Re: svds test failure

[Daniel J Sebald]

On 07/31/2012 03:04 PM, Rik wrote:
> On 07/31/2012 11:26 AM, Daniel J Sebald wrote:
[snip]
> > %!testif HAVE_ARPACK
> > %! s = svds (speye (10));
> > %! assert (s, ones (6, 1), 2*eps);
> >
> > To expect a numerical routine to be accurate within two times the
> > machine precision is asking for quite a bit.  The tests which have
> > 'opts' passed in are asking for accuracy within 1e-10, which seems more
> > reasonable.
> The special case of the identity matrix and a matrix of all zeros are just
> that -- special cases.  ARPACK should be able in these instances to arrive
> at a nearly exact solution.

The identity matrix probably isn't a special case.  I mean, 
theoretically identity matrix is special, but algorithm wise ARPACK 
probably proceeds the same as other matrices until the stopping criteria 
is met.

In the case of the zero matrix I would guess that ARPACK proceeds by 
trying to diagonalize some matrix using a rotation of sorts, but because 
the sum of any terms (be they the diagonal) turns out to be zero the 
algorithm likely stops right away because of some potential division by 
zero in the rotation algorithm.


> > I realize one would expect the result to be deterministic and not fail
> > in one case and pass in the other, but who knows how ARPACK is set up?
> > From what I can tell from the API, ARPACK chooses a random initial seed
> ONLY if a seed is not provided to them.  Other than this, the algorithm is
> deterministic.

That would explain the result from my followup post on the identity 
matrix randomness.

Dan