Re: variability in a test for eigs.cc

[Ben Abbott]

On Mar 28, 2010, at 7:01 PM, David Bateman wrote:

> Ben Abbott wrote:
>> On Mar 28, 2010, at 4:07 PM, Michael D Godfrey wrote:
>> 
>>  
>>> On 03/28/2010 12:42 PM, Ben Abbott wrote:
>>>    
>>>> Thanks. Perhaps the right thing to do is to loop through the test 3 times 
>>>> and check that at least one result is less than 1e-11.
>>>> 
>>>> If there is no objection, I'll try to push that change later today.
>>>> 
>>>> Ben
>>>>        
>>> I think it would be a good idea to let whoever has had responsibility
>>> for this algorithm to take a look and determine a few things like: what
>>> inputs produce largest errors and can anything be done about improving
>>> accuracy.
>>> 
>>> Michael
>>>    
>> 
>> ok. It looks to me like David introduced these tests.
>> 
>> I've cc'd him.
>> 
>> David, do you have any suggestion for how to deal with the variability in 
>> the eigs.cc test?
>> 
>> The start of this thread is at the link below.
>> 
>>      
>> https://www-old.cae.wisc.edu/pipermail/octave-maintainers/2010-March/015680.html
>> 
>> Ben
>> 
> 
> This test as you've written it shouldn't use 'li'. The matrix is hermitian 
> and the eigenvalues as real and so looking for the largest imaginary part of 
> the eigenvalues will just give you noise. You should use 'lr' instead in this 
> case.
> 
> D.

David thanks for responding so quickly. If I infer correctly this test was 
intended to use "li".

        http://hg.savannah.gnu.org/hgweb/octave/rev/654bcfb937bf

How may the test below be rewritten so that a stable result is obtained?

 %!test
 %! [v1,d1] = eigs(A, k, 'li');
 %! d1 = diag(d1);
 %! for i=1:k
 %!  assert(max(abs((A - d1(i)*speye(n))*v1(:,i))),0.,1e-12)
 %! endfor

Ben