[Developers] [Patches] Make ADMConstraints GF public

David Rideout dprideout at gmail.com
Sun Sep 17 16:27:30 CDT 2006


Let me clarify my proposal.  Why not just leave everything as it is,
except turn off the absolute error checking for values which exceed
some threshold?  This threshold could be set to 1.  Or maybe 10.  Then
everthing should work fine, _including_ testing large values such as
those returned by sum reduction operators.  This has the added benefit
of being easy to implement...

Cheers,
David

On 9/17/06, David Rideout <dprideout at gmail.com> wrote:
> IMHO the test mechanism should be changed, not the tests themselves.
> e.g. what if one wants to test the reduction operators themselves?  As
> Jonathan says, it makes little sense to worry about absolute errors
> except for in small quantities.  The test mechanism could turn off the
> absolute error check if the value is above 1, say.
>
> -David
>
> On 9/17/06, Jonathan Thornburg <jthorn at aei.mpg.de> wrote:
> > Hi, Erik,
> >
> > > The "sum" reduction has the problem that it can easily lead to large
> > > absolute
> > > differences that are small relative differences.  The "average" reduction
> > > behaves better in that respect, and, apart from that, tests the same
> > > thing.  I
> > > suggest to avoid using the sum reduction in test cases.
> >
> > | I'm confused:  Since    average := sum / sum_of_weights   , why does
> > |  average   not also "lead to large absolute differences that are small
> > | relative differences"?
> >
> > > Because of the division by "sum_of_weights".  If you assume 10^6 grid points,
> > > then the absolute difference in the sum is 10^6 times the absolution
> > > difference in the average.  If you allow an absolute difference of 10^-12,
> > > then there are often cases where the average is deemed accurate enough, while
> > > the sum is deemed inaccurate.
> > >
> > > Let me give an example:
> > >
> > > Assume there are 10^6 grid points, all having the value 1.0 plus a small error
> > > of the order of 10^-14.  Then we have
> > >
> > > the exact values:
> > >
> > >       average: 1.0
> > >       sum: 10^6
> > >
> > > the perturbed values:
> > >
> > >       average: 1.0 + 10^-14
> > >       sum: 10^6 + 10^-8
> > >
> > > The relative error of the perturbed values with respect to the accurate values
> > > is 10^-14 for both the average and the sum.  The absolute errors differ; the
> > > absolute error for the average is 10^-14, while the absolute error of the sum
> > > is 10^-8.
> >
> > Ok, I see your point.  I hadn't realised we (are so foolish as to)
> > compare non-O(1) values with absolute tolerances.  Using relative
> > tolerances is *much* preferred...
> >
> > ciao,
> >
> > --
> > -- Jonathan Thornburg <jthorn at aei.mpg.de>
> >    Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),
> >    Golm, Germany, "Old Europe"     http://www.aei.mpg.de/~jthorn/home.html
> >    "Washing one's hands of the conflict between the powerful and the
> >     powerless means to side with the powerful, not to be neutral."
> >                                       -- quote by Freire / poster by Oxfam
> >
> > _______________________________________________
> > Developers mailing list
> > Developers at cactuscode.org
> > http://www.cactuscode.org/mailman/listinfo/developers
> >
>


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