[petsc-users] Slepc: Nonlinear eigenvalue problem

[Jose E. Roman]

> 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
>>> 
>>