debug output of eigs?

[David Bateman]

Dear All,

In implementing eigs and trying to make it matlab compatible I've run 
across an issue with the debugging output when opts.disp > 0 (default 
value of 1 in matlab). The problem is that ARPACK returns to the calling 
function several times to ask for operations like A*x to be done, but a 
single iteration as defined by ARPACK is when its internal 
representation of the Ritz values are updated, and this counter is not 
returned and several A*x calls are needed for a single iteration. 
However, it is this internal counter that matlab uses for display such as

Iteration 27: a few Ritz values of the 20-by-20 matrix:
   5.9659
   5.9848
   5.9848
   5.9962
   5.9962

and so matlab certainly has a modified version of ARPACK that they use 
for this purpose. We have several choices.

1) Include ARPACK into the octave source tree and make the necessary 
modifications to return the iteration counter
  in the same manner as matlab.
2) Print out each time we come back from ARPACK. This means that the 
iteration count is meaningless and that the Ritz values will not change 
at  each nominal iteration.
3) Try to fool ARPACK into giving information about the iteration 
counter by setting the output value workl[ipntr(5)-1]  to a NaN, and 
then test when it isn't a NaN for printing. There are several downsides 
to this. If ARPACK terminates on an iteration, the returned eigenvalues 
will contain this NaN, so the termination needs to check for the NaN, 
and without in depth understanding of the ARPACK code there is no 
guarantee that this value is not in fact used in some cases and so there 
is a some potential of adding a difficult to find bug to eigs
4) Store a local copy of the Ritz values and consider that there is an 
iteration when these values have changed. This is rather messy, require 
an overhead in terms of testing for equality of the Ritz values and 
storing them, but it will work.
5) Ignore the whole mess of the matlab debugging arguments and just 
don't display these messages

What is the preferred solution, of people on this list? In any case 
apart of this and a couple of issues with the general eigenvalue 
equation (when B is set) I now have most of eigs working...

Cheers
David

--
David Bateman                                address@hidden
Motorola Labs - Paris                        +33 1 69 35 48 04 (Ph) 
Parc Les Algorithmes, Commune de St Aubin    +33 1 69 35 77 01 (Fax) 
91193 Gif-Sur-Yvette FRANCE

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