Expand: Difference between revisions
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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 | ||
Revision as of 22:04, 10 September 2022
\ ⍀
|
Expand (\, ⍀) 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 (<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
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'
a bbb cc </source>
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'
a b c
1 0 0 1 0 1/'a b c'
abc </source>
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>⍀</source>, and the last axis for <syntaxhighlight lang=apl inline>\</source>.
<syntaxhighlight lang=apl>
⎕←A←3 4⍴⎕A
ABCD EFGH IJKL
1 0 3 2 ¯2 1\A
A BBBCC D E FFFGG H I JJJKK L
3 1 ¯1 2⍀A
ABCD ABCD ABCD EFGH
IJKL IJKL </source>
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'
a aaa b bbb c ccc </source>
External Links
Lessons
Documentation