class Bidiagonal Divide and Conquer SVD More...

#include <ForwardDeclarations.h>

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

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

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

Index	cols () const

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

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

bool	computeU () const

bool	computeV () const

Index	rows () const

void	setSwitchSize (int s)

	~BDCSVD ()

Public Attributes
int	m_numIters

Protected Attributes
int	m_algoswap

bool	m_compU

MatrixXr	m_computed

bool	m_computeFullU

bool	m_computeFullV

bool	m_computeThinU

bool	m_computeThinV

bool	m_compV

Index	m_diagSize

ComputationInfo	m_info

bool	m_isInitialized

bool	m_isTranspose

MatrixUType	m_matrixU

MatrixVType	m_matrixV

MatrixXr	m_naiveU

MatrixXr	m_naiveV

Index	m_nonzeroSingularValues

Index	m_nRec

SingularValuesType	m_singularValues

ArrayXr	m_workspace

ArrayXi	m_workspaceI

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)

Detailed Description

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 performs 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 279 of file ForwardDeclarations.h.

Member Typedef Documentation

◆ ArrayRef

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

Definition at line 106 of file BDCSVD.h.

◆ ArrayXi

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

Definition at line 105 of file BDCSVD.h.

◆ ArrayXr

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

Definition at line 104 of file BDCSVD.h.

◆ Base

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

private

Definition at line 75 of file BDCSVD.h.

◆ IndicesRef

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

Definition at line 107 of file BDCSVD.h.

◆ Literal

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

Definition at line 86 of file BDCSVD.h.

◆ MatrixType

typedef _MatrixType Eigen::BDCSVD::MatrixType

Definition at line 83 of file BDCSVD.h.

◆ MatrixUType

typedef Base::MatrixUType Eigen::BDCSVD::MatrixUType

Definition at line 97 of file BDCSVD.h.

◆ MatrixVType

typedef Base::MatrixVType Eigen::BDCSVD::MatrixVType

Definition at line 98 of file BDCSVD.h.

◆ MatrixX

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

Definition at line 101 of file BDCSVD.h.

◆ MatrixXr

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

Definition at line 102 of file BDCSVD.h.

◆ RealScalar

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

Definition at line 85 of file BDCSVD.h.

◆ Scalar

typedef MatrixType::Scalar Eigen::BDCSVD::Scalar

Definition at line 84 of file BDCSVD.h.

◆ SingularValuesType

typedef Base::SingularValuesType Eigen::BDCSVD::SingularValuesType

Definition at line 99 of file BDCSVD.h.

◆ VectorType

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

Definition at line 103 of file BDCSVD.h.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Enumerator
RowsAtCompileTime
ColsAtCompileTime
DiagSizeAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime
MaxDiagSizeAtCompileTime
MatrixOptions

Definition at line 87 of file BDCSVD.h.

Constructor & Destructor Documentation

◆ BDCSVD() [1/3]

Eigen::BDCSVD::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 114 of file BDCSVD.h.

◆ BDCSVD() [2/3]

Eigen::BDCSVD::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 124 of file BDCSVD.h.

◆ BDCSVD() [3/3]

Eigen::BDCSVD::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 140 of file BDCSVD.h.

◆ ~BDCSVD()

Eigen::BDCSVD::~BDCSVD ( )

inline

Definition at line 146 of file BDCSVD.h.

Member Function Documentation

◆ allocate()

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

private

Definition at line 222 of file BDCSVD.h.

◆ cols()

Index Eigen::SVDBase::cols

inline

Definition at line 213 of file SVDBase.h.

◆ compute() [1/2]

BDCSVD& Eigen::BDCSVD::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 168 of file BDCSVD.h.

◆ compute() [2/2]

BDCSVD< MatrixType > & Eigen::BDCSVD::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 245 of file BDCSVD.h.

◆ computeSingVals()

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

private

Definition at line 739 of file BDCSVD.h.

◆ computeSingVecs()

void Eigen::BDCSVD::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 1066 of file BDCSVD.h.

◆ computeSVDofM()

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

private

Definition at line 595 of file BDCSVD.h.

◆ computeU()

bool Eigen::SVDBase::computeU

inline

Returns: true if U (full or thin) is asked for in this SVD decomposition

Definition at line 208 of file SVDBase.h.

◆ computeV()

bool Eigen::SVDBase::computeV

inline

Returns: true if V (full or thin) is asked for in this SVD decomposition

Definition at line 210 of file SVDBase.h.

◆ copyUV()

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

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

private

Definition at line 332 of file BDCSVD.h.

◆ deflation()

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

private

Definition at line 1180 of file BDCSVD.h.

◆ deflation43()

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

private

Definition at line 1111 of file BDCSVD.h.

◆ deflation44()

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

private

Definition at line 1140 of file BDCSVD.h.

◆ divide()

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

private

Definition at line 411 of file BDCSVD.h.

◆ perturbCol0()

void Eigen::BDCSVD::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 986 of file BDCSVD.h.

◆ rows()

Index Eigen::SVDBase::rows

inline

Definition at line 212 of file SVDBase.h.

◆ secularEq()

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

staticprivate

Definition at line 723 of file BDCSVD.h.

◆ setSwitchSize()

void Eigen::BDCSVD::setSwitchSize ( int s )

inline

Definition at line 173 of file BDCSVD.h.

◆ structured_update()

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

private

Definition at line 360 of file BDCSVD.h.

Member Data Documentation

◆ m_algoswap

int Eigen::BDCSVD::m_algoswap

protected

Definition at line 200 of file BDCSVD.h.

◆ m_compU

bool Eigen::BDCSVD::m_compU

protected

Definition at line 201 of file BDCSVD.h.

◆ m_computed

MatrixXr Eigen::BDCSVD::m_computed

protected

Definition at line 196 of file BDCSVD.h.

◆ m_computeFullU

bool Eigen::SVDBase::m_computeFullU

protected

Definition at line 277 of file SVDBase.h.

◆ m_computeFullV

bool Eigen::SVDBase::m_computeFullV

protected

Definition at line 278 of file SVDBase.h.

◆ m_computeThinU

bool Eigen::SVDBase::m_computeThinU

protected

Definition at line 277 of file SVDBase.h.

◆ m_computeThinV

bool Eigen::SVDBase::m_computeThinV

protected

Definition at line 278 of file SVDBase.h.

◆ m_compV

bool Eigen::BDCSVD::m_compV

protected

Definition at line 201 of file BDCSVD.h.

◆ m_diagSize

Index Eigen::SVDBase::m_diagSize

protected

Definition at line 280 of file SVDBase.h.

◆ m_info

ComputationInfo Eigen::SVDBase::m_info

protected

Definition at line 275 of file SVDBase.h.

◆ m_isInitialized

bool Eigen::SVDBase::m_isInitialized

protected

Definition at line 276 of file SVDBase.h.

◆ m_isTranspose

bool Eigen::BDCSVD::m_isTranspose

protected

Definition at line 201 of file BDCSVD.h.

◆ m_matrixU

MatrixUType Eigen::SVDBase::m_matrixU

protected

Definition at line 272 of file SVDBase.h.

◆ m_matrixV

MatrixVType Eigen::SVDBase::m_matrixV

protected

Definition at line 273 of file SVDBase.h.

◆ m_naiveU

MatrixXr Eigen::BDCSVD::m_naiveU

protected

Definition at line 195 of file BDCSVD.h.

◆ m_naiveV

MatrixXr Eigen::BDCSVD::m_naiveV

protected

Definition at line 195 of file BDCSVD.h.

◆ m_nonzeroSingularValues

Index Eigen::SVDBase::m_nonzeroSingularValues

protected

Definition at line 280 of file SVDBase.h.

◆ m_nRec

Index Eigen::BDCSVD::m_nRec

protected

Definition at line 197 of file BDCSVD.h.

◆ m_numIters

int Eigen::BDCSVD::m_numIters

Definition at line 216 of file BDCSVD.h.

◆ m_singularValues

SingularValuesType Eigen::SVDBase::m_singularValues

protected

Definition at line 274 of file SVDBase.h.

◆ m_workspace

ArrayXr Eigen::BDCSVD::m_workspace

protected

Definition at line 198 of file BDCSVD.h.

◆ m_workspaceI

ArrayXi Eigen::BDCSVD::m_workspaceI

protected

Definition at line 199 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

Detailed Description

Member Typedef Documentation

◆ ArrayRef

◆ ArrayXi

◆ ArrayXr

◆ Base

◆ IndicesRef

◆ Literal

◆ MatrixType

◆ MatrixUType

◆ MatrixVType

◆ MatrixX

◆ MatrixXr

◆ RealScalar

◆ Scalar

◆ SingularValuesType

◆ VectorType

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ BDCSVD() [1/3]

◆ BDCSVD() [2/3]

◆ BDCSVD() [3/3]

◆ ~BDCSVD()

Member Function Documentation

◆ allocate()

◆ cols()

◆ compute() [1/2]

◆ compute() [2/2]

◆ computeSingVals()

◆ computeSingVecs()

◆ computeSVDofM()

◆ computeU()

◆ computeV()

◆ copyUV()

◆ deflation()

◆ deflation43()

◆ deflation44()

◆ divide()

◆ perturbCol0()

◆ rows()

◆ secularEq()

◆ setSwitchSize()

◆ structured_update()

Member Data Documentation

◆ m_algoswap

◆ m_compU

◆ m_computed

◆ m_computeFullU

◆ m_computeFullV

◆ m_computeThinU

◆ m_computeThinV

◆ m_compV

◆ m_diagSize

◆ m_info

◆ m_isInitialized

◆ m_isTranspose

◆ m_matrixU

◆ m_matrixV

◆ m_naiveU

◆ m_naiveV

◆ m_nonzeroSingularValues

◆ m_nRec

◆ m_numIters

◆ m_singularValues

◆ m_workspace

◆ m_workspaceI