Visual Servoing Platform
version 3.2.0 under development (2019-01-22)
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#include <visp3/core/vpSubMatrix.h>
Public Types | |
enum | vpDetMethod { LU_DECOMPOSITION } |
Public Member Functions | |
vpSubMatrix () | |
vpSubMatrix (vpMatrix &m, const unsigned int &row, const unsigned int &col, const unsigned int &nrows, const unsigned int &ncols) | |
virtual | ~vpSubMatrix () |
void | init (vpMatrix &m, const unsigned int &row, const unsigned int &col, const unsigned int &nrows, const unsigned int &ncols) |
void | checkParentStatus () const |
vpSubMatrix & | operator= (const vpSubMatrix &B) |
vpSubMatrix & | operator= (const vpMatrix &B) |
vpSubMatrix & | operator= (const double &x) |
void | clear () |
Setting a diagonal matrix | |
void | diag (const double &val=1.0) |
void | diag (const vpColVector &A) |
void | eye () |
Assignment operators | |
vpMatrix & | operator<< (double *) |
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 |
double | detByLUEigen3 () const |
double | detByLUGsl () const |
double | detByLULapack () const |
double | detByLUOpenCV () const |
vpMatrix | expm () const |
vpMatrix & | operator+= (const vpMatrix &B) |
vpMatrix & | operator+= (const double x) |
vpMatrix & | operator-= (const vpMatrix &B) |
vpMatrix & | operator-= (const double x) |
vpMatrix | operator* (const vpMatrix &B) const |
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 double x) const |
vpMatrix | operator+ (const vpMatrix &B) const |
vpMatrix | operator- (const vpMatrix &B) const |
vpMatrix | operator- () const |
vpMatrix & | operator*= (const double x) |
vpMatrix & | operator/= (double x) |
vpMatrix | operator/ (const double x) const |
double | sum () const |
double | sumSquare () const |
Hadamard product | |
vpMatrix | hadamard (const vpMatrix &m) const |
Inherited functionalities from vpArray2D | |
vpArray2D< double > | hadamard (const vpArray2D< double > &m) const |
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 |
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 | inverseByLUEigen3 () const |
vpMatrix | inverseByLUGsl () const |
vpMatrix | inverseByLULapack () const |
vpMatrix | inverseByLUOpenCV () const |
vpMatrix | inverseByCholesky () const |
vpMatrix | inverseByCholeskyLapack () const |
vpMatrix | inverseByCholeskyOpenCV () const |
vpMatrix | inverseByQR () const |
vpMatrix | inverseByQRLapack () 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 |
vpMatrix | pseudoInverseLapack (double svThreshold=1e-6) const |
unsigned int | pseudoInverseLapack (vpMatrix &Ap, double svThreshold=1e-6) const |
unsigned int | pseudoInverseLapack (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const |
unsigned int | pseudoInverseLapack (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const |
vpMatrix | pseudoInverseEigen3 (double svThreshold=1e-6) const |
unsigned int | pseudoInverseEigen3 (vpMatrix &Ap, double svThreshold=1e-6) const |
unsigned int | pseudoInverseEigen3 (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const |
unsigned int | pseudoInverseEigen3 (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const |
vpMatrix | pseudoInverseOpenCV (double svThreshold=1e-6) const |
unsigned int | pseudoInverseOpenCV (vpMatrix &Ap, double svThreshold=1e-6) const |
unsigned int | pseudoInverseOpenCV (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const |
unsigned int | pseudoInverseOpenCV (vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const |
vpMatrix | pseudoInverseGsl (double svThreshold=1e-6) const |
unsigned int | pseudoInverseGsl (vpMatrix &Ap, double svThreshold=1e-6) const |
unsigned int | pseudoInverseGsl (vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const |
unsigned int | pseudoInverseGsl (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) |
void | svdEigen3 (vpColVector &w, vpMatrix &V) |
void | svdGsl (vpColVector &w, vpMatrix &V) |
void | svdLapack (vpColVector &w, vpMatrix &V) |
void | svdOpenCV (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 |
Static Public Member Functions | |
Stacking with Static Public Member Functions | |
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) |
static vpMatrix | juxtaposeMatrices (const vpMatrix &A, const vpMatrix &B) |
static void | juxtaposeMatrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C) |
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) |
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) |
Setting a diagonal matrix with Static Public Member Functions | |
static void | createDiagonalMatrix (const vpColVector &A, vpMatrix &DA) |
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) |
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 | pRowNum |
unsigned int | pColNum |
vpMatrix * | parent |
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) |
Definition of the vpSubMatrix vpSubMatrix class provides a mask on a vpMatrix all properties of vpMatrix are available with a vpSubMatrix.
Definition at line 62 of file vpSubMatrix.h.
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Method used to compute the determinant of a square matrix.
Enumerator | |
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LU_DECOMPOSITION |
LU decomposition method. |
Definition at line 111 of file vpMatrix.h.
vpSubMatrix::vpSubMatrix | ( | ) |
Default constructor.
Definition at line 45 of file vpSubMatrix.cpp.
vpSubMatrix::vpSubMatrix | ( | vpMatrix & | m, |
const unsigned int & | row_offset, | ||
const unsigned int & | col_offset, | ||
const unsigned int & | nrows, | ||
const unsigned int & | ncols | ||
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Constructor.
m | : parent matrix |
row_offset | : row offset |
col_offset | : col offset |
nrows | : number of rows of the sub matrix |
ncols | : number of columns of the sub matrix |
Definition at line 55 of file vpSubMatrix.cpp.
References vpMatrix::init().
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virtual |
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Computes the operation
Definition at line 426 of file vpMatrix.cpp.
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Compute the AAt operation such as .
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.
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.
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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).
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 vpMatrix::operator+().
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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).
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.
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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).
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.
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Compute the AtA operation such as
Definition at line 524 of file vpMatrix.cpp.
Referenced by vpMbDepthDenseTracker::computeVVS(), vpMbDepthNormalTracker::computeVVS(), vpMbGenericTracker::computeVVS(), vpMbEdgeMultiTracker::computeVVSFirstPhasePoseEstimation(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbTracker::computeVVSPoseEstimation(), vpTemplateTrackerWarpHomographySL3::findWarp(), vpNurbs::globalCurveApprox(), vpMbGenericTracker::track(), and vpTemplateTrackerWarp::warp().
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Compute the AtA operation such as .
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.
Definition at line 480 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, and vpArray2D< Type >::rowNum.
void vpSubMatrix::checkParentStatus | ( | ) | const |
Check is parent vpRowVector has changed since initialization.
This method can be used to detect if the parent matrix always exits or its size have not changed and throw an exception is not.
Definition at line 104 of file vpSubMatrix.cpp.
References vpArray2D< double >::data, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrixException::incorrectMatrixSizeError, parent, pColNum, and pRowNum.
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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().
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should be replaced with:
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().
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Compute the covariance matrix of the parameters x from a least squares minimisation defined as: Ax = b
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(), vpMatrix::pseudoInverse(), and vpMatrix::t().
Referenced by vpMatrix::computeCovarianceMatrixVVS(), vpPoseFeatures::computePose(), and vpPose::poseVirtualVSrobust().
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Compute the covariance matrix of the parameters x from a least squares minimisation defined as: WAx = Wb
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 vpMatrix::t().
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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.
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 vpMatrix::computeCovarianceMatrix(), vpHomogeneousMatrix::extract(), vpMatrix::eye(), vpArray2D< Type >::getRows(), vpMatrix::pseudoInverse(), vpMath::sinc(), vpTranslationVector::skew(), vpColVector::skew(), vpMath::sqr(), and vpColVector::sumSquare().
Referenced by vpMatrix::computeCovarianceMatrixVVS(), vpMbTracker::computeCovarianceMatrixVVS(), and vpPose::poseVirtualVS().
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Compute the covariance matrix of an image-based virtual visual servoing. This assumes the optimization has been done via v = Ls.pseudoInverse() * DeltaS.
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 vpMatrix::computeCovarianceMatrix(), and vpMatrix::computeCovarianceMatrixVVS().
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Compute
H | : input Matrix . This matrix should be square. |
alpha | : Scalar |
HLM | : Resulting operation. |
Definition at line 5071 of file vpMatrix.cpp.
References vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), and vpArray2D< Type >::resize().
Referenced by vpTemplateTrackerWarpHomographySL3::findWarp(), vpTemplateTrackerSSDESM::initCompInverse(), vpTemplateTrackerSSDInverseCompositional::initCompInverse(), vpTemplateTrackerZNCCForwardAdditional::initHessienDesired(), vpTemplateTrackerMIForwardCompositional::initHessienDesired(), vpTemplateTrackerZNCCInverseCompositional::initHessienDesired(), vpTemplateTrackerMIESM::initHessienDesired(), vpTemplateTrackerMIForwardAdditional::initHessienDesired(), vpTemplateTrackerMIInverseCompositional::initHessienDesired(), vpTemplateTracker::setHDes(), vpTemplateTrackerSSDForwardCompositional::trackNoPyr(), vpTemplateTrackerMIForwardCompositional::trackNoPyr(), vpTemplateTrackerSSDESM::trackNoPyr(), vpTemplateTrackerSSDForwardAdditional::trackNoPyr(), vpTemplateTrackerMIESM::trackNoPyr(), vpTemplateTrackerMIForwardAdditional::trackNoPyr(), vpTemplateTrackerMIInverseCompositional::trackNoPyr(), and vpTemplateTrackerWarp::warp().
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Definition at line 5045 of file vpMatrix.cpp.
References vpArray2D< Type >::getCols(), and vpMatrix::svd().
Referenced by vpTemplateTrackerMIForwardCompositional::trackNoPyr(), vpTemplateTrackerMIESM::trackNoPyr(), vpTemplateTrackerMIForwardAdditional::trackNoPyr(), and vpTemplateTrackerMIInverseCompositional::trackNoPyr().
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Perform a 2D convolution similar to Matlab conv2 function: .
M | : First matrix. |
kernel | : Second matrix. |
mode | : Convolution mode: "full" (default), "same", "valid". |
Definition at line 5164 of file vpMatrix.cpp.
Referenced by vpImageFilter::getSobelKernelY().
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Perform a 2D convolution similar to Matlab conv2 function: .
M | : First matrix. |
kernel | : Second matrix. |
res | : Result. |
mode | : Convolution mode: "full" (default), "same", "valid". |
Definition at line 5183 of file vpMatrix.cpp.
References vpArray2D< Type >::data, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrix::insert(), and vpArray2D< Type >::resize().
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Print to be used as part of a C++ code later.
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:
It produces the following output that could be copy/paste in a C++ code:
Definition at line 4438 of file vpMatrix.cpp.
References vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().
Referenced by vpColVector::clear().
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Create a diagonal matrix with the element of a vector .
A | : Vector which element will be put in the diagonal. |
DA | : Diagonal matrix DA[i][i] = A[i] |
Definition at line 712 of file vpMatrix.cpp.
References vpArray2D< Type >::getRows(), and vpArray2D< Type >::resize().
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Print/save a matrix in csv format.
The following code
produces log.csv file that contains:
Definition at line 4389 of file vpMatrix.cpp.
References vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().
Referenced by vpColVector::clear().
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Compute the determinant of a n-by-n matrix.
method | : Method used to compute the determinant. Default LU decomposition method is faster than the method based on Gaussian elimination. |
Definition at line 4906 of file vpMatrix.cpp.
References vpMatrix::detByLU(), and vpMatrix::LU_DECOMPOSITION.
Referenced by vpTriangle::buildFrom(), vpHomography::computeDisplacement(), vpMatrix::detByLUGsl(), vpMatrix::detByLULapack(), vpMatrix::detByLUOpenCV(), and vpTemplateTrackerTriangle::init().
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inherited |
Compute the determinant of a square matrix using the LU decomposition.
This function calls the first following function that is available:
If none of these previous 3rd parties is installed, we use by default detByLULapack() with a Lapack built-in version.
Definition at line 180 of file vpMatrix_lu.cpp.
References vpArray2D< double >::colNum, vpMatrix::detByLUEigen3(), vpMatrix::detByLUGsl(), vpMatrix::detByLULapack(), vpMatrix::detByLUOpenCV(), vpException::fatalError, and vpArray2D< double >::rowNum.
Referenced by vpMatrix::det().
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inherited |
Compute the determinant of a square matrix using the LU decomposition with Eigen3 3rd party.
Definition at line 624 of file vpMatrix_lu.cpp.
References vpArray2D< double >::colNum, vpArray2D< double >::data, vpException::fatalError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), and vpArray2D< double >::rowNum.
Referenced by vpMatrix::detByLU().
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inherited |
Compute the determinant of a square matrix using the LU decomposition with GSL 3rd party.
Definition at line 301 of file vpMatrix_lu.cpp.
References vpArray2D< double >::colNum, vpMatrix::det(), vpException::fatalError, and vpArray2D< double >::rowNum.
Referenced by vpMatrix::detByLU().
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inherited |
Compute the determinant of a square matrix using the LU decomposition with GSL 3rd party.
Definition at line 421 of file vpMatrix_lu.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpMatrix::det(), vpException::fatalError, and vpArray2D< double >::rowNum.
Referenced by vpMatrix::detByLU().
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inherited |
Compute the determinant of a n-by-n matrix using the LU decomposition with OpenCV 3rd party.
Definition at line 533 of file vpMatrix_lu.cpp.
References vpArray2D< double >::colNum, vpArray2D< double >::data, vpMatrix::det(), vpException::fatalError, and vpArray2D< double >::rowNum.
Referenced by vpMatrix::detByLU().
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inherited |
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.
val | : Value to set. |
Matrix A is now equal to:
Definition at line 693 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, and vpArray2D< double >::rowNum.
Referenced by vpMbTracker::computeCovarianceMatrixVVS(), and vpQuadProg::fromCanonicalCost().
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inherited |
Create a diagonal matrix with the element of a vector.
A | : Vector which element will be put in the diagonal. |
Matrix A is now equal to:
Definition at line 653 of file vpMatrix.cpp.
References vpArray2D< Type >::getRows(), and vpArray2D< double >::resize().
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inherited |
Compute the eigenvalues of a n-by-n real symmetric matrix.
vpException::dimensionError | If the matrix is not square. |
vpException::fatalError | If the matrix is not symmetric. |
vpException::functionNotImplementedError | If the GSL library is not detected. |
Here an example:
Definition at line 4624 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpException::dimensionError, vpException::fatalError, vpException::functionNotImplementedError, vpArray2D< double >::rowNum, and vpMatrix::t().
Referenced by vpQuadProg::fromCanonicalCost().
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inherited |
Compute the eigenvalues of a n-by-n real symmetric matrix.
evalue | : Eigenvalues of the matrix. |
evector | : Eigenvector of the matrix. |
vpException::dimensionError | If the matrix is not square. |
vpException::fatalError | If the matrix is not symmetric. |
vpException::functionNotImplementedError | If the GSL library is not detected. |
Here an example:
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 vpMatrix::t().
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inherited |
Compute and return the Euclidean norm .
Definition at line 5096 of file vpMatrix.cpp.
References vpArray2D< double >::data, and vpArray2D< double >::dsize.
Referenced by vpColVector::deg2rad().
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inherited |
Compute the exponential matrix of a square matrix.
Definition at line 4924 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< double >::data, vpArray2D< Type >::data, vpException::dimensionError, vpMatrix::eye(), vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrix::inverseByLU(), vpMatrix::row(), vpArray2D< double >::rowNum, and vpMatrix::sum().
Referenced by vpTemplateTrackerWarpHomographySL3::computeCoeff().
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inherited |
Extract a sub matrix from a matrix M.
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:
It produces the following output:
Definition at line 319 of file vpMatrix.cpp.
References vpException::dimensionError, vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().
Referenced by vpLinProg::colReduction(), vpLinProg::rowReduction(), vpMatrix::solveByQR(), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().
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inherited |
Set an m-by-n matrix to identity with ones on the diagonal and zeros else where.
Definition at line 360 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, and vpArray2D< double >::rowNum.
Referenced by vpLinProg::colReduction(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrixVVS(), vpServo::computeProjectionOperators(), vpMbDepthDenseTracker::computeVVS(), vpMbDepthNormalTracker::computeVVS(), vpMbGenericTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpMbEdgeMultiTracker::computeVVSFirstPhasePoseEstimation(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbTracker::computeVVSPoseEstimation(), vpMatrix::expm(), vpMatrix::eye(), vpTemplateTrackerWarpHomographySL3::getdW0(), vpTemplateTrackerWarpHomographySL3::getdWdp0(), vpFeatureThetaU::interaction(), vpMeLine::leastSquare(), vpPose::poseFromRectangle(), vpMeEllipse::printParameters(), vpServo::setServo(), vpLinProg::solveLP(), vpMbGenericTracker::track(), vpMbTracker::vpMbTracker(), vpRobotCamera::vpRobotCamera(), vpServo::vpServo(), vpSimulatorCamera::vpSimulatorCamera(), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().
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inherited |
Extract a column vector from a matrix.
j | : Index of the column to extract. If j=0, the first column is extracted. |
The following example shows how to use this function:
It produces the following output:
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(), vpMatrix::kernel(), vpPose::poseFromRectangle(), vpServo::secondaryTaskJointLimitAvoidance(), and vpLinProg::simplex().
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inherited |
Extract a column vector from a matrix.
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. |
The following example shows how to use this function:
It produces the following output:
Definition at line 3749 of file vpMatrix.cpp.
References vpException::dimensionError, vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().
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inlineinherited |
Return the number of columns of the 2D array.
Definition at line 146 of file vpArray2D.h.
References vpArray2D< Type >::colNum, vpArray2D< Type >::getMaxValue(), and vpArray2D< Type >::getMinValue().
Referenced by vpRowVector::cppPrint(), vpMatrix::cppPrint(), vpRowVector::csvPrint(), vpMatrix::csvPrint(), vpMatrix::detByLUEigen3(), vpMatrix::extract(), vpRotationMatrix::getCol(), vpHomogeneousMatrix::getCol(), vpMatrix::getCol(), vpMatrix::getRow(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByQRLapack(), vpMatrix::kernel(), vpRowVector::maplePrint(), vpMatrix::maplePrint(), vpRowVector::matlabPrint(), vpMatrix::matlabPrint(), vpRowVector::operator*(), vpRowVector::operator+(), vpRowVector::operator+=(), vpRowVector::operator-(), vpRowVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpRowVector::print(), vpMatrix::print(), vpMatrix::pseudoInverse(), vpMatrix::row(), vpMatrix::svdEigen3(), vpMatrix::svdGsl(), vpMatrix::svdLapack(), and vpMatrix::svdOpenCV().
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inherited |
Return the array max value.
|
inherited |
Return the array min value.
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inherited |
Extract a row vector from a matrix.
i | : Index of the row to extract. If i=0, the first row is extracted. |
The following example shows how to use this function:
It produces the following output:
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().
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inherited |
Extract a row vector from a matrix.
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. |
The following example shows how to use this function:
It produces the following output:
Definition at line 3896 of file vpMatrix.cpp.
References vpException::dimensionError, vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().
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inlineinherited |
Return the number of rows of the 2D array.
Definition at line 156 of file vpArray2D.h.
References vpArray2D< Type >::rowNum.
Referenced by vpMatrix::column(), vpColVector::cppPrint(), vpMatrix::cppPrint(), vpColVector::csvPrint(), vpMatrix::csvPrint(), vpMatrix::detByLUEigen3(), vpMatrix::extract(), vpRotationMatrix::getCol(), vpHomogeneousMatrix::getCol(), vpMatrix::getCol(), vpMatrix::getRow(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByQRLapack(), vpMatrix::kernel(), vpColVector::maplePrint(), vpMatrix::maplePrint(), vpColVector::matlabPrint(), vpMatrix::matlabPrint(), vpColVector::operator+(), vpColVector::operator+=(), vpColVector::operator-(), vpColVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpPoseVector::print(), vpColVector::print(), vpMatrix::print(), vpMatrix::pseudoInverse(), vpMatrix::svdEigen3(), vpMatrix::svdGsl(), vpMatrix::svdLapack(), and vpMatrix::svdOpenCV().
Compute the Hadamard product (element wise matrix multiplication).
m | : Second matrix; |
Compute the Hadamard product (element wise matrix multiplication).
m | : Second matrix; |
Definition at line 1513 of file vpMatrix.cpp.
References vpCPUFeatures::checkSSE2(), vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::dimensionError, vpArray2D< double >::dsize, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::resize(), and vpArray2D< double >::rowNum.
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inherited |
Compute and return the infinity norm with where is the matrix size.
Definition at line 5117 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.
Referenced by vpLinProg::colReduction(), and vpColVector::extract().
void vpSubMatrix::init | ( | vpMatrix & | m, |
const unsigned int & | row_offset, | ||
const unsigned int & | col_offset, | ||
const unsigned int & | nrows, | ||
const unsigned int & | ncols | ||
) |
Initialisation of vpMatrix.
Initialisation of a sub matrix.
m | : parent matrix |
row_offset | : row offset |
col_offset | : col offset |
nrows | : number of rows of the sub matrix |
ncols | : number of columns of the sub matrix |
Definition at line 70 of file vpSubMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpArray2D< double >::dsize, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrixException::incorrectMatrixSizeError, parent, pColNum, pRowNum, vpArray2D< double >::rowNum, vpArray2D< double >::rowPtrs, and vpMatrixException::subMatrixError.
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inherited |
Initialize the matrix from a part of an input matrix M.
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:
It produces the following output:
Definition at line 258 of file vpMatrix.cpp.
References vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::resize(), and vpArray2D< double >::rowPtrs.
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inlineinherited |
Definition at line 686 of file vpMatrix.h.
Referenced by vpColVector::extract(), vpMatrix::vpMatrix(), and vpSubMatrix().
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inherited |
Insert matrix A at the given position in the current matrix.
A | : The matrix to insert. |
r | : The index of the row to begin to insert data. |
c | : The index of the column to begin to insert data. |
Definition at line 4570 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::rowNum, and vpArray2D< Type >::size().
Referenced by vpMbEdgeKltTracker::computeVVS(), vpMbEdgeMultiTracker::computeVVS(), vpMbDepthDenseTracker::computeVVSInteractionMatrixAndResidu(), vpMbDepthNormalTracker::computeVVSInteractionMatrixAndResidu(), vpMbKltMultiTracker::computeVVSInteractionMatrixAndResidu(), vpMbEdgeMultiTracker::computeVVSInteractionMatrixAndResidu(), vpMbEdgeKltMultiTracker::computeVVSInteractionMatrixAndResidu(), vpMbGenericTracker::computeVVSInteractionMatrixAndResidu(), vpMatrix::conv2(), vpNurbs::curveKnotIns(), vpColVector::extract(), vpMatrix::insert(), vpMatrix::juxtaposeMatrices(), vpMatrix::kernel(), vpMatrix::pseudoInverse(), vpMatrix::stack(), vpColVector::stackMatrices(), and vpMbGenericTracker::track().
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staticinherited |
Insert matrix B in matrix A at the given position.
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. |
Definition at line 4061 of file vpMatrix.cpp.
References vpMatrix::insert().
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staticinherited |
Insert matrix B in matrix A at the given position.
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. |
Definition at line 4083 of file vpMatrix.cpp.
References vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), and vpArray2D< Type >::resize().
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inherited |
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:
If none of these 3rd parties is installed we use a Lapack built-in version.
Here an example:
Definition at line 105 of file vpMatrix_cholesky.cpp.
References vpException::fatalError, vpMatrix::inverseByCholeskyLapack(), and vpMatrix::inverseByCholeskyOpenCV().
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inherited |
Compute the inverse of a n-by-n matrix using the Cholesky decomposition with Lapack 3rd party. The matrix must be real symmetric positive defined.
Here an example:
Definition at line 155 of file vpMatrix_cholesky.cpp.
References vpException::badValue, vpArray2D< double >::colNum, vpArray2D< Type >::data, vpException::fatalError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::getRows(), vpMatrixException::matrixError, and vpArray2D< double >::rowNum.
Referenced by vpMatrix::inverseByCholesky().
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inherited |
Compute the inverse of a n-by-n matrix using the Cholesky decomposition with OpenCV 3rd party. The matrix must be real symmetric positive defined.
Here an example:
Definition at line 224 of file vpMatrix_cholesky.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::fatalError, and vpArray2D< double >::rowNum.
Referenced by vpMatrix::inverseByCholesky().
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inherited |
Compute the inverse of a n-by-n matrix using the LU decomposition.
This function calls the first following function that is available:
If none of these previous 3rd parties is installed, we use by default inverseByLULapack() with a Lapack built-in version.
Here an example:
Definition at line 130 of file vpMatrix_lu.cpp.
References vpException::fatalError, vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByLUGsl(), vpMatrix::inverseByLULapack(), and vpMatrix::inverseByLUOpenCV().
Referenced by vpTriangle::buildFrom(), vpMatrix::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().
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inherited |
Compute the inverse of a n-by-n matrix using the LU decomposition with Eigen3 3rd party.
Here an example:
Definition at line 582 of file vpMatrix_lu.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::fatalError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), and vpArray2D< double >::rowNum.
Referenced by vpMatrix::inverseByLU().
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inherited |
Compute the inverse of a n-by-n matrix using the LU decomposition with GSL 3rd party.
Here an example:
Definition at line 237 of file vpMatrix_lu.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpException::fatalError, and vpArray2D< double >::rowNum.
Referenced by vpMatrix::inverseByLU().
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inherited |
Compute the inverse of a n-by-n matrix using the LU decomposition with Lapack 3rd party.
Here an example:
Definition at line 366 of file vpMatrix_lu.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpException::fatalError, and vpArray2D< double >::rowNum.
Referenced by vpMatrix::inverseByLU().
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inherited |
Compute the inverse of a n-by-n matrix using the LU decomposition with OpenCV 3rd party.
Here an example:
Definition at line 492 of file vpMatrix_lu.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::data, vpException::fatalError, and vpArray2D< double >::rowNum.
Referenced by vpMatrix::inverseByLU().
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inherited |
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.
Here an example:
Definition at line 273 of file vpMatrix_qr.cpp.
References vpException::fatalError, and vpMatrix::inverseByQRLapack().
Referenced by vpLinProg::simplex().
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inherited |
Compute the inverse of a n-by-n matrix using the QR decomposition with Lapack 3rd party.
Here an example:
Definition at line 112 of file vpMatrix_qr.cpp.
References vpException::badValue, vpArray2D< double >::colNum, vpArray2D< Type >::data, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpArray2D< Type >::getRows(), vpMatrixException::matrixError, and vpArray2D< double >::rowNum.
Referenced by vpMatrix::inverseByQR().
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inherited |
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.
upper | : if it is an upper triangular matrix |
The function does not check if the matrix is actually upper or lower triangular.
Definition at line 713 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 vpMatrix::solveByQR().
Juxtapose to matrices C = [ A B ].
A | : Left matrix. |
B | : Right matrix. |
Definition at line 4114 of file vpMatrix.cpp.
Referenced by vpLinProg::colReduction().
Juxtapose to matrices C = [ A B ].
A | : Left matrix. |
B | : Right matrix. |
C | : Juxtaposed matrix C = [ A B ] |
Definition at line 4135 of file vpMatrix.cpp.
References vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrix::insert(), and vpArray2D< Type >::resize().
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inherited |
Function to compute the null space (the kernel) of a m-by-n matrix .
The null space of a matrix is defined as .
kerAt | The matrix that contains the null space (kernel) of defined by the matrix . If matrix is full rank, the dimension of kerAt is (0, n), otherwise the dimension is (n-r, n). This matrix is thus the transpose of . |
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. |
Definition at line 4821 of file vpMatrix.cpp.
References vpMatrix::getCol(), vpArray2D< double >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::getRows(), vpMatrix::insert(), vpArray2D< Type >::resize(), vpColVector::sumSquare(), and vpMatrix::svd().
Compute Kronecker product matrix.
m | : vpMatrix. |
out | : If m1.kron(m2) out contains the kronecker product's result : . |
Definition at line 1579 of file vpMatrix.cpp.
Referenced by vpMatrix::kron().
Compute Kronecker product matrix.
m | : vpMatrix; |
Definition at line 1617 of file vpMatrix.cpp.
References vpMatrix::kron().
Compute Kronecker product matrix.
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.
Compute Kronecker product matrix.
Definition at line 1587 of file vpMatrix.cpp.
References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().
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inlinestaticinherited |
Load a matrix from a file.
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. |
Definition at line 322 of file vpArray2D.h.
References vpException::badValue, and vpArray2D< Type >::resize().
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inlinestaticinherited |
Load a matrix from a file. This function overloads vpArray2D::load().
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 |
Definition at line 618 of file vpMatrix.h.
References vpArray2D< Type >::load().
Referenced by vpDot2::defineDots().
|
inlinestaticinherited |
Load a matrix from a YAML-formatted file. This function overloads vpArray2D::loadYAML().
filename | : absolute file name. |
M | : matrix to be loaded from the file. |
header | : Header of the file is loaded in this parameter. |
Definition at line 634 of file vpMatrix.h.
References vpArray2D< Type >::loadYAML().
|
inlinestaticinherited |
Load an array from a YAML-formatted file.
filename | : absolute file name. |
A | : array to be loaded from the file. |
header | : header of the file is loaded in this parameter. |
Definition at line 434 of file vpArray2D.h.
References vpArray2D< Type >::resize().
|
inherited |
Print using Maple syntax, to copy/paste in Maple later.
The following code
produces this output:
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().
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inherited |
Print using Matlab syntax, to copy/paste in Matlab later.
The following code
produces this output:
that could be copy/paste in Matlab:
Definition at line 4304 of file vpMatrix.cpp.
References vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().
Referenced by vpColVector::extract().
|
staticinherited |
Operation C = A * B.
The result is placed in the third parameter C and not returned. A new matrix won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).
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 vpMatrix::operator*().
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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).
vpException::dimensionError | If 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.
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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).
vpException::dimensionError | If 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.
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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).
Definition at line 932 of file vpMatrix.cpp.
References vpMatrix::multMatrixVector().
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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).
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 vpMatrix::mult2Matrices(), and vpMatrix::operator*().
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).
Definition at line 1301 of file vpMatrix.cpp.
References vpArray2D< Type >::colNum, vpArray2D< Type >::resize(), vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.
Referenced by vpMatrix::operator-().
Operation C = A * B (A is unchanged).
Definition at line 941 of file vpMatrix.cpp.
References vpMatrix::mult2Matrices().
Referenced by vpColVector::operator[](), vpColVector::stackMatrices(), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().
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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.
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Operator that allow to multiply a matrix by a velocity twist matrix. The matrix should be of dimension m-by-6.
Definition at line 981 of file vpMatrix.cpp.
References vpCPUFeatures::checkSSE2(), vpArray2D< double >::colNum, vpArray2D< Type >::colNum, vpArray2D< double >::data, vpArray2D< Type >::data, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.
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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.
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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.
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Operation w = A * v (matrix A is unchanged, v and w are column vectors).
Definition at line 750 of file vpMatrix.cpp.
References vpMatrix::multMatrixVector().
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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.
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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[]().
Operation C = A + B (A is unchanged).
Definition at line 1171 of file vpMatrix.cpp.
References vpMatrix::add2Matrices().
Referenced by vpColVector::operator[]().
Operation A = A + B.
Definition at line 1260 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::rowNum, vpArray2D< Type >::rowPtrs, and vpArray2D< double >::rowPtrs.
Referenced by vpColVector::operator[]().
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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.
Operation C = A - B (A is unchanged).
Definition at line 1251 of file vpMatrix.cpp.
References vpMatrix::sub2Matrices().
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Operation C = -A (A is unchanged).
Definition at line 1319 of file vpMatrix.cpp.
References vpMatrix::negateMatrix().
Referenced by vpColVector::operator[]().
Operation A = A - B.
Definition at line 1277 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::rowNum, vpArray2D< Type >::rowPtrs, and vpArray2D< double >::rowPtrs.
Referenced by vpColVector::operator[]().
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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.
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Cij = Aij / x (A is unchanged)
Definition at line 1380 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpException::divideByZeroError, vpArray2D< Type >::resize(), vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.
Referenced by vpColVector::operator[]().
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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[]().
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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.
vpSubMatrix & vpSubMatrix::operator= | ( | const vpSubMatrix & | B | ) |
Operation such as subA = subB.
Operation A = B.
B | : a subMatrix |
Definition at line 140 of file vpSubMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrixException::incorrectMatrixSizeError, parent, pColNum, pRowNum, vpArray2D< double >::rowNum, vpArray2D< double >::rowPtrs, and vpArray2D< Type >::rowPtrs.
vpSubMatrix & vpSubMatrix::operator= | ( | const vpMatrix & | B | ) |
Operation such as subA = B.
Operation A = B.
B | : a matrix |
Definition at line 120 of file vpSubMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrixException::incorrectMatrixSizeError, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.
vpSubMatrix & vpSubMatrix::operator= | ( | const double & | x | ) |
Operation such as subA = x.
Operation A = x.
x | : a scalar |
Definition at line 166 of file vpSubMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.
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Set element using A[i][j] = x.
Definition at line 266 of file vpArray2D.h.
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Get element using x = A[i][j].
Definition at line 268 of file vpArray2D.h.
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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.
s | Stream used for the printing. |
length | The suggested width of each matrix element. The actual width grows in order to accomodate the whole integral part, and shrinks if the whole extent is not needed for all the numbers. |
intro | The introduction which is printed before the matrix. Can be set to zero (or omitted), in which case the introduction is not printed. |
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().
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Definition at line 502 of file vpMatrix.h.
References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().
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Compute and return the Moore-Penros pseudo inverse of a m-by-n matrix .
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. |
Here an example to compute the pseudo-inverse of a 2-by-3 matrix.
Once build, the previous example produces the following output:
Definition at line 1932 of file vpMatrix.cpp.
References vpException::fatalError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpMatrix::insert(), vpMatrix::pseudoInverseEigen3(), vpMatrix::pseudoInverseGsl(), vpMatrix::pseudoInverseLapack(), vpMatrix::pseudoInverseOpenCV(), vpArray2D< Type >::resize(), vpColVector::resize(), vpArray2D< Type >::size(), vpMatrix::svdEigen3(), vpMatrix::svdGsl(), vpMatrix::svdLapack(), vpMatrix::svdOpenCV(), and vpMatrix::t().
Referenced by vpSimulatorAfma6::computeArticularVelocity(), vpSimulatorViper850::computeArticularVelocity(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), vpMatrix::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(), vpMatrix::pseudoInverse(), vpHomography::robust(), vpMatrix::solveBySVD(), and vpQuadProg::solveQPi().
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Compute the Moore-Penros pseudo inverse of a m-by-n matrix and return the rank r of the matrix.
Ap | : The Moore-Penros pseudo inverse . |
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. |
Here an example to compute the pseudo-inverse of a 2-by-3 matrix.
Once build, the previous example produces the following output:
Definition at line 1863 of file vpMatrix.cpp.
References vpException::fatalError, vpMatrix::pseudoInverseEigen3(), vpMatrix::pseudoInverseGsl(), vpMatrix::pseudoInverseLapack(), and vpMatrix::pseudoInverseOpenCV().
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Compute the Moore-Penros pseudo inverse of a m-by-n matrix along with singular values and return the rank r of the matrix.
Ap | : The Moore-Penros pseudo inverse . |
sv | Vector corresponding to matrix 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. |
Here an example to compute the pseudo-inverse of a 2-by-3 matrix.
Once build, the previous example produces the following output:
Definition at line 3449 of file vpMatrix.cpp.
References vpException::fatalError, vpMatrix::pseudoInverseEigen3(), vpMatrix::pseudoInverseGsl(), vpMatrix::pseudoInverseLapack(), and vpMatrix::pseudoInverseOpenCV().
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Compute the Moore-Penros pseudo inverse of a m-by-n matrix along with singular values, and and return the rank r of the matrix.
See pseudoInverse(vpMatrix &, vpColVector &, double, vpMatrix &, vpMatrix &, vpMatrix &) const for a complete description of this function.
Ap | : The Moore-Penros pseudo inverse . |
sv | Vector corresponding to matrix 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 | that is a m-by-r matrix. |
imAt | that is n-by-r matrix. |
Here an example to compute the pseudo-inverse of a 2-by-3 matrix.
Once build, the previous example produces the following output:
Definition at line 3543 of file vpMatrix.cpp.
References vpMatrix::pseudoInverse().
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Compute the Moore-Penros pseudo inverse of a m-by-n matrix along with singular values, , and and return the rank r of the matrix.
Using singular value decomposition, we have:
where the diagonal of corresponds to the matrix singular values.
This equation could be reformulated in a minimal way:
where the diagonal of corresponds to the matrix first r singular values.
The null space of a matrix is defined as .
Ap | The Moore-Penros pseudo inverse . |
sv | Vector corresponding to matrix 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 | that is a m-by-r matrix. |
imAt | that is n-by-r matrix. |
kerAt | The matrix that contains the null space (kernel) of defined by the matrix . If matrix is full rank, the dimension of kerAt is (0, n), otherwise the dimension is (n-r, n). This matrix is thus the transpose of . |
Here an example to compute the pseudo-inverse of a 2-by-3 matrix.
Once build, the previous example produces the following output:
Definition at line 3684 of file vpMatrix.cpp.
References vpException::fatalError, vpMatrix::pseudoInverseEigen3(), vpMatrix::pseudoInverseGsl(), vpMatrix::pseudoInverseLapack(), and vpMatrix::pseudoInverseOpenCV().
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Referenced by vpMatrix::pseudoInverse().
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Referenced by vpMatrix::pseudoInverse().
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Referenced by vpMatrix::pseudoInverse().
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Referenced by vpMatrix::pseudoInverse().
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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.
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. |
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:
Definition at line 337 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().
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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.
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. |
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:
Definition at line 537 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 vpMatrix::solveByQR().
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Set the size of the array and initialize all the values to zero.
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. |
Definition at line 171 of file vpArray2D.h.
References vpArray2D< Type >::colNum, vpArray2D< Type >::dsize, vpException::memoryAllocationError, vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.
Referenced by vpMatrix::diag(), vpMatrix::eye(), vpMatrix::init(), vpMatrix::operator=(), vpMatrix::stack(), and vpMatrix::svdOpenCV().
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should be replaced with:
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 vpMatrix::expm().
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Save a matrix to a file.
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. |
Warning : If you save the matrix as in a text file the precision is less than if you save it in a binary file.
Definition at line 519 of file vpArray2D.h.
References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().
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Save a matrix to a file. This function overloads vpArray2D::load().
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. |
Warning : If you save the matrix as in a text file the precision is less than if you save it in a binary file.
Definition at line 653 of file vpMatrix.h.
References vpArray2D< Type >::save().
Referenced by vpDot2::defineDots().
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Save a matrix in a YAML-formatted file. This function overloads vpArray2D::saveYAML().
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. |
Definition at line 671 of file vpMatrix.h.
References vpArray2D< Type >::saveYAML().
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Save an array in a YAML-formatted file.
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. |
Here is an example of outputs.
Content of matrix.yml:
Content of matrixIndent.yml:
Definition at line 612 of file vpArray2D.h.
References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().
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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().
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Return the number of elements of the 2D array.
Definition at line 158 of file vpArray2D.h.
References vpArray2D< Type >::rowNum.
Referenced by vpRowVector::insert(), vpColVector::insert(), vpColVector::operator*(), vpMatrix::stack(), vpRotationVector::toStdVector(), vpRowVector::toStdVector(), and vpColVector::toStdVector().
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Solve a linear system Ax = b using QR Decomposition.
Non destructive wrt. A and b.
b | : Vector b |
x | : Vector x |
Here an example:
Definition at line 792 of file vpMatrix_qr.cpp.
References vpArray2D< double >::colNum, vpMatrix::extract(), vpMatrix::inverseTriangular(), vpMatrix::qrPivot(), and vpMatrix::t().
Referenced by vpMatrix::solveByQR().
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Solve a linear system Ax = b using QR Decomposition.
Non destructive wrt. A and B.
b | : Vector b |
Here an example:
Definition at line 844 of file vpMatrix_qr.cpp.
References vpArray2D< double >::colNum, and vpMatrix::solveByQR().
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Solve a linear system using Singular Value Decomposition (SVD).
Non destructive wrt. A and B.
b | : Vector . |
x | : Vector . |
Here an example:
Definition at line 1669 of file vpMatrix.cpp.
References vpMatrix::pseudoInverse().
Referenced by vpQuadProg::solveByProjection(), vpMatrix::solveBySVD(), and vpQuadProg::solveQPe().
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Solve a linear system using Singular Value Decomposition (SVD).
Non destructive wrt. A and B.
B | : Vector . |
Here an example:
Definition at line 1720 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, and vpMatrix::solveBySVD().
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Stack A at the end of the current matrix, or copy if the matrix has no dimensions : this = [ this A ]^T.
Definition at line 4462 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpException::dimensionError, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpMatrix::insert(), vpArray2D< double >::resize(), and vpArray2D< double >::rowNum.
Referenced by vpPoseFeatures::addFeatureSegment(), vpColVector::cross(), vpFeatureVanishingPoint::interaction(), vpFeatureEllipse::interaction(), vpFeatureSegment::interaction(), vpGenericFeature::interaction(), vpFeaturePoint::interaction(), vpFeatureMoment::interaction(), vpFeatureLine::interaction(), vpFeaturePoint3D::interaction(), vpFeatureThetaU::interaction(), vpFeaturePointPolar::interaction(), vpFeatureTranslation::interaction(), vpColVector::resize(), vpLinProg::rowReduction(), vpMatrix::stack(), vpColVector::stackMatrices(), and vpMatrix::stackMatrices().
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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 :
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().
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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 :
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().
Stack matrix B to the end of matrix A and return the resulting matrix [ A B ]^T
A | : Upper matrix. |
B | : Lower matrix. |
Definition at line 3916 of file vpMatrix.cpp.
References vpMatrix::stack().
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Stack row vector r to matrix A and return the resulting matrix [ A r ]^T
A | : Upper matrix. |
r | : Lower row vector. |
Definition at line 3980 of file vpMatrix.cpp.
References vpMatrix::stack().
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Stack column vector c to matrix A and return the resulting matrix [ A c ]
A | : Left matrix. |
c | : Right column vector. |
Definition at line 4019 of file vpMatrix.cpp.
References vpMatrix::stack().
Stack matrix B to the end of matrix A and return the resulting matrix in C.
A | : Upper matrix. |
B | : Lower matrix. |
C | : Stacked matrix C = [ A B ]^T |
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().
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Stack row vector r to the end of matrix A and return the resulting matrix in C.
A | : Upper matrix. |
r | : Lower row vector. |
C | : Stacked matrix C = [ A r ]^T |
Definition at line 3999 of file vpMatrix.cpp.
References vpArray2D< Type >::data, and vpMatrix::stack().
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Stack column vector c to the end of matrix A and return the resulting matrix in C.
A | : Left matrix. |
c | : Right column vector. |
C | : Stacked matrix C = [ A c ] |
Definition at line 4038 of file vpMatrix.cpp.
References vpArray2D< Type >::data, and vpMatrix::stack().
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Stacks columns of a matrix in a vector.
out | : a vpColVector. |
Definition at line 1457 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpColVector::resize(), vpArray2D< Type >::rowNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.
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Stacks columns of a matrix in a vector.
Definition at line 1474 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, and vpArray2D< double >::rowNum.
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Definition at line 691 of file vpMatrix.h.
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Definition at line 696 of file vpMatrix.h.
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Definition at line 701 of file vpMatrix.h.
References operator*().
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Definition at line 5254 of file vpMatrix.cpp.
References vpMatrix::stack().
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Definition at line 5256 of file vpMatrix.cpp.
References vpMatrix::stack().
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Definition at line 5244 of file vpMatrix.cpp.
References vpColVector::stack().
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Definition at line 5249 of file vpMatrix.cpp.
References vpColVector::stack().
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Stacks rows of a matrix in a vector
out | : a vpRowVector. |
Definition at line 1485 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< double >::data, vpArray2D< Type >::data, vpArray2D< double >::dsize, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), vpRowVector::resize(), and vpArray2D< double >::rowNum.
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Stacks rows of a matrix in a vector.
Definition at line 1500 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, and vpArray2D< double >::rowNum.
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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).
vpException::dimensionError | If A and B matrices have not the same size. |
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 vpMatrix::operator-().
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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).
vpException::dimensionError | If A and B vectors have not the same size. |
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.
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Return the sum of all the elements of the matrix.
Definition at line 1326 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.
Referenced by vpMatrix::expm(), and vpColVector::resize().
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Return the sum square of all the elements of the matrix .
Definition at line 5138 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.
Referenced by vpColVector::resize().
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Matrix singular value decomposition (SVD).
This function calls the first following function that is available:
If none of these previous 3rd parties is installed, we use by default svdLapack() with a Lapack built-in version.
Given matrix , this function computes it singular value decomposition such as
w | : Vector of singular values: . |
V | : Matrix . |
Here an example of SVD decomposition of a non square Matrix M.
Definition at line 1792 of file vpMatrix.cpp.
References vpException::fatalError, vpMatrix::svdEigen3(), vpMatrix::svdGsl(), vpMatrix::svdLapack(), and vpMatrix::svdOpenCV().
Referenced by vpHomography::computeDisplacement(), vpMatrix::cond(), vpHomography::DLT(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), vpMatrix::kernel(), and vpMatrix::svdEigen3().
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Singular value decomposition (SVD) using Eigen3 3rd party.
Given matrix , this function computes it singular value decomposition such as
w | : Vector of singular values: . |
V | : Matrix . |
Here an example of SVD decomposition of a non square Matrix M.
Definition at line 451 of file vpMatrix_svd.cpp.
References vpArray2D< double >::data, vpArray2D< Type >::data, vpArray2D< Type >::getCols(), vpArray2D< double >::getCols(), vpArray2D< Type >::getRows(), vpArray2D< double >::getRows(), vpArray2D< Type >::resize(), vpColVector::resize(), vpArray2D< Type >::size(), and vpMatrix::svd().
Referenced by vpMatrix::pseudoInverse(), and vpMatrix::svd().
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Singular value decomposition (SVD) using GSL 3rd party.
Given matrix , this function computes it singular value decomposition such as
w | : Vector of singular values: . |
V | : Matrix . |
Here an example of SVD decomposition of a non square Matrix M.
Definition at line 346 of file vpMatrix_svd.cpp.
References vpArray2D< double >::data, vpArray2D< Type >::data, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpArray2D< Type >::resize(), and vpColVector::resize().
Referenced by vpMatrix::pseudoInverse(), and vpMatrix::svd().
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Singular value decomposition (SVD) using Lapack 3rd party.
Given matrix , this function computes it singular value decomposition such as
w | : Vector of singular values: . |
V | : Matrix . |
Here an example of SVD decomposition of a non square Matrix M.
Definition at line 237 of file vpMatrix_svd.cpp.
References vpArray2D< Type >::data, vpArray2D< double >::data, vpException::fatalError, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpArray2D< Type >::resize(), vpColVector::resize(), and vpMatrix::transpose().
Referenced by vpMatrix::pseudoInverse(), and vpMatrix::svd().
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Singular value decomposition (SVD) using OpenCV 3rd party.
Given matrix , this function computes it singular value decomposition such as
w | : Vector of singular values: . |
V | : Matrix . |
Here an example of SVD decomposition of a non square Matrix M.
Definition at line 150 of file vpMatrix_svd.cpp.
References vpArray2D< double >::data, vpArray2D< Type >::data, vpArray2D< double >::getCols(), vpArray2D< double >::getRows(), vpArray2D< Type >::resize(), vpArray2D< double >::resize(), vpColVector::resize(), and vpMatrix::transpose().
Referenced by vpMatrix::pseudoInverse(), and vpMatrix::svd().
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Compute and return the transpose of the matrix.
Definition at line 375 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< Type >::resize(), and vpArray2D< double >::rowNum.
Referenced by vpLinProg::colReduction(), vpServo::computeControlLaw(), vpMatrix::computeCovarianceMatrix(), vpTemplateTracker::computeOptimalBrentGain(), vpMatrix::eigenValues(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), vpKalmanFilter::filtering(), vpTemplateTrackerWarpHomographySL3::findWarp(), vpQuadProg::fromCanonicalCost(), vpImageFilter::getSobelKernelX(), vpRotationMatrix::mean(), vpHomogeneousMatrix::mean(), vpKalmanFilter::prediction(), vpMatrix::pseudoInverse(), vpColVector::resize(), vpLinProg::simplex(), vpMatrix::solveByQR(), vpColVector::vpColVector(), vpTemplateTrackerWarp::warp(), and vpVelocityTwistMatrix::~vpVelocityTwistMatrix().
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Compute and return the transpose of the matrix.
Definition at line 394 of file vpMatrix.cpp.
Referenced by vpLinProg::colReduction(), vpServo::computeProjectionOperators(), vpQuadProg::fromCanonicalCost(), vpTemplateTrackerWarpSRT::getParamInverse(), vpTemplateTrackerWarpRT::getParamInverse(), vpColVector::resize(), vpLinProg::rowReduction(), vpLinProg::solveLP(), vpQuadProg::solveQPi(), vpMatrix::svdLapack(), and vpMatrix::svdOpenCV().
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Compute At the transpose of the matrix.
At | (output) : Resulting transpose matrix. |
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.
Allow to multiply a scalar by a matrix.
Definition at line 1350 of file vpMatrix.cpp.
References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().
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Enumeration of the operations applied on matrices in vpGEMM() function.
Operations are :
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Number of columns in the array.
Definition at line 76 of file vpArray2D.h.
Referenced by vpMatrix::AAt(), vpMatrix::AtA(), vpColVector::clear(), vpMatrix::detByLU(), vpMatrix::detByLUEigen3(), vpMatrix::detByLUGsl(), vpMatrix::detByLULapack(), vpMatrix::detByLUOpenCV(), vpMatrix::diag(), vpMatrix::eigenValues(), vpMatrix::expm(), vpMatrix::eye(), vpMatrix::getRow(), vpColVector::hadamard(), vpMatrix::hadamard(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), init(), vpRowVector::insert(), vpMatrix::insert(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByCholeskyOpenCV(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByLUGsl(), vpMatrix::inverseByLULapack(), vpMatrix::inverseByLUOpenCV(), vpMatrix::inverseByQRLapack(), vpMatrix::inverseTriangular(), vpRotationMatrix::operator*(), vpRowVector::operator*(), vpMatrix::operator*(), vpRotationMatrix::operator*=(), vpRowVector::operator*=(), vpMatrix::operator*=(), vpRowVector::operator+(), vpRowVector::operator+=(), vpMatrix::operator+=(), vpRowVector::operator-(), vpRowVector::operator-=(), vpMatrix::operator-=(), vpRowVector::operator/(), vpMatrix::operator/(), vpRowVector::operator/=(), vpMatrix::operator/=(), vpMatrix::operator<<(), vpColVector::operator<<(), vpSubRowVector::operator=(), operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpColVector::operator==(), vpMatrix::qr(), vpMatrix::qrPivot(), vpRowVector::reshape(), vpMatrix::setIdentity(), vpMatrix::solveByQR(), vpMatrix::solveBySVD(), vpMatrix::stack(), vpRowVector::stack(), vpMatrix::stackColumns(), vpMatrix::stackRows(), vpRowVector::sum(), vpMatrix::sum(), vpRowVector::sumSquare(), vpMatrix::sumSquare(), vpRowVector::t(), vpMatrix::t(), vpMatrix::transpose(), vpColVector::vpColVector(), and vpMatrix::vpMatrix().
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Address of the first element of the data array.
Definition at line 84 of file vpArray2D.h.
Referenced by vpMatrix::AtA(), vpQuaternionVector::buildFrom(), vpHomogeneousMatrix::buildFrom(), vpRzyzVector::buildFrom(), vpThetaUVector::buildFrom(), vpRxyzVector::buildFrom(), vpRzyxVector::buildFrom(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), checkParentStatus(), vpColVector::clear(), vpHomogeneousMatrix::convert(), vpMatrix::detByLUEigen3(), vpMatrix::detByLUOpenCV(), vpTranslationVector::euclideanNorm(), vpRowVector::euclideanNorm(), vpMatrix::euclideanNorm(), vpMatrix::expm(), vpThetaUVector::extract(), vpMatrix::getRow(), vpThetaUVector::getTheta(), vpThetaUVector::getU(), vpColVector::hadamard(), vpMatrix::hadamard(), vpSubColVector::init(), vpSubRowVector::init(), init(), vpColVector::insert(), vpMatrix::insert(), vpMatrix::inverseByCholeskyOpenCV(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByLUOpenCV(), vpTranslationVector::operator*(), vpRowVector::operator*(), vpColVector::operator*(), vpHomography::operator*(), vpMatrix::operator*(), vpTranslationVector::operator-(), vpRowVector::operator-(), vpColVector::operator-(), vpTranslationVector::operator/(), vpRowVector::operator/(), vpColVector::operator/(), vpHomography::operator/(), vpHomography::operator/=(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpQuaternionVector::operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpRzyzVector::operator=(), vpRxyzVector::operator=(), vpRzyxVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpThetaUVector::operator=(), vpColVector::operator==(), vpColVector::operator[](), vpMatrix::qr(), vpMatrix::qrPivot(), vpRowVector::reshape(), vpColVector::reshape(), vpQuaternionVector::set(), vpMatrix::stack(), vpMatrix::stackRows(), vpColVector::sum(), vpColVector::sumSquare(), vpMatrix::svdEigen3(), vpMatrix::svdGsl(), vpMatrix::svdLapack(), vpMatrix::svdOpenCV(), vpRotationVector::t(), vpTranslationVector::t(), vpPoseVector::t(), vpRowVector::t(), vpColVector::t(), vpRotationVector::toStdVector(), vpRowVector::toStdVector(), vpColVector::toStdVector(), vpColVector::vpColVector(), vpMatrix::vpMatrix(), vpQuaternionVector::w(), vpQuaternionVector::x(), vpQuaternionVector::y(), vpQuaternionVector::z(), vpSubColVector::~vpSubColVector(), ~vpSubMatrix(), and vpSubRowVector::~vpSubRowVector().
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Current array size (rowNum * colNum)
Definition at line 80 of file vpArray2D.h.
Referenced by vpColVector::clear(), vpTranslationVector::euclideanNorm(), vpRowVector::euclideanNorm(), vpMatrix::euclideanNorm(), vpColVector::hadamard(), vpMatrix::hadamard(), vpSubColVector::init(), vpSubRowVector::init(), init(), vpTranslationVector::operator*(), vpRotationVector::operator*(), vpTranslationVector::operator-(), vpTranslationVector::operator/(), vpRzyzVector::operator=(), vpRxyzVector::operator=(), vpRzyxVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpThetaUVector::operator=(), vpRowVector::reshape(), vpColVector::reshape(), vpMatrix::stackRows(), vpRotationVector::t(), vpColVector::vpColVector(), and vpMatrix::vpMatrix().
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Definition at line 76 of file vpSubMatrix.h.
Referenced by checkParentStatus(), init(), and operator=().
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Definition at line 75 of file vpSubMatrix.h.
Referenced by checkParentStatus(), init(), and operator=().
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Definition at line 74 of file vpSubMatrix.h.
Referenced by checkParentStatus(), init(), and operator=().
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Number of rows in the array.
Definition at line 74 of file vpArray2D.h.
Referenced by vpMatrix::AAt(), vpMatrix::AtA(), vpColVector::clear(), vpMatrix::detByLU(), vpMatrix::detByLUEigen3(), vpMatrix::detByLUGsl(), vpMatrix::detByLULapack(), vpMatrix::detByLUOpenCV(), vpMatrix::diag(), vpMatrix::eigenValues(), vpMatrix::expm(), vpColVector::extract(), vpMatrix::eye(), vpColVector::hadamard(), vpMatrix::hadamard(), vpColVector::infinityNorm(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), init(), vpMatrix::insert(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByCholeskyOpenCV(), vpMatrix::inverseByLUEigen3(), vpMatrix::inverseByLUGsl(), vpMatrix::inverseByLULapack(), vpMatrix::inverseByLUOpenCV(), vpMatrix::inverseByQRLapack(), vpMatrix::inverseTriangular(), vpRotationMatrix::operator*(), vpTranslationVector::operator*(), vpHomogeneousMatrix::operator*(), vpColVector::operator*(), vpMatrix::operator*(), vpRotationMatrix::operator*=(), vpTranslationVector::operator*=(), vpColVector::operator*=(), vpMatrix::operator*=(), vpColVector::operator+(), vpColVector::operator+=(), vpMatrix::operator+=(), vpColVector::operator-(), vpColVector::operator-=(), vpMatrix::operator-=(), vpColVector::operator/(), vpMatrix::operator/(), vpTranslationVector::operator/=(), vpColVector::operator/=(), vpMatrix::operator/=(), vpMatrix::operator<<(), vpColVector::operator<<(), vpSubColVector::operator=(), vpSubRowVector::operator=(), operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpColVector::operator==(), vpMatrix::qr(), vpMatrix::qrPivot(), vpColVector::reshape(), vpMatrix::setIdentity(), vpMatrix::stack(), vpColVector::stack(), vpMatrix::stackColumns(), vpMatrix::stackRows(), vpColVector::sum(), vpMatrix::sum(), vpRotationVector::sumSquare(), vpTranslationVector::sumSquare(), vpColVector::sumSquare(), vpMatrix::sumSquare(), vpTranslationVector::t(), vpPoseVector::t(), vpColVector::t(), vpMatrix::t(), vpMatrix::transpose(), vpColVector::vpColVector(), and vpMatrix::vpMatrix().
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Address of the first element of each rows.
Definition at line 78 of file vpArray2D.h.
Referenced by vpMatrix::AAt(), vpColVector::clear(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), init(), vpRowVector::init(), vpColVector::init(), vpMatrix::init(), vpRotationMatrix::operator*(), vpForceTwistMatrix::operator*(), vpVelocityTwistMatrix::operator*(), vpHomogeneousMatrix::operator*(), vpMatrix::operator*(), vpRotationMatrix::operator*=(), vpMatrix::operator*=(), vpMatrix::operator+=(), vpMatrix::operator-=(), vpMatrix::operator/(), vpMatrix::operator/=(), vpMatrix::operator<<(), vpColVector::operator<<(), operator=(), vpRotationMatrix::operator=(), vpHomogeneousMatrix::operator=(), vpForceTwistMatrix::operator=(), vpVelocityTwistMatrix::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpMatrix::stack(), vpMatrix::stackColumns(), vpRowVector::sum(), vpMatrix::sum(), vpRotationVector::sumSquare(), vpTranslationVector::sumSquare(), vpRowVector::sumSquare(), vpMatrix::sumSquare(), vpMatrix::transpose(), vpColVector::vpColVector(), and vpMatrix::vpMatrix().