[petsc-users] MatCreateMPIAIJWithSplitArrays for symmetric matrix?

Jed Brown jed at 59A2.org
Mon Nov 8 06:31:58 CST 2010

```On Mon, Nov 8, 2010 at 13:07, Daniel Langr <daniel.langr at gmail.com> wrote:

> Ok, that's a good idea and I will try it. I can estimate total number of
> nonzeros (limited by the amount of memory), but I can hardly estimate number
> of nonzeros per particular rows (d_nnz, o_nnz). So I need to use d_nz and
> o_nz, right? And for symmetric matrix, what do d_nz and o_nz mean? Is it
> number of nonzeros for whole matrix row, or just upper triangular part? (I
> don't see this in manual page.)
>

It is only for the upper triangular part.  If you have no way to guess the
number per row, then just set {d,o}_nz, but note that this is pessimistic
because the last rows of the matrix necessarily have fewer nonzeros in the
upper triangular part.

> (That was my point, through MatMPISBAIJSetPreallocation I need to estimate
> number of nonzeros per row. Not just number of nonzeros of whole local part.
> If I construct CSR arrays directly, I don't need this row-estimates.)
>

Here's a little secret: if you assemble the matrix row-by-row, in-order,
then you need only estimate the average number of nonzeros per row.  The
implementation is not stupid, so early rows can blow over their initial
estimates as long as later rows make up for it by being under the estimate.
For example, with a 5-point Laplacian, you can
MatSeqSBAIJSetPreallocation(A,1,3,PETSC_NULL) and you will see something
like

Matrix Object:
type: seqsbaij
rows=400, cols=400
total: nonzeros=1160, allocated nonzeros=1200
total number of mallocs used during MatSetValues calls =0
block size is 1

So no mallocs even though the early rows have more than 3 nonzeros in the
upper triangular part.  If you assemble out-of-order, or in a scattered
fashion (such as for a finite element method) then this will be costly.
Does this help?

Jed
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