numpy.dot 的意外结果

Question

I have two matrices:

>>> a.shape
(100, 3, 1)
>>> b.shape
(100, 3, 3)

I'd like to perform a dot product such that my end result is (100, 3, 1). However, currently I receive:

>>> c = np.dot(b, a)
>>> c.shape
(100, 3, 100, 1)

Could somebody explain what is happening? I'm reading thedocs and can't figure it out.

Edit:

So per the docs (overlooked it):

If both a and b are 2-D arrays, it is matrix multiplication, but using matmul or a @ b is preferred.

And that gives the desired result, but I'm still curious, what is taking place here? What rule of the np.dot function is being applied to yield a result of (100, 3, 100, 1) ?

Answer 1

This is how dot works in your case:

dot(b, a)[i,j,k,m] = sum(b[i,j,:] * a[k,:,m])

Your output shape is exactly how the docs specify it:

(b.shape[0], b.shape[1], a.shape[0], a.shape[2])

If it's not what you expected, you might be looking for another matrix multiplication.

Answer 2

dot will return all the possible products of the matrices stored in the last two dimensions of your arrays. Use matmul aka the @ operator to broadcast the leading dimensions instead of combining them:

np.matmul(b, a)

Or

b @ a

The Swiss Army knife of sum-products is einsum , so you can use that too:

np.einsum('aij,ajk->aik', b, a)

Or

np.einsum('ajk,aij->aik', a, b)