org.ejml.alg.dense.decomposition.qr

Class QRColPivDecompositionHouseholderColumn

java.lang.Object

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

org.ejml.alg.dense.decomposition.qr.QRColPivDecompositionHouseholderColumn

All Implemented Interfaces:

DecompositionInterface<DenseMatrix64F>, QRDecomposition<DenseMatrix64F>, QRPDecomposition<DenseMatrix64F>

public class QRColPivDecompositionHouseholderColumn
extends QRDecompositionHouseholderColumn
implements QRPDecomposition<DenseMatrix64F>

Performs QR decomposition with column pivoting. To prevent overflow/underflow the whole matrix is normalized by the max value, but columns are not normalized individually any more. To enable code reuse it extends QRDecompositionHouseholderColumn and functions from that class are used whenever possible. Columns are transposed into single arrays, which allow for fast pivots.

Decomposition: A*P = Q*R

Based off the description in "Fundamentals of Matrix Computations", 2nd by David S. Watkins.

Author:

Peter Abeles

Field Summary

Fields

Modifier and Type	Field and Description
protected double[]	normsCol
protected int[]	pivots
protected int	rank
protected double	singularThreshold

Fields inherited from class org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholderColumn

dataQR, error, gamma, gammas, minLength, numCols, numRows, tau, v

Constructor Summary

Constructors

Constructor and Description
QRColPivDecompositionHouseholderColumn()
QRColPivDecompositionHouseholderColumn(double singularThreshold) Configure parameters.

Method Summary

Methods

Modifier and Type	Method and Description
boolean	decompose(DenseMatrix64F A) To decompose the matrix 'A' it must have full rank.
DenseMatrix64F	getPivotMatrix(DenseMatrix64F P) Creates the pivot matrix.
int[]	getPivots() Ordering of each column after pivoting.
DenseMatrix64F	getQ(DenseMatrix64F Q, boolean compact) Computes the Q matrix from the information stored in the QR matrix.
int	getRank() Returns the rank as determined by the algorithm.
protected boolean	householderPivot(int j) Computes the householder vector "u" for the first column of submatrix j.
void	setExpectedMaxSize(int numRows, int numCols)
void	setSingularThreshold(double threshold) Specifies the threshold used to flag a column as being singular.

Methods inherited from class org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholderColumn

convertToColumnMajor, getGammas, getQR, getR, householder, inputModified, updateA

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.ejml.factory.QRDecomposition

getR

Methods inherited from interface org.ejml.factory.DecompositionInterface

inputModified

Field Detail

pivots

protected int[] pivots

normsCol

protected double[] normsCol

singularThreshold

protected double singularThreshold

rank

protected int rank

Constructor Detail

QRColPivDecompositionHouseholderColumn

public QRColPivDecompositionHouseholderColumn(double singularThreshold)

Configure parameters.

Parameters:

singularThreshold - The singular threshold.

QRColPivDecompositionHouseholderColumn

public QRColPivDecompositionHouseholderColumn()

Method Detail

setSingularThreshold

public void setSingularThreshold(double threshold)

Description copied from interface: QRPDecomposition

Specifies the threshold used to flag a column as being singular. The optimal threshold (if one exists) varies by the matrix being processed. A reasonable value would be the maximum absolute value of the matrix's elements multiplied by EPS:
decomposition.setSingularThreshold(CommonOps.elementMaxAbs(A)*UtilEjml.EPS)

Specified by:

setSingularThreshold in interface QRPDecomposition<DenseMatrix64F>

Parameters:

threshold - Singular threshold.

setExpectedMaxSize

public void setExpectedMaxSize(int numRows,
                      int numCols)

Overrides:

setExpectedMaxSize in class QRDecompositionHouseholderColumn

getQ

public DenseMatrix64F getQ(DenseMatrix64F 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<DenseMatrix64F>

Overrides:

getQ in class QRDecompositionHouseholderColumn

Parameters:

Q - The orthogonal Q matrix.

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

Returns:

The Q 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>

Overrides:

decompose in class QRDecompositionHouseholderColumn

Parameters:

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

Returns:

Returns if it was able to decompose the matrix.

householderPivot

protected boolean householderPivot(int j)

Computes the householder vector "u" for the first column of submatrix j. The already computed norm is used and checks to see if the matrix is singular at this point.

Q = I - γuu^T

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

Parameters:

j - Which submatrix to work off of.

Returns:

false if it is degenerate

getRank

public int getRank()

Description copied from interface: QRPDecomposition

Returns the rank as determined by the algorithm. This is dependent upon a fixed threshold and might not be appropriate for some applications.

Specified by:

getRank in interface QRPDecomposition<DenseMatrix64F>

Returns:

Matrix's rank

getPivots

public int[] getPivots()

Description copied from interface: QRPDecomposition

Ordering of each column after pivoting. The current column i was original at column pivot[i].

Specified by:

getPivots in interface QRPDecomposition<DenseMatrix64F>

Returns:

Order of columns.

getPivotMatrix

public DenseMatrix64F getPivotMatrix(DenseMatrix64F P)

Description copied from interface: QRPDecomposition

Creates the pivot matrix.

Specified by:

getPivotMatrix in interface QRPDecomposition<DenseMatrix64F>

Parameters:

P - Optional storage for pivot matrix. If null a new matrix will be created.

Returns:

The pivot matrix.