Householder QR decomposition of a matrix. More...

#include <HouseholderQR.h>

Inheritance diagram for Eigen::HouseholderQR< _MatrixType >:

Public Types
enum	{ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime , MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }

typedef _MatrixType	MatrixType

typedef SolverBase< HouseholderQR >	Base

typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime,(MatrixType::Flags &RowMajorBit) ? RowMajor :ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime >	MatrixQType

typedef internal::plain_diag_type< MatrixType >::type	HCoeffsType

typedef internal::plain_row_type< MatrixType >::type	RowVectorType

typedef HouseholderSequence< MatrixType, typename internal::remove_all< typename HCoeffsType::ConjugateReturnType >::type >	HouseholderSequenceType

Public Types inherited from Eigen::SolverBase< HouseholderQR< _MatrixType > >
enum

typedef EigenBase< HouseholderQR< _MatrixType > >	Base

typedef internal::traits< HouseholderQR< _MatrixType > >::Scalar	Scalar

typedef Scalar	CoeffReturnType

typedef Transpose< const HouseholderQR< _MatrixType > >	ConstTransposeReturnType

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

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

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

Public Member Functions
	HouseholderQR ()
	Default Constructor.

	HouseholderQR (Index rows, Index cols)
	Default Constructor with memory preallocation.

template<typename InputType >
	HouseholderQR (const EigenBase< InputType > &matrix)
	Constructs a QR factorization from a given matrix.

template<typename InputType >
	HouseholderQR (EigenBase< InputType > &matrix)
	Constructs a QR factorization from a given matrix.

HouseholderSequenceType	householderQ () const
	This method returns an expression of the unitary matrix Q as a sequence of Householder transformations.

const MatrixType &	matrixQR () const

template<typename InputType >
HouseholderQR &	compute (const EigenBase< InputType > &matrix)

MatrixType::RealScalar	absDeterminant () const

MatrixType::RealScalar	logAbsDeterminant () const

Index	rows () const

Index	cols () const

const HCoeffsType &	hCoeffs () const

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< HouseholderQR< _MatrixType > >
	SolverBase ()
	Default constructor.

const Solve< HouseholderQR< _MatrixType >, Rhs >	solve (const MatrixBase< Rhs > &b) const

const ConstTransposeReturnType	transpose () const

const AdjointReturnType	adjoint () const

EIGEN_DEVICE_FUNC HouseholderQR< _MatrixType > &	derived ()

EIGEN_DEVICE_FUNC const HouseholderQR< _MatrixType > &	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	computeInPlace ()
	Performs the QR factorization of the given matrix matrix.

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

Static Protected Member Functions
static void	check_template_parameters ()

Protected Attributes
MatrixType	m_qr

HCoeffsType	m_hCoeffs

RowVectorType	m_temp

bool	m_isInitialized

Friends
class	SolverBase< HouseholderQR >

Detailed Description

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

Householder QR decomposition of a matrix.

Template Parameters

_MatrixType the type of the matrix of which we are computing the QR decomposition

This class performs a QR decomposition of a matrix A into matrices Q and R such that

$\mathbf{A} = \mathbf{Q} \, \mathbf{R}$

by using Householder transformations. Here, Q a unitary matrix and R an upper triangular matrix. The result is stored in a compact way compatible with LAPACK.

Note that no pivoting is performed. This is not a rank-revealing decomposition. If you want that feature, use FullPivHouseholderQR or ColPivHouseholderQR instead.

This Householder QR decomposition is faster, but less numerically stable and less feature-full than FullPivHouseholderQR or ColPivHouseholderQR.

This class supports the inplace decomposition mechanism.

See also: MatrixBase::householderQr()

Constructor & Destructor Documentation

◆ HouseholderQR() [1/4]

template<typename _MatrixType >

Eigen::HouseholderQR< _MatrixType >::HouseholderQR ( )

inline

Default Constructor.

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

◆ HouseholderQR() [2/4]

template<typename _MatrixType >

Eigen::HouseholderQR< _MatrixType >::HouseholderQR	(	Index	rows,
		Index	cols
	)

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: HouseholderQR()

◆ HouseholderQR() [3/4]

template<typename _MatrixType >

template<typename InputType >

Eigen::HouseholderQR< _MatrixType >::HouseholderQR ( const EigenBase< InputType > & matrix )

inlineexplicit

Constructs a QR factorization from a given matrix.

This constructor computes the QR factorization of the matrix matrix by calling the method compute(). It is a short cut for:

HouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());

qr.compute(matrix);

Eigen::MatrixBase

Base class for all dense matrices, vectors, and expressions.

Definition MatrixBase.h:50

See also: compute()

◆ HouseholderQR() [4/4]

template<typename _MatrixType >

template<typename InputType >

Eigen::HouseholderQR< _MatrixType >::HouseholderQR ( EigenBase< InputType > & matrix )

inlineexplicit

Constructs a QR factorization from a given matrix.

This overloaded constructor is provided for inplace decomposition when MatrixType is a Eigen::Ref.

See also: HouseholderQR(const EigenBase&)

Member Function Documentation

◆ absDeterminant()

template<typename MatrixType >

MatrixType::RealScalar Eigen::HouseholderQR< MatrixType >::absDeterminant ( ) const

Returns: the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.

Note: This is only for square matrices.

Warning: a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow. One way to work around that is to use logAbsDeterminant() instead.

See also: logAbsDeterminant(), MatrixBase::determinant()

◆ computeInPlace()

template<typename MatrixType >

void Eigen::HouseholderQR< MatrixType >::computeInPlace ( )

protected

Performs the QR factorization of the given matrix matrix.

The result of the factorization is stored into *this, and a reference to *this is returned.

See also: class HouseholderQR, HouseholderQR(const MatrixType&)

◆ hCoeffs()

template<typename _MatrixType >

const HCoeffsType & Eigen::HouseholderQR< _MatrixType >::hCoeffs ( ) const

inline

Returns: a const reference to the vector of Householder coefficients used to represent the factor Q.

For advanced uses only.

◆ householderQ()

template<typename _MatrixType >

HouseholderSequenceType Eigen::HouseholderQR< _MatrixType >::householderQ ( ) const

inline

This method returns an expression of the unitary matrix Q as a sequence of Householder transformations.

The returned expression can directly be used to perform matrix products. It can also be assigned to a dense Matrix object. Here is an example showing how to recover the full or thin matrix Q, as well as how to perform matrix products using operator*:

Example:

Output:

◆ logAbsDeterminant()

template<typename MatrixType >

MatrixType::RealScalar Eigen::HouseholderQR< MatrixType >::logAbsDeterminant ( ) const

Returns: the natural log of the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.

Note: This is only for square matrices.; This method is useful to work around the risk of overflow/underflow that's inherent to determinant computation.

See also: absDeterminant(), MatrixBase::determinant()

◆ matrixQR()

template<typename _MatrixType >

const MatrixType & Eigen::HouseholderQR< _MatrixType >::matrixQR ( ) const

inline

Returns: a reference to the matrix where the Householder QR decomposition is stored in a LAPACK-compatible way.

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

External/Eigen/src/Core/util/ForwardDeclarations.h
External/Eigen/src/QR/HouseholderQR.h

Public Types

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ HouseholderQR() [1/4]

◆ HouseholderQR() [2/4]

◆ HouseholderQR() [3/4]

◆ HouseholderQR() [4/4]

Member Function Documentation

◆ absDeterminant()

◆ computeInPlace()

◆ hCoeffs()

◆ householderQ()

◆ logAbsDeterminant()

◆ matrixQR()