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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Table is equivalent to [[reshape|reshaping]] with the shape where all trailing axis lengths have been replaced by their [[product], or alternatively, the tally concatenated to the [[bound]] divided by the tally:
Table is equivalent to [[reshape|reshaping]] with the shape where all trailing axis lengths have been replaced by their [[product]] or, alternatively, the tally concatenated to the [[bound]] divided by the tally: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>
<source lang=apl>
       ⍪2 3 4 2⍴⎕A
       ⍪2 3 4 2⍴⎕A
Line 59: Line 59:
YZABCDEFGHIJKLMNOPQRSTUV
YZABCDEFGHIJKLMNOPQRSTUV
</source>
</source>
In languages where [function axis] is available, Table is equivalent to <source lang=apl inline>,[1↓⍳≢⍴Y]</source>:
In languages where [[function axis]] is available, Table is equivalent to <source lang=apl inline>,[1↓⍳≢⍴Y]</source>:
<source lang=apl>
<source lang=apl>
       {,[1↓⍳≢⍴⍵]⍵}2 3 4 2⍴⎕A
       {,[1↓⍳≢⍴⍵]⍵}2 3 4 2⍴⎕A

Revision as of 08:44, 9 July 2020

⍪

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Table is equivalent to reshaping with the shape where all trailing axis lengths have been replaced by their product or, alternatively, the tally concatenated to the bound divided by the tally: 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]
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
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