Ah, yes, I didn't notice the difference. Now its working. Thank you!
Michael
Am 27.09.19 um 15:54 schrieb Jose E. Roman:
> 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
>>>>>
>>
>>
>>
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