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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]] < | {{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 == | ||
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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 29: | Line 29: | ||
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 | ||
┌───┬───┐ | ┌───┬───┐ | ||
| Line 41: | Line 41: | ||
Table is equivalent to [[reshape|reshaping]] with the shape where all trailing axis lengths have been replaced by their [[product]] or, alternatively, the tally concatenated to the [[bound]] divided by the tally: | Table is equivalent to [[reshape|reshaping]] with the shape where all trailing axis lengths have been replaced by their [[product]] or, alternatively, the tally concatenated to the [[bound]] divided by the tally: | ||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 53: | Line 53: | ||
</syntaxhighlight> | </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> | </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 | ||
Revision as of 10:59, 11 September 2022
⍪
|
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 ⍪ with the dyadic function Catenate First.
Examples
For arrays of rank 1 or higher, the result is identical to applying Ravel to major cells:
{⍵(⍴⍵)}⍪5⍴⎕A
┌─┬───┐
│A│5 1│
│B│ │
│C│ │
│D│ │
│E│ │
└─┴───┘
{⍵(⍴⍵)}⍪3 4⍴⎕A
┌────┬───┐
│ABCD│3 4│
│EFGH│ │
│IJKL│ │
└────┴───┘
{⍵(⍴⍵)}⍪2 3 4⍴⎕A
┌────────────┬────┐
│ABCDEFGHIJKL│2 12│
│MNOPQRSTUVWX│ │
└────────────┴────┘
A scalar argument is converted to a 1-by-1 matrix:
{⍵(⍴⍵)}⍪123
┌───┬───┐
│123│1 1│
└───┴───┘
Properties
Table preserves the array's Tally (the number of major cells).
Table is equivalent to 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:
⍪2 3 4 2⍴⎕A
ABCDEFGHIJKLMNOPQRSTUVWX
YZABCDEFGHIJKLMNOPQRSTUV
{⍵⍴⍨(≢⍵),(×/⍴⍵)÷≢⍵}2 3 4 2⍴⎕A
ABCDEFGHIJKLMNOPQRSTUVWX
YZABCDEFGHIJKLMNOPQRSTUV
{⍵⍴⍨(1↑⍴⍵),(×/1↓⍴⍵)}2 3 4 2⍴⎕A
ABCDEFGHIJKLMNOPQRSTUVWX
YZABCDEFGHIJKLMNOPQRSTUV
In languages where the Rank operator is available, Table is equivalent to ,⍤¯1:
(,⍤¯1)2 3 4 2⍴⎕A ABCDEFGHIJKLMNOPQRSTUVWX YZABCDEFGHIJKLMNOPQRSTUV
In languages where function axis is available, Table is equivalent to ,[1↓⍳≢⍴Y]:
{,[1↓⍳≢⍴⍵]⍵}2 3 4 2⍴⎕A
ABCDEFGHIJKLMNOPQRSTUVWX
YZABCDEFGHIJKLMNOPQRSTUV
External links
Lessons
Documentation