[petsc-dev] Tao unusable from complex??

[Stefano Zampini]

Il giorno Mer 12 Dic 2018, 20:04 Stefano Zampini <stefano.zampini at gmail.com>
ha scritto:

> My problems are all real.
>

And my mental issues all imaginary....


> I was just building a complex version of petsc and noticed these issue. As
> far as it is made clear (as it is) that Tao only supports real valued
> objective functions, there's no need to disable the solvers suite when
> petsc is compiled with complexes, since all the vectors and matrices used
> in TAO solvers will be zero in their  imaginary part. But probably there
> are other issues that I'm not considering?
>
> Il giorno Mer 12 Dic 2018, 18:46 Munson, Todd <tmunson at mcs.anl.gov> ha
> scritto:
>
>>
>> Yes; the optimization problems do not make sense if the objective
>> function is
>> from C^n to C, as there is not a natural ordering for complex numbers.  If
>> your objective is from C^n to R (and the constraints are from C^n to
>> R^m),
>> then the problem can be well defined.  Then we need to get into what bound
>> constraints mean, etc.
>>
>> One challenge from the optimization perspective is dealing with the
>> complex
>> vectors and creating complex Hessian approximations.  I think its
>> possible,
>> but has never been a priority.  If the bounds are on the magnitude of the
>> complex values, then we need appropriate nonlinear constraints to enforce
>> them.
>>
>> Todd.
>>
>> > On Dec 12, 2018, at 9:18 AM, Stefano Zampini via petsc-dev <
>> petsc-dev at mcs.anl.gov> wrote:
>> >
>> >
>> >
>> > Il giorno mer 12 dic 2018 alle ore 18:06 Dener, Alp <adener at anl.gov>
>> ha scritto:
>> > Hi Stefano,
>> >
>> > I can’t really speak to why the entirety of TAO is disabled in complex
>> builds. Todd can probably offer historical insight to the reason(s).
>> >
>> > However, we do have some methods in TAO that are not tested or
>> guaranteed to be correct for complex-valued objective functions.
>> >
>> > As far as I understands, TAO is clear in requiring  real objective
>> functions, having PetscReal on the prototype for the callback
>> >
>> > The limited-memory quasi-Newton codes, for instance, currently only
>> construct the approximate Hessian for the real part of the function and do
>> not generate step directions in the complex part. I also don’t know whether
>> any of the CG methods or line searches require any modifications to be
>> correct in complex builds either.
>> >
>> > In your itemized list, I agree that at minimum we should be supporting
>> #3 even if TAO itself does not work correctly for complex-valued functions.
>> >
>> > In the meantime, TAO can test real gradients or Hessians internally
>> with `-tao_test_gradient` or `-tao_test_hessian`. Or you can also call
>> `TaoTestHessian()` too. It’s a finite-difference test though, and not a
>> complex-step test.
>> >
>> > ——
>> > Alp Dener
>> > Argonne National Laboratory
>> > https://www.anl.gov/profile/alp-dener
>> >
>> >
>> >> On Dec 12, 2018, at 8:23 AM, Stefano Zampini via petsc-dev <
>> petsc-dev at mcs.anl.gov> wrote:
>> >>
>> >> If I compile PETSc with complex support, all of the TAO methods are
>> not registered.
>> >> Fare enough? not really, I can imagine at least three valid reasons to
>> use those
>> >>
>> >> 1) I want to check that my code works for complex builds, even if I
>> have pure real function evaluations. I may need complex support in other
>> parts or the code (not when using TAO), or I just want to be a diligent
>> PETSc developer
>> >> 2) I want to test REAL gradients or Hessians using built-in
>> capability, instead of writing my own
>> >> 3) I want to use the complex differentiation trick to compute REAL
>> gradients
>> >>
>> >> Last time I checked, at least option 2) was available; However, from
>> commit 5921d7004dad83427f45468906667b100d2e2b6e, no Tao methods are
>> registered when PETSC_USE_COMPLEX is defined, and code like the one below
>> fail at runtime:
>> >>
>> >> TaoCreate()
>> >> TaoSetFromOption()
>> >> TaoSetObjectiveRoutine()
>> >> TaoTestGradient()
>> >>
>> >> [0]PETSC ERROR: Unknown type. Check for miss-spelling or missing
>> package:
>> http://www.mcs.anl.gov/petsc/documentation/installation.html#external
>> >> [0]PETSC ERROR: Unable to find requested Tao type lmvm
>> >>
>> >>
>> >> --
>> >> Stefano
>> >
>> >
>> >
>> > --
>> > Stefano
>>
>>
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