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

#include <SVD.h>

Public Member Functions
void	compute (const MatrixType &matrix)

template<typename PositiveType , typename UnitaryType >
void	computePositiveUnitary (PositiveType positive, UnitaryType unitary) const

template<typename UnitaryType , typename PositiveType >
void	computePositiveUnitary (UnitaryType positive, PositiveType 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	computeUnitaryPositive (UnitaryType unitary, PositiveType positive) const

const MatrixUType &	matrixU () const

const MatrixVType &	matrixV () const

const SingularValuesType &	singularValues () const

template<typename OtherDerived , typename ResultType >
bool	solve (const MatrixBase< OtherDerived > &b, ResultType *result) const

SVD &	sort ()

	SVD ()

	SVD (const MatrixType &matrix)

Protected Attributes
MatrixUType	m_matU

MatrixVType	m_matV

SingularValuesType	m_sigma

Private Types
enum	{ PacketSize = internal::packet_traits<Scalar>::size, AlignmentMask = int(PacketSize)-1, MinSize = EIGEN_SIZE_MIN_PREFER_DYNAMIC(MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime) }

typedef Matrix< Scalar, MatrixType::RowsAtCompileTime, 1 >	ColVector

typedef Matrix< Scalar, MatrixType::RowsAtCompileTime, MinSize >	MatrixUType

typedef Matrix< Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime >	MatrixVType

typedef NumTraits< typename MatrixType::Scalar >::Real	RealScalar

typedef Matrix< Scalar, MatrixType::ColsAtCompileTime, 1 >	RowVector

typedef MatrixType::Scalar	Scalar

typedef Matrix< Scalar, MinSize, 1 >	SingularValuesType

Detailed Description

template<typename MatrixType>
class Eigen::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()

Definition at line 30 of file SVD.h.

Member Typedef Documentation

◆ ColVector

template<typename MatrixType>

typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> Eigen::SVD< MatrixType >::ColVector

private

Definition at line 42 of file SVD.h.

◆ MatrixUType

template<typename MatrixType>

typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MinSize> Eigen::SVD< MatrixType >::MatrixUType

private

Definition at line 45 of file SVD.h.

◆ MatrixVType

template<typename MatrixType>

typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> Eigen::SVD< MatrixType >::MatrixVType

private

Definition at line 46 of file SVD.h.

◆ RealScalar

template<typename MatrixType>

typedef NumTraits<typename MatrixType::Scalar>::Real Eigen::SVD< MatrixType >::RealScalar

private

Definition at line 34 of file SVD.h.

◆ RowVector

template<typename MatrixType>

typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> Eigen::SVD< MatrixType >::RowVector

private

Definition at line 43 of file SVD.h.

◆ Scalar

template<typename MatrixType>

typedef MatrixType::Scalar Eigen::SVD< MatrixType >::Scalar

private

Definition at line 33 of file SVD.h.

◆ SingularValuesType

template<typename MatrixType>

typedef Matrix<Scalar, MinSize, 1> Eigen::SVD< MatrixType >::SingularValuesType

private

Definition at line 47 of file SVD.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename MatrixType>

anonymous enum

private

Enumerator
PacketSize
AlignmentMask
MinSize

Definition at line 36 of file SVD.h.

Constructor & Destructor Documentation

◆ SVD() [1/2]

template<typename MatrixType>

Eigen::SVD< MatrixType >::SVD ( )

inline

Definition at line 51 of file SVD.h.

◆ SVD() [2/2]

template<typename MatrixType>

Eigen::SVD< MatrixType >::SVD ( const MatrixType & matrix )

inline

Definition at line 53 of file SVD.h.

Member Function Documentation

◆ compute()

template<typename MatrixType >

void Eigen::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)

Definition at line 94 of file SVD.h.

◆ computePositiveUnitary() [1/2]

template<typename MatrixType>

template<typename PositiveType , typename UnitaryType >

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

◆ computePositiveUnitary() [2/2]

template<typename MatrixType>

template<typename UnitaryType , typename PositiveType >

void Eigen::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()

Definition at line 565 of file SVD.h.

◆ computeRotationScaling()

template<typename MatrixType >

template<typename RotationType , typename ScalingType >

void Eigen::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()

Definition at line 584 of file SVD.h.

◆ computeScalingRotation()

template<typename MatrixType >

template<typename ScalingType , typename RotationType >

void Eigen::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()

Definition at line 610 of file SVD.h.

◆ computeUnitaryPositive()

template<typename MatrixType >

template<typename UnitaryType , typename PositiveType >

void Eigen::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()

Definition at line 547 of file SVD.h.

◆ matrixU()

template<typename MatrixType>

const MatrixUType& Eigen::SVD< MatrixType >::matrixU ( ) const

inline

Definition at line 64 of file SVD.h.

◆ matrixV()

template<typename MatrixType>

const MatrixVType& Eigen::SVD< MatrixType >::matrixV ( ) const

inline

Definition at line 66 of file SVD.h.

◆ singularValues()

template<typename MatrixType>

const SingularValuesType& Eigen::SVD< MatrixType >::singularValues ( ) const

inline

Definition at line 65 of file SVD.h.

◆ solve()

template<typename MatrixType >

template<typename OtherDerived , typename ResultType >

bool Eigen::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()

Definition at line 513 of file SVD.h.

◆ sort()

template<typename MatrixType >

SVD< MatrixType > & Eigen::SVD< MatrixType >::sort ( )

Definition at line 470 of file SVD.h.

Member Data Documentation

◆ m_matU

template<typename MatrixType>

MatrixUType Eigen::SVD< MatrixType >::m_matU

protected

Definition at line 82 of file SVD.h.

◆ m_matV

template<typename MatrixType>

MatrixVType Eigen::SVD< MatrixType >::m_matV

protected

Definition at line 84 of file SVD.h.

◆ m_sigma

template<typename MatrixType>

SingularValuesType Eigen::SVD< MatrixType >::m_sigma

protected

Definition at line 86 of file SVD.h.

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

SVD.h

Public Member Functions

Protected Attributes

Private Types

Detailed Description

template<typename MatrixType> class Eigen::SVD< MatrixType >

Member Typedef Documentation

◆ ColVector

◆ MatrixUType

◆ MatrixVType

◆ RealScalar

◆ RowVector

◆ Scalar

◆ SingularValuesType

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ SVD() [1/2]

◆ SVD() [2/2]

Member Function Documentation

◆ compute()

◆ computePositiveUnitary() [1/2]

◆ computePositiveUnitary() [2/2]

◆ computeRotationScaling()

◆ computeScalingRotation()

◆ computeUnitaryPositive()

◆ matrixU()

◆ matrixV()

◆ singularValues()

◆ solve()

◆ sort()

Member Data Documentation

◆ m_matU

◆ m_matV

◆ m_sigma

template<typename MatrixType>
class Eigen::SVD< MatrixType >