[Users] Definitions of different reductions in CarpetIOScalar

[Roland Haas]

Hello Shamin,

> CarpetIOScalar thorn has the following options from outscalar_reductions:
> 
> count minimum maximum sum average norm1 norm2 norm_inf icount iaverage
> inorm1 inorm2
> 
> What are the expressions/definitions for each? I could not find them in the
> ETK documentation. Please help.

They are defined by CarpetReduce
(https://bitbucket.org/eschnett/carpet/src/master/CarpetReduce/) and
mostly match the corresponding ones in LocalReduce (which has docs):

http://einsteintoolkit.org/thornguide/CactusNumerical/LocalReduce/documentation.html

The difference between the "i" and non "i" flavors is that the regular
ones weigh the influence of a grid point by the volume of its cell so
that eg the "sum" reduction becomes (up to a constant factor of the
cell volume on the coarsest grid) the Riemann sum (integral) of the
data.

The "i" ones leave out that factor so just sum up the values.

For reductions that do not perform sums (min/max) I don't think there
is is a difference between the two.

Yours,
Roland

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