[SciPy-dev] QR factorization: modifications

[Bart Vandereycken]

Hi all,

I've modified the QR routine in scipy.linalg.qr in 3 ways, to make it 
faster and more compatible with Matlab.

This is my first patch so any feedback is appreciated... you can find 
the files here: http://www.cs.kuleuven.be/~bartvde/scipy/

1) The original method used only one LAPACK-routine (GEQRF) to compute 
the R factor, but NOT the (xORGQR and xUNGQR) to compute the Q factor.
This is a huge efficiency loss, see the figure at my site for a 
comparison of the old and new qr method.

I included the 2 LAPACK-wrappers in patch_flapack.diff and the new qr 
method in patch_qr.diff. (I don't use clapack, so I can't test this.) 
The old qr method is still available as qr_old in case you want to 
compare the results, use test_qr.py ;-)


2) You can compute economy-sized (as Matlab calls it) or skinny QR 
factorizations for tall matrices (more rows than cols). The performance 
gain should be obvious now.


3) If you only want the R factor and not the Q, the method stops early 
and is 2 times faster.


Testing for test_decompy.py is included in patch_test.diff.

There are 2 new parameters for scipy.decomp.qr:
   econ=False: economy size or not
     -> Matlab's qr(A,0)

   mode='qr': 'qr' or 'r' (or 'qre', qr with Givens rotations, maybe I'll
                           do this later)
     -> Matlab's Q,R=qr(A) or R=qr(A) or Q,R,E=qr(A)


Bart