Inner Product (`f.g`)¶

Syntax¶

X f.g Y

f and g are dyadic scalar functions. X and Y are arrays.

Description¶

Generalised inner product. Applies g to corresponding pairs along the last axis of X and the first axis of Y, then reduces the results with f.

The classic case is +.× (matrix multiply / dot product).

Vector dot product¶

      1 2 3 +.× 4 5 6
32

Computes (1×4)+(2×5)+(3×6).

Matrix multiply¶

      (2 3⍴⍳6) +.× 3 2⍴⍳6
22 28
49 64

The left array has shape 2 3, the right has shape 3 2, and the result has shape 2 2.

Other inner products¶

You can use any pair of dyadic functions. For example, ∧.= tests whether two vectors are identical element-wise:

      1 2 3 ∧.= 1 2 3
1
      1 2 3 ∧.= 1 2 4
0

Shape rules¶

Left shape	Right shape	Result shape
`n`	`n`	scalar
`m n`	`n p`	`m p`
`n`	`n p`	`p`

The last axis of the left argument must equal the first axis of the right argument (LENGTH ERROR otherwise).

Inner Product (f.g)¶