org.ejml.alg.dense.decomposition.qr

Class QRDecompositionHouseholderColumn_D64

java.lang.Object

org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholderColumn_D64

All Implemented Interfaces:

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

Direct Known Subclasses:

QRColPivDecompositionHouseholderColumn_D64

public class QRDecompositionHouseholderColumn_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 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_D64()

Method Summary

Modifier and Type	Method and Description
protected void	convertToColumnMajor(org.ejml.data.DenseMatrix64F A) Converts the standard row-major matrix into a column-major vector that is advantageous for this problem.
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 imformation stored in the QR matrix.
double[][]	getQR() Returns the combined QR matrix in a 2D array format that is column major.
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

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_D64

public QRDecompositionHouseholderColumn_D64()

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 org.ejml.data.DenseMatrix64F getQ(org.ejml.data.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 org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.DenseMatrix64F>

Parameters:

Q - The orthogonal Q matrix.

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. If compact then the input expected to be size = [min(rows,cols) , numCols] otherwise size = [numRows,numCols].

Specified by:

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

Parameters:

R - Storage for upper triangular matrix.

compact - If true then a compact matrix is expected.

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>

convertToColumnMajor

protected void convertToColumnMajor(org.ejml.data.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()