[petsc-users] Construct Matrix based on row and column values

[Jed Brown]

Elias Karabelas <karabelaselias at gmail.com> writes:

> Dear Users,
>
> I want to implement a FCT (flux corrected transport) scheme with PETSc. 
> To this end I have amongst other things create a Matrix whose entries 
> are given by
>
> L_ij = -max(0, A_ij, A_ji) for i neq j
>
> L_ii = Sum_{j=0,..n, j neq i} L_ij
>
> where Mat A is an (non-symmetric) Input Matrix created beforehand.
>
> I was wondering how to do this. My first search brought me to 
> https://www.mcs.anl.gov/petsc/petsc-current/src/mat/examples/tutorials/ex16.c.html 
>
>
> but this just goes over the rows of one matrix to set new values and now 
> I would need to run over the rows and columns of the matrix. My Idea was 
> to just create a transpose of A and do the same but then the row-layout 
> will be different and I can't use the same for loop for A and AT and 
> thus also won't be able to calculate the max's above.

Does your matrix have symmetric nonzero structure?  (It's typical for
finite element methods.)

If so, all the indices will match up so I think you can do something like:

for (row=rowstart; row<rowend; row++) {
  PetscScalar Lvals[MAX_LEN];
  PetscInt diag;
  MatGetRow(A, row, &ncols, &cols, &vals);
  MatGetRow(At, row, &ncolst, &colst, &valst);
  assert(ncols == ncolst); // symmetric structure
  PetscScalar sum = 0;
  for (c=0; c<ncols; c++) {
    assert(cols[c] == colst[c]); // symmetric structure
    if (cols[c] == row) diag = c;
    else sum -= (Lvals[c] = -max(0, vals[c], valst[c]));
  }
  Lvals[diag] = sum;
  MatSetValues(L, 1, &row, ncols, cols, Lvals, INSERT_VALUES);
  MatRestoreRow(A, row, &ncols, &cols, &vals);
  MatRestoreRow(At, row, &ncolst, &colst, &valst);
}