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Visual Servoing Platform
version 3.2.0
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#include <vpMatrix.h>
Public Types | |
enum | vpDetMethod { LU_DECOMPOSITION } |
Public Member Functions | |
vpMatrix () | |
vpMatrix (unsigned int r, unsigned int c) | |
vpMatrix (unsigned int r, unsigned int c, double val) | |
vpMatrix (const vpMatrix &M, unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols) | |
vpMatrix (const vpArray2D< double > &A) | |
vpMatrix (const vpMatrix &A) | |
vpMatrix (vpMatrix &&A) | |
virtual | ~vpMatrix () |
void | clear () |
Setting a diagonal matrix | |
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void | diag (const double &val=1.0) |
void | diag (const vpColVector &A) |
void | eye () |
void | eye (unsigned int n) |
void | eye (unsigned int m, unsigned int n) |
Assignment operators | |
vpMatrix & | operator<< (double *) |
vpMatrix & | operator= (const vpArray2D< double > &A) |
vpMatrix & | operator= (const vpMatrix &A) |
vpMatrix & | operator= (vpMatrix &&A) |
vpMatrix & | operator= (const double x) |
Stacking | |
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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 | |
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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 vpMatrix &B) |
vpMatrix | operator* (const vpMatrix &B) const |
vpMatrix | operator* (const vpRotationMatrix &R) const |
vpMatrix | operator* (const vpVelocityTwistMatrix &V) const |
vpMatrix | operator* (const vpForceTwistMatrix &V) const |
vpTranslationVector | operator* (const vpTranslationVector &tv) const |
vpColVector | operator* (const vpColVector &v) const |
vpMatrix | operator+ (const vpMatrix &B) const |
vpMatrix | operator- (const vpMatrix &B) const |
vpMatrix | operator- () const |
vpMatrix & | operator+= (const double x) |
vpMatrix & | operator-= (const double x) |
vpMatrix & | operator*= (const double x) |
vpMatrix & | operator/= (double x) |
vpMatrix | operator* (const double x) const |
vpMatrix | operator/ (const double x) const |
double | sum () const |
double | sumSquare () const |
Hadamard product | |
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vpMatrix | hadamard (const vpMatrix &m) const |
Kronecker product | |
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void | kron (const vpMatrix &m1, vpMatrix &out) const |
vpMatrix | kron (const vpMatrix &m1) const |
Transpose | |
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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 | |
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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 | |
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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 | |
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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 | |
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vpColVector | eigenValues () const |
void | eigenValues (vpColVector &evalue, vpMatrix &evector) const |
Norms | |
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double | euclideanNorm () const |
double | infinityNorm () const |
Printing | |
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std::ostream & | cppPrint (std::ostream &os, const std::string &matrixName="A", bool octet=false) const |
std::ostream & | csvPrint (std::ostream &os) const |
std::ostream & | maplePrint (std::ostream &os) const |
std::ostream & | matlabPrint (std::ostream &os) const |
int | print (std::ostream &s, unsigned int length, char const *intro=0) const |
void | printSize () const |
Inherited functionalities from vpArray2D | |
unsigned int | getCols () const |
double | getMaxValue () const |
double | getMinValue () const |
unsigned int | getRows () const |
unsigned int | size () const |
void | resize (const unsigned int nrows, const unsigned int ncols, const bool flagNullify=true, const bool recopy_=true) |
double * | operator[] (unsigned int i) |
double * | operator[] (unsigned int i) const |
vpArray2D< double > | hadamard (const vpArray2D< double > &m) const |
Static Public Member Functions | |
Setting a diagonal matrix with Static Public Member Functions | |
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static void | createDiagonalMatrix (const vpColVector &A, vpMatrix &DA) |
Matrix insertion with Static Public Member Functions | |
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static vpMatrix | insert (const vpMatrix &A, const vpMatrix &B, const unsigned int r, const unsigned int c) |
static void | insert (const vpMatrix &A, const vpMatrix &B, vpMatrix &C, const unsigned int r, const unsigned int c) |
Stacking with Static Public Member Functions | |
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static vpMatrix | juxtaposeMatrices (const vpMatrix &A, const vpMatrix &B) |
static void | juxtaposeMatrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C) |
static vpMatrix | stack (const vpMatrix &A, const vpMatrix &B) |
static vpMatrix | stack (const vpMatrix &A, const vpRowVector &r) |
static vpMatrix | stack (const vpMatrix &A, const vpColVector &c) |
static void | stack (const vpMatrix &A, const vpMatrix &B, vpMatrix &C) |
static void | stack (const vpMatrix &A, const vpRowVector &r, vpMatrix &C) |
static void | stack (const vpMatrix &A, const vpColVector &c, vpMatrix &C) |
Matrix operations with Static Public Member Functions | |
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static void | add2Matrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C) |
static void | add2Matrices (const vpColVector &A, const vpColVector &B, vpColVector &C) |
static void | add2WeightedMatrices (const vpMatrix &A, const double &wA, const vpMatrix &B, const double &wB, vpMatrix &C) |
static void | computeHLM (const vpMatrix &H, const double &alpha, vpMatrix &HLM) |
static void | mult2Matrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C) |
static void | mult2Matrices (const vpMatrix &A, const vpMatrix &B, vpRotationMatrix &C) |
static void | mult2Matrices (const vpMatrix &A, const vpMatrix &B, vpHomogeneousMatrix &C) |
static void | mult2Matrices (const vpMatrix &A, const vpColVector &B, vpColVector &C) |
static void | multMatrixVector (const vpMatrix &A, const vpColVector &v, vpColVector &w) |
static void | negateMatrix (const vpMatrix &A, vpMatrix &C) |
static void | sub2Matrices (const vpMatrix &A, const vpMatrix &B, vpMatrix &C) |
static void | sub2Matrices (const vpColVector &A, const vpColVector &B, vpColVector &C) |
Kronecker product with Static Public Member Functions | |
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static void | kron (const vpMatrix &m1, const vpMatrix &m2, vpMatrix &out) |
static vpMatrix | kron (const vpMatrix &m1, const vpMatrix &m2) |
2D Convolution with Static Public Member Functions | |
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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 | |
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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 | |
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static bool | loadMatrix (const std::string &filename, vpArray2D< double > &M, const bool binary=false, char *header=NULL) |
static bool | loadMatrixYAML (const std::string &filename, vpArray2D< double > &M, char *header=NULL) |
static bool | saveMatrix (const std::string &filename, const vpArray2D< double > &M, const bool binary=false, const char *header="") |
static bool | saveMatrixYAML (const std::string &filename, const vpArray2D< double > &M, const char *header="") |
Inherited I/O from vpArray2D with Static Public Member Functions | |
static bool | load (const std::string &filename, vpArray2D< double > &A, const bool binary=false, char *header=NULL) |
static bool | loadYAML (const std::string &filename, vpArray2D< double > &A, char *header=NULL) |
static bool | save (const std::string &filename, const vpArray2D< double > &A, const bool binary=false, const char *header="") |
static bool | saveYAML (const std::string &filename, const vpArray2D< double > &A, const char *header="") |
Public Attributes | |
double * | data |
Protected Attributes | |
unsigned int | rowNum |
unsigned int | colNum |
double ** | rowPtrs |
unsigned int | dsize |
Related Functions | |
(Note that these are not member functions.) | |
vpMatrix | operator* (const double &x, const vpMatrix &B) |
enum | vpGEMMmethod |
void | vpGEMM (const vpArray2D< double > &A, const vpArray2D< double > &B, const double &alpha, const vpArray2D< double > &C, const double &beta, vpArray2D< double > &D, const unsigned int &ops=0) |
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) |
Implementation of a matrix and operations on matrices.
This class needs one of the following third-party to compute matrix inverse, pseudo-inverse, singular value decomposition, determinant:
vpMatrix class provides a data structure for the matrices as well as a set of operations on these matrices.
The vpMatrix class is derived from vpArray2D<double>.
Definition at line 103 of file vpMatrix.h.
Method used to compute the determinant of a square matrix.
Enumerator | |
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LU_DECOMPOSITION | LU decomposition method. |
Definition at line 110 of file vpMatrix.h.
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Basic constructor of a matrix of double. Number of columns and rows are zero.
Definition at line 119 of file vpMatrix.h.
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Constructor that initialize a matrix of double with 0.
r | : Matrix number of rows. |
c | : Matrix number of columns. |
Definition at line 126 of file vpMatrix.h.
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Constructor that initialize a matrix of double with val.
r | : Matrix number of rows. |
c | : Matrix number of columns. |
val | : Each element of the matrix is set to val. |
Definition at line 134 of file vpMatrix.h.
vpMatrix::vpMatrix | ( | const vpMatrix & | M, |
unsigned int | r, | ||
unsigned int | c, | ||
unsigned int | nrows, | ||
unsigned int | ncols | ||
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Construct a matrix as a sub-matrix of the input matrix M.
Definition at line 180 of file vpMatrix.cpp.
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Create a matrix from a 2D array that could be one of the following container that inherit from vpArray2D such as vpMatrix, vpRotationMatrix, vpHomogeneousMatrix, vpPoseVector, vpColVector, vpRowVector... The following example shows how to create a matrix from an homogeneous matrix:
Definition at line 148 of file vpMatrix.h.
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Definition at line 151 of file vpMatrix.h.
vpMatrix::vpMatrix | ( | vpMatrix && | A | ) |
Definition at line 195 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< double >::data, vpArray2D< double >::dsize, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.
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Destructor (Memory de-allocation)
Definition at line 157 of file vpMatrix.h.
vpMatrix vpMatrix::AAt | ( | ) | const |
Computes the operation
Definition at line 425 of file vpMatrix.cpp.
void vpMatrix::AAt | ( | vpMatrix & | B | ) | const |
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 445 of file vpMatrix.cpp.
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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 1145 of file vpMatrix.cpp.
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 1112 of file vpMatrix.cpp.
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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 1083 of file vpMatrix.cpp.
vpMatrix vpMatrix::AtA | ( | ) | const |
Compute the AtA operation such as
Definition at line 523 of file vpMatrix.cpp.
Referenced by vpMbDepthDenseTracker::computeVVS(), vpMbDepthNormalTracker::computeVVS(), vpMbGenericTracker::computeVVS(), vpMbEdgeMultiTracker::computeVVSFirstPhasePoseEstimation(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), and vpTemplateTrackerWarpHomographySL3::findWarp().
void vpMatrix::AtA | ( | vpMatrix & | B | ) | const |
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 479 of file vpMatrix.cpp.
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Removes all elements from the matrix (which are destroyed), leaving the container with a size of 0.
Definition at line 163 of file vpMatrix.h.
vpColVector vpMatrix::column | ( | const unsigned int | j | ) |
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 5301 of file vpMatrix.cpp.
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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 58 of file vpMatrix_covariance.cpp.
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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 90 of file vpMatrix_covariance.cpp.
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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 123 of file vpMatrix_covariance.cpp.
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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 148 of file vpMatrix_covariance.cpp.
Referenced by vpMbTracker::computeCovarianceMatrixVVS().
Compute
H | : input Matrix ![]() |
alpha | : Scalar ![]() |
HLM | : Resulting operation. |
Definition at line 5070 of file vpMatrix.cpp.
Referenced by vpTemplateTrackerWarpHomographySL3::findWarp(), vpTemplateTrackerSSDESM::initCompInverse(), vpTemplateTrackerSSDInverseCompositional::initCompInverse(), vpTemplateTrackerZNCCForwardAdditional::initHessienDesired(), vpTemplateTrackerZNCCInverseCompositional::initHessienDesired(), vpTemplateTrackerMIESM::initHessienDesired(), vpTemplateTrackerMIForwardAdditional::initHessienDesired(), vpTemplateTrackerSSDForwardCompositional::trackNoPyr(), vpTemplateTrackerMIForwardCompositional::trackNoPyr(), vpTemplateTrackerSSDESM::trackNoPyr(), vpTemplateTrackerSSDForwardAdditional::trackNoPyr(), vpTemplateTrackerMIESM::trackNoPyr(), vpTemplateTrackerMIForwardAdditional::trackNoPyr(), and vpTemplateTrackerMIInverseCompositional::trackNoPyr().
double vpMatrix::cond | ( | ) | const |
Definition at line 5044 of file vpMatrix.cpp.
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 5163 of file vpMatrix.cpp.
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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 5182 of file vpMatrix.cpp.
std::ostream & vpMatrix::cppPrint | ( | std::ostream & | os, |
const std::string & | matrixName = "A" , |
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bool | octet = false |
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) | const |
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 4437 of file vpMatrix.cpp.
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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 711 of file vpMatrix.cpp.
std::ostream & vpMatrix::csvPrint | ( | std::ostream & | os | ) | const |
Print/save a matrix in csv format.
The following code
produces log.csv file that contains:
Definition at line 4388 of file vpMatrix.cpp.
double vpMatrix::det | ( | vpDetMethod | method = LU_DECOMPOSITION | ) | const |
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 4905 of file vpMatrix.cpp.
double vpMatrix::detByLU | ( | ) | const |
Compute the determinant of a square matrix using the LU decomposition.
This function calls the first following function that is available:
If none of these previous 3rd parties is installed, we use by default detByLULapack() with a Lapack built-in version.
Definition at line 179 of file vpMatrix_lu.cpp.
double vpMatrix::detByLUEigen3 | ( | ) | const |
Compute the determinant of a square matrix using the LU decomposition with Eigen3 3rd party.
Definition at line 623 of file vpMatrix_lu.cpp.
double vpMatrix::detByLUGsl | ( | ) | const |
Compute the determinant of a square matrix using the LU decomposition with GSL 3rd party.
Definition at line 300 of file vpMatrix_lu.cpp.
double vpMatrix::detByLULapack | ( | ) | const |
Compute the determinant of a square matrix using the LU decomposition with GSL 3rd party.
Definition at line 420 of file vpMatrix_lu.cpp.
double vpMatrix::detByLUOpenCV | ( | ) | const |
Compute the determinant of a n-by-n matrix using the LU decomposition with OpenCV 3rd party.
Definition at line 532 of file vpMatrix_lu.cpp.
void vpMatrix::diag | ( | const double & | val = 1.0 | ) |
Set the matrix as a diagonal matrix where each element on the diagonal is set to val. Elements that are not on the diagonal are set to 0.
val | : Value to set. |
Matrix A is now equal to:
Definition at line 692 of file vpMatrix.cpp.
void vpMatrix::diag | ( | const vpColVector & | A | ) |
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 652 of file vpMatrix.cpp.
vpColVector vpMatrix::eigenValues | ( | ) | const |
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 4623 of file vpMatrix.cpp.
Referenced by vpQuadProg::fromCanonicalCost().
void vpMatrix::eigenValues | ( | vpColVector & | evalue, |
vpMatrix & | evector | ||
) | const |
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 4734 of file vpMatrix.cpp.
References vpException::dimensionError, vpException::fatalError, vpException::functionNotImplementedError, vpArray2D< Type >::resize(), and t().
double vpMatrix::euclideanNorm | ( | ) | const |
Compute and return the Euclidean norm .
Definition at line 5095 of file vpMatrix.cpp.
vpMatrix vpMatrix::expm | ( | ) | const |
Compute the exponential matrix of a square matrix.
Definition at line 4923 of file vpMatrix.cpp.
Referenced by vpTemplateTrackerWarpHomographySL3::computeCoeff().
vpMatrix vpMatrix::extract | ( | unsigned int | r, |
unsigned int | c, | ||
unsigned int | nrows, | ||
unsigned int | ncols | ||
) | const |
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 318 of file vpMatrix.cpp.
void vpMatrix::eye | ( | ) |
Set an m-by-n matrix to identity with ones on the diagonal and zeros else where.
Definition at line 359 of file vpMatrix.cpp.
Referenced by vpMbDepthDenseTracker::computeVVS(), vpMbDepthNormalTracker::computeVVS(), vpMbGenericTracker::computeVVS(), vpMbTracker::computeVVSPoseEstimation(), vpTemplateTrackerWarpHomographySL3::getdW0(), and vpTemplateTrackerWarpHomographySL3::getdWdp0().
void vpMatrix::eye | ( | unsigned int | m, |
unsigned int | n | ||
) |
Set an m-by-n matrix to identity with ones on the diagonal and zeros else where.
Definition at line 348 of file vpMatrix.cpp.
void vpMatrix::eye | ( | unsigned int | n | ) |
Set an n-by-n matrix to identity with ones on the diagonal and zeros else where.
Definition at line 342 of file vpMatrix.cpp.
vpColVector vpMatrix::getCol | ( | const unsigned int | j | ) | const |
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 3797 of file vpMatrix.cpp.
Referenced by vpMbtFaceDepthNormal::estimatePlaneEquationSVD().
vpColVector vpMatrix::getCol | ( | const unsigned int | j, |
const unsigned int | i_begin, | ||
const unsigned int | column_size | ||
) | const |
Extract a column vector from a matrix.
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 3748 of file vpMatrix.cpp.
|
inlineinherited |
Return the number of columns of the 2D array.
Definition at line 145 of file vpArray2D.h.
|
inherited |
Return the array max value.
Definition at line 693 of file vpArray2D.h.
|
inherited |
Return the array min value.
Definition at line 676 of file vpArray2D.h.
vpRowVector vpMatrix::getRow | ( | const unsigned int | i | ) | const |
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 3843 of file vpMatrix.cpp.
vpRowVector vpMatrix::getRow | ( | const unsigned int | i, |
const unsigned int | j_begin, | ||
const unsigned int | row_size | ||
) | const |
Extract a row vector from a matrix.
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 3895 of file vpMatrix.cpp.
|
inlineinherited |
Return the number of rows of the 2D array.
Definition at line 155 of file vpArray2D.h.
Compute the Hadamard product (element wise matrix multiplication).
m | : Second matrix; |
Definition at line 713 of file vpArray2D.h.
Compute the Hadamard product (element wise matrix multiplication).
m | : Second matrix; |
Definition at line 1512 of file vpMatrix.cpp.
double vpMatrix::infinityNorm | ( | ) | const |
Compute and return the infinity norm with
where
is the matrix size.
Definition at line 5116 of file vpMatrix.cpp.
|
inline |
Definition at line 685 of file vpMatrix.h.
void vpMatrix::init | ( | const vpMatrix & | M, |
unsigned int | r, | ||
unsigned int | c, | ||
unsigned int | nrows, | ||
unsigned int | ncols | ||
) |
Initialize the matrix from a part of an input matrix M.
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 257 of file vpMatrix.cpp.
void vpMatrix::insert | ( | const vpMatrix & | A, |
const unsigned int | r, | ||
const unsigned int | c | ||
) |
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 4569 of file vpMatrix.cpp.
Referenced by vpMbEdgeMultiTracker::computeVVS(), vpMbDepthDenseTracker::computeVVSInteractionMatrixAndResidu(), vpMbDepthNormalTracker::computeVVSInteractionMatrixAndResidu(), vpMbKltMultiTracker::computeVVSInteractionMatrixAndResidu(), vpMbEdgeMultiTracker::computeVVSInteractionMatrixAndResidu(), vpMbEdgeKltMultiTracker::computeVVSInteractionMatrixAndResidu(), and vpMbGenericTracker::computeVVSInteractionMatrixAndResidu().
|
static |
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 4060 of file vpMatrix.cpp.
|
static |
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 4082 of file vpMatrix.cpp.
vpMatrix vpMatrix::inverseByCholesky | ( | ) | const |
Compute the inverse of a n-by-n matrix using the Cholesky decomposition. The matrix must be real symmetric positive defined.
This function calls the first following function that is available:
If none of these 3rd parties is installed we use a Lapack built-in version.
Here an example:
Definition at line 104 of file vpMatrix_cholesky.cpp.
vpMatrix vpMatrix::inverseByCholeskyLapack | ( | ) | const |
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 154 of file vpMatrix_cholesky.cpp.
vpMatrix vpMatrix::inverseByCholeskyOpenCV | ( | ) | const |
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 223 of file vpMatrix_cholesky.cpp.
vpMatrix vpMatrix::inverseByLU | ( | ) | const |
Compute the inverse of a n-by-n matrix using the LU decomposition.
This function calls the first following function that is available:
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 129 of file vpMatrix_lu.cpp.
Referenced by vpTemplateTrackerWarpHomographySL3::findWarp(), vpTemplateTrackerSSDInverseCompositional::initCompInverse(), vpTemplateTrackerZNCCForwardAdditional::initHessienDesired(), vpTemplateTrackerZNCCInverseCompositional::initHessienDesired(), vpTemplateTrackerMIESM::initHessienDesired(), vpTemplateTrackerMIForwardAdditional::initHessienDesired(), vpTemplateTrackerSSDForwardCompositional::trackNoPyr(), vpTemplateTrackerMIForwardCompositional::trackNoPyr(), vpTemplateTrackerSSDForwardAdditional::trackNoPyr(), vpTemplateTrackerMIESM::trackNoPyr(), vpTemplateTrackerMIForwardAdditional::trackNoPyr(), and vpTemplateTrackerMIInverseCompositional::trackNoPyr().
vpMatrix vpMatrix::inverseByLUEigen3 | ( | ) | const |
Compute the inverse of a n-by-n matrix using the LU decomposition with Eigen3 3rd party.
Here an example:
Definition at line 581 of file vpMatrix_lu.cpp.
vpMatrix vpMatrix::inverseByLUGsl | ( | ) | const |
Compute the inverse of a n-by-n matrix using the LU decomposition with GSL 3rd party.
Here an example:
Definition at line 236 of file vpMatrix_lu.cpp.
vpMatrix vpMatrix::inverseByLULapack | ( | ) | const |
Compute the inverse of a n-by-n matrix using the LU decomposition with Lapack 3rd party.
Here an example:
Definition at line 365 of file vpMatrix_lu.cpp.
vpMatrix vpMatrix::inverseByLUOpenCV | ( | ) | const |
Compute the inverse of a n-by-n matrix using the LU decomposition with OpenCV 3rd party.
Here an example:
Definition at line 491 of file vpMatrix_lu.cpp.
vpMatrix vpMatrix::inverseByQR | ( | ) | const |
Compute the inverse of a n-by-n matrix using the QR decomposition. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.
Here an example:
Definition at line 272 of file vpMatrix_qr.cpp.
vpMatrix vpMatrix::inverseByQRLapack | ( | ) | const |
Compute the inverse of a n-by-n matrix using the QR decomposition with Lapack 3rd party.
Here an example:
Definition at line 111 of file vpMatrix_qr.cpp.
vpMatrix vpMatrix::inverseTriangular | ( | bool | upper = true | ) | const |
Compute the inverse of a full-rank n-by-n triangular matrix. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.
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 712 of file vpMatrix_qr.cpp.
Juxtapose to matrices C = [ A B ].
A | : Left matrix. |
B | : Right matrix. |
Definition at line 4113 of file vpMatrix.cpp.
Juxtapose to matrices C = [ A B ].
A | : Left matrix. |
B | : Right matrix. |
C | : Juxtaposed matrix C = [ A B ] |
Definition at line 4134 of file vpMatrix.cpp.
unsigned int vpMatrix::kernel | ( | vpMatrix & | kerAt, |
double | svThreshold = 1e-6 |
||
) | const |
Function to compute the null space (the kernel) of a m-by-n matrix .
The null space of a matrix is defined as
.
kerAt | The matrix that contains the null space (kernel) 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 4820 of file vpMatrix.cpp.
Compute Kronecker product matrix.
m | : vpMatrix; |
Definition at line 1616 of file vpMatrix.cpp.
Compute Kronecker product matrix.
Definition at line 1586 of file vpMatrix.cpp.
Compute Kronecker product matrix.
Definition at line 1545 of file vpMatrix.cpp.
Compute Kronecker product matrix.
m | : vpMatrix. |
out | : If m1.kron(m2) out contains the kronecker product's result : ![]() |
Definition at line 1578 of file vpMatrix.cpp.
|
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 321 of file vpArray2D.h.
|
inlinestatic |
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 617 of file vpMatrix.h.
|
inlinestatic |
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 633 of file vpMatrix.h.
|
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 433 of file vpArray2D.h.
std::ostream & vpMatrix::maplePrint | ( | std::ostream & | os | ) | const |
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 4347 of file vpMatrix.cpp.
std::ostream & vpMatrix::matlabPrint | ( | std::ostream & | os | ) | const |
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 4303 of file vpMatrix.cpp.
|
static |
Operation C = A * B.
The result is placed in the third parameter C and not returned. A new matrix won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).
Definition at line 931 of file vpMatrix.cpp.
|
static |
Operation C = A * B.
The result is placed in the third parameter C and not returned. A new matrix won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).
vpException::dimensionError | If matrices are not 4-by-4 dimension. |
Definition at line 893 of file vpMatrix.cpp.
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 805 of file vpMatrix.cpp.
|
static |
Operation C = A * B.
The result is placed in the third parameter C and not returned. A new matrix won't be allocated for every use of the function (speed gain if used many times with the same result matrix size).
vpException::dimensionError | If matrices are not 3-by-3 dimension. |
Definition at line 854 of file vpMatrix.cpp.
|
static |
Operation w = A * v (v and w are vectors).
A new matrix won't be allocated for every use of the function (Speed gain if used many times with the same result matrix size).
Definition at line 764 of file vpMatrix.cpp.
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 1300 of file vpMatrix.cpp.
vpMatrix vpMatrix::operator* | ( | const double | x | ) | const |
Operator that allows to multiply all the elements of a matrix by a scalar.
Definition at line 1367 of file vpMatrix.cpp.
vpColVector vpMatrix::operator* | ( | const vpColVector & | v | ) | const |
Operation w = A * v (matrix A is unchanged, v and w are column vectors).
Definition at line 749 of file vpMatrix.cpp.
vpMatrix vpMatrix::operator* | ( | const vpForceTwistMatrix & | V | ) | const |
Operator that allow to multiply a matrix by a force/torque twist matrix. The matrix should be of dimension m-by-6.
Definition at line 1049 of file vpMatrix.cpp.
Operation C = A * B (A is unchanged).
Definition at line 940 of file vpMatrix.cpp.
vpMatrix vpMatrix::operator* | ( | const vpRotationMatrix & | R | ) | const |
Operator that allow to multiply a matrix by a rotation matrix. The matrix should be of dimension m-by-3.
Definition at line 953 of file vpMatrix.cpp.
vpTranslationVector vpMatrix::operator* | ( | const vpTranslationVector & | tv | ) | const |
Operator that allows to multiply a matrix by a translation vector. The matrix should be of dimension (3x3)
Definition at line 724 of file vpMatrix.cpp.
vpMatrix vpMatrix::operator* | ( | const vpVelocityTwistMatrix & | V | ) | const |
Operator that allow to multiply a matrix by a velocity twist matrix. The matrix should be of dimension m-by-6.
Definition at line 980 of file vpMatrix.cpp.
vpMatrix & vpMatrix::operator*= | ( | const double | x | ) |
Multiply all the element of the matrix by x : Aij = Aij * x.
Operator that allows to multiply all the elements of a matrix by a scalar.
Definition at line 1423 of file vpMatrix.cpp.
Operation C = A + B (A is unchanged).
Definition at line 1170 of file vpMatrix.cpp.
vpMatrix & vpMatrix::operator+= | ( | const double | x | ) |
Add x to all the element of the matrix : Aij = Aij + x.
Definition at line 1400 of file vpMatrix.cpp.
Operation A = A + B.
Definition at line 1259 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.
vpMatrix vpMatrix::operator- | ( | void | ) | const |
Operation C = -A (A is unchanged).
Definition at line 1318 of file vpMatrix.cpp.
Operation C = A - B (A is unchanged).
Definition at line 1250 of file vpMatrix.cpp.
vpMatrix & vpMatrix::operator-= | ( | const double | x | ) |
Substract x to all the element of the matrix : Aij = Aij - x.
Definition at line 1410 of file vpMatrix.cpp.
Operation A = A - B.
Definition at line 1276 of file vpMatrix.cpp.
vpMatrix vpMatrix::operator/ | ( | const double | x | ) | const |
Cij = Aij / x (A is unchanged)
Definition at line 1379 of file vpMatrix.cpp.
vpMatrix & vpMatrix::operator/= | ( | double | x | ) |
Divide all the element of the matrix by x : Aij = Aij / x.
Definition at line 1433 of file vpMatrix.cpp.
vpMatrix & vpMatrix::operator<< | ( | double * | x | ) |
Assigment from an array of double. This method has to be used carefully since the array allocated behind x pointer should have the same dimension than the matrix.
Definition at line 606 of file vpMatrix.cpp.
vpMatrix & vpMatrix::operator= | ( | const double | x | ) |
Set all the element of the matrix A to x.
Definition at line 595 of file vpMatrix.cpp.
Copy operator that allows to convert on of the following container that inherit from vpArray2D such as vpMatrix, vpRotationMatrix, vpHomogeneousMatrix, vpPoseVector, vpColVector, vpRowVector... into a vpMatrix.
A | : 2D array to be copied. |
The following example shows how to create a matrix from an homogeneous matrix:
Definition at line 548 of file vpMatrix.cpp.
Definition at line 560 of file vpMatrix.cpp.
References vpArray2D< double >::data, vpArray2D< Type >::data, vpArray2D< double >::dsize, vpArray2D< Type >::getCols(), vpArray2D< Type >::getRows(), and vpArray2D< double >::resize().
Definition at line 571 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< double >::data, vpArray2D< double >::dsize, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.
|
inlineinherited |
Set element using A[i][j] = x.
Definition at line 265 of file vpArray2D.h.
|
inlineinherited |
Get element using x = A[i][j].
Definition at line 267 of file vpArray2D.h.
int vpMatrix::print | ( | std::ostream & | s, |
unsigned int | length, | ||
char const * | intro = 0 |
||
) | const |
Pretty print a matrix. The data are tabulated. The common widths before and after the decimal point are set with respect to the parameter maxlen.
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 4180 of file vpMatrix.cpp.
|
inline |
Definition at line 501 of file vpMatrix.h.
vpMatrix vpMatrix::pseudoInverse | ( | double | svThreshold = 1e-6 | ) | const |
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 1931 of file vpMatrix.cpp.
Referenced by vpSimulatorAfma6::computeArticularVelocity(), vpMbEdgeMultiTracker::computeVVSFirstPhasePoseEstimation(), vpMbEdgeTracker::computeVVSFirstPhasePoseEstimation(), vpMbTracker::computeVVSPoseEstimation(), vpQuadProg::fromCanonicalCost(), and vpMeEllipse::initTracking().
unsigned int vpMatrix::pseudoInverse | ( | vpMatrix & | Ap, |
double | svThreshold = 1e-6 |
||
) | const |
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 1862 of file vpMatrix.cpp.
unsigned int vpMatrix::pseudoInverse | ( | vpMatrix & | Ap, |
vpColVector & | sv, | ||
double | svThreshold, | ||
vpMatrix & | imA, | ||
vpMatrix & | imAt | ||
) | const |
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 ![]() |
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 | ![]() |
imAt | ![]() |
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 3542 of file vpMatrix.cpp.
unsigned int vpMatrix::pseudoInverse | ( | vpMatrix & | Ap, |
vpColVector & | sv, | ||
double | svThreshold, | ||
vpMatrix & | imA, | ||
vpMatrix & | imAt, | ||
vpMatrix & | kerAt | ||
) | const |
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 ![]() |
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 | ![]() |
imAt | ![]() |
kerAt | The matrix that contains the null space (kernel) 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 3683 of file vpMatrix.cpp.
unsigned int vpMatrix::pseudoInverse | ( | vpMatrix & | Ap, |
vpColVector & | sv, | ||
double | svThreshold = 1e-6 |
||
) | const |
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 ![]() |
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 3448 of file vpMatrix.cpp.
vpMatrix vpMatrix::pseudoInverseEigen3 | ( | double | svThreshold = 1e-6 | ) | const |
unsigned int vpMatrix::pseudoInverseEigen3 | ( | vpMatrix & | Ap, |
double | svThreshold = 1e-6 |
||
) | const |
unsigned int vpMatrix::pseudoInverseEigen3 | ( | vpMatrix & | Ap, |
vpColVector & | sv, | ||
double | svThreshold, | ||
vpMatrix & | imA, | ||
vpMatrix & | imAt, | ||
vpMatrix & | kerAt | ||
) | const |
unsigned int vpMatrix::pseudoInverseEigen3 | ( | vpMatrix & | Ap, |
vpColVector & | sv, | ||
double | svThreshold = 1e-6 |
||
) | const |
vpMatrix vpMatrix::pseudoInverseGsl | ( | double | svThreshold = 1e-6 | ) | const |
unsigned int vpMatrix::pseudoInverseGsl | ( | vpMatrix & | Ap, |
double | svThreshold = 1e-6 |
||
) | const |
unsigned int vpMatrix::pseudoInverseGsl | ( | vpMatrix & | Ap, |
vpColVector & | sv, | ||
double | svThreshold, | ||
vpMatrix & | imA, | ||
vpMatrix & | imAt, | ||
vpMatrix & | kerAt | ||
) | const |
unsigned int vpMatrix::pseudoInverseGsl | ( | vpMatrix & | Ap, |
vpColVector & | sv, | ||
double | svThreshold = 1e-6 |
||
) | const |
vpMatrix vpMatrix::pseudoInverseLapack | ( | double | svThreshold = 1e-6 | ) | const |
unsigned int vpMatrix::pseudoInverseLapack | ( | vpMatrix & | Ap, |
double | svThreshold = 1e-6 |
||
) | const |
unsigned int vpMatrix::pseudoInverseLapack | ( | vpMatrix & | Ap, |
vpColVector & | sv, | ||
double | svThreshold, | ||
vpMatrix & | imA, | ||
vpMatrix & | imAt, | ||
vpMatrix & | kerAt | ||
) | const |
unsigned int vpMatrix::pseudoInverseLapack | ( | vpMatrix & | Ap, |
vpColVector & | sv, | ||
double | svThreshold = 1e-6 |
||
) | const |
vpMatrix vpMatrix::pseudoInverseOpenCV | ( | double | svThreshold = 1e-6 | ) | const |
unsigned int vpMatrix::pseudoInverseOpenCV | ( | vpMatrix & | Ap, |
double | svThreshold = 1e-6 |
||
) | const |
unsigned int vpMatrix::pseudoInverseOpenCV | ( | vpMatrix & | Ap, |
vpColVector & | sv, | ||
double | svThreshold, | ||
vpMatrix & | imA, | ||
vpMatrix & | imAt, | ||
vpMatrix & | kerAt | ||
) | const |
unsigned int vpMatrix::pseudoInverseOpenCV | ( | vpMatrix & | Ap, |
vpColVector & | sv, | ||
double | svThreshold = 1e-6 |
||
) | const |
unsigned int vpMatrix::qr | ( | vpMatrix & | Q, |
vpMatrix & | R, | ||
bool | full = false , |
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bool | squareR = false , |
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double | tol = 1e-6 |
||
) | const |
Compute the QR decomposition of a (m x n) matrix of rank r. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.
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 336 of file vpMatrix_qr.cpp.
unsigned int vpMatrix::qrPivot | ( | vpMatrix & | Q, |
vpMatrix & | R, | ||
vpMatrix & | P, | ||
bool | full = false , |
||
bool | squareR = false , |
||
double | tol = 1e-6 |
||
) | const |
Compute the QR pivot decomposition of a (m x n) matrix of rank r. Only available if Lapack 3rd party is installed. If Lapack is not installed we use a Lapack built-in version.
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 536 of file vpMatrix_qr.cpp.
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inlineinherited |
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 170 of file vpArray2D.h.
vpRowVector vpMatrix::row | ( | const unsigned int | i | ) |
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 5275 of file vpMatrix.cpp.
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inlinestaticinherited |
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 518 of file vpArray2D.h.
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inlinestatic |
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 652 of file vpMatrix.h.
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inlinestatic |
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 670 of file vpMatrix.h.
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inlinestaticinherited |
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 611 of file vpArray2D.h.
void vpMatrix::setIdentity | ( | const double & | val = 1.0 | ) |
Set the matrix diagonal elements to val. More generally set M[i][i] = val.
Definition at line 5316 of file vpMatrix.cpp.
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inlineinherited |
Return the number of elements of the 2D array.
Definition at line 157 of file vpArray2D.h.
vpColVector vpMatrix::solveByQR | ( | const vpColVector & | b | ) | const |
Solve a linear system Ax = b using QR Decomposition.
Non destructive wrt. A and B.
b | : Vector b |
Here an example:
Definition at line 843 of file vpMatrix_qr.cpp.
void vpMatrix::solveByQR | ( | const vpColVector & | b, |
vpColVector & | x | ||
) | const |
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 791 of file vpMatrix_qr.cpp.
vpColVector vpMatrix::solveBySVD | ( | const vpColVector & | B | ) | const |
Solve a linear system using Singular Value Decomposition (SVD).
Non destructive wrt. A and B.
B | : Vector ![]() |
Here an example:
Definition at line 1719 of file vpMatrix.cpp.
void vpMatrix::solveBySVD | ( | const vpColVector & | b, |
vpColVector & | x | ||
) | const |
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 1668 of file vpMatrix.cpp.
void vpMatrix::stack | ( | const vpColVector & | c | ) |
Stack column vector c at the right of the current matrix, or copy if the matrix has no dimensions: this = [ this c ].
Here an example for a robot velocity log :
Definition at line 4531 of file vpMatrix.cpp.
void vpMatrix::stack | ( | const vpMatrix & | A | ) |
Stack A at the end of the current matrix, or copy if the matrix has no dimensions : this = [ this A ]^T.
Definition at line 4461 of file vpMatrix.cpp.
Referenced by stackMatrices().
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static |
Stack column vector c to matrix A and return the resulting matrix [ A c ]
A | : Left matrix. |
c | : Right column vector. |
Definition at line 4018 of file vpMatrix.cpp.
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static |
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 4037 of file vpMatrix.cpp.
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 3915 of file vpMatrix.cpp.
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 3935 of file vpMatrix.cpp.
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static |
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 3979 of file vpMatrix.cpp.
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static |
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 3998 of file vpMatrix.cpp.
void vpMatrix::stack | ( | const vpRowVector & | r | ) |
Stack row vector r at the end of the current matrix, or copy if the matrix has no dimensions: this = [ this r ]^T.
Here an example for a robot velocity log :
Definition at line 4492 of file vpMatrix.cpp.
vpColVector vpMatrix::stackColumns | ( | ) |
Stacks columns of a matrix in a vector.
Definition at line 1473 of file vpMatrix.cpp.
void vpMatrix::stackColumns | ( | vpColVector & | out | ) |
Stacks columns of a matrix in a vector.
out | : a vpColVector. |
Definition at line 1456 of file vpMatrix.cpp.
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static |
Definition at line 5243 of file vpMatrix.cpp.
References vpColVector::stack().
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static |
Definition at line 5248 of file vpMatrix.cpp.
References vpColVector::stack().
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inline |
Definition at line 690 of file vpMatrix.h.
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inlinestatic |
Definition at line 695 of file vpMatrix.h.
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inlinestatic |
Definition at line 700 of file vpMatrix.h.
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static |
Definition at line 5253 of file vpMatrix.cpp.
References stack().
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static |
Definition at line 5255 of file vpMatrix.cpp.
References stack().
vpRowVector vpMatrix::stackRows | ( | ) |
Stacks rows of a matrix in a vector.
Definition at line 1499 of file vpMatrix.cpp.
void vpMatrix::stackRows | ( | vpRowVector & | out | ) |
Stacks rows of a matrix in a vector
out | : a vpRowVector. |
Definition at line 1484 of file vpMatrix.cpp.
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static |
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 1192 of file vpMatrix.cpp.
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 1225 of file vpMatrix.cpp.
double vpMatrix::sum | ( | ) | const |
Return the sum of all the elements of the matrix.
Definition at line 1325 of file vpMatrix.cpp.
References vpArray2D< double >::colNum, vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.
double vpMatrix::sumSquare | ( | ) | const |
Return the sum square of all the elements of the matrix
.
Definition at line 5137 of file vpMatrix.cpp.
void vpMatrix::svd | ( | vpColVector & | w, |
vpMatrix & | V | ||
) |
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 1791 of file vpMatrix.cpp.
Referenced by vpMbtFaceDepthNormal::estimatePlaneEquationSVD().
void vpMatrix::svdEigen3 | ( | vpColVector & | w, |
vpMatrix & | V | ||
) |
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 450 of file vpMatrix_svd.cpp.
void vpMatrix::svdGsl | ( | vpColVector & | w, |
vpMatrix & | V | ||
) |
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 345 of file vpMatrix_svd.cpp.
void vpMatrix::svdLapack | ( | vpColVector & | w, |
vpMatrix & | V | ||
) |
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 236 of file vpMatrix_svd.cpp.
void vpMatrix::svdOpenCV | ( | vpColVector & | w, |
vpMatrix & | V | ||
) |
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 149 of file vpMatrix_svd.cpp.
vpMatrix vpMatrix::t | ( | ) | const |
Compute and return the transpose of the matrix.
Definition at line 374 of file vpMatrix.cpp.
Referenced by vpTemplateTracker::computeOptimalBrentGain(), eigenValues(), vpMbtFaceDepthNormal::estimatePlaneEquationSVD(), vpTemplateTrackerWarpHomographySL3::findWarp(), and vpQuadProg::fromCanonicalCost().
vpMatrix vpMatrix::transpose | ( | ) | const |
Compute and return the transpose of the matrix.
Definition at line 393 of file vpMatrix.cpp.
Referenced by vpServo::computeProjectionOperators(), vpQuadProg::fromCanonicalCost(), vpTemplateTrackerWarpSRT::getParamInverse(), and vpTemplateTrackerWarpRT::getParamInverse().
void vpMatrix::transpose | ( | vpMatrix & | At | ) | const |
Compute At the transpose of the matrix.
At | (output) : Resulting transpose matrix. |
Definition at line 405 of file vpMatrix.cpp.
Allow to multiply a scalar by a matrix.
Definition at line 1349 of file vpMatrix.cpp.
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related |
This function performs generalized matrix multiplication: D = alpha*op(A)*op(B) + beta*op(C), where op(X) is X or X^T. Operation on A, B and C matrices is described by enumeration vpGEMMmethod().
For example, to compute D = alpha*A^T*B^T+beta*C we need to call :
If C is not used, vpGEMM must be called using an empty array null. Thus to compute D = alpha*A^T*B, we have to call:
vpException::incorrectMatrixSizeError | if the sizes of the matrices do not allow the operations. |
A | : An array that could be a vpMatrix. |
B | : An array that could be a vpMatrix. |
alpha | : A scalar. |
C | : An array that could be a vpMatrix. |
beta | : A scalar. |
D | : The resulting array that could be a vpMatrix. |
ops | : A scalar describing operation applied on the matrices. Possible values are the one defined in vpGEMMmethod(): VP_GEMM_A_T, VP_GEMM_B_T, VP_GEMM_C_T. |
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related |
Enumeration of the operations applied on matrices in vpGEMM() function.
Operations are :
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protectedinherited |
Number of columns in the array.
Definition at line 75 of file vpArray2D.h.
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inherited |
Address of the first element of the data array.
Definition at line 83 of file vpArray2D.h.
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protectedinherited |
Current array size (rowNum * colNum)
Definition at line 79 of file vpArray2D.h.
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protectedinherited |
Number of rows in the array.
Definition at line 73 of file vpArray2D.h.
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protectedinherited |
Address of the first element of each rows.
Definition at line 77 of file vpArray2D.h.