Partitioned Enclose: Difference between revisions

Jump to navigation Jump to search

Partitioned Enclose (view source)

Revision as of 21:33, 28 January 2024

1,818 bytes added ,  28 January
m
Text replacement - "KAP" to "Kap"
No edit summary
m (Text replacement - "KAP" to "Kap")
 
(13 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Built-in|Partitioned Enclose|⊂}} is a [[dyadic function]] which splits its right argument into differently sized pieces as determined by the non-negative integer<ref group=note name=max>Most dialects restrict this number to a maximum of 1.</ref> left argument.
:''In the [[APL2]] family and many related dialects, <syntaxhighlight lang=apl inline>⊂</syntaxhighlight> indicates [[Partition]].''


On a vector right argument, the corresponding element in the left argument indicate how many<ref group=note name=max></ref> '''divisions''' to begin there:
{{Built-in|Partitioned Enclose|⊂}} is a [[dyadic function]] which splits its right argument into differently sized pieces as determined by the left argument. It was introduced by [[NARS]] and appears in [[Dyalog APL]] and some newer dialects influenced by it.
<source lang=apl>
== Description ==
In the simplest case, and on a vector right argument, the corresponding element in the left argument indicates where '''divisions''' begin:
<syntaxhighlight lang=apl>
       1 0 1 0 0 0 0⊂'HiEarth'
       1 0 1 0 0 0 0⊂'HiEarth'
┌──┬─────┐
┌──┬─────┐
│Hi│Earth│
│Hi│Earth│
└──┴─────┘
└──┴─────┘
</source>
</syntaxhighlight>
{{Works in|[[Dyalog APL]]}}
{{Works in|[[Dyalog APL]], [[Extended Dyalog APL]]}}
Empty divisions can be inserted by beginning more than 1 division at a particular index<ref group=note name=not>Most dialects do not support this.</ref>:
=== Non-Boolean left argument ===
<source lang=apl>
Older dialects restrict the left argument to provide only the above functionality. However, the left argument can be interpreted as a count of how many partitions begin with a particular position:
<syntaxhighlight lang=apl>
       2 0 3 0 0 0 0⊂'HiEarth'
       2 0 3 0 0 0 0⊂'HiEarth'
┌┬──┬┬┬─────┐
┌┬──┬┬┬─────┐
││Hi│││Earth│
││Hi│││Earth│
└┴──┴┴┴─────┘
└┴──┴┴┴─────┘
</source>
</syntaxhighlight>
Additional trailing empty divisions are created by adding an additional division count corresponding to the index beyond the end of the right argument<ref group=note name=not></ref>:
=== Short left argument ===
<source lang=apl>
The dialects that support this extension also allow omission of trailing zeros, which is useful if the partitioning vector is generated by [[indices#Inverse|where's inverse]]:
<syntaxhighlight lang=apl>
      ⍸⍣¯1⊢1 1 3 3 3
2 0 3
      2 0 3⊂'HiEarth'
┌┬──┬┬┬─────┐
││Hi│││Earth│
└┴──┴┴┴─────┘
</syntaxhighlight>
=== Long left argument ===
Additional trailing empty divisions are created by adding an additional division count corresponding to the position beyond the end of the right argument:
<syntaxhighlight lang=apl>
       1 0 1 0 0 0 0 1⊂'HiEarth'
       1 0 1 0 0 0 0 1⊂'HiEarth'
┌──┬─────┬┐
┌──┬─────┬┐
│Hi│Earth││
│Hi│Earth││
└──┴─────┴┘
└──┴─────┴┘
</source>
</syntaxhighlight>
Partition allows a simple definition<ref group=note>In dialects that implement the full functionality of Partitioned Enclose.</ref> of a split-into-lengths function:
 
== Split into lengths ==
The above extensions allow a simple definition of a split-into-lengths function:


[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/qLdP/VHf1GBXvZRHbROqNQxtH3UufNS7S/NRx/JHvWvAnC1AvhVQEVABkJWSVqJg8Ki7BSKQkllcABSshQgAjdEAUuHB6uquZal5JerqGurqwanFxZn5eQFFmSABBXX1FHV1zUddi4EKnSOBvLS8YqCA@v/ggpzMEpAjHvVuVXjU1fSod4XCo94dj3oXH1pvqKAdowCkHrVNNtQB2ff/v7GCsYKJAliTgrpHfrljUWpkfqm9OgA Try it online!]
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/qLdP/VHf1GBXvZRHbROqNQxtH3UufNS7S/NRx/JHvWvAnC1AvhVQEVABkJWSVqJg8Ki7BSKQkllcABSshQgAjdEAUuHB6uquZal5JerqGurqwanFxZn5eQFFmSABBXX1FHV1zUddi4EKnSOBvLS8YqCA@v/ggpzMEpAjHvVuVXjU1fSod4XCo94dj3oXH1pvqKAdowCkHrVNNtQB2ff/v7GCsYKJAliTgrpHfrljUWpkfqm9OgA Try it online!]
<source lang=apl>
<syntaxhighlight lang=apl>
       Split←{⍵ ⊂⍨ ⍸⍣¯1 +\ ¯1↓1,⍺}
       Split←{⍵ ⊂⍨ ⍸⍣¯1 +\ ¯1↓1,⍺}
       3 3 4 Split 'HowAreYou?'
       3 3 4 Split 'HowAreYou?'
Line 32: Line 48:
│How│Are│You?│
│How│Are│You?│
└───┴───┴────┘
└───┴───┴────┘
</source>
</syntaxhighlight>
{{Works in|[[Extended Dyalog APL]]}}
 
==Notes==
== Extension support ==
<references group="note"/>
The following table shows which of the extensions to <syntaxhighlight lang=apl inline>⍺</syntaxhighlight> introduced by [[Dyalog APL 18.0]] are supported in various dialects. [[dzaima/APL]] doesn't support extended lengths but instead requires a short <syntaxhighlight lang=apl inline>⍺</syntaxhighlight>, assuming the first value is 1. This means it can't drop elements as the original Partitioned Enclose typically does, but also means it can't produce leading or trailing empty partitions.
{| class=wikitable
! Languages                !! Non-boolean !! Left argument length
|-
| [[NARS]]                  || {{No}}      || <syntaxhighlight lang=apl inline>=≢⍵</syntaxhighlight>
|-
| [[Dyalog APL]], [[April]] || {{Yes}}     || <syntaxhighlight lang=apl inline>≤1+≢⍵</syntaxhighlight>
|-
| [[dzaima/APL]]            || {{Yes}}    || <syntaxhighlight lang=apl inline>=¯1+≢⍵</syntaxhighlight> (first entry assumed 1)
|-
| [[Kap]] (<syntaxhighlight lang=apl inline>⊆</syntaxhighlight>) || {{Yes}}          || <syntaxhighlight lang=apl inline>=≢⍵</syntaxhighlight>
|}
 
== See also ==
* [[Partition]]
* [[Cut (K)]]
* [[Partition representations]]
 
==External links==
==External links==
===Tutorials===
===Tutorials===
Line 41: Line 74:
===Documentation===
===Documentation===
* [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Partitioned%20Enclose.htm Dyalog]
* [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Partitioned%20Enclose.htm Dyalog]
{{APL built-ins}}
{{APL built-ins}}[[Category:Primitive functions]]
Retrieved from ‘https://aplwiki.com/wiki/Special:MobileDiff/2559...10784’

Navigation menu