org.ejml.alg.dense.decomposition.qr

Class QRDecompositionHouseholderColumn

java.lang.Object

org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholderColumn

All Implemented Interfaces:

DecompositionInterface<DenseMatrix64F>, QRDecomposition<DenseMatrix64F>

Direct Known Subclasses:

QRColPivDecompositionHouseholderColumn

public class QRDecompositionHouseholderColumn
extends Object
implements QRDecomposition<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.

Author:

Peter Abeles

See Also:

QRDecompositionHouseholder

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
QRDecompositionHouseholderColumn()

Method Summary

Methods

Modifier and Type	Method and Description
protected void	convertToColumnMajor(DenseMatrix64F A) Converts the standard row-major matrix into a column-major vector that is advantageous for this problem.
boolean	decompose(DenseMatrix64F A) To decompose the matrix 'A' it must have full rank.
double[]	getGammas()
DenseMatrix64F	getQ(DenseMatrix64F Q, boolean compact) Computes the Q matrix from the imformation stored in the QR matrix.
double[][]	getQR() Returns the combined QR matrix in a 2D array format that is column major.
DenseMatrix64F	getR(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() Is the input matrix to DecompositionInterface.decompose(org.ejml.data.Matrix64F) is modified during the decomposition process.
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

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

QRDecompositionHouseholderColumn

public QRDecompositionHouseholderColumn()

Method Detail

setExpectedMaxSize

public void setExpectedMaxSize(int numRows,
                      int numCols)

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 DenseMatrix64F getQ(DenseMatrix64F Q,
                  boolean compact)

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

Specified by:

getQ in interface QRDecomposition<DenseMatrix64F>

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 DenseMatrix64F getR(DenseMatrix64F R,
                  boolean compact)

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

Specified by:

getR in interface QRDecomposition<DenseMatrix64F>

Parameters:

R - An upper triangular matrix.

compact -

Returns:

The R matrix.

decompose

public boolean decompose(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 DecompositionInterface<DenseMatrix64F>

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.Matrix64F) is modified during the decomposition process.

Specified by:

inputModified in interface DecompositionInterface<DenseMatrix64F>

Returns:

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

convertToColumnMajor

protected void convertToColumnMajor(DenseMatrix64F 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()