Re: svds test failure

[Daniel J Sebald]

On 07/31/2012 03:23 PM, Ed Meyer wrote:
> On Tue, Jul 31, 2012 at 12:31 PM, Daniel J Sebald
> <address@hidden <mailto:address@hidden>> wrote:
>
>     On 07/31/2012 02:22 PM, Ed Meyer wrote:
>
>         As I pointed out in the "make check" thread the problem is that we
>         should not be
>         using absolute tolerances because that does not account for the
>         size of
>         the matrix
>         elements.  What we should do is to estimate if the result lies
>         in the
>         interval we would
>         get with roundoff perturbations in the matrix.  If it does,
>         that's as
>         good as can be expected.
>         Eispack used to do something like that with their "performance
>         index"
>         but I think you can
>         get better estimates.
>
>
>     Give us an idea of what code you are suggesting Ed.  Something like
>
>     eps*size(s,1)*size(s,2)
>
>     ?  Something concerning the rank of the input matrix?
>
>     Dan
>
>     PS: Did you mean to CC to the maintainers list?
>
>
> oops - I did mean to CC
> I'm attaching a page from a manual I wrote describing how I judge
> results.  It's more
> involved than the old eispack tests and maybe more work than we want to do.
> Much simpler would be to just use the norm of the matrix times some
> factor times
> machine epsilon instead of the absolute tolerances.

We're talking the linear case here, so what does equation (7) become in 
that case?  A'(lambda) should be simply a constant matrix?  Does that 
then turn out to be Frobenius norm or something?  So

tol = 100*eps*norm(A, 'fro');

and

%!testif HAVE_ARPACK
%! s = svds (speye (10));
%! assert (s, ones (6, 1), tol);

Something like that?

And what of the degenerative case of

%!testif HAVE_ARPACK
%! [u2,s2,v2,flag] = svds (zeros (10), k);
%! assert (u2, eye (10, k));
%! assert (s2, zeros (k));
%! assert (v2, eye (10, 7));

where the norm is zero?  Just leave as is, because we aren't really 
testing the performance in this case so much as the library's ability to 
handle the degenerate case?

Dan