[petsc-dev] proposed minor PetscPartitioner changes

[Matthew Knepley]

On Sat, Nov 11, 2017 at 1:12 PM, Jed Brown <jed at jedbrown.org> wrote:

> 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.
>

That is one operator. This is argument by anecdote. An arbitrary graph is
not
a linear operator, but an arbitrary matrix definitely is (the coordinate
representation of one).

  Matt

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
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