Re: debug output of eigs?

[David Bateman]

Keith Goodman wrote:

> On 5/18/05, David Bateman <address@hidden> wrote:
>  
>
> > 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).
> >    
>
> For what it's worth, I always set opts.disp to zero since I'm calling
> eigs hundreds of time and since I don't understand what the output
> means anyway.
>
> My typical call is
>
> OPTS.disp = 0;
> [eigvec,eigval] = eigs(x,n,'LM',OPTS);
>
>  
On another point was is the best way to treat the ordering of the 
eigenvalues returned from eigs. Matlab seems to be inconsistent here are 
depending on the type of matrix and the value of sigma does different 
things. The returned eigenvalues from the matlab eigs function are 
ordered in the fashion

Sigma        Real Postive Definite               Complex or unsymmetric

"lm"             D                                    abs D
"sm"             D                                    abs I
"la"             D                                    -
"sa"             I                                    -
"lr"             -                                    real D
"sr"             -                                    real I
"li"             -                                    imag D
"si"             -                                    imag I
"be"             I                                    -
value            D                                    abs (eigenvalue - value) I


where D is for monotonically decreasing and I for montonically 
increasing. So there are inconsistence is the ordering in most of the 
above cases, and they also down correspond to the ordering given back by 
ARPACK itself. Is it important to respect the same ordering as matlab? 
Should I define a specific ordering (eg. abs value always monotonically 
decreasing), or should I just accept the output of ARPACK as it is 
given? If I don't respect the matlab ordering, the problem is something like

e = eigs (A);

% Get largest eigenvalue
emax  = e(1);

won't work consistently.... Then again doing something like

e = eigs (A,5,'sm')
emin = e(1);

in matlab will work or not depending on wether A is positive definite or 
not... To me this seems like a misfeature in matlab, but before I 
pronounce it as that, and just do my own things, some feedback would be 
helpful..

Regards
David

--
David Bateman                                address@hidden
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