Visual Servoing Platform  version 3.2.0 under development (2018-10-19)
vpMatrix Class Reference

#include <visp3/core/vpMatrix.h>

+ Inheritance diagram for vpMatrix:

Public Types

enum  vpDetMethod { LU_DECOMPOSITION }
 

Public Member Functions

 vpMatrix ()
 
 vpMatrix (unsigned int r, unsigned int c)
 
 vpMatrix (unsigned int r, unsigned int c, double val)
 
 vpMatrix (const vpMatrix &M, unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols)
 
 vpMatrix (const vpArray2D< double > &A)
 
 vpMatrix (const vpMatrix &A)
 
 vpMatrix (vpMatrix &&A)
 
virtual ~vpMatrix ()
 
void clear ()
 
Setting a diagonal matrix
void diag (const double &val=1.0)
 
void diag (const vpColVector &A)
 
void eye ()
 
void eye (unsigned int n)
 
void eye (unsigned int m, unsigned int n)
 
Assignment operators
vpMatrixoperator<< (double *)
 
vpMatrixoperator= (const vpArray2D< double > &A)
 
vpMatrixoperator= (const vpMatrix &A)
 
vpMatrixoperator= (vpMatrix &&A)
 
vpMatrixoperator= (const double x)
 
Stacking
void stack (const vpMatrix &A)
 
void stack (const vpRowVector &r)
 
void stack (const vpColVector &c)
 
void stackColumns (vpColVector &out)
 
vpColVector stackColumns ()
 
void stackRows (vpRowVector &out)
 
vpRowVector stackRows ()
 
Matrix insertion
void insert (const vpMatrix &A, const unsigned int r, const unsigned int c)
 
Columns, rows, sub-matrices extraction
vpMatrix extract (unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols) const
 
vpColVector getCol (const unsigned int j) const
 
vpColVector getCol (const unsigned int j, const unsigned int i_begin, const unsigned int size) const
 
vpRowVector getRow (const unsigned int i) const
 
vpRowVector getRow (const unsigned int i, const unsigned int j_begin, const unsigned int size) const
 
void init (const vpMatrix &M, unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols)
 
Matrix operations
double det (vpDetMethod method=LU_DECOMPOSITION) const
 
double detByLU () const
 
vpMatrix expm () const
 
vpMatrixoperator+= (const vpMatrix &B)
 
vpMatrixoperator-= (const vpMatrix &B)
 
vpMatrix operator* (const vpMatrix &B) const
 
vpMatrix operator* (const vpRotationMatrix &R) const
 
vpMatrix operator* (const vpVelocityTwistMatrix &V) const
 
vpMatrix operator* (const vpForceTwistMatrix &V) const
 
vpTranslationVector operator* (const vpTranslationVector &tv) const
 
vpColVector operator* (const vpColVector &v) const
 
vpMatrix operator+ (const vpMatrix &B) const
 
vpMatrix operator- (const vpMatrix &B) const
 
vpMatrix operator- () const
 
vpMatrixoperator+= (const double x)
 
vpMatrixoperator-= (const double x)
 
vpMatrixoperator*= (const double x)
 
vpMatrixoperator/= (double x)
 
vpMatrix operator* (const double x) const
 
vpMatrix operator/ (const double x) const
 
double sum () const
 
double sumSquare () const
 
Hadamard product
vpMatrix hadamard (const vpMatrix &m) const
 
Kronecker product
void kron (const vpMatrix &m1, vpMatrix &out) const
 
vpMatrix kron (const vpMatrix &m1) const
 
Transpose
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
 
Matrix inversion
vpMatrix inverseByLU () const
 
vpMatrix inverseByCholesky () const
 
vpMatrix inverseByQR () const
 
vpMatrix inverseTriangular (bool upper=true) 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 &kerAt) const
 
SVD decomposition
double cond () const
 
unsigned int kernel (vpMatrix &kerAt, double svThreshold=1e-6) const
 
void solveBySVD (const vpColVector &B, vpColVector &x) const
 
vpColVector solveBySVD (const vpColVector &B) const
 
void svd (vpColVector &w, vpMatrix &V)
 
QR decomposition
unsigned int qr (vpMatrix &Q, vpMatrix &R, bool full=false, bool squareR=false, double tol=1e-6) const
 
unsigned int qrPivot (vpMatrix &Q, vpMatrix &R, vpMatrix &P, bool full=false, bool squareR=false, double tol=1e-6) const
 
void solveByQR (const vpColVector &b, vpColVector &x) const
 
vpColVector solveByQR (const vpColVector &b) const
 
Eigen values
vpColVector eigenValues () const
 
void eigenValues (vpColVector &evalue, vpMatrix &evector) const
 
Norms
double euclideanNorm () const
 
double infinityNorm () const
 
Printing
std::ostream & cppPrint (std::ostream &os, const std::string &matrixName="A", bool octet=false) const
 
std::ostream & csvPrint (std::ostream &os) const
 
std::ostream & maplePrint (std::ostream &os) const
 
std::ostream & matlabPrint (std::ostream &os) const
 
int print (std::ostream &s, unsigned int length, char const *intro=0) const
 
void printSize () const
 
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)
 
double * operator[] (unsigned int i)
 
double * operator[] (unsigned int i) const
 
vpArray2D< double > hadamard (const vpArray2D< double > &m) const
 

Static Public Member Functions

Setting a diagonal matrix with Static Public Member Functions
static void createDiagonalMatrix (const vpColVector &A, vpMatrix &DA)
 
Matrix insertion with Static Public Member Functions
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)
 
Stacking with Static Public Member Functions
static vpMatrix juxtaposeMatrices (const vpMatrix &A, const vpMatrix &B)
 
static void juxtaposeMatrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)
 
static vpMatrix stack (const vpMatrix &A, const vpMatrix &B)
 
static vpMatrix stack (const vpMatrix &A, const vpRowVector &r)
 
static vpMatrix stack (const vpMatrix &A, const vpColVector &c)
 
static void stack (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)
 
static void stack (const vpMatrix &A, const vpRowVector &r, vpMatrix &C)
 
static void stack (const vpMatrix &A, const vpColVector &c, vpMatrix &C)
 
Matrix operations with Static Public Member Functions
static void add2Matrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)
 
static void add2Matrices (const vpColVector &A, const vpColVector &B, vpColVector &C)
 
static void add2WeightedMatrices (const vpMatrix &A, const double &wA, const vpMatrix &B, const double &wB, vpMatrix &C)
 
static void computeHLM (const vpMatrix &H, const double &alpha, vpMatrix &HLM)
 
static void mult2Matrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)
 
static void mult2Matrices (const vpMatrix &A, const vpMatrix &B, vpRotationMatrix &C)
 
static void mult2Matrices (const vpMatrix &A, const vpMatrix &B, vpHomogeneousMatrix &C)
 
static void mult2Matrices (const vpMatrix &A, const vpColVector &B, vpColVector &C)
 
static void multMatrixVector (const vpMatrix &A, const vpColVector &v, vpColVector &w)
 
static void negateMatrix (const vpMatrix &A, vpMatrix &C)
 
static void sub2Matrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)
 
static void sub2Matrices (const vpColVector &A, const vpColVector &B, vpColVector &C)
 
Kronecker product with Static Public Member Functions
static void kron (const vpMatrix &m1, const vpMatrix &m2, vpMatrix &out)
 
static vpMatrix kron (const vpMatrix &m1, const vpMatrix &m2)
 
2D Convolution with Static Public Member Functions
static vpMatrix conv2 (const vpMatrix &M, const vpMatrix &kernel, const std::string &mode="full")
 
static void conv2 (const vpMatrix &M, const vpMatrix &kernel, vpMatrix &res, const std::string &mode="full")
 
Covariance computation with Static Public Member Functions
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 vpMatrix computeCovarianceMatrixVVS (const vpHomogeneousMatrix &cMo, const vpColVector &deltaS, const vpMatrix &Ls, const vpMatrix &W)
 
static vpMatrix computeCovarianceMatrixVVS (const vpHomogeneousMatrix &cMo, const vpColVector &deltaS, const vpMatrix &Ls)
 
Matrix I/O with Static Public Member Functions
static bool loadMatrix (const std::string &filename, vpArray2D< double > &M, const bool binary=false, char *header=NULL)
 
static bool loadMatrixYAML (const std::string &filename, vpArray2D< double > &M, char *header=NULL)
 
static bool saveMatrix (const std::string &filename, const vpArray2D< double > &M, const bool binary=false, const char *header="")
 
static bool saveMatrixYAML (const std::string &filename, const vpArray2D< double > &M, const char *header="")
 
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.)

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

Deprecated functions

vp_deprecated void init ()
 
vp_deprecated void stackMatrices (const vpMatrix &A)
 
vp_deprecated void setIdentity (const double &val=1.0)
 
vp_deprecated vpRowVector row (const unsigned int i)
 
vp_deprecated vpColVector column (const unsigned int j)
 
static vp_deprecated vpMatrix stackMatrices (const vpMatrix &A, const vpMatrix &B)
 
static vp_deprecated void stackMatrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C)
 
static vp_deprecated vpMatrix stackMatrices (const vpMatrix &A, const vpRowVector &B)
 
static vp_deprecated void stackMatrices (const vpMatrix &A, const vpRowVector &B, vpMatrix &C)
 
static vp_deprecated vpMatrix stackMatrices (const vpColVector &A, const vpColVector &B)
 
static vp_deprecated void stackMatrices (const vpColVector &A, const vpColVector &B, vpColVector &C)
 

Detailed Description

Implementation of a matrix and operations on matrices.

This class needs one of the following third-party to compute matrix inverse, pseudo-inverse, singular value decomposition, determinant:

  • If Lapack is installed and detected by ViSP, this 3rd party is used by vpMatrix. Installation instructions are provided here https://visp.inria.fr/3rd_lapack;
  • else if Eigen3 is installed and detected by ViSP, this 3rd party is used by vpMatrix. Installation instructions are provided here https://visp.inria.fr/3rd_eigen;
  • else if OpenCV is installed and detected by ViSP, this 3rd party is used, Installation instructions are provided here https://visp.inria.fr/3rd_opencv;
  • else if GSL is installed and detected by ViSP, we use this other 3rd party. Installation instructions are provided here https://visp.inria.fr/3rd_gsl.
  • If none of these previous 3rd parties is installed, we use by default a Lapack built-in version.

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

The vpMatrix class is derived from vpArray2D<double>.

See also
vpArray2D, vpRowVector, vpColVector, vpHomogeneousMatrix, vpRotationMatrix, vpVelocityTwistMatrix, vpForceTwistMatrix, vpHomography
Examples:
manServo4PointsDisplay.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, photometricVisualServoing.cpp, quadprog.cpp, quadprog_eq.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocityKalman.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoMomentImage.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPioneerPoint2DDepthWithoutVpServo.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimu4Points.cpp, servoSimuCylinder.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuSphere.cpp, servoViper650FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DArtVelocityInteractionDesired.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, servoViper850Point2DArtVelocity-jointAvoidance-large.cpp, servoViper850Point2DArtVelocity.cpp, servoViper850Point2DCamVelocityKalman.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testColVector.cpp, testFeature.cpp, testFrankaCartVelocity-2.cpp, testImageFilter.cpp, testMatrix.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixException.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testPoseFeatures.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testRowVector.cpp, testSvd.cpp, testTranslationVector.cpp, tutorial-image-filter.cpp, tutorial-matlab.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 104 of file vpMatrix.h.

Member Enumeration Documentation

Method used to compute the determinant of a square matrix.

See also
det()
Enumerator
LU_DECOMPOSITION 

LU decomposition method.

Definition at line 111 of file vpMatrix.h.

Constructor & Destructor Documentation

vpMatrix::vpMatrix ( )
inline

Basic constructor of a matrix of double. Number of columns and rows are zero.

Definition at line 120 of file vpMatrix.h.

vpMatrix::vpMatrix ( unsigned int  r,
unsigned int  c 
)
inline

Constructor that initialize a matrix of double with 0.

Parameters
r: Matrix number of rows.
c: Matrix number of columns.

Definition at line 127 of file vpMatrix.h.

vpMatrix::vpMatrix ( unsigned int  r,
unsigned int  c,
double  val 
)
inline

Constructor that initialize a matrix of double with val.

Parameters
r: Matrix number of rows.
c: Matrix number of columns.
val: Each element of the matrix is set to val.

Definition at line 135 of file vpMatrix.h.

vpMatrix::vpMatrix ( const vpMatrix M,
unsigned int  r,
unsigned int  c,
unsigned int  nrows,
unsigned int  ncols 
)

Construct a matrix as a sub-matrix of the input matrix M.

See also
init(const vpMatrix &M, unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols)

Definition at line 181 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, init(), and vpArray2D< Type >::rowNum.

vpMatrix::vpMatrix ( const vpArray2D< double > &  A)
inline

Create a matrix from a 2D array that could be one of the following container that inherit from vpArray2D such as vpMatrix, vpRotationMatrix, vpHomogeneousMatrix, vpPoseVector, vpColVector, vpRowVector...

The following example shows how to create a matrix from an homogeneous matrix:

Definition at line 149 of file vpMatrix.h.

vpMatrix::vpMatrix ( const vpMatrix A)
inline

Definition at line 152 of file vpMatrix.h.

virtual vpMatrix::~vpMatrix ( )
inlinevirtual

Destructor (Memory de-allocation)

Definition at line 158 of file vpMatrix.h.

Member Function Documentation

vpMatrix vpMatrix::AAt ( ) const

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

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

Definition at line 426 of file vpMatrix.cpp.

void vpMatrix::AAt ( vpMatrix B) const

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 446 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpArray2D< double >::colNum, vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, vpArray2D< Type >::rowNum, and vpArray2D< double >::rowPtrs.

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

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 1113 of file vpMatrix.cpp.

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

Referenced by operator+().

void vpMatrix::add2Matrices ( const vpColVector A,
const vpColVector B,
vpColVector C 
)
static
Warning
This function is provided for compat with previous releases. You should rather use the functionalities provided in vpColVector class.

Operation C = A + B.

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

See also
vpColVector::operator+()

Definition at line 1146 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpColVector::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

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

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 1084 of file vpMatrix.cpp.

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

void vpMatrix::AtA ( vpMatrix B) const

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 480 of file vpMatrix.cpp.

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

void vpMatrix::clear ( )
inline

Removes all elements from the matrix (which are destroyed), leaving the container with a size of 0.

Definition at line 164 of file vpMatrix.h.

References vpArray2D< Type >::hadamard(), operator*(), vpArray2D< Type >::operator<<, and vpArray2D< Type >::operator=().

Referenced by vpPose::init().

vpColVector vpMatrix::column ( const unsigned int  j)
Deprecated:
This method is deprecated. You should rather use getCol(). More precisely, the following code:
unsigned int column_index = ...;
... = L.column(column_index);

should be replaced with:

... = L.getCol(column_index - 1);
Warning
Notice column(1) is the 0-th column. This function returns the j-th columns of the matrix.
Parameters
j: Index of the column to extract noting that column index start at 1 to get the first column.

Definition at line 5302 of file vpMatrix.cpp.

References vpArray2D< double >::getRows().

vpMatrix vpMatrix::computeCovarianceMatrix ( const vpMatrix A,
const vpColVector x,
const vpColVector b 
)
static

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 59 of file vpMatrix_covariance.cpp.

References vpException::divideByZeroError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), pseudoInverse(), and t().

Referenced by computeCovarianceMatrixVVS(), vpPoseFeatures::computePose(), and vpPose::poseVirtualVSrobust().

vpMatrix vpMatrix::computeCovarianceMatrix ( const vpMatrix A,
const vpColVector x,
const vpColVector b,
const vpMatrix W 
)
static

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 91 of file vpMatrix_covariance.cpp.

References vpException::divideByZeroError, vpArray2D< Type >::getCols(), and t().

vpMatrix vpMatrix::computeCovarianceMatrixVVS ( const vpHomogeneousMatrix cMo,
const vpColVector deltaS,
const vpMatrix Ls,
const vpMatrix W 
)
static

Compute the covariance matrix of an image-based virtual visual servoing. This assumes the optimization has been done via v = (W * Ls).pseudoInverse() W * DeltaS.

Parameters
cMo: Pose matrix that has been computed with the v.
deltaS: Error vector used in v = (W * Ls).pseudoInverse() * W * DeltaS.
Ls: interaction matrix used in v = (W * Ls).pseudoInverse() * W * DeltaS.
W: Weight matrix used in v = (W * Ls).pseudoInverse() * W * DeltaS.

Definition at line 149 of file vpMatrix_covariance.cpp.

References computeCovarianceMatrix(), vpHomogeneousMatrix::extract(), eye(), vpArray2D< Type >::getRows(), pseudoInverse(), vpMath::sinc(), vpTranslationVector::skew(), vpColVector::skew(), vpMath::sqr(), and vpColVector::sumSquare().

Referenced by computeCovarianceMatrixVVS(), vpMbTracker::computeCovarianceMatrixVVS(), and vpPose::poseVirtualVS().

vpMatrix vpMatrix::computeCovarianceMatrixVVS ( const vpHomogeneousMatrix cMo,
const vpColVector deltaS,
const vpMatrix Ls 
)
static

Compute the covariance matrix of an image-based virtual visual servoing. This assumes the optimization has been done via v = Ls.pseudoInverse() * DeltaS.

Parameters
cMo: Pose matrix that has been computed with the v.
deltaS: Error vector used in v = Ls.pseudoInverse() * DeltaS
Ls: interaction matrix used in v = Ls.pseudoInverse() * DeltaS

Definition at line 124 of file vpMatrix_covariance.cpp.

References computeCovarianceMatrix(), and computeCovarianceMatrixVVS().

double vpMatrix::cond ( ) const
Returns
The condition number, the ratio of the largest singular value of the matrix to the smallest.

Definition at line 5045 of file vpMatrix.cpp.

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

Referenced by vpTemplateTrackerMIForwardCompositional::trackNoPyr(), vpTemplateTrackerMIESM::trackNoPyr(), vpTemplateTrackerMIForwardAdditional::trackNoPyr(), and vpTemplateTrackerMIInverseCompositional::trackNoPyr().

vpMatrix vpMatrix::conv2 ( const vpMatrix M,
const vpMatrix kernel,
const std::string &  mode = "full" 
)
static

Perform a 2D convolution similar to Matlab conv2 function: $ M \star kernel $.

Parameters
M: First matrix.
kernel: Second matrix.
mode: Convolution mode: "full" (default), "same", "valid".
vpMatrix-conv2-mode.jpg
Convolution mode: full, same, valid (image credit: Theano doc).
Note
This is a very basic implementation that does not use FFT.
Examples:
testMatrixConvolution.cpp.

Definition at line 5164 of file vpMatrix.cpp.

Referenced by vpImageFilter::getSobelKernelY().

void vpMatrix::conv2 ( const vpMatrix M,
const vpMatrix kernel,
vpMatrix res,
const std::string &  mode = "full" 
)
static

Perform a 2D convolution similar to Matlab conv2 function: $ M \star kernel $.

Parameters
M: First matrix.
kernel: Second matrix.
res: Result.
mode: Convolution mode: "full" (default), "same", "valid".
vpMatrix-conv2-mode.jpg
Convolution mode: full, same, valid (image credit: Theano doc).
Note
This is a very basic implementation that does not use FFT.

Definition at line 5183 of file vpMatrix.cpp.

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

std::ostream & vpMatrix::cppPrint ( std::ostream &  os,
const std::string &  matrixName = "A",
bool  octet = false 
) const

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

Parameters
os: the stream to be printed in.
matrixName: name of the matrix, "A" by default.
octet: if false, print using double, if true, print byte per byte each bytes of the double array.

The following code shows how to use this function:

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix M(2,3);
int cpt = 0;
for (unsigned int i=0; i<M.getRows(); i++)
for (unsigned int j=0; j<M.getCols(); j++)
M[i][j] = cpt++;
M.cppPrint(std::cout, "M");
}

It produces the following output that could be copy/paste in a C++ code:

vpMatrix M (2, 3);
M[0][0] = 0;
M[0][1] = 1;
M[0][2] = 2;
M[1][0] = 3;
M[1][1] = 4;
M[1][2] = 5;

Definition at line 4438 of file vpMatrix.cpp.

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

Referenced by vpColVector::clear().

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

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 712 of file vpMatrix.cpp.

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

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

Print/save a matrix in csv format.

The following code

#include <visp3/core/vpMatrix.h>
int main()
{
std::ofstream ofs("log.csv", std::ofstream::out);
vpMatrix M(2,3);
int cpt = 0;
for (unsigned int i=0; i<M.getRows(); i++)
for (unsigned int j=0; j<M.getCols(); j++)
M[i][j] = cpt++;
M.csvPrint(ofs);
ofs.close();
}

produces log.csv file that contains:

0, 1, 2
3, 4, 5

Definition at line 4389 of file vpMatrix.cpp.

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

Referenced by vpColVector::clear().

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

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

Parameters
method: Method used to compute the determinant. Default LU decomposition method is faster than the method based on Gaussian elimination.
Returns
Determinant of the matrix.
#include <iostream>
#include <visp3/core/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.detByLU() << std::endl;
std:: cout << "Determinant by LU decomposition (Lapack): " << A.detByLULapack() << std::endl;
std:: cout << "Determinant by LU decomposition (OpenCV): " << A.detByLUOpenCV() << std::endl;
std:: cout << "Determinant by LU decomposition (GSL) : " << A.detByLUGsl() << std::endl;
}
Examples:
testMatrixInverse.cpp.

Definition at line 4906 of file vpMatrix.cpp.

References detByLU(), and LU_DECOMPOSITION.

Referenced by vpTriangle::buildFrom(), vpHomography::computeDisplacement(), detByLU(), and vpTemplateTrackerTriangle::init().

double vpMatrix::detByLU ( ) const

Compute the determinant of a square matrix using the LU decomposition.

This function calls the first following function that is available:

  • detByLULapack() if Lapack 3rd party is installed
  • detByLUEigen3() if Eigen3 3rd party is installed
  • detByLUOpenCV() if OpenCV 3rd party is installed
  • detByLUGsl() if GSL 3rd party is installed.

If none of these previous 3rd parties is installed, we use by default detByLULapack() with a Lapack built-in version.

Returns
The determinant of the matrix if the matrix is square.
#include <iostream>
#include <visp3/core/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.detByLU() << std::endl;
}
See also
detByLULapack(), detByLUEigen3(), detByLUOpenCV(), detByLUGsl()

Definition at line 180 of file vpMatrix_lu.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, det(), vpException::fatalError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), and vpArray2D< double >::rowNum.

Referenced by det().

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

Set the matrix as a diagonal matrix where each element on the diagonal is set to val. Elements that are not on the diagonal are set to 0.

Parameters
val: Value to set.
See also
eye()
#include <iostream>
#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix A(3, 4);
A.diag(2);
std::cout << "A:\n" << A << std::endl;
}

Matrix A is now equal to:

2 0 0 0
0 2 0 0
0 0 2 0
Examples:
testSvd.cpp.

Definition at line 693 of file vpMatrix.cpp.

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

Referenced by vpMbTracker::computeCovarianceMatrixVVS(), and vpQuadProg::fromCanonicalCost().

void vpMatrix::diag ( const vpColVector A)

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 <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
v[0] = 1;
v[1] = 2;
v[2] = 3;
A.diag(v);
std::cout << "A:\n" << A << std::endl;
}

Matrix A is now equal to:

1 0 0
0 2 0
0 0 3

Definition at line 653 of file vpMatrix.cpp.

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

vpColVector vpMatrix::eigenValues ( ) const

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
vpException::dimensionErrorIf the matrix is not square.
vpException::fatalErrorIf the matrix is not symmetric.
vpException::functionNotImplementedErrorIf the GSL library is not detected.

Here an example:

#include <iostream>
#include <visp3/core/vpColVector.h>
#include <visp3/core/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 4624 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::dimensionError, vpException::fatalError, vpException::functionNotImplementedError, vpArray2D< double >::rowNum, and t().

Referenced by vpQuadProg::fromCanonicalCost().

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

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
vpException::dimensionErrorIf the matrix is not square.
vpException::fatalErrorIf the matrix is not symmetric.
vpException::functionNotImplementedErrorIf the GSL library is not detected.

Here an example:

#include <iostream>
#include <visp3/core/vpColVector.h>
#include <visp3/core/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;
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 4735 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::dimensionError, vpException::fatalError, vpException::functionNotImplementedError, vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, and t().

double vpMatrix::euclideanNorm ( ) const

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

Returns
The Euclidean norm if the matrix is initialized, 0 otherwise.
See also
infinityNorm()
Examples:
testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 5096 of file vpMatrix.cpp.

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

Referenced by vpColVector::deg2rad().

vpMatrix vpMatrix::expm ( ) const
vpMatrix vpMatrix::extract ( unsigned int  r,
unsigned int  c,
unsigned int  nrows,
unsigned int  ncols 
) const

Extract a sub matrix from a matrix M.

Parameters
r: row index in matrix M.
c: column index in matrix M.
nrows: Number of rows of the matrix that should be extracted.
ncols: Number of columns of the matrix that should be extracted.

The following code shows how to use this function:

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix M(4,5);
int val = 0;
for(size_t i=0; i<M.getRows(); i++) {
for(size_t j=0; j<M.getCols(); j++) {
M[i][j] = val++;
}
}
M.print (std::cout, 4, "M ");
vpMatrix N = M.extract(0, 1, 2, 3);
N.print (std::cout, 4, "N ");
}

It produces the following output:

M [4,5]=
0 1 2 3 4
5 6 7 8 9
10 11 12 13 14
15 16 17 18 19
N [2,3]=
1 2 3
6 7 8
See also
init(const vpMatrix &, unsigned int, unsigned int, unsigned int, unsigned int)

Definition at line 319 of file vpMatrix.cpp.

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

Referenced by vpLinProg::colReduction(), vpLinProg::rowReduction(), solveByQR(), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().

void vpMatrix::eye ( unsigned int  n)

Set an n-by-n matrix to identity with ones on the diagonal and zeros else where.

Definition at line 343 of file vpMatrix.cpp.

References eye().

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

Set an m-by-n matrix to identity with ones on the diagonal and zeros else where.

Definition at line 349 of file vpMatrix.cpp.

References eye(), and vpArray2D< double >::resize().

vpColVector vpMatrix::getCol ( const unsigned int  j) const

Extract a column vector from a matrix.

Warning
All the indexes start from 0 in this function.
Parameters
j: Index of the column to extract. If j=0, the first column is extracted.
Returns
The extracted column vector.

The following example shows how to use this function:

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix A(4,4);
for(unsigned int i=0; i < A.getRows(); i++)
for(unsigned int j=0; j < A.getCols(); j++)
A[i][j] = i*A.getCols()+j;
A.print(std::cout, 4);
vpColVector cv = A.getCol(1);
std::cout << "Column vector: \n" << cv << std::endl;
}

It produces the following output:

[4,4]=
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
column vector:
1
5
9
13
Examples:
testMatrix.cpp.

Definition at line 3798 of file vpMatrix.cpp.

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

Referenced by vpLinProg::colReduction(), vpHomography::DLT(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), kernel(), vpPose::poseFromRectangle(), vpServo::secondaryTaskJointLimitAvoidance(), and vpLinProg::simplex().

vpColVector vpMatrix::getCol ( const unsigned int  j,
const unsigned int  i_begin,
const unsigned int  column_size 
) const

Extract a column vector from a matrix.

Warning
All the indexes start from 0 in this function.
Parameters
j: Index of the column to extract. If col=0, the first column is extracted.
i_begin: Index of the row that gives the location of the first element of the column vector to extract.
column_size: Size of the column vector to extract.
Returns
The extracted column vector.

The following example shows how to use this function:

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix A(4,4);
for(unsigned int i=0; i < A.getRows(); i++)
for(unsigned int j=0; j < A.getCols(); j++)
A[i][j] = i*A.getCols()+j;
A.print(std::cout, 4);
vpColVector cv = A.getCol(1, 1, 3);
std::cout << "Column vector: \n" << cv << std::endl;
}

It produces the following output:

[4,4]=
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
column vector:
5
9
13

Definition at line 3749 of file vpMatrix.cpp.

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

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.
vpRowVector vpMatrix::getRow ( const unsigned int  i) const

Extract a row vector from a matrix.

Warning
All the indexes start from 0 in this function.
Parameters
i: Index of the row to extract. If i=0, the first row is extracted.
Returns
The extracted row vector.

The following example shows how to use this function:

#include <visp3/core/vpMatrix.h>
#include <visp3/core/vpRowVector.h>
int main()
{
vpMatrix A(4,4);
for(unsigned int i=0; i < A.getRows(); i++)
for(unsigned int j=0; j < A.getCols(); j++)
A[i][j] = i*A.getCols()+j;
A.print(std::cout, 4);
vpRowVector rv = A.getRow(1);
std::cout << "Row vector: \n" << rv << std::endl;
}

It produces the following output:

[4,4]=
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
Row vector:
4 5 6 7
Examples:
testMatrix.cpp.

Definition at line 3844 of file vpMatrix.cpp.

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

Referenced by vpLinProg::allClose(), vpLinProg::allLesser(), vpLinProg::solveLP(), and vpQuadProg::solveQPi().

vpRowVector vpMatrix::getRow ( const unsigned int  i,
const unsigned int  j_begin,
const unsigned int  row_size 
) const

Extract a row vector from a matrix.

Warning
All the indexes start from 0 in this function.
Parameters
i: Index of the row to extract. If i=0, the first row is extracted.
j_begin: Index of the column that gives the location of the first element of the row vector to extract.
row_size: Size of the row vector to extract.
Returns
The extracted row vector.

The following example shows how to use this function:

#include <visp3/core/vpMatrix.h>
#include <visp3/core/vpRowVector.h>
int main()
{
vpMatrix A(4,4);
for(unsigned int i=0; i < A.getRows(); i++)
for(unsigned int j=0; j < A.getCols(); j++)
A[i][j] = i*A.getCols()+j;
A.print(std::cout, 4);
vpRowVector rv = A.getRow(1, 1, 3);
std::cout << "Row vector: \n" << rv << std::endl;
}

It produces the following output:

[4,4]=
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
Row vector:
5 6 7

Definition at line 3896 of file vpMatrix.cpp.

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

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.
vpMatrix vpMatrix::hadamard ( const vpMatrix m) const

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:
testMatrix.cpp.

Definition at line 1513 of file vpMatrix.cpp.

References vpCPUFeatures::checkSSE2(), vpArray2D< double >::colNum, vpArray2D< double >::data, vpArray2D< Type >::data, vpException::dimensionError, vpArray2D< double >::dsize, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::resize(), and vpArray2D< double >::rowNum.

double vpMatrix::infinityNorm ( ) const

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 5117 of file vpMatrix.cpp.

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

Referenced by vpColVector::extract().

void vpMatrix::init ( const vpMatrix M,
unsigned int  r,
unsigned int  c,
unsigned int  nrows,
unsigned int  ncols 
)

Initialize the matrix from a part of an input matrix M.

Parameters
M: Input matrix used for initialization.
r: row index in matrix M.
c: column index in matrix M.
nrows: Number of rows of the matrix that should be initialized.
ncols: Number of columns of the matrix that should be initialized.

The sub-matrix starting from M[r][c] element and ending on M[r+nrows-1][c+ncols-1] element is used to initialize the matrix.

The following code shows how to use this function:

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix M(4,5);
int val = 0;
for(size_t i=0; i<M.getRows(); i++) {
for(size_t j=0; j<M.getCols(); j++) {
M[i][j] = val++;
}
}
M.print (std::cout, 4, "M ");
N.init(M, 0, 1, 2, 3);
N.print (std::cout, 4, "N ");
}

It produces the following output:

M [4,5]=
0 1 2 3 4
5 6 7 8 9
10 11 12 13 14
15 16 17 18 19
N [2,3]=
1 2 3
6 7 8
See also
extract()
Examples:
testMatrix.cpp.

Definition at line 258 of file vpMatrix.cpp.

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

vp_deprecated void vpMatrix::init ( )
inline
Deprecated:
Only provided for compatibilty with ViSP previous releases. This function does nothing.

Definition at line 698 of file vpMatrix.h.

Referenced by vpColVector::extract(), vpMatrix(), and vpSubMatrix::vpSubMatrix().

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

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 4061 of file vpMatrix.cpp.

References insert().

void insert ( const vpMatrix A,
const vpMatrix B,
vpMatrix C,
const unsigned int  r,
const unsigned int  c 
)
static

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 4083 of file vpMatrix.cpp.

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

vpMatrix vpMatrix::inverseByCholesky ( ) const

Compute the inverse of a n-by-n matrix using the Cholesky decomposition. The matrix must be real symmetric positive defined.

This function calls the first following function that is available:

  • inverseByCholeskyLapack() if Lapack 3rd party is installed
  • inverseByLUOpenCV() if OpenCV 3rd party is installed.

If none of these 3rd parties is installed we use a Lapack built-in version.

Returns
The inverse matrix.

Here an example:

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix A(4,4);
// Symmetric matrix
A[0][0] = 1/1.; A[0][1] = 1/5.; A[0][2] = 1/6.; A[0][3] = 1/7.;
A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.; A[1][3] = 1/5.;
A[2][0] = 1/6.; A[2][1] = 1/3.; A[2][2] = 1/2.; A[2][3] = 1/6.;
A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.; A[3][3] = 1/7.;
// Compute the inverse
vpMatrix A_1; // A^-1
A_1 = A.inverseByCholesky();
std::cout << "Inverse by Cholesky: \n" << A_1 << std::endl;
std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}
See also
pseudoInverse()

Definition at line 105 of file vpMatrix_cholesky.cpp.

References vpException::badValue, vpArray2D< double >::colNum, vpArray2D< double >::data, vpArray2D< Type >::data, vpException::fatalError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::getRows(), vpMatrixException::matrixError, and vpArray2D< double >::rowNum.

vpMatrix vpMatrix::inverseByLU ( ) const

Compute the inverse of a n-by-n matrix using the LU decomposition.

This function calls the first following function that is available:

  • inverseByLULapack() if Lapack 3rd party is installed
  • inverseByLUEigen3() if Eigen3 3rd party is installed
  • inverseByLUOpenCV() if OpenCV 3rd party is installed
  • inverseByLUGsl() if GSL 3rd party is installed.

If none of these previous 3rd parties is installed, we use by default inverseByLULapack() with a Lapack built-in version.

Returns
The inverse matrix.

Here an example:

#include <visp3/core/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.inverseByLU();
std::cout << "Inverse by LU ";
#if defined(VISP_HAVE_LAPACK)
std::cout << "(using Lapack)";
#elif defined(VISP_HAVE_EIGEN3)
std::cout << "(using Eigen3)";
#elif (VISP_HAVE_OPENCV_VERSION >= 0x020101)
std::cout << "(using OpenCV)";
#elif defined (VISP_HAVE_GSL)
std::cout << "(using GSL)";
#endif
std::cout << ": \n" << A_1 << std::endl;
std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}
See also
inverseByLULapack(), inverseByLUEigen3(), inverseByLUOpenCV(), inverseByLUGsl(), pseudoInverse()
Examples:
photometricVisualServoing.cpp.

Definition at line 130 of file vpMatrix_lu.cpp.

References vpException::fatalError.

Referenced by vpTriangle::buildFrom(), expm(), vpKalmanFilter::filtering(), vpTemplateTrackerWarpHomographySL3::findWarp(), vpTemplateTrackerWarpAffine::getParamInverse(), vpTemplateTrackerTriangle::init(), vpTemplateTrackerSSDInverseCompositional::initCompInverse(), vpTemplateTrackerZNCCForwardAdditional::initHessienDesired(), vpTemplateTrackerMIForwardCompositional::initHessienDesired(), vpTemplateTrackerZNCCInverseCompositional::initHessienDesired(), vpTemplateTrackerMIESM::initHessienDesired(), vpTemplateTrackerMIForwardAdditional::initHessienDesired(), vpTemplateTrackerMIInverseCompositional::initHessienDesired(), vpTemplateTracker::setHDes(), vpTemplateTrackerSSDForwardCompositional::trackNoPyr(), vpTemplateTrackerMIForwardCompositional::trackNoPyr(), vpTemplateTrackerSSDForwardAdditional::trackNoPyr(), vpTemplateTrackerMIESM::trackNoPyr(), vpTemplateTrackerMIForwardAdditional::trackNoPyr(), vpTemplateTrackerMIInverseCompositional::trackNoPyr(), and vpTemplateTrackerWarp::warp().

vpMatrix vpMatrix::inverseByQR ( ) const

Compute the inverse of a n-by-n matrix using the QR decomposition. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.

Returns
The inverse matrix.

Here an example:

#include <visp3/core/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.inverseByQR();
std::cout << "Inverse by QR: \n" << A_1 << std::endl;
std::cout << "A*A^-1: \n" << A * A_1 << std::endl;
}
See also
inverseByLU(), inverseByCholesky()

Definition at line 275 of file vpMatrix_qr.cpp.

References vpException::fatalError.

Referenced by vpLinProg::simplex().

vpMatrix vpMatrix::inverseTriangular ( bool  upper = true) const

Compute the inverse of a full-rank n-by-n triangular matrix. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.

Parameters
upper: if it is an upper triangular matrix

The function does not check if the matrix is actually upper or lower triangular.

Returns
The inverse matrix

Definition at line 715 of file vpMatrix_qr.cpp.

References vpException::badValue, vpArray2D< double >::colNum, vpArray2D< Type >::data, vpException::dimensionError, vpException::fatalError, vpMatrixException::rankDeficient, and vpArray2D< double >::rowNum.

Referenced by vpLinProg::colReduction(), vpLinProg::rowReduction(), and solveByQR().

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

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 rows.
Examples:
testMatrix.cpp.

Definition at line 4114 of file vpMatrix.cpp.

Referenced by vpLinProg::colReduction().

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

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 rows.

Definition at line 4135 of file vpMatrix.cpp.

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

unsigned int vpMatrix::kernel ( vpMatrix kerAt,
double  svThreshold = 1e-6 
) const

Function to compute the null space (the kernel) of a m-by-n matrix $\bf A$.

The null space of a matrix $\bf A$ is defined as $\mbox{Ker}({\bf A}) = { {\bf X} : {\bf A}*{\bf X} = {\bf 0}}$.

Parameters
kerAtThe matrix that contains the null space (kernel) of $\bf A$ defined by the matrix ${\bf X}^T$. If matrix $\bf A$ is full rank, the dimension of kerAt is (0, n), otherwise the dimension is (n-r, n). This matrix is thus the transpose of $\mbox{Ker}({\bf A})$.
svThresholdThreshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.
Returns
The rank r of the matrix.
Examples:
servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp.

Definition at line 4821 of file vpMatrix.cpp.

References getCol(), vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpArray2D< Type >::getRows(), insert(), vpArray2D< Type >::resize(), vpColVector::sumSquare(), and svd().

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

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 1579 of file vpMatrix.cpp.

Referenced by kron().

vpMatrix vpMatrix::kron ( const vpMatrix m) const

Compute Kronecker product matrix.

Parameters
m: vpMatrix;
Returns
m1.kron(m2) The kronecker product : $ m1 \otimes m2 $

Definition at line 1617 of file vpMatrix.cpp.

References kron().

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

Compute Kronecker product matrix.

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

Definition at line 1546 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::rowNum, and vpERROR_TRACE.

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

Compute Kronecker product matrix.

Parameters
m1: vpMatrix;
m2: vpMatrix;
Returns
The kronecker product : $ m1 \otimes m2 $

Definition at line 1587 of file vpMatrix.cpp.

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

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 vpMatrix::loadMatrix ( const std::string &  filename,
vpArray2D< double > &  M,
const bool  binary = false,
char *  header = NULL 
)
inlinestatic

Load a matrix from a file. This function overloads vpArray2D::load().

Parameters
filename: absolute file name.
M: matrix to be loaded.
binary:If true the matrix is loaded from a binary file, else from a text file.
header: Header of the file is loaded in this parameter
Returns
Returns true if no problem appends.
Examples:
testMatrix.cpp.

Definition at line 630 of file vpMatrix.h.

References vpArray2D< Type >::load().

Referenced by vpDot2::defineDots().

static bool vpMatrix::loadMatrixYAML ( const std::string &  filename,
vpArray2D< double > &  M,
char *  header = NULL 
)
inlinestatic

Load a matrix from a YAML-formatted file. This function overloads vpArray2D::loadYAML().

Parameters
filename: absolute file name.
M: matrix to be loaded from the file.
header: Header of the file is loaded in this parameter.
Returns
Returns true if no problem appends.
Examples:
testMatrix.cpp.

Definition at line 646 of file vpMatrix.h.

References vpArray2D< Type >::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:
servoFrankaPBVS.cpp.

Definition at line 424 of file vpArray2D.h.

References vpArray2D< Type >::resize().

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

Print using Maple syntax, to copy/paste in Maple later.

The following code

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix M(2,3);
int cpt = 0;
for (unsigned int i=0; i<M.getRows(); i++)
for (unsigned int j=0; j<M.getCols(); j++)
M[i][j] = cpt++;
std::cout << "M = "; M.maplePrint(std::cout);
}

produces this output:

M = ([
[0, 1, 2, ],
[3, 4, 5, ],
])

that could be copy/paste in Maple.

Definition at line 4348 of file vpMatrix.cpp.

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

Referenced by vpColVector::extract().

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

Print using Matlab syntax, to copy/paste in Matlab later.

The following code

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix M(2,3);
int cpt = 0;
for (unsigned int i=0; i<M.getRows(); i++)
for (unsigned int j=0; j<M.getCols(); j++)
M[i][j] = cpt++;
std::cout << "M = "; M.matlabPrint(std::cout);
}

produces this output:

M = [ 0, 1, 2, ;
3, 4, 5, ]

that could be copy/paste in Matlab:

>> M = [ 0, 1, 2, ;
3, 4, 5, ]
M =
0 1 2
3 4 5
>>

Definition at line 4304 of file vpMatrix.cpp.

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

Referenced by vpColVector::extract().

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

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 806 of file vpMatrix.cpp.

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

Referenced by operator*().

void vpMatrix::mult2Matrices ( const vpMatrix A,
const vpMatrix B,
vpRotationMatrix C 
)
static
Warning
This function is provided for compat with previous releases. You should rather use the functionalities provided in vpRotationMatrix class.

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).

Exceptions
vpException::dimensionErrorIf matrices are not 3-by-3 dimension.

Definition at line 855 of file vpMatrix.cpp.

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

void vpMatrix::mult2Matrices ( const vpMatrix A,
const vpMatrix B,
vpHomogeneousMatrix C 
)
static
Warning
This function is provided for compat with previous releases. You should rather use the functionalities provided in vpHomogeneousMatrix class.

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).

Exceptions
vpException::dimensionErrorIf matrices are not 4-by-4 dimension.

Definition at line 894 of file vpMatrix.cpp.

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

void vpMatrix::mult2Matrices ( const vpMatrix A,
const vpColVector B,
vpColVector C 
)
static
Warning
This function is provided for compat with previous releases. You should rather use multMatrixVector() that is more explicit.

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
multMatrixVector()

Definition at line 932 of file vpMatrix.cpp.

References multMatrixVector().

void vpMatrix::multMatrixVector ( const vpMatrix A,
const vpColVector v,
vpColVector w 
)
static

Operation w = A * v (v and w are vectors).

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 &v) const

Definition at line 765 of file vpMatrix.cpp.

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

Referenced by mult2Matrices(), and operator*().

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

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 1301 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpArray2D< Type >::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

Referenced by operator-().

vpMatrix vpMatrix::operator* ( const vpMatrix B) const

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

See also
mult2Matrices() to avoid matrix allocation for each use.

Definition at line 941 of file vpMatrix.cpp.

References mult2Matrices().

Referenced by vpColVector::operator[](), vpColVector::stackMatrices(), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().

vpMatrix vpMatrix::operator* ( const vpRotationMatrix R) const

Operator that allow to multiply a matrix by a rotation matrix. The matrix should be of dimension m-by-3.

Definition at line 954 of file vpMatrix.cpp.

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

vpMatrix vpMatrix::operator* ( const vpForceTwistMatrix V) const

Operator that allow to multiply a matrix by a force/torque twist matrix. The matrix should be of dimension m-by-6.

Definition at line 1050 of file vpMatrix.cpp.

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

vpTranslationVector vpMatrix::operator* ( const vpTranslationVector tv) const

Operator that allows to multiply a matrix by a translation vector. The matrix should be of dimension (3x3)

Definition at line 725 of file vpMatrix.cpp.

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

vpColVector vpMatrix::operator* ( const vpColVector v) const

Operation w = A * v (matrix A is unchanged, v and w are column vectors).

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

Definition at line 750 of file vpMatrix.cpp.

References multMatrixVector().

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

Operator that allows to multiply all the elements of a matrix by a scalar.

Definition at line 1368 of file vpMatrix.cpp.

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

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

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

Operator that allows to multiply all the elements of a matrix by a scalar.

Definition at line 1424 of file vpMatrix.cpp.

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

Referenced by vpColVector::operator[]().

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

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

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

Definition at line 1171 of file vpMatrix.cpp.

References add2Matrices().

Referenced by vpColVector::operator[]().

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

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

Definition at line 1401 of file vpMatrix.cpp.

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

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

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

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

Definition at line 1251 of file vpMatrix.cpp.

References sub2Matrices().

vpMatrix vpMatrix::operator- ( void  ) const

Operation C = -A (A is unchanged).

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

Definition at line 1319 of file vpMatrix.cpp.

References negateMatrix().

Referenced by vpColVector::operator[]().

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

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

Definition at line 1411 of file vpMatrix.cpp.

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

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

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

Definition at line 1434 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpException::divideByZeroError, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

Referenced by vpColVector::operator[]().

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

Assigment from an array of double. This method has to be used carefully since the array allocated behind x pointer should have the same dimension than the matrix.

Definition at line 607 of file vpMatrix.cpp.

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

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

Copy operator that allows to convert on of the following container that inherit from vpArray2D such as vpMatrix, vpRotationMatrix, vpHomogeneousMatrix, vpPoseVector, vpColVector, vpRowVector... into a vpMatrix.

Parameters
A: 2D array to be copied.

The following example shows how to create a matrix from an homogeneous matrix:

Definition at line 549 of file vpMatrix.cpp.

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

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

Set all the element of the matrix A to x.

Definition at line 596 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< double >::data, and vpArray2D< double >::rowNum.

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

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

Definition at line 262 of file vpArray2D.h.

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

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

Definition at line 264 of file vpArray2D.h.

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

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<<(std::ostream &s, const vpArray2D<Type> &A)
Examples:
testMatrix.cpp.

Definition at line 4181 of file vpMatrix.cpp.

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

Referenced by vpServo::computeControlLaw(), vpColVector::operator[](), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().

void vpMatrix::printSize ( ) const
inline

Definition at line 514 of file vpMatrix.h.

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

vpMatrix vpMatrix::pseudoInverse ( double  svThreshold = 1e-6) const

Compute and return the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$.

Note
By default, this function uses Lapack 3rd party. It is also possible to use a specific 3rd party suffixing this function name with one of the following 3rd party names (Lapack, Eigen3, OpenCV or Gsl).
Warning
To inverse a square n-by-n matrix, you have to use rather one of the following functions inverseByLU(), inverseByQR(), inverseByCholesky() that are kwown as faster.
Parameters
svThreshold: Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.
Returns
The Moore-Penros pseudo inverse $ A^+ $.

Here an example to compute the pseudo-inverse of a 2-by-3 matrix.

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix A(2, 3);
A[0][0] = 2; A[0][1] = 3; A[0][2] = 5;
A[1][0] = -4; A[1][1] = 2; A[1][2] = 3;
A.print(std::cout, 10, "A: ");
A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
}

Once build, the previous example produces the following output:

A: [2,3]=
2 3 5
-4 2 3
A^+ (pseudo-inverse): [3,2]=
0.117899 -0.190782
0.065380 0.039657
0.113612 0.052518
Examples:
testFrankaCartVelocity-2.cpp, testRobotViper650-frames.cpp, and testRobotViper850-frames.cpp.

Definition at line 1932 of file vpMatrix.cpp.

References vpException::fatalError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), insert(), vpArray2D< Type >::resize(), vpColVector::resize(), vpArray2D< Type >::size(), and t().

Referenced by vpSimulatorAfma6::computeArticularVelocity(), vpSimulatorViper850::computeArticularVelocity(), vpServo::computeControlLaw(), computeCovarianceMatrix(), computeCovarianceMatrixVVS(), vpPoseFeatures::computePose(), vpMbEdgeMultiTracker::computeVVSFirstPhasePoseEstimation(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbTracker::computeVVSPoseEstimation(), vpQuadProg::fromCanonicalCost(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), vpMeEllipse::initTracking(), vpHomography::inverse(), vpMeLine::leastSquare(), vpRotationMatrix::mean(), vpHomogeneousMatrix::mean(), vpPose::poseDementhonNonPlan(), vpPose::poseDementhonPlan(), vpPose::poseFromRectangle(), vpPose::poseVirtualVS(), vpMeEllipse::printParameters(), pseudoInverse(), vpHomography::robust(), solveBySVD(), and vpQuadProg::solveQPi().

unsigned int vpMatrix::pseudoInverse ( vpMatrix Ap,
double  svThreshold = 1e-6 
) const

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ and return the rank r of the matrix.

Note
By default, this function uses Lapack 3rd party. It is also possible to use a specific 3rd party suffixing this function name with one of the following 3rd party names (Lapack, Eigen3, OpenCV or Gsl).
Warning
To inverse a square n-by-n matrix, you have to use rather one of the following functions inverseByLU(), inverseByQR(), inverseByCholesky() that are kwown as faster.
Parameters
Ap: The Moore-Penros pseudo inverse $ A^+ $.
svThreshold: Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.
Returns
The rank r of the matrix.

Here an example to compute the pseudo-inverse of a 2-by-3 matrix.

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix A(2, 3);
A[0][0] = 2; A[0][1] = 3; A[0][2] = 5;
A[1][0] = -4; A[1][1] = 2; A[1][2] = 3;
A.print(std::cout, 10, "A: ");
vpMatrix A_p;
unsigned int rank = A.pseudoInverse(A_p);
A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
std::cout << "Rank: " << rank << std::endl;
}

Once build, the previous example produces the following output:

A: [2,3]=
2 3 5
-4 2 3
A^+ (pseudo-inverse): [3,2]=
0.117899 -0.190782
0.065380 0.039657
0.113612 0.052518
Rank: 2

Definition at line 1863 of file vpMatrix.cpp.

References vpException::fatalError.

unsigned int vpMatrix::pseudoInverse ( vpMatrix Ap,
vpColVector sv,
double  svThreshold = 1e-6 
) const

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ along with singular values and return the rank r of the matrix.

Note
By default, this function uses Lapack 3rd party. It is also possible to use a specific 3rd party suffixing this function name with one of the following 3rd party names (Lapack, Eigen3, OpenCV or Gsl).
Warning
To inverse a square n-by-n matrix, you have to use rather one of the following functions inverseByLU(), inverseByQR(), inverseByCholesky() that are kwown as faster.
Parameters
Ap: The Moore-Penros pseudo inverse $ A^+ $.
svVector corresponding to matrix $A$ singular values. The size of this vector is equal to min(m, n).
svThreshold: Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.
Returns
The rank r of the matrix $\bf A$.

Here an example to compute the pseudo-inverse of a 2-by-3 matrix.

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix A(2, 3);
A[0][0] = 2; A[0][1] = 3; A[0][2] = 5;
A[1][0] = -4; A[1][1] = 2; A[1][2] = 3;
A.print(std::cout, 10, "A: ");
vpMatrix A_p;
unsigned int rank = A.pseudoInverse(A_p, sv);
A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
std::cout << "Rank: " << rank << std::endl;
std::cout << "Singular values: " << sv.t() << std::endl;
}

Once build, the previous example produces the following output:

A: [2,3]=
2 3 5
-4 2 3
A^+ (pseudo-inverse): [3,2]=
0.117899 -0.190782
0.065380 0.039657
0.113612 0.052518
Rank: 2
Singular values: 6.874359351 4.443330227

Definition at line 3449 of file vpMatrix.cpp.

References vpException::fatalError.

unsigned int vpMatrix::pseudoInverse ( vpMatrix Ap,
vpColVector sv,
double  svThreshold,
vpMatrix imA,
vpMatrix imAt 
) const

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ along with singular values, $\mbox{Im}(A)$ and $\mbox{Im}(A^T)$ and return the rank r of the matrix.

See pseudoInverse(vpMatrix &, vpColVector &, double, vpMatrix &, vpMatrix &, vpMatrix &) const for a complete description of this function.

Warning
To inverse a square n-by-n matrix, you have to use rather one of the following functions inverseByLU(), inverseByQR(), inverseByCholesky() that are kwown as faster.
Parameters
Ap: The Moore-Penros pseudo inverse $ A^+ $.
svVector corresponding to matrix $A$ singular values. The size of this vector is equal to min(m, n).
svThreshold: Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.
imA$\mbox{Im}({\bf A})$ that is a m-by-r matrix.
imAt$\mbox{Im}({\bf A}^T)$ that is n-by-r matrix.
Returns
The rank r of the matrix $\bf A$.

Here an example to compute the pseudo-inverse of a 2-by-3 matrix.

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix A(2, 3);
A[0][0] = 2; A[0][1] = 3; A[0][2] = 5;
A[1][0] = -4; A[1][1] = 2; A[1][2] = 3;
A.print(std::cout, 10, "A: ");
vpMatrix A_p;
vpMatrix imA, imAt;
unsigned int rank = A.pseudoInverse(A_p, sv, 1e-6, imA, imAt);
A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
std::cout << "Rank: " << rank << std::endl;
std::cout << "Singular values: " << sv.t() << std::endl;
imA.print(std::cout, 10, "Im(A): ");
imAt.print(std::cout, 10, "Im(A^T): ");
}

Once build, the previous example produces the following output:

A: [2,3]=
2 3 5
-4 2 3
A^+ (pseudo-inverse): [3,2]=
0.117899 -0.190782
0.065380 0.039657
0.113612 0.052518
Rank: 2
Singular values: 6.874359351 4.443330227
Im(A): [2,2]=
0.81458 -0.58003
0.58003 0.81458
Im(A^T): [3,2]=
-0.100515 -0.994397
0.524244 -0.024967
0.845615 -0.102722

Definition at line 3543 of file vpMatrix.cpp.

References pseudoInverse().

unsigned int vpMatrix::pseudoInverse ( vpMatrix Ap,
vpColVector sv,
double  svThreshold,
vpMatrix imA,
vpMatrix imAt,
vpMatrix kerAt 
) const

Compute the Moore-Penros pseudo inverse $A^+$ of a m-by-n matrix $\bf A$ along with singular values, $\mbox{Im}(A)$, $\mbox{Im}(A^T)$ and $\mbox{Ker}(A)$ and return the rank r of the matrix.

Note
By default, this function uses Lapack 3rd party. It is also possible to use a specific 3rd party suffixing this function name with one of the following 3rd party names (Lapack, Eigen3, OpenCV or Gsl).
Warning
To inverse a square n-by-n matrix, you have to use rather inverseByLU(), inverseByCholesky(), or inverseByQR() that are kwown as faster.

Using singular value decomposition, we have:

\[ {\bf A}_{m\times n} = {\bf U}_{m\times m} \; {\bf S}_{m\times n} \; {\bf V^\top}_{n\times n} \]

\[ {\bf A}_{m\times n} = \left[\begin{array}{ccc}\mbox{Im} ({\bf A}) & | & \mbox{Ker} ({\bf A}^\top) \end{array} \right] {\bf S}_{m\times n} \left[ \begin{array}{c} \left[\mbox{Im} ({\bf A}^\top)\right]^\top \\ \\ \hline \\ \left[\mbox{Ker}({\bf A})\right]^\top \end{array}\right] \]

where the diagonal of ${\bf S}_{m\times n}$ corresponds to the matrix $A$ singular values.

This equation could be reformulated in a minimal way:

\[ {\bf A}_{m\times n} = \mbox{Im} ({\bf A}) \; {\bf S}_{r\times n} \left[ \begin{array}{c} \left[\mbox{Im} ({\bf A}^\top)\right]^\top \\ \\ \hline \\ \left[\mbox{Ker}({\bf A})\right]^\top \end{array}\right] \]

where the diagonal of ${\bf S}_{r\times n}$ corresponds to the matrix $A$ first r singular values.

The null space of a matrix $\bf A$ is defined as $\mbox{Ker}({\bf A}) = { {\bf X} : {\bf A}*{\bf X} = {\bf 0}}$.

Parameters
ApThe Moore-Penros pseudo inverse $ {\bf A}^+ $.
svVector corresponding to matrix $A$ singular values. The size of this vector is equal to min(m, n).
svThresholdThreshold used to test the singular values. If a singular value is lower than this threshold we consider that the matrix is not full rank.
imA$\mbox{Im}({\bf A})$ that is a m-by-r matrix.
imAt$\mbox{Im}({\bf A}^T)$ that is n-by-r matrix.
kerAtThe matrix that contains the null space (kernel) of $\bf A$ defined by the matrix ${\bf X}^T$. If matrix $\bf A$ is full rank, the dimension of kerAt is (0, n), otherwise the dimension is (n-r, n). This matrix is thus the transpose of $\mbox{Ker}({\bf A})$.
Returns
The rank r of the matrix $\bf A$.

Here an example to compute the pseudo-inverse of a 2-by-3 matrix.

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix A(2, 3);
A[0][0] = 2; A[0][1] = 3; A[0][2] = 5;
A[1][0] = -4; A[1][1] = 2; A[1][2] = 3;
A.print(std::cout, 10, "A: ");
vpMatrix A_p, imA, imAt, kerAt;
unsigned int rank = A.pseudoInverse(A_p, sv, 1e-6, imA, imAt, kerAt);
A_p.print(std::cout, 10, "A^+ (pseudo-inverse): ");
std::cout << "Rank: " << rank << std::endl;
std::cout << "Singular values: " << sv.t() << std::endl;
imA.print(std::cout, 10, "Im(A): ");
imAt.print(std::cout, 10, "Im(A^T): ");
if (kerAt.size()) {
kerAt.t().print(std::cout, 10, "Ker(A): ");
}
else {
std::cout << "Ker(A) empty " << std::endl;
}
// Reconstruct matrix A from ImA, ImAt, KerAt
vpMatrix S(rank, A.getCols());
for(unsigned int i = 0; i< rank; i++)
S[i][i] = sv[i];
vpMatrix Vt(A.getCols(), A.getCols());
Vt.insert(imAt.t(), 0, 0);
Vt.insert(kerAt, rank, 0);
(imA * S * Vt).print(std::cout, 10, "Im(A) * S * [Im(A^T) | Ker(A)]^T:");
}

Once build, the previous example produces the following output:

A: [2,3]=
2 3 5
-4 2 3
A^+ (pseudo-inverse): [3,2]=
0.117899 -0.190782
0.065380 0.039657
0.113612 0.052518
Rank: 2
Singular values: 6.874359351 4.443330227
Im(A): [2,2]=
0.81458 -0.58003
0.58003 0.81458
Im(A^T): [3,2]=
-0.100515 -0.994397
0.524244 -0.024967
0.845615 -0.102722
Ker(A): [3,1]=
-0.032738
-0.851202
0.523816
Im(A) * S * [Im(A^T) | Ker(A)]^T:[2,3]=
2 3 5
-4 2 3

Definition at line 3684 of file vpMatrix.cpp.

References vpException::fatalError.

unsigned int vpMatrix::qr ( vpMatrix Q,
vpMatrix R,
bool  full = false,
bool  squareR = false,
double  tol = 1e-6 
) const

Compute the QR decomposition of a (m x n) matrix of rank r. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.

Parameters
Q: orthogonal matrix (will be modified).
R: upper-triangular matrix (will be modified).
full: whether or not we want full decomposition.
squareR: will return only the square (min(m,n) x min(m,n)) part of R.
tol: tolerance to test the rank of R.
Returns
The rank r of the matrix.

If full is false (default) then Q is (m x min(n,m)) and R is (min(n,m) x n). We then have this = QR.

If full is true and m > n then Q is (m x m) and R is (n x n). In this case this = Q (R, 0)^T

If squareR is true and n > m then R is (m x m). If r = m then R is invertible.

Here an example:

#include <visp3/core/vpMatrix.h>
double residual(vpMatrix M1, vpMatrix M2)
{
return (M1 - M2).euclideanNorm();
}
int main()
{
vpMatrix A(4,3);
A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/3.;
A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.;
A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/2.;
A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/6.;
// Economic QR (Q 4x3, R 3x3)
vpMatrix Q, R;
int r = A.qr(A, R);
std::cout << "QR Residual: "
<< residual(A, Q*R) << std::endl;
// Full QR (Q 4x4, R 3x3)
r = A.qr(Q, R, true);
std::cout << "Full QR Residual: "
<< residual(A, Q.extract(0, 0, 4, 3)*R) << std::endl;
}
See also
qrPivot()

Definition at line 339 of file vpMatrix_qr.cpp.

References vpException::badValue, vpArray2D< double >::colNum, vpArray2D< double >::data, vpException::fatalError, vpArray2D< Type >::resize(), and vpArray2D< double >::rowNum.

Referenced by vpLinProg::colReduction().

unsigned int vpMatrix::qrPivot ( vpMatrix Q,
vpMatrix R,
vpMatrix P,
bool  full = false,
bool  squareR = false,
double  tol = 1e-6 
) const

Compute the QR pivot decomposition of a (m x n) matrix of rank r. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.

Parameters
Q: orthogonal matrix (will be modified).
R: upper-triangular matrix (will be modified).
P: the (n x n) permutation matrix.
full: whether or not we want full decomposition.
squareR: will return only the (r x r) part of R and the (r x n) part of P.
tol: tolerance to test the rank of R.
Returns
The rank r of the matrix.

If full is false (default) then Q is (m x min(n,m)) and R is (min(n,m) x n). We then have this.P = Q.R.

If full is true and m > n then Q is (m x m) and R is (n x n). In this case this.P = Q (R, 0)^T

If squareR is true then R is (r x r) invertible.

Here an example:

#include <visp3/core/vpMatrix.h>
double residual(vpMatrix M1, vpMatrix M2)
{
return (M1 - M2).euclideanNorm();
}
int main()
{
vpMatrix A(4,3);
A[0][0] = 1/1.; A[0][1] = 1/2.; A[0][2] = 1/2.;
A[1][0] = 1/5.; A[1][1] = 1/3.; A[1][2] = 1/3.;
A[2][0] = 1/6.; A[2][1] = 1/4.; A[2][2] = 1/4.;
A[3][0] = 1/7.; A[3][1] = 1/5.; A[3][2] = 1/5.;
// A is rank (4x3) but rank 2
// Economic QR (Q 4x3, R 3x3)
vpMatrix Q, R, P;
int r = A.qrPivot(Q, R, P);
std::cout << "A rank: " << r << std::endl;
std::cout << "Residual: " << residual(A*P, Q*R) << std::endl;
// Full QR (Q 4x4, R 3x3)
r = A.qrPivot(Q, R, P, true);
std::cout << "QRPivot Residual: " <<
residual(A*P, Q.extract(0, 0, 4, 3)*R) << std::endl;
// Using permutation matrix: keep only non-null part of R
Q.resize(4, r, false); // Q is 4 x 2
R = R.extract(0, 0, r, 3)*P.t(); // R is 2 x 3
std::cout << "Full QRPivot Residual: " <<
residual(A, Q*R) << std::endl;
}
See also
qrPivot()

Definition at line 539 of file vpMatrix_qr.cpp.

References vpException::badValue, vpArray2D< double >::colNum, vpArray2D< double >::data, vpException::fatalError, vpArray2D< Type >::resize(), and vpArray2D< double >::rowNum.

Referenced by vpLinProg::colReduction(), vpLinProg::rowReduction(), and solveByQR().

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 diag(), eye(), init(), operator=(), and stack().

vpRowVector vpMatrix::row ( const unsigned int  i)
Deprecated:
This method is deprecated. You should rather use getRow(). More precisely, the following code:
unsigned int row_index = ...;
... = L.row(row_index);

should be replaced with:

... = L.getRow(row_index - 1);
Warning
Notice row(1) is the 0th row. This function returns the i-th row of the matrix.
Parameters
i: Index of the row to extract noting that row index start at 1 to get the first row.

Definition at line 5276 of file vpMatrix.cpp.

References vpArray2D< double >::getCols().

Referenced by expm().

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 vpMatrix::saveMatrix ( const std::string &  filename,
const vpArray2D< double > &  M,
const bool  binary = false,
const char *  header = "" 
)
inlinestatic

Save a matrix to a file. This function overloads vpArray2D::load().

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.

Examples:
testMatrix.cpp.

Definition at line 665 of file vpMatrix.h.

References vpArray2D< Type >::save().

Referenced by vpDot2::defineDots().

static bool vpMatrix::saveMatrixYAML ( const std::string &  filename,
const vpArray2D< double > &  M,
const char *  header = "" 
)
inlinestatic

Save a matrix in a YAML-formatted file. This function overloads vpArray2D::saveYAML().

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

Definition at line 683 of file vpMatrix.h.

References vpArray2D< Type >::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::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, and tutorial-franka-acquire-calib-data.cpp.

Definition at line 595 of file vpArray2D.h.

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

void vpMatrix::setIdentity ( const double &  val = 1.0)
Deprecated:
You should rather use diag(const double &)
Deprecated:
You should rather use diag(const double &)

Set the matrix diagonal elements to val. More generally set M[i][i] = val.

Definition at line 5317 of file vpMatrix.cpp.

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

Referenced by vpVelocityTwistMatrix::init(), vpColVector::rows(), and vpServo::secondaryTask().

void vpMatrix::solveByQR ( const vpColVector b,
vpColVector x 
) const

Solve a linear system Ax = b using QR Decomposition.

Non destructive wrt. A and b.

Parameters
b: Vector b
x: Vector x
Warning
If Ax = b does not have a solution, this method does not return the least-square minimizer. Use solveBySVD() to get this vector.

Here an example:

#include <visp3/core/vpColVector.h>
#include <visp3/core/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.solveByQR(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
qrPivot()

Definition at line 794 of file vpMatrix_qr.cpp.

References vpArray2D< double >::colNum, extract(), inverseTriangular(), qrPivot(), and t().

Referenced by solveByQR().

vpColVector vpMatrix::solveByQR ( const vpColVector b) const

Solve a linear system Ax = b using QR Decomposition.

Non destructive wrt. A and B.

Parameters
b: Vector b
Returns
Vector x
Warning
If Ax = b does not have a solution, this method does not return the least-square minimizer. Use solveBySVD() to get this vector.

Here an example:

#include <visp3/core/vpColVector.h>
#include <visp3/core/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.solveByQR(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
qrPivot()

Definition at line 846 of file vpMatrix_qr.cpp.

References vpArray2D< double >::colNum, and solveByQR().

void vpMatrix::solveBySVD ( const vpColVector b,
vpColVector x 
) const

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 <visp3/core/vpColVector.h>
#include <visp3/core/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 &)
Examples:
quadprog.cpp, and quadprog_eq.cpp.

Definition at line 1669 of file vpMatrix.cpp.

References pseudoInverse().

Referenced by vpQuadProg::solveByProjection(), solveBySVD(), and vpQuadProg::solveQPe().

vpColVector vpMatrix::solveBySVD ( const vpColVector B) const

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 <visp3/core/vpColVector.h>
#include <visp3/core/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 1720 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, and solveBySVD().

void vpMatrix::stack ( const vpRowVector r)

Stack row vector r at the end of the current matrix, or copy if the matrix has no dimensions: this = [ this r ]^T.

Here an example for a robot velocity log :

for(unsigned int i = 0;i<100;i++)
{
robot.getVelocity(vpRobot::ARTICULAR_FRAME, v);
Velocities.stack(v.t());
}

Definition at line 4493 of file vpMatrix.cpp.

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

void vpMatrix::stack ( const vpColVector c)

Stack column vector c at the right of the current matrix, or copy if the matrix has no dimensions: this = [ this c ].

Here an example for a robot velocity log :

for(unsigned int i = 0;i<100;i++)
{
robot.getVelocity(vpRobot::ARTICULAR_FRAME, v);
Velocities.stack(v);
}

Definition at line 4532 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::dimensionError, vpArray2D< Type >::getRows(), vpArray2D< double >::resize(), vpArray2D< double >::rowNum, vpArray2D< double >::rowPtrs, and vpArray2D< Type >::size().

vpMatrix vpMatrix::stack ( const vpMatrix A,
const vpMatrix B 
)
static

Stack matrix B to the end of matrix A and return the resulting matrix [ A B ]^T

Parameters
A: Upper matrix.
B: Lower matrix.
Returns
Stacked matrix [ A B ]^T
Warning
A and B must have the same number of columns.

Definition at line 3916 of file vpMatrix.cpp.

References stack().

vpMatrix vpMatrix::stack ( const vpMatrix A,
const vpRowVector r 
)
static

Stack row vector r to matrix A and return the resulting matrix [ A r ]^T

Parameters
A: Upper matrix.
r: Lower row vector.
Returns
Stacked matrix [ A r ]^T
Warning
A and r must have the same number of columns.

Definition at line 3980 of file vpMatrix.cpp.

References stack().

vpMatrix vpMatrix::stack ( const vpMatrix A,
const vpColVector c 
)
static

Stack column vector c to matrix A and return the resulting matrix [ A c ]

Parameters
A: Left matrix.
c: Right column vector.
Returns
Stacked matrix [ A c ]
Warning
A and c must have the same number of rows.

Definition at line 4019 of file vpMatrix.cpp.

References stack().

void vpMatrix::stack ( const vpMatrix A,
const vpMatrix B,
vpMatrix C 
)
static

Stack matrix B to the end of matrix A and return the resulting matrix in C.

Parameters
A: Upper matrix.
B: Lower matrix.
C: Stacked matrix C = [ A B ]^T
Warning
A and B must have the same number of columns. A and C, B and C must be two different objects.

Definition at line 3936 of file vpMatrix.cpp.

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

void vpMatrix::stack ( const vpMatrix A,
const vpRowVector r,
vpMatrix C 
)
static

Stack row vector r to the end of matrix A and return the resulting matrix in C.

Parameters
A: Upper matrix.
r: Lower row vector.
C: Stacked matrix C = [ A r ]^T
Warning
A and r must have the same number of columns. A and C must be two different objects.

Definition at line 3999 of file vpMatrix.cpp.

References vpArray2D< Type >::data, and stack().

void vpMatrix::stack ( const vpMatrix A,
const vpColVector c,
vpMatrix C 
)
static

Stack column vector c to the end of matrix A and return the resulting matrix in C.

Parameters
A: Left matrix.
c: Right column vector.
C: Stacked matrix C = [ A c ]
Warning
A and c must have the same number of rows. A and C must be two different objects.

Definition at line 4038 of file vpMatrix.cpp.

References vpArray2D< Type >::data, and stack().

void vpMatrix::stackColumns ( vpColVector out)
vpColVector vpMatrix::stackColumns ( )

Stacks columns of a matrix in a vector.

Returns
a vpColVector.

Definition at line 1474 of file vpMatrix.cpp.

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

vp_deprecated void vpMatrix::stackMatrices ( const vpMatrix A)
inline
Deprecated:
You should rather use stack(const vpMatrix &A)

Definition at line 703 of file vpMatrix.h.

static vp_deprecated vpMatrix vpMatrix::stackMatrices ( const vpMatrix A,
const vpMatrix B 
)
inlinestatic
Deprecated:
You should rather use stack(const vpMatrix &A, const vpMatrix &B)

Definition at line 708 of file vpMatrix.h.

static vp_deprecated void vpMatrix::stackMatrices ( const vpMatrix A,
const vpMatrix B,
vpMatrix C 
)
inlinestatic
Deprecated:
You should rather use stack(const vpMatrix &A, const vpMatrix &B, vpMatrix &C)

Definition at line 713 of file vpMatrix.h.

References operator*().

vpMatrix vpMatrix::stackMatrices ( const vpMatrix A,
const vpRowVector B 
)
static
Deprecated:
You should rather use stack(const vpMatrix &A, const vpMatrix &B)

Definition at line 5254 of file vpMatrix.cpp.

References stack().

void vpMatrix::stackMatrices ( const vpMatrix A,
const vpRowVector B,
vpMatrix C 
)
static
Deprecated:
You should rather use stack(const vpMatrix &A, const vpRowVector &B, vpMatrix &C)

Definition at line 5256 of file vpMatrix.cpp.

References stack().

vpMatrix vpMatrix::stackMatrices ( const vpColVector A,
const vpColVector B 
)
static
Deprecated:
You should rather use vpColVector::stack(const vpColVector &A, const vpColVector &B)

Definition at line 5244 of file vpMatrix.cpp.

References vpColVector::stack().

void vpMatrix::stackMatrices ( const vpColVector A,
const vpColVector B,
vpColVector C 
)
static
Deprecated:
You should rather use vpColVector::stack(const vpColVector &A, const vpColVector &B, vpColVector &C)

Definition at line 5249 of file vpMatrix.cpp.

References vpColVector::stack().

vpRowVector vpMatrix::stackRows ( )

Stacks rows of a matrix in a vector.

Returns
a vpRowVector.

Definition at line 1500 of file vpMatrix.cpp.

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

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

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).

Exceptions
vpException::dimensionErrorIf A and B matrices have not the same size.
See also
operator-()

Definition at line 1226 of file vpMatrix.cpp.

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

Referenced by operator-().

void vpMatrix::sub2Matrices ( const vpColVector A,
const vpColVector B,
vpColVector C 
)
static
Warning
This function is provided for compat with previous releases. You should rather use the functionalities provided in vpColVector class.

Operation C = A - B on column vectors.

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

Exceptions
vpException::dimensionErrorIf A and B vectors have not the same size.
See also
vpColVector::operator-()

Definition at line 1193 of file vpMatrix.cpp.

References vpArray2D< Type >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpColVector::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

double vpMatrix::sum ( ) const

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

Returns
Value of $\sum a_{ij}$

Definition at line 1326 of file vpMatrix.cpp.

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

Referenced by expm(), and vpColVector::resize().

double vpMatrix::sumSquare ( ) const

Return the sum square of all the $A_{ij}$ elements of the matrix $A(m, n)$.

Returns
The value $\sum A_{ij}^{2}$.

Definition at line 5138 of file vpMatrix.cpp.

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

Referenced by vpColVector::resize().

void vpMatrix::svd ( vpColVector w,
vpMatrix V 
)

Matrix singular value decomposition (SVD).

This function calls the first following function that is available:

  • svdLapack() if Lapack 3rd party is installed
  • svdEigen3() if Eigen3 3rd party is installed
  • svdOpenCV() if OpenCV 3rd party is installed
  • svdGsl() if GSL 3rd party is installed.

If none of these previous 3rd parties is installed, we use by default svdLapack() with a Lapack built-in version.

Given matrix $M$, this function computes it singular value decomposition such as

\[ M = U \Sigma V^{\top} \]

Warning
This method is destructive wrt. to the matrix $ M $ to decompose. You should make a COPY of that matrix if needed.
Parameters
w: Vector of singular values: $ \Sigma = diag(w) $.
V: Matrix $ V $.
Returns
Matrix $ U $.
Note
The singular values are ordered in decreasing fashion in w. It means that the highest singular value is in w[0].

Here an example of SVD decomposition of a non square Matrix M.

#include <visp3/core/vpMatrix.h>
int main()
{
vpMatrix M(3,2);
M[0][0] = 1; M[0][1] = 6;
M[1][0] = 2; M[1][1] = 8;
M[2][0] = 0.5; M[2][1] = 9;
vpMatrix V, Sigma, U = M;
U.svd(w, V);
// Construct the diagonal matrix from the singular values
Sigma.diag(w);
// Reconstruct the initial matrix using the decomposition
vpMatrix Mrec = U * Sigma * V.t();
// Here, Mrec is obtained equal to the initial value of M
// Mrec[0][0] = 1; Mrec[0][1] = 6;
// Mrec[1][0] = 2; Mrec[1][1] = 8;
// Mrec[2][0] = 0.5; Mrec[2][1] = 9;
std::cout << "Reconstructed M matrix: \n" << Mrec << std::endl;
}
See also
svdLapack(), svdEigen3(), svdOpenCV(), svdGsl()
Examples:
servoMomentImage.cpp.

Definition at line 1792 of file vpMatrix.cpp.

References vpException::fatalError.

Referenced by vpHomography::computeDisplacement(), cond(), vpHomography::DLT(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), and kernel().

void vpMatrix::transpose ( vpMatrix At) const

Compute At the transpose of the matrix.

Parameters
At(output) : Resulting transpose matrix.
See also
t()

Definition at line 406 of file vpMatrix.cpp.

References vpArray2D< double >::colNum, vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, vpArray2D< Type >::rowPtrs, and vpArray2D< double >::rowPtrs.

Friends And Related Function Documentation

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

Allow to multiply a scalar by a matrix.

Definition at line 1350 of file vpMatrix.cpp.

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

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

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 AtA(), vpQuaternionVector::buildFrom(), vpHomogeneousMatrix::buildFrom(), vpRzyzVector::buildFrom(), vpThetaUVector::buildFrom(), vpRxyzVector::buildFrom(), vpRzyxVector::buildFrom(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpColVector::clear(), vpHomogeneousMatrix::convert(), detByLU(), vpTranslationVector::euclideanNorm(), vpRowVector::euclideanNorm(), euclideanNorm(), expm(), vpThetaUVector::extract(), getRow(), vpThetaUVector::getTheta(), vpThetaUVector::getU(), vpColVector::hadamard(), hadamard(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpColVector::insert(), insert(), inverseByCholesky(), vpTranslationVector::operator*(), vpRowVector::operator*(), vpColVector::operator*(), vpHomography::operator*(), operator*(), vpTranslationVector::operator-(), vpRowVector::operator-(), vpColVector::operator-(), vpTranslationVector::operator/(), vpRowVector::operator/(), vpColVector::operator/(), vpHomography::operator/(), vpHomography::operator/=(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpQuaternionVector::operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpRzyzVector::operator=(), vpRxyzVector::operator=(), vpRzyxVector::operator=(), vpColVector::operator=(), operator=(), vpThetaUVector::operator=(), vpColVector::operator==(), vpColVector::operator[](), qr(), qrPivot(), vpRowVector::reshape(), vpColVector::reshape(), vpQuaternionVector::set(), stack(), stackRows(), vpColVector::sum(), vpColVector::sumSquare(), vpRotationVector::t(), vpTranslationVector::t(), vpPoseVector::t(), vpRowVector::t(), vpColVector::t(), vpRotationVector::toStdVector(), vpRowVector::toStdVector(), vpColVector::toStdVector(), vpColVector::vpColVector(), vpMatrix(), vpQuaternionVector::w(), vpQuaternionVector::x(), vpQuaternionVector::y(), vpQuaternionVector::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 AAt(), AtA(), vpColVector::clear(), detByLU(), diag(), eigenValues(), expm(), vpColVector::extract(), eye(), vpColVector::hadamard(), hadamard(), vpColVector::infinityNorm(), infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), insert(), inverseByCholesky(), inverseTriangular(), vpRotationMatrix::operator*(), vpTranslationVector::operator*(), vpHomogeneousMatrix::operator*(), vpColVector::operator*(), operator*(), vpRotationMatrix::operator*=(), vpTranslationVector::operator*=(), vpColVector::operator*=(), operator*=(), vpColVector::operator+(), vpColVector::operator+=(), operator+=(), vpColVector::operator-(), vpColVector::operator-=(), operator-=(), vpColVector::operator/(), operator/(), vpTranslationVector::operator/=(), vpColVector::operator/=(), operator/=(), operator<<(), vpColVector::operator<<(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpSubMatrix::operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), operator=(), vpColVector::operator==(), qr(), qrPivot(), vpColVector::reshape(), setIdentity(), stack(), vpColVector::stack(), stackColumns(), stackRows(), vpColVector::sum(), sum(), vpRotationVector::sumSquare(), vpTranslationVector::sumSquare(), vpColVector::sumSquare(), sumSquare(), vpTranslationVector::t(), vpPoseVector::t(), vpColVector::t(), t(), transpose(), vpColVector::vpColVector(), and vpMatrix().