From APL Wiki
Revision as of 10:24, 11 September 2022 by Adám Brudzewsky (talk | contribs) (Text replacement - "</source>" to "</syntaxhighlight>")
Jump to navigation Jump to search

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 <source lang=apl inline>↓</syntaxhighlight> with the dyadic function Drop. Split is the inverse of Mix in the sense that the latter undoes the enclosing that Split introduced.


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

<source lang=apl>

     ⎕←Y←2 3 4⍴⎕A  ⍝ 3D array



     ↓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.

<source lang=apl>


1 </syntaxhighlight>


Most dialects do not have Split. Instead, they can use Enclose (<source lang=apl inline>⊂</syntaxhighlight>) with bracket axis or the Rank operator: <source lang=apl>


┌────┬────┬────┐ │ABCD│EFGH│IJKL│ ├────┼────┼────┤ │MNOP│QRST│UVWX│ └────┴────┴────┘


┌────┬────┬────┐ │ABCD│EFGH│IJKL│ ├────┼────┼────┤ │MNOP│QRST│UVWX│ └────┴────┴────┘


┌────┬────┬────┐ │ABCD│EFGH│IJKL│ ├────┼────┼────┤ │MNOP│QRST│UVWX│ └────┴────┴────┘ </syntaxhighlight> 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 for vectors or arrays of higher rank than 2. Instead, the solution is to use or <source lang=apl inline>⊂[1↓⍳≢⍴Y]Y</syntaxhighlight> or <source lang=apl inline>⊂⍤¯1⊢Y</syntaxhighlight>: <source lang=apl>


┌────┬────┐ │ABCD│MNOP│ │EFGH│QRST│ │IJKL│UVWX│ └────┴────┘


┌────┬────┐ │ABCD│MNOP│ │EFGH│QRST│ │IJKL│UVWX│ └────┴────┘ </syntaxhighlight>

External links



APL built-ins [edit]
Primitive functions
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndex
Selector Index generatorGradeIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)
Quad names
Arrays Index originMigration levelAtomic vector
Functions Name classCase convertUnicode convert
Operators SearchReplace