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 MatrixType::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

typedef internal::plain_row_type< MatrixType >::type	RowType

typedef internal::plain_col_type< MatrixType >::type	ColType

typedef Matrix< Scalar, Dynamic, Dynamic >	MatrixX

typedef Matrix< RealScalar, Dynamic, Dynamic >	MatrixXr

typedef Matrix< RealScalar, Dynamic, 1 >	VectorType

Public Types inherited from Eigen::SVDBase< _MatrixType >
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 MatrixType::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

typedef internal::plain_row_type< MatrixType >::type	RowType

typedef internal::plain_col_type< MatrixType >::type	ColType

typedef Matrix< Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime >	WorkMatrixType

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...

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

SVDBase< MatrixType > &	compute (const MatrixType &matrix)
	Method performing the decomposition of given matrix using current options. More...

void	setSwitchSize (int s)

template<typename Rhs >
const internal::solve_retval< BDCSVD, Rhs >	solve (const MatrixBase< Rhs > &b) const

const MatrixUType &	matrixU () const

const MatrixVType &	matrixV () const

template<>
SVDBase< Matrix< int, Dynamic, Dynamic > > &	compute (const MatrixType &matrix, unsigned int computationOptions)

Public Member Functions inherited from Eigen::SVDBase< _MatrixType >
SVDBase &	compute (const MatrixType &matrix, unsigned int computationOptions)
	Method performing the decomposition of given matrix using custom options. More...

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

const MatrixUType &	matrixU () const

const MatrixVType &	matrixV () const

const SingularValuesType &	singularValues () const

Index	nonzeroSingularValues () const

bool	computeU () const

bool	computeV () const

Index	rows () const

Index	cols () const

Protected Attributes
MatrixXr	m_naiveU

MatrixXr	m_naiveV

MatrixXr	m_computed

Index	nRec

int	algoswap

bool	isTranspose

bool	compU

bool	compV

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

MatrixVType	m_matrixV

SingularValuesType	m_singularValues

bool	m_isInitialized

bool	m_isAllocated

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

Additional Inherited Members
Protected Member Functions inherited from Eigen::SVDBase< _MatrixType >
bool	allocate (Index rows, Index cols, unsigned int computationOptions)

	SVDBase ()
	Default Constructor. More...

Detailed Description

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

class Bidiagonal Divide and Conquer SVD

Parameters

MatrixType the type of the matrix of which we are computing the SVD decomposition We plan to have a very similar interface to JacobiSVD on this class. It should be used to speed up the calcul of SVD for big matrices.

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 >

SVDBase< 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.

§ compute() [2/2]

template<typename _MatrixType>

SVDBase<MatrixType>& 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).

§ solve()

template<typename _MatrixType>

template<typename Rhs >

const internal::solve_retval<BDCSVD, Rhs> Eigen::BDCSVD< _MatrixType >::solve ( const MatrixBase< Rhs > & b ) const

inline

Returns: a (least squares) solution of \( A x = b \) using the current SVD decomposition of A.

Parameters

b	the right - hand - side of the equation to solve.

Note: Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.; SVD solving is implicitly least - squares. Thus, this method serves both purposes of exact solving and least - squares solving. In other words, the returned solution is guaranteed to minimize the Euclidean norm \( \Vert A x - b \Vert \).

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

vendor/eigen/unsupported/Eigen/src/SVD/BDCSVD.h

Public Types

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

§ BDCSVD() [1/3]

§ BDCSVD() [2/3]

§ BDCSVD() [3/3]

Member Function Documentation

§ compute() [1/2]

§ compute() [2/2]

§ solve()

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