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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]] <source lang=apl inline>⍪</syntaxhighlight> with the dyadic function [[catenate|Catenate First]].
:''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:


<source lang=apl>
<syntaxhighlight lang=apl>
       {⍵(⍴⍵)}⍪5⍴⎕A
       {⍵(⍴⍵)}⍪5⍴⎕A
┌─┬───┐
┌─┬───┐
Line 29: Line 30:
A [[scalar]] [[argument]] is converted to a 1-by-1 matrix:
A [[scalar]] [[argument]] is converted to a 1-by-1 matrix:


<source lang=apl>
<syntaxhighlight lang=apl>
       {⍵(⍴⍵)}⍪123
       {⍵(⍴⍵)}⍪123
┌───┬───┐
┌───┬───┐
Line 41: Line 42:


Table is equivalent to [[reshape|reshaping]] with the shape where all trailing axis lengths have been replaced by their [[product]] or, alternatively, the tally concatenated to the [[bound]] divided by the tally:
Table is equivalent to [[reshape|reshaping]] with the shape where all trailing axis lengths have been replaced by their [[product]] or, alternatively, the tally concatenated to the [[bound]] divided by the tally:
<source lang=apl>
<syntaxhighlight lang=apl>
       ⍪2 3 4 2⍴⎕A
       ⍪2 3 4 2⍴⎕A
ABCDEFGHIJKLMNOPQRSTUVWX
ABCDEFGHIJKLMNOPQRSTUVWX
Line 53: Line 54:
</syntaxhighlight>
</syntaxhighlight>


In languages where the [[Rank (operator)|Rank operator]] is available, Table is equivalent to <source lang=apl inline>,⍤¯1</syntaxhighlight>:
In languages where the [[Rank (operator)|Rank operator]] is available, Table is equivalent to <syntaxhighlight lang=apl inline>,⍤¯1</syntaxhighlight>:
<source lang=apl>
<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 <source lang=apl inline>,[1↓⍳≢⍴Y]</syntaxhighlight>:
In languages where [[function axis]] is available, Table is equivalent to <syntaxhighlight lang=apl inline>,[1↓⍳≢⍴Y]</syntaxhighlight>:
<source lang=apl>
<syntaxhighlight lang=apl>
       {,[1↓⍳≢⍴⍵]⍵}2 3 4 2⍴⎕A
       {,[1↓⍳≢⍴⍵]⍵}2 3 4 2⍴⎕A
ABCDEFGHIJKLMNOPQRSTUVWX
ABCDEFGHIJKLMNOPQRSTUVWX
YZABCDEFGHIJKLMNOPQRSTUV
YZABCDEFGHIJKLMNOPQRSTUV
</syntaxhighlight>
</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 ==

Latest revision as of 15:33, 17 March 2024

This page is about the function that reshapes into a table. For the operator that generates a table of all combinations, see Outer Product.
⍪

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

History

Table was implemented in SHARP APL release 19.0,[1] 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.[2] 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

Lessons

Documentation


APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
  1. ↑ Robert Bernecky. An Introduction to Function Rank at APL88. APL Quote Quad, Volume 18, Issue 2. December 1987.
  2. ↑ F.H.D. van Batenburg. Conformity of APL Implementations to the ISO APL Standard. Vector journal Volume 21, No.3. 2005-05.
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