Multiplying lists of matrices without loops

Question

Hi everyone and thank you for your assistance. I am new to python and failed to find an efficient alternative to for loops for the following task.

I want to multiply ndarrays A and B of dimension (d,n,m) and (d,m), respectively. With some abuse of terminology to help understanding, A is a list of nxm matrices and B is a list of vectors in R^m.

For example:

A = np.array([[[0,0,0,0,0],[1,1,1,1,1],[2,2,2,2,2]],[[3,3,3,3,3],[4,4,4,4,4],[5,5,5,5,5]]])
B = np.array([[1,2,3,4,5],[5,6,7,8,9]])

My solution uses a for loop

for i in range(2):
    print(A[i]*B[i])

Is there any cheaper alternative (no loops)?

Thank you again

Asked By: bud

||

Source

Answer 1

In this case, you can use broadcasting by adding in a new dimension in the "middle" for B:

>>> import numpy as np
>>> A = np.array([[[0,0,0,0,0],[1,1,1,1,1],[2,2,2,2,2]],[[3,3,3,3,3],[4,4,4,4,4],[5,5,5,5,5]]])
>>> B = np.array([[1,2,3,4,5],[5,6,7,8,9]])
>>> A * B[:, None, :]
array([[[ 0,  0,  0,  0,  0],
        [ 1,  2,  3,  4,  5],
        [ 2,  4,  6,  8, 10]],

       [[15, 18, 21, 24, 27],
        [20, 24, 28, 32, 36],
        [25, 30, 35, 40, 45]]])

Here is a link to the official docs

Note, your original solution already relied on broadcasting:

>>> A[0]
array([[0, 0, 0, 0, 0],
       [1, 1, 1, 1, 1],
       [2, 2, 2, 2, 2]])
>>> B[0]
array([1, 2, 3, 4, 5])
>>> A[0] * B[0]
array([[ 0,  0,  0,  0,  0],
       [ 1,  2,  3,  4,  5],
       [ 2,  4,  6,  8, 10]])

Answered By: juanpa.arrivillaga

Multiplying lists of matrices without loops

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