org.ejml.alg.dense.decompose.qr

Class QRDecompositionHouseholder_CD64

java.lang.Object

org.ejml.alg.dense.decompose.qr.QRDecompositionHouseholder_CD64

All Implemented Interfaces:

DecompositionInterface<CDenseMatrix64F>, QRDecomposition<CDenseMatrix64F>

public class QRDecompositionHouseholder_CD64
extends java.lang.Object
implements QRDecomposition<CDenseMatrix64F>

This variation of complex 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^H) 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
QRDecompositionHouseholder_CD64()

Method Summary

Modifier and Type	Method and Description
boolean	decompose(CDenseMatrix64F A) In order to decompose the matrix 'A' it must have full rank.
double[]	getGammas()
CDenseMatrix64F	getQ(CDenseMatrix64F Q, boolean compact) Computes the Q matrix from the information stored in the QR matrix.
CDenseMatrix64F	getQR() Returns a single matrix which contains the combined values of Q and R.
CDenseMatrix64F	getR(CDenseMatrix64F R, boolean compact) Returns an upper triangular matrix which is the R in the QR decomposition.
boolean	inputModified() Is the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix) is modified during the decomposition process.
void	setExpectedMaxSize(int numRows, int numCols)

Methods inherited from class java.lang.Object

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

Constructor Detail

QRDecompositionHouseholder_CD64

public QRDecompositionHouseholder_CD64()

Method Detail

setExpectedMaxSize

public void setExpectedMaxSize(int numRows,
                               int numCols)

getQR

public CDenseMatrix64F 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 CDenseMatrix64F getQ(CDenseMatrix64F Q,
                            boolean compact)

Computes the Q matrix from the information stored in the QR matrix. This operation requires about 4(m²n-mn²+n³/3) flops.

Specified by:

getQ in interface QRDecomposition<CDenseMatrix64F>

Parameters:

Q - The orthogonal Q matrix.

compact - If true an m by n matrix is created, otherwise n by n.

Returns:

The Q matrix.

getR

public CDenseMatrix64F getR(CDenseMatrix64F R,
                            boolean compact)

Returns an upper triangular matrix which is the R in the QR decomposition.

Specified by:

getR in interface QRDecomposition<CDenseMatrix64F>

Parameters:

R - An upper triangular matrix.

compact -

Returns:

The R matrix.

decompose

public boolean decompose(CDenseMatrix64F 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 DecompositionInterface<CDenseMatrix64F>

Parameters:

A - The matrix which is being decomposed. Modification is implementation dependent.

Returns:

Returns if it was able to decompose the matrix.

inputModified

public boolean inputModified()

Description copied from interface: DecompositionInterface

Is the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix) is modified during the decomposition process.

Specified by:

inputModified in interface DecompositionInterface<CDenseMatrix64F>

Returns:

true if the input matrix to decompose() is modified.

getGammas

public double[] getGammas()