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== Examples ==
== Examples ==


For arrays of [[rank]] 1 or higher, the result is identical to applying Ravel to major cells. In languages where [[Rank (operator)|Rank operator]] is available, Table is equivalent to <source lang=apl inline>,⍤¯1</source>.
For arrays of [[rank]] 1 or higher, the result is identical to applying Ravel to major cells:


<source lang=apl>
<source lang=apl>
Line 49: Line 49:
YZABCDEFGHIJKLMNOPQRSTUV
YZABCDEFGHIJKLMNOPQRSTUV
       {⍵⍴⍨(1↑⍴⍵),(×/1↓⍴⍵)}2 3 4 2⍴⎕A
       {⍵⍴⍨(1↑⍴⍵),(×/1↓⍴⍵)}2 3 4 2⍴⎕A
ABCDEFGHIJKLMNOPQRSTUVWX
YZABCDEFGHIJKLMNOPQRSTUV
</source>
In languages where the [[Rank (operator)|Rank operator]] is available, Table is equivalent to <source lang=apl inline>,⍤¯1</source>:
<source lang=apl>
      (,⍤¯1)2 3 4 2⍴⎕A
ABCDEFGHIJKLMNOPQRSTUVWX
YZABCDEFGHIJKLMNOPQRSTUV
</source>
In languages where [function axis] is available, Table is equivalent to <source lang=apl inline>,[1↓⍳≢⍴Y]</source>:
<source lang=apl>
      {,[1↓⍳≢⍴⍵]⍵}2 3 4 2⍴⎕A
ABCDEFGHIJKLMNOPQRSTUVWX
ABCDEFGHIJKLMNOPQRSTUVWX
YZABCDEFGHIJKLMNOPQRSTUV
YZABCDEFGHIJKLMNOPQRSTUV

Revision as of 08:43, 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Table is equivalent to reshaping with the shape where all trailing axis lengths have been replaced by their [[product], or alternatively, the tally concatenated to the bound divided by the tally: 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
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
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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