Householder QR decomposition of a matrix. More...

#include <HouseholderQR.h>

Public Types
enum	{ RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, Options = MatrixType::Options, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }
typedef _MatrixType	MatrixType
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::Index	Index
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, HCoeffsType > ::ConjugateReturnType	HouseholderSequenceType
Public Member Functions
	HouseholderQR ()
	Default Constructor.
	HouseholderQR (Index rows, Index cols)
	Default Constructor with memory preallocation.
	HouseholderQR (const MatrixType &matrix)
template<typename Rhs >
const internal::solve_retval < HouseholderQR, Rhs >	solve (const MatrixBase< Rhs > &b) const
HouseholderSequenceType	householderQ () const
const MatrixType &	matrixQR () const
HouseholderQR &	compute (const MatrixType &matrix)
MatrixType::RealScalar	absDeterminant () const
MatrixType::RealScalar	logAbsDeterminant () const
Index	rows () const
Index	cols () const
const HCoeffsType &	hCoeffs () const
Protected Attributes
MatrixType	m_qr
HCoeffsType	m_hCoeffs
RowVectorType	m_temp
bool	m_isInitialized

Detailed Description

template<typename _MatrixType>
class HouseholderQR< _MatrixType >

Householder QR decomposition of a matrix.

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.

See also:: MatrixBase::householderQr()

Member Typedef Documentation

template<typename _MatrixType>

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

template<typename _MatrixType>

typedef HouseholderSequence<MatrixType,HCoeffsType>::ConjugateReturnType HouseholderQR< _MatrixType >::HouseholderSequenceType

template<typename _MatrixType>

typedef MatrixType::Index HouseholderQR< _MatrixType >::Index

template<typename _MatrixType>

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

template<typename _MatrixType>

typedef _MatrixType HouseholderQR< _MatrixType >::MatrixType

template<typename _MatrixType>

typedef MatrixType::RealScalar HouseholderQR< _MatrixType >::RealScalar

template<typename _MatrixType>

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

template<typename _MatrixType>

typedef MatrixType::Scalar HouseholderQR< _MatrixType >::Scalar

Member Enumeration Documentation

template<typename _MatrixType>

anonymous enum

Enumerator:

RowsAtCompileTime
ColsAtCompileTime
Options
MaxRowsAtCompileTime
MaxColsAtCompileTime

Constructor & Destructor Documentation

template<typename _MatrixType>

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&).

template<typename _MatrixType>

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()

template<typename _MatrixType>

HouseholderQR< _MatrixType >::HouseholderQR ( const MatrixType & matrix ) [inline]

Member Function Documentation

template<typename _MatrixType>

MatrixType::RealScalar 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()

template<typename _MatrixType>

Index HouseholderQR< _MatrixType >::cols ( void ) const [inline]

template<typename _MatrixType>

HouseholderQR& HouseholderQR< _MatrixType >::compute ( const MatrixType & matrix )

template<typename _MatrixType>

const HCoeffsType& HouseholderQR< _MatrixType >::hCoeffs ( ) const [inline]

template<typename _MatrixType>

HouseholderSequenceType HouseholderQR< _MatrixType >::householderQ ( void ) const [inline]

template<typename _MatrixType>

MatrixType::RealScalar 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()

template<typename _MatrixType>

const MatrixType& HouseholderQR< _MatrixType >::matrixQR ( ) const [inline]

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

template<typename _MatrixType>

Index HouseholderQR< _MatrixType >::rows ( void ) const [inline]

template<typename _MatrixType>

template<typename Rhs >

const internal::solve_retval<HouseholderQR, Rhs> HouseholderQR< _MatrixType >::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:: The case where b is a matrix is not yet implemented. Also, this code is space inefficient.

Example:

Output:

Member Data Documentation

template<typename _MatrixType>

HCoeffsType HouseholderQR< _MatrixType >::m_hCoeffs [protected]

template<typename _MatrixType>

bool HouseholderQR< _MatrixType >::m_isInitialized [protected]

template<typename _MatrixType>

MatrixType HouseholderQR< _MatrixType >::m_qr [protected]

template<typename _MatrixType>

RowVectorType HouseholderQR< _MatrixType >::m_temp [protected]

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

/home/hauberg/Dokumenter/Capture/humim-tracker-0.1/src/ntk/geometry/Eigen/src/QR/HouseholderQR.h

HouseholderQR< _MatrixType > Class Template Reference

Public Types

Public Member Functions

Protected Attributes

Detailed Description

template<typename _MatrixType> class HouseholderQR< _MatrixType >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename _MatrixType>
class HouseholderQR< _MatrixType >