Two-sided Jacobi SVD decomposition of a rectangular matrix. More...

#include <JacobiSVD.h>

Inheritance diagram for Eigen::JacobiSVD< _MatrixType, QRPreconditioner >:

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 }
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::plain_col_type < MatrixType >::type	ColType
typedef internal::plain_col_type < MatrixType >::type	ColType
typedef MatrixType::Index	Index
typedef MatrixType::Index	Index
typedef _MatrixType	MatrixType
typedef _MatrixType	MatrixType
typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime >	MatrixUType
typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime >	MatrixUType
typedef Matrix< Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime >	MatrixVType
typedef Matrix< Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime >	MatrixVType
typedef NumTraits< typename MatrixType::Scalar >::Real	RealScalar
typedef NumTraits< typename MatrixType::Scalar >::Real	RealScalar
typedef internal::plain_row_type < MatrixType >::type	RowType
typedef internal::plain_row_type < MatrixType >::type	RowType
typedef MatrixType::Scalar	Scalar
typedef MatrixType::Scalar	Scalar
typedef internal::plain_diag_type < MatrixType, RealScalar > ::type	SingularValuesType
typedef internal::plain_diag_type < MatrixType, RealScalar > ::type	SingularValuesType
typedef Matrix< Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime >	WorkMatrixType
typedef Matrix< Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime >	WorkMatrixType
Public Member Functions
Index	cols () const
SVDBase< MatrixType > &	compute (const MatrixType &matrix, unsigned int computationOptions)
	Method performing the decomposition of given matrix using custom options.
SVDBase< MatrixType > &	compute (const MatrixType &matrix)
	Method performing the decomposition of given matrix using current options.
JacobiSVD &	compute (const MatrixType &matrix, unsigned int computationOptions)
	Method performing the decomposition of given matrix using custom options.
JacobiSVD &	compute (const MatrixType &matrix)
	Method performing the decomposition of given matrix using current options.
bool	computeU () const
bool	computeV () const
	JacobiSVD ()
	Default Constructor.
	JacobiSVD (Index rows, Index cols, unsigned int computationOptions=0)
	Default Constructor with memory preallocation.
	JacobiSVD ()
	Default Constructor.
	JacobiSVD (Index rows, Index cols, unsigned int computationOptions=0)
	Default Constructor with memory preallocation.
	JacobiSVD (const MatrixType &matrix, unsigned int computationOptions=0)
	Constructor performing the decomposition of given matrix.
	JacobiSVD (const MatrixType &matrix, unsigned int computationOptions=0)
	Constructor performing the decomposition of given matrix.
const MatrixUType &	matrixU () const
const MatrixVType &	matrixV () const
Index	nonzeroSingularValues () const
Index	rank () const
Index	rows () const
JacobiSVD &	setThreshold (const RealScalar &threshold)
JacobiSVD &	setThreshold (Default_t)
const SingularValuesType &	singularValues () const
template<typename Rhs >
const internal::solve_retval < JacobiSVD, Rhs >	solve (const MatrixBase< Rhs > &b) const
template<typename Rhs >
const internal::solve_retval < JacobiSVD, Rhs >	solve (const MatrixBase< Rhs > &b) const
RealScalar	threshold () const
Protected Attributes
Index	m_cols
unsigned int	m_computationOptions
bool	m_computeFullU
bool	m_computeFullV
bool	m_computeThinU
bool	m_computeThinV
Index	m_diagSize
bool	m_isAllocated
bool	m_isInitialized
MatrixUType	m_matrixU
MatrixVType	m_matrixV
Index	m_nonzeroSingularValues
RealScalar	m_prescribedThreshold
internal::qr_preconditioner_impl < MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows >	m_qr_precond_morecols
internal::qr_preconditioner_impl < MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols >	m_qr_precond_morerows
Index	m_rows
MatrixType	m_scaledMatrix
SingularValuesType	m_singularValues
bool	m_usePrescribedThreshold
WorkMatrixType	m_workMatrix
Private Member Functions
void	allocate (Index rows, Index cols, unsigned int computationOptions)
void	allocate (Index rows, Index cols, unsigned int computationOptions)
Static Private Member Functions
static void	check_template_parameters ()
Friends
struct	internal::qr_preconditioner_impl
struct	internal::svd_precondition_2x2_block_to_be_real

Detailed Description

template<typename _MatrixType, int QRPreconditioner>
class Eigen::JacobiSVD< _MatrixType, QRPreconditioner >

Two-sided Jacobi SVD decomposition of a rectangular matrix.

Parameters:

MatrixType	the type of the matrix of which we are computing the SVD decomposition
QRPreconditioner	this optional parameter allows to specify the type of QR decomposition that will be used internally for the R-SVD step for non-square matrices. See discussion of possible values below.

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.

This JacobiSVD decomposition computes only the singular values by default. If you want U or V, you need to ask for them explicitly.

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.

Here's an example demonstrating basic usage:

Output:

This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The downside is that it's slower than bidiagonalizing SVD algorithms for large square matrices; however its complexity is still $ O(n^2p) $ where n is the smaller dimension and p is the greater dimension, meaning that it is still of the same order of complexity as the faster bidiagonalizing R-SVD algorithms. In particular, like any R-SVD, it takes advantage of non-squareness in that its complexity is only linear in the greater dimension.

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.

The possible values for QRPreconditioner are:

ColPivHouseholderQRPreconditioner is the default. In practice it's very safe. It uses column-pivoting QR.
FullPivHouseholderQRPreconditioner, is the safest and slowest. It uses full-pivoting QR. Contrary to other QRs, it doesn't allow computing thin unitaries.
HouseholderQRPreconditioner is the fastest, and less safe and accurate than the pivoting variants. It uses non-pivoting QR. This is very similar in safety and accuracy to the bidiagonalization process used by bidiagonalizing SVD algorithms (since bidiagonalization is inherently non-pivoting). However the resulting SVD is still more reliable than bidiagonalizing SVDs because the Jacobi-based iterarive process is more reliable than the optimized bidiagonal SVD iterations.
NoQRPreconditioner allows not to use a QR preconditioner at all. This is useful if you know that you will only be computing JacobiSVD decompositions of square matrices. Non-square matrices require a QR preconditioner. Using this option will result in faster compilation and smaller executable code. It won't significantly speed up computation, since JacobiSVD is always checking if QR preconditioning is needed before applying it anyway.

See also:: MatrixBase::jacobiSvd()

Definition at line 500 of file Eigen/src/SVD/JacobiSVD.h.

Member Typedef Documentation

template<typename _MatrixType, int QRPreconditioner>

typedef internal::plain_col_type<MatrixType>::type Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::ColType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 519 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef internal::plain_col_type<MatrixType>::type Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::ColType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 526 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef MatrixType::Index Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::Index

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 500 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef MatrixType::Index Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::Index

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 507 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef _MatrixType Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::MatrixType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 497 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef _MatrixType Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::MatrixType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 504 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::MatrixUType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 513 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::MatrixUType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 520 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::MatrixVType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 516 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::MatrixVType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 523 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef NumTraits<typename MatrixType::Scalar>::Real Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::RealScalar

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 499 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef NumTraits<typename MatrixType::Scalar>::Real Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::RealScalar

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 506 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef internal::plain_row_type<MatrixType>::type Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::RowType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 518 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef internal::plain_row_type<MatrixType>::type Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::RowType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 525 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef MatrixType::Scalar Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::Scalar

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 498 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef MatrixType::Scalar Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::Scalar

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 505 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef internal::plain_diag_type<MatrixType, RealScalar>::type Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::SingularValuesType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 517 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef internal::plain_diag_type<MatrixType, RealScalar>::type Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::SingularValuesType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 524 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime> Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::WorkMatrixType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 522 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime> Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::WorkMatrixType

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 529 of file Eigen/src/SVD/JacobiSVD.h.

Member Enumeration Documentation

template<typename _MatrixType, int QRPreconditioner>

anonymous enum

Enumerator:

RowsAtCompileTime
ColsAtCompileTime
DiagSizeAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime
MaxDiagSizeAtCompileTime
MatrixOptions

Definition at line 508 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

anonymous enum

Enumerator:

RowsAtCompileTime
ColsAtCompileTime
DiagSizeAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime
MaxDiagSizeAtCompileTime
MatrixOptions

Definition at line 501 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

Constructor & Destructor Documentation

template<typename _MatrixType, int QRPreconditioner>

Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::JacobiSVD ( ) [inline]

Default Constructor.

The default constructor is useful in cases in which the user intends to perform decompositions via JacobiSVD::compute(const MatrixType&).

Definition at line 536 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::JacobiSVD	(	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:: JacobiSVD()

Definition at line 551 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::JacobiSVD	(	const MatrixType &	matrix,
		unsigned int	computationOptions = `0`
	)		`[inline]`

Constructor performing the decomposition of given matrix.

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.

Definition at line 571 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::JacobiSVD ( ) [inline]

Default Constructor.

The default constructor is useful in cases in which the user intends to perform decompositions via JacobiSVD::compute(const MatrixType&).

Definition at line 529 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::JacobiSVD	(	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:: JacobiSVD()

Definition at line 540 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::JacobiSVD	(	const MatrixType &	matrix,
		unsigned int	computationOptions = `0`
	)		`[inline]`

Constructor performing the decomposition of given matrix.

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.

Definition at line 556 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

Member Function Documentation

template<typename _MatrixType, int QRPreconditioner>

void Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::allocate	(	Index	rows,
		Index	cols,
		unsigned int	computationOptions
	)		`[private]`

Reimplemented from Eigen::SVDBase< _MatrixType >.

template<typename MatrixType , int QRPreconditioner>

void Eigen::JacobiSVD< MatrixType, QRPreconditioner >::allocate	(	Index	rows,
		Index	cols,
		unsigned int	computationOptions
	)		`[private]`

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 774 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

static void Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::check_template_parameters ( ) [inline, static, private]

Definition at line 746 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Index Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::cols ( void ) const [inline]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 741 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

SVDBase<MatrixType>& Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::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 from Eigen::SVDBase< _MatrixType >.

template<typename _MatrixType, int QRPreconditioner>

SVDBase<MatrixType>& Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::compute ( const MatrixType & matrix ) [inline]

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 from Eigen::SVDBase< _MatrixType >.

Definition at line 580 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename MatrixType , int QRPreconditioner>

SVDBase< MatrixType > & Eigen::JacobiSVD< MatrixType, QRPreconditioner >::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 from Eigen::SVDBase< _MatrixType >.

Definition at line 824 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

JacobiSVD& Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::compute ( const MatrixType & matrix ) [inline]

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 from Eigen::SVDBase< _MatrixType >.

Definition at line 599 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

bool Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::computeU ( ) const [inline]

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

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 648 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

bool Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::computeV ( ) const [inline]

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

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 650 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

const MatrixUType& Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::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.

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 613 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

const MatrixVType& Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::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 from Eigen::SVDBase< _MatrixType >.

Definition at line 629 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Index Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::nonzeroSingularValues ( ) const [inline]

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

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 671 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Index Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::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 683 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Index Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::rows ( void ) const [inline]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 740 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

JacobiSVD& Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::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 708 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

JacobiSVD& Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::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 723 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

const SingularValuesType& Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::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.

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 641 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

template<typename Rhs >

const internal::solve_retval<JacobiSVD, Rhs> Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::solve ( const MatrixBase< Rhs > & b ) const [inline]

Returns:: a (least squares) solution of 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 $\Vert A x - b \Vert$ .

Definition at line 596 of file unsupported/Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

template<typename Rhs >

const internal::solve_retval<JacobiSVD, Rhs> Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::solve ( const MatrixBase< Rhs > & b ) const [inline]

Returns:: a (least squares) solution of 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 $\Vert A x - b \Vert$ .

Definition at line 663 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

RealScalar Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::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 733 of file Eigen/src/SVD/JacobiSVD.h.

Friends And Related Function Documentation

template<typename _MatrixType, int QRPreconditioner>

internal::qr_preconditioner_impl [friend]

Definition at line 766 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

internal::svd_precondition_2x2_block_to_be_real [friend]

Definition at line 764 of file Eigen/src/SVD/JacobiSVD.h.

Member Data Documentation

template<typename _MatrixType, int QRPreconditioner>

Index Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_cols [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 760 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

unsigned int Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_computationOptions [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 759 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

bool Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_computeFullU [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 757 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

bool Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_computeFullV [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 758 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

bool Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_computeThinU [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 757 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

bool Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_computeThinV [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 758 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Index Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_diagSize [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 760 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

bool Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_isAllocated [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 756 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

bool Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_isInitialized [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 756 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

MatrixUType Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_matrixU [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 752 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

MatrixVType Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_matrixV [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 753 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Index Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_nonzeroSingularValues [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 760 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

RealScalar Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_prescribedThreshold [protected]

Definition at line 761 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

internal::qr_preconditioner_impl< MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows > Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_qr_precond_morecols [protected]

Definition at line 768 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

internal::qr_preconditioner_impl< MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols > Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_qr_precond_morerows [protected]

Definition at line 769 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

Index Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_rows [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 760 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

MatrixType Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_scaledMatrix [protected]

Definition at line 770 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

SingularValuesType Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_singularValues [protected]

Reimplemented from Eigen::SVDBase< _MatrixType >.

Definition at line 754 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

bool Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_usePrescribedThreshold [protected]

Definition at line 756 of file Eigen/src/SVD/JacobiSVD.h.

template<typename _MatrixType, int QRPreconditioner>

WorkMatrixType Eigen::JacobiSVD< _MatrixType, QRPreconditioner >::m_workMatrix [protected]

Definition at line 755 of file Eigen/src/SVD/JacobiSVD.h.

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

Public Types

Public Member Functions

Protected Attributes

Private Member Functions

Static Private Member Functions

Friends

Detailed Description

template<typename _MatrixType, int QRPreconditioner> class Eigen::JacobiSVD< _MatrixType, QRPreconditioner >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<typename _MatrixType, int QRPreconditioner>
class Eigen::JacobiSVD< _MatrixType, QRPreconditioner >