Householder QR decomposition of a matrix. More...

#include <ForwardDeclarations.h>

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

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

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

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

typedef _MatrixType	MatrixType

typedef MatrixType::RealScalar	RealScalar

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

typedef MatrixType::Scalar	Scalar

typedef MatrixType::StorageIndex	StorageIndex

Public Member Functions
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

MatrixType::RealScalar	absDeterminant () const

Index	cols () const

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

const HCoeffsType &	hCoeffs () const

HouseholderSequenceType	householderQ () const

	HouseholderQR ()
	Default Constructor. More...

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

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

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

MatrixType::RealScalar	logAbsDeterminant () const

const MatrixType &	matrixQR () const

Index	rows () const

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

Protected Member Functions
void	computeInPlace ()

Static Protected Member Functions
static void	check_template_parameters ()

Protected Attributes
HCoeffsType	m_hCoeffs

bool	m_isInitialized

MatrixType	m_qr

RowVectorType	m_temp

Detailed Description

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()

Definition at line 254 of file ForwardDeclarations.h.

Member Typedef Documentation

◆ HCoeffsType

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

Definition at line 60 of file HouseholderQR.h.

◆ HouseholderSequenceType

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

Definition at line 62 of file HouseholderQR.h.

◆ MatrixQType

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

Definition at line 59 of file HouseholderQR.h.

◆ MatrixType

typedef _MatrixType Eigen::HouseholderQR::MatrixType

Definition at line 48 of file HouseholderQR.h.

◆ RealScalar

typedef MatrixType::RealScalar Eigen::HouseholderQR::RealScalar

Definition at line 56 of file HouseholderQR.h.

◆ RowVectorType

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

Definition at line 61 of file HouseholderQR.h.

◆ Scalar

typedef MatrixType::Scalar Eigen::HouseholderQR::Scalar

Definition at line 55 of file HouseholderQR.h.

◆ StorageIndex

typedef MatrixType::StorageIndex Eigen::HouseholderQR::StorageIndex

Definition at line 58 of file HouseholderQR.h.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Enumerator
RowsAtCompileTime
ColsAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime

Definition at line 49 of file HouseholderQR.h.

Constructor & Destructor Documentation

◆ HouseholderQR() [1/4]

Eigen::HouseholderQR::HouseholderQR ( )

inline

Default Constructor.

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

Definition at line 70 of file HouseholderQR.h.

◆ HouseholderQR() [2/4]

Eigen::HouseholderQR::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()

Definition at line 78 of file HouseholderQR.h.

◆ HouseholderQR() [3/4]

template<typename InputType >

Eigen::HouseholderQR::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);

See also: compute()

Definition at line 97 of file HouseholderQR.h.

◆ HouseholderQR() [4/4]

template<typename InputType >

Eigen::HouseholderQR::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&)

Definition at line 115 of file HouseholderQR.h.

Member Function Documentation

◆ _solve_impl() [1/2]

template<typename RhsType , typename DstType >

EIGEN_DEVICE_FUNC void Eigen::HouseholderQR::_solve_impl	(	const RhsType &	rhs,
		DstType &	dst
	)		const

◆ _solve_impl() [2/2]

template<typename RhsType , typename DstType >

void Eigen::HouseholderQR::_solve_impl	(	const RhsType &	rhs,
		DstType &	dst
	)		const

Definition at line 350 of file HouseholderQR.h.

◆ absDeterminant()

MatrixType::RealScalar Eigen::HouseholderQR::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()

Definition at line 236 of file HouseholderQR.h.

◆ check_template_parameters()

static void Eigen::HouseholderQR::check_template_parameters ( )

inlinestaticprotected

Definition at line 222 of file HouseholderQR.h.

◆ cols()

Index Eigen::HouseholderQR::cols ( ) const

inline

Definition at line 206 of file HouseholderQR.h.

◆ compute()

template<typename InputType >

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

inline

Definition at line 170 of file HouseholderQR.h.

◆ computeInPlace()

void Eigen::HouseholderQR::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&)

Definition at line 379 of file HouseholderQR.h.

◆ hCoeffs()

const HCoeffsType& Eigen::HouseholderQR::hCoeffs ( ) const

inline

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

For advanced uses only.

Definition at line 212 of file HouseholderQR.h.

◆ householderQ()

HouseholderSequenceType Eigen::HouseholderQR::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:

Definition at line 154 of file HouseholderQR.h.

◆ logAbsDeterminant()

MatrixType::RealScalar Eigen::HouseholderQR::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()

Definition at line 245 of file HouseholderQR.h.

◆ matrixQR()

const MatrixType& Eigen::HouseholderQR::matrixQR ( ) const

inline

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

Definition at line 163 of file HouseholderQR.h.

◆ rows()

Index Eigen::HouseholderQR::rows ( ) const

inline

Definition at line 205 of file HouseholderQR.h.

◆ solve()

template<typename Rhs >

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

inline

This method finds a solution x to the equation Ax=b, where A is the matrix of which *this is the QR decomposition, if any exists.

Parameters

b	the right-hand-side of the equation to solve.

Returns: a solution.

\note_about_checking_solutions

\note_about_arbitrary_choice_of_solution

Example:

Output:

Definition at line 140 of file HouseholderQR.h.

Member Data Documentation

◆ m_hCoeffs

HCoeffsType Eigen::HouseholderQR::m_hCoeffs

protected

Definition at line 230 of file HouseholderQR.h.

◆ m_isInitialized

bool Eigen::HouseholderQR::m_isInitialized

protected

Definition at line 232 of file HouseholderQR.h.

◆ m_qr

MatrixType Eigen::HouseholderQR::m_qr

protected

Definition at line 229 of file HouseholderQR.h.

◆ m_temp

RowVectorType Eigen::HouseholderQR::m_temp

protected

Definition at line 231 of file HouseholderQR.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

Detailed Description

Member Typedef Documentation

◆ HCoeffsType

◆ HouseholderSequenceType

◆ MatrixQType

◆ MatrixType

◆ RealScalar

◆ RowVectorType

◆ Scalar

◆ StorageIndex

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ HouseholderQR() [1/4]

◆ HouseholderQR() [2/4]

◆ HouseholderQR() [3/4]

◆ HouseholderQR() [4/4]

Member Function Documentation

◆ _solve_impl() [1/2]

◆ _solve_impl() [2/2]

◆ absDeterminant()

◆ check_template_parameters()

◆ cols()

◆ compute()

◆ computeInPlace()

◆ hCoeffs()

◆ householderQ()

◆ logAbsDeterminant()

◆ matrixQR()

◆ rows()

◆ solve()

Member Data Documentation

◆ m_hCoeffs

◆ m_isInitialized

◆ m_qr

◆ m_temp