Eigen: Eigen::BDCSVD< MatrixType_, Options

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#include <Eigen/src/SVD/BDCSVD.h>

Detailed Description

template<typename MatrixType_, int Options_>
class Eigen::BDCSVD< MatrixType_, Options_ >

class Bidiagonal Divide and Conquer SVD

Template Parameters

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

Options_ this optional parameter allows one to specify options for computing unitaries U and V. Possible values are ComputeThinU, ComputeThinV, ComputeFullU, ComputeFullV, and DisableQRDecomposition. It is not possible to request both the thin and full version of U or V. By default, unitaries are not computed. BDCSVD uses R-Bidiagonalization to improve performance on tall and wide matrices. For backwards compatility, the option DisableQRDecomposition can be used to disable this optimization.

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

Inheritance diagram for Eigen::BDCSVD< MatrixType_, Options_ >:

Public Member Functions
	BDCSVD ()
	Default Constructor.

template<typename Derived>
	BDCSVD (const MatrixBase< Derived > &matrix)
	Constructor performing the decomposition of given matrix, using the custom options specified with the Options template parameter.

template<typename Derived>
	BDCSVD (const MatrixBase< Derived > &matrix, unsigned int computationOptions)
	Constructor performing the decomposition of given matrix using specified options for computing unitaries.

	BDCSVD (Index rows, Index cols)
	Default Constructor with memory preallocation.

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

template<typename Derived>
BDCSVD &	compute (const MatrixBase< Derived > &matrix)
	Method performing the decomposition of given matrix. Computes Thin/Full unitaries U/V if specified using the Options template parameter or the class constructor.

template<typename Derived>
BDCSVD &	compute (const MatrixBase< Derived > &matrix, unsigned int computationOptions)
	Method performing the decomposition of given matrix, as specified by the `computationOptions` parameter.

bool	computeU () const

bool	computeV () const

Public Member Functions inherited from Eigen::SVDBase< BDCSVD< MatrixType_, Options_ > >
bool	computeU () const

bool	computeV () const

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

const MatrixUType &	matrixU () const

const MatrixVType &	matrixV () const

Index	nonzeroSingularValues () const

Index	rank () const

BDCSVD< MatrixType_, Options_ > &	setThreshold (const RealScalar &threshold)

BDCSVD< MatrixType_, Options_ > &	setThreshold (Default_t)

const SingularValuesType &	singularValues () const

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

RealScalar	threshold () const

Public Member Functions inherited from Eigen::SolverBase< SVDBase< BDCSVD< MatrixType_, Options_ > > >
const AdjointReturnType	adjoint () const

constexpr SVDBase< BDCSVD< MatrixType_, Options_ > > &	derived ()

constexpr const SVDBase< BDCSVD< MatrixType_, Options_ > > &	derived () const

const Solve< SVDBase< BDCSVD< MatrixType_, Options_ > >, Rhs >	solve (const MatrixBase< Rhs > &b) const

	SolverBase ()

const ConstTransposeReturnType	transpose () const

Public Member Functions inherited from Eigen::EigenBase< SVDBase< BDCSVD< MatrixType_, Options_ > > >
constexpr Index	cols () const noexcept

constexpr SVDBase< BDCSVD< MatrixType_, Options_ > > &	derived ()

constexpr const SVDBase< BDCSVD< MatrixType_, Options_ > > &	derived () const

constexpr Index	rows () const noexcept

constexpr Index	size () const noexcept

Additional Inherited Members
Public Types inherited from Eigen::EigenBase< SVDBase< BDCSVD< MatrixType_, Options_ > > >
typedef Eigen::Index	Index
	The interface type of indices.

Protected Member Functions inherited from Eigen::SVDBase< BDCSVD< MatrixType_, Options_ > >
	SVDBase ()
	Default Constructor.

Constructor & Destructor Documentation

◆ BDCSVD() [1/5]

template<typename MatrixType_, int Options_>

Eigen::BDCSVD< MatrixType_, Options_ >::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() [2/5]

template<typename MatrixType_, int Options_>

Eigen::BDCSVD< MatrixType_, Options_ >::BDCSVD	(	Index	rows,
		Index	cols )

inline

Default Constructor with memory preallocation.

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

See also: BDCSVD()

◆ BDCSVD() [3/5]

template<typename MatrixType_, int Options_>

Eigen::BDCSVD< MatrixType_, Options_ >::BDCSVD	(	Index	rows,
		Index	cols,
		unsigned int	computationOptions )

inline

Default Constructor with memory preallocation.

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

One cannot request unitaries using both the Options template parameter and the constructor. If possible, prefer using the Options template parameter.

Parameters

rows	number of rows for the input matrix
cols	number of columns for the input matrix
computationOptions	specification for computing Thin/Full unitaries U/V

See also: BDCSVD()

◆ BDCSVD() [4/5]

template<typename MatrixType_, int Options_>

template<typename Derived>

Eigen::BDCSVD< MatrixType_, Options_ >::BDCSVD ( const MatrixBase< Derived > & matrix )

inline

Constructor performing the decomposition of given matrix, using the custom options specified with the Options template parameter.

Parameters

matrix the matrix to decompose

◆ BDCSVD() [5/5]

template<typename MatrixType_, int Options_>

template<typename Derived>

Eigen::BDCSVD< MatrixType_, Options_ >::BDCSVD	(	const MatrixBase< Derived > &	matrix,
		unsigned int	computationOptions )

inline

Constructor performing the decomposition of given matrix using specified options for computing unitaries.

One cannot request unitaries using both the Options template parameter and the constructor. If possible, prefer using the Options template parameter.

Parameters

matrix	the matrix to decompose
computationOptions	specification for computing Thin/Full unitaries U/V

Member Function Documentation

◆ compute() [1/2]

template<typename MatrixType_, int Options_>

template<typename Derived>

BDCSVD & Eigen::BDCSVD< MatrixType_, Options_ >::compute ( const MatrixBase< Derived > & matrix )

inline

Method performing the decomposition of given matrix. Computes Thin/Full unitaries U/V if specified using the Options template parameter or the class constructor.

Parameters

matrix the matrix to decompose

◆ compute() [2/2]

template<typename MatrixType_, int Options_>

template<typename Derived>

BDCSVD & Eigen::BDCSVD< MatrixType_, Options_ >::compute	(	const MatrixBase< Derived > &	matrix,
		unsigned int	computationOptions )

inline

Method performing the decomposition of given matrix, as specified by the computationOptions parameter.

Parameters

matrix	the matrix to decompose
computationOptions	specify whether to compute Thin/Full unitaries U/V

◆ computeU()

template<typename MatrixType_, int Options_>

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

inline

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

◆ computeV()

template<typename MatrixType_, int Options_>

bool Eigen::SVDBase< BDCSVD >::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:

/builds/libeigen/eigen/Eigen/src/Core/util/ForwardDeclarations.h
/builds/libeigen/eigen/Eigen/src/SVD/BDCSVD.h

Detailed Description

Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ BDCSVD() [1/5]

◆ BDCSVD() [2/5]

◆ BDCSVD() [3/5]

◆ BDCSVD() [4/5]

◆ BDCSVD() [5/5]

Member Function Documentation

◆ compute() [1/2]

◆ compute() [2/2]

◆ computeU()

◆ computeV()