetaUVector &  tu) const

Extract the rotation as a Theta U vector.

Definition at line 321 of file vpHomogeneousMatrix.cpp.

References vpThetaUVector::buildFrom().

void vpHomogeneousMatrix::extract ( vpQuaternionVector &  q) const

Extract the rotation as a quaternion.

Definition at line 333 of file vpHomogeneousMatrix.cpp.

References vpQuaternionVector::buildFrom().

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 1130 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 1150 of file vpMatrix.cpp.

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

void vpHomogeneousMatrix::eye ( )

Set transformation to identity.

Examples:
calibrateTsai.cpp.

Definition at line 423 of file vpHomogeneousMatrix.cpp.

unsigned int vpMatrix::getCols ( ) const
inlineinherited

Return the number of columns of the matrix.

Examples:
servoViper850Point2DArtVelocity-jointAvoidance-basic.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::juxtaposeMatrices(), vpMatrix::kernel(), vpMatrix::kron(), 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 3654 of file vpMatrix.cpp.

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

double vpMatrix::getMinValue ( ) const
inherited
Examples:
servoMomentImage.cpp.

Definition at line 3640 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:
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(), vpHomography::computeResidual(), vpHomography::computeTransformation(), vpMbEdgeTracker::computeVVS(), vpMatrix::cppPrint(), vpMatrix::createDiagonalMatrix(), vpColVector::crossProd(), vpDot2::defineDots(), vpHomography::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::inverseByLU(), vpColVector::invSort(), vpMatrix::juxtaposeMatrices(), vpMatrix::kernel(), vpScale::KernelDensity(), vpScale::KernelDensityGradient(), vpMatrix::kron(), 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=(), vpSubRowVector::operator=(), vpSubMatrix::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().

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 2809 of file vpMatrix.cpp.

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

void vpHomogeneousMatrix::init ( )

Basic initialisation (identity).

Initialize a 4x4 momogeneous matrix as identity.

Examples:
HelloWorldOgreAdvanced.cpp.

Definition at line 66 of file vpHomogeneousMatrix.cpp.

References vpMatrix::resize(), and vpERROR_TRACE.

Referenced by buildFrom(), operator=(), setIdentity(), and vpHomogeneousMatrix().

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

subvpMatrix extraction

Definition at line 261 of file vpMatrix.cpp.

References vpMatrix::resize(), and vpERROR_TRACE.

void vpHomogeneousMatrix::insert ( const vpRotationMatrix &  R)

Insert the rotational component of the homogeneous matrix.

Examples:
testDisplacement.cpp.

Definition at line 344 of file vpHomogeneousMatrix.cpp.

Referenced by buildFrom(), vpCalibration::calibrationTsai(), vpExponentialMap::direct(), insert(), inverse(), operator*(), vpPose::poseLowe(), and vpHomogeneousMatrix().

void vpHomogeneousMatrix::insert ( const vpThetaUVector &  tu)

Insert the rotational component of the homogeneous matrix from a theta u rotation vector.

Definition at line 360 of file vpHomogeneousMatrix.cpp.

References insert().

void vpHomogeneousMatrix::insert ( const vpTranslationVector &  T)

Insert the translational component in a homogeneous matrix.

Definition at line 370 of file vpHomogeneousMatrix.cpp.

void vpHomogeneousMatrix::insert ( const vpQuaternionVector &  q)

Insert the rotational component of the homogeneous matrix from a quaternion rotation vector.

Definition at line 384 of file vpHomogeneousMatrix.cpp.

References insert().

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 2908 of file vpMatrix.cpp.

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

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

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

Insert matrix B in matrix A at the given position.

Parameters
A: Main matrix.
B: Matrix to insert.
r: Index of the row where to add the matrix.
c: Index of the column where to add the matrix.
Returns
Matrix with B insert in A.
Warning
Throw exception if the sizes of the matrices do not allow the insertion.

Definition at line 2346 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 2377 of file vpMatrix.cpp.

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

vpHomogeneousMatrix vpHomogeneousMatrix::inverse ( ) const

Invert the homogeneous matrix

Returns
$\left[\begin{array}{cc} {\bf R} & {\bf t} \\ {\bf 0}_{1\times 3} & 1 \end{array} \right]^{-1} = \left[\begin{array}{cc} {\bf R}^T & -{\bf R}^T {\bf t} \\ {\bf 0}_{1\times 3} & 1 \end{array} \right]$
Examples:
calibrateTsai.cpp, servoAfma62DhalfCamVelocity.cpp, servoSimu3D_cdMc_CamVelocity.cpp, servoSimu3D_cdMc_CamVelocityWithoutVpServo.cpp, servoSimu3D_cMcd_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimu4Points.cpp, servoSimuCylinder.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuSphere.cpp, and servoSimuThetaUCamVelocity.cpp.

Definition at line 403 of file vpHomogeneousMatrix.cpp.

References extract(), insert(), and vpRotationMatrix::t().

Referenced by vpSimulatorViper850::compute_fMi(), vpHomography::computeDisplacement(), vpPtu46::computeMGD(), vpBiclops::computeMGD(), vpMbEdgeTracker::computeVVS(), vpProjectionDisplay::displayCamera(), vpPtu46::get_cMe(), vpAfma4::get_cMe(), vpViper::get_cMe(), vpAfma6::get_cMe(), vpRobotSimulator::get_cMo(), vpAfma4::get_cVf(), vpViper::get_eJe(), vpViper::get_fJe(), vpBiclops::get_fMc(), vpRobotBiclops::getDisplacement(), vpRobotAfma6::getDisplacement(), vpSimulator::getExternalCameraPosition(), vpSimulatorAfma6::getExternalImage(), vpSimulatorViper850::getExternalImage(), vpWireFrameSimulator::getExternalImage(), vpWireFrameSimulator::getInternalImage(), vpRobotSimulator::getInternalView(), vpViper::getInverseKinematics(), vpAfma6::getInverseKinematics(), vpRobotAfma4::getVelocity(), vpRobotAfma6::getVelocity(), vpRobotViper850::getVelocity(), vpSimulatorAfma6::initialiseCameraRelativeToObject(), vpSimulatorViper850::initialiseCameraRelativeToObject(), inverse(), vpSimulator::moveInternalCamera(), vpPose::poseVirtualVS(), vpPose::poseVirtualVSrobust(), vpWireFrameSimulator::projectCameraTrajectory(), vpBiclops::set_cMe(), vpWireFrameSimulator::set_fMo(), vpRobotCamera::setArticularVelocity(), vpWireFrameSimulator::setCameraPositionRelObj(), vpWireFrameSimulator::setCameraPositionRelWorld(), vpRobotCamera::setCameraVelocity(), vpWireFrameSimulator::setExternalCameraPosition(), vpSimulatorAfma6::setPosition(), and vpKinect::vpKinect().

void vpHomogeneousMatrix::inverse ( vpHomogeneousMatrix &  M) const

Invert the homogeneous matrix.

Parameters
M: The inverted homogenous matrix: $\left[\begin{array}{cc} {\bf R} & {\bf t} \\ {\bf 0}_{1\times 3} & 1 \end{array} \right]^{-1} = \left[\begin{array}{cc} {\bf R}^T & -{\bf R}^T {\bf t} \\ {\bf 0}_{1\times 3} & 1 \end{array} \right]$

Definition at line 453 of file vpHomogeneousMatrix.cpp.

References inverse().

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().

bool vpHomogeneousMatrix::isAnHomogeneousMatrix ( ) const

Test if the 3x3 rotational part of the homogeneous matrix is really a rotation matrix.

Definition at line 285 of file vpHomogeneousMatrix.cpp.

References extract(), and vpRotationMatrix::isARotationMatrix().

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 2420 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 2449 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 3186 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 284 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 1475 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 1516 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 1441 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 1485 of file vpMatrix.cpp.

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

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

Read an homogeneous matrix from an input file stream. The homogeneous matrix is considered as a 4 by 4 matrix.

Parameters
f: Input file stream.

The code below shows how to get an homogenous matrix from a file.

vpHomogeneousMatrix M;
std::ifstream f("homogeneous.dat");
M.load(f);
See also
save()
Examples:
servoAfma6Points2DCamVelocityEyeToHand.cpp.

Definition at line 515 of file vpHomogeneousMatrix.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 3482 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 217 of file vpMatrix.h.

References vpMatrix::loadMatrix().

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 2704 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 391 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 809 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 707 of file vpMatrix.cpp.

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

Referenced by vpMatrix::operator-().

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

Multiply two homogeneous matrices: aMb = aMc*cMb.

Allow homogeneous matrix multiplication.

#include <visp/vpHomogeneousMatrix.h>
int main()
{
vpHomogeneousMatrix aMb, bMc;
// Initialize aMb and bMc...
// Compute aMc * bMc
vpHomogeneousMatrix aMc = aMb * bMc;
}

Definition at line 237 of file vpHomogeneousMatrix.cpp.

References extract(), and insert().

vpColVector vpHomogeneousMatrix::operator* ( vpColVector &  v) const

Multiply by a vector ! size 4 !!!

Definition at line 262 of file vpHomogeneousMatrix.cpp.

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

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 434 of file vpMatrix.cpp.

References vpMatrix::mult2Matrices().

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 844 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 853 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 928 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 1056 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 542 of file vpMatrix.cpp.

References vpMatrix::add2Matrices().

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

Operation A = A + B.

Definition at line 622 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 1008 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 613 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 749 of file vpMatrix.cpp.

References vpMatrix::negateMatrix().

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

Operation A = A - B.

Definition at line 662 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 1032 of file vpMatrix.cpp.

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

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

Cij = Aij / x (A is unchanged)

Definition at line 963 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 1071 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 366 of file vpMatrix.cpp.

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

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

Copy operator from vpHomogeneousMatrix.

Affectation of two homogeneous matrices.

Parameters
M: *this = M

Definition at line 204 of file vpHomogeneousMatrix.cpp.

References init(), and vpMatrix::rowPtrs.

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

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

Definition at line 247 of file vpMatrix.h.

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

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

Definition at line 249 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
sStream used for the printing.
lengthThe 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.
introThe 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 2613 of file vpMatrix.cpp.

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

void vpHomogeneousMatrix::print ( )

Print the matrix as a vector [T thetaU].

Examples:
servoAfma6Points2DCamVelocityEyeToHand.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, and servoSimuViper850FourPoints2DCamVelocity.cpp.

Definition at line 534 of file vpHomogeneousMatrix.cpp.

References vpColVector::t().

void vpMatrix::printSize ( )
inlineinherited

Definition at line 182 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 1810 of file vpMatrix.cpp.

Referenced by vpCalibration::calibrationTsai(), vpSimulatorAfma6::computeArticularVelocity(), vpSimulatorViper850::computeArticularVelocity(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), vpHomography::computeDisplacement(), vpHomography::computeRotation(), vpMbEdgeTracker::computeVVS(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), vpMeEllipse::initTracking(), vpHomography::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 $ A^+ $.
svThreshold: Threshold used to test the singular values.
Returns
Return the rank of the matrix A

Definition at line 1770 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 $ A^+ $.
sv: Singular values.
svThreshold: Threshold used to test the singular values.
Returns
Return the rank of the matrix A

Definition at line 1826 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 $ A^+ $.
sv: Singular values.
svThreshold: Threshold used to test the singular values.
imAt: Image A^T
imAImage A
Returns
Return the rank of the matrix A

Definition at line 1865 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 $ A^+ $.
sv: Singular values.
svThreshold: Threshold used to test the singular values.
imAImage A
imAt: Image A^T
kerA: null space of A
Returns
Return the rank of the matrix A

Definition at line 2043 of file vpMatrix.cpp.

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

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, 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.

Referenced by vpMatrix::AAt(), vpMatrix::add2Matrices(), vpMatrix::add2WeightedMatrices(), vpMatrix::AtA(), vpServo::computeControlLaw(), vpMbTracker::computeJTR(), vpMatrix::createDiagonalMatrix(), vpMatrix::diag(), vpProjectionDisplay::display(), vpHomography::DLT(), vpMatrix::eigenValues(), vpMatrix::eye(), vpPtu46::get_eJe(), vpAfma4::get_eJe(), vpAfma6::get_eJe(), vpBiclops::get_eJe(), vpPtu46::get_fJe(), vpAfma4::get_fJe(), vpAfma6::get_fJe(), vpBiclops::get_fJe(), vpAfma4::get_fJe_inverse(), vpViper::get_fJw(), vpCameraParameters::get_K(), vpRobotCamera::init(), vpRotationMatrix::init(), vpProjectionDisplay::init(), vpVelocityTwistMatrix::init(), vpForceTwistMatrix::init(), vpKalmanFilter::init(), init(), vpMatrix::init(), vpMatrix::insert(), vpFeatureEllipse::interaction(), vpFeatureVanishingPoint::interaction(), vpFeatureLuminance::interaction(), vpFeatureSegment::interaction(), vpGenericFeature::interaction(), vpFeatureDepth::interaction(), vpFeaturePoint::interaction(), vpFeatureLine::interaction(), vpFeaturePoint3D::interaction(), vpFeaturePointPolar::interaction(), vpFeatureThetaU::interaction(), vpFeatureTranslation::interaction(), vpMatrix::juxtaposeMatrices(), vpMatrix::kernel(), vpMatrix::loadMatrix(), vpMatrix::mult2Matrices(), vpMatrix::negateMatrix(), vpMatrix::operator*(), vpMatrix::operator/(), vpMatrix::operator=(), vpPose::poseDementhonNonPlan(), vpPose::poseDementhonPlan(), vpPose::poseVirtualVSrobust(), vpMatrix::pseudoInverse(), vpIoTools::readConfigVar(), vpRowVector::reshape(), vpColVector::reshape(), vpRowVector::resize(), vpColVector::resize(), vpServo::secondaryTask(), vpColVector::skew(), vpMatrix::skew(), vpMatrix::stackMatrices(), vpMatrix::sub2Matrices(), vpMatrix::svd(), vpMatrix::t(), vpMatrix::transpose(), and vpMatrix::vpMatrix().

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 2223 of file vpMatrix.cpp.

References vpMatrix::getCols().

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

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

Write an homogeneous matrix in an output file stream.

Parameters
f: Output file stream. The homogeneous matrix is saved as a 4 by 4 matrix.

The code below shows how to save an homogenous matrix in a file.

// Contruct an homogeneous matrix
vpTranslationVector t(1,2,3);
vpRxyzVector r(M_PI, 0, -M_PI/4.);
vpRotationMatrix R(r);
vpHomogeneousMatrix M(t, R);
// Save the content of the matrix in "homogeneous.dat"
std::ofstream f("homogeneous.dat");
M.save(f);
See also
load()
Examples:
servoAfma6Points2DCamVelocityEyeToHand.cpp.

Definition at line 482 of file vpHomogeneousMatrix.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 3409 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 200 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 1108 of file vpMatrix.cpp.

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

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

void vpHomogeneousMatrix::setIdentity ( )

Basic initialisation (identity)

Definition at line 541 of file vpHomogeneousMatrix.cpp.

References init().

Referenced by vpPose::computeTransformation(), vpViper::get_wMe(), vpMbTracker::initClick(), vpMbEdgeTracker::resetTracker(), vpAfma6::vpAfma6(), vpViper::vpViper(), and vpWireFrameSimulator::vpWireFrameSimulator().

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 $ B $.
x: Vector $ X $.

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 1571 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 $ B $.
Returns
Vector $ X $.

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 1626 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 1371 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 1395 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 2261 of file vpMatrix.cpp.

References vpCERROR.

Referenced by vpCalibration::calibrationTsai(), vpHomography::computeDisplacement(), vpHomography::computeRotation(), vpFeatureSegment::error(), vpFeatureEllipse::error(), vpFeatureVanishingPoint::error(), vpFeatureMomentAlpha::error(), vpGenericFeature::error(), vpFeaturePoint::error(), vpFeatureLine::error(), vpFeaturePoint3D::error(), vpFeaturePointPolar::error(), vpFeatureThetaU::error(), vpFeatureTranslation::error(), vpBasicFeature::get_s(), vpFeatureEllipse::interaction(), vpFeatureVanishingPoint::interaction(), vpFeatureSegment::interaction(), vpFeatureMoment::interaction(), vpGenericFeature::interaction(), vpFeaturePoint::interaction(), vpFeatureLine::interaction(), vpFeaturePoint3D::interaction(), vpFeaturePointPolar::interaction(), vpFeatureThetaU::interaction(), vpFeatureTranslation::interaction(), and vpMatrix::stackMatrices().

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 2290 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 2889 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 1406 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 1428 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 560 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, and servoMomentImage.cpp.

Definition at line 758 of file vpMatrix.cpp.

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

Referenced by vpPose::calculArbreDementhon(), vpCalibration::calibrationTsai(), vpHomography::computeDisplacement(), vpHomography::computeResidual(), vpHomography::computeRotation(), 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 $ M $ 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 $ V $.
Returns
Matrix $ U $.
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 1700 of file vpMatrix.cpp.

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

Referenced by vpHomography::computeDisplacement(), vpHomography::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 1174 of file vpMatrix.cpp.

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

Referenced by vpVelocityTwistMatrix::buildFrom(), vpForceTwistMatrix::buildFrom(), buildFrom(), vpCalibration::calibrationTsai(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), vpHomography::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 1204 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 1216 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 
)
related

Multiplication by a scalar Cij = x*Bij.

Definition at line 884 of file vpMatrix.cpp.

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

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

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

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

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

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

For example, to compute 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::incorrectMatrixSizeErrorif 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
related

Enumeration of the operations applied on matrices in vpGEMM function.

Operations are :

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

Definition at line 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::inverseByLU(), 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(), vpHomography::computeResidual(), vpPose::computeTransformation(), vpHomography::computeTransformation(), vpColVector::dotProd(), vpMatrix::eigenValues(), vpMatrix::euclideanNorm(), vpRobotViper850::getForceTorque(), vpMatrix::getMaxValue(), vpMatrix::getMinValue(), vpRobotViper850::getPosition(), vpRobotViper850::getVelocity(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpMatrix::init(), vpRobotViper850::init(), vpColVector::invSort(), vpMatrix::kill(), vpColVector::mean(), vpColVector::median(), vpRowVector::operator*(), vpColVector::operator*(), vpTranslationVector::operator*(), vpHomography::operator*(), vpColVector::operator+(), vpTranslationVector::operator-(), vpColVector::operator-(), vpHomography::operator/(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpTranslationVector::operator=(), vpMatrix::operator=(), vpRowVector::operator[](), vpColVector::operator[](), vpPose::ransac(), vpHomography::ransac(), vpRowVector::reshape(), vpColVector::reshape(), vpMatrix::resize(), vpRobotAfma4::setPosition(), vpRobotViper850::setPosition(), vpRobotAfma4::setVelocity(), vpRobotAfma6::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::inverseByLU(), vpMatrix::kron(), vpMatrix::mult2Matrices(), vpMatrix::multMatrixVector(), vpMatrix::negateMatrix(), vpColVector::operator*(), 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(), 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.

Referenced by vpMatrix::AAt(), vpMatrix::add2Matrices(), vpMatrix::add2WeightedMatrices(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpMatrix::init(), vpMatrix::kill(), vpMatrix::mult2Matrices(), vpMatrix::multMatrixVector(), vpMatrix::negateMatrix(), vpRotationMatrix::operator*(), vpVelocityTwistMatrix::operator*(), vpForceTwistMatrix::operator*(), operator*(), vpMatrix::operator*(), vpMatrix::operator*=(), vpMatrix::operator+=(), vpMatrix::operator-=(), vpMatrix::operator/(), vpMatrix::operator/=(), vpColVector::operator<<(), vpMatrix::operator<<(), vpRowVector::operator=(), vpSubMatrix::operator=(), vpRotationMatrix::operator=(), vpVelocityTwistMatrix::operator=(), vpForceTwistMatrix::operator=(), operator=(), vpMatrix::operator=(), vpMatrix::resize(), vpMatrix::stackColumns(), vpMatrix::sub2Matrices(), vpMatrix::sumSquare(), vpMatrix::transpose(), vpSubColVector::vpSubColVector(), vpSubMatrix::vpSubMatrix(), and vpSubRowVector::vpSubRowVector().

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().