[SciPy-User] why is GMRES slow ? [py=3.4.3 numpy=1.10 scipy=0.16]

[zimon toutoune]

On 2 December 2015 at 12:26, Pauli Virtanen <pav at iki.fi> wrote:
> Tue, 01 Dec 2015 21:48:27 -0300, zimon toutoune kirjoitti:
>> I am looking for an explanation why GMRes [scipy.sparse.linalg.gmres]
>> running 'Niter' iterations is much more slower than applying 'Niter'
>> times 'matvec' (or 'dot').
>
> Each gmres outer iteration requires ~ `restart` matrix-vector products.
> restart=None means the default value, restart=20.
> The returned `info` contains the number of outer iterations.

Sorry for the naive question.
Now completely clear.

This means that by default gmres is not gmres(full).
And the docstring of 'info' is a bit disturbing.
So clearly the total of number of iterations is always: Niter = maxiter*restart.

However, the only way to use gmres(full) is to set: 'maxiter=1' and
'restart=val'.
Which is also a bit confusing.
The matlab behavior seems clearer, no ?
 - if restart==None then gmres does not restart.
 - if maxiter!=None and restart==None then the maximum number of total
iterations is maxiter (instead of restart*maxiter).

Last, why not collect more information in info, as the residual
history, the number of outer iterations, the number of inner
iteration, etc. ?
Is there a reason ? or just because nobody has added it ?

Thanks for your times and your quick and clear answer.

All the best,
simon