Enclose: Difference between revisions
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== Examples == | == Examples == | ||
An enclosed array is a [[scalar]], which is subject to [[scalar extension]]. This can be used to simulate [[Outer Product|outer product]] by a [[scalar function]] or one-sided [[Each]] (pair the entire right argument with each element of the left argument, or vice versa). A notable application of this behavior is the "chipmunk idiom" < | An enclosed array is a [[scalar]], which is subject to [[scalar extension]]. This can be used to simulate [[Outer Product|outer product]] by a [[scalar function]] or one-sided [[Each]] (pair the entire right argument with each element of the left argument, or vice versa). A notable application of this behavior is the "chipmunk idiom" <syntaxhighlight lang=apl inline>X⊃¨⊂Y</syntaxhighlight>, which simulates <syntaxhighlight lang=apl inline>Y[X]</syntaxhighlight> for (possibly nested) [[vector]] Y and [[simple]] X. | ||
< | <syntaxhighlight lang=apl> | ||
1 2 3+⊂4 5 6 ⍝ Computes (1+4 5 6)(2+4 5 6)(3+4 5 6) | 1 2 3+⊂4 5 6 ⍝ Computes (1+4 5 6)(2+4 5 6)(3+4 5 6) | ||
┌─────┬─────┬─────┐ | ┌─────┬─────┬─────┐ | ||
| Line 20: | Line 20: | ||
│3 4│1 2│ | │3 4│1 2│ | ||
└───┴───┘ | └───┴───┘ | ||
</ | </syntaxhighlight> | ||
Enclose with function axis can be used to move one or more axes to an extra level of nesting. | Enclose with function axis can be used to move one or more axes to an extra level of nesting. | ||
< | <syntaxhighlight lang=apl> | ||
⎕←M←2 3 4⍴⎕A | ⎕←M←2 3 4⍴⎕A | ||
ABCD | ABCD | ||
| Line 51: | Line 51: | ||
⍴⊃⊂[1 3]N ⍝ Shape of each element is the enclosed axes | ⍴⊃⊂[1 3]N ⍝ Shape of each element is the enclosed axes | ||
2 4 | 2 4 | ||
</ | </syntaxhighlight>{{Works in|[[Dyalog APL]]}} | ||
== Description == | == Description == | ||
With no [[function axis]], Enclose returns a [[scalar]] array whose only [[element]] is the argument. In the [[flat array model]] this means that the argument is placed in a [[box]], and the result is this box as a scalar. In the [[nested array model]] it can simply be viewed as creating a new array. However, if the argument is a [[simple scalar]], then the result will match the argument because nested array theory dicatates that simple scalars [[float]]. | |||
Enclose (without axis) is the [[inverse]] of [[Mix]] and [[First]] in the sense that | == Properties == | ||
Enclose (without axis) is the [[inverse]] of both [[Mix]] and [[First]] in the sense that either of these undoes the additional nesting introduced by Enclose. | |||
== External links == | == External links == | ||
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=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Enclose.htm Dyalog], [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Enclose%20with%20Axes.htm with axes] | ||
* [http://microapl.com/apl_help/ch_020_020_580.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_580.htm APLX] | ||
* J [https://www.jsoftware.com/help/dictionary/d010.htm Vocabulary], [https://code.jsoftware.com/wiki/Vocabulary/lt NuVoc] | * J [https://www.jsoftware.com/help/dictionary/d010.htm Vocabulary], [https://code.jsoftware.com/wiki/Vocabulary/lt NuVoc] (as <syntaxhighlight lang=j inline><</syntaxhighlight>) | ||
* [https://mlochbaum.github.io/BQN/doc/enclose.html BQN] (as <code><</code>) | |||
{{APL built-ins}}[[Category:Primitive functions]] | {{APL built-ins}}[[Category:Primitive functions]] | ||
Latest revision as of 22:17, 10 September 2022
⊂ <
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Enclose (⊂, <), or Box, is a monadic primitive function which creates a nested scalar by wrapping its argument under one level of nesting. When used with function axis, only the selected axes of the given array are enclosed. This can be seen as a more general form of Split, which can only enclose (or split) one selected axis.
Examples
An enclosed array is a scalar, which is subject to scalar extension. This can be used to simulate outer product by a scalar function or one-sided Each (pair the entire right argument with each element of the left argument, or vice versa). A notable application of this behavior is the "chipmunk idiom" X⊃¨⊂Y, which simulates Y[X] for (possibly nested) vector Y and simple X.
1 2 3+⊂4 5 6 ⍝ Computes (1+4 5 6)(2+4 5 6)(3+4 5 6)
┌─────┬─────┬─────┐
│5 6 7│6 7 8│7 8 9│
└─────┴─────┴─────┘
1 2 3,¨⊂4 5 6 ⍝ Computes (1,4 5 6)(2,4 5 6)(3,4 5 6)
┌───────┬───────┬───────┐
│1 4 5 6│2 4 5 6│3 4 5 6│
└───────┴───────┴───────┘
(2 2⍴1 2 2 1)⊃¨⊂(1 2)(3 4)(5 6) ⍝ "chipmunk" idiom
┌───┬───┐
│1 2│3 4│
├───┼───┤
│3 4│1 2│
└───┴───┘
Enclose with function axis can be used to move one or more axes to an extra level of nesting.
⎕←M←2 3 4⍴⎕A
ABCD
EFGH
IJKL
MNOP
QRST
UVWX
⊂[3]M ⍝ Enclose last axis; same as ↓M
┌────┬────┬────┐
│ABCD│EFGH│IJKL│
├────┼────┼────┤
│MNOP│QRST│UVWX│
└────┴────┴────┘
⊂[2 3]M ⍝ Enclose two axes at once
┌────┬────┐
│ABCD│MNOP│
│EFGH│QRST│
│IJKL│UVWX│
└────┴────┘
N←2 3 4 5⍴⎕A
⍴⊂[1 3]N ⍝ Shape of the array is enclosed axes removed
3 5
⍴⊃⊂[1 3]N ⍝ Shape of each element is the enclosed axes
2 4Description
With no function axis, Enclose returns a scalar array whose only element is the argument. In the flat array model this means that the argument is placed in a box, and the result is this box as a scalar. In the nested array model it can simply be viewed as creating a new array. However, if the argument is a simple scalar, then the result will match the argument because nested array theory dicatates that simple scalars float.
Properties
Enclose (without axis) is the inverse of both Mix and First in the sense that either of these undoes the additional nesting introduced by Enclose.
External links
Documentation