Split

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 a right inverse to Mix.

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

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APL built-ins [edit]
Primitives (Timeline)	Functions
Scalar
		Monadic	Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root
		Dyadic	Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
		Structural	Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
		Selection	First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
		Selector	Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
		Computational	Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators	Monadic	Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis
Operators	Dyadic	Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator)
Quad names	Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector

Split

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Split

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