2.2.23. averageDown
Purpose
Average each data block of size 'packing' into single values thus reducing the former grid to grid/packing.
Usage
> averageDown options ASCII table(s)
Options

c
/ coordinates
[ pos ]  column label of coordinates

p
/ =packing=[ 2 2 2 ]  size of packed group
 =shift=[ 0 0 0 ]
 shift vector of packing stencil

g
/ grid
 grid in x,y,z (optional)

s
/ size
 size in x,y,z (optional)
Details

 
 Figure 1: Packing stencil concept exemplified in two dimensions.  
For a periodic and regular grid stored in an
ASCII table with x as fastest and z as slowest varying coordinate, calculate the average per block of given size.
Grid resolution is reduced by the factor resulting from the chosen size of the packing stencil.
Figure
1 illustrates the concept in two dimensions with a 2 by 2 packing stencil.
The original 4 by 4 grid is shown in light gray and might result from a 2 by 2 finite element mesh (black lines) with linear interpolation functions, thus containing four integration points each.
During averaging, the stencil is moved across the whole grid in steps of 2 grid points along x and 2 grid points along y, i.e., in a nonoverlapping fashion.
The (black) points of the resulting 4/2 by 4/2 = 2 by 2 grid fall into the center of the finite elements since a stencil shift of (0, 0) was employed in this example.
Using a stencil shift of either (1,1), (1,1), (1,1), or (1,1) in the example of Figure
1 would result in the new grid coinciding with the nodes of the finite elements and averaged from their four neighboring integration points (light gray; periodicity of the original data is always implied).