如何制作2D和3D矩阵的点积（分别针对每个维进行计算）

Question

I need to calculate dot product of two matrices. Probably tensordot would do the job, however I am struggling to figure out exact solution.

The simple option

res = np.dot(x, fullkernel[:, :-1].transpose())

works fine, where x is of shape (9999,), fullkernel of shape (980,10000), and res is of shape (1, 980).

Now I need to do similar thing with 2 dimensions. Thus my x now has shape (9999, 2), fullkernel (2, 980, 10000).

Literally I want my result "res" to be of 2 dimensions, where each one is dot.product of one column of x and one dimension of fullkernel.

Answer 1

You can do that like this:

res = np.einsum('ki,ijk->ij', x, fullkernel[:, :, :-1])
print(res.shape)
# (2, 980)

If you want to have the additional singleton dimension in the middle just do:

res = np.expand_dims(res, 1)

An equivalent solution with @ / np.matmul would be:

res = np.expand_dims(x.T, 1) @ np.moveaxis(fullkernel[:, :, :-1], 2, 1)
print(res.shape)
# (2, 1, 980)