[petsc-dev] proposed minor PetscPartitioner changes

[Jed Brown]

Matthew Knepley <knepley at gmail.com> writes:

>> Matrix and graph are equivalent concepts.
>
>
> This is clearly wrong. A matrix is the coordinate representation of a
> linear operator, and thus has a specific
> behavior under coordinate transformations. A graph is just connectivity,
> and really just a relation. I cannot
> count the number of times Barry has ranted about this on petsc-maint
> (usually about Vecs and arrays). The
> mathematical object is not its data structure.

A graph Laplacian certainly does transform under coordinate
transformation and indeed, we use that property to design effective
coarsening strategies.  That one basis strikes you as intrinsically
"more canonical" does not mean it isn't a linear operator.