Each: Difference between revisions

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Note that this operator has no effect on [https://mastering.dyalog.com/Appendices.html#scalar-functions scalar functions], since these functions map to each array elements by default.   
The Each operator has no effect on [[scalar function]]s, since these functions already map over each array element.   


For example, both expression below has the same meaning, since + is a scalar function.
For example, both expressions below have the same meaning, since <source lang=apl inline>+</source> is a scalar function.
<source lang=apl>
<source lang=apl>
       1 + 1 2 3 4
       1 + 1 2 3 4

Revision as of 11:30, 3 September 2021

¨

Each (¨) is a primitive monadic operator which applies its operand to each element of the arguments, and returns an array whose elements are the results. If two arguments are given, their elements are matched using conformability rules.

Each is defined only in nested APLs. Some flat APLs obtain analogous functionality by using an Under operator with close composition along with the rank-0 function Disclose (or Unbox). In SHARP APL this is written f¨>. In J it is f&.>.

Each differs from the Rank operator with rank 0 in that the operand arguments and results are not enclosed. As the elements of a nested array they need not be scalar.

For example,

      1,1 2 3 ⍝ join 1 with 1 2 3
1 1 2 3
      1,¨1 2 3 ⍝ join 1 with each element of 1 2 3
┌───┬───┬───┐
│1 1│1 2│1 3│
└───┴───┴───┘

The Each operator has no effect on scalar functions, since these functions already map over each array element.

For example, both expressions below have the same meaning, since + is a scalar function.

      1 + 1 2 3 4
2 3 4 5
      1 +¨ 1 2 3 4
2 3 4 5

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