Numpy：如何逐个乘以两个向量，shape（n，1）和（n，）？

Question

Elementwise multiplication of two vectors is no problem if they both have the same shape, say both (n,1) or both (n,). If one vector has shape (n,1) and the other (n,), though, the * -operator returns something funny.

a = np.ones((3,1))
b = np.ones((3,))
print a * b

The resulting nxn-matrix contains A_{i,j}=a_i*b_j.

How can I do elementwise multiplication for the a and b then?

Answer 1

Slice the vectors in a way that makes their shape match:

a[:, 0] * b

or

a * b[:, None]

Answer 2

Add a second axis to b to that a and b have the same dimensions:

>>> a * b[:,np.newaxis]
array([[ 1.],
       [ 1.],
       [ 1.]])

Alternatively, transpose a so that broadcasting works:

>>> a.T * b
array([[ 1.,  1.,  1.]])

(You'd probably want to transpose the result.)