Numpy: Compute dot product of 2d arrays with a condition before summation

Question

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

Asked By: agctute

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Answer 1

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

Numpy: Compute dot product of 2d arrays with a condition before summation

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