Windowed Reduce: Difference between revisions
m (Text replacement  "</source>" to "</syntaxhighlight>") 
m (Text replacement  "<source" to "<syntaxhighlight") 

Line 3:  Line 3:  
== Description ==  == Description ==  
When applied to a [[vector]] argument, <  When applied to a [[vector]] argument, <syntaxhighlight lang=apl inline>n f/x</syntaxhighlight> evaluates to the expression <syntaxhighlight lang=apl inline>(a f b f c)(b f c f d)</syntaxhighlight>… where <syntaxhighlight lang=apl inline>a</syntaxhighlight>, <syntaxhighlight lang=apl inline>b</syntaxhighlight>, <syntaxhighlight lang=apl inline>c</syntaxhighlight>, <syntaxhighlight lang=apl inline>d</syntaxhighlight>, … are the elements of <syntaxhighlight lang=apl inline>x</syntaxhighlight>, grouped into windows of size <syntaxhighlight lang=apl inline>n</syntaxhighlight>. It works like [[Reduce]], except applied on overlapping segments of an array, and borrows most of its functionality from it. When  
<  <syntaxhighlight lang=apl inline>n</syntaxhighlight>is negative, each window is reversed before the reduction is done.  
== Examples ==  == Examples ==  
Windowed reduce is used to apply functions on overlapping sections of array e.g. when you need the deltas of an array.  Windowed reduce is used to apply functions on overlapping sections of array e.g. when you need the deltas of an array.  
<  <syntaxhighlight lang=apl>  
3+/5 1 4 1 8  3+/5 1 4 1 8  
10 6 13  10 6 13  
Line 24:  Line 24:  
== Notable uses ==  == 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, <  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, <syntaxhighlight lang=apl inline>1,2≠/v</syntaxhighlight> indicates the elements that differ from their neighbour on the left. For a Boolean vector <syntaxhighlight lang=apl inline>b</syntaxhighlight>, the expression <syntaxhighlight lang=apl inline>2</0,b</syntaxhighlight> indicates the first 1 in each contiguous run of 1s.  
== See also ==  == See also ==  
* [[Stencil]] which can be seen as a generalisation of Windowed Reduce in that for a vector argument, <  * [[Stencil]] which can be seen as a generalisation of Windowed Reduce in that for a vector argument, <syntaxhighlight lang=apl inline>({⊂f/⍵}⌺n)v</syntaxhighlight> is equivalent to <syntaxhighlight lang=apl inline>n f/ v</syntaxhighlight> except in how they deal with the ends of the vector; Stencil includes "shards" and Windowed Reduce does not.  
== External links ==  == External links == 
Latest revision as of 10:36, 11 September 2022
/ ⌿

Windowed Reduce (/
, ⌿
), also called Nwise Reduce, is a primitive dyadic operator which takes a dyadic function, and a number as its left argument, inserts it between the overlapping "windows" of the size of its left argument, and evaluates it into a single array in righttoleft order.
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.
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