(Petsc SNES) Reevaluating Function right after evaluating the Jacobian

[Edson Tadeu]

 Barry,

It's not that I'm changing the definition of the function... the problem is
that the function have some "ifs" on it. This comes ultimately from the
physics of the problem... there is some change of dependency between the
variables, like this:

A is an unknown, B is an unknown, C is dependent (not on the system):

   C = 1 - A - B + delta_C

(where delta_C is also dependent from some other variables).

But if C == 0 and delta_C == 0, then the dependency changes:

A is an unknown, but B is now dependent:

   B = 1 - A

This is why, when this happens, the Jacobian row of B becomes linearly
dependent with the row of A. So, actually, B should be taken out of the
system! [See that there is a real change here, because now the derivative
dB/dA == -1, but before, A and B were unrelated.]

Well... this scheme was working before using full Newton steps... ;)

But thanks for the tip, I'll also try to treat accordingly the null space
that appears with the linear dependence. Hmm... but by removing the null
space of J, I'll be effectively removing the row corresponding to the B
unknown... so, I would need to define delta_B = -delta_A later, anyway,
wouldn't I (or maybe PETSc would define it automatically, given the basis
vector [1 -1 0 0 0...] for the null space)?

  Thanks,
Edson


On Mon, Dec 1, 2008 at 6:29 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
>   The mathematician side of me cringes (actually every side of me cringes)
> when I read this.
>
>   You are changing the definition of the function you are finding the zero
> of WHILE you are
> finding the zero of it. Yuck. How do you know what you get at the end is
> anything but garbage?
>
>  It seems to me that either
> 1) there is a bug in your Jacobian or
> 2) near (or at) the solution (when F(x) = 0) the Jacobian is singular
>
> For 1) you can run with -snes_ls_type test to do some simple tests on the
> Jacobian.
>
> For 2) I submit that what you really want to do (instead of changing the
> "Jacobian" to something
> that is not the Jacobian) is to properly solve the singular linear system.
> How to do this
> depends on the nature of the null space of the Jacobian and if you have a
> handle on what
> the null space is). In PETSc the simplest thing to try (sequentially) is
> -pc_type lu -pc_factor_shift_nonzero
> and see what happens.
>
>   Barry
>
>
>
>
> On Dec 1, 2008, at 2:04 PM, Edson Tadeu wrote:
>
>  Barry,
>>
>>  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
>> this:
>>
>> 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!
>>
>>  Thanks,
>> Edson
>>
>>
>
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