How to express the dot product of 3 dimensions arrays with numpy?

How do I do the following dot product in 3 dimensions with numpy?

I tried:

x = np.array([[[-1, 2, -4]], [[-1, 2, -4]]])
W = np.array([[[2, -4, 3], [-3, -4, 3]], 
              [[2, -4, 3], [-3, -4, 3]]])
y = np.dot(W, x.transpose())

but received this error message:

    y = np.dot(W, x)
ValueError: shapes (2,2,3) and (2,1,3) not aligned: 3 (dim 2) != 1 (dim 1)

It's 2 dimensions equivalent is:

x = np.array([-1, 2, -4])
W = np.array([[2, -4, 3],
              [-3, -4, 3]])
y = np.dot(W,x)
print(f'{y=}')

which will return:

y=array([-22, -17])

Also, y = np.dot(W,x.transpose()) will return the same answer.

The issue comes from the 3D transposition which does not transpose the axes you want by default. You need to specify the right axes during this call:

W @ x.transpose(0, 2, 1)

# Output:
# array([[[-22],
#         [-17]],
# 
#        [[-22],
#         [-17]]])