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{{Built-ins|Expand|<nowiki>\</nowiki>|⍀}} is a [[dyadic function]] or [[monadic operator]] that copies each [[element]] of the right [[argument]] a given number of times and inserts [[prototype]] elements, ordering the copies along a specified [[axis]]. Typically < | {{Built-ins|Expand|<nowiki>\</nowiki>|⍀}} is a [[dyadic function]] or [[monadic operator]] that copies each [[element]] of the right [[argument]] a given number of times and inserts [[prototype]] elements, ordering the copies along a specified [[axis]]. Typically <syntaxhighlight lang=apl inline>\</source> is called Expand while <syntaxhighlight lang=apl inline>⍀</source> is called "Expand First" or an equivalent. | ||
Expand is usually associated with [[Replicate]] (< | Expand is usually associated with [[Replicate]] (<syntaxhighlight lang=apl inline>/</source>), and the two functions are related to [[Mesh]] and [[Mask]]. It shares a [[glyph]] with [[Scan]] even though Expand is naturally a [[function]] and Scan must be an [[operator]]. This incongruity is sometimes resolved by making Expand an operator itself, and sometimes by [[function-operator overloading]] allowing both syntactic elements to coexist. | ||
== Examples == | == Examples == | ||
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If the right argument is a [[vector]], the number of positive values in the left argument must match the length of the right argument. Each positive value produces copies of the corresponding item on the right argument; a zero or negative value produces one or more prototype elements. | If the right argument is a [[vector]], the number of positive values in the left argument must match the length of the right argument. Each positive value produces copies of the corresponding item on the right argument; a zero or negative value produces one or more prototype elements. | ||
< | <syntaxhighlight lang=apl> | ||
1 0 3 ¯2 2\'abc' | 1 0 3 ¯2 2\'abc' | ||
a bbb cc | a bbb cc | ||
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For [[Boolean]] left argument, Expand is the right inverse of [[Replicate]], as Expand inserts prototype elements at the exact places which Replicate will remove: | For [[Boolean]] left argument, Expand is the right inverse of [[Replicate]], as Expand inserts prototype elements at the exact places which Replicate will remove: | ||
< | <syntaxhighlight lang=apl> | ||
1 0 0 1 0 1\'abc' | 1 0 0 1 0 1\'abc' | ||
a b c | a b c | ||
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=== High-rank arrays === | === High-rank arrays === | ||
Expand works along a particular [[axis]], which can be specified in languages with [[function axis]] and otherwise is the first axis for < | Expand works along a particular [[axis]], which can be specified in languages with [[function axis]] and otherwise is the first axis for <syntaxhighlight lang=apl inline>⍀</source>, and the last axis for <syntaxhighlight lang=apl inline>\</source>. | ||
< | <syntaxhighlight lang=apl> | ||
⎕←A←3 4⍴⎕A | ⎕←A←3 4⍴⎕A | ||
ABCD | ABCD | ||
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Some implementations allow the right argument to have length 1 along the expansion axis even if other axes have lengths not equal to 1. | Some implementations allow the right argument to have length 1 along the expansion axis even if other axes have lengths not equal to 1. | ||
< | <syntaxhighlight lang=apl> | ||
1 ¯2 3 \ ⍪'abc' | 1 ¯2 3 \ ⍪'abc' | ||
a aaa | a aaa | ||