Outer Product {R}←X∘.gY

g may be any dyadic function. The left operand of the operator is the symbol ∘. X and Y may be any arrays whose elements are appropriate to the function g.

Function g is applied to all combinations of the elements of X and Y. If function g returns a result, the shape of R is (⍴X),⍴Y. Each element of R is the item returned by function g when applied to the particular combination of elements of X and Y.

If X or Y is empty, the result R is a conformable empty array, and the operand function is applied once between the first items of X and Y to determine the prototype of R.

Examples

      1 2 3∘.×10 20 30 40
10 20 30  40
20 40 60  80
30 60 90 120

      1 2 3∘.⍴'AB'
 A    B
 AA   BB
 AAA  BBB

      1 2∘.,1 2 3
 1 1  1 2  1 3
 2 1  2 2  2 3

      (⍳3)∘.=⍳3
1 0 0
0 1 0
0 0 1