Index Generator

• Monadic iota (⍳R) is extended to negative right arguments, returning a vector of length |R whose values complement on the left the corresponding values from ⍳|R.

  For example, in origin-0

        ⍳3
  0 1 2

        ⍳¯3
  ¯3 ¯2 ¯1

  and in origin-1

        ⍳3
  1 2 3

        ⍳¯3
  

  ¯2 ¯1 0

• Monadic iota (⍳R) is extended to length > 1 vector right arguments, returning a nested array of shape R whose items are each integer vectors of length ⍴⍴R.

  For example, in origin-0

        ⍳2 3
   0 0  0 1  0 2
   1 0  1 1  1 2

        ⍳2 ¯3
   0 ¯3  0 ¯2  0 ¯1
   1 ¯3  1 ¯2  1 ¯1

  and in origin-1

        ⍳2 3
   1 1  1 2  1 3
   2 1  2 2  2 3

        ⍳2 ¯3
   1 ¯2  1 ¯1  1 0
   2 ¯2  2 ¯1  2 0

  This extension is implemented via an internal magic function due to Carl M. Cheney:

      ∇ Z←F V
  [1]   Z←⊃∘.,/⍳¨V
  

      ∇