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Re: Good eigenvalue/eigenvector test problems for eigs?


From: Quentin Spencer
Subject: Re: Good eigenvalue/eigenvector test problems for eigs?
Date: Sat, 23 Sep 2006 01:33:02 -0500
User-agent: Thunderbird 1.5.0.7 (Windows/20060909)

David Bateman wrote:
Sebastien Loisel wrote:
    This was my thinking as well, the the problem should be easy. By try the
    code I supplied under matlab and see what you get for "det(A - lamba *
    eye(n))".


for k=1:n foo(k)=det(B-ei(k)*eye(n)); end;
plot(foo);

for the complex matrices shows that the det is <= 10^-20.

S├ębastien Loisel


Ok, I have to kill my sysadmin... It seems he only partially fixed the
-ffloat-store problem with atlas on my machine, as octave works fine for
the first matrix if I disable atlas... Could someone on fedora or debian
check

n=200;
A = spdiags([ones(n,1),4*ones(n,1),-ones(n,1)],[-2,0,2],n,n);
d0=eig(A);
merr=0.
for i=1:200
  newerr = abs(det(A - d0(i)*eye(n)));
  if (newerr > merr)
     merr = newerr;
  endif
endfor
printf("Max error: %g\n", merr);

and see that you get an error around 1e-20 and not 1e+200 like I do with
my atlas. I'd like to know if this atlas issue exists elsewhere, and if
not point my sysadmin to a distrib that has the right fix..

On Fedora, running plain atlas (no sse or sse2) I get:
Max error: 8.60406e-21

Come to think of it, I think the eig function that is shipped in both the Debian and Fedora atlas packages is taken straight out of lapack because it's not provided directly by atlas. So, I think you're using the same eig function with or without atlas installed.

-Quentin


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