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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, they can use [[Enclose]] (< | 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|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 < | 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 == | ||