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Windowed Reduce: Difference between revisions
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== 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 == | ||
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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 | ||
2-/1 2 3 4 5 | 2-/1 2 3 4 5 | ||
¯1 ¯1 ¯1 ¯1 | ¯1 ¯1 ¯1 ¯1 | ||
¯2-/1 2 3 4 5 | |||
1 1 1 1 | |||
4,/35 56 67 79 91 | 4,/35 56 67 79 91 | ||
┌───────────┬───────────┐ | ┌───────────┬───────────┐ | ||
│35 56 67 79│56 67 79 91│ | │35 56 67 79│56 67 79 91│ | ||
└───────────┴───────────┘ | └───────────┴───────────┘ | ||
</ | </syntaxhighlight> | ||
== 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, <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 == | |||
* [[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 == | ||