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{{Built- | {{Built-ins|Unique|∪|↑}}, or '''Nub''', is a [[monadic]] [[set function]] which removes duplicate [[major cells]] from an array. It returns only the distinct cells (those which do not [[match]] an earlier distinct cell) in the order they appeared in the array. | ||
== Examples == | == Examples == | ||
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In some languages, such as [[J]] and [[Dyalog APL 17.0]] and later, Unique applies to the [[major cells]] of an array, including those with rank greater than 1: | In some languages, such as [[J]] and [[Dyalog APL 17.0]] and later, Unique applies to the [[major cells]] of an array, including those with rank greater than 1: | ||
<source lang=apl> | <source lang=apl> | ||
⎕←x ← (⍳10)∘.∨2 3 6 | |||
1 1 1 | 1 1 1 | ||
2 1 2 | 2 1 2 | ||
| Line 49: | Line 49: | ||
⎕CT←1e¯14 | ⎕CT←1e¯14 | ||
⎕PP←18 ⍝ Print all digits | ⎕PP←18 ⍝ Print all digits | ||
⎕←x←1+⎕CT×0 0.6 1.2 | |||
1 1.000000000000006 1.000000000000012 | 1 1.000000000000006 1.000000000000012 | ||
⍳⍨x ⍝ Each element equal to the previous | ⍳⍨x ⍝ Each element equal to the previous | ||
| Line 61: | Line 61: | ||
</source> | </source> | ||
{{Works in|[[Dyalog APL]]}} | {{Works in|[[Dyalog APL]]}} | ||
== History == | |||
The function Nub was proposed in 1978 by [[Ken Iverson|Iverson]] as one of a collection of set functions (including [[Union]], [[Intersection]], and [[Difference]]) with the symbol <source lang=apl inline>∪</source> and definition <source lang=apl inline>∪w</source> {{←→}} <source lang=apl inline>((⍳⍴w)=w⍳w)/w←,w</source>.<ref>[[Ken Iverson|Iverson, Ken]]. [https://www.jsoftware.com/papers/opfns.htm ''Operators and Functions'']. IBM Research Report #RC7091. 1978-04-26.</ref> It was implemented as part of [[STSC]]'s [[NARS]] in 1981 with the name Unique and the same definition, except that the argument was restricted to be a vector or scalar.<ref>Cheney, Carl. ''APL*PLUS Nested Arrays Reference Manual. [[STSC]] Inc. 1981.</ref> Later APLs such as [[Dyalog APL]] generally adopted this version of the primitive, and it is featured in the [[ISO/IEC 13751:2001]] standard. Dyalog extended Unique to higher-rank arrays in [[Dyalog APL 17.0]], following the much earlier extension made by [[J]]. | |||
Iverson continued to refine his definition of Nub. He included it in his [[Rationalized APL]] specification with no changes in 1983, but modified it to work on [[major cell]]s (thus aligning it with [[leading axis theory]]) in his 1987 [[A Dictionary of APL]]. Iverson's dictionary also changed the symbol for Nub to <source lang=apl inline>↑</source>, added the functions [[Nub Sieve]] (<source lang=apl inline>≠</source>) and [[Nub in]] (<source lang=apl inline>=</source>), and defined Nub in terms of Nub Sieve. These definitions were adopted by [[IPSA]] in the [[SHARP APL]] successor [[SAX]]. [[J]] uses similar definitions: its Nub-related functions are Nub (<source lang=j inline>~.</source>), [[Nub Sieve]] (<source lang=j inline>~:</source>), and [[Self-classify]] (<source lang=j inline>=</source>). However, Self-classify is indicated as deprecated in J's NuVoc because its result can be much larger than its argument. | |||
[[A+]] does not include Unique or any related functions, but [[K]]'s function range (<code>?</code>) gives the unique elements of a list argument. In later versions it is called "distinct" or "unique". While APLs allow a [[scalar]] argument ([[scalar rank extension]]), K gives a [[RANK ERROR]] if the argument is not a list. | |||
== APL model == | == APL model == | ||
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{{Works in|[[Dyalog APL]]}} | {{Works in|[[Dyalog APL]]}} | ||
While the model <source lang=apl inline>{((⍳≢⍵)=(⍵⍳⍵))⌿⍵}</source>, based on [[Nub Sieve]], is often described as an implementation of Unique, it does not correctly handle [[tolerant comparison]]. A correct implementation of Nub Sieve could be used to implement Unique, but writing such an implementation is no easier than implementing Unique directly. | While the model <source lang=apl inline>{((⍳≢⍵)=(⍵⍳⍵))⌿⍵}</source>, based on [[Nub Sieve]], is often described as an implementation of Unique, it does not correctly handle [[tolerant comparison]].<ref>Hui, Roger. [https://dyalog.tv/Dyalog17/?v=fPWky9IOG40 Tolerant Unique]. [[Dyalog '17]].</ref> A correct implementation of Nub Sieve could be used to implement Unique, but writing such an implementation is no easier than implementing Unique directly. | ||
== Properties == | == Properties == | ||
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* [https://www.jsoftware.com/help/dictionary/d221.htm J Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/tildedot J NuVoc] (as <source lang=apl inline>~.</source>) | * [https://www.jsoftware.com/help/dictionary/d221.htm J Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/tildedot J NuVoc] (as <source lang=apl inline>~.</source>) | ||
{{APL built-ins}} | |||
== References == | |||
<references /> | |||
{{APL built-ins}}[[Category:Primitive functions]][[Category:Set functions]] | |||