Re: new snapshot?

[Michael D. Godfrey]

On 2/28/10 6:19 AM, David Bateman wrote:
> Michael D. Godfrey wrote:
> > On 2/26/10 2:28 PM, John W. Eaton wrote:
> > > On 26-Feb-2010, Michael D. Godfrey wrote:
> > >
> > > | On 2/26/10 10:15 AM, Jaroslav Hajek wrote:
> > > | > Are you sure? This is exactly the opposite of what I get. 
> > Sometimes
> > > | > the assert fails with
> > > | >
> > > | > !!!!! test failed
> > > | > 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
> > > | >
> > > | > and the latter result is correct, AFAIK.
> > > | >
> > > | > > | The latter result is s2  in the test.  This is what I get 
> > too.  s2, > | computed from:
> > > | [u2,s2,v2,flag] = svds(a,k,0);
> > > | s2 = diag(s2);
> > > | is correct.  It is the "expected" vector that is wrong.  This 
> > comes from:
> > > | 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);
> > > | > | Agree?
> > >
> > > The problem is with svds, not svd on the full matrix.  I should have
> > > put the arguments to assert in the opposite order.
> > >
> > > Sorry for the confusion,
> > >
> > > jwe
> > >   A bit more reading of svds.m finds that if sigma=0, it calls eigs 
> > requesting 2*k
> > eigenvalues instead of k.  This helps to explain things, but still 
> > does not isolate
> > exactly why in one case eigs returns extra eigenvalues but in another 
> > context,
> > with the same arguments, it returns k eigenvalues.
> >
> > In any case, it now appears that my suggested change of sigma from 0 
> > to 0.05
> > is appropriate in order to prevent "extra" eigenvalues.
> >
> > Michael
> The function svds creates the matrix [0, b; b', 0] and finds the 
> eigenvalues of this matrix and the positive eigenvalues of this matrix 
> are the singular values of b. Note that the eigenvalues of [0,b;b',0] 
> are symmetric about 0 and so if we want the singular values with sigma 
> of zero then we have to call eigs with 2*k and ignore the negative 
> values. In fact with small values of sigma, one of the negative 
> eigenvalues of [0,b;b',0] might be closer to sigma than the k singular 
> values of b that are desired. The only way to avoid this issue would 
> be to always call eigs with 2*k but at the cost of at least two times 
> more iterations in eigs.. When writing svds I chose speed over a 
> guarantee that svds would return the right value as the case described 
> should be relatively rare in real life.. This however doesn't explain 
> the original issue..
>
> D.
>
>
> --
> David Bateman address@hidden
> 35 rue Gambetta                              +33 1 46 04 02 18 (Home)
> 92100 Boulogne-Billancourt FRANCE            +33 6 72 01 06 33 (Mob)
I understand this and agree with your last statement.  It would be good 
to try to resolve the
underlying inconsistency.   However,  in the test that is failing, use 
of a small non-zero sigma
in the call to svds is not unreasonable for the reason that you 
described in the code.

Michael