nmrPInverseSolver Class Reference

#include <nmrPInverseSolver.h>

Public Member Functions
	nmrPInverseSolver (void)
	nmrPInverseSolver (CISSTNETLIB_INTEGER m, CISSTNETLIB_INTEGER n, bool storageOrder=VCT_COL_MAJOR)
	nmrPInverseSolver (const vctDynamicMatrix< CISSTNETLIB_DOUBLE > &A)
void	Allocate (CISSTNETLIB_INTEGER m, CISSTNETLIB_INTEGER n, bool storageOrder)
void	Allocate (const vctDynamicMatrix< CISSTNETLIB_DOUBLE > &A)
template<class _matrixOwnerType>
void	Solve (vctDynamicMatrixBase< _matrixOwnerType, CISSTNETLIB_DOUBLE > &A) throw (std::runtime_error)
const vctDynamicMatrix< CISSTNETLIB_DOUBLE > &	GetS (void) const
const vctDynamicMatrix< CISSTNETLIB_DOUBLE > &	GetU (void) const
const vctDynamicMatrix< CISSTNETLIB_DOUBLE > &	GetV (void) const
const vctDynamicMatrix< CISSTNETLIB_DOUBLE > &	GetPInverse (void) const

Protected Attributes
CISSTNETLIB_INTEGER	M
CISSTNETLIB_INTEGER	N
CISSTNETLIB_INTEGER	MaxMN
CISSTNETLIB_INTEGER	MinMN
CISSTNETLIB_DOUBLE	EPS
vctDynamicMatrix< CISSTNETLIB_DOUBLE >	S
vctDynamicMatrix< CISSTNETLIB_DOUBLE >	U
vctDynamicMatrix< CISSTNETLIB_DOUBLE >	V
vctDynamicMatrix< CISSTNETLIB_DOUBLE >	PInverseA
bool	StorageOrder
nmrSVDSolver	svd

Detailed Description

Algorithm P-Inverse: Moore-Penrose pseudo-inverse Calculates the Moore-Penrose pseudo-inverse of the M by N matrix A, and stores the result in PInverseA. The singular values of A are returned in S. The left singular vectors are returned in U, and the right singular vectors are returned in V.

\( A^{+} = V * \Sigma^{+} * U^{T} \)

where \( \Sigma^{+} \) is a \( N \times M \) matrix which is zero except for its min(m,n) diagonal elements, U is a \( M \times M \) orthogonal matrix, and V is a \( N \times N \) orthogonal matrix. The diagonal elements of \( \Sigma^{+} \) are the reciprocal of non-zero singular values of A; they are real and non-negative, and are returned in descending order. The first \( \mbox{min}(m,n) \) columns of U and V are the left and right singular vectors of A.

The data members of this class are:

• M: The number of rows of the input matrix A. M >= 0.
• N: The number of columns of the input matrix A. N >= 0.
• MaxMN: leading dimension of all 2-dim. arrays. MaxMN must be greater than or equal to max(N,M).
• MinMN: min(N,M);
• A: On entry, the \( M \times N \) matrix A. On exit, the content of A is altered.

Note

The input matrix must be compact (see vctDynamicMatrix::IsCompact() or vctFixedSizeMatrix::IsCompact()).

This code relies on the ERC CISST cnetlib library. Since cnetlib is optional, make sure that CISST_HAS_CNETLIB has been turned ON during the configuration with CMake.

Deprecated

This class has been replaced by nmrPInverse, nmrPInverseDynamicData and nmrPInverseFixedSizeData.

Constructor & Destructor Documentation

nmrPInverseSolver() [1/3]

nmrPInverseSolver::nmrPInverseSolver ( void )

inline

Default constructor. This constructor doesn't allocate any memory. If you use this constructor, you will need to use one of the Allocate() methods before you can use the Solve method.

nmrPInverseSolver() [2/3]

nmrPInverseSolver::nmrPInverseSolver ( CISSTNETLIB_INTEGER m, CISSTNETLIB_INTEGER n, bool storageOrder = VCT_COL_MAJOR )

inline

Constructor with memory allocation. This constructor allocates the memory based on M and N. It relies on the method Allocate(). The next call to the Solve() method will check that the parameters match the dimension.

Parameters

m	Number of rows of A
n	Number of columns of A
storageOrder	Storage order used for the input matrix. This order will be used for the output as well.

nmrPInverseSolver() [3/3]

nmrPInverseSolver::nmrPInverseSolver ( const vctDynamicMatrix< CISSTNETLIB_DOUBLE > & A )

inline

Constructor with memory allocation. This constructor allocates the memory based on the actual input of the Solve() method. It relies on the method Allocate(). The next call to the Solve() method will check that the parameters match the dimension and storage order.

Member Function Documentation

Allocate() [1/2]

void nmrPInverseSolver::Allocate ( CISSTNETLIB_INTEGER m, CISSTNETLIB_INTEGER n, bool storageOrder )

inline

This method allocates the memory based on M and N. The next call to the Solve() method will check that the parameters match the dimension.

Parameters

m	Number of rows of A
n	Number of columns of A
storageOrder	Storage order used for all the matrices

Allocate() [2/2]

void nmrPInverseSolver::Allocate ( const vctDynamicMatrix< CISSTNETLIB_DOUBLE > & A )

inline

Allocate memory to solve this problem. This method provides a convenient way to extract the required sizes from the input containers. The next call to the Solve() method will check that the parameters match the dimension.

GetPInverse()

const vctDynamicMatrix< CISSTNETLIB_DOUBLE > & nmrPInverseSolver::GetPInverse ( void ) const

inline

GetS()

const vctDynamicMatrix< CISSTNETLIB_DOUBLE > & nmrPInverseSolver::GetS ( void ) const

inline

GetU()

const vctDynamicMatrix< CISSTNETLIB_DOUBLE > & nmrPInverseSolver::GetU ( void ) const

inline

GetV()

const vctDynamicMatrix< CISSTNETLIB_DOUBLE > & nmrPInverseSolver::GetV ( void ) const

inline

Solve()

template<class _matrixOwnerType>

void nmrPInverseSolver::Solve ( vctDynamicMatrixBase< _matrixOwnerType, CISSTNETLIB_DOUBLE > & A ) throw ( std::runtime_error )

inline

This computes the Moore-Penrose pseudo-inverse of a real \( M \times N \) matrix A, optionally computing the left and/or right singular vectors. The SVD is written:

\( A^{+} = V * \Sigma^{+} * U^{T} \)

Note

This method requires a compact matrix with the same size and storage order used to Allocate. An std::runtime_error exception will be thrown if these conditions are not met.

Member Data Documentation

EPS

CISSTNETLIB_DOUBLE nmrPInverseSolver::EPS

protected

M

CISSTNETLIB_INTEGER nmrPInverseSolver::M

protected

MaxMN

CISSTNETLIB_INTEGER nmrPInverseSolver::MaxMN

protected

MinMN

CISSTNETLIB_INTEGER nmrPInverseSolver::MinMN

protected

N

CISSTNETLIB_INTEGER nmrPInverseSolver::N

protected

PInverseA

vctDynamicMatrix<CISSTNETLIB_DOUBLE> nmrPInverseSolver::PInverseA

protected

S

vctDynamicMatrix<CISSTNETLIB_DOUBLE> nmrPInverseSolver::S

protected

StorageOrder

bool nmrPInverseSolver::StorageOrder

protected

svd

nmrSVDSolver nmrPInverseSolver::svd

protected

U

vctDynamicMatrix<CISSTNETLIB_DOUBLE> nmrPInverseSolver::U

protected

V

vctDynamicMatrix<CISSTNETLIB_DOUBLE> nmrPInverseSolver::V

protected

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The documentation for this class was generated from the following file:

• tmp/cisst-saw/cisst/cisstNumerical/nmrPInverseSolver.h