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Power (operator): Difference between revisions
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== Description == | == Description == | ||
A call to Power is of the form < | A call to Power is of the form <syntaxhighlight lang=apl inline>X(f⍣g)Y</syntaxhighlight>, where | ||
* < | * <syntaxhighlight lang=apl inline>X</syntaxhighlight> is an optional argument. | ||
* < | * <syntaxhighlight lang=apl inline>f</syntaxhighlight> is a function. If <syntaxhighlight lang=apl inline>X</syntaxhighlight> is given, then it is bound to <syntaxhighlight lang=apl inline>f</syntaxhighlight> so <syntaxhighlight lang=apl inline>X f⍣g Y</syntaxhighlight> is equivalent to <syntaxhighlight lang=apl inline>X∘f⍣g Y</syntaxhighlight>. | ||
* < | * <syntaxhighlight lang=apl inline>g</syntaxhighlight> can be an [[array]] or a function. | ||
Power repeatedly applies < | Power repeatedly applies <syntaxhighlight lang=apl inline>f</syntaxhighlight> to <syntaxhighlight lang=apl inline>Y</syntaxhighlight> based on the type of operand <syntaxhighlight lang=apl inline>g</syntaxhighlight>: | ||
* '''Function''': Must be dyadic and must return a boolean [[singleton]]. The previous iteration value is provided as the right argument to < | * '''Function''': Must be dyadic and must return a boolean [[singleton]]. The previous iteration value is provided as the right argument to <syntaxhighlight lang=apl inline>f</syntaxhighlight>, and the current iteration value is given as the left argument. <syntaxhighlight lang=apl inline>f</syntaxhighlight> is repeatedly applied until this function returns 1. | ||
* '''Integer''': Applies < | * '''Integer''': Applies <syntaxhighlight lang=apl inline>f</syntaxhighlight> <syntaxhighlight lang=apl inline>g</syntaxhighlight> times to <syntaxhighlight lang=apl inline>Y</syntaxhighlight>. If <syntaxhighlight lang=apl inline>g</syntaxhighlight> is negative, then the inverse of <syntaxhighlight lang=apl inline>f</syntaxhighlight> (if available) is applied. | ||
* '''Integer Array''': In [[Extended Dyalog APL]], < | * '''Integer Array''': In [[Extended Dyalog APL]], <syntaxhighlight lang=apl inline>g</syntaxhighlight> can be an integer array. Each integer <syntaxhighlight lang=apl inline>i</syntaxhighlight> in <syntaxhighlight lang=apl inline>g</syntaxhighlight> will be replaced by <syntaxhighlight lang=apl inline>⊂(f⍣i)Y</syntaxhighlight>. | ||
== Examples == | == Examples == | ||
Some basic examples: | Some basic examples: | ||
< | <syntaxhighlight lang=apl> 1 (+⍣3) 5 ⍝ Fixed number of iterations | ||
8 | 8 | ||
(2∘×⍣3) 5 ⍝ No X given | (2∘×⍣3) 5 ⍝ No X given | ||
40 | 40 | ||
1 +∘÷⍣= 1 ⍝ iterate till fixed point | 1 +∘÷⍣= 1 ⍝ iterate till fixed point | ||
1.618033989</ | 1.618033989</syntaxhighlight> | ||
A well-known use for Power is iterating until a fixed point is reached. | A well-known use for Power is iterating until a fixed point is reached. | ||
< | <syntaxhighlight lang=apl> | ||
(∨.∧⍨∨⊢)⍣≡3 3⍴0 0 1 1 0 1 1 0 1 ⍝ Transitive closure of an adjacency matrix | (∨.∧⍨∨⊢)⍣≡3 3⍴0 0 1 1 0 1 1 0 1 ⍝ Transitive closure of an adjacency matrix | ||
1 0 1 | 1 0 1 | ||
1 0 1 | 1 0 1 | ||
1 0 1</ | 1 0 1</syntaxhighlight> | ||
Power is also used to access function inverses. | Power is also used to access function inverses. | ||
< | <syntaxhighlight lang=apl> 2(⊥⍣¯1)5 | ||
1 0 1</ | 1 0 1</syntaxhighlight> | ||
== External Links == | == External Links == | ||
=== Lessons === | === Lessons === | ||