Skip to content
⍉

Transpose (Dyadic) R←X⍉Y

Y may be any array. X must be a simple scalar or vector whose elements are included in the set ⍳⍴⍴Y. Integer values in X may be repeated but all integers in the set ⍳⌈/X must be included. The length of X must equal the rank of Y.

R is an array formed by the transposition of the axes of Y as specified by X. The Ith element of X gives the new position for the Ith axis of Y. If X repositions two or more axes of Y to the same axis, the elements used to fill this axis are those whose indices on the relevant axes of Y are equal.

⎕IO is an implicit argument of Dyadic Transpose.

Examples

      A
 1  2  3  4
 5  6  7  8
 9 10 11 12

13 14 15 16
17 18 19 20
21 22 23 24

      2 1 3⍉A
 1  2  3  4
13 14 15 16

 5  6  7  8
17 18 19 20

 9 10 11 12
21 22 23 24

      1 1 1⍉A
1 18

      1 1 2⍉A
 1  2  3  4
17 18 19 20

Alternative Explanation

Assign a distinct letter for each unique integer in X : 

0 1 2 3 …
i j k l

If R←X⍉Y, then R[i;j;k;…] equals Y indexed by the letters corresponding to elements of X .

For example

      ⎕IO←0

      Y← ? 5 13 19 17 11 ⍴ 100

      X← 2 1 2 0 1
      ⍝  k j k i j

      R←X⍉Y

      i←?17 ⋄ j←?11 ⋄ k←?5
      R[i;j;k] = Y[k;j;k;i;j]
1
      R[i;j;k]=Y[⊂⍎¨'ijk'[X]]
1

From the above it can be seen that:

  • the rank of R is 0⌈1+⌈/X
  • the shape of R is (⍴Y)⌊.+(⌈/⍴Y)×X∘.≠⍳0⌈1+⌈/X