Re: QR failing 1 test without qrupdate library

[Jaroslav Hajek]

On Sat, May 8, 2010 at 7:54 PM, Rik <address@hidden> wrote:
> While trying to debug another problem, I had occasion to compile octave
> without most of it's helper libraries.  When running 'make check' the qr
> test suite failed on this test:
>
>  AA = single([0.091364  0.613038  0.027504  0.999083;
>              0.594638  0.425302  0.562834  0.603537;
>              0.383594  0.291238  0.742073  0.085574;
>              0.265712  0.268003  0.783553  0.238409;
>              0.669966  0.743851  0.457255  0.445057 ]);
>
>  [Q,R] = qr(AA);
>  [Q,R] = qrdelete(Q,R,3,'row');
>  assert(norm(vec(Q'*Q - eye(4,'single')),Inf) < 1e1*eps('single'))
>
> The norm as calculated by Octave is 1.4305e-06, whereas the tolerance is
> 1.1921e-06.
>
> According to Octave when running the qrdelete step
>
> warning: In this version of Octave, QR & Cholesky updating routines
> simply update the matrix and recalculate factorizations.
> To use fast algorithms, link Octave with the qrupdate library.
>
> My understanding is that the QR routines from qrupdate are not only faster
> but more accurate.  When I link against them the error is always less than
> the tolerance in the assert block.
>

If qrupdate is not available, then

[Q,R] = qrdelete(Q,R,3,'row');

is performed simply by doing

TMP = Q*R;
TMP(3,:) = [];
[Q,R] = qr (TMP);

it's not clear whether this should be more or less accurate that
qrupdate's direct update using Givens rotations. But in any case, the
resulting Q matrix is from a standard QR factorization.

> My solution would be to transform this test into two tests with one
> protected by a testif HAVE_QRUPDATE which uses the lower tolerance and an
> ordinary block which uses a higher tolerance.  On the other hand, I thought
> I would post in case someone believes that the tolerance should be the same
> and there is another reason why this is failing.
>

I'm OK with this solution.

-- 
RNDr. Jaroslav Hajek, PhD
computing expert & GNU Octave developer
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz