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. It is not possible to request both the thin and full version of U or V. By default, unitaries are not computed.

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. More...

	BDCSVD (const MatrixType &matrix)
	Constructor performing the decomposition of given matrix, using the custom options specified with the Options template paramter. More...

EIGEN_DEPRECATED	BDCSVD (const MatrixType &matrix, unsigned int computationOptions)
	Constructor performing the decomposition of given matrix using specified options for computing unitaries. More...

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

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

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

BDCSVD &	compute (const MatrixType &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. More...

EIGEN_DEPRECATED BDCSVD &	compute (const MatrixType &matrix, unsigned int computationOptions)
	Method performing the decomposition of given matrix, as specified by the `computationOptions` parameter. More...

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

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. More...

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< Derived >
const AdjointReturnType	adjoint () const

Derived &	derived ()

const Derived &	derived () const

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

	SolverBase ()

const ConstTransposeReturnType	transpose () const

Public Member Functions inherited from Eigen::EigenBase< Derived >
EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

Derived &	derived ()

const Derived &	derived () const

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

Additional Inherited Members
Public Types inherited from Eigen::SVDBase< BDCSVD< MatrixType_, Options_ > >
typedef Eigen::Index	Index

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

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

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_DEPRECATED 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 unitiaries using both the Options template parameter and the constructor. If possible, prefer using the Options template parameter.

Parameters

computationOptions specifification for computing Thin/Full unitaries U/V

See also: BDCSVD()

Deprecated:: Will be removed in the next major Eigen version. Options should be specified in the Options template parameter.

◆ BDCSVD() [4/5]

template<typename MatrixType_ , int Options_>

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

inline

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

Parameters

matrix the matrix to decompose

◆ BDCSVD() [5/5]

template<typename MatrixType_ , int Options_>

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

inline

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

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

Parameters

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

Deprecated:: Will be removed in the next major Eigen version. Options should be specified in the Options template parameter.

Member Function Documentation

◆ cols()

template<typename MatrixType_ , int Options_>

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

inline

Returns: the number of columns.

See also: rows(), ColsAtCompileTime

◆ compute() [1/2]

template<typename MatrixType_ , int Options_>

BDCSVD& Eigen::BDCSVD< MatrixType_, Options_ >::compute ( const MatrixType & 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_>

EIGEN_DEPRECATED BDCSVD& Eigen::BDCSVD< MatrixType_, Options_ >::compute	(	const MatrixType &	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

Deprecated:: Will be removed in the next major Eigen version. Options should be specified in the Options template parameter.

◆ rows()

template<typename MatrixType_ , int Options_>

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

inline

Returns: the number of rows.

See also: cols(), RowsAtCompileTime

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

BDCSVD.h

Detailed Description

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

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

◆ cols()

◆ compute() [1/2]

◆ compute() [2/2]

◆ rows()

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