mikera.matrixx.decompose.impl.qr

Class HouseholderQR

java.lang.Object

mikera.matrixx.decompose.impl.qr.HouseholderQR

All Implemented Interfaces:

QRDecomposition

public class HouseholderQR
extends java.lang.Object
implements QRDecomposition

This variation of QR decomposition uses reflections to compute the Q matrix. Each reflection uses a householder operations, hence its name. To provide a meaningful solution the original matrix must have full rank. This is intended for processing of small to medium matrices.

Both Q and R are stored in the same m by n matrix. Q is not stored directly, instead the u from Q_k=(I-γ*u*u^T) is stored. Decomposition requires about 2n*m²-2m²/3 flops.

See the QR reflections algorithm described in:
David S. Watkins, "Fundamentals of Matrix Computations" 2nd Edition, 2002

For the most part this is a straight forward implementation. To improve performance on large matrices a column is written to an array and the order of some of the loops has been changed. This will degrade performance noticeably on small matrices. Since it is unlikely that the QR decomposition would be a bottle neck when small matrices are involved only one implementation is provided.

Constructor Summary

Constructors

Constructor and Description
HouseholderQR(boolean compact)

Method Summary

Modifier and Type	Method and Description
QRResult	decompose(AMatrix A) In order to decompose the matrix 'A' it must have full rank.
double[]	getGammas()
AMatrix	getQ()
AMatrix	getQR() Returns a single matrix which contains the combined values of Q and R.
AMatrix	getR()

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

HouseholderQR

public HouseholderQR(boolean compact)

Method Detail

getQR

public AMatrix getQR()

Returns a single matrix which contains the combined values of Q and R. This is possible since Q is symmetric and R is upper triangular.

Returns:

The combined Q R matrix.

getQ

public AMatrix getQ()

Returns:

The Q matrix from the decomposition.

getR

public AMatrix getR()

Returns:

The R matrix from the decomposition.

decompose

public QRResult decompose(AMatrix A)

In order to decompose the matrix 'A' it must have full rank. 'A' is a 'm' by 'n' matrix. It requires about 2n*m²-2m²/3 flops.

The matrix provided here can be of different dimension than the one specified in the constructor. It just has to be smaller than or equal to it.

Specified by:

decompose in interface QRDecomposition

getGammas

public double[] getGammas()