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< typenameMatrixType::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< typenameMatrixType::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 Transpose< const Derived >	ConstTransposeReturnType

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

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

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

Public Member Functions
	BDCSVD ()
	Default Constructor.

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

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

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

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

void	setSwitchSize (int s)

Index	rows () const

Index	cols () const

bool	computeU () const

bool	computeV () const

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)
	Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(), which need to determine when singular values are to be considered nonzero.

BDCSVD< _MatrixType > &	setThreshold (Default_t)
	Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold.

RealScalar	threshold () const
	Returns the threshold that will be used by certain methods such as rank().

bool	computeU () const

bool	computeV () const

Index	rows () const

Index	cols () const

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

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 ()
	Default constructor.

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

const ConstTransposeReturnType	transpose () const

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

Data Fields
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

SingularValuesType	m_singularValues

Index	m_diagSize

bool	m_computeFullU

bool	m_computeFullV

bool	m_computeThinU

bool	m_computeThinV

MatrixUType	m_matrixU

MatrixVType	m_matrixV

ComputationInfo	m_info

bool	m_isInitialized

Index	m_nonzeroSingularValues

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

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.

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

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.

Member Function Documentation

◆ 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.

◆ computeU()

template<typename _MatrixType >

bool Eigen::SVDBase< Derived >::computeU ( ) const

inline

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

◆ computeV()

template<typename _MatrixType >

bool Eigen::SVDBase< Derived >::computeV ( ) const

inline

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

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

External/Eigen/src/Core/util/ForwardDeclarations.h
External/Eigen/src/SVD/BDCSVD.h

Public Types

Public Member Functions

Data Fields

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ BDCSVD() [1/3]

◆ BDCSVD() [2/3]

◆ BDCSVD() [3/3]

Member Function Documentation

◆ compute() [1/2]

◆ compute() [2/2]

◆ computeU()

◆ computeV()