Issue
I have a problem where I have two arrays with dimensions n x d and d x h, where n, d, and h are positive integers that may or may not be the same. I am trying to find the dot product of the two matrices but with the condition that for each multiplication, I apply a function g to the term.
For example, in a case where n=2, d=3, and h=3 If I had the following matrices:
a = [[1, 2, 3],
[4, 5, 6]]
b = [[1, 2, 3],
[4, 5, 6],
[1, 1, 1]]
I would want to find c such that
c = [[g(1*1)+g(2*4)+g(3*1), g(1*2)+g(2*5)+g(3*1), g(1*3)+g(2*6)+g(3*1)],
[g(4*1)+g(5*4)+g(6*1), g(4*2)+g(5*5)+g(6*1), g(4*3)+g(5*6)+g(6*1)]]
Any help would be appreciated
Solution
I was able to do this by first doing the multiplications with broadcasting, applying g()
, and then summing across the correct axis:
import numpy as np
def g(x):
return 1 / (1 + np.exp(-x))
a = np.array([[1, 2, 3],
[4, 5, 6]])
b = np.array([[1, 2, 3],
[4, 5, 6],
[1, 1, 1]])
First, the multiplication a[:, None] * b.T
(probably a nicer way to do this), then evaluate g(x)
, then sum across axis 2:
>>> g(a[:, None] * b.T).sum(axis=2)
array([[2.68329736, 2.83332581, 2.90514211],
[2.97954116, 2.99719203, 2.99752123]])
Verifying that the first row indeed matches your desired result:
>>> g(1*1) + g(2*4) + g(3*1)
2.683297355321972
>>> g(1*2) + g(2*5) + g(3*1)
2.8333258069316134
>>> g(1*3) + g(2*6) + g(3*1)
2.9051421094702645
Answered By - ddejohn
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