## Index Range Functions

Range functions are executed from left to right if more than one appears in a single index list. The following range functions reduce the rank of the result, like a scalar index:

min   minimum of values along index
max   maximum of values along index
sum   sum of values along index
avg   average of values along index
rms   root mean square of values along index
ptp   peak-to-peak of values along index
mnx   index at which minimum occurs
mxx   index at which maximum occurs

The following functions do not change the rank of the result, like an index range. However, the length of the index is changed as indicated by +1, -1, or 0 (no change):

cum, psum   +1, 0, partial sums of values along index
dif         -1, pairwise differences of adjacent values
zcen        -1, pairwise averages of adjacent values
pcen        +1, pairwise averages of adjacent interior values
uncp        -1, inverse of pcen (point center) operation

For example, given a two-dimensional array x, x(min,max) returns the largest of the smallest elements along the first dimension. To get the smallest of the largest elements along the second dimension, use x(,max)(min).