[petsc-users] Off-diagonal matrix-vector product y=(A-diag(A))x

[Jed Brown]

Ingo Gaertner <ingogaertner.tus at gmail.com> writes:

> I have 2*ndim+1 entries per row (including the diagonal).
> In 2 dimensions, the suggested solution is 6 multiplications + 5 additions
> = 11 flops per row.
> The optimized solution is 4 multiplications + 3 additions = 7 flops per row.

Run it.  Flops are not the performance limiting factor for these
operations.  Your algorithm still needs to traverse the matrix, which
for 2D is 5*sizeof(PetscScalar)+6*sizeof(PetscInt) = 64 bytes per dof.
It almost certainly does not cost less to apply the matrix than to apply
it while skipping the diagonal entry.  A custom implementation also will
not be able to use vector-friendly matrix formats without extra masking
which may indeed impact performance and in any case, would require a
custom implementation for that format.  I think you're wasting your
time, but please run it to see.

> I call this significant.
>
> Thanks
> Ingo
>
>
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> 2017-04-14 16:50 GMT+02:00 Jed Brown <jed at jedbrown.org>:
>
>> Ingo Gaertner <ingogaertner.tus at gmail.com> writes:
>>
>> > Does PETSc include an efficient implementation for the operation
>> > y=(A-diag(A))x or y_i=\sum_{j!=i}A_{ij}x_j on a sparse matrix A?
>> >
>> > In words, I need a matrix-vector product after the matrix diagonal has
>> been
>> > set to zero. For efficiency reasons I can't copy and modify the matrix or
>> > first calculate the full product and then subtract the diagonal
>> > contribution.
>>
>> How many entries per row in your matrix?  There isn't a special function
>> for this, but I'm skeptical that the performance gains of a custom
>> implementation would be significant.  Do you have a profile showing that
>> it is?
>>
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