This variation of QR decomposition uses reflections to compute the Q matrix. Each reflection uses a householder operations, hence its name. To provide a meaningful solution the original matrix must have full rank. This is intended for processing of small to medium matrices.
Both Q and R are stored in the same m by n matrix. Q is not stored directly, instead the u from Qk=(I-γ*u*uT) is stored. Decomposition requires about 2n*m2-2m2/3 flops.
See the QR reflections algorithm described in:
David S. Watkins, "Fundamentals of Matrix Computations" 2nd Edition, 2002
For the most part this is a straight forward implementation. To improve performance on large matrices a column is writen to an array and the order of some of the loops has been changed. This will degrade performance noticeably on small matrices. Since it is unlikely that the QR decomposition would be a bottle neck when small matrices are involved only one implementation is provided.
@author Peter Abeles | |