org.ejml.alg.dense.decomposition.qr

Class QRDecompositionHouseholderTran_D64

java.lang.Object

org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholderTran_D64

All Implemented Interfaces:

org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DenseMatrix64F>, org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.DenseMatrix64F>

public class QRDecompositionHouseholderTran_D64
extends java.lang.Object
implements org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.DenseMatrix64F>

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.

See Also:

QRDecompositionHouseholder_D64

Field Summary

Fields

Modifier and Type	Field and Description
protected boolean	error
protected double	gamma
protected double[]	gammas
protected int	minLength
protected int	numCols
protected int	numRows
protected org.ejml.data.DenseMatrix64F	QR Where the Q and R matrices are stored.
protected double	tau
protected double[]	v

Constructor Summary

Constructors

Constructor and Description
QRDecompositionHouseholderTran_D64()

Method Summary

Modifier and Type	Method and Description
void	applyQ(org.ejml.data.DenseMatrix64F A) A = Q*A
void	applyTranQ(org.ejml.data.DenseMatrix64F A) A = QT*A
boolean	decompose(org.ejml.data.DenseMatrix64F A) To decompose the matrix 'A' it must have full rank.
double[]	getGammas()
org.ejml.data.DenseMatrix64F	getQ(org.ejml.data.DenseMatrix64F Q, boolean compact) Computes the Q matrix from the information stored in the QR matrix.
org.ejml.data.DenseMatrix64F	getQR() Inner matrix that stores the decomposition
org.ejml.data.DenseMatrix64F	getR(org.ejml.data.DenseMatrix64F 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)
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

QR

protected org.ejml.data.DenseMatrix64F QR

Where the Q and R matrices are stored. For speed reasons this is transposed

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

QRDecompositionHouseholderTran_D64

public QRDecompositionHouseholderTran_D64()

Method Detail

setExpectedMaxSize

public void setExpectedMaxSize(int numRows,
                               int numCols)

getQR

public org.ejml.data.DenseMatrix64F getQR()

Inner matrix that stores the decomposition

getQ

public org.ejml.data.DenseMatrix64F getQ(org.ejml.data.DenseMatrix64F Q,
                                         boolean compact)

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

Specified by:

getQ in interface org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.DenseMatrix64F>

Parameters:

Q - The orthogonal Q matrix.

applyQ

public void applyQ(org.ejml.data.DenseMatrix64F A)

A = Q*A

Parameters:

A - Matrix that is being multiplied by Q. Is modified.

applyTranQ

public void applyTranQ(org.ejml.data.DenseMatrix64F A)

A = Q^T*A

Parameters:

A - Matrix that is being multiplied by Q^T. Is modified.

getR

public org.ejml.data.DenseMatrix64F getR(org.ejml.data.DenseMatrix64F 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.DenseMatrix64F>

Parameters:

R - An upper triangular matrix.

compact -

decompose

public boolean decompose(org.ejml.data.DenseMatrix64F 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 org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DenseMatrix64F>

inputModified

public boolean inputModified()

Specified by:

inputModified in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.DenseMatrix64F>

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^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()