Index (function)

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This article describes a dyadic primitive function that performs indexing into an array. For the concept of array indices, see Index. For the concept of extracting items from an array, see Indexing.
⌷

Index (⌷), also called Squad Indexing after the name of the glyph, is a dyadic primitive function. The result of X⌷Y is an array formed with items of Y extracted by the index specification X. Index is a proper function alternative to a mode of bracket indexing (which uses a dedicated syntax Y[X]), making it usable within tacit programming. It shares its glyph with the monadic Materialise function.

Examples

The left argument X must be a vector whose length equals the rank of the right argument Y and depth does not exceed 2. Each element of X selects one or more indices over the corresponding axis of the right argument Y. The result is identical to that of bracket indexing in that Y[X1;X2;…;Xn] ≡ X1 X2 … Xn⌷Y. The resulting shape equals the concatenation of the shapes of each element of X. 

      VEC←111 222 333 444
      3⌷VEC
333
      (⊂4 3)⌷VEC
444 333
      (⊂2 3⍴3 1 4 1 2 3)⌷VEC
333 111 444
111 222 333

      ⎕←MAT←10⊥¨⍳3 4
11 12 13 14
21 22 23 24
31 32 33 34
      3(2 1)⌷MAT
32 31
      ⍴(2 1⍴1)(3 4⍴2)⌷MAT
2 1 3 4

When used with function axis in the form of X⌷[K]Y, K specifies a subset of axes of Y to apply indexing on. The axes not mentioned in K are selected without modification; this corresponds to omitted axes in bracket indexing. 

     ⎕←CUBE←10⊥¨⍳2 3 4
111 112 113 114
121 122 123 124
131 132 133 134
               
211 212 213 214
221 222 223 224
231 232 233 234
 
      2⌷[1]CUBE
211 212 213 214
221 222 223 224
231 232 233 234
 
      2⌷[3]CUBE
112 122 132
212 222 232
 
      CUBE[;;2] ≡ 2⌷[3]CUBE
1

In some dialects that support leading axis theory, short X in X⌷Y selects from leading axes of Y. In that case, the trailing axes are selected without modification. 

      MAT←10⊥¨⍳3 4  ⍝ Same as the first example
      2⌷MAT  ⍝ Second axis omitted
21 22 23 24
Works in: Dyalog APL

Implementation support

This form of indexing is supported in J as boxed left argument of From {.

See also

External links

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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