Numpy equivalent of dot(A,B,3)

Question

Say I have two 3 dimensional matrices, like so (taken from this matlab example http://www.mathworks.com/help/matlab/ref/dot.html):

A = cat(3,[1 1;1 1],[2 3;4 5],[6 7;8 9])
B = cat(3,[2 2;2 2],[10 11;12 13],[14 15; 16 17])

If I want to take pairwise dot products along the third dimension, I could do so like this in matlab:

C = dot(A,B,3)

Which would give the result:

C =
  106   140
  178   220

What would be the equivalent operation in numpy, preferably a vectorized option, to avoid having to write a double for loop through the entire array. I can't seem to make sense of what np.tensordot or np.inner are supposed to do, but they might be options.

Answer 1

In [169]:

A = np.dstack([[[1, 1],[1 ,1]],[[2 ,3],[4, 5]],[[6, 7],[8, 9]]])
B = np.dstack([[[2, 2],[2, 2]],[[10, 11],[12, 13]],[[14, 15], [16, 17]]])
c=np.tensordot(A, B.T,1)
np.vstack([np.diag(c[:,i,i]) for i in range(A.shape[0])]).T
Out[169]:
array([[106, 140],
       [178, 220]])

But surprisingly it is the slowest:

In [170]:

%%timeit
c=np.tensordot(A, B.T,1)
np.vstack([np.diag(c[:,i,i]) for i in range(A.shape[0])]).T
10000 loops, best of 3: 95.2 µs per loop
In [171]:

%timeit np.einsum('i...,i...',a,b)
100000 loops, best of 3: 6.93 µs per loop
In [172]:

%timeit inner1d(A,B)
100000 loops, best of 3: 4.51 µs per loop

Answer 2

Using np.einsum:

In [9]: B = np.array([[[2, 2],[2, 2]],[[10, 11],[12, 13]],[[14, 15],[16, 17]]])

In [10]: A = np.array([[[1, 1],[1, 1]],[[2, 3],[4, 5]],[[6, 7],[8, 9]]]) 

In [11]: np.einsum('i...,i...',A,B)
Out[11]:
array([[106, 140],
       [178, 220]])

Or here's another fun one:

In [37]: from numpy.core.umath_tests import inner1d

In [38]: inner1d(A,B)
Out[38]:
array([[106, 140],
       [178, 220]])

Edit in response to @flebool's comment, inner1d works for both (2,2,3) and (3,2,2) shaped arrays:

In [41]: A = dstack([[[1, 1],[1 ,1]],[[2 ,3],[4, 5]],[[6, 7],[8, 9]]])

In [42]: B = dstack([[[2, 2],[2, 2]],[[10, 11],[12, 13]],[[14, 15], [16, 17]]])

In [43]: inner1d(A,B)
Out[43]:
array([[106, 140],
       [178, 220]])