BDCSVD< _MatrixType > Class Template Reference

---

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 >:

List of all members.

Public Member Functions
	BDCSVD ()
	Default Constructor.
	BDCSVD (Index rows, Index cols, unsigned int computationOptions=0)
	Default Constructor with memory preallocation.
	BDCSVD (const MatrixType &matrix, unsigned int computationOptions=0)
	Constructor performing the decomposition of given matrix.
SVDBase< MatrixType > &	compute (const MatrixType &matrix, unsigned int computationOptions)
	Method performing the decomposition of given matrix using custom options.
SVDBase< MatrixType > &	compute (const MatrixType &matrix)
	Method performing the decomposition of given matrix using current options.
template<>
SVDBase< Matrix< int, Dynamic, Dynamic > > &	compute (const MatrixType &matrix, unsigned int computationOptions)
	Method performing the decomposition of given matrix using custom options.
bool	computeU () const
bool	computeV () const
const MatrixUType &	matrixU () const
const MatrixVType &	matrixV () 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.

Reimplemented from SVDBase< _MatrixType >.

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

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).

Reimplemented from SVDBase< _MatrixType >.

References BDCSVD< _MatrixType >::compute().

SVDBase< Matrix< int, Dynamic, Dynamic > > & 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.

Reimplemented from SVDBase< _MatrixType >.

bool computeU

(

)

const [inline, inherited]

Returns:

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

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

bool computeV

(

)

const [inline, inherited]

Returns:

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

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

const MatrixUType& matrixU

(

)

const [inline]

Returns:

the U matrix.

For the SVDBase decomposition of a n-by-p matrix, letting m be the minimum of n and p, the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.

The m first columns of U are the left singular vectors of the matrix being decomposed.

This method asserts that you asked for U to be computed.

Reimplemented from SVDBase< _MatrixType >.

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

const MatrixVType& matrixV

(

)

const [inline]

Returns:

the V matrix.

For the SVD decomposition of a n-by-p matrix, letting m be the minimum of n and p, the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.

The m first columns of V are the right singular vectors of the matrix being decomposed.

This method asserts that you asked for V to be computed.

Reimplemented from SVDBase< _MatrixType >.

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

Index nonzeroSingularValues

(

)

const [inline, inherited]

Returns:

the number of singular values that are not exactly 0

const SingularValuesType& singularValues

(

)

const [inline, inherited]

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.

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 .

---

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

• BDCSVD.h