SVD Class Reference

Singular value decomposition of a rectangular matrix. More...

Collaboration diagram for SVD:

Public Member Functions
	SVD (const scalarRectangularMatrix &A, const scalar minCondition=0)
	Construct from a rectangular Matrix. More...
const scalarRectangularMatrix &	U () const
	Return U. More...
const scalarRectangularMatrix &	V () const
	Return the square matrix V. More...
const scalarDiagonalMatrix &	S () const
	Return the singular values. More...
const scalarRectangularMatrix &	VSinvUt () const
	Return VSinvUt (the pseudo inverse) More...
label	nZeros () const
	Return the number of zero singular values. More...
scalar	minNonZeroS () const
	Return the minimum non-zero singular value. More...

Private Member Functions
	SVD (const SVD &)
	Disallow default bitwise copy construct. More...
void	operator= (const SVD &)
	Disallow default bitwise assignment. More...
template<class T >
const T	sign (const T &a, const T &b)

Private Attributes
scalarRectangularMatrix	U_
	Rectangular matrix with the same dimensions as the input. More...
scalarRectangularMatrix	V_
	Square matrix V. More...
DiagonalMatrix< scalar >	S_
	The singular values. More...
scalarRectangularMatrix	VSinvUt_
	The matrix product V S^(-1) U^T. More...
label	nZeros_
	The number of zero singular values. More...

Detailed Description

Singular value decomposition of a rectangular matrix.

Source files

• SVD.H
• SVDI.H
• SVD.C

Definition at line 52 of file SVD.H.

Constructor & Destructor Documentation

SVD() [1/2]

SVD ( const SVD &  )

private

Disallow default bitwise copy construct.

SVD() [2/2]

SVD	(	const scalarRectangularMatrix &	A,
		const scalar	minCondition = 0
	)

Construct from a rectangular Matrix.

Definition at line 33 of file SVD.C.

References A(), Foam::constant::universal::c, Foam::endl(), f(), Foam::findMax(), forAll, g, Foam::constant::universal::h, Foam::inv(), k, Matrix::m(), Foam::mag(), Foam::max(), Foam::min(), Foam::multiply(), Matrix::n(), SVD::nZeros_, s(), SVD::S_, SVD::sign(), Foam::sqrt(), Foam::sqrtSumSqr(), Matrix::T(), SVD::U_, SVD::V_, SVD::VSinvUt_, WarningInFunction, x, and y.

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Member Function Documentation

operator=()

void operator= ( const SVD &  )

private

Disallow default bitwise assignment.

sign()

const T sign ( const T &  a, const T &  b  )

inlineprivate

Definition at line 29 of file SVDI.H.

References Foam::constant::physicoChemical::b.

Referenced by SVD::SVD().

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U()

const Foam::scalarRectangularMatrix & U ( ) const

inline

Return U.

Definition at line 37 of file SVDI.H.

V()

const Foam::scalarRectangularMatrix & V ( ) const

inline

Return the square matrix V.

Definition at line 42 of file SVDI.H.

S()

const Foam::scalarDiagonalMatrix & S ( ) const

inline

Return the singular values.

Definition at line 47 of file SVDI.H.

Referenced by CentredFitSnGradData< Polynomial >::calcFit().

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VSinvUt()

const Foam::scalarRectangularMatrix & VSinvUt ( ) const

inline

Return VSinvUt (the pseudo inverse)

Definition at line 52 of file SVDI.H.

Referenced by CentredFitSnGradData< Polynomial >::calcFit(), FitData< CentredFitSnGradData< Polynomial >, extendedCentredCellToFaceStencil, Polynomial >::calcFit(), and Foam::SVDinv().

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nZeros()

Foam::label nZeros ( ) const

inline

Return the number of zero singular values.

Definition at line 57 of file SVDI.H.

minNonZeroS()

Foam::scalar minNonZeroS ( ) const

inline

Return the minimum non-zero singular value.

Definition at line 62 of file SVDI.H.

References s().

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Field Documentation

U_

scalarRectangularMatrix U_

private

Rectangular matrix with the same dimensions as the input.

Definition at line 57 of file SVD.H.

Referenced by SVD::SVD().

V_

scalarRectangularMatrix V_

private

Square matrix V.

Definition at line 60 of file SVD.H.

Referenced by SVD::SVD().

S_

DiagonalMatrix<scalar> S_

private

The singular values.

Definition at line 63 of file SVD.H.

Referenced by SVD::SVD().

VSinvUt_

scalarRectangularMatrix VSinvUt_

private

The matrix product V S^(-1) U^T.

Definition at line 66 of file SVD.H.

Referenced by SVD::SVD().

nZeros_

label nZeros_

private

The number of zero singular values.

Definition at line 69 of file SVD.H.

Referenced by SVD::SVD().

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

• src/OpenFOAM/matrices/scalarMatrices/SVD/SVD.H
• src/OpenFOAM/matrices/scalarMatrices/SVD/SVD.C
• src/OpenFOAM/matrices/scalarMatrices/SVD/SVDI.H