[petsc-users] Question about MATMPIAIJ and column indexes ordering

[Deuse, Mathieu via petsc-users]

Hello,

I have a piece of code which generates a matrix in CSR format, but the without 
sorting the column indexes in increasing order within each row. This seems not 
to be 100% compatible with the MATMPIAIJ format: the documentation of 
MatCreateMPIAIJWithArrays indeed mentions 'row-major ordering'.

For example, consider the 2x2 matrix (1 2; 3 4), which in my code could be 
stored as i=[0, 2, 4], j=[1, 0, 0, 1], v=[2, 1, 3, 4]. I can generate the 
matrix as follows (on 1 proc): MatCreateMPIAIJWithArrays(PETSC_COMM_SELF, 2, 2, 
2, 2, i, j, v, &matrix). This appears to work fine, and I can then use the 
matrix in a KSP for example. However, if I try to update the entry values (same 
order and values v=[2, 1, 3, 4]) with MatUpdateMPIAIJWithArray(matrix, v), it 
seems that PETSc does not memorize the order of the column indexes and the 
matrix that I get now is (2 1; 3 4). I get the same result with 
MatUpdateMPIAIJWithArrays(matrix, 2, 2, 2, 2, i, j, v). On the other hand, if 
the column indexes are sorted within each row (i=[0, 2, 4], j=[0, 1, 0, 1], 
v=[1, 2, 3, 4]), then it works fine. I have attached a minimal working example 
(C++).

Can I safely rely on MatCreateMPIAIJWithArrays working fine with unsorted 
column indexes as long as I do not use MatUpdateMPIAIJWithArray(s)? Or should I 
do the sorting myself before calling MatCreateMPIAIJWithArrays? (or 
alternatively use another matrix format).

Thanks in advance for the help.

Kind regards,

Mathieu Deuse

#include <iostream>

#include "petsc.h"

int main(int argc, char** argv)
{
    PetscCall(PetscInitialize(&argc, &argv, nullptr, nullptr));

    PetscInt    m   = 2;
    PetscInt    n   = 2;
    PetscInt    i[] = {0, 2, 4};
    PetscInt    j[] = {1, 0, 0, 1};
    PetscScalar v[] = {2, 1, 3, 4};

    Mat mat;
    PetscCall(MatCreateMPIAIJWithArrays(PETSC_COMM_SELF, m, n, m, n, i, j, v, 
&mat));

    std::cout << "=== Before update ===" << std::endl;
    for (PetscInt row = 0; row < m; ++row)
    {
        for (PetscInt col = 0; col < n; ++col)
        {
            PetscScalar x;
            PetscCall(MatGetValue(mat, row, col, &x));
            std::cout << ' ' << x;
        }
        std::cout << std::endl;
    }

    PetscCall(MatUpdateMPIAIJWithArray(mat, v));

    std::cout << "=== After update ===" << std::endl;
    for (PetscInt row = 0; row < m; ++row)
    {
        for (PetscInt col = 0; col < n; ++col)
        {
            PetscScalar x;
            PetscCall(MatGetValue(mat, row, col, &x));
            std::cout << ' ' << x;
        }
        std::cout << std::endl;
    }

    PetscCall(MatDestroy(&mat));

    PetscCall(PetscFinalize());
}