Problem with Singular Value Decomposition Algorithm

[Brian Gough]

Jim Love writes:
 > I still think their is a problem with your API.  I have done this problem using a pencil and paper, using Matlab, using Mathematica, and using the LAPACK DGESVD routine.  These 4 implementations all produce the same exact solution for the U S and Q matrix - only yours is different.  How do you explain this?
 > 

Matlab uses LAPACK.  I believe Mathematica might use that too now.  So
that's probably why they are giving the same results.

Provided the results returned by GSL satisfy u'*u = I, v'*v = I and
u*diag(s)*v' = A then it's a valid singular value decomposition.  From
my own testing this checks out ok, and also with the numbers you sent
in your emails.  If you have an example that doesn't then that would
be a bug.