jhplot.math

Class QRDecomposition

java.lang.Object

jhplot.math.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

Constructors

Constructor and Description
QRDecomposition(double[][] A) QR Decomposition, computed by Householder reflections.

Method Summary

Modifier and Type	Method and Description
double[][]	getH() Return the Householder vectors
double[][]	getQ() Generate and return the (economy-sized) orthogonal factor
double[][]	getR() Return the upper triangular factor
boolean	isFullRank() Is the matrix full rank?
double[][]	solve(double[][] B) Least squares solution of A*X = B

Methods inherited from class java.lang.Object

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

Constructor Detail

QRDecomposition

public QRDecomposition(double[][] A)

QR Decomposition, computed by Householder reflections.

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 double[][] getH()

Return the Householder vectors

Returns:

Lower trapezoidal matrix whose columns define the reflections

getR

public double[][] getR()

Return the upper triangular factor

Returns:

R

getQ

public double[][] getQ()

Generate and return the (economy-sized) orthogonal factor

Returns:

Q

solve

public double[][] solve(double[][] 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.