[petsc-users] question about MatSetLocalToGlobalMapping

[Matthew Knepley]

On Thu, Apr 20, 2023 at 6:13 AM Karthikeyan Chockalingam - STFC UKRI via
petsc-users <petsc-users at mcs.anl.gov> wrote:

> Hello,
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> I created a new thread, thought would it be more appropriate (and is a
> continuation of my previous post). I want to construct the below K matrix
> (which is composed of submatrices)
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> K = [A P^T
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>        P   0]
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> Where K is of type MatMPIAIJ. I first constructed the top left [A] using
> MatSetValues().
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> Now, I would like to construct the bottom left [p] and top right [p^T] using
> MatSetValuesLocal().
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> To use  MatSetValuesLocal(),  I first have to create a local-to-global
> mapping using ISLocalToGlobalMappingCreate. I have created two mapping
> row_mapping and column_mapping.
>

I do not understand why they are not the same map. Maybe I was unclear
before. It looks like you have two fields, say phi and lambda, where lambda
is a Lagrange multiplier imposing some constraint. Then you get a saddle
point like this. You can imagine matrices

  (phi, phi)        --> A
  (phi, lambda) --> P^T
  (lambda, phi) --> P

So you make a L2G map for the phi field and the lambda field. Oh, you are
calling them row and col map, but they are my phi and lambda
maps. I do not like the row and col names since in P they reverse.


> Q1) At what point should I declare MatSetLocalToGlobalMapping – is it
> just before I use MatSetValuesLocal()?
>

Okay, it is good you are asking this because my thinking was somewhat
confused. I think the precise steps are:

  1) Create the large saddle point matrix K

    1a) We must call
https://petsc.org/main/manualpages/Mat/MatSetLocalToGlobalMapping/ on it.
In the simplest case, this just maps
           the local rows numbers [0, Nrows) to the global rows numbers
[rowStart, rowStart + Nrows).

  2) To form each piece:

    2a) Extract that block using
https://petsc.org/main/manualpages/Mat/MatGetLocalSubMatrix/

           This gives back a Mat object that you subsequently restore using
https://petsc.org/main/manualpages/Mat/MatRestoreLocalSubMatrix/

     2b) Insert values using
https://petsc.org/main/manualpages/Mat/MatSetValuesLocal/

            The local indices used for insertion here are indices relative
to the block itself, and the L2G map for this matrix
            has been rewritten to insert into that block in the larger
matrix. Thus this looks like just calling MatSetValuesLocal()
            on the smaller matrix block, but inserts correctly into the
larger matrix.

Therefore, the code you write code in 2) could work equally well making the
large matrix from 1), or independent smaller matrix blocks.

Does this make sense?

  Thanks,

     Matt


> I will use MatSetLocalToGlobalMapping(K, row_mapping, column_mapping) to
> build the bottom left [P].
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> Q2) Can now I reset the mapping as MatSetLocalToGlobalMapping(K,
> column_mapping, row_mapping) to build the top right [P^T]?
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> Many thanks!
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> Kind regards,
>
> Karthik.
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-- 
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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