org.openmali.decomposition
Class QRDecomposition

java.lang.Object
  org.openmali.decomposition.QRDecomposition

public class QRDecomposition
extends java.lang.Object

QR Decomposition.

For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q*R.

The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns false.

Constructor Summary

QRDecomposition(MatrixMxNf A)
QR Decomposition, computed by Householder reflections.

Method Summary

MatrixMxNf	getH() Returns the Householder vectors.
MatrixMxNf	getQ()
MatrixMxNf	getR()
boolean	isFullRank() Is the matrix full rank?
MatrixMxNf	solve(MatrixMxNf B, MatrixMxNf result) Least squares solution of A * X = B.

Methods inherited from class java.lang.Object

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

Constructor Detail

QRDecomposition

public QRDecomposition(MatrixMxNf A)

QR Decomposition, computed by Householder reflections.

Parameters:

A - Rectangular matrix

Method Detail

isFullRank

public final boolean isFullRank()

Is the matrix full rank?

Returns:

true if R, and hence A, has full rank.

getH

public MatrixMxNf getH()

Returns the Householder vectors.

Returns:

Lower trapezoidal matrix whose columns define the reflections

getR

public MatrixMxNf getR()

Returns:

the upper triangular factor.

getQ

public MatrixMxNf getQ()

Returns:

Generates and returns the (economy-sized) orthogonal factor.

solve

public final MatrixMxNf solve(MatrixMxNf B,
                              MatrixMxNf result)

Least squares solution of A * X = B.

Parameters:

B - A Matrix with as many rows as A and any number of columns.

Returns:

X that minimizes the two norm of Q*R*X-B.

Throws:

java.lang.IllegalArgumentException - Matrix row dimensions must agree.

java.lang.RuntimeException - Matrix is rank deficient.