[petsc-users] question about MatSetLocalToGlobalMapping

[Zhang, Hong]

Karthik,
We built a KKT matrix in  TaoSNESJacobian_PDIPM() (see petsc/src/tao/constrained/impls/ipm/pdipm.c) which assembles several small matrices into a large KKT matrix in mpiaij format. You could take the same approach to insert P and P^T into your K.
FYI, I attached our paper.
Hong
________________________________
From: petsc-users <petsc-users-bounces at mcs.anl.gov> on behalf of Matthew Knepley <knepley at gmail.com>
Sent: Thursday, April 20, 2023 5:37 AM
To: Karthikeyan Chockalingam - STFC UKRI <karthikeyan.chockalingam at stfc.ac.uk>
Cc: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] question about MatSetLocalToGlobalMapping

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

Hello,



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)



K = [A P^T

       P   0]



Where K is of type MatMPIAIJ. I first constructed the top left [A] using MatSetValues().



Now, I would like to construct the bottom left [p] and top right [p^T] using MatSetValuesLocal().



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].





Q2) Can now I reset the mapping as MatSetLocalToGlobalMapping(K, column_mapping, row_mapping) to build the top right [P^T]?





Many thanks!



Kind regards,

Karthik.




















--
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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