[petsc-dev] Jacobian checking options

[Andrs, David]

On Mon, Jan 20, 2014 at 11:39 AM, Dmitry Karpeyev <karpeev at mcs.anl.gov>wrote:

> Forwarding this to petsc-dev because of (*) below.
>
> The behavior of -snes_check_jacobian, is, unfortunately, controlled by
> several options with different prefixes.
> This is because a mix of PETSc objects are involved.  In particular, we
> have -snes_test_xxx and -mat_fd_xxx determining the choice of the
> differencing parameter h in J(u)v ~ (F(u+hv) - F(u))/h.
> In particular, -mat_fd_type ds|wp controls the order of magnitude of h:
> (1) wp uses h = (1+||u||)*epsilon,
> (2) ds (default) uses h = u_j*epsilon, where j is the column of the
> Jacobian being computed (i.e., v = e_j).
>
> Furthermore, epsilon is controlled by -snes_test_err (and no programmatic
> option?).
> By default epsilon is the square root of the machine epsilon. However, if
> h ends up being too small (< 1e-16, which
> generally should only possible with -mat_fd_type ds), then h =
> 0.1*sign(u_j)*epsilon is used.
>
> (*) Maybe control of -snes_check_jacobian, -snes_test (do we need this to
> be separate from -snes_check_jacobian?  maybe this can be a suboption that
> causes an early exit from the solve?), and -mat_fd can be made more
> consistent?
>
> David, are you computing the Jacobian at u = 0? Then h = 0.1*epsilon, and
> the differenced residual should be h^2/h =
> (0.01*machine_epsilon)/(0.1*sqrt_machine_epsilon) and should evaluate to
> zero, it seems to me.
>
​Yes, I am.  Let me double check the code so that something else is not
kicking in...

--
David​



>
> Dmitry.
>
>
>
> On Mon, Jan 20, 2014 at 10:48 AM, Andrs, David <david.andrs at inl.gov>wrote:
>
>>  Is there a PETSc option to control the finite differencing parameter
>> for -snes_check_jacobian?
>>
>>  The reason why I ask is that if I have a term like: u^2 (u is the
>> velocity), then the FD value for this entry is something like 1e-5, but my
>> exact one is correctly zero. Then the difference from PETSc is rather
>> larger then 1e-8 (which PETSc suggest is the order of the difference it
>> should be).
>>
>>  --
>> David
>>
>>
>> On Sat, Jan 18, 2014 at 10:37 AM, Dmitry Karpeyev <karpeev at mcs.anl.gov>wrote:
>>
>>> You might know this already:
>>> Run the smallest (fewest dofs) case possible. Identify incorrect
>>> Jacobian entries. Trace them back to the faulty mesh nodes/variables. Debug
>>> the corresponding Jacobian code. -start_in_debugger (-start_in_debugger
>>> lldb on macos) can be helpful there.
>>>
>>> Let me know, if you need further help.
>>> Also let me know what test cases are good for testing the element-based
>>> FD Jacobian code that I am writing.
>>>
>>> Cheers,
>>> Dmitry
>>> On Jan 18, 2014 11:26 AM, "Zou (Non-US), Ling" <ling.zou at inl.gov> wrote:
>>>
>>>>  Dmitry, this tool is VERY helpful.
>>>> I showed you last time, the first several iterations were good as I
>>>> could check the Jacobians for the very first iteration. It then became
>>>> worse but I don't know why since I was not able to check the Jacobians.
>>>>
>>>>  With this new feature, I was able to find out in later steps the
>>>> hand-coded Jacobians are far away from the FD Jacobians for whatever reason
>>>> (bugs I bet). I am investigating my codes.
>>>>
>>>>  Best,
>>>>
>>>>  Ling
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> On Tue, Jan 14, 2014 at 5:10 PM, Dmitry Karpeyev <karpeev at mcs.anl.gov>wrote:
>>>>
>>>>> Sounds good.  Let me know, if you need help.
>>>>>
>>>>>
>>>>>  On Tue, Jan 14, 2014 at 5:02 PM, Zou (Non-US), Ling <ling.zou at inl.gov
>>>>> > wrote:
>>>>>
>>>>>>  Thank you Dmitry.
>>>>>> I will at first work to update my petsc version, which may need some
>>>>>> help from MOOSE team though.
>>>>>> I will then update you the status of the Jacobian status.
>>>>>>
>>>>>>  Best,
>>>>>>
>>>>>>  Ling
>>>>>>
>>>>>>
>>>>>>  On Tue, Jan 14, 2014 at 4:59 PM, Dmitry Karpeyev <
>>>>>> karpeev at mcs.anl.gov> wrote:
>>>>>>
>>>>>>> Hi Ling,
>>>>>>>
>>>>>>>  You can check Jacobian at EVERY SNES solve in petsc-3.4 using
>>>>>>> -snes_check_jacobian
>>>>>>> and view the difference between two Jacobians using
>>>>>>> -snes_check_jacobian_view.
>>>>>>>
>>>>>>>  Naturally, this is best done on the smallest problem possible, so
>>>>>>> that
>>>>>>> (a) the FD Jacobian calculation doesn't take too much time,
>>>>>>> (b) matrix viewing doesn't overwhelm the output.
>>>>>>>
>>>>>>>  MOOSE works with petsc-3.4.
>>>>>>>
>>>>>>>  Cheers,
>>>>>>> Dmitry.
>>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>
>>
>
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