Scan R←f\[K]Y

f may be any dyadic function that returns a result.  Y may be any array whose items in the sub-arrays along the Kth axis are appropriate to the function f.

The axis specification is optional.  If present, K must identify an axis of Y.  If absent, the last axis of Y is implied.  The form R←f⍀Y implies the first axis of Y.

R is an array formed by successive reductions along the Kth axis of Y.  If V is a typical vector taken from the Kth axis of Y, then the Ith element of the result is determined as f/I↑V.

The shape of R is the same as the shape of Y.  If Y is an empty array, then R is the same empty array.

Examples

      ∨\0 0 1 0 0 1 0
0 0 1 1 1 1 1
 
      ^\1 1 1 0 1 1 1
1 1 1 0 0 0 0
 
      +\1 2 3 4 5
1 3 6 10 15
 
      +\(1 2 3)(4 5 6)(7 8 9)
 1 2 3  5 7 9  12 15 18

 

      M
1 2 3
4 5 6
 
      +\M
1 3  6
4 9 15
 
      +⍀M
1 2 3
5 7 9
 
      +\[1]M
1 2 3
5 7 9
 
      ,\'ABC'
A AB  ABC
 
      T←'ONE(TWO) BOOK(S)'
 
      ≠\T∊'()'
0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0
 
      ((T∊'()')⍱≠\T∊'()')/T
ONE BOOK