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{{Built-in|Table|⍪}}, or '''Ravel Items''', is a [[monadic]] [[primitive function]] which returns a [[matrix]] formed by applying [[Ravel]] to each [[major cell]] of the given array. Table shares its [[glyph]] < | :''This page is about the function that reshapes into a table. For the operator that generates a table of all combinations, see [[Outer Product]].'' | ||
{{Built-in|Table|⍪}}, or '''Ravel Items''', is a [[monadic]] [[primitive function]] which returns a [[matrix]] formed by applying [[Ravel]] to each [[major cell]] of the given array. Table shares its [[glyph]] <syntaxhighlight lang=apl inline>⍪</syntaxhighlight> with the dyadic function [[catenate|Catenate First]]. | |||
== Examples == | == Examples == | ||
| Line 5: | Line 6: | ||
For arrays of [[rank]] 1 or higher, the result is identical to applying Ravel to major cells: | For arrays of [[rank]] 1 or higher, the result is identical to applying Ravel to major cells: | ||
< | <syntaxhighlight lang=apl> | ||
{⍵(⍴⍵)}⍪5⍴⎕A | {⍵(⍴⍵)}⍪5⍴⎕A | ||
┌─┬───┐ | ┌─┬───┐ | ||
| Line 25: | Line 26: | ||
│MNOPQRSTUVWX│ │ | │MNOPQRSTUVWX│ │ | ||
└────────────┴────┘ | └────────────┴────┘ | ||
</ | </syntaxhighlight> | ||
A [[scalar]] [[argument]] is converted to a 1-by-1 matrix: | A [[scalar]] [[argument]] is converted to a 1-by-1 matrix: | ||
< | <syntaxhighlight lang=apl> | ||
{⍵(⍴⍵)}⍪123 | {⍵(⍴⍵)}⍪123 | ||
┌───┬───┐ | ┌───┬───┐ | ||
│123│1 1│ | │123│1 1│ | ||
└───┴───┘ | └───┴───┘ | ||
</ | </syntaxhighlight> | ||
== Properties == | == Properties == | ||
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Table preserves the array's [[Tally]] (the number of major cells). | Table preserves the array's [[Tally]] (the number of major cells). | ||
Table is equivalent to [[reshape|reshaping]] with the shape where all trailing axis lengths have been replaced by their [[product], | Table is equivalent to [[reshape|reshaping]] with the shape where all trailing axis lengths have been replaced by their [[product]] or, alternatively, the tally concatenated to the [[bound]] divided by the tally: | ||
< | <syntaxhighlight lang=apl> | ||
⍪2 3 4 2⍴⎕A | ⍪2 3 4 2⍴⎕A | ||
ABCDEFGHIJKLMNOPQRSTUVWX | ABCDEFGHIJKLMNOPQRSTUVWX | ||
| Line 51: | Line 52: | ||
ABCDEFGHIJKLMNOPQRSTUVWX | ABCDEFGHIJKLMNOPQRSTUVWX | ||
YZABCDEFGHIJKLMNOPQRSTUV | YZABCDEFGHIJKLMNOPQRSTUV | ||
</ | </syntaxhighlight> | ||
In languages where the [[Rank (operator)|Rank operator]] is available, Table is equivalent to < | In languages where the [[Rank (operator)|Rank operator]] is available, Table is equivalent to <syntaxhighlight lang=apl inline>,⍤¯1</syntaxhighlight>: | ||
< | <syntaxhighlight lang=apl> | ||
(,⍤¯1)2 3 4 2⍴⎕A | (,⍤¯1)2 3 4 2⍴⎕A | ||
ABCDEFGHIJKLMNOPQRSTUVWX | ABCDEFGHIJKLMNOPQRSTUVWX | ||
YZABCDEFGHIJKLMNOPQRSTUV | YZABCDEFGHIJKLMNOPQRSTUV | ||
</ | </syntaxhighlight> | ||
In languages where [function axis] is available, Table is equivalent to < | In languages where [[function axis]] is available, Table is equivalent to <syntaxhighlight lang=apl inline>,[1↓⍳≢⍴Y]</syntaxhighlight>: | ||
< | <syntaxhighlight lang=apl> | ||
{,[1↓⍳≢⍴⍵]⍵}2 3 4 2⍴⎕A | {,[1↓⍳≢⍴⍵]⍵}2 3 4 2⍴⎕A | ||
ABCDEFGHIJKLMNOPQRSTUVWX | ABCDEFGHIJKLMNOPQRSTUVWX | ||
YZABCDEFGHIJKLMNOPQRSTUV | YZABCDEFGHIJKLMNOPQRSTUV | ||
</ | </syntaxhighlight> | ||
== History == | |||
Table was implemented in [[SHARP APL]] release 19.0,<ref>[[Robert Bernecky]]. [https://dl.acm.org/citation.cfm?id=55632 An Introduction to Function Rank] at [[APL88]]. [[APL Quote Quad]], Volume 18, Issue 2. December 1987.</ref> and included in [[A Dictionary of APL]] in the same year. It was eventually included [[ISO/IEC 13751:2001]] standard, although other dialects had generally not adopted it: a 2005 review lists only a non-conforming implementation in [[APLX]].<ref>F.H.D. van Batenburg. [http://archive.vector.org.uk/art10000930 Conformity of APL Implementations to the ISO APL Standard]. [[Vector journal]] Volume 21, No.3. 2005-05.</ref> Table was added in [[Dyalog APL 12.1]], released in 2009, and it generally appears in modern dialects (for example [[ngn/apl]] and [[Kap]]). | |||
== External links == | == External links == | ||
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=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Enlist.htm Dyalog] | ||
* J [https://www.jsoftware.com/help/dictionary/d321.htm Vocabulary], [https://code.jsoftware.com/wiki/Vocabulary/commadot NuVoc] | * J [https://www.jsoftware.com/help/dictionary/d321.htm Vocabulary], [https://code.jsoftware.com/wiki/Vocabulary/commadot NuVoc] | ||
{{APL built-ins}}[[Category:Primitive functions]] | {{APL built-ins}}[[Category:Primitive functions]] | ||