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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]] < | {{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]] <syntaxhighlight 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. | ||
== Examples == | == Examples == | ||
The result of Split on a non-[[scalar]] array is always a [[nested array]] whose elements are [[vector|vectors]]. The [[rank]] of < | The result of Split on a non-[[scalar]] array is always a [[nested array]] whose elements are [[vector|vectors]]. The [[rank]] of <syntaxhighlight lang=apl inline>↓[K]Y</syntaxhighlight> is <syntaxhighlight lang=apl inline>¯1+≢⍴Y</syntaxhighlight> (original rank minus 1), its [[shape]] is <syntaxhighlight lang=apl inline>(K≠⍳≢⍴Y)/⍴Y</syntaxhighlight> (original shape with K-th axis removed), and the shape of each element is <syntaxhighlight lang=apl inline>(⍴Y)[K]</syntaxhighlight>. | ||
< | <syntaxhighlight lang=apl> | ||
⎕←Y←2 3 4⍴⎕A ⍝ 3D array | ⎕←Y←2 3 4⍴⎕A ⍝ 3D array | ||
ABCD | ABCD | ||
| Line 37: | Line 37: | ||
(≡↓Y)(≢⍴↓Y) ⍝ Split array is depth 1+1, rank 3-1 | (≡↓Y)(≢⍴↓Y) ⍝ Split array is depth 1+1, rank 3-1 | ||
2 2 | 2 2 | ||
</ | </syntaxhighlight>{{Works in|[[Dyalog APL]]}} | ||
Split is a no-op to a [[scalar]]. | Split is a no-op to a [[scalar]]. | ||
< | <syntaxhighlight lang=apl> | ||
2≡↓2 | 2≡↓2 | ||
1 | 1 | ||
</ | </syntaxhighlight> | ||
== Alternatives == | == Alternatives == | ||
Most dialects do not have Split. Instead, | Most dialects do not have Split. Instead, they can use [[Enclose]] (<syntaxhighlight lang=apl inline>⊂</syntaxhighlight>) with [[bracket axis]] or the [[Rank operator]]: | ||
< | <syntaxhighlight lang=apl> | ||
↓Y | ↓Y | ||
┌────┬────┬────┐ | ┌────┬────┬────┐ | ||
| Line 67: | Line 67: | ||
│MNOP│QRST│UVWX│ | │MNOP│QRST│UVWX│ | ||
└────┴────┴────┘ | └────┴────┴────┘ | ||
</ | </syntaxhighlight> | ||
It is common to split a higher-[[rank]] array into its constituent [[major cell]] | It is common to split a higher-[[rank]] array into its constituent [[major cell|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 <syntaxhighlight lang=apl inline>⊂[1↓⍳≢⍴Y]Y</syntaxhighlight> or <syntaxhighlight lang=apl inline>⊂⍤¯1⊢Y</syntaxhighlight>: | ||
< | <syntaxhighlight lang=apl> | ||
⊂[1↓⍳≢⍴Y]Y | ⊂[1↓⍳≢⍴Y]Y | ||
┌────┬────┐ | ┌────┬────┐ | ||
| Line 82: | Line 82: | ||
│IJKL│UVWX│ | │IJKL│UVWX│ | ||
└────┴────┘ | └────┴────┘ | ||
</ | </syntaxhighlight> | ||
== External links == | == External links == | ||
| Line 91: | Line 92: | ||
=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Split.htm Dyalog] | ||
{{APL built-ins}}[[Category:Primitive functions]] | {{APL built-ins}}[[Category:Primitive functions]] | ||
Latest revision as of 10:55, 11 September 2022
↓
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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 2Works in: Dyalog APL
Split is a no-op to a scalar.
2≡↓2 1
Alternatives
Most dialects do not have Split. Instead, they 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 for 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