[petsc-users] Obtaining bytes per second

[Jed Brown]

Justin Chang <jychang48 at gmail.com> writes:
> I already have speedup/strong scaling results that essentially depict the
> difference between the KSPSolve() and TaoSolve(). However, I have been told
> by someone that strong-scaling isn't enough - that I should somehow include
> something to show the "efficiency" of these two methodologies. 

"Efficiency" is irrelevant if one is wrong.  Can you set up a problem
where both get the right answer and vary a parameter to get to the case
where one fails?  Then you can look at efficiency for a given accuracy
(and you might have to refine the grid differently) as you vary the
parameter.

It's really hard to demonstrate that an implicit solver is optimal in
terms of mathematical convergence rate.  Improvements there can dwarf
any differences in implementation efficiency.

> That is, how much of the wall-clock time reported by these two very
> different solvers is spent doing useful work.
>
> Is such an "efficiency" metric necessary to report in addition to
> strong-scaling results? The overall computational framework is the same for
> both problems, the only difference being one uses a linear solver and the
> other uses an optimization solver. My first thought was to use PAPI to
> include hardware counters, but these are notoriously inaccurate. Then I
> thought about simply reporting the manual FLOPS and FLOPS/s via PETSc, but
> these metrics ignore memory bandwidth. And so here I am looking at the idea
> of implementing the Roofline model, but now I am wondering if any of this
> is worth the trouble.

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