class Bidiagonal Divide and Conquer SVD More...

#include <BDCSVD.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 _MatrixType	MatrixType

typedef MatrixType::Scalar	Scalar

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

typedef NumTraits< RealScalar >::Literal	Literal

typedef Base::MatrixUType	MatrixUType

typedef Base::MatrixVType	MatrixVType

typedef Base::SingularValuesType	SingularValuesType

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

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

typedef Matrix< RealScalar, Dynamic, 1 >	VectorType

typedef Array< RealScalar, Dynamic, 1 >	ArrayXr

typedef Array< Index, 1, Dynamic >	ArrayXi

typedef Ref< ArrayXr >	ArrayRef

typedef Ref< ArrayXi >	IndicesRef

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

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

typedef MatrixType::Scalar	Scalar

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

typedef Eigen::internal::traits< SVDBase >::StorageIndex	StorageIndex

typedef Eigen::Index	Index

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

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

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

Public Types inherited from Eigen::SolverBase< Derived >
enum	{ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime , ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime , SizeAtCompileTime , MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime , MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime , MaxSizeAtCompileTime , IsVectorAtCompileTime , NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 : bool(IsVectorAtCompileTime) ? 1 : 2 }

typedef EigenBase< Derived >	Base

typedef internal::traits< Derived >::Scalar	Scalar

typedef Scalar	CoeffReturnType

typedef internal::add_const< Transpose< const Derived > >::type	ConstTransposeReturnType

typedef internal::conditional< NumTraits< Scalar >::IsComplex, CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, ConstTransposeReturnType >, ConstTransposeReturnType >::type	AdjointReturnType

Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index	Index
	The interface type of indices. More...

typedef internal::traits< Derived >::StorageKind	StorageKind

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 ()

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)

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

Public Member Functions inherited from Eigen::SVDBase< BDCSVD< _MatrixType > >
BDCSVD< _MatrixType > &	derived ()

const BDCSVD< _MatrixType > &	derived () const

const MatrixUType &	matrixU () const

const MatrixVType &	matrixV () const

const SingularValuesType &	singularValues () const

Index	nonzeroSingularValues () const

Index	rank () const

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

BDCSVD< _MatrixType > &	setThreshold (Default_t)

RealScalar	threshold () const

bool	computeU () const

bool	computeV () const

Index	rows () const

Index	cols () const

EIGEN_DEVICE_FUNC ComputationInfo	info () const
	Reports whether previous computation was successful. More...

void	_solve_impl (const RhsType &rhs, DstType &dst) const

void	_solve_impl_transposed (const RhsType &rhs, DstType &dst) const

Public Member Functions inherited from Eigen::SolverBase< Derived >
	SolverBase ()

	~SolverBase ()

template<typename Rhs >
const Solve< Derived, Rhs >	solve (const MatrixBase< Rhs > &b) const

ConstTransposeReturnType	transpose () const

AdjointReturnType	adjoint () const

EIGEN_DEVICE_FUNC Derived &	derived ()

EIGEN_DEVICE_FUNC const Derived &	derived () const

Public Member Functions inherited from Eigen::EigenBase< Derived >
EIGEN_DEVICE_FUNC Derived &	derived ()

EIGEN_DEVICE_FUNC const Derived &	derived () const

EIGEN_DEVICE_FUNC Derived &	const_cast_derived () const

EIGEN_DEVICE_FUNC const Derived &	const_derived () const

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

template<typename Dest >
EIGEN_DEVICE_FUNC void	evalTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	addTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	subTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheRight (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheLeft (Dest &dst) const

Public Attributes
int	m_numIters

Protected Attributes
MatrixXr	m_naiveU

MatrixXr	m_naiveV

MatrixXr	m_computed

Index	m_nRec

ArrayXr	m_workspace

ArrayXi	m_workspaceI

int	m_algoswap

bool	m_isTranspose

bool	m_compU

bool	m_compV

Protected Attributes inherited from Eigen::SVDBase< BDCSVD< _MatrixType > >
MatrixUType	m_matrixU

MatrixVType	m_matrixV

SingularValuesType	m_singularValues

ComputationInfo	m_info

bool	m_isInitialized

bool	m_isAllocated

bool	m_usePrescribedThreshold

bool	m_computeFullU

bool	m_computeThinU

bool	m_computeFullV

bool	m_computeThinV

unsigned int	m_computationOptions

Index	m_nonzeroSingularValues

Index	m_rows

Index	m_cols

Index	m_diagSize

RealScalar	m_prescribedThreshold

Private Types
typedef SVDBase< BDCSVD >	Base

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

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

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

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

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

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

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

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 > >
void	_check_compute_assertions () const

void	_check_solve_assertion (const Rhs &b) const

bool	allocate (Index rows, Index cols, unsigned int computationOptions)

	SVDBase ()
	Default Constructor. More...

Protected Member Functions inherited from Eigen::SolverBase< Derived >
template<bool Transpose_, typename Rhs >
void	_check_solve_assertion (const Rhs &b) const

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 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

Member Typedef Documentation

◆ ArrayRef

template<typename _MatrixType >

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

◆ ArrayXi

template<typename _MatrixType >

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

◆ ArrayXr

template<typename _MatrixType >

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

◆ Base

template<typename _MatrixType >

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

private

◆ IndicesRef

template<typename _MatrixType >

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

◆ Literal

template<typename _MatrixType >

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

◆ MatrixType

template<typename _MatrixType >

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

◆ MatrixUType

template<typename _MatrixType >

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

◆ MatrixVType

template<typename _MatrixType >

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

◆ MatrixX

template<typename _MatrixType >

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

◆ MatrixXr

template<typename _MatrixType >

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

◆ RealScalar

template<typename _MatrixType >

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

◆ Scalar

template<typename _MatrixType >

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

◆ SingularValuesType

template<typename _MatrixType >

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

◆ VectorType

template<typename _MatrixType >

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

Member Enumeration Documentation

◆ anonymous enum

template<typename _MatrixType >

anonymous enum

Enumerator
RowsAtCompileTime
ColsAtCompileTime
DiagSizeAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime
MaxDiagSizeAtCompileTime
MatrixOptions

Constructor & Destructor Documentation

◆ BDCSVD() [1/3]

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&).

◆ BDCSVD() [2/3]

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()

◆ BDCSVD() [3/3]

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.

◆ ~BDCSVD()

template<typename _MatrixType >

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

inline

Member Function Documentation

◆ allocate()

template<typename MatrixType >

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

private

◆ cols()

template<typename _MatrixType >

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index Eigen::EigenBase< Derived >::cols ( void )

inline

Returns: the number of columns.

See also: rows(), ColsAtCompileTime

◆ compute() [1/2]

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).

◆ compute() [2/2]

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.

◆ computeSingVals()

template<typename MatrixType >

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

private

◆ computeSingVecs()

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

◆ computeSVDofM()

template<typename MatrixType >

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

private

◆ copyUV()

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

◆ deflation()

template<typename MatrixType >

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

private

◆ deflation43()

template<typename MatrixType >

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

private

◆ deflation44()

template<typename MatrixType >

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

private

◆ divide()

template<typename MatrixType >

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

private

◆ perturbCol0()

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

◆ rows()

template<typename _MatrixType >

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index Eigen::EigenBase< Derived >::rows ( void )

inline

Returns: the number of rows.

See also: cols(), RowsAtCompileTime

◆ secularEq()

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

◆ setSwitchSize()

template<typename _MatrixType >

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

inline

◆ structured_update()

template<typename MatrixType >

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

private

Member Data Documentation

◆ m_algoswap

template<typename _MatrixType >

int Eigen::BDCSVD< _MatrixType >::m_algoswap

protected

◆ m_compU

template<typename _MatrixType >

bool Eigen::BDCSVD< _MatrixType >::m_compU

protected

◆ m_computed

template<typename _MatrixType >

MatrixXr Eigen::BDCSVD< _MatrixType >::m_computed

protected

◆ m_compV

template<typename _MatrixType >

bool Eigen::BDCSVD< _MatrixType >::m_compV

protected

◆ m_isTranspose

template<typename _MatrixType >

bool Eigen::BDCSVD< _MatrixType >::m_isTranspose

protected

◆ m_naiveU

template<typename _MatrixType >

MatrixXr Eigen::BDCSVD< _MatrixType >::m_naiveU

protected

◆ m_naiveV

template<typename _MatrixType >

MatrixXr Eigen::BDCSVD< _MatrixType >::m_naiveV

protected

◆ m_nRec

template<typename _MatrixType >

Index Eigen::BDCSVD< _MatrixType >::m_nRec

protected

◆ m_numIters

template<typename _MatrixType >

int Eigen::BDCSVD< _MatrixType >::m_numIters

◆ m_workspace

template<typename _MatrixType >

ArrayXr Eigen::BDCSVD< _MatrixType >::m_workspace

protected

◆ m_workspaceI

template<typename _MatrixType >

ArrayXi Eigen::BDCSVD< _MatrixType >::m_workspaceI

protected

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

/home/runner/work/NDDEM/NDDEM/src/CoarseGraining/Eigen/src/Core/util/ForwardDeclarations.h
/home/runner/work/NDDEM/NDDEM/src/CoarseGraining/Eigen/src/SVD/BDCSVD.h

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

◆ 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()

◆ copyUV()

◆ deflation()

◆ deflation43()

◆ deflation44()

◆ divide()

◆ perturbCol0()

◆ rows()

◆ secularEq()

◆ setSwitchSize()

◆ structured_update()

Member Data Documentation

◆ m_algoswap

◆ m_compU

◆ m_computed

◆ m_compV

◆ m_isTranspose

◆ m_naiveU

◆ m_naiveV

◆ m_nRec

◆ m_numIters

◆ m_workspace

◆ m_workspaceI

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