numpy element-wise multiplication of an array and a vector

Question

I want to do something like this:

a =  # multi-dimensional numpy array
ares = # multi-dim array, same shape as a
a.shape
>>> (45, 72, 37, 24)  # the relevant point is that all dimension are different
v = # 1D numpy array, i.e. a vector
v.shape
>>> (37)  # note that v has the same length as the 3rd dimension of a
for i in range(37):
    ares[:,:,i,:] = a[:,:,i,:]*v[i]

I'm thinking there has to be a more compact way to do this with numpy, but I haven't figured it out. I guess I could replicate v and then calculate a*v , but I am guessing there is something better than that too. So I need to do element wise multiplication "over a given axis", so to speak. Anyone know how I can do this? Thanks. (BTW, I did find a close duplicate question, but because of the nature of the OP's particular problem there, the discussion was very short and got tracked into other issues.)

Answer 1

你可以使用numpy的einsum函数用爱因斯坦求和符号来做到这一点：

ares = np.einsum('ijkl,k->ijkl', a, v)

Answer 2

You can automatically broadcast the vector against the outermost axis of an array. So, you can transpose the array to swap the axis you want to the outside, multiply, then transpose it back:

ares = (a.transpose(0,1,3,2) * v).transpose(0,1,3,2)

Answer 3

I tend to do something like

b = a * v[None, None, :, None]

where I think I'm officially supposed to write np.newaxis instead of None .

For example:

>>> import numpy as np
>>> a0 = np.random.random((45,72,37,24))
>>> a = a0.copy()
>>> v = np.random.random(37)
>>> for i in range(len(v)):
...     a[:,:,i,:] *= v[i]
...     
>>> b = a0 * v[None,None,:,None]
>>> 
>>> np.allclose(a,b)
True

Answer 4

Here is one more:

b = a * v.reshape(-1, 1)

IMHO, this is more readable than transpose , einsum and maybe even v[:, None] , but pick the one that suits your style.