Outer product of more than two vectors

[mkitti]

I was thinking about this after viewing the following video by Conor Hoekstra:

APL vs BQN vs J vs Q vs NumPy vs Julia vs R

Julia gets dinged around minute 15 since broadcasting does not equate directly with an outer product in all circumstances. This gets explained further around minute 32 where he takes issues with transpose on Vector. See also this prior post:

Should transpose of a Vector be a Matrix?

As Julia has a true 1D vector data type, shouldn’t the transpose of a Vector just be a Vector (essentially an identity operation)? See Conor Hoekstra’s comments in APL vs BQN vs J vs Q vs NumPy vs Julia vs R - YouTube I assume this stems from MATLAB where a vector is actually a 2D array and that you can, of course, transpose. What are your thoughts about this?

ThIs thread clearly shows that a true outer product is also accessible in Julia.

Hoekstra’s original version without using I is as follows:

# check fo see if matrix is an X matrix
# where only the main diagonals are non-zero
function checkmatrix(grid)
    n = size(grid, 1)
    i = 1:n .== 1:n |> transpose
    min.(grid, 1) == max.(i, reverse(i, dims=1))
end

Using Iterators.product, map, and allequal we could do the following.

function checkmatrix2(grid)
    n = size(grid, 1)
    i = map(allequal, Iterators.product(1:n, 1:n))
    min.(grid, 1) == max.(i, reverse(i, dims=1))
end