Visual Servoing Platform  version 3.5.0 under development (2022-02-15)
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vpVelocityTwistMatrix Class Reference
core: Core module » Mathematics » Tranformations

#include <visp3/core/vpVelocityTwistMatrix.h>

+ Inheritance diagram for vpVelocityTwistMatrix:

Public Member Functions

 vpVelocityTwistMatrix ()
 
 vpVelocityTwistMatrix (const vpVelocityTwistMatrix &V)
 
 vpVelocityTwistMatrix (const vpHomogeneousMatrix &M, bool full=true)
 
 vpVelocityTwistMatrix (const vpTranslationVector &t, const vpRotationMatrix &R)
 
 vpVelocityTwistMatrix (const vpTranslationVector &t, const vpThetaUVector &thetau)
 
 vpVelocityTwistMatrix (double tx, double ty, double tz, double tux, double tuy, double tuz)
 
 vpVelocityTwistMatrix (const vpRotationMatrix &R)
 
 vpVelocityTwistMatrix (const vpThetaUVector &thetau)
 
virtual ~vpVelocityTwistMatrix ()
 
vpVelocityTwistMatrix buildFrom (const vpTranslationVector &t, const vpRotationMatrix &R)
 
vpVelocityTwistMatrix buildFrom (const vpTranslationVector &t, const vpThetaUVector &thetau)
 
vpVelocityTwistMatrix buildFrom (const vpHomogeneousMatrix &M, bool full=true)
 
vpVelocityTwistMatrix buildFrom (const vpRotationMatrix &R)
 
vpVelocityTwistMatrix buildFrom (const vpThetaUVector &thetau)
 
void extract (vpRotationMatrix &R) const
 
void extract (vpTranslationVector &t) const
 
void eye ()
 
vpVelocityTwistMatrix inverse () const
 
void inverse (vpVelocityTwistMatrix &V) const
 
vpVelocityTwistMatrix operator* (const vpVelocityTwistMatrix &V) const
 
vpMatrix operator* (const vpMatrix &M) const
 
vpColVector operator* (const vpColVector &v) const
 
vpVelocityTwistMatrix & operator= (const vpVelocityTwistMatrix &V)
 
int print (std::ostream &s, unsigned int length, char const *intro=0) const
 
void resize (unsigned int nrows, unsigned int ncols, bool flagNullify=true)
 
bool operator== (const vpArray2D< float > &A) const
 
Deprecated functions
vp_deprecated void init ()
 
vp_deprecated void setIdentity ()
 
Inherited functionalities from vpArray2D
unsigned int getCols () const
 
double getMaxValue () const
 
double getMinValue () const
 
unsigned int getRows () const
 
unsigned int size () const
 
void resize (unsigned int nrows, unsigned int ncols, bool flagNullify=true, bool recopy_=true)
 
void reshape (unsigned int nrows, unsigned int ncols)
 
bool operator== (const vpArray2D< double > &A) const
 
bool operator!= (const vpArray2D< double > &A) const
 
double * operator[] (unsigned int i)
 
double * operator[] (unsigned int i) const
 
vpArray2D< double > hadamard (const vpArray2D< double > &m) const
 

Static Public Member Functions

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

Public Attributes

double * data
 

Protected Attributes

unsigned int rowNum
 
unsigned int colNum
 
double ** rowPtrs
 
unsigned int dsize
 

Friends

class vpMatrix
 

Related Functions

(Note that these are not member functions.)

enum  vpGEMMmethod
 
bool operator== (const vpArray2D< double > &A) const
 
void vpGEMM (const vpArray2D< double > &A, const vpArray2D< double > &B, const double &alpha, const vpArray2D< double > &C, const double &beta, vpArray2D< double > &D, const unsigned int &ops=0)
 

Detailed Description

This class derived from vpArray2D<double> implements the 6 by 6 matrix which transforms velocities from one frame to another. This matrix is also called velocity twist transformation matrix.

The full velocity twist transformation matrix allows to compute the velocity at point a expressed in frame a knowing its velocity at point b expressed in frame b. This matrix is defined as:

\[ ^a{\bf V}_b = \left[\begin{array}{cc} ^a{\bf R}_b & [^a{\bf t}_b]_\times \; ^a{\bf R}_b\\ {\bf 0}_{3\times 3} & ^a{\bf R}_b \end{array} \right] \]

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

There are different ways to initialize such a full velocity twist matrix. The following example shows how to proceed setting the translation and rotation matrix transformations:

#include <visp3/core/vpVelocityTwistMatrix.h>
int main()
{
vpTranslationVector cte(0.1, 0.2, 0.3);
vpRotationMatrix cRe( {0, 0, -1,
0, -1, 0,
-1, 0, 0} );
vpVelocityTwistMatrix cVe(cte, cRe);
std::cout << "cVe:\n" << cVe << std::endl;
}

It produces the following printings:

cVe:
0 0 -1 -0.2 0.3 0
0 -1 0 0.1 0 -0.3
-1 0 0 0 -0.1 0.2
0 0 0 0 0 -1
0 0 0 0 -1 0
0 0 0 -1 0 0

When the point where the velocity is expressed doesn't change, the matrix becomes block diagonal. It allows than to compute the velocity at point b expressed in frame a knowing its velocity at point b expressed in frame b :

\[ ^a{\bf V}_b = \left[\begin{array}{cc} ^a{\bf R}_b & {\bf 0}_{3\times 3} \\ {\bf 0}_{3\times 3} & ^a{\bf R}_b \end{array} \right] \]

To initialize such a velocity twist matrix where translation is not taken into account you can proceed like in the following code:

#include <visp3/core/vpVelocityTwistMatrix.h>
int main()
{
vpRotationMatrix cRe( {0, 0, -1,
0, -1, 0,
-1, 0, 0} );
vpVelocityTwistMatrix cVe(cRe);
std::cout << "cVe:\n" << cVe << std::endl;
}

It produces the following printings:

cVe:
0 0 -1 0 0 0
0 -1 0 0 0 0
-1 0 0 0 0 0
0 0 0 0 0 -1
0 0 0 0 -1 0
0 0 0 -1 0 0

The code below shows how to convert a velocity skew expressed at the origin of the camera frame into the origin of the fix frame using the full velocity twist matrix.

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpVelocityTwistMatrix.h>
int main()
{
vpVelocityTwistMatrix fVc; // Twist transformation matrix from fix to camera frame
vpHomogeneousMatrix fMc; // Fix to camera frame transformation
// ... fMc need here to be initialized
fVc.buildFrom(fMc);
vpColVector c_v(6); // Velocity in the camera frame: vx,vy,vz,wx,wy,wz
// ... c_v should here have an initial value
vpColVector f_v(6); // Velocity in the fix frame: vx,vy,vz,wx,wy,wz
// Compute the velocity in the fix frame
f_v = fVc * c_v;
}
Examples:
manServo4PointsDisplay.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoBebop2.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoFlirPtuIBVS.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPioneerPoint2DDepthWithoutVpServo.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu4Points.cpp, servoSimuCylinder.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuSphere.cpp, servoViper650FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testMatrix.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testTwistMatrix.cpp, testVirtuoseAfma6.cpp, testVirtuoseHapticBox.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 166 of file vpVelocityTwistMatrix.h.

Constructor & Destructor Documentation

◆ vpVelocityTwistMatrix() [1/8]

vpVelocityTwistMatrix::vpVelocityTwistMatrix ( )

Initialize a velocity twist transformation matrix as identity.

Definition at line 85 of file vpVelocityTwistMatrix.cpp.

References eye().

◆ vpVelocityTwistMatrix() [2/8]

vpVelocityTwistMatrix::vpVelocityTwistMatrix ( const vpVelocityTwistMatrix &  V)

Initialize a velocity twist transformation matrix from another velocity twist matrix.

Parameters
V: Velocity twist matrix used as initializer.

Definition at line 93 of file vpVelocityTwistMatrix.cpp.

◆ vpVelocityTwistMatrix() [3/8]

vpVelocityTwistMatrix::vpVelocityTwistMatrix ( const vpHomogeneousMatrix &  M,
bool  full = true 
)
explicit

Initialize a velocity twist transformation matrix from an homogeneous matrix $M$ with

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

Parameters
M: Homogeneous matrix $\bf M$ used to initialize the velocity twist transformation matrix.
full: Boolean used to indicate which matrix should be filled.
  • When set to true, use the complete velocity skew transformation :

    \[ {\bf V} = \left[\begin{array}{cc} {\bf R} & [{\bf t}]_\times \; {\bf R} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

  • When set to false, use the block diagonal velocity skew transformation:

    \[ {\bf V} = \left[\begin{array}{cc} {\bf R} & {\bf 0}_{3\times 3} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

Definition at line 113 of file vpVelocityTwistMatrix.cpp.

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

◆ vpVelocityTwistMatrix() [4/8]

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

Initialize a velocity twist transformation matrix from a translation vector t and a rotation matrix R.

\[ {\bf V} = \left[\begin{array}{cc} {\bf R} & [{\bf t}]_\times \; {\bf R} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

Parameters
t: Translation vector.
R: Rotation matrix.

Definition at line 171 of file vpVelocityTwistMatrix.cpp.

References buildFrom().

◆ vpVelocityTwistMatrix() [5/8]

vpVelocityTwistMatrix::vpVelocityTwistMatrix ( const vpTranslationVector &  t,
const vpThetaUVector &  thetau 
)

Initialize a velocity twist transformation matrix from a translation vector t and a rotation vector with $\theta u $ parametrization.

\[ {\bf V} = \left[\begin{array}{cc} {\bf R} & [{\bf t}]_\times \; {\bf R} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

Parameters
t: Translation vector.
thetau: $\theta u$ rotation vector used to initialize rotation vector $R$ .

Definition at line 135 of file vpVelocityTwistMatrix.cpp.

References buildFrom().

◆ vpVelocityTwistMatrix() [6/8]

vpVelocityTwistMatrix::vpVelocityTwistMatrix ( double  tx,
double  ty,
double  tz,
double  tux,
double  tuy,
double  tuz 
)

Initialize a velocity twist transformation matrix from a translation vector ${\bf t}=(t_x, t_y, t_z)^T$ and a rotation vector with $\theta {\bf u}=(\theta u_x, \theta u_y, \theta u_z)^T $ parametrization.

\[ {\bf V} = \left[\begin{array}{cc} {\bf R} & [{\bf t}]_\times \; {\bf R} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

Parameters
tx,ty,tz: Translation vector in meters.
tux,tuy,tuz: $\theta {\bf u}$ rotation vector expressed in radians used to initialize $R$.

Definition at line 205 of file vpVelocityTwistMatrix.cpp.

References buildFrom().

◆ vpVelocityTwistMatrix() [7/8]

vpVelocityTwistMatrix::vpVelocityTwistMatrix ( const vpRotationMatrix &  R)

Initialize a velocity twist transformation matrix from a rotation matrix R.

\[ {\bf V} = \left[\begin{array}{cc} {\bf R} & {\bf 0}_{3\times 3} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

Parameters
R: Rotation matrix.

Definition at line 188 of file vpVelocityTwistMatrix.cpp.

References buildFrom().

◆ vpVelocityTwistMatrix() [8/8]

vpVelocityTwistMatrix::vpVelocityTwistMatrix ( const vpThetaUVector &  thetau)

Initialize a velocity twist transformation matrix from a rotation vector with $\theta u $ parametrization.

\[ {\bf V} = \left[\begin{array}{cc} {\bf R} & {\bf 0}_{3\times 3}\\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

Parameters
thetau: $\theta u$ rotation vector used to initialize rotation vector $R$ .

Definition at line 153 of file vpVelocityTwistMatrix.cpp.

References buildFrom().

◆ ~vpVelocityTwistMatrix()

virtual vpVelocityTwistMatrix::~vpVelocityTwistMatrix ( )
inlinevirtual

Destructor.

Definition at line 190 of file vpVelocityTwistMatrix.h.

References vpMatrix::extract(), vpMatrix::eye(), vpMatrix::operator*(), vpArray2D< Type >::operator=(), vpMatrix::print(), and vpMatrix::t().

Member Function Documentation

◆ buildFrom() [1/5]

vpVelocityTwistMatrix vpVelocityTwistMatrix::buildFrom ( const vpTranslationVector &  t,
const vpRotationMatrix &  R 
)

Build a velocity twist transformation matrix from a translation vector t and a rotation matrix R.

\[ {\bf V} = \left[\begin{array}{cc} {\bf R} & [{\bf t}]_\times \; {\bf R} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

Parameters
t: Translation vector.
R: Rotation matrix.

Definition at line 364 of file vpVelocityTwistMatrix.cpp.

References vpTranslationVector::skew().

Referenced by buildFrom(), vpMbDepthDenseTracker::computeVVS(), vpMbDepthNormalTracker::computeVVS(), vpMbEdgeKltTracker::computeVVS(), vpMbKltTracker::computeVVS(), vpMbGenericTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbTracker::computeVVSPoseEstimation(), vpUnicycle::get_cVe(), vpPtu46::get_cVe(), vpRobotPtu46::get_cVe(), vpRobotBiclops::get_cVe(), vpRobotFlirPtu::get_cVe(), vpAfma4::get_cVe(), vpViper::get_cVe(), vpBiclops::get_cVe(), vpAfma6::get_cVe(), vpSimulatorAfma6::get_cVe(), vpRobotAfma4::get_cVe(), vpSimulatorViper850::get_cVe(), vpRobotAfma6::get_cVe(), vpRobotViper650::get_cVe(), vpRobotViper850::get_cVe(), vpAfma4::get_cVf(), inverse(), vpRobotAfma4::setVelocity(), vpMbGenericTracker::track(), and vpVelocityTwistMatrix().

◆ buildFrom() [2/5]

vpVelocityTwistMatrix vpVelocityTwistMatrix::buildFrom ( const vpTranslationVector &  t,
const vpThetaUVector &  thetau 
)

Initialize a velocity twist transformation matrix from a translation vector t and a rotation vector with $\theta u $ parametrization.

\[ {\bf V} = \left[\begin{array}{cc} {\bf R} & [{\bf t}]_\times \; {\bf R} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

Parameters
t: Translation vector.
thetau: $\theta {\bf u}$ rotation vector used to create rotation matrix ${\bf R}$.

Definition at line 394 of file vpVelocityTwistMatrix.cpp.

References buildFrom().

◆ buildFrom() [3/5]

vpVelocityTwistMatrix vpVelocityTwistMatrix::buildFrom ( const vpHomogeneousMatrix &  M,
bool  full = true 
)

Initialize a velocity twist transformation matrix from an homogeneous matrix $M$ with

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

Parameters
M: Homogeneous matrix $M$ used to initialize the velocity twist transformation matrix.
full: Boolean used to indicate which matrix should be filled.
  • When set to true, use the complete velocity skew transformation :

    \[ {\bf V} = \left[\begin{array}{cc} {\bf R} & [{\bf t}]_\times \; {\bf R} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

  • When set to false, use the block diagonal velocity skew transformation:

    \[ {\bf V} = \left[\begin{array}{cc} {\bf R} & {\bf 0}_{3\times 3} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

Definition at line 436 of file vpVelocityTwistMatrix.cpp.

References buildFrom(), vpHomogeneousMatrix::getRotationMatrix(), and vpHomogeneousMatrix::getTranslationVector().

◆ buildFrom() [4/5]

vpVelocityTwistMatrix vpVelocityTwistMatrix::buildFrom ( const vpRotationMatrix &  R)

Build a velocity twist transformation block diagonal matrix from a rotation matrix R.

\[ {\bf V} = \left[\begin{array}{cc} {\bf R} & {\bf 0}_{3\times 3} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

Parameters
R: Rotation matrix.

Definition at line 338 of file vpVelocityTwistMatrix.cpp.

◆ buildFrom() [5/5]

vpVelocityTwistMatrix vpVelocityTwistMatrix::buildFrom ( const vpThetaUVector &  thetau)

Initialize a velocity twist transformation matrix from a rotation vector with $\theta u $ parametrization.

\[ {\bf V} = \left[\begin{array}{cc} {\bf R} & {\bf 0}_{3\times 3} \\ {\bf 0}_{3\times 3} & {\bf R} \end{array} \right] \]

Parameters
thetau: $\theta {\bf u}$ rotation vector used to create rotation matrix ${\bf R}$.

Definition at line 412 of file vpVelocityTwistMatrix.cpp.

References buildFrom().

◆ extract() [1/2]

void vpVelocityTwistMatrix::extract ( vpRotationMatrix &  R) const

Extract the rotation matrix from the velocity twist matrix.

Definition at line 466 of file vpVelocityTwistMatrix.cpp.

Referenced by extract(), and inverse().

◆ extract() [2/2]

void vpVelocityTwistMatrix::extract ( vpTranslationVector &  t) const

Extract the translation vector from the velocity twist matrix.

Definition at line 474 of file vpVelocityTwistMatrix.cpp.

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

◆ eye()

void vpVelocityTwistMatrix::eye ( )

Initialize a 6x6 velocity twist matrix as identity.

Definition at line 72 of file vpVelocityTwistMatrix.cpp.

Referenced by setIdentity(), and vpVelocityTwistMatrix().

◆ getCols()

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

Return the number of columns of the 2D array.

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

Definition at line 279 of file vpArray2D.h.

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

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

◆ getMaxValue()

double vpArray2D< double >::getMaxValue ( ) const
inherited

Return the array max value.

Examples:
servoMomentImage.cpp, and testArray2D.cpp.

Definition at line 912 of file vpArray2D.h.

References vpArray2D< Type >::data.

◆ getMinValue()

double vpArray2D< double >::getMinValue ( ) const
inherited

Return the array min value.

Examples:
servoMomentImage.cpp, and testArray2D.cpp.

Definition at line 895 of file vpArray2D.h.

References vpArray2D< Type >::data.

◆ getRows()

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

Return the number of rows of the 2D array.

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

Definition at line 289 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

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

◆ hadamard()

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

Compute the Hadamard product (element wise matrix multiplication).

Parameters
m: Second matrix;
Returns
m1.hadamard(m2) The Hadamard product : $ m1 \circ m2 = (m1 \circ m2)_{i,j} = (m1)_{i,j} (m2)_{i,j} $
Examples:
testArray2D.cpp.

Definition at line 932 of file vpArray2D.h.

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

◆ init()

vp_deprecated void vpVelocityTwistMatrix::init ( )
inline
Deprecated:
Provided only for compat with previous releases. This function does nothing.

Definition at line 237 of file vpVelocityTwistMatrix.h.

References vpMatrix::setIdentity().

◆ inverse() [1/2]

vpVelocityTwistMatrix vpVelocityTwistMatrix::inverse ( ) const

Invert the velocity twist matrix.

Definition at line 447 of file vpVelocityTwistMatrix.cpp.

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

Referenced by inverse().

◆ inverse() [2/2]

void vpVelocityTwistMatrix::inverse ( vpVelocityTwistMatrix &  V) const

Invert the velocity twist matrix.

Definition at line 463 of file vpVelocityTwistMatrix.cpp.

References inverse().

◆ load()

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

Load a matrix from a file.

Parameters
filename: Absolute file name.
A: Array to be loaded
binary: If true the matrix is loaded from a binary file, else from a text file.
header: Header of the file is loaded in this parameter.
Returns
Returns true if success.
See also
save()

Definition at line 540 of file vpArray2D.h.

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

◆ loadYAML()

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

Load an array from a YAML-formatted file.

Parameters
filename: absolute file name.
A: array to be loaded from the file.
header: header of the file is loaded in this parameter.
Returns
Returns true on success.
See also
saveYAML()
Examples:
servoFlirPtuIBVS.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, tutorial-flir-ptu-ibvs.cpp, and tutorial-hand-eye-calibration.cpp.

Definition at line 652 of file vpArray2D.h.

References vpArray2D< Type >::resize().

◆ operator!=()

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

Not equal to comparison operator of a 2D array.

Definition at line 996 of file vpArray2D.h.

◆ operator*() [1/3]

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

Operator that allows to multiply a velocity twist transformation matrix by an other velocity twist transformation matrix.

Definition at line 219 of file vpVelocityTwistMatrix.cpp.

References vpArray2D< double >::rowPtrs, and vpArray2D< Type >::rowPtrs.

◆ operator*() [2/3]

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

Operator that allows to multiply a velocity twist transformation matrix by a matrix.

As shown in the example below, this operator can be used to compute the corresponding camera velocity skew from the joint velocities knowing the robot jacobian.

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpConfig.h>
#include <visp3/core/vpVelocityTwistMatrix.h>
#include <visp3/robot/vpSimulatorCamera.h>
int main()
{
vpSimulatorCamera robot;
vpColVector q_vel(6); // Joint velocity on the 6 joints
// ... q_vel need here to be initialized
vpColVector c_v(6); // Velocity in the camera frame: vx,vy,vz,wx,wy,wz
vpVelocityTwistMatrix cVe; // Velocity skew transformation from camera frame to end-effector
robot.get_cVe(cVe);
vpMatrix eJe; // Robot jacobian
robot.get_eJe(eJe);
// Compute the velocity in the camera frame
c_v = cVe * eJe * q_vel;
return 0;
}
Exceptions
vpException::dimensionErrorIf M is not a 6 rows dimension matrix.

Definition at line 273 of file vpVelocityTwistMatrix.cpp.

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

◆ operator*() [3/3]

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

Operator that allows to multiply a twist transformation matrix by a 6-dimension column vector.

Parameters
v: Velocity skew vector.
Exceptions
vpException::dimensionErrorIf v is not a 6 dimension column vector.

Definition at line 303 of file vpVelocityTwistMatrix.cpp.

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

◆ operator=()

vpVelocityTwistMatrix & vpVelocityTwistMatrix::operator= ( const vpVelocityTwistMatrix &  V)

Copy operator that allow to set a velocity twist matrix from an other one.

Parameters
V: Velocity twist matrix to copy.

Definition at line 58 of file vpVelocityTwistMatrix.cpp.

References vpArray2D< double >::rowPtrs, and vpArray2D< Type >::rowPtrs.

◆ operator==() [1/2]

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

Equal to comparison operator of a 2D array.

Definition at line 948 of file vpArray2D.h.

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

◆ operator==() [2/2]

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

Definition at line 981 of file vpArray2D.h.

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

◆ operator[]() [1/2]

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

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

Definition at line 484 of file vpArray2D.h.

◆ operator[]() [2/2]

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

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

Definition at line 486 of file vpArray2D.h.

◆ print()

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

Pretty print a velocity twist 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<<(std::ostream &s, const vpArray2D<Type> &A)
Examples:
testTwistMatrix.cpp.

Definition at line 508 of file vpVelocityTwistMatrix.cpp.

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

◆ reshape()

void vpArray2D< double >::reshape ( unsigned int  nrows,
unsigned int  ncols 
)
inlineinherited
Examples:
testMatrixInitialization.cpp.

Definition at line 379 of file vpArray2D.h.

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

◆ resize() [1/2]

void vpVelocityTwistMatrix::resize ( unsigned int  nrows,
unsigned int  ncols,
bool  flagNullify = true 
)
inline

This function is not applicable to a velocity twist matrix that is always a 6-by-6 matrix.

Exceptions
vpException::fatalErrorWhen this function is called.

Definition at line 220 of file vpVelocityTwistMatrix.h.

References vpException::fatalError.

◆ resize() [2/2]

void vpArray2D< double >::resize ( unsigned int  nrows,
unsigned int  ncols,
bool  flagNullify = true,
bool  recopy_ = true 
)
inlineinherited

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

Parameters
nrows: number of rows.
ncols: number of column.
flagNullify: if true, then the array is re-initialized to 0 after resize. If false, the initial values from the common part of the array (common part between old and new version of the array) are kept. Default value is true.
recopy_: if true, will perform an explicit recopy of the old data.
Examples:
testArray2D.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixDeterminant.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 304 of file vpArray2D.h.

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

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

◆ save()

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

Save a matrix to a file.

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

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

See also
load()

Definition at line 737 of file vpArray2D.h.

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

◆ saveYAML()

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

Save an array in a YAML-formatted file.

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

Here is an example of outputs.

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

Content of matrix.yml:

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

Content of matrixIndent.yml:

example:
- a YAML-formatted header
- with inner indentation
rows: 3
cols: 4
data:
- [0, 0, 0, 0]
- [0, 0, 0, 0]
- [0, 0, 0, 0]
See also
loadYAML()
Examples:
tutorial-chessboard-pose.cpp, tutorial-franka-acquire-calib-data.cpp, and tutorial-hand-eye-calibration.cpp.

Definition at line 830 of file vpArray2D.h.

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

◆ setIdentity()

void vpVelocityTwistMatrix::setIdentity ( )
Deprecated:
You should rather use eye().
Deprecated:
You should rather use eye().

Set the velocity twist transformation matrix to identity.

Definition at line 603 of file vpVelocityTwistMatrix.cpp.

References eye().

◆ size()

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

Return the number of elements of the 2D array.

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

Definition at line 291 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

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

Friends And Related Function Documentation

◆ operator==()

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

Definition at line 966 of file vpArray2D.h.

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

◆ vpGEMM()

void vpGEMM ( const vpArray2D< double > &  A,
const vpArray2D< double > &  B,
const double &  alpha,
const vpArray2D< double > &  C,
const double &  beta,
vpArray2D< double > &  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 D = alpha*A^T*B^T+beta*C we need to call :

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

If C is not used, vpGEMM must be called using an empty array null. Thus to compute D = alpha*A^T*B, we have to call:

vpGEMM(A, B, alpha, null, 0, D, VP_GEMM_B_T);
Exceptions
vpException::incorrectMatrixSizeErrorif the sizes of the matrices do not allow the operations.
Parameters
A: An array that could be a vpMatrix.
B: An array that could be a vpMatrix.
alpha: A scalar.
C: An array that could be a vpMatrix.
beta: A scalar.
D: The resulting array that could be a vpMatrix.
ops: A scalar describing operation applied on the matrices. Possible values are the one defined in vpGEMMmethod(): VP_GEMM_A_T, VP_GEMM_B_T, VP_GEMM_C_T.

Definition at line 393 of file vpGEMM.h.

References vpException::functionNotImplementedError.

◆ vpGEMMmethod

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 57 of file vpGEMM.h.

◆ vpMatrix

friend class vpMatrix
friend

Definition at line 168 of file vpVelocityTwistMatrix.h.

Member Data Documentation

◆ colNum

unsigned int vpArray2D< double >::colNum
protectedinherited

Number of columns in the array.

Definition at line 137 of file vpArray2D.h.

Referenced by vpMatrix::AAt(), vpMatrix::AtA(), vpColVector::clear(), vpMatrix::detByLU(), vpMatrix::detByLUEigen3(), vpMatrix::detByLULapack(), vpMatrix::detByLUOpenCV(), vpMatrix::diag(), vpMatrix::eigenValues(), vpMatrix::expm(), vpMatrix::eye(), vpMatrix::getDiag(), vpMatrix::getRow(), vpColVector::hadamard(), vpMatrix::hadamard(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpRowVector::insert(), vpMatrix::insert(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByCholeskyOpenCV(), vpMatrix::inverseByLU(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByLULapack(), vpMatrix::inverseByLUOpenCV(), vpMatrix::inverseByQRLapack(), vpMatrix::inverseTriangular(), vpRotationMatrix::operator*(), vpRowVector::operator*(), vpMatrix::operator*(), vpRotationMatrix::operator*=(), vpRowVector::operator*=(), vpMatrix::operator*=(), vpRowVector::operator+(), vpRowVector::operator+=(), vpMatrix::operator+=(), vpRowVector::operator,(), vpMatrix::operator,(), vpRowVector::operator-(), vpRowVector::operator-=(), vpMatrix::operator-=(), vpRowVector::operator/(), vpMatrix::operator/(), vpRowVector::operator/=(), vpMatrix::operator/=(), vpColVector::operator<<(), vpMatrix::operator<<(), vpSubRowVector::operator=(), vpSubMatrix::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpRowVector::operator==(), vpColVector::operator==(), vpMatrix::qr(), vpMatrix::qrPivot(), vpRowVector::reshape(), vpMatrix::setIdentity(), vpMatrix::solveByQR(), vpMatrix::solveBySVD(), vpRowVector::stack(), vpMatrix::stack(), vpMatrix::stackColumns(), vpMatrix::stackRows(), vpRowVector::sum(), vpMatrix::sum(), vpRowVector::sumSquare(), vpMatrix::sumSquare(), vpMatrix::svdLapack(), vpRowVector::t(), vpMatrix::transpose(), vpColVector::vpColVector(), vpMatrix::vpMatrix(), and vpRowVector::vpRowVector().

◆ data

double * vpArray2D< double >::data
inherited

Address of the first element of the data array.

Examples:
testArray2D.cpp, testDisplacement.cpp, testEigenConversion.cpp, testImageFilter.cpp, testMatrix.cpp, testTranslationVector.cpp, tutorial-bridge-opencv-matrix.cpp, and tutorial-matlab.cpp.

Definition at line 145 of file vpArray2D.h.

Referenced by vpMatrix::AAt(), vpMatrix::AtA(), vpQuaternionVector::buildFrom(), vpHomogeneousMatrix::buildFrom(), vpThetaUVector::buildFrom(), vpRzyzVector::buildFrom(), vpRxyzVector::buildFrom(), vpRzyxVector::buildFrom(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpColVector::clear(), vpHomogeneousMatrix::convert(), vpMatrix::detByLUEigen3(), vpMatrix::detByLUOpenCV(), vpMatrix::expm(), vpThetaUVector::extract(), vpMatrix::frobeniusNorm(), vpMatrix::getRow(), vpThetaUVector::getTheta(), vpThetaUVector::getU(), vpColVector::hadamard(), vpMatrix::hadamard(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpColVector::insert(), vpMatrix::insert(), vpMatrix::inverseByCholeskyOpenCV(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByLUOpenCV(), vpTranslationVector::operator*(), vpRowVector::operator*(), vpHomography::operator*(), vpColVector::operator*(), vpMatrix::operator*(), vpRotationVector::operator,(), vpTranslationVector::operator,(), vpRotationMatrix::operator,(), vpHomogeneousMatrix::operator,(), vpRowVector::operator,(), vpColVector::operator,(), vpTranslationVector::operator-(), vpRowVector::operator-(), vpColVector::operator-(), vpTranslationVector::operator/(), vpRowVector::operator/(), vpHomography::operator/(), vpColVector::operator/(), vpHomography::operator/=(), vpRotationVector::operator<<(), vpTranslationVector::operator<<(), vpRotationMatrix::operator<<(), vpHomogeneousMatrix::operator<<(), vpRowVector::operator<<(), vpColVector::operator<<(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpQuaternionVector::operator=(), vpTranslationVector::operator=(), vpRotationMatrix::operator=(), vpRxyzVector::operator=(), vpRzyzVector::operator=(), vpRzyxVector::operator=(), vpRowVector::operator=(), vpThetaUVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpRowVector::operator==(), vpColVector::operator==(), vpColVector::operator[](), vpMatrix::qr(), vpMatrix::qrPivot(), vpRowVector::reshape(), vpColVector::reshape(), vpQuaternionVector::set(), vpMatrix::stack(), vpMatrix::stackRows(), vpColVector::sum(), vpColVector::sumSquare(), vpMatrix::svdEigen3(), vpMatrix::svdLapack(), vpMatrix::svdOpenCV(), vpRotationVector::t(), vpTranslationVector::t(), vpPoseVector::t(), vpRowVector::t(), vpColVector::t(), vpRotationVector::toStdVector(), vpRowVector::toStdVector(), vpColVector::toStdVector(), vpMatrix::transpose(), vpColVector::vpColVector(), vpHomogeneousMatrix::vpHomogeneousMatrix(), vpMatrix::vpMatrix(), vpRowVector::vpRowVector(), vpQuaternionVector::w(), vpQuaternionVector::x(), vpQuaternionVector::y(), vpQuaternionVector::z(), vpSubColVector::~vpSubColVector(), vpSubMatrix::~vpSubMatrix(), and vpSubRowVector::~vpSubRowVector().

◆ dsize

unsigned int vpArray2D< double >::dsize
protectedinherited

Current array size (rowNum * colNum)

Definition at line 141 of file vpArray2D.h.

Referenced by vpColVector::clear(), vpMatrix::frobeniusNorm(), vpMatrix::hadamard(), vpMatrix::inducedL2Norm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpRotationVector::operator*(), vpTranslationVector::operator*(), vpTranslationVector::operator-(), vpTranslationVector::operator/(), vpRotationMatrix::operator=(), vpRxyzVector::operator=(), vpRzyzVector::operator=(), vpRzyxVector::operator=(), vpThetaUVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpRowVector::reshape(), vpColVector::reshape(), vpRotationVector::t(), vpColVector::vpColVector(), vpMatrix::vpMatrix(), and vpRowVector::vpRowVector().

◆ rowNum

unsigned int vpArray2D< double >::rowNum
protectedinherited

Number of rows in the array.

Definition at line 135 of file vpArray2D.h.

Referenced by vpMatrix::AAt(), vpMatrix::AtA(), vpColVector::clear(), vpMatrix::detByLU(), vpMatrix::detByLUEigen3(), vpMatrix::detByLULapack(), vpMatrix::detByLUOpenCV(), vpMatrix::diag(), vpMatrix::eigenValues(), vpMatrix::expm(), vpColVector::extract(), vpMatrix::eye(), vpMatrix::getCol(), vpMatrix::getDiag(), vpMatrix::getRow(), vpColVector::hadamard(), vpMatrix::hadamard(), vpColVector::infinityNorm(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpMatrix::insert(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByCholeskyOpenCV(), vpMatrix::inverseByLU(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByLULapack(), vpMatrix::inverseByLUOpenCV(), vpMatrix::inverseByQRLapack(), vpMatrix::inverseTriangular(), vpTranslationVector::operator*(), vpRotationMatrix::operator*(), vpHomogeneousMatrix::operator*(), vpColVector::operator*(), vpMatrix::operator*(), vpTranslationVector::operator*=(), vpRotationMatrix::operator*=(), vpColVector::operator*=(), vpMatrix::operator*=(), vpColVector::operator+(), vpColVector::operator+=(), vpMatrix::operator+=(), vpColVector::operator,(), vpColVector::operator-(), vpColVector::operator-=(), vpMatrix::operator-=(), vpColVector::operator/(), vpMatrix::operator/(), vpTranslationVector::operator/=(), vpColVector::operator/=(), vpMatrix::operator/=(), vpColVector::operator<<(), vpMatrix::operator<<(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpSubMatrix::operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpRowVector::operator==(), vpColVector::operator==(), vpMatrix::qr(), vpMatrix::qrPivot(), vpColVector::reshape(), vpMatrix::setIdentity(), vpMatrix::stack(), vpColVector::stack(), vpMatrix::stackColumns(), vpMatrix::stackRows(), vpColVector::sum(), vpMatrix::sum(), vpRotationVector::sumSquare(), vpTranslationVector::sumSquare(), vpColVector::sumSquare(), vpMatrix::sumSquare(), vpMatrix::svdLapack(), vpTranslationVector::t(), vpPoseVector::t(), vpColVector::t(), vpMatrix::transpose(), vpColVector::vpColVector(), vpMatrix::vpMatrix(), and vpRowVector::vpRowVector().

◆ rowPtrs

double ** vpArray2D< double >::rowPtrs
protectedinherited

Address of the first element of each rows.

Definition at line 139 of file vpArray2D.h.

Referenced by vpMatrix::AAt(), vpColVector::clear(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpRowVector::init(), vpColVector::init(), vpMatrix::init(), vpRotationMatrix::operator*(), vpForceTwistMatrix::operator*(), operator*(), vpHomogeneousMatrix::operator*(), vpMatrix::operator*(), vpRotationMatrix::operator*=(), vpMatrix::operator*=(), vpMatrix::operator+=(), vpMatrix::operator,(), vpMatrix::operator-=(), vpMatrix::operator/(), vpMatrix::operator/=(), vpColVector::operator<<(), vpMatrix::operator<<(), vpSubMatrix::operator=(), vpRotationMatrix::operator=(), vpForceTwistMatrix::operator=(), operator=(), vpHomogeneousMatrix::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpMatrix::stack(), vpMatrix::stackColumns(), vpRowVector::sum(), vpMatrix::sum(), vpRotationVector::sumSquare(), vpTranslationVector::sumSquare(), vpRowVector::sumSquare(), vpMatrix::sumSquare(), vpColVector::vpColVector(), vpMatrix::vpMatrix(), and vpRowVector::vpRowVector().