I now see what is happening. In the expression of the paper the antishift has
different sign compared to the expression used in SLEPc (see the users manual):
(A-sigma*B)^{-1}*(A+nu*B)x = \theta x
So nu=-sigma is a forbidden value, otherwise both factors cancel out (I will
fix the interface so that this is catched).
In your case you should do -eps_target -1 -st_cayley_antishift -1
Jose
> El 27 sept 2019, a las 13:54, Michael Werner <[email protected]> escribió:
>
> Yes, with sinvert its working. And using -eps_target instead of
> -st_shift didn't change anything.
>
> I also just sent you the matrices for reproduction of the issue.
>
> Michael
>
> Am 27.09.19 um 13:32 schrieb Jose E. Roman:
>> Try setting -eps_target -1 instead of -st_shift -1
>> Does sinvert work with target -1?
>> Can you send me the matrices so that I can reproduce the issue?
>>
>> Jose
>>
>>
>>> El 27 sept 2019, a las 13:11, Michael Werner <[email protected]>
>>> escribió:
>>>
>>> Thank you for the link to the paper, it's quite interesting and pretty
>>> close to what I'm doing. I'm currently also using the "inexact" approach
>>> for my application, and in general it works, as long as the ksp
>>> tolerance is low enough. However, I was hoping to speed up convergence
>>> towards the "interesting" eigenvalues by using Cayley.
>>>
>>> Now as a test I tried to follow the approach from your paper, choosing
>>> mu = -sigma, and mu in the order of magnitude of the imaginary part of
>>> the most amplified eigenvalue. I know the most amplified eigenvalue for
>>> my problem is -0.0398+0.724i, so I tried running SLEPc with the
>>> following settings:
>>> -st_type cayley
>>> -st_shift -1
>>> -st_cayley_antishift 1
>>>
>>> But I never get the correct eigenvalue, instead SLEPc returns only the
>>> value of st_shift:
>>> [0] Number of iterations of the method: 1
>>> [0] Solution method: krylovschur
>>> [0] Number of requested eigenvalues: 1
>>> [0] Stopping condition: tol=1e-08, maxit=19382
>>> [0] Number of converged eigenpairs: 16
>>> [0]
>>> [0] k ||Ax-kx||/||kx||
>>> [0] ----------------- ------------------
>>> [0] -1.000000 0.0281754
>>> [0] -1.000000 0.0286815
>>> [0] -1.000000 0.0109186
>>> [0] -1.000000 0.140883
>>> [0] -1.000000 0.203036
>>> [0] -1.000000 0.00801616
>>> [0] -1.000000 0.0526871
>>> [0] -1.000000 0.022244
>>> [0] -1.000000 0.0182197
>>> [0] -1.000000 0.0107924
>>> [0] -1.000000 0.00963378
>>> [0] -1.000000 0.0239422
>>> [0] -1.000000 0.00472435
>>> [0] -1.000000 0.00607732
>>> [0] -1.000000 0.0124056
>>> [0] -1.000000 0.00557715
>>>
>>> Also, it doesn't matter if I'm using exact or inexact solves. Changing
>>> the values of shift and antishift also doesn't change the behaviour. Do
>>> I need to make additional adjustments to get cayley to work?
>>>
>>> Best regards,
>>> Michael
>>>
>>>
>>>
>>> Am 25.09.19 um 17:21 schrieb Jose E. Roman:
>>>>> El 25 sept 2019, a las 16:18, Michael Werner via petsc-users
>>>>> <[email protected]> escribió:
>>>>>
>>>>> Hello,
>>>>>
>>>>> I'm looking for advice on how to set shift and antishift for the cayley
>>>>> spectral transformation. So far I've been using sinvert to find the
>>>>> eigenvalues with the smallest real part (but possibly large imaginary
>>>>> part). For this, I use the following options:
>>>>> -st_type sinvert
>>>>> -eps_target -0.05
>>>>> -eps_target_real
>>>>>
>>>>> With sinvert, it is easy to understand how to chose the target, but for
>>>>> Cayley I'm not sure how to set shift and antishift. What is the
>>>>> mathematical meaning of the antishift?
>>>>>
>>>>> Best regards,
>>>>> Michael Werner
>>>> In exact arithmetic, both shift-and-invert and Cayley build the same
>>>> Krylov subspace, so no difference. If the linear solves are computed
>>>> "inexactly" (iterative solver) then Cayley may have some advantage, but it
>>>> depends on the application. Also, iterative solvers usually are not robust
>>>> enough in this context. You can see the discussion here
>>>> https://doi.org/10.1108/09615530410544328
>>>>
>>>> Jose
>>>>
>
>
>
>
