by **sven** » Wed Mar 22, 2006 9:45 am

See:

@BOOK{GV:96,

AUTHOR = {Golub, G. H. and Van Loan, C. F.},

TITLE = {Matrix Computations},

EDITION = {3rd},

PUBLISHER = {The Johns Hopkins University Press},

ADDRESS = {Baltimore, MD, USA},

YEAR = {1996},

ISBN = {0-8018-5414-8} }

section 5.1. Golub and Van Loan call them Householder reflections. For efficiency, LAPACK itself applies several reflections at once in block form whenever possible, because then the Level 3 BLAS can be used. This approach is described in section 5.1.7 of the above reference. DLARFX only uses the Level 2 BLAS. I suspect that it will be hard to optimize the routine as most of the computational effort is in the Level 2 BLAS routines DGEMV and DGER.

Best wishes,

Sven Hammarling.

P.S. Julien Langou reminded me that there already is some optimization in the form of loop unrolling for Householder reflections up to 10 by 10.