SVD< MatrixType > Class Template Reference

Standard SVD decomposition of a matrix and associated features. More...

#include <SVD.h>

List of all members.

Public Member Functions
	SVD ()
	SVD (const MatrixType &matrix)
template<typename OtherDerived , typename ResultType >
bool	solve (const MatrixBase< OtherDerived > &b, ResultType *result) const
const MatrixUType &	matrixU () const
const SingularValuesType &	singularValues () const
const MatrixVType &	matrixV () const
void	compute (const MatrixType &matrix)
SVD &	sort ()
template<typename UnitaryType , typename PositiveType >
void	computeUnitaryPositive (UnitaryType *unitary, PositiveType *positive) const
template<typename PositiveType , typename UnitaryType >
void	computePositiveUnitary (PositiveType *positive, UnitaryType *unitary) const
template<typename RotationType , typename ScalingType >
void	computeRotationScaling (RotationType *unitary, ScalingType *positive) const
template<typename ScalingType , typename RotationType >
void	computeScalingRotation (ScalingType *positive, RotationType *unitary) const
template<typename UnitaryType , typename PositiveType >
void	computePositiveUnitary (UnitaryType *positive, PositiveType *unitary) const
Protected Attributes
MatrixUType	m_matU
MatrixVType	m_matV
SingularValuesType	m_sigma

---

Detailed Description

template<typename MatrixType>
class SVD< MatrixType >

Standard SVD decomposition of a matrix and associated features.

Parameters:

MatrixType

the type of the matrix of which we are computing the SVD decomposition

This class performs a standard SVD decomposition of a real matrix A of size M x N with M >= N.

See also:

MatrixBase::SVD()

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Constructor & Destructor Documentation

template<typename MatrixType>

SVD< MatrixType >::SVD

(

)

[inline]

template<typename MatrixType>

SVD< MatrixType >::SVD

(

const MatrixType &

matrix

)

[inline]

---

Member Function Documentation

template<typename MatrixType >

void SVD< MatrixType >::compute

(

const MatrixType &

matrix

)

Computes / recomputes the SVD decomposition A = U S V^* of matrix

Note:

this code has been adapted from JAMA (public domain)

template<typename MatrixType>

template<typename PositiveType , typename UnitaryType >

void SVD< MatrixType >::computePositiveUnitary	(	PositiveType *	positive,
		UnitaryType *	unitary
	)			const

template<typename MatrixType>

template<typename UnitaryType , typename PositiveType >

void SVD< MatrixType >::computePositiveUnitary	(	UnitaryType *	positive,
		PositiveType *	unitary
	)			const

Computes the polar decomposition of the matrix, as a product positive x unitary.

If either pointer is zero, the corresponding computation is skipped.

Only for square matrices.

See also:

computeUnitaryPositive(), computeRotationScaling()

template<typename MatrixType >

template<typename RotationType , typename ScalingType >

void SVD< MatrixType >::computeRotationScaling	(	RotationType *	rotation,
		ScalingType *	scaling
	)			const

decomposes the matrix as a product rotation x scaling, the scaling being not necessarily positive.

If either pointer is zero, the corresponding computation is skipped.

This method requires the Geometry module.

See also:

computeScalingRotation(), computeUnitaryPositive()

template<typename MatrixType >

template<typename ScalingType , typename RotationType >

void SVD< MatrixType >::computeScalingRotation	(	ScalingType *	scaling,
		RotationType *	rotation
	)			const

decomposes the matrix as a product scaling x rotation, the scaling being not necessarily positive.

If either pointer is zero, the corresponding computation is skipped.

This method requires the Geometry module.

See also:

computeRotationScaling(), computeUnitaryPositive()

template<typename MatrixType >

template<typename UnitaryType , typename PositiveType >

void SVD< MatrixType >::computeUnitaryPositive	(	UnitaryType *	unitary,
		PositiveType *	positive
	)			const

Computes the polar decomposition of the matrix, as a product unitary x positive.

If either pointer is zero, the corresponding computation is skipped.

Only for square matrices.

See also:

computePositiveUnitary(), computeRotationScaling()

template<typename MatrixType>

const MatrixUType& SVD< MatrixType >::matrixU

(

)

const [inline]

template<typename MatrixType>

const MatrixVType& SVD< MatrixType >::matrixV

(

)

const [inline]

template<typename MatrixType>

const SingularValuesType& SVD< MatrixType >::singularValues

(

)

const [inline]

template<typename MatrixType >

template<typename OtherDerived , typename ResultType >

bool SVD< MatrixType >::solve	(	const MatrixBase< OtherDerived > &	b,
		ResultType *	result
	)			const

Returns:

the solution of using the current SVD decomposition of A. The parts of the solution corresponding to zero singular values are ignored.

See also:

MatrixBase::svd(), LU::solve(), LLT::solve()

template<typename MatrixType >

SVD< MatrixType > & SVD< MatrixType >::sort

(

)

---

Member Data Documentation

template<typename MatrixType>

MatrixUType SVD< MatrixType >::m_matU [protected]

template<typename MatrixType>

MatrixVType SVD< MatrixType >::m_matV [protected]

template<typename MatrixType>

SingularValuesType SVD< MatrixType >::m_sigma [protected]

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

• /home/hauberg/Dokumenter/Capture/humim-tracker-0.1/src/ntk/geometry/Eigen/src/Eigen2Support/SVD.h