Numpy: multiplying matrix elements with array of matrices

Question

I need to multiply the elements of a, let's say, 2x2 matrix, x, with a matrix, y, whose elements are 2x2 matrices. When I use the conventional numpy multiplication it takes the entire matrix, x, and multiples it with each matrix in y. I have been searching the numpy doc. for something that will replicate this:

>>> x = np.array([[1, 0], [0, 1]])
>>> x
array([[1, 0],
       [0, 1]])
>>> y = np.ones((2, 2, 2, 2))
>>> y
array([[[[ 1.,  1.],
         [ 1.,  1.]],
    [[ 1.,  1.],
     [ 1.,  1.]]],
   [[[ 1.,  1.],
     [ 1.,  1.]],
    [[ 1.,  1.],
     [ 1.,  1.]]]])
>>> multiply(x,y)
[[[[1, 1],
   [1, 1]],
  [[0, 0],
   [0, 0]]],
 [[[0, 0],
   [0, 0]],
  [[1, 1],
   [1, 1]]]]

How do I multiply each element of matrix x as if it were a scalar with the corresponding matrix in y. basically I need something that will replicate the multiply function that I gave in the example code. — user2909415
– user2909415, Commented Sep 19, 2014 at 14:41
@user2909415 It seems you are looking for np.tensordot(x, y, axes=[[0, 1], [0, 1]]), but your question is unclear... what is the expected result? — Saullo G. P. Castro
– Saullo G. P. Castro, Commented Sep 19, 2014 at 14:46
Ones and zeros make for confusing examples for multiplication since is 1: just 1, or maybe 1*1, or maybe 1*1 + 0*1, etc.. — tom10
– tom10, Commented Sep 19, 2014 at 15:00

Saullo G. P. Castro · Accepted Answer · 2014-09-19 15:38:29Z

3

EDIT: From the comments of @Dalek and @DSM it seems that actually what you want is:

np.einsum('ij, ijkl-> ijkl', x, y)

edited Sep 19, 2014 at 15:38

answered Sep 19, 2014 at 15:05

Saullo G. P. Castro

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2 Comments

Dalek Over a year ago

I think he/she is looking for a way to multiply each element of matrix x in each element of matrix y, which is a 2x2 matrix, the example of the requested answer is given in the question.

DSM Over a year ago

IIUC the einsum version of what the OP is looking for is np.einsum('ij,ijkl->ijkl', x, y). I haven't had my coffee yet though.

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