Windowed Reduce

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/ ⌿

Windowed Reduce (/, ⌿), also called N-wise 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 right-to-left order.

Description

When applied to a vector argument, <source lang=apl inline>n f/x</syntaxhighlight> evaluates to the expression <source lang=apl inline>(a f b f c)(b f c f d)</syntaxhighlight>… where <source lang=apl inline>a</syntaxhighlight>, <source lang=apl inline>b</syntaxhighlight>, <source lang=apl inline>c</syntaxhighlight>, <source lang=apl inline>d</syntaxhighlight>, … are the elements of <source lang=apl inline>x</syntaxhighlight>, grouped into windows of size <source 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 <source lang=apl inline>n</syntaxhighlight>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.

<source lang=apl> 

     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│ └───────────┴───────────┘ </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, <source lang=apl inline>1,2≠/v</syntaxhighlight> indicates the elements that differ from their neighbour on the left. For a Boolean vector <source lang=apl inline>b</syntaxhighlight>, the expression <source 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, <source lang=apl inline>({⊂f/⍵}⌺n)v</syntaxhighlight> is equivalent to <source 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

Lessons

Documentation


APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
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Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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