Catalano.Math.Decompositions

Class QRDecomposition

java.lang.Object

Catalano.Math.Decompositions.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

Constructors

Constructor and Description
QRDecomposition(double[][] matrix) Initializes a new instance of the QRDecomposition class.

Method Summary

Modifier and Type	Method and Description
double[][]	getH() Get the Householder vectors.
double[][]	getQ() Generate the (economy-sized) orthogonal factor.
double[][]	getR() Get the upper triangular factor.
boolean	isFullRank() Check if the matrix is 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[][] matrix)

Initializes a new instance of the QRDecomposition class.

Parameters:

matrix - Matrix.

Method Detail

isFullRank

public boolean isFullRank()

Check if the matrix is full rank.

Returns:

True if R, and hence A has full rank, otherwise false.

getH

public double[][] getH()

Get the Householder vectors.

Returns:

Lower trapezoidal matrix whose columns define the reflections.

getR

public double[][] getR()

Get the upper triangular factor.

Returns:

Upper triangular factor.

getQ

public double[][] getQ()

Generate the (economy-sized) orthogonal factor.

Returns:

Economy-sized orthogonal factor.

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.