Base class of SVD algorithms. More...

#include <SVDBase.h>

Inheritance diagram for Eigen::SVDBase< Derived >:

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 Eigen::internal::traits< SVDBase >::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 Types inherited from Eigen::SolverBase< SVDBase< Derived > >
enum

typedef EigenBase< SVDBase< Derived > >	Base

typedef internal::traits< SVDBase< Derived > >::Scalar	Scalar

typedef Scalar	CoeffReturnType

typedef internal::add_const< Transpose< const SVDBase< Derived > > >::type	ConstTransposeReturnType

typedef internal::conditional< NumTraits< Scalar >::IsComplex, CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, ConstTransposeReturnType >, ConstTransposeReturnType >::type	AdjointReturnType

Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index	Index
	The interface type of indices. More...

typedef internal::traits< Derived >::StorageKind	StorageKind

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)

Derived &	setThreshold (Default_t)

RealScalar	threshold () const

bool	computeU () const

bool	computeV () const

Index	rows () const

Index	cols () const

EIGEN_DEVICE_FUNC ComputationInfo	info () const
	Reports whether previous computation was successful. More...

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

template<bool Conjugate, typename RhsType , typename DstType >
void	_solve_impl_transposed (const RhsType &rhs, DstType &dst) const

Public Member Functions inherited from Eigen::SolverBase< SVDBase< Derived > >
	SolverBase ()

	~SolverBase ()

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

ConstTransposeReturnType	transpose () const

AdjointReturnType	adjoint () const

EIGEN_DEVICE_FUNC SVDBase< Derived > &	derived ()

EIGEN_DEVICE_FUNC const SVDBase< Derived > &	derived () const

Public Member Functions inherited from Eigen::EigenBase< Derived >
EIGEN_DEVICE_FUNC Derived &	derived ()

EIGEN_DEVICE_FUNC const Derived &	derived () const

EIGEN_DEVICE_FUNC Derived &	const_cast_derived () const

EIGEN_DEVICE_FUNC const Derived &	const_derived () const

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

template<typename Dest >
EIGEN_DEVICE_FUNC void	evalTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	addTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	subTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheRight (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheLeft (Dest &dst) const

Protected Member Functions
void	_check_compute_assertions () const

template<bool Transpose_, typename Rhs >
void	_check_solve_assertion (const Rhs &b) const

bool	allocate (Index rows, Index cols, unsigned int computationOptions)

	SVDBase ()
	Default Constructor. More...

Protected Member Functions inherited from Eigen::SolverBase< SVDBase< Derived > >
void	_check_solve_assertion (const Rhs &b) const

Static Protected Member Functions
static void	check_template_parameters ()

Protected Attributes
MatrixUType	m_matrixU

MatrixVType	m_matrixV

SingularValuesType	m_singularValues

ComputationInfo	m_info

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

Friends
template<typename Derived_ >
struct	internal::solve_assertion

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.

The status of the computation can be retrived using the info() method. Unless info() returns Success, the results should be not considered well defined.

If the input matrix has inf or nan coefficients, the result of the computation is undefined, and info() will return InvalidInput, 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

◆ MatrixType

template<typename Derived >

typedef internal::traits<Derived>::MatrixType Eigen::SVDBase< Derived >::MatrixType

◆ MatrixUType

template<typename Derived >

typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> Eigen::SVDBase< Derived >::MatrixUType

◆ MatrixVType

template<typename Derived >

typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> Eigen::SVDBase< Derived >::MatrixVType

◆ RealScalar

template<typename Derived >

typedef NumTraits<typename MatrixType::Scalar>::Real Eigen::SVDBase< Derived >::RealScalar

◆ Scalar

template<typename Derived >

typedef MatrixType::Scalar Eigen::SVDBase< Derived >::Scalar

◆ SingularValuesType

template<typename Derived >

typedef internal::plain_diag_type<MatrixType, RealScalar>::type Eigen::SVDBase< Derived >::SingularValuesType

◆ StorageIndex

template<typename Derived >

typedef Eigen::internal::traits<SVDBase>::StorageIndex Eigen::SVDBase< Derived >::StorageIndex

Member Enumeration Documentation

◆ anonymous enum

template<typename Derived >

anonymous enum

Enumerator
RowsAtCompileTime
ColsAtCompileTime
DiagSizeAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime
MaxDiagSizeAtCompileTime
MatrixOptions

Constructor & Destructor Documentation

◆ SVDBase()

template<typename Derived >

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

inlineprotected

Default Constructor.

Default constructor of SVDBase

Member Function Documentation

◆ _check_compute_assertions()

template<typename Derived >

void Eigen::SVDBase< Derived >::_check_compute_assertions ( ) const

inlineprotected

◆ _check_solve_assertion()

template<typename Derived >

template<bool Transpose_, typename Rhs >

void Eigen::SVDBase< Derived >::_check_solve_assertion ( const Rhs & b ) const

inlineprotected

◆ _solve_impl()

template<typename Derived >

template<typename RhsType , typename DstType >

void Eigen::SVDBase< Derived >::_solve_impl	(	const RhsType &	rhs,
		DstType &	dst
	)		const

◆ _solve_impl_transposed()

template<typename Derived >

template<bool Conjugate, typename RhsType , typename DstType >

void Eigen::SVDBase< Derived >::_solve_impl_transposed	(	const RhsType &	rhs,
		DstType &	dst
	)		const

◆ allocate()

template<typename MatrixType >

bool Eigen::SVDBase< MatrixType >::allocate	(	Index	rows,
		Index	cols,
		unsigned int	computationOptions
	)

protected

◆ check_template_parameters()

template<typename Derived >

static void Eigen::SVDBase< Derived >::check_template_parameters ( )

inlinestaticprotected

◆ cols()

template<typename Derived >

Index Eigen::SVDBase< Derived >::cols ( void ) const

inline

◆ 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

◆ derived() [1/2]

template<typename Derived >

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

inline

◆ derived() [2/2]

template<typename Derived >

const Derived& Eigen::SVDBase< Derived >::derived ( ) const

inline

◆ info()

template<typename Derived >

EIGEN_DEVICE_FUNC ComputationInfo Eigen::SVDBase< Derived >::info ( ) const

inline

Reports whether previous computation was successful.

Returns: Success if computation was successful.

◆ 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&).

◆ rows()

template<typename Derived >

Index Eigen::SVDBase< Derived >::rows ( void ) const

inline

◆ 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);

Eigen::Default

@ Default

Definition: Constants.h:362

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.

◆ 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&).

Friends And Related Function Documentation

◆ internal::solve_assertion

template<typename Derived >

template<typename Derived_ >

friend struct internal::solve_assertion

friend

Member Data Documentation

◆ m_cols

template<typename Derived >

Index Eigen::SVDBase< Derived >::m_cols

protected

◆ m_computationOptions

template<typename Derived >

unsigned int Eigen::SVDBase< Derived >::m_computationOptions

protected

◆ m_computeFullU

template<typename Derived >

bool Eigen::SVDBase< Derived >::m_computeFullU

protected

◆ m_computeFullV

template<typename Derived >

bool Eigen::SVDBase< Derived >::m_computeFullV

protected

◆ m_computeThinU

template<typename Derived >

bool Eigen::SVDBase< Derived >::m_computeThinU

protected

◆ m_computeThinV

template<typename Derived >

bool Eigen::SVDBase< Derived >::m_computeThinV

protected

◆ m_diagSize

template<typename Derived >

Index Eigen::SVDBase< Derived >::m_diagSize

protected

◆ m_info

template<typename Derived >

ComputationInfo Eigen::SVDBase< Derived >::m_info

protected

◆ m_isAllocated

template<typename Derived >

bool Eigen::SVDBase< Derived >::m_isAllocated

protected

◆ m_isInitialized

template<typename Derived >

bool Eigen::SVDBase< Derived >::m_isInitialized

protected

◆ m_matrixU

template<typename Derived >

MatrixUType Eigen::SVDBase< Derived >::m_matrixU

protected

◆ m_matrixV

template<typename Derived >

MatrixVType Eigen::SVDBase< Derived >::m_matrixV

protected

◆ m_nonzeroSingularValues

template<typename Derived >

Index Eigen::SVDBase< Derived >::m_nonzeroSingularValues

protected

◆ m_prescribedThreshold

template<typename Derived >

RealScalar Eigen::SVDBase< Derived >::m_prescribedThreshold

protected

◆ m_rows

template<typename Derived >

Index Eigen::SVDBase< Derived >::m_rows

protected

◆ m_singularValues

template<typename Derived >

SingularValuesType Eigen::SVDBase< Derived >::m_singularValues

protected

◆ m_usePrescribedThreshold

template<typename Derived >

bool Eigen::SVDBase< Derived >::m_usePrescribedThreshold

protected

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

/home/runner/work/NDDEM/NDDEM/src/CoarseGraining/Eigen/src/Core/util/ForwardDeclarations.h
/home/runner/work/NDDEM/NDDEM/src/CoarseGraining/Eigen/src/SVD/SVDBase.h

Public Types

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Friends

Detailed Description

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

Member Typedef Documentation

◆ Index

◆ MatrixType

◆ MatrixUType

◆ MatrixVType

◆ RealScalar

◆ Scalar

◆ SingularValuesType

◆ StorageIndex

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ SVDBase()

Member Function Documentation

◆ _check_compute_assertions()

◆ _check_solve_assertion()

◆ _solve_impl()

◆ _solve_impl_transposed()

◆ allocate()

◆ check_template_parameters()

◆ cols()

◆ computeU()

◆ computeV()

◆ derived() [1/2]

◆ derived() [2/2]

◆ info()

◆ matrixU()

◆ matrixV()

◆ nonzeroSingularValues()

◆ rank()

◆ rows()

◆ setThreshold() [1/2]

◆ setThreshold() [2/2]

◆ singularValues()

◆ threshold()

Friends And Related Function Documentation

◆ internal::solve_assertion

Member Data Documentation

◆ m_cols

◆ m_computationOptions

◆ m_computeFullU

◆ m_computeFullV

◆ m_computeThinU

◆ m_computeThinV

◆ m_diagSize

◆ m_info

◆ m_isAllocated

◆ m_isInitialized

◆ m_matrixU

◆ m_matrixV

◆ m_nonzeroSingularValues

◆ m_prescribedThreshold

◆ m_rows

◆ m_singularValues

◆ m_usePrescribedThreshold

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