f must be a dyadic function. Y may be any array whose items in the sub-arrays along the Kth axis are appropriate to 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 applying function f between items of the vectors along the Kth (or implied) axis of Y. For a typical vector Y, the result R is:
R ←→ ⊂(1⊃Y)f(2⊃Y)f......f(n⊃Y)
The shape S of R is the shape of Y excluding the Kth axis, i.e.
S ←→ ⍴R ←→ (K≠⍳⍴⍴Y)/⍴Y
If Y is a scalar then for any function f, R is Y.
If the length of the Kth axis of Y is 1, or if the length of any other axis of Y is 0, then f is not applied and R is S⍴Y.
Otherwise, if the length of the Kth axis is 0 then the result depends on f and on ⊃Y (the prototypical item of Y) as follows:
If f is one of the functions listed in Table 39 then R is S⍴⊂I, where I is formed from ⊃Y by replacing each depth-zero item of ⊃Y with the identity element from the table.
Otherwise if f is Catenate, R is S⍴⊂0/⊃Y. If f is Catenate First, R is S⍴⊂0⌿⊃Y. If f is Catenate along the Jth axis, R is S⍴⊂0/[J]⊃Y. See Catenate/Laminate.
Otherwise, DOMAIN ERROR is reported.
| Function | Identity | |
|---|---|---|
| Add | + | 0 |
| Subtract | - | 0 |
| Multiply | × | 1 |
| Divide | ÷ | 1 |
| Residue | | | 0 |
| Minimum | ⌊ | M1 |
| Maximum | ⌈ | -M |
| Power | * | 1 |
| Binomial | ! | 1 |
| And | ∧ | 1 |
| Or | ∨ | 0 |
| Less | < | 0 |
| Less or Equal | ≤ | 1 |
| Equal | = | 1 |
| Greater | > | 0 |
| Greater or Equal | ≥ | 1 |
| Not Equal | ≠ | 0 |
| Encode | ⊤ | 0 |
| Union | ∪ | ⍬ |
| Replicate | /⌿ | 1 |
| Expand | \⍀ | 1 |
| Rotate | ⌽⊖ | 0 |
Examples
∨/0 0 1 0 0 1 0 1 MAT 1 2 3 4 5 6 +/MAT 6 15
+⌿MAT 5 7 9 +/[1]MAT 5 7 9 +/(1 2 3)(4 5 6)(7 8 9) 12 15 18 ,/'ONE' 'NESS' ONENESS +/⍳0 0
(⊂⍬)≡,/⍬
1
(⊂'')≡,/0⍴'Hello' 'World'
1
(⊂0 3 4⍴0)≡⍪/0⍴⊂2 3 4⍴0
1