Windowed Reduce: Difference between revisions
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{{Built-ins|Windowed Reduce|/|⌿}}, also called '''N-wise Reduce''', is a [[primitive operator|primitive]] [[ | {{Built-ins|Windowed Reduce|/|⌿}}, also called '''N-wise Reduce''', is a [[primitive operator|primitive]] [[monadic operator]] which takes a [[dyadic function]], and derives a [[dyadic function]] which [[reduce]]s each overlapping "window" in its right [[argument]] of the size given by its left argument. | ||
== 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. | ||
The magnitude of <syntaxhighlight lang=apl inline>n</syntaxhighlight> must be no more than 1 greater than the size of <syntaxhighlight lang=apl inline>x</syntaxhighlight> along the relevant [[axis]]. | |||
== 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 20: | Line 23: | ||
│35 56 67 79│56 67 79 91│ | │35 56 67 79│56 67 79 91│ | ||
└───────────┴───────────┘ | └───────────┴───────────┘ | ||
</ | </syntaxhighlight> | ||
== Notable uses == | == Notable uses == | ||
Windowed Reduce is especially common with a left argument of 2 or ¯2, as it is then a pair-wise 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 pair-wise 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 21:47, 18 May 2024
/ ⌿
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Windowed Reduce (/, ⌿), also called N-wise 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 pair-wise 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)vis equivalent ton f/ vexcept in how they deal with the ends of the vector; Stencil includes "shards" and Windowed Reduce does not.
External links
Lessons
Documentation