Numpy 二维数组和长一维数组的乘积，结果应该是 3d 数组

Question

Given two arrays, a and b, with shapes; (3, 3) and (1000,). How do I multiply them to get an array with shape (3, 3, 1000)?

a = np.array([[1,2,3],[4,5,6],[7,8,9]])
b = np.linspace(1, 1000, 1000)

c = a * b # does not work
c = np.outer(a, b) # does not work
c = np.outer(a, b[None,] # nope

I have tried a lot of things, too many to remember them all.

I have also googled (and searched on SO) but to no avail.

Answer 1

IIUC, use numpy.einsum :

c = np.einsum("ij,k->ijk", a, b)

Output:

c.shape
# (3, 3, 1000)

Answer 2

You can do it with multiplication by reshaping your arrays:

M,N = a.shape
B = b.size
c = a.reshape(M,N,1) * b.reshape(1,1,B)
print(c.shape)
print(c[:,:,0])
print(c[:,:,B-1])

Output:

% python3 script.py
(3, 3, 1000)
[[1. 2. 3.]
 [4. 5. 6.]
 [7. 8. 9.]]
[[1000. 2000. 3000.]
 [4000. 5000. 6000.]
 [7000. 8000. 9000.]]

Answer 3

You need to understand the broadcasting rules . The bottomline is:

• both arrays need to have the same number of axes and
• the sizes along each axis must be the same or one of them must be 1.

You can multiply and array with shape (3,3) only by another with shape (3,3), (3,1) or (1,3). There are other broadcasting rules. Read them.

Your shapes are (3,3) and (1000,). As you said, you need the final shape to be 3-dimensional. The 3 needs to match an axis with length 1. Same with the 1000 . So you can add axes to each to end up with shapes (3, 3, 1) and (1, 1, 1000):

c = a[:, :, np.newaxis]* b[np.newaxis,np.newaxis]