Re: eigs compatibility

[John W. Eaton]

On 07/04/2013 03:03 PM, Daniel J Sebald wrote:

> I guess a sparse matrix of 2x2 isn't really all that sparse. Anyway, if
> it is important to have compatibility or just handle all dimensions, and
> it is only 2x2 and 1x1 that must be dealt with, rather than require a
> different math package be used to offer those results, it might be just
> as easy to write out the formulas for the solution to the eigenvalues.
> If one were to study the math, it probably breaks down into some simple
> inversion formulas which aren't so challenging until getting above 3x3.
> Why isn't there support in the sparse math package?

I have no clue why ARPACK has the limitation of providing at most N-2 
eigenvalues, but that's the way it works.  I'm not going to try to fix 
that problem.

Apparently Matlab's eigs function automatically handles the cases of 
computing N or N-1 eigenvalues.  I don't know how to do that other than 
by calling eig and sorting the results as needed.

I think Matlab does not issue a warning until N >= 8, then it says that 
you should use "eig (full (A))" or something similar, but still goes 
ahead and does the calculation anyway.  Would someone like to confirm 
that behavior?

I don't think it makes sense to try to write out the analyical solution 
for eigenvalues for N == 6, or 5, ...

I'm also not trying to defend this behavior.  I just want to make it 
work because a paying customer wants it to work.

jwe