Power (operator)

From APL Wiki
Revision as of 21:14, 10 September 2022 by Adám Brudzewsky (talk | contribs) (Text replacement - "<source" to "<syntaxhighlight")
Jump to navigation Jump to search

Power () is a primitive dyadic operator that performs bounded looping, unbounded looping, and function inverses in NARS2000, Dyalog APL, and related implementations like ngn/apl, dzaima/APL, and Extended Dyalog APL.

Description

A call to Power is of the form <syntaxhighlight lang=apl inline>X(f⍣g)Y</source>, where

  • <syntaxhighlight lang=apl inline>X</source> is an optional argument.
  • <syntaxhighlight lang=apl inline>f</source> is a function. If <syntaxhighlight lang=apl inline>X</source> is given, then it is bound to <syntaxhighlight lang=apl inline>f</source> so <syntaxhighlight lang=apl inline>X f⍣g Y</source> is equivalent to <syntaxhighlight lang=apl inline>X∘f⍣g Y</source>.
  • <syntaxhighlight lang=apl inline>g</source> can be an array or a function.

Power repeatedly applies <syntaxhighlight lang=apl inline>f</source> to <syntaxhighlight lang=apl inline>Y</source> based on the type of operand <syntaxhighlight lang=apl inline>g</source>:

  • 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</source>, and the current iteration value is given as the left argument. <syntaxhighlight lang=apl inline>f</source> is repeatedly applied until this function returns 1.
  • Integer: Applies <syntaxhighlight lang=apl inline>f</source> <syntaxhighlight lang=apl inline>g</source> times to <syntaxhighlight lang=apl inline>Y</source>. If <syntaxhighlight lang=apl inline>g</source> is negative, then the inverse of <syntaxhighlight lang=apl inline>f</source> (if available) is applied.
  • Integer Array: In Extended Dyalog APL, <syntaxhighlight lang=apl inline>g</source> can be an integer array. Each integer <syntaxhighlight lang=apl inline>i</source> in <syntaxhighlight lang=apl inline>g</source> will be replaced by <syntaxhighlight lang=apl inline>⊂(f⍣i)Y</source>.

Examples

Some basic examples: <syntaxhighlight lang=apl> 1 (+⍣3) 5 ⍝ Fixed number of iterations 8

     (2∘×⍣3) 5 ⍝ No X given

40

     1 +∘÷⍣= 1 ⍝ iterate till fixed point

1.618033989</source> 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

1 0 1 1 0 1 1 0 1</source> Power is also used to access function inverses. <syntaxhighlight lang=apl> 2(⊥⍣¯1)5 1 0 1</source>

External Links

Lessons

Documentation

APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentityStopSelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndexCartesian ProductSort
Selector Index generatorGradeIndex OfInterval IndexIndicesDealPrefix and suffix vectors
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductDeterminantPowerAtUnderRankDepthVariantStencilCutDirect definition (operator)
Quad names Index originComparison toleranceMigration levelAtomic vector