[petsc-users] Slepc: Nonlinear eigenvalue problem

[Manav Bhatia]

Really interesting! 

So this is a limitation of the algorithm and not the implementation. 

The challenge is that the eigenvalue solution  in my workflow is a small component of a large computation done with real numbers in an optimization problem. I could do the whole thing with complex numbers, but would be wasting a lot of cpu cycles doing that. 

Do you know if there is anyway to link to both real and complex versions of the library or switch between them at runtime? 

-Manav

Sent from my iPhone

> On Oct 23, 2018, at 9:42 AM, Jose E. Roman <jroman at dsic.upv.es> wrote:
> 
> 
> 
>> El 23 oct 2018, a las 16:10, Manav Bhatia <bhatiamanav at gmail.com> escribió:
>> 
>> Thanks for the clarification. 
>> 
>> Does this also apply to the standard non-hermitian eigenvalue problem? Do I need to compile with complex numbers if I want to capture the complex eigenvalues? Or does it work with real number support? 
> 
> No, linear eigenproblems (EPS) can be solved with real scalars for complex eigenvalues, but nonlinear eigenproblems (NEP) cannot.
> 
> Jose
> 
>> 
>> Thanks
>> Manav
>> 
>> Sent from my iPhone
>> 
>>> On Oct 23, 2018, at 3:43 AM, Jose E. Roman <jroman at dsic.upv.es> wrote:
>>> 
>>> If eigenvalues are complex then NLEIGS also needs to work in complex arithmetic because it needs a region of the complex plane containing the wanted eigenvalues. It seems that complex arithmetic is the only change in your problem.
>>> 
>>> Jose
>>> 
>>> 
>>>> El 22 oct 2018, a las 22:01, Manav Bhatia <bhatiamanav at gmail.com> escribió:
>>>> 
>>>> Thanks, Jose. 
>>>> 
>>>> How difficult would it be to add the support for the general case (if at all possible)? 
>>>> 
>>>> My eigenvalue problem is of the form shown in the attachment. Beta is the eigenvalue and X_s^\Delta is the eigenvector. While some of the matrices are known, others are defined only as matrix vector products. 
>>>> 
>>>> I am interested in eigenvalues with the largest real part. I expect to find complex eigenvalues, although for a small subset of cases these will be real. 
>>>> 
>>>> What is your recommendation for attacking this problem with the nonlinear eigenvalue support in Slepc? 
>>>> 
>>>> Would appreciate your guidance. 
>>>> 
>>>> Regards,
>>>> Manav
>>>> 
>>>> <PastedGraphic-1.pdf>
>>>> 
>>>> 
>>>>> On Oct 22, 2018, at 2:40 PM, Jose E. Roman <jroman at dsic.upv.es> wrote:
>>>>> 
>>>>> 
>>>>> 
>>>>>> El 22 oct 2018, a las 21:05, Manav Bhatia <bhatiamanav at gmail.com> escribió:
>>>>>> 
>>>>>> Hi, 
>>>>>> 
>>>>>> I am exploring the nonlinear eigenvalue problem solver in Slepc. 
>>>>>> 
>>>>>> From the notes in "Sec 6.4: Retrieving the Solution”, it appears that if I expect to find complex eigenpairs then I must compile the library (and Petsc) with complex scalars. Is that correct? 
>>>>>> 
>>>>>> Is there a way to include support for complex eigenpairs in a library complied with real scalars? 
>>>>>> 
>>>>>> Regards,
>>>>>> Manav
>>>>>> 
>>>>>> 
>>>>> 
>>>>> Currently, the only combination that supports complex eigenpairs with real scalars is the split form for the nonlinear function with the NLEIGS solver.
>>>>> 
>>>>> Jose
>>>> 
>>> 
>