Is bsxfun really applied element-wise?

Question

Suppose that I have the following function:

function x = printAndKeepX(x, y)
    x
    y
end

and I invoke bsxfun like so:

bsxfun(@printAndKeepX, 1:4, 1);

Were bsxfun really element-by-element, I would expect printAndKeepX to be called 4 times, with the arguments (x, y) being (1, 1), (2, 1), (3, 1) and (4, 1), respectively. But the output shows that it is called just once with (x, y) being ([1 2 3 4], 1):

x =
     1     2     3     4

y =
     1

Why? How can I know what's considered an "element"?

Edit:
The documentation suggests that sometimes the called function can receive two scalars and sometimes a vector/matrix and a scalar. Can I know for sure which of these is going to happen?

I'm interested in both the regular and GPU versions of bsxfun.

Answer 1

The documentation also states that:

fun must also support scalar expansion, such that if A or B is a scalar, C is the result of applying the scalar to every element in the other input array.

In your case B is in fact a scalar, so your function is applied on A only once.

The same applies when the input arrays are matrices. For example, consider a case where bsxfun is invoked with a matrix A={ a_ij } of size m×n and a vector B={ b_ij } of size m×1. B would be replicated n times along the second dimension, and the function would be called as follows:

function([a11, ..., a1n], b1)
function([a21, ..., a2n], b2)
...
function([am1, ..., amn], bm)

This results in n function calls for vector-scalar inputs rather then mn function calls for pairs of scalars. If the function is vectorized, it may be reflected in a possibly significant performance gain.