mpv2
Class QRDecomposition

java.lang.Object
  mpv2.QRDecomposition

All Implemented Interfaces:

java.io.Serializable

public class QRDecomposition
extends java.lang.Object
implements java.io.Serializable

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.

See Also:

Serialized Form

Constructor Summary

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

Method Summary

JamaMatrix	getH() Return the Householder vectors
JamaMatrix	getQ() Generate and return the (economy-sized) orthogonal factor
JamaMatrix	getR() Return the upper triangular factor
boolean	isFullRank() Is the matrix full rank?
JamaMatrix	solve(JamaMatrix B) 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(JamaMatrix A)

QR Decomposition, computed by Householder reflections. Constructor returns a structure to access R and the Householder vectors and compute Q.

Parameters:

A - Rectangular matrix

Method Detail

isFullRank

public boolean isFullRank()

Is the matrix full rank?

Returns:

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

getH

public JamaMatrix getH()

Return the Householder vectors

Returns:

Lower trapezoidal matrix whose columns define the reflections

getR

public JamaMatrix getR()

Return the upper triangular factor

Returns:

R

getQ

public JamaMatrix getQ()

Generate and return the (economy-sized) orthogonal factor

Returns:

Q

solve

public JamaMatrix solve(JamaMatrix B)

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.