Base class of SVD algorithms. More...

#include <ForwardDeclarations.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 Eigen::Index	Index

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

typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime >	MatrixUType

typedef Matrix< Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime >	MatrixVType

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

typedef MatrixType::Scalar	Scalar

typedef internal::plain_diag_type< MatrixType, RealScalar >::type	SingularValuesType

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

Public Types inherited from Eigen::SolverBase< SVDBase< Derived > >
enum

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

typedef EigenBase< SVDBase< Derived > >	Base

typedef Scalar	CoeffReturnType

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

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

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
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

Index	cols () const

bool	computeU () const

bool	computeV () const

Derived &	derived ()

const Derived &	derived () const

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

const MatrixUType &	matrixU () const

const MatrixVType &	matrixV () const

Index	nonzeroSingularValues () const

Index	rank () const

Index	rows () const

Derived &	setThreshold (const RealScalar &threshold)

Derived &	setThreshold (Default_t)

const SingularValuesType &	singularValues () const

RealScalar	threshold () const

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

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

	SolverBase ()

ConstTransposeReturnType	transpose () const

	~SolverBase ()

Public Member Functions inherited from Eigen::EigenBase< Derived >
template<typename Dest >
EIGEN_DEVICE_FUNC void	addTo (Dest &dst) const

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

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

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC Derived &	const_cast_derived () const

EIGEN_DEVICE_FUNC const Derived &	const_derived () const

EIGEN_DEVICE_FUNC Derived &	derived ()

EIGEN_DEVICE_FUNC const Derived &	derived () const

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

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

template<typename Dest >
EIGEN_DEVICE_FUNC void	subTo (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
Index	m_cols

unsigned int	m_computationOptions

bool	m_computeFullU

bool	m_computeFullV

bool	m_computeThinU

bool	m_computeThinV

Index	m_diagSize

ComputationInfo	m_info

bool	m_isAllocated

bool	m_isInitialized

MatrixUType	m_matrixU

MatrixVType	m_matrixV

Index	m_nonzeroSingularValues

RealScalar	m_prescribedThreshold

Index	m_rows

SingularValuesType	m_singularValues

bool	m_usePrescribedThreshold

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

Definition at line 277 of file ForwardDeclarations.h.

Member Typedef Documentation

◆ Index

template<typename Derived>

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

Deprecated:: since Eigen 3.3

Definition at line 74 of file SVDBase.h.

◆ MatrixType

template<typename Derived>

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

Definition at line 70 of file SVDBase.h.

◆ MatrixUType

template<typename Derived>

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

Definition at line 85 of file SVDBase.h.

◆ MatrixVType

template<typename Derived>

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

Definition at line 86 of file SVDBase.h.

◆ RealScalar

template<typename Derived>

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

Definition at line 72 of file SVDBase.h.

◆ Scalar

template<typename Derived>

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

Definition at line 71 of file SVDBase.h.

◆ SingularValuesType

template<typename Derived>

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

Definition at line 87 of file SVDBase.h.

◆ StorageIndex

template<typename Derived>

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

Definition at line 73 of file SVDBase.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename Derived>

anonymous enum

Enumerator
RowsAtCompileTime
ColsAtCompileTime
DiagSizeAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime
MaxDiagSizeAtCompileTime
MatrixOptions

Definition at line 75 of file SVDBase.h.

Constructor & Destructor Documentation

◆ SVDBase()

template<typename Derived>

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

inlineprotected

Default Constructor.

Default constructor of SVDBase

Definition at line 287 of file SVDBase.h.

Member Function Documentation

◆ _check_compute_assertions()

template<typename Derived>

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

inlineprotected

Definition at line 257 of file SVDBase.h.

◆ _check_solve_assertion()

template<typename Derived>

template<bool Transpose_, typename Rhs >

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

inlineprotected

Definition at line 262 of file SVDBase.h.

◆ _solve_impl()

template<typename Derived >

template<typename RhsType , typename DstType >

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

Definition at line 308 of file SVDBase.h.

◆ _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

Definition at line 322 of file SVDBase.h.

◆ allocate()

template<typename MatrixType >

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

protected

Definition at line 337 of file SVDBase.h.

◆ check_template_parameters()

template<typename Derived>

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

inlinestaticprotected

Definition at line 252 of file SVDBase.h.

◆ cols()

template<typename Derived>

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

inline

Definition at line 213 of file SVDBase.h.

◆ 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

Definition at line 208 of file SVDBase.h.

◆ 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

Definition at line 210 of file SVDBase.h.

◆ derived() [1/2]

template<typename Derived>

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

inline

Definition at line 89 of file SVDBase.h.

◆ derived() [2/2]

template<typename Derived>

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

inline

Definition at line 90 of file SVDBase.h.

◆ 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.

Definition at line 236 of file SVDBase.h.

◆ 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.

Definition at line 101 of file SVDBase.h.

◆ 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.

Definition at line 117 of file SVDBase.h.

◆ nonzeroSingularValues()

template<typename Derived>

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

inline

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

Definition at line 136 of file SVDBase.h.

◆ 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&).

Definition at line 148 of file SVDBase.h.

◆ rows()

template<typename Derived>

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

inline

Definition at line 212 of file SVDBase.h.

◆ 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)

Definition at line 173 of file SVDBase.h.

◆ 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&).

Definition at line 188 of file SVDBase.h.

◆ 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.

Definition at line 129 of file SVDBase.h.

◆ 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&).

Definition at line 198 of file SVDBase.h.

Friends And Related Function Documentation

◆ internal::solve_assertion

template<typename Derived>

template<typename Derived_ >

friend struct internal::solve_assertion

friend

Definition at line 68 of file SVDBase.h.

Member Data Documentation

◆ m_cols

template<typename Derived>

Index Eigen::SVDBase< Derived >::m_cols

protected

Definition at line 280 of file SVDBase.h.

◆ m_computationOptions

template<typename Derived>

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

protected

Definition at line 279 of file SVDBase.h.

◆ m_computeFullU

template<typename Derived>

bool Eigen::SVDBase< Derived >::m_computeFullU

protected

Definition at line 277 of file SVDBase.h.

◆ m_computeFullV

template<typename Derived>

bool Eigen::SVDBase< Derived >::m_computeFullV

protected

Definition at line 278 of file SVDBase.h.

◆ m_computeThinU

template<typename Derived>

bool Eigen::SVDBase< Derived >::m_computeThinU

protected

Definition at line 277 of file SVDBase.h.

◆ m_computeThinV

template<typename Derived>

bool Eigen::SVDBase< Derived >::m_computeThinV

protected

Definition at line 278 of file SVDBase.h.

◆ m_diagSize

template<typename Derived>

Index Eigen::SVDBase< Derived >::m_diagSize

protected

Definition at line 280 of file SVDBase.h.

◆ m_info

template<typename Derived>

ComputationInfo Eigen::SVDBase< Derived >::m_info

protected

Definition at line 275 of file SVDBase.h.

◆ m_isAllocated

template<typename Derived>

bool Eigen::SVDBase< Derived >::m_isAllocated

protected

Definition at line 276 of file SVDBase.h.

◆ m_isInitialized

template<typename Derived>

bool Eigen::SVDBase< Derived >::m_isInitialized

protected

Definition at line 276 of file SVDBase.h.

◆ m_matrixU

template<typename Derived>

MatrixUType Eigen::SVDBase< Derived >::m_matrixU

protected

Definition at line 272 of file SVDBase.h.

◆ m_matrixV

template<typename Derived>

MatrixVType Eigen::SVDBase< Derived >::m_matrixV

protected

Definition at line 273 of file SVDBase.h.

◆ m_nonzeroSingularValues

template<typename Derived>

Index Eigen::SVDBase< Derived >::m_nonzeroSingularValues

protected

Definition at line 280 of file SVDBase.h.

◆ m_prescribedThreshold

template<typename Derived>

RealScalar Eigen::SVDBase< Derived >::m_prescribedThreshold

protected

Definition at line 281 of file SVDBase.h.

◆ m_rows

template<typename Derived>

Index Eigen::SVDBase< Derived >::m_rows

protected

Definition at line 280 of file SVDBase.h.

◆ m_singularValues

template<typename Derived>

SingularValuesType Eigen::SVDBase< Derived >::m_singularValues

protected

Definition at line 274 of file SVDBase.h.

◆ m_usePrescribedThreshold

template<typename Derived>

bool Eigen::SVDBase< Derived >::m_usePrescribedThreshold

protected

Definition at line 276 of file SVDBase.h.

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

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 >