It Complies, links, & runs...

[Brian Gough]

Thanks, I've had a look at your complex SVD routine now.  I think that
is a good exercise, but the comments like "I'm not sure if this needs
to be conjugated" gave me bad flashbacks to 3-month production runs
going down the toilet for that reason ;-)

My suggestion for getting on the right track is to always be 100% sure
of the algorithm before coding.  I always like to implement the
algorithm of a published paper, so a literature search is important,
and may turn up useful information, as well a precise definitions of
algorithms.  Perhaps there are some papers which deal specifically
with the complex case.

The existing real-valued algorithm has some problems, as noted in the
comments about the convergence condition.  We really need to rewrite
the existing SVD to use bidiagonalisation, as the convergence results
for the Jacobi algorithm have only been proved for positive definite
matrices, iirc, so it's difficult to know when to terminate the
algorithm with zero singular values which are subject to roundoff.

regards
Brian Gough