Eigen::BDCSVD< _MatrixType > Class Template Reference

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

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 perfroms 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 >:

Public Member Functions
	BDCSVD ()
	Default Constructor.
	BDCSVD (const MatrixType &matrix, unsigned int computationOptions=0)
	Constructor performing the decomposition of given matrix.
	BDCSVD (Index rows, Index cols, unsigned int computationOptions=0)
	Default Constructor with memory preallocation.
BDCSVD &	compute (const MatrixType &matrix)
	Method performing the decomposition of given matrix using current options.
BDCSVD &	compute (const MatrixType &matrix, unsigned int computationOptions)
	Method performing the decomposition of given matrix using custom options.
bool	computeU () const
bool	computeV () const
Public Member Functions inherited from Eigen::SVDBase< BDCSVD< _MatrixType > >
bool	computeU () const
bool	computeV () const
const MatrixUType &	matrixU () const
const MatrixVType &	matrixV () const
Index	nonzeroSingularValues () const
Index	rank () const
BDCSVD< _MatrixType > &	setThreshold (const RealScalar &threshold)
BDCSVD< _MatrixType > &	setThreshold (Default_t)
const SingularValuesType &	singularValues () const
const Solve< BDCSVD< _MatrixType >, Rhs >	solve (const MatrixBase< Rhs > &b) const
RealScalar	threshold () const

Additional Inherited Members
Public Types inherited from Eigen::SVDBase< BDCSVD< _MatrixType > >
typedef Eigen::Index	Index
Protected Member Functions inherited from Eigen::SVDBase< BDCSVD< _MatrixType > >
	SVDBase ()
	Default Constructor.

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< BDCSVD >::computeU ( ) const

inline

Returns

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

computeV()

template<typename _MatrixType>

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