Jama

Class QRDecomposition

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(Matrix A)
QR Decomposition, computed by Householder reflections.

Method Summary

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

Constructor Details

QRDecomposition

public QRDecomposition(Matrix A)
QR Decomposition, computed by Householder reflections.
Parameters:
A - Rectangular matrix

Method Details

getH

public Matrix getH()
Return the Householder vectors
Returns:
Lower trapezoidal matrix whose columns define the reflections

getQ

public Matrix getQ()
Generate and return the (economy-sized) orthogonal factor
Returns:
Q

getR

public Matrix getR()
Return the upper triangular factor
Returns:
R

isFullRank

public boolean isFullRank()
Is the matrix full rank?
Returns:
true if R, and hence A, has full rank.

solve

public Matrix solve(Matrix 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.