Visual Servoing Platform  version 3.2.0 under development (2018-12-11)
vpQuaternionVector Class Reference

#include <visp3/core/vpQuaternionVector.h>

+ Inheritance diagram for vpQuaternionVector:

Public Member Functions

 vpQuaternionVector ()
 
 vpQuaternionVector (const vpQuaternionVector &q)
 
 vpQuaternionVector (const double qx, const double qy, const double qz, const double qw)
 
 vpQuaternionVector (const vpRotationMatrix &R)
 
 vpQuaternionVector (const vpThetaUVector &tu)
 
 vpQuaternionVector (const vpColVector &q)
 
 vpQuaternionVector (const std::vector< double > &q)
 
virtual ~vpQuaternionVector ()
 
vpQuaternionVector buildFrom (const double qx, const double qy, const double qz, const double qw)
 
vpQuaternionVector buildFrom (const vpRotationMatrix &R)
 
vpQuaternionVector buildFrom (const vpThetaUVector &tu)
 
vpQuaternionVector buildFrom (const vpColVector &q)
 
vpQuaternionVector buildFrom (const std::vector< double > &q)
 
void set (const double x, const double y, const double z, const double w)
 
double x () const
 
double y () const
 
double z () const
 
double w () const
 
vpQuaternionVector operator+ (const vpQuaternionVector &q) const
 
vpQuaternionVector operator- (const vpQuaternionVector &q) const
 
vpQuaternionVector operator- () const
 
vpQuaternionVector operator* (const double l) const
 
vpQuaternionVector operator* (const vpQuaternionVector &rq) const
 
vpQuaternionVector operator/ (const double l) const
 
vpQuaternionVectoroperator= (const vpColVector &q)
 
vpQuaternionVector conjugate () const
 
vpQuaternionVector inverse () const
 
double magnitude () const
 
void normalize ()
 
Inherited functionalities from vpRotationVector
double & operator[] (unsigned int i)
 
const double & operator[] (unsigned int i) const
 
double sumSquare () const
 
vpRowVector t () const
 
std::vector< double > toStdVector ()
 
Inherited functionalities from vpArray2D
unsigned int getCols () const
 
double getMaxValue () const
 
double getMinValue () const
 
unsigned int getRows () const
 
unsigned int size () const
 
void resize (const unsigned int nrows, const unsigned int ncols, const bool flagNullify=true, const bool recopy_=true)
 
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, const bool binary=false, char *header=NULL)
 
static bool loadYAML (const std::string &filename, vpArray2D< double > &A, char *header=NULL)
 
static bool save (const std::string &filename, const vpArray2D< double > &A, const bool binary=false, const char *header="")
 
static bool saveYAML (const std::string &filename, const vpArray2D< double > &A, const char *header="")
 

Public Attributes

double * data
 

Protected Attributes

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

Related Functions

(Note that these are not member functions.)

vpColVector operator* (const double &x, const vpRotationVector &v)
 
enum  vpGEMMmethod
 

Detailed Description

Implementation of a rotation vector as quaternion angle minimal representation.

Defines a quaternion and its basic operations.

The vpQuaternionVector class is derived from vpRotationVector.

A quaternion is defined by four values: ${\bf q} = (x, y, z, w)$.

This class allows to compute a quaternion from a rotation matrix using either vpQuaternionVector(const vpRotationMatrix &) constructor or buildFrom() method.

It also defines common operations on a quaternion such as:

  • multiplication (scalar and quaternion)
  • addition
  • substraction.
Examples:
tutorial-pose-from-qrcode-image.cpp.

Definition at line 79 of file vpQuaternionVector.h.

Constructor & Destructor Documentation

vpQuaternionVector::vpQuaternionVector ( )

Default constructor that initialize all the 4 angles to zero.

Definition at line 54 of file vpQuaternionVector.cpp.

Referenced by conjugate(), operator*(), operator+(), operator-(), and operator/().

vpQuaternionVector::vpQuaternionVector ( const vpQuaternionVector q)

Copy constructor.

Definition at line 57 of file vpQuaternionVector.cpp.

vpQuaternionVector::vpQuaternionVector ( const double  qx,
const double  qy,
const double  qz,
const double  qw 
)

Constructor from doubles.

Definition at line 60 of file vpQuaternionVector.cpp.

vpQuaternionVector::vpQuaternionVector ( const vpRotationMatrix R)
explicit

Constructs a quaternion from a rotation matrix.

Parameters
R: Matrix containing a rotation.

Definition at line 83 of file vpQuaternionVector.cpp.

References buildFrom().

vpQuaternionVector::vpQuaternionVector ( const vpThetaUVector tu)
explicit

Constructor that initialize $R_{xyz}=(\varphi,\theta,\psi)$ Euler angles vector from a $\theta {\bf u}$ vector.

Parameters
tu: $\theta {\bf u}$ representation of a rotation used here as input to initialize the Euler angles.

Definition at line 91 of file vpQuaternionVector.cpp.

References buildFrom().

vpQuaternionVector::vpQuaternionVector ( const vpColVector q)
explicit

Constructor from a 4-dimension vector of doubles.

Definition at line 67 of file vpQuaternionVector.cpp.

References buildFrom().

vpQuaternionVector::vpQuaternionVector ( const std::vector< double > &  q)
explicit

Constructor from a 4-dimension vector of doubles.

Definition at line 73 of file vpQuaternionVector.cpp.

References buildFrom().

virtual vpQuaternionVector::~vpQuaternionVector ( )
inlinevirtual

Destructor.

Definition at line 94 of file vpQuaternionVector.h.

References vpRotationVector::operator*(), and vpRotationVector::operator=().

Member Function Documentation

vpQuaternionVector vpQuaternionVector::buildFrom ( const double  qx,
const double  qy,
const double  qz,
const double  qw 
)

Manually change values of a quaternion.

Parameters
qx: x quaternion parameter.
qy: y quaternion parameter.
qz: z quaternion parameter.
qw: w quaternion parameter.
See also
set()

Definition at line 116 of file vpQuaternionVector.cpp.

Referenced by buildFrom(), vpPoseVector::extract(), vpHomogeneousMatrix::extract(), and vpQuaternionVector().

vpQuaternionVector vpQuaternionVector::buildFrom ( const vpRotationMatrix R)

Constructs a quaternion from a rotation matrix.

Parameters
R: Rotation matrix.

Definition at line 257 of file vpQuaternionVector.cpp.

References vpThetaUVector::extract().

vpQuaternionVector vpQuaternionVector::buildFrom ( const vpThetaUVector tu)

Convert a $\theta {\bf u}$ vector into a quaternion.

Parameters
tu: $\theta {\bf u}$ representation of a rotation used here as input.
Returns
Quaternion vector.

Definition at line 128 of file vpQuaternionVector.cpp.

References buildFrom().

vpQuaternionVector vpQuaternionVector::buildFrom ( const vpColVector q)

Construct a quaternion vector from a 4-dim vector (x,y,z,w).

Definition at line 139 of file vpQuaternionVector.cpp.

References vpArray2D< double >::data, vpException::dimensionError, and vpArray2D< Type >::size().

vpQuaternionVector vpQuaternionVector::buildFrom ( const std::vector< double > &  q)

Construct a quaternion vector from a 4-dim vector (x,y,z,w).

Definition at line 154 of file vpQuaternionVector.cpp.

References vpArray2D< double >::data, and vpException::dimensionError.

vpQuaternionVector vpQuaternionVector::conjugate ( ) const

Quaternion conjugate.

Returns
The conjugate quaternion.

Definition at line 276 of file vpQuaternionVector.cpp.

References vpQuaternionVector(), w(), x(), y(), and z().

Referenced by inverse().

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

Return the array max value.

Examples:
servoMomentImage.cpp, testArray2D.cpp, and testMatrix.cpp.
double vpArray2D< double >::getMinValue ( ) const
inherited

Return the array min value.

Examples:
servoMomentImage.cpp, testArray2D.cpp, and testMatrix.cpp.
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.
vpQuaternionVector vpQuaternionVector::inverse ( ) const

Quaternion inverse.

Returns
The inverse quaternion.

Definition at line 283 of file vpQuaternionVector.cpp.

References conjugate(), vpMath::nul(), w(), x(), y(), and z().

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

Load a matrix from a file.

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

Definition at line 316 of file vpArray2D.h.

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

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:
servoFrankaPBVS.cpp, and tutorial-hand-eye-calibration.cpp.

Definition at line 424 of file vpArray2D.h.

References vpArray2D< Type >::resize().

double vpQuaternionVector::magnitude ( ) const

Quaternion magnitude or norm.

Returns
The magnitude or norm of the quaternion.

Definition at line 302 of file vpQuaternionVector.cpp.

References w(), x(), y(), and z().

Referenced by normalize().

void vpQuaternionVector::normalize ( )

Normalize the quaternion.

Definition at line 307 of file vpQuaternionVector.cpp.

References magnitude(), vpMath::nul(), w(), x(), y(), and z().

vpQuaternionVector vpQuaternionVector::operator* ( const double  l) const

Multiplication by scalar. Returns a quaternion defined by (lx,ly,lz,lw).

Definition at line 193 of file vpQuaternionVector.cpp.

References vpQuaternionVector(), w(), x(), y(), and z().

vpQuaternionVector vpQuaternionVector::operator* ( const vpQuaternionVector rq) const

Multiply two quaternions.

Definition at line 199 of file vpQuaternionVector.cpp.

References vpQuaternionVector(), w(), x(), y(), and z().

vpQuaternionVector vpQuaternionVector::operator+ ( const vpQuaternionVector q) const

Quaternion addition.

Adds two quaternions. Addition is component-wise.

Parameters
q: quaternion to add.

Definition at line 173 of file vpQuaternionVector.cpp.

References vpQuaternionVector(), w(), x(), y(), and z().

vpQuaternionVector vpQuaternionVector::operator- ( const vpQuaternionVector q) const

Quaternion substraction.

Substracts a quaternion from another. Substraction is component-wise.

Parameters
q: quaternion to substract.

Definition at line 184 of file vpQuaternionVector.cpp.

References vpQuaternionVector(), w(), x(), y(), and z().

vpQuaternionVector vpQuaternionVector::operator- ( void  ) const

Negate operator. Returns a quaternion defined by (-x,-y,-z-,-w).

Definition at line 190 of file vpQuaternionVector.cpp.

References vpQuaternionVector(), w(), x(), y(), and z().

vpQuaternionVector vpQuaternionVector::operator/ ( const double  l) const

Division by scalar. Returns a quaternion defined by (x/l,y/l,z/l,w/l).

Definition at line 208 of file vpQuaternionVector.cpp.

References vpException::fatalError, vpMath::nul(), vpQuaternionVector(), w(), x(), y(), and z().

vpQuaternionVector & vpQuaternionVector::operator= ( const vpColVector q)

Copy operator that initializes a quaternion vector from a 4-dimension column vector q.

Parameters
q: 4-dimension vector containing the values of the quaternion vector.
#include <visp3/core/vpQuaternionVector.h>
int main()
{
v[0] = 0.1;
v[1] = 0.2;
v[2] = 0.3;
v[3] = 0.4;
q = v;
// q is now equal to v : 0.1, 0.2, 0.3, 0.4
}

Definition at line 240 of file vpQuaternionVector.cpp.

References vpArray2D< double >::data, vpException::dimensionError, and vpArray2D< Type >::size().

double& vpRotationVector::operator[] ( unsigned int  i)
inlineinherited

Operator that allows to set the value of an element of the rotation vector: r[i] = value

Definition at line 127 of file vpRotationVector.h.

const double& vpRotationVector::operator[] ( unsigned int  i) const
inlineinherited

Operator that allows to get the value of an element of the rotation vector: value = r[i]

Definition at line 132 of file vpRotationVector.h.

void vpArray2D< double >::resize ( const unsigned int  nrows,
const unsigned int  ncols,
const bool  flagNullify = true,
const 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 if needed and if flagNullify is set to false.
Examples:
testArray2D.cpp, testMatrix.cpp, testMatrixDeterminant.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 171 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=(), and vpMatrix::stack().

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

Save a matrix to a file.

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

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

See also
load()

Definition at line 506 of file vpArray2D.h.

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

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::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
- [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
- [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 595 of file vpArray2D.h.

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

void vpQuaternionVector::set ( const double  qx,
const double  qy,
const double  qz,
const double  qw 
)

Manually change values of a quaternion.

Parameters
qx: x quaternion parameter.
qy: y quaternion parameter.
qz: z quaternion parameter.
qw: w quaternion parameter.

Definition at line 100 of file vpQuaternionVector.cpp.

References vpArray2D< double >::data.

double vpRotationVector::sumSquare ( ) const
inherited

Return the sum square of all the elements $r_{i}$ of the rotation vector r(m).

Returns
The value

\[\sum{i=0}^{m} r_i^{2}\]

.
Examples:
servoFrankaPBVS.cpp.

Definition at line 115 of file vpRotationVector.cpp.

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

vpRowVector vpRotationVector::t ( ) const
inherited

Return the transpose of the rotation vector.

Examples:
testViper650.cpp, and testViper850.cpp.

Definition at line 56 of file vpRotationVector.cpp.

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

std::vector< double > vpRotationVector::toStdVector ( )
inherited

Converts the vpRotationVector to a std::vector.

Returns
The corresponding std::vector<double>.

Definition at line 70 of file vpRotationVector.cpp.

References vpArray2D< double >::data, and vpArray2D< double >::size().

double vpQuaternionVector::w ( ) const

Returns w-component of the quaternion.

Definition at line 322 of file vpQuaternionVector.cpp.

References vpArray2D< double >::data.

Referenced by vpRotationMatrix::buildFrom(), conjugate(), inverse(), magnitude(), normalize(), operator*(), operator+(), operator-(), and operator/().

double vpQuaternionVector::x ( ) const

Returns x-component of the quaternion.

Definition at line 316 of file vpQuaternionVector.cpp.

References vpArray2D< double >::data.

Referenced by vpRotationMatrix::buildFrom(), conjugate(), inverse(), magnitude(), normalize(), operator*(), operator+(), operator-(), and operator/().

double vpQuaternionVector::y ( ) const

Returns y-component of the quaternion.

Definition at line 318 of file vpQuaternionVector.cpp.

References vpArray2D< double >::data.

Referenced by vpRotationMatrix::buildFrom(), conjugate(), inverse(), magnitude(), normalize(), operator*(), operator+(), operator-(), and operator/().

double vpQuaternionVector::z ( ) const

Returns z-component of the quaternion.

Definition at line 320 of file vpQuaternionVector.cpp.

References vpArray2D< double >::data.

Referenced by vpRotationMatrix::buildFrom(), conjugate(), inverse(), magnitude(), normalize(), operator*(), operator+(), operator-(), and operator/().

Friends And Related Function Documentation

vpColVector operator* ( const double &  x,
const vpRotationVector v 
)
related

Allows to multiply a scalar by rotaion vector.

Definition at line 102 of file vpRotationVector.cpp.

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.

Member Data Documentation

unsigned int vpArray2D< double >::colNum
protectedinherited

Number of columns in the array.

Definition at line 76 of file vpArray2D.h.

Referenced by vpMatrix::AAt(), vpMatrix::AtA(), vpColVector::clear(), vpMatrix::detByLU(), vpMatrix::diag(), vpMatrix::eigenValues(), vpMatrix::expm(), vpMatrix::eye(), vpMatrix::getRow(), vpColVector::hadamard(), vpMatrix::hadamard(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpRowVector::insert(), vpMatrix::insert(), vpMatrix::inverseByCholesky(), vpMatrix::inverseTriangular(), vpRotationMatrix::operator*(), vpRowVector::operator*(), vpMatrix::operator*(), vpRotationMatrix::operator*=(), vpRowVector::operator*=(), vpMatrix::operator*=(), vpRowVector::operator+(), vpRowVector::operator+=(), vpMatrix::operator+=(), vpRowVector::operator-(), vpRowVector::operator-=(), vpMatrix::operator-=(), vpRowVector::operator/(), vpMatrix::operator/(), vpRowVector::operator/=(), vpMatrix::operator/=(), vpMatrix::operator<<(), vpColVector::operator<<(), vpSubRowVector::operator=(), vpSubMatrix::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpColVector::operator==(), vpMatrix::qr(), vpMatrix::qrPivot(), vpRowVector::reshape(), vpMatrix::setIdentity(), vpMatrix::solveByQR(), vpMatrix::solveBySVD(), vpMatrix::stack(), vpRowVector::stack(), vpMatrix::stackColumns(), vpMatrix::stackRows(), vpRowVector::sum(), vpMatrix::sum(), vpRowVector::sumSquare(), vpMatrix::sumSquare(), vpRowVector::t(), vpMatrix::t(), vpMatrix::transpose(), vpColVector::vpColVector(), and vpMatrix::vpMatrix().

double * vpArray2D< double >::data
inherited

Address of the first element of the data array.

Examples:
testArray2D.cpp, testDisplacement.cpp, testImageFilter.cpp, testMatrix.cpp, testPoseVector.cpp, testTranslationVector.cpp, and tutorial-matlab.cpp.

Definition at line 84 of file vpArray2D.h.

Referenced by vpMatrix::AtA(), buildFrom(), vpHomogeneousMatrix::buildFrom(), vpRzyzVector::buildFrom(), vpThetaUVector::buildFrom(), vpRxyzVector::buildFrom(), vpRzyxVector::buildFrom(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpColVector::clear(), vpHomogeneousMatrix::convert(), vpMatrix::detByLU(), vpTranslationVector::euclideanNorm(), vpRowVector::euclideanNorm(), vpMatrix::euclideanNorm(), vpMatrix::expm(), vpThetaUVector::extract(), vpMatrix::getRow(), vpThetaUVector::getTheta(), vpThetaUVector::getU(), vpColVector::hadamard(), vpMatrix::hadamard(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpColVector::insert(), vpMatrix::insert(), vpMatrix::inverseByCholesky(), vpTranslationVector::operator*(), vpRowVector::operator*(), vpColVector::operator*(), vpHomography::operator*(), vpMatrix::operator*(), vpTranslationVector::operator-(), vpRowVector::operator-(), vpColVector::operator-(), vpTranslationVector::operator/(), vpRowVector::operator/(), vpColVector::operator/(), vpHomography::operator/(), vpHomography::operator/=(), vpSubColVector::operator=(), vpSubRowVector::operator=(), operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpRzyzVector::operator=(), vpRxyzVector::operator=(), vpRzyxVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpThetaUVector::operator=(), vpColVector::operator==(), vpColVector::operator[](), vpMatrix::qr(), vpMatrix::qrPivot(), vpRowVector::reshape(), vpColVector::reshape(), set(), vpMatrix::stack(), vpMatrix::stackRows(), vpColVector::sum(), vpColVector::sumSquare(), vpRotationVector::t(), vpTranslationVector::t(), vpPoseVector::t(), vpRowVector::t(), vpColVector::t(), vpRotationVector::toStdVector(), vpRowVector::toStdVector(), vpColVector::toStdVector(), vpColVector::vpColVector(), vpMatrix::vpMatrix(), w(), x(), y(), z(), vpSubColVector::~vpSubColVector(), vpSubMatrix::~vpSubMatrix(), and vpSubRowVector::~vpSubRowVector().

unsigned int vpArray2D< double >::rowNum
protectedinherited

Number of rows in the array.

Definition at line 74 of file vpArray2D.h.

Referenced by vpMatrix::AAt(), vpMatrix::AtA(), vpColVector::clear(), vpMatrix::detByLU(), vpMatrix::diag(), vpMatrix::eigenValues(), vpMatrix::expm(), vpColVector::extract(), vpMatrix::eye(), vpColVector::hadamard(), vpMatrix::hadamard(), vpColVector::infinityNorm(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpMatrix::insert(), vpMatrix::inverseByCholesky(), vpMatrix::inverseTriangular(), vpRotationMatrix::operator*(), vpTranslationVector::operator*(), vpHomogeneousMatrix::operator*(), vpColVector::operator*(), vpMatrix::operator*(), vpRotationMatrix::operator*=(), vpTranslationVector::operator*=(), vpColVector::operator*=(), vpMatrix::operator*=(), vpColVector::operator+(), vpColVector::operator+=(), vpMatrix::operator+=(), vpColVector::operator-(), vpColVector::operator-=(), vpMatrix::operator-=(), vpColVector::operator/(), vpMatrix::operator/(), vpTranslationVector::operator/=(), vpColVector::operator/=(), vpMatrix::operator/=(), vpMatrix::operator<<(), vpColVector::operator<<(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpSubMatrix::operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::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(), vpTranslationVector::t(), vpPoseVector::t(), vpColVector::t(), vpMatrix::t(), vpMatrix::transpose(), vpColVector::vpColVector(), and vpMatrix::vpMatrix().