[petsc-users] Question about residue norm in PETSc

[Matthew Knepley]

On Sun, Jul 2, 2023 at 7:53 AM 王赫萌 <wanghemeng at 163.com> wrote:

> Thanks for your reply!
> So sorry that I made a mistake in the description.
> I set the tolerances by:
> PetscCall(KSPSetTolerances(ksp, 1e-12, DBL_MIN, PETSC_DEFAULT,
> PETSC_DEFAULT));
> and got (by passing `-ksp_norm_type unpreconditioned
> -ksp_monitor_true_residual`)
> 74 KSP unpreconditioned resid norm 7.256655641876e-08 true resid norm
> 7.256655641876e-08 ||r(i)||/||b|| 9.975738158726e-13
> I'm wondering why the ` ||r(i)||/||b||` is different with mine which
> calculated by:
> ```
>   PetscCall(VecNorm(b, NORM_2, &norm_b)); // (main.c, line 74) (which is
> 72743.044439)
>   PetscCall(VecDuplicate(b, &u)); // (main.c, line 105)
>   PetscCall(MatMult(A, x, u));
>   PetscCall(VecAXPY(b, -1.0, u));
>   PetscCall(VecNorm(b, NORM_2, &norm_delta)); // (which is 0.039608)
> ```
> and (norm_delta) / (norm_b) = 5.44496e-07 which is higher and different
> with the rtol I set (1e-12).
> Sorry again for the waste of your time. I would really appreciated if you
> could help me again!
>

1) 7.256655641876e-08 / 72743.044439 = 9.975738158726e-13 so ||r_i||/||b||
is correct in the output

2) You are asking why you calculate a different residual? I will have to
run your code.

  Thanks,

     Matt


> Best regards!
> Hemeng Wang
>
>
> ---- Replied Message ----
> From Matthew Knepley<knepley at gmail.com> <knepley at gmail.com>
> Date 7/2/2023 18:51
> To 王赫萌<wanghemeng at 163.com> <wanghemeng at 163.com>
> Cc petsc-users at mcs.anl.gov<petsc-users at mcs.anl.gov>
> <petsc-users at mcs.anl.gov>
> Subject Re: [petsc-users] Question about residue norm in PETSc
> On Sun, Jul 2, 2023 at 2:24 AM 王赫萌 <wanghemeng at 163.com> wrote:
>
>> Dear PETSc Team,
>>
>> Sorry to bother! My name is Hemeng Wang, and I am currently learning the
>> use of PETSc software package. I am confused while calculating the norm of
>> residue.
>>
>> I calculated residue norm by myself with:
>> ```
>>   PetscCall(VecNorm(b, NORM_2, &norm_b)); // (main.c, line 74)
>>
>>   PetscCall(VecDuplicate(b, &u)); // (main.c, line 105)
>>   PetscCall(MatMult(A, x, u));
>>   PetscCall(VecAXPY(b, -1.0, u));
>>   PetscCall(VecNorm(b, NORM_2, &norm_delta));
>> ```
>> and check the (norm_delta) / (norm_b). It seems not the `atol` which set
>> by `KSPSetTolerances()`.
>> (I set atol as 1e-12, but got 5e-7 finally)
>> (options:  -ksp_type cg -pc_type gamg -ksp_converged_reason
>> -ksp_norm_type unpreconditioned -ksp_monitor_true_residual)
>>
>
> If you are using the default convergence test, there is an absolute
> tolerance (atol) _and_ a relative tolerance (rtol). It seems likely you hit
> the relative tolerance. You can check this using
>
>   -ksp_converged_reason
>
> You could make rtol really small if you want to just see the atol
>
>   -ksp_rtol 1e-20
>
>   Thanks,
>
>      Matt
>
>
>> I also check the soure code of `KSPSolve_CG` in
>> `petsc/src/ksp/ksp/impls/cg/cg.c`. And could not figure out where is the
>> difference.
>>
>> I will really really appreciated if someone can explain the calculation
>> of `resid norm` in petsc. And where is my mistake.
>>
>> To provide you with more context, here are the source code about my
>> implementation. And the output of my test.
>>
>> main.c
>> Main code of my program
>>
>> mmio.h  mmloader.h
>> Headers for matrix read
>>
>> Makefile
>> For compiling, same as sample provided
>>
>> task.sh
>> A script for running program in `slurm`
>>
>> slurm-4803840.out
>> Output of my test
>>
>> Thank you very much for your time and attention. I greatly appreciate
>> your support and look forward to hearing from you soon.
>> Best regards,
>> Hemeng Wang
>>
>>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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