Inner Product R←Xf.gY

f and g are dyadic functions. The last axis of X must have the same length as the first axis of Y, or one of X and Y is single (^/1=⍴X or ^/1=⍴Y).

The result of the derived function has shape (¯1↓⍴X),1↓⍴Y; each item is f/x g¨y where x and y are vectors taken from all the combinations of vectors along the last axis of X and the first axis of Y.

Note

g must return a result.
f must return a result with the possible exception of the case when 1=⍴x g¨y.
The expression f/x g¨y applies even when R or x g¨y or X or Y is empty. When X or Y is empty, the vector x is X reshaped to the appropriate length (y is Y reshaped to appropriate length).
x is just X itself if X is a scalar. Likewise y and Y.

Examples

      1 2 3+.×10 12 14
76
      +/1 2 3×10 12 14
76

      NAMES
HENRY
WILLIAM
JAMES
SEBASTIAN

      NAMES^.='WILLIAM  '
0 1 0 0