QR Decomposition. Can be used to solve least squares problems. More...

#include <Qrd.h>

Public Types
enum	Mode { Mode::full, Mode::reduced }

typedef Matrix< matrix::dynamic, matrix::dynamic, Real >	Matrix

Public Member Functions
	Qrd ()

template<class T >
	Qrd (const MatrixBase< T > &a, Mode mode=Mode::reduced)
	Calculate the QRD of matrix A. More...

template<class T >
Qrd &	calc (const MatrixBase< T > &a, Mode mode=Mode::reduced)
	Calculate the QRD of matrix A. More...

bool	isFullRank () const
	Check if the decomposed matrix has full rank (ie. all vectors are linearly independent; no vector is a linear combination of others) More...

template<class B , class X >
void	solve (const MatrixBase< B > &b, MatrixBase< X > &x)
	Solve the linear system where A is the decomposed matrix. A and B row sizes must match. A must have full rank. More...

const Matrix &	q () const
	Get Q of the decomposition. More...

const Matrix &	r () const
	Get R of the decomposition. More...

const Matrix &	h () const
	Get the Householder column vectors that define the reflections. H is a (m x n) lower trapazoidal matrix. More...

Detailed Description

template<class Real>
class honey::Qrd< Real >

QR Decomposition. Can be used to solve least squares problems.

The reduced QRD of (m x n) matrix A with m >= n is: $ A = Q R $ where Q is an orthogonal (m x n) matrix, and R is an upper triangular (n x n) matrix.

The full QRD is: $A = Q \begin{bmatrix} R \\ 0 \end{bmatrix}$ where Q is (m x m) and 0 is (m-n x n).

Most linear systems do not require the full QRD to solve.

Complexity: $ O(n^2 m) $

Member Typedef Documentation

template<class Real >

typedef Matrix<matrix::dynamic, matrix::dynamic, Real> honey::Qrd< Real >::Matrix

Member Enumeration Documentation

template<class Real >

enum honey::Qrd::Mode

strong

Enumerator
full	compute full QRD
reduced	compute reduced QRD

Constructor & Destructor Documentation

template<class Real >

honey::Qrd< Real >::Qrd ( )

inline

template<class Real >

template<class T >

honey::Qrd< Real >::Qrd	(	const MatrixBase< T > &	a,
		Mode	mode = `Mode::reduced`
	)

inline

Calculate the QRD of matrix A.

Member Function Documentation

template<class Real >

template<class T >

Qrd& honey::Qrd< Real >::calc	(	const MatrixBase< T > &	a,
		Mode	mode = `Mode::reduced`
	)

inline

Calculate the QRD of matrix A.

template<class Real >

const Matrix& honey::Qrd< Real >::h ( ) const

inline

Get the Householder column vectors that define the reflections. H is a (m x n) lower trapazoidal matrix.

template<class Real >

bool honey::Qrd< Real >::isFullRank ( ) const

inline

Check if the decomposed matrix has full rank (ie. all vectors are linearly independent; no vector is a linear combination of others)

template<class Real >

const Matrix& honey::Qrd< Real >::q ( ) const

inline

Get Q of the decomposition.

template<class Real >

const Matrix& honey::Qrd< Real >::r ( ) const

inline

Get R of the decomposition.

template<class Real >

template<class B , class X >

void honey::Qrd< Real >::solve	(	const MatrixBase< B > &	b,
		MatrixBase< X > &	x
	)

inline

Solve the linear system $ Ax = B $ where A is the decomposed matrix. A and B row sizes must match. A must have full rank.

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

src/common/Honey/Math/NumAnalysis/Qrd.h
src/common/Honey/Math/NumAnalysis/Qrd.cpp

Public Types

Public Member Functions

Detailed Description

template<class Real> class honey::Qrd< Real >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<class Real>
class honey::Qrd< Real >