在没有for循环的情况下在python中获取两个数组的点积

Question

I have two arrays W and x . W has the shape (16, 10) and x has the shape (10000, 16) . I need to take the dot product between the transpose of W and x . The problem is that the shapes of x and W are very different so I keep getting an error when trying to do this. Of course I can do this with for loops but I want to do it without using any for loops.

for i in range(x.shape[0])
    s = (np.dot(W.transpose(), x[i])) + b

The above code produces an array, s , which consists of 10 entries. I'm trying to get s to be 10,000 lines with 10 entries in each line (without using a for loop).

Answer 1

You're probably looking for

s = x.dot(W)

Or

s = x @ W

dot behaves as a for product for simple 1D vectors, but is full blown matrix multiplication otherwise. Since you want a (10000, 10) result shape, you need to set up your matrices to have that shape in the outer dimensions, and match the inner ones:

(10000, 16) x (16, 10) -> (10000, 10)

To perform the sum in whatever order you want, you can use np.einsum :

s= np.einsum('ik,ji->jk', W, x)

Or simply

s = np.einsum('ik,ji', W, x)