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SVDBase< _MatrixType > Class Template Reference
[SVD module]

Mother class of SVD classes algorithms. More...

Inheritance diagram for SVDBase< _MatrixType >:

List of all members.

Public Member Functions

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

Protected Member Functions

 SVDBase ()
 Default Constructor.

Detailed Description

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

Mother class of SVD classes algorithms.

Parameters:
MatrixType the type of the matrix of which we are computing the SVD decomposition SVD decomposition consists in decomposing any n-by-p matrix A as a product

\[ A = U S V^* \]

where U is a n-by-n unitary, V is a p-by-p unitary, and S is a n-by-p real positive matrix which is zero outside of its main diagonal; the diagonal entries of S are known as the singular values of A and the columns of U and V are known as the left and right singular vectors of A respectively.

Singular values are always sorted in decreasing order.

You can ask for only thin U or V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting m be the smaller value among n and p, there are only m singular vectors; the remaining columns of U and V do not correspond to actual singular vectors. Asking for thin U or V means asking for only their m first columns to be formed. So U is then a n-by-m matrix, and V is then a p-by-m matrix. Notice that thin U and V are all you need for (least squares) solving.

If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to terminate in finite (and reasonable) time.

See also:
MatrixBase::genericSvd()

Constructor & Destructor Documentation

SVDBase (  )  [inline, protected]

Default Constructor.

Default constructor of SVDBase


Member Function Documentation

SVDBase& compute ( const MatrixType &  matrix  ) 

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 in BDCSVD< _MatrixType >, and JacobiSVD< _MatrixType, QRPreconditioner >.

SVDBase& 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 in BDCSVD< _MatrixType >, JacobiSVD< _MatrixType, QRPreconditioner >, and BDCSVD< _MatrixType >.

bool computeU (  )  const [inline]
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]
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 in BDCSVD< _MatrixType >.

References SVDBase< _MatrixType >::computeU().

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 in BDCSVD< _MatrixType >.

References SVDBase< _MatrixType >::computeV().

Index nonzeroSingularValues (  )  const [inline]
Returns:
the number of singular values that are not exactly 0
const SingularValuesType& singularValues (  )  const [inline]
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.


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