Question

Suppose I have three arrays (that is, of type numpy.array):

>>> w.shape
(113,)
>>> X.shape
(113,1)
>>> Y.shape
(113,)

The numpy help pages suggest that on arrays every multiplication is element-wise. Since all above three vectors are of size 113 in the first dimension, I thought multiplication would in all cases give a 113 length vector, but it doesn’t:

>>> (w * Y).shape     # expected
(113,)
>>> (w * X).shape     # ?!?!?!?!
(113,113)

Where does the 113 on the second axis come from? Doesn’t look so element-wise to me.

Answer 1

When operating on two arrays, NumPy compares their shapes
element-wise. It starts with the trailing dimensions, and works its
way forward. Two dimensions are compatible when they are equal, or one
of them is 1.

The smaller of two axes is stretched or “copied” to match
the other.

Numpy’s broadcasting rules are being applied here.

w      (1d array):       113
X      (2d array): 113 x   1   
Result (2d array): 113 x 113