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{{Built-in|Split|↓}} is a [[monadic]] [[primitive function]] which reduces the [[rank]] of its [[argument]] by converting one of its [[axis|axes]] to one level of [[nested array model|nesting]]. The axis to move defaults to the last axis, but a different axis can be chosen using [[function axis]]. It shares its [[glyph]] <source lang=apl inline>↓</source> with the dyadic function [[Drop]]. Split is a right inverse to [[Mix]].
{{Built-in|Split|↓}} is a [[monadic]] [[primitive function]] which reduces the [[rank]] of its [[argument]] by converting one of its [[axis|axes]] to one level of [[nested array model|nesting]]. The axis to move defaults to the last axis, but a different axis can be chosen using [[function axis]]. It shares its [[glyph]] <source lang=apl inline>↓</source> with the dyadic function [[Drop]]. Split is the inverse of [[Mix]] in the sense that the latter undoes the enclosing that Split introduced.


== Examples ==
== Examples ==

Revision as of 11:47, 16 June 2020

Split () is a monadic primitive function which reduces the rank of its argument by converting one of its axes to one level of nesting. The axis to move defaults to the last axis, but a different axis can be chosen using function axis. It shares its glyph with the dyadic function Drop. Split is the inverse of Mix in the sense that the latter undoes the enclosing that Split introduced.

Examples

The result of Split on a non-scalar array is always a nested array whose elements are vectors. The rank of ↓[K]Y is ¯1+≢⍴Y (original rank minus 1), its shape is (K≠⍳≢⍴Y)/⍴Y (original shape with K-th axis removed), and the shape of each element is (⍴Y)[K].

      ⎕←Y←2 3 4⍴⎕A  ⍝ 3D array
ABCD
EFGH
IJKL
    
MNOP
QRST
UVWX
      ↓Y  ⍝ Last axis split; 2×3 array of length-4 vectors
┌────┬────┬────┐
│ABCD│EFGH│IJKL│
├────┼────┼────┤
│MNOP│QRST│UVWX│
└────┴────┴────┘
      ↓[2]Y  ⍝ 2nd axis split; 2×4 array of length-3 vectors
┌───┬───┬───┬───┐
│AEI│BFJ│CGK│DHL│
├───┼───┼───┼───┤
│MQU│NRV│OSW│PTX│
└───┴───┴───┴───┘
      ↓↓Y  ⍝ Split twice
┌────────────────┬────────────────┐
│┌────┬────┬────┐│┌────┬────┬────┐│
││ABCD│EFGH│IJKL│││MNOP│QRST│UVWX││
│└────┴────┴────┘│└────┴────┴────┘│
└────────────────┴────────────────┘

      (≡Y)(≢⍴Y)  ⍝ Original array is depth 1, rank 3
1 3
      (≡↓Y)(≢⍴↓Y)  ⍝ Split array is depth 1+1, rank 3-1
2 2
Works in: Dyalog APL

Split is a no-op to a scalar.

      2≡↓2
1

Alternatives

Most dialects do not have Split. Instead, the can use Enclose () with bracket axis or the Rank operator:

      ↓Y
┌────┬────┬────┐
│ABCD│EFGH│IJKL│
├────┼────┼────┤
│MNOP│QRST│UVWX│
└────┴────┴────┘
      ⊂[3]Y
┌────┬────┬────┐
│ABCD│EFGH│IJKL│
├────┼────┼────┤
│MNOP│QRST│UVWX│
└────┴────┴────┘
      ⊂⍤1⊢Y
┌────┬────┬────┐
│ABCD│EFGH│IJKL│
├────┼────┼────┤
│MNOP│QRST│UVWX│
└────┴────┴────┘

It is common to split a higher-rank array into its constituent major cells. The behaviour of Split on matrices might mislead to the belief that this is what the primitive does. However, it isn't so vectors or arrays of higher rank than 2. Instead, the solution is to use or ⊂[1↓⍳≢⍴Y]Y or ⊂⍤¯1⊢Y:

      ⊂[1↓⍳≢⍴Y]Y
┌────┬────┐
│ABCD│MNOP│
│EFGH│QRST│
│IJKL│UVWX│
└────┴────┘
      ⊂⍤¯1⊢Y
┌────┬────┐
│ABCD│MNOP│
│EFGH│QRST│
│IJKL│UVWX│
└────┴────┘

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