(Petsc SNES) Reevaluating Function right after evaluating the Jacobian

Edson Tadeu e.tadeu at gmail.com
Mon Dec 1 14:04:56 CST 2008


  Thanks for the reply;

On Mon, Dec 1, 2008 at 4:56 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

> On Dec 1, 2008, at 12:28 PM, Edson Tadeu wrote:
>   Hi,
>>   I'm solving non-linear problems with Line Search, and sometimes I need
>> to change an entire row of the Jacobian together with the corresponding
>> element in the Function, but I only know which rows/elements need to be
>> changed when I'm computing the Jacobian. So, what I'd like to know first is:
>   Maybe if you explain why you need to "change an entire row of the
> Jacobian together with the corresponding element in the Function" we could
> come up
> with some suggestions on how to proceed.

It's because, depending on some conditions, I need to make some change of
variables in the original equations, otherwise the Jacobian will have linear
dependent rows. For example, I need to tell that x(4) = 1.0-x(3) (instead of
the original equation for x(4)). I would do it by changing the Jacobian like

J(4,3) = 1; J(4,4) = 1; all other columns of row 4 of J are zero. F(4) = 0.

This way, I would have delta_x(4) = -delta_x(3). I've solved this now by
directly changing the delta solution vector (delta_x) in the pre check
phase... it seems to be working, but it doesn't seem to be the right way, I
don't know...

>>  1) Am I allowed to change the Function vector from inside FormJacobian?
>> (I've looked inside SNESSolve_LS, and it seems that this is not allowed,
>> because "fnorm" is evaluated before SNESComputeJacobian, and if I change F
>> inside FormJacobian, fnorm would be wrong).
>>  or
>>  2) Am I allowed to change the Function vector from PreCheck routine?
>>  If none of that is allowed, another solution that I thought was to
>> compute the Jacobian while computing the Function. The FAQ says that "You
>> are free to have your 'FormFunction' compute as much of the Jacobian at that
>> point as you like, keep the information in the user context (the final
>> argument to FormFunction and FormJacobian) and then retreive the information
>> in your FormJacobian() function". The problem is that FormFunction is called
>> many times more than FormJacobian, and Jacobian calculation is slow, so:
>>  3) Is there any way to know when I should really recompute the Jacobian
>> from inside FormFunction? (I don't think so, but...)
>  No. But if you do not use any line search at all then each function
> evaluation will have an associated Jacobian so you can compute them
> together. (Of course you lose the globalization of the line search so SNES
> may not converge).  You can turn off all line searches with -snes_ls basic
> from the command line or from the code
> SNESLineSearchSet(snes,SNESLineSeachNo,PETSC_NULL);
>   Barry

 Ok, but the whole reason that I'm using SNES is to speed up my computations
by using the Line Search algorithms (or maybe Trust Region). I had coded an
algorithm before that manually computed using full steps, and it were
working, but were slow!

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