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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 <syntaxhighlight lang=apl inline>\</ | {{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>\</syntaxhighlight> is called Expand while <syntaxhighlight lang=apl inline>⍀</syntaxhighlight> is called "Expand First" or an equivalent. | ||
Expand is usually associated with [[Replicate]] (<syntaxhighlight lang=apl inline>/</ | Expand is usually associated with [[Replicate]] (<syntaxhighlight lang=apl inline>/</syntaxhighlight>), 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 == | ||
| Line 10: | Line 10: | ||
1 0 3 ¯2 2\'abc' | 1 0 3 ¯2 2\'abc' | ||
a bbb cc | a bbb cc | ||
</ | </syntaxhighlight> | ||
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: | ||
| Line 19: | Line 19: | ||
1 0 0 1 0 1/'a b c' | 1 0 0 1 0 1/'a b c' | ||
abc | abc | ||
</ | </syntaxhighlight> | ||
=== 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 <syntaxhighlight lang=apl inline>⍀</ | 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>⍀</syntaxhighlight>, and the last axis for <syntaxhighlight lang=apl inline>\</syntaxhighlight>. | ||
<syntaxhighlight lang=apl> | <syntaxhighlight lang=apl> | ||
| Line 42: | Line 42: | ||
IJKL | IJKL | ||
IJKL | IJKL | ||
</ | </syntaxhighlight> | ||
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. | ||
| Line 50: | Line 50: | ||
b bbb | b bbb | ||
c ccc | c ccc | ||
</ | </syntaxhighlight> | ||
== External Links == | == External Links == | ||