[petsc-users] Auto sparsity detection?

[Matthew Knepley]

On Thu, Jan 16, 2025 at 10:43 PM Zou, Ling <lzou at anl.gov> wrote:

> Thank you, Matt.
>
> Seems that at least the matrix coloring part I am following the ‘best
> practice’.
>

Yes, for FD approximations of the Jacobian.

If you have a stencil operation (like FEM or FVM), then AD can be very
useful because you
only have to differentiate the kernel to get the Jacobian kernel.

  Thanks,

     Matt


>
>
> -Ling
>
>
>
> *From: *Matthew Knepley <knepley at gmail.com>
> *Date: *Thursday, January 16, 2025 at 9:01 PM
> *To: *Zou, Ling <lzou at anl.gov>
> *Cc: *petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> *Subject: *Re: [petsc-users] Auto sparsity detection?
>
> On Thu, Jan 16, 2025 at 9: 50 PM Zou, Ling via petsc-users <petsc-users@
> mcs. anl. gov> wrote: Hi all, Does PETSc has some automatic matrix
> sparsity detection algorithm available? Something like: https: //docs.
> sciml. ai/NonlinearSolve/stable/basics/sparsity_detection/
>
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> On Thu, Jan 16, 2025 at 9:50 PM Zou, Ling via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
> Hi all,
>
>
>
> Does PETSc has some automatic matrix sparsity detection algorithm
> available?
>
> Something like:
> https://urldefense.us/v3/__https://docs.sciml.ai/NonlinearSolve/stable/basics/sparsity_detection/__;!!G_uCfscf7eWS!cWyHnKq-Gzasz3ooIUAgTl0RTGrzg0fW8jwVOi0AHE_Ydv4dnayXiG06EPQYvp6guWhXYTv8DMnOu2Z-6riZ$ 
> <https://urldefense.us/v3/__https:/docs.sciml.ai/NonlinearSolve/stable/basics/sparsity_detection/__;!!G_uCfscf7eWS!ccEx6zmuNrVADqtN50hO2N0k4Qs-A70nztAjMLu-JElnjhK5w84BpYC8CAINd6KihSxaS2rx_LgpqUVM49U$>
>
>
>
> Sparsity detection would rely on introspection of the user code for
> ComputeFunction(), which is not
>
> possible in C (unless you were to code up your evaluation in some symbolic
> framework).
>
>
>
> The background is that I use finite differencing plus matrix coloring to
> (efficiently) get the Jacobian.
>
> For the matrix coloring part, I color the matrix based on mesh
> connectivity and variable dependencies, which is not bad, but just try to
> be lazy to even eliminating this part.
>
>
>
> This is how the automatic frameworks also work. This is how we compute the
> sparsity pattern for PetscFE and PetscFV.
>
>
>
> A related but different question, how much does PETSc support automatic
> differentiation?
>
> I see some old paper:
>
> https://ftp.mcs.anl.gov/pub/tech_reports/reports/P922.pdf
>
> and discussion in the roadmap:
>
> https://urldefense.us/v3/__https://petsc.org/release/community/roadmap/__;!!G_uCfscf7eWS!cWyHnKq-Gzasz3ooIUAgTl0RTGrzg0fW8jwVOi0AHE_Ydv4dnayXiG06EPQYvp6guWhXYTv8DMnOu9i64gyw$ 
> <https://urldefense.us/v3/__https:/petsc.org/release/community/roadmap/__;!!G_uCfscf7eWS!ccEx6zmuNrVADqtN50hO2N0k4Qs-A70nztAjMLu-JElnjhK5w84BpYC8CAINd6KihSxaS2rx_Lgpw6v6hKE$>
>
> I am thinking that if AD works so I don’t even need to do finite
> differencing Jacobian, or have it as another option.
>
>
>
> Other people understand that better than I do.
>
>
>
>   Thanks,
>
>
>
>      Matt
>
>
>
> Best,
>
>
>
> -Ling
>
>
>
>
> --
>
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
>
>
> https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!cWyHnKq-Gzasz3ooIUAgTl0RTGrzg0fW8jwVOi0AHE_Ydv4dnayXiG06EPQYvp6guWhXYTv8DMnOu7qfipNL$ 
> <https://urldefense.us/v3/__http:/www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!d-7O5V0pNvm_fDSKhNk_ilXP0jG-_MBnectBJ0BfVPOSzARXvYWAahGyRNf1cKCh9dJKEiFt2caV$>
>


-- 
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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!cWyHnKq-Gzasz3ooIUAgTl0RTGrzg0fW8jwVOi0AHE_Ydv4dnayXiG06EPQYvp6guWhXYTv8DMnOu7qfipNL$  <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!cWyHnKq-Gzasz3ooIUAgTl0RTGrzg0fW8jwVOi0AHE_Ydv4dnayXiG06EPQYvp6guWhXYTv8DMnOu7xNNzJR$ >
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