Windowed Reduce
/ ⌿

Windowed Reduce (/
, ⌿
), also called Nwise Reduce, is a primitive monadic operator which takes a dyadic function, and derives a dyadic function which reduces each overlapping "window" in its right argument of the size given by its left argument.
Description
When applied to a vector argument, n f/x
evaluates to the expression (a f b f c)(b f c f d)
… where a
, b
, c
, d
, … are the elements of x
, grouped into windows of size n
. It works like Reduce, except applied on overlapping segments of an array, and borrows most of its functionality from it. When
n
is negative, each window is reversed before the reduction is done.
The magnitude of n
must be no more than 1 greater than the size of x
along the relevant axis.
Examples
Windowed reduce is used to apply functions on overlapping sections of array e.g. when you need the deltas of an array.
3+/5 1 4 1 8 10 6 13 2/1 2 3 4 5 ¯1 ¯1 ¯1 ¯1 ¯2/1 2 3 4 5 1 1 1 1 4,/35 56 67 79 91 ┌───────────┬───────────┐ │35 56 67 79│56 67 79 91│ └───────────┴───────────┘
Notable uses
Windowed Reduce is especially common with a left argument of 2 or ¯2, as it is then a pairwise application of the operand between neighbouring elements, and especially so with comparison functions. For example, 1,2≠/v
indicates the elements that differ from their neighbour on the left. For a Boolean vector b
, the expression 2</0,b
indicates the first 1 in each contiguous run of 1s.
See also
 Stencil which can be seen as a generalisation of Windowed Reduce in that for a vector argument,
({⊂f/⍵}⌺n)v
is equivalent ton f/ v
except in how they deal with the ends of the vector; Stencil includes "shards" and Windowed Reduce does not.
External links
Lessons
Documentation