[petsc-users] Questions about matrix permutation

[Mark Adams]

On Wed, Oct 26, 2022 at 11:00 PM 晓峰 何 <tlanyan at hotmail.com> wrote:

> Dear developers,
>
> To avoid zero pivot error in IC/ILU preconditioners,  I plan to permute
> matrix before solving the linear system. I referred example ex10(
> https://petsc.org/main/src/ksp/ksp/tutorials/ex10.c.html) and ex18(
> https://petsc.org/main/src/ksp/ksp/tutorials/ex18.c.html), and was
> confused that why vector b is permuted by column permutation index set:
>
> // in ex18.c
>
> 174:   if (permute) {175:     Mat <https://petsc.org/main/docs/manualpages/Mat/Mat/> Aperm;176:     MatGetOrdering <https://petsc.org/main/docs/manualpages/MatOrderings/MatGetOrdering/>(A, ordering, &rowperm, &colperm);177:     MatPermute <https://petsc.org/main/docs/manualpages/Mat/MatPermute/>(A, rowperm, colperm, &Aperm);178:     VecPermute <https://petsc.org/main/docs/manualpages/Vec/VecPermute/>(b, colperm, PETSC_FALSE <https://petsc.org/main/docs/manualpages/Sys/PETSC_FALSE/>);179:     MatDestroy <https://petsc.org/main/docs/manualpages/Mat/MatDestroy/>(&A);180:     A = Aperm; /* Replace original operator with permuted version */181:   }
>
> As far as I understand, vector b should be only  affected by permuting
> rows in matrix A, instead of column permutation. How to understand that
> permuting vector b with column permutation index set of matrix A?
>
>
I get confused by this also. I just test it. Try one and if thats wrong,
its the other!
As I recall a permutation vector has the place where the equation sould _go_

Another question is why  MatReorderForNonzeroDiagonal function only works
> for type MATSEQAIJ? If it works for other matrix types, then this function
> will meet my requirement.
>
>
It has not been implemented. You could do this, clone the MATSEQAIJ one for
the matrix type that you want.
See https://petsc.org/release/developers/contributing/  for instructions on
contributing to PETSc.

Thanks,
Mark


>
> Thanks,
>
> Xiaofeng
>
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