Base class of SVD algorithms. More...

#include <SVDBase.h>

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 internal::traits< Derived >::MatrixType	MatrixType

typedef MatrixType::Scalar	Scalar

typedef NumTraits< typename MatrixType::Scalar >::Real	RealScalar

typedef MatrixType::StorageIndex	StorageIndex

typedef Eigen::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

Public Member Functions
Derived &	derived ()

const Derived &	derived () const

const MatrixUType &	matrixU () const

const MatrixVType &	matrixV () const

const SingularValuesType &	singularValues () const

Index	nonzeroSingularValues () const

Index	rank () const

Derived &	setThreshold (const RealScalar &threshold)
	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. More...

Derived &	setThreshold (Default_t)
	Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold. More...

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

bool	computeU () const

bool	computeV () const

Index	rows () const

Index	cols () const

template<typename Rhs >
const Solve< Derived, Rhs >	solve (const MatrixBase< Rhs > &b) const

template<typename RhsType , typename DstType >
EIGEN_DEVICE_FUNC void	_solve_impl (const RhsType &rhs, DstType &dst) const

template<typename RhsType , typename DstType >
void	_solve_impl (const RhsType &rhs, DstType &dst) const

Protected Member Functions
bool	allocate (Index rows, Index cols, unsigned int computationOptions)

	SVDBase ()
	Default Constructor. More...

Static Protected Member Functions
static void	check_template_parameters ()

Protected Attributes
MatrixUType	m_matrixU

MatrixVType	m_matrixV

SingularValuesType	m_singularValues

bool	m_isInitialized

bool	m_isAllocated

bool	m_usePrescribedThreshold

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

RealScalar	m_prescribedThreshold

Detailed Description

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

Base class of SVD algorithms.

Template Parameters

Derived the type of the actual 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: class BDCSVD, class JacobiSVD

Member Typedef Documentation

§ Index

template<typename Derived>

typedef Eigen::Index Eigen::SVDBase< Derived >::Index

Deprecated:: since Eigen 3.3

Constructor & Destructor Documentation

§ SVDBase()

template<typename Derived>

Eigen::SVDBase< Derived >::SVDBase ( )

inlineprotected

Default Constructor.

Default constructor of SVDBase

Member Function Documentation

§ computeU()

template<typename Derived>

bool Eigen::SVDBase< Derived >::computeU ( ) const

inline

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

§ computeV()

template<typename Derived>

bool Eigen::SVDBase< Derived >::computeV ( ) const

inline

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

§ matrixU()

template<typename Derived>

const MatrixUType& Eigen::SVDBase< Derived >::matrixU ( ) const

inline

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.

§ matrixV()

template<typename Derived>

const MatrixVType& Eigen::SVDBase< Derived >::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.

§ nonzeroSingularValues()

template<typename Derived>

Index Eigen::SVDBase< Derived >::nonzeroSingularValues ( ) const

inline

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

§ rank()

template<typename Derived>

Index Eigen::SVDBase< Derived >::rank ( ) const

inline

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&).

§ setThreshold() [1/2]

template<typename Derived>

Derived& Eigen::SVDBase< Derived >::setThreshold ( const RealScalar & threshold )

inline

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

threshold The 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)

§ setThreshold() [2/2]

template<typename Derived>

Derived& Eigen::SVDBase< Derived >::setThreshold ( Default_t )

inline

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&).

§ singularValues()

template<typename Derived>

const SingularValuesType& Eigen::SVDBase< Derived >::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.

§ solve()

template<typename Derived>

template<typename Rhs >

const Solve<Derived, Rhs> Eigen::SVDBase< Derived >::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 \( \Vert A x - b \Vert \).

§ threshold()

template<typename Derived>

RealScalar Eigen::SVDBase< Derived >::threshold ( ) const

inline

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 file:

third-party-libs/eigen3/Eigen/src/SVD/SVDBase.h

Public Types

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

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

Member Typedef Documentation

§ Index

Constructor & Destructor Documentation

§ SVDBase()

Member Function Documentation

§ computeU()

§ computeV()

§ matrixU()

§ matrixV()

§ nonzeroSingularValues()

§ rank()

§ setThreshold() [1/2]

§ setThreshold() [2/2]

§ singularValues()

§ solve()

§ threshold()

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