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 XY 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 XnY. The resulting shape equals the concatenation of the shapes of each element of X.

      VEC111 222 333 444
      3VEC
333
      (4 3)VEC
444 333
      (2 33 1 4 1 2 3)VEC
333 111 444
111 222 333

      MAT10¨3 4
11 12 13 14
21 22 23 24
31 32 33 34
      3(2 1)MAT
32 31
      (2 11)(3 42)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.

     CUBE10¨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 XY selects from leading axes of Y. In that case, the trailing axes are selected without modification.

      MAT10¨3 4  ⍝ Same as the first example
      2MAT  ⍝ 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


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