class Bidiagonal Divide and Conquer SVD More...

#include <ForwardDeclarations.h>

Inheritance diagram for Eigen::BDCSVD< _MatrixType >:

Public Types
enum	{ RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime), MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime, MaxColsAtCompileTime), MatrixOptions = MatrixType::Options }

typedef Ref< ArrayXr >	ArrayRef

typedef Array< Index, 1, Dynamic >	ArrayXi

typedef Array< RealScalar, Dynamic, 1 >	ArrayXr

typedef Ref< ArrayXi >	IndicesRef

typedef NumTraits< RealScalar >::Literal	Literal

typedef _MatrixType	MatrixType

typedef Base::MatrixUType	MatrixUType

typedef Base::MatrixVType	MatrixVType

typedef Matrix< Scalar, Dynamic, Dynamic, ColMajor >	MatrixX

typedef Matrix< RealScalar, Dynamic, Dynamic, ColMajor >	MatrixXr

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

typedef MatrixType::Scalar	Scalar

typedef Base::SingularValuesType	SingularValuesType

typedef Matrix< RealScalar, Dynamic, 1 >	VectorType

Public Types inherited from Eigen::SVDBase< BDCSVD< _MatrixType > >
enum

typedef Eigen::Index	Index

typedef internal::traits< BDCSVD< _MatrixType > >::MatrixType	MatrixType

typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime >	MatrixUType

typedef Matrix< Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime >	MatrixVType

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

typedef MatrixType::Scalar	Scalar

typedef internal::plain_diag_type< MatrixType, RealScalar >::type	SingularValuesType

typedef MatrixType::StorageIndex	StorageIndex

Public Member Functions
	BDCSVD ()
	Default Constructor. More...

	BDCSVD (Index rows, Index cols, unsigned int computationOptions=0)
	Default Constructor with memory preallocation. More...

	BDCSVD (const MatrixType &matrix, unsigned int computationOptions=0)
	Constructor performing the decomposition of given matrix. More...

BDCSVD &	compute (const MatrixType &matrix, unsigned int computationOptions)
	Method performing the decomposition of given matrix using custom options. More...

BDCSVD &	compute (const MatrixType &matrix)
	Method performing the decomposition of given matrix using current options. More...

void	setSwitchSize (int s)

	~BDCSVD ()

Public Member Functions inherited from Eigen::SVDBase< BDCSVD< _MatrixType > >
EIGEN_DEVICE_FUNC void	_solve_impl (const RhsType &rhs, DstType &dst) const

Index	cols () const

bool	computeU () const

bool	computeV () const

BDCSVD< _MatrixType > &	derived ()

const BDCSVD< _MatrixType > &	derived () const

const MatrixUType &	matrixU () const

const MatrixVType &	matrixV () const

Index	nonzeroSingularValues () const

Index	rank () const

Index	rows () const

BDCSVD< _MatrixType > &	setThreshold (const RealScalar &threshold)

BDCSVD< _MatrixType > &	setThreshold (Default_t)

const SingularValuesType &	singularValues () const

const Solve< BDCSVD< _MatrixType >, Rhs >	solve (const MatrixBase< Rhs > &b) const

RealScalar	threshold () const

Public Attributes
int	m_numIters

Protected Attributes
int	m_algoswap

bool	m_compU

MatrixXr	m_computed

bool	m_compV

bool	m_isTranspose

MatrixXr	m_naiveU

MatrixXr	m_naiveV

Index	m_nRec

ArrayXr	m_workspace

ArrayXi	m_workspaceI

Protected Attributes inherited from Eigen::SVDBase< BDCSVD< _MatrixType > >
Index	m_cols

unsigned int	m_computationOptions

bool	m_computeFullU

bool	m_computeFullV

bool	m_computeThinU

bool	m_computeThinV

Index	m_diagSize

bool	m_isAllocated

bool	m_isInitialized

MatrixUType	m_matrixU

MatrixVType	m_matrixV

Index	m_nonzeroSingularValues

RealScalar	m_prescribedThreshold

Index	m_rows

SingularValuesType	m_singularValues

bool	m_usePrescribedThreshold

Private Types
typedef SVDBase< BDCSVD >	Base

Private Member Functions
void	allocate (Index rows, Index cols, unsigned int computationOptions)

void	computeSingVals (const ArrayRef &col0, const ArrayRef &diag, const IndicesRef &perm, VectorType &singVals, ArrayRef shifts, ArrayRef mus)

void	computeSingVecs (const ArrayRef &zhat, const ArrayRef &diag, const IndicesRef &perm, const VectorType &singVals, const ArrayRef &shifts, const ArrayRef &mus, MatrixXr &U, MatrixXr &V)

void	computeSVDofM (Index firstCol, Index n, MatrixXr &U, VectorType &singVals, MatrixXr &V)

template<typename HouseholderU , typename HouseholderV , typename NaiveU , typename NaiveV >
void	copyUV (const HouseholderU &householderU, const HouseholderV &householderV, const NaiveU &naiveU, const NaiveV &naivev)

void	deflation (Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift)

void	deflation43 (Index firstCol, Index shift, Index i, Index size)

void	deflation44 (Index firstColu, Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size)

void	divide (Index firstCol, Index lastCol, Index firstRowW, Index firstColW, Index shift)

void	perturbCol0 (const ArrayRef &col0, const ArrayRef &diag, const IndicesRef &perm, const VectorType &singVals, const ArrayRef &shifts, const ArrayRef &mus, ArrayRef zhat)

void	structured_update (Block< MatrixXr, Dynamic, Dynamic > A, const MatrixXr &B, Index n1)

Static Private Member Functions
static RealScalar	secularEq (RealScalar x, const ArrayRef &col0, const ArrayRef &diag, const IndicesRef &perm, const ArrayRef &diagShifted, RealScalar shift)

Additional Inherited Members
Protected Member Functions inherited from Eigen::SVDBase< BDCSVD< _MatrixType > >
bool	allocate (Index rows, Index cols, unsigned int computationOptions)

	SVDBase ()
	Default Constructor. More...

Static Protected Member Functions inherited from Eigen::SVDBase< BDCSVD< _MatrixType > >
static void	check_template_parameters ()

Detailed Description

template<typename _MatrixType>
class Eigen::BDCSVD< _MatrixType >

class Bidiagonal Divide and Conquer SVD

Template Parameters

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

This class first reduces the input matrix to bi-diagonal form using class UpperBidiagonalization, and then performs a divide-and-conquer diagonalization. Small blocks are diagonalized using class JacobiSVD. You can control the switching size with the setSwitchSize() method, default is 16. For small matrice (<16), it is thus preferable to directly use JacobiSVD. For larger ones, BDCSVD is highly recommended and can several order of magnitude faster.

Warning: this algorithm is unlikely to provide accurate result when compiled with unsafe math optimizations. For instance, this concerns Intel's compiler (ICC), which perfroms such optimization by default unless you compile with the -fp-model precise option. Likewise, the -ffast-math option of GCC or clang will significantly degrade the accuracy.

See also: class JacobiSVD

Definition at line 259 of file ForwardDeclarations.h.

Member Typedef Documentation

template<typename _MatrixType>

typedef Ref<ArrayXr> Eigen::BDCSVD< _MatrixType >::ArrayRef

Definition at line 100 of file BDCSVD.h.

template<typename _MatrixType>

typedef Array<Index,1,Dynamic> Eigen::BDCSVD< _MatrixType >::ArrayXi

Definition at line 99 of file BDCSVD.h.

template<typename _MatrixType>

typedef Array<RealScalar, Dynamic, 1> Eigen::BDCSVD< _MatrixType >::ArrayXr

Definition at line 98 of file BDCSVD.h.

template<typename _MatrixType>

typedef SVDBase<BDCSVD> Eigen::BDCSVD< _MatrixType >::Base

private

Definition at line 69 of file BDCSVD.h.

template<typename _MatrixType>

typedef Ref<ArrayXi> Eigen::BDCSVD< _MatrixType >::IndicesRef

Definition at line 101 of file BDCSVD.h.

template<typename _MatrixType>

typedef NumTraits<RealScalar>::Literal Eigen::BDCSVD< _MatrixType >::Literal

Definition at line 80 of file BDCSVD.h.

template<typename _MatrixType>

typedef _MatrixType Eigen::BDCSVD< _MatrixType >::MatrixType

Definition at line 77 of file BDCSVD.h.

template<typename _MatrixType>

typedef Base::MatrixUType Eigen::BDCSVD< _MatrixType >::MatrixUType

Definition at line 91 of file BDCSVD.h.

template<typename _MatrixType>

typedef Base::MatrixVType Eigen::BDCSVD< _MatrixType >::MatrixVType

Definition at line 92 of file BDCSVD.h.

template<typename _MatrixType>

typedef Matrix<Scalar, Dynamic, Dynamic, ColMajor> Eigen::BDCSVD< _MatrixType >::MatrixX

Definition at line 95 of file BDCSVD.h.

template<typename _MatrixType>

typedef Matrix<RealScalar, Dynamic, Dynamic, ColMajor> Eigen::BDCSVD< _MatrixType >::MatrixXr

Definition at line 96 of file BDCSVD.h.

template<typename _MatrixType>

typedef NumTraits<typename MatrixType::Scalar>::Real Eigen::BDCSVD< _MatrixType >::RealScalar

Definition at line 79 of file BDCSVD.h.

template<typename _MatrixType>

typedef MatrixType::Scalar Eigen::BDCSVD< _MatrixType >::Scalar

Definition at line 78 of file BDCSVD.h.

template<typename _MatrixType>

typedef Base::SingularValuesType Eigen::BDCSVD< _MatrixType >::SingularValuesType

Definition at line 93 of file BDCSVD.h.

template<typename _MatrixType>

typedef Matrix<RealScalar, Dynamic, 1> Eigen::BDCSVD< _MatrixType >::VectorType

Definition at line 97 of file BDCSVD.h.

Member Enumeration Documentation

template<typename _MatrixType>

anonymous enum

Enumerator
RowsAtCompileTime
ColsAtCompileTime
DiagSizeAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime
MaxDiagSizeAtCompileTime
MatrixOptions

Definition at line 81 of file BDCSVD.h.

Constructor & Destructor Documentation

template<typename _MatrixType>

Eigen::BDCSVD< _MatrixType >::BDCSVD ( )

inline

Default Constructor.

The default constructor is useful in cases in which the user intends to perform decompositions via BDCSVD::compute(const MatrixType&).

Definition at line 108 of file BDCSVD.h.

template<typename _MatrixType>

Eigen::BDCSVD< _MatrixType >::BDCSVD	(	Index	rows,
		Index	cols,
		unsigned int	computationOptions = `0`
	)

inline

Default Constructor with memory preallocation.

Like the default constructor but with preallocation of the internal data according to the specified problem size.

See also: BDCSVD()

Definition at line 118 of file BDCSVD.h.

template<typename _MatrixType>

Eigen::BDCSVD< _MatrixType >::BDCSVD	(	const MatrixType &	matrix,
		unsigned int	computationOptions = `0`
	)

inline

Constructor performing the decomposition of given matrix.

Parameters

matrix	the matrix to decompose
computationOptions	optional parameter allowing to specify if you want full or thin U or V unitaries to be computed. By default, none is computed. This is a bit - field, the possible bits are ComputeFullU, ComputeThinU, ComputeFullV, ComputeThinV.

Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not available with the (non - default) FullPivHouseholderQR preconditioner.

Definition at line 134 of file BDCSVD.h.

template<typename _MatrixType>

Eigen::BDCSVD< _MatrixType >::~BDCSVD ( )

inline

Definition at line 140 of file BDCSVD.h.

Member Function Documentation

template<typename MatrixType >

void Eigen::BDCSVD< MatrixType >::allocate	(	Index	rows,
		Index	cols,
		unsigned int	computationOptions
	)

private

Definition at line 215 of file BDCSVD.h.

template<typename MatrixType >

BDCSVD< MatrixType > & Eigen::BDCSVD< MatrixType >::compute	(	const MatrixType &	matrix,
		unsigned int	computationOptions
	)

Method performing the decomposition of given matrix using custom options.

Parameters

matrix	the matrix to decompose
computationOptions	optional parameter allowing to specify if you want full or thin U or V unitaries to be computed. By default, none is computed. This is a bit - field, the possible bits are ComputeFullU, ComputeThinU, ComputeFullV, ComputeThinV.

Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not available with the (non - default) FullPivHouseholderQR preconditioner.

Definition at line 238 of file BDCSVD.h.

template<typename _MatrixType>

BDCSVD& Eigen::BDCSVD< _MatrixType >::compute ( const MatrixType & matrix )

inline

Method performing the decomposition of given matrix using current options.

Parameters

matrix the matrix to decompose

This method uses the current computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).

Definition at line 162 of file BDCSVD.h.

template<typename MatrixType >

void Eigen::BDCSVD< MatrixType >::computeSingVals	(	const ArrayRef &	col0,
		const ArrayRef &	diag,
		const IndicesRef &	perm,
		VectorType &	singVals,
		ArrayRef	shifts,
		ArrayRef	mus
	)

private

Definition at line 708 of file BDCSVD.h.

template<typename MatrixType >

void Eigen::BDCSVD< MatrixType >::computeSingVecs	(	const ArrayRef &	zhat,
		const ArrayRef &	diag,
		const IndicesRef &	perm,
		const VectorType &	singVals,
		const ArrayRef &	shifts,
		const ArrayRef &	mus,
		MatrixXr &	U,
		MatrixXr &	V
	)

private

Definition at line 945 of file BDCSVD.h.

template<typename MatrixType >

void Eigen::BDCSVD< MatrixType >::computeSVDofM	(	Index	firstCol,
		Index	n,
		MatrixXr &	U,
		VectorType &	singVals,
		MatrixXr &	V
	)

private

Definition at line 571 of file BDCSVD.h.

template<typename MatrixType >

template<typename HouseholderU , typename HouseholderV , typename NaiveU , typename NaiveV >

void Eigen::BDCSVD< MatrixType >::copyUV	(	const HouseholderU &	householderU,
		const HouseholderV &	householderV,
		const NaiveU &	naiveU,
		const NaiveV &	naivev
	)

private

Definition at line 312 of file BDCSVD.h.

template<typename MatrixType >

void Eigen::BDCSVD< MatrixType >::deflation	(	Index	firstCol,
		Index	lastCol,
		Index	k,
		Index	firstRowW,
		Index	firstColW,
		Index	shift
	)

private

Definition at line 1059 of file BDCSVD.h.

template<typename MatrixType >

void Eigen::BDCSVD< MatrixType >::deflation43	(	Index	firstCol,
		Index	shift,
		Index	i,
		Index	size
	)

private

Definition at line 990 of file BDCSVD.h.

template<typename MatrixType >

void Eigen::BDCSVD< MatrixType >::deflation44	(	Index	firstColu,
		Index	firstColm,
		Index	firstRowW,
		Index	firstColW,
		Index	i,
		Index	j,
		Index	size
	)

private

Definition at line 1019 of file BDCSVD.h.

template<typename MatrixType >

void Eigen::BDCSVD< MatrixType >::divide	(	Index	firstCol,
		Index	lastCol,
		Index	firstRowW,
		Index	firstColW,
		Index	shift
	)

private

Definition at line 391 of file BDCSVD.h.

template<typename MatrixType >

void Eigen::BDCSVD< MatrixType >::perturbCol0	(	const ArrayRef &	col0,
		const ArrayRef &	diag,
		const IndicesRef &	perm,
		const VectorType &	singVals,
		const ArrayRef &	shifts,
		const ArrayRef &	mus,
		ArrayRef	zhat
	)

private

Definition at line 896 of file BDCSVD.h.

template<typename MatrixType >

BDCSVD< MatrixType >::RealScalar Eigen::BDCSVD< MatrixType >::secularEq	(	RealScalar	x,
		const ArrayRef &	col0,
		const ArrayRef &	diag,
		const IndicesRef &	perm,
		const ArrayRef &	diagShifted,
		RealScalar	shift
	)

staticprivate

Definition at line 692 of file BDCSVD.h.

template<typename _MatrixType>

void Eigen::BDCSVD< _MatrixType >::setSwitchSize ( int s )

inline

Definition at line 167 of file BDCSVD.h.

template<typename MatrixType >

void Eigen::BDCSVD< MatrixType >::structured_update	(	Block< MatrixXr, Dynamic, Dynamic >	A,
		const MatrixXr &	B,
		Index	n1
	)

private

Definition at line 340 of file BDCSVD.h.

Member Data Documentation

template<typename _MatrixType>

int Eigen::BDCSVD< _MatrixType >::m_algoswap

protected

Definition at line 194 of file BDCSVD.h.

template<typename _MatrixType>

bool Eigen::BDCSVD< _MatrixType >::m_compU

protected

Definition at line 195 of file BDCSVD.h.

template<typename _MatrixType>

MatrixXr Eigen::BDCSVD< _MatrixType >::m_computed

protected

Definition at line 190 of file BDCSVD.h.

template<typename _MatrixType>

bool Eigen::BDCSVD< _MatrixType >::m_compV

protected

Definition at line 195 of file BDCSVD.h.

template<typename _MatrixType>

bool Eigen::BDCSVD< _MatrixType >::m_isTranspose

protected

Definition at line 195 of file BDCSVD.h.

template<typename _MatrixType>

MatrixXr Eigen::BDCSVD< _MatrixType >::m_naiveU

protected

Definition at line 189 of file BDCSVD.h.

template<typename _MatrixType>

MatrixXr Eigen::BDCSVD< _MatrixType >::m_naiveV

protected

Definition at line 189 of file BDCSVD.h.

template<typename _MatrixType>

Index Eigen::BDCSVD< _MatrixType >::m_nRec

protected

Definition at line 191 of file BDCSVD.h.

template<typename _MatrixType>

int Eigen::BDCSVD< _MatrixType >::m_numIters

Definition at line 209 of file BDCSVD.h.

template<typename _MatrixType>

ArrayXr Eigen::BDCSVD< _MatrixType >::m_workspace

protected

Definition at line 192 of file BDCSVD.h.

template<typename _MatrixType>

ArrayXi Eigen::BDCSVD< _MatrixType >::m_workspaceI

protected

Definition at line 193 of file BDCSVD.h.

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

Public Types

Public Member Functions

Public Attributes

Protected Attributes

Private Types

Private Member Functions

Static Private Member Functions

Additional Inherited Members

Detailed Description

template<typename _MatrixType> class Eigen::BDCSVD< _MatrixType >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename _MatrixType>
class Eigen::BDCSVD< _MatrixType >