Computing histograms
Mathematically, a
histogram
is a discretised representation of a probability distribution. A
histogram computation takes as input a collection of elements, maps
each to one of k bins, and counts the number of elements that
fall into each bin (discarding invalid bins). In Futhark,
histogram-like computations can be done with reduce_by_index:
def histogram [n] (k: i64) (is: [n]i64): [k]i32 =
let bins = replicate k 0
in reduce_by_index bins (+) 0 is (replicate n 1)For example, histogram 3 [0, 1, 3, 2, 1, 0, 0, 1] produces
[3, 3, 1]. Note that out-of-bounds bins (the 3) are
ignored.
reduce_by_index is a surprisingly flexible function. In
imperative pseudocode, we can describe the behaviour of
reduce_by_index dest f ne is as as:
for j < length is:
i = is[j]
a = as[j]
if i >= 0 && i < length dest:
dest[i] = f(dest[i], a)The f function must be associative and have ne as its neutral
element (like with scans and reductions).
Furthermore, it must also be commutative, which simply means that
f x y == f y x.