Essays/Transpose

The verb |: (transpose) can be modelled as follows:

mask        =: = /: ~.
rho         =: <./@#
ind         =: (#:i.)@:rho +/ .* #.~
transposeAPL=: (mask@[ ind $@]) { ,@]

rank        =: #@$
pfill       =: (i.@[ -. |) , |
en          =: - #@;
ci          =: (/:@pfill ;) { i.@en , en + (#&> # i.@#)@]
tsp2        =: (rank@] ci [) transposeAPL ]
transpose   =: (i.@-@rank tsp2 ]) : tsp2

tranposeAPL is dyadic transpose in APL. transpose models the verb |: . For example:

   y=: 3 5 7 11 13 17 ?@$ 1e6

   (|: -: transpose) y
1
   (?~ #$y) (|: -: transpose) y
1
   (4 0;1 3 2) (|: -: transpose) y
1

transposeAPL is a translation into J of a model in Dictionary APL that appeared in Section 3.1 of R.K.W. Hui, Some Uses of { and }, APL87, 1987-05-10.

⍺⍉⍵: ((>{⍳¨>(⍴⍵)⌊.+¯×~k)+.×(⍴⍵)⊥k){,⍵ ⊣ k←⍺∘.=⍳1+⌈/⍺

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Contributed by Roger Hui.