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.

Inheritance diagram for BDCSVD< _MatrixType >:

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...

bool	computeU () const

bool	computeV () const

Index	nonzeroSingularValues () const

const SingularValuesType &	singularValues () const

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

Constructor & Destructor Documentation

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	(	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	(	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.

References BDCSVD< _MatrixType >::compute().

Member Function Documentation

SVDBase< 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.

References SVDBase< _MatrixType >::computeU(), SVDBase< _MatrixType >::computeV(), SVDBase< _MatrixType >::matrixU(), SVDBase< _MatrixType >::matrixV(), and SVDBase< _MatrixType >::singularValues().

Referenced by BDCSVD< _MatrixType >::BDCSVD(), BDCSVD< _MatrixType >::compute(), and BDCSVD< _MatrixType >::solve().

SVDBase<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).

References BDCSVD< _MatrixType >::compute().

bool computeU ( ) const

inlineinherited

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

Referenced by BDCSVD< _MatrixType >::compute(), SVDBase< _MatrixType >::matrixU(), and BDCSVD< _MatrixType >::solve().

bool computeV ( ) const

inlineinherited

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

Referenced by BDCSVD< _MatrixType >::compute(), SVDBase< _MatrixType >::matrixV(), and BDCSVD< _MatrixType >::solve().

Index nonzeroSingularValues ( ) const

inlineinherited

Returns: the number of singular values that are not exactly 0

const SingularValuesType& singularValues ( ) const

inlineinherited

Returns: the vector of singular values.

For the SVD decomposition of a n-by-p matrix, letting m be the minimum of n and p, the returned vector has size m. Singular values are always sorted in decreasing order.

Referenced by BDCSVD< _MatrixType >::compute().

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

inline

Returns: a (least squares) solution of 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 $\Vert A x - b \Vert$ .

References BDCSVD< _MatrixType >::compute(), SVDBase< _MatrixType >::computeU(), and SVDBase< _MatrixType >::computeV().

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

BDCSVD.h

Detailed Description

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

Public Member Functions

Constructor & Destructor Documentation

Member Function Documentation

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