Jama
Class QRDecomposition
- 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.
QRDecomposition
public QRDecomposition(Matrix A)
QR Decomposition, computed by Householder reflections.
getH
public Matrix getH()
Return the Householder vectors
- Lower trapezoidal matrix whose columns define the reflections
getQ
public Matrix getQ()
Generate and return the (economy-sized) orthogonal factor
getR
public Matrix getR()
Return the upper triangular factor
isFullRank
public boolean isFullRank()
Is the matrix full rank?
- true if R, and hence A, has full rank.
solve
public Matrix solve(Matrix B)
Least squares solution of A*X = B
B
- A Matrix with as many rows as A and any number of columns.
- X that minimizes the two norm of Q*R*X-B.