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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]].
{{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:


<source lang=apl>
<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:


<source lang=apl>
<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Table is equivalent to [[reshape|reshaping]] with the shape where all trailing axis lengths have been replaced by their [[product]] or, alternatively, the tally concatenated to the [[bound]] divided by the tally:
Table is equivalent to [[reshape|reshaping]] with the shape where all trailing axis lengths have been replaced by their [[product]] or, alternatively, the tally concatenated to the [[bound]] divided by the tally:
<source lang=apl>
<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 <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

Latest 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


APL built-ins [edit]
Primitive functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root
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 ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Primitive operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut (J)
Quad names
Arrays Index origin ∙ Migration level ∙ Atomic vector
Functions Name class ∙ Case convert ∙ Unicode convert
Operators Search ∙ Replace
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