Re: 3.2.3 RC2

[David Bateman]

Dmitri A. Sergatskov wrote:
> On Wed, Sep 2, 2009 at 1:29 PM, John W. Eaton<address@hidden> wrote:
>
>   
> > The test is:
> >
> >  n = 100;
> >  k = 7;
> >  a = 
> > sparse([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),0.4*n*ones(1,n),ones(1,n-2)]);
> >  [u,s,v] = svd(full(a));
> >  s = diag(s);
> >  [dum, idx] = sort(abs(s));
> >  s = s(idx);
> >  u = u(:,idx);
> >  v = v(:,idx);
> >  [u2,s2,v2,flag] = svds(a,k,0);
> >  s2 = diag(s2);
> >  assert(flag,!1);
> >  assert(s(k:-1:1), s2, 1e-10);
> >
> > If you run this repeatedly, do you see some successes and some
> > failures?  If it does fail, do you see that the first assert sometimes
> > fails, and other times it is the second?
> >     
>
>   
I'd always had problems with ARPACK with matrices with lots of 
eigenvalues very close to each other and this test case was deliberately 
create to make life hard for ARPACK in this manner. Basically it seems 
iterative eigensolvers don't seem to like cases like that.

This test matrix has 100 real eigenvalues between 38 and 40, and it used 
to run fine for me, but I too am now seeing the same errors.. I suspect 
minor changes in the optimizations of the compiler that mean that the 
eigensolver no longer converges.

Choose a sigma of zero was to ensure that the smallest eigenvalues were 
always found and choosing a sigma closer to the actual minimum 
eigenvalue  will improve the convergence. Changing the line

 [u2,s2,v2,flag] = svds(a,k,0);

to

 [u2,s2,v2,flag] = svds(a,k,38);

or even

 [u2,s2,v2,flag] = svds(a,k,0.1);

removes this issue for me. So if we just assume that this is a 
particularly nasty problem, that ARPACK has difficulties handling then 
I'd suggest making this change as a means of getting the tests to pass 
while still testing the functionality of svds

D.

> It is alway seems to be in the second, but I get different warnings from
> time to time.  Most often it is:
>
> warning: returning fewer singular values than requested
> warning: try increasing the value of sigma
> error: assert (s (k:-1:1),s2,1e-10) expected
>    38.034
>    38.034
>    38.015
>    38.015
>    38.004
>    38.004
> but got
>    38.060
>    38.034
>    38.034
>    38.015
>    38.015
>    38.004
>    38.004
> Dimensions don't match
>   
WIth this issue you get a warning, so I'd consider this less of a problem..

> but sometimes it is just:
>
> error: assert (s (k:-1:1),s2,1e-10) expected
>    38.060
>    38.060
>    38.034
>    38.034
>    38.015
>    38.015
>    38.004
> but got
>    38.060
>    38.034
>    38.034
>    38.015
>    38.015
>    38.004
>    38.004
> maximum absolute error 0.0263523 exceeds tolerance 1e-10
>   

This one you don't get a warning and you're missing one of the pair of 
the minimum eigenvalue..

D.

>   
> > I have not tried to debug the problem yet.
> >
> > David, I'm copying you because you wrote svds and might be able to see
> > the problem and perhaps a fix more quickly than I could.
> >
> > Thanks,
> >
> > jwe
> >
> >     
>
> Dmitri.
> --
>
>   



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