Package org.ejml.dense.row.decompose.qr

Class QRDecompositionHouseholder_ZDRM

java.lang.Object

org.ejml.dense.row.decompose.qr.QRDecompositionHouseholder_ZDRM

All Implemented Interfaces:

org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.ZMatrixRMaj>, org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.ZMatrixRMaj>

public class QRDecompositionHouseholder_ZDRM
extends Object
implements org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.ZMatrixRMaj>

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.

Field Summary

Fields

Modifier and Type	Field	Description
protected double[]	dataQR
protected boolean	error
protected double[]	gammas
protected int	minLength
protected int	numCols
protected int	numRows
protected org.ejml.data.ZMatrixRMaj	QR	Where the Q and R matrices are stored.
protected org.ejml.data.Complex_F64	tau
protected double[]	u
protected double[]	v

Constructor Summary

Constructors

Constructor	Description
QRDecompositionHouseholder_ZDRM()

Method Summary

Modifier and Type	Method	Description
protected void	commonSetup(org.ejml.data.ZMatrixRMaj A)	This function performs sanity check on the input for decompose and sets up the QR matrix.
boolean	decompose(org.ejml.data.ZMatrixRMaj A)	In order to decompose the matrix 'A' it must have full rank.
double[]	getGammas()
org.ejml.data.ZMatrixRMaj	getQ(@Nullable org.ejml.data.ZMatrixRMaj Q, boolean compact)	Computes the Q matrix from the information stored in the QR matrix.
org.ejml.data.ZMatrixRMaj	getQR()	Returns a single matrix which contains the combined values of Q and R.
org.ejml.data.ZMatrixRMaj	getR(@Nullable org.ejml.data.ZMatrixRMaj R, boolean compact)	Returns an upper triangular matrix which is the R in the QR decomposition.
protected void	householder(int j)	Computes the householder vector "u" for the first column of submatrix j.
boolean	inputModified()
void	setExpectedMaxSize(int numRows, int numCols)

Methods inherited from class java.lang.Object

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

Field Details

QR

protected org.ejml.data.ZMatrixRMaj QR

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^H).

u

protected double[] u

v

protected double[] v

numCols

protected int numCols

numRows

protected int numRows

minLength

protected int minLength

dataQR

protected double[] dataQR

gammas

protected double[] gammas

tau

protected org.ejml.data.Complex_F64 tau

error

protected boolean error

Constructor Details

QRDecompositionHouseholder_ZDRM

public QRDecompositionHouseholder_ZDRM()

Method Details

setExpectedMaxSize

public void setExpectedMaxSize(int numRows,
 int numCols)

getQR

public org.ejml.data.ZMatrixRMaj 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 org.ejml.data.ZMatrixRMaj getQ(@Nullable
 @Nullable org.ejml.data.ZMatrixRMaj 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 org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.ZMatrixRMaj>

Parameters:

Q - The orthogonal Q matrix.

getR

public org.ejml.data.ZMatrixRMaj getR(@Nullable
 @Nullable org.ejml.data.ZMatrixRMaj R,
 boolean compact)

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

Specified by:

getR in interface org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.ZMatrixRMaj>

Parameters:

R - An upper triangular matrix.

decompose

public boolean decompose(org.ejml.data.ZMatrixRMaj 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 org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.ZMatrixRMaj>

inputModified

public boolean inputModified()

Specified by:

inputModified in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.ZMatrixRMaj>

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 overflow and underflow.

Q = I - γuu^H

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

Parameters:

j - Which submatrix to work off of.

commonSetup

protected void commonSetup(org.ejml.data.ZMatrixRMaj A)

This function performs sanity check on the input for decompose and sets up the QR matrix.

getGammas

public double[] getGammas()