Eigen  3.2.91
Eigen::BDCSVD< _MatrixType > Class Template Reference

Detailed Description

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

class Bidiagonal Divide and Conquer SVD

Parameters
MatrixTypethe 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 Eigen::BDCSVD< _MatrixType >:

Public Types

typedef Eigen::Index Index
 

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...
 
BDCSVDcompute (const MatrixType &matrix, unsigned int computationOptions)
 Method performing the decomposition of given matrix using custom options. More...
 
BDCSVDcompute (const MatrixType &matrix)
 Method performing the decomposition of given matrix using current options. More...
 
bool computeU () const
 
bool computeV () const
 
const MatrixUTypematrixU () const
 
const MatrixVTypematrixV () 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
 

Member Typedef Documentation

typedef Eigen::Index Eigen::SVDBase< BDCSVD< _MatrixType > >::Index
inherited
Deprecated:
since Eigen 3.3

Constructor & Destructor Documentation

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&).

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()
template<typename _MatrixType>
Eigen::BDCSVD< _MatrixType >::BDCSVD ( const MatrixType &  matrix,
unsigned int  computationOptions = 0 
)
inline

Constructor performing the decomposition of given matrix.

Parameters
matrixthe matrix to decompose
computationOptionsoptional 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 Eigen::BDCSVD< _MatrixType >::compute().

Member Function Documentation

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
matrixthe matrix to decompose
computationOptionsoptional 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 Eigen::MatrixBase< Derived >::adjoint(), Eigen::SVDBase< JacobiSVD< _MatrixType, QRPreconditioner > >::matrixU(), Eigen::SVDBase< JacobiSVD< _MatrixType, QRPreconditioner > >::matrixV(), Eigen::SVDBase< JacobiSVD< _MatrixType, QRPreconditioner > >::nonzeroSingularValues(), and Eigen::SVDBase< JacobiSVD< _MatrixType, QRPreconditioner > >::singularValues().

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

template<typename _MatrixType>
BDCSVD& Eigen::BDCSVD< _MatrixType >::compute ( const MatrixType &  matrix)
inline

Method performing the decomposition of given matrix using current options.

Parameters
matrixthe matrix to decompose

This method uses the current computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).

References Eigen::BDCSVD< _MatrixType >::compute().

bool Eigen::SVDBase< BDCSVD< _MatrixType > >::computeU ( ) const
inlineinherited
Returns
true if U (full or thin) is asked for in this SVD decomposition
bool Eigen::SVDBase< BDCSVD< _MatrixType > >::computeV ( ) const
inlineinherited
Returns
true if V (full or thin) is asked for in this SVD decomposition
const MatrixUType& Eigen::SVDBase< BDCSVD< _MatrixType > >::matrixU ( ) const
inlineinherited
Returns
the U matrix.

For the SVD 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.

References Eigen::SVDBase< Derived >::computeU().

const MatrixVType& Eigen::SVDBase< BDCSVD< _MatrixType > >::matrixV ( ) const
inlineinherited
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.

References Eigen::SVDBase< Derived >::computeV().

Index Eigen::SVDBase< BDCSVD< _MatrixType > >::nonzeroSingularValues ( ) const
inlineinherited
Returns
the number of singular values that are not exactly 0
Index Eigen::SVDBase< BDCSVD< _MatrixType > >::rank ( ) const
inlineinherited
Returns
the rank of the matrix of which *this is the SVD.
Note
This method has to determine which singular values should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).

References Eigen::SVDBase< Derived >::threshold().

BDCSVD< _MatrixType > & Eigen::SVDBase< BDCSVD< _MatrixType > >::setThreshold ( const RealScalar &  threshold)
inlineinherited

Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(), which need to determine when singular values are to be considered nonzero. This is not used for the SVD decomposition itself.

When it needs to get the threshold value, Eigen calls threshold(). The default is NumTraits<Scalar>::epsilon()

Parameters
thresholdThe new value to use as the threshold.

A singular value will be considered nonzero if its value is strictly greater than $ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert $.

If you want to come back to the default behavior, call setThreshold(Default_t)

References Eigen::SVDBase< Derived >::threshold().

BDCSVD< _MatrixType > & Eigen::SVDBase< BDCSVD< _MatrixType > >::setThreshold ( Default_t  )
inlineinherited

Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold.

You should pass the special object Eigen::Default as parameter here.

svd.setThreshold(Eigen::Default);

See the documentation of setThreshold(const RealScalar&).

const SingularValuesType& Eigen::SVDBase< BDCSVD< _MatrixType > >::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.

const Solve<BDCSVD< _MatrixType > , Rhs> Eigen::SVDBase< BDCSVD< _MatrixType > >::solve ( const MatrixBase< Rhs > &  b) const
inlineinherited
Returns
a (least squares) solution of $ A x = b $ using the current SVD decomposition of A.
Parameters
bthe 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 Eigen::SVDBase< Derived >::computeU(), and Eigen::SVDBase< Derived >::computeV().

RealScalar Eigen::SVDBase< BDCSVD< _MatrixType > >::threshold ( ) const
inlineinherited

Returns the threshold that will be used by certain methods such as rank().

See the documentation of setThreshold(const RealScalar&).


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