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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>\</syntaxhighlight> is called Expand while <syntaxhighlight lang=apl inline>⍀</syntaxhighlight> is called "Expand First" or an equivalent. | ||
Expand is usually associated with [[Replicate]] (< | 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 == | ||
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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 | ||
</ | </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: | ||
< | <syntaxhighlight lang=apl> | ||
1 0 0 1 0 1\'abc' | 1 0 0 1 0 1\'abc' | ||
a b c | a b c | ||
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 < | 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> | ||
⎕←A←3 4⍴⎕A | ⎕←A←3 4⍴⎕A | ||
ABCD | ABCD | ||
| 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. | ||
< | <syntaxhighlight lang=apl> | ||
1 ¯2 3 \ ⍪'abc' | 1 ¯2 3 \ ⍪'abc' | ||
a aaa | a aaa | ||
b bbb | b bbb | ||
c ccc | c ccc | ||
</ | </syntaxhighlight> | ||
== External Links == | == External Links == | ||
Latest revision as of 22:11, 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 \ is called Expand while ⍀ is called "Expand First" or an equivalent.
Expand is usually associated with Replicate (/), 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.
1 0 3 ¯2 2\'abc' a bbb cc
For Boolean left argument, Expand is the right inverse of Replicate, as Expand inserts prototype elements at the exact places which Replicate will remove:
1 0 0 1 0 1\'abc'
a b c
1 0 0 1 0 1/'a b c'
abc
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 ⍀, and the last axis for \.
⎕←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
Some implementations allow the right argument to have length 1 along the expansion axis even if other axes have lengths not equal to 1.
1 ¯2 3 \ ⍪'abc' a aaa b bbb c ccc
External Links
Lessons
Documentation