Jama Class QRDecomposition

java.lang.Object Jama.QRDecomposition
All Implemented Interfaces:
Serializable

public class QRDecomposition
extends Object
implements 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.

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

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

QRDecomposition

public QRDecomposition(Matrix A)
QR Decomposition, computed by Householder reflections. 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 Matrix getH()
Return the Householder vectors

Returns:
Lower trapezoidal matrix whose columns define the reflections

getR

public Matrix getR()
Return the upper triangular factor

Returns:
R

getQ

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

Returns:
Q

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.
Throws:
IllegalArgumentException - Matrix row dimensions must agree.
RuntimeException - Matrix is rank deficient.