Re: 'make check' errors for Mac OS X

[Daniel J Sebald]

On 11/03/2013 05:53 AM, c. wrote:
> On 3 Nov 2013, at 09:05, Dmitri A. Sergatskov<address@hidden>  wrote:
>
> > On my Fedora 19 (x86_64) it passes with reference BLAS  but fails with ATLAS
> > and OpenBLAS.
> >
> > Dmitri.
>
> I am using ATLAS on OSX too, is the error you get the same as for me?
>
> svds.m
>   ***** testif HAVE_ARPACK
> [u2,s2,v2,flag] = svds (A,k);
> s2 = diag (s2);
> assert (flag, !1);
> tol = 10 * eps() * norm(s2, 1);
> assert (s2, s(end:-1:end-k+1), tol);
>
> !!!!! test failed
> ASSERT errors for:  assert (s2,s (end:-1:end - k + 1),tol)
>
>   Location  |  Observed  |  Expected  |  Reason
>     (6)         41.966       41.966      Abs err 6.8923e-13 exceeds tol 
> 6.5244e-13
>
> c.

This certainly looks like a tolerance issue, but there is something not 
exactly right--at least something that warrants a bit of investigation. 
 With the norm() scaling in the tolerance it seems a pretty loose 
bound, but I suppose it is the nature of the problem given the A matrix 
looks to be rank 7.  The weak eigenvalues that should theoretically be 
zero will probably have a large degree of noise, and being sorted might 
taper off (one of the reasons I added a vector tolerance for assert as 
opposed to just a scalar tolerance).

A few things.

First, this norm(s2,1) is done on the sparse matrix, which represents 
the non-zero eigenvalue portion (i.e., those theoretically with rank, or 
singular values) of the matrix.  There is this whole other set of 
near-zero eigenvalues (93 of them?) for which that subspace is adding 
noise to the result.  Perhaps there needs to be a term introduced into 
the tolerance for that.

Second, having not looked too closely at the matrix itself, from the way 
it is constructed I would guess it is of rank 7.  Maybe it isn't of rank 
7, but if that were the case, my guess would be it is the last singular 
value where the most discrepancy is, not the second last.

Lastly, if there is some inaccuracy here, we aren't sure if it is the 
sparse SVD routine or the non-sparse SVD routine which is worse.  It 
might be nice to have a test that compares against some theoretical result.

In any case, David, could you investigate this issue a bit to see if you 
are comfortable with the result?

Dan