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[[K]] takes advantage of this relationship by removing the primitive Replicate entirely: the glyph <code>&</code> is paired with [[Minimum]] instead. In K, Replicate is performed by using Where and then [[Bracket indexing|indexing]]. | [[K]] takes advantage of this relationship by removing the primitive Replicate entirely: the glyph <code>&</code> is paired with [[Minimum]] instead. In K, Replicate is performed by using Where and then [[Bracket indexing|indexing]]. | ||
== Inverse == | |||
The [[inverse]] of Indices, <source lang=apl inline>⍸⍣¯1</source>, is the mapping from an ordered (multi-)set of indices to an array where each element is the count for its position. For a simple non-empty vector <source lang=apl inline>Y</source> without duplicates, the expression <source lang=apl inline>R←(⍸⍣¯1)Y</source> gives a Boolean vector <source lang=apl inline>R</source> with ones at the indices in <source lang=apl inline>Y</source>. This is equivalent to <source lang=apl inline>R←(1@Y)0⍴⍨⌈/Y</source> which is useful in conversion between [[partition representations]]. | |||
It should be noted that the inverse is not unique because <source lang=apl inline>(⍸Y) ≡ (⍸Z)</source> if <source lang=apl inline>Y</source> and <source lang=apl inline>Z</source> differ only by the number of trailing zeros. <source lang=apl inline>⍸⍣¯1</source> does not add any trailing zeros, and it may be necessary to add those separately, for example using [[overtake]]. | |||
== History == | == History == | ||
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Indices (<source lang=apl inline>⍸</source>) was first introduced to APL, and the [[nested array model]], by [[NARS2000]]. Originally defined only for vectors, the generalised definition <source lang=apl inline>(,R)/,⍳⍴1/R</source> was introduced in about 2013 after some experimentation with alternatives.<ref>NARS2000 Wiki. [http://wiki.nars2000.org/index.php?title=Indices&direction=next&oldid=863 Indices]. Old revision: 2013-05-26.</ref> Where (<source lang=apl inline>⍸</source>) was added to [[Dyalog APL 16.0]] (June 2017), with the nearly-identical definition <source lang=apl inline>{(,⍵)⌿,⍳⍴⍵}</source>, but also with the restriction that the argument be Boolean. This restriction that was lifted to allow non-negative integers in [[Dyalog APL 18.0|18.0]] (2020). For a [[scalar]] <source lang=apl inline>I</source>, Dyalog's definition gives <source lang=apl inline>I⍴⊂⍬</source> for <source lang=apl inline>⍸I</source>, while NARS2000 returned <source lang=apl inline>I⍴1</source>. By January 2018, NARS2000 switched to Dyalog's definition, removing the discrepancy for scalar arguments. | Indices (<source lang=apl inline>⍸</source>) was first introduced to APL, and the [[nested array model]], by [[NARS2000]]. Originally defined only for vectors, the generalised definition <source lang=apl inline>(,R)/,⍳⍴1/R</source> was introduced in about 2013 after some experimentation with alternatives.<ref>NARS2000 Wiki. [http://wiki.nars2000.org/index.php?title=Indices&direction=next&oldid=863 Indices]. Old revision: 2013-05-26.</ref> Where (<source lang=apl inline>⍸</source>) was added to [[Dyalog APL 16.0]] (June 2017), with the nearly-identical definition <source lang=apl inline>{(,⍵)⌿,⍳⍴⍵}</source>, but also with the restriction that the argument be Boolean. This restriction that was lifted to allow non-negative integers in [[Dyalog APL 18.0|18.0]] (2020). For a [[scalar]] <source lang=apl inline>I</source>, Dyalog's definition gives <source lang=apl inline>I⍴⊂⍬</source> for <source lang=apl inline>⍸I</source>, while NARS2000 returned <source lang=apl inline>I⍴1</source>. By January 2018, NARS2000 switched to Dyalog's definition, removing the discrepancy for scalar arguments. | ||
The [[#inverse|inverse]] of Indices became supported with [[Dyalog APL 18.0]]. | |||
== External links == | == External links == | ||