mikera.matrixx.decompose.impl.qr

Class HouseholderColQR

java.lang.Object

mikera.matrixx.decompose.impl.qr.HouseholderColQR

All Implemented Interfaces:

QRDecomposition

public class HouseholderColQR
extends Object
implements QRDecomposition

Householder QR decomposition is rich in operations along the columns of the matrix. This can be taken advantage of by solving for the Q matrix in a column major format to reduce the number of CPU cache misses and the number of copies that are performed.

Author:

Peter Abeles

Field Summary

Fields

Modifier and Type	Field and Description
protected double[][]	dataQR Where the Q and R matrices are stored.
protected boolean	error
protected double	gamma
protected double[]	gammas
protected int	minLength
protected int	numCols
protected int	numRows
protected double	tau
protected double[]	v

Constructor Summary

Constructors

Constructor and Description
HouseholderColQR(boolean compact)

Method Summary

Modifier and Type	Method and Description
protected AMatrix	computeQ() Computes Q.
protected AMatrix	computeR() Computes R.
protected void	convertToColumnMajor(AMatrix A) Converts the standard row-major matrix into a column-major vector that is advantageous for this problem.
QRResult	decompose(AMatrix A) To decompose the matrix 'A' it must have full rank.
double[]	getGammas()
AMatrix	getQ()
double[][]	getQR() Returns the combined QR matrix in a 2D array format that is column major.
AMatrix	getR()
protected void	householder(int j) Computes the householder vector "u" for the first column of submatrix j.
protected void	updateA(int w) Takes the results from the householder computation and updates the 'A' matrix. A = (I - γ*u*uT)A

Methods inherited from class java.lang.Object

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

Field Detail

dataQR

protected double[][] dataQR

Where the Q and R matrices are stored. R is stored in the upper triangular portion and Q on the lower bit. Lower columns are where u is stored. Q_k = (I - gamma_k*u_k*u_k^T).

v

protected double[] v

numCols

protected int numCols

numRows

protected int numRows

minLength

protected int minLength

gammas

protected double[] gammas

gamma

protected double gamma

tau

protected double tau

error

protected boolean error

Constructor Detail

HouseholderColQR

public HouseholderColQR(boolean compact)

Method Detail

getQR

public double[][] getQR()

Returns the combined QR matrix in a 2D array format that is column major.

Returns:

The QR matrix in a 2D matrix column major format. [ column ][ row ]

getQ

public AMatrix getQ()

Returns:

The Q matrix from the decomposition.

getR

public AMatrix getR()

Returns:

The R matrix from the decomposition.

computeQ

protected AMatrix computeQ()

Computes Q.

computeR

protected AMatrix computeR()

Computes R.

decompose

public QRResult decompose(AMatrix A)

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

convertToColumnMajor

protected void convertToColumnMajor(AMatrix A)

Converts the standard row-major matrix into a column-major vector that is advantageous for this problem.

Parameters:

A - original matrix that is to be decomposed.

householder

protected void householder(int j)

Computes the householder vector "u" for the first column of submatrix j. Note this is a specialized householder for this problem. There is some protection against overfloaw and underflow.

Q = I - γuu^T

This function finds the values of 'u' and 'γ'.

Parameters:

j - Which submatrix to work off of.

updateA

protected void updateA(int w)

Takes the results from the householder computation and updates the 'A' matrix.

A = (I - γ*u*u^T)A

Parameters:

w - The submatrix.

getGammas

public double[] getGammas()