Is there any way to merge two numpy arrays with a given cost function?

Question

For my neural network, I am trying to create a cost function. I am using the following cost function:

C = sum((an - yn)^2)
# C = Cost Function, sum = sigma, an = actual_output, yn = desired_output

Here is a way in which I implemented it in python:

def cost(actual_outputs, desired_outputs):
    # actual_outputs and desired outputs are numpy arrays
    costs = [(actual_output - desired_output) ** 2 for actual_output, desired_output in zip(actual_outputs, desired_outputs)]
    return sum(costs)

Is there a more efficient way of doing this using numpy (or any other method)?

Answer 1

You could use linalg.norm :

import numpy as np

def cost(actual_outputs, desired_outputs):
    return np.linalg.norm(np.array(actual_outputs) -  np.array(desired_outputs)) ** 2

This answer assumes your input are not numpy arrays, otherwise you can compute using actual_outputs and desired_outputs directly.

Answer 2

import timeit
import random
import numpy as np
def cost(actual_outputs, desired_outputs):
    # actual_outputs and desired outputs are numpy arrays
    costs = [(actual_output - desired_output) ** 2 for actual_output, desired_output in zip(actual_outputs, desired_outputs)]
    return sum(costs)

def cost2(actual_outputs,desired_outputs):
    return ((actual_outputs-desired_outputs)**2).sum()

actual = [random.random() for _ in range(1000)]
desired = [random.random() for _ in range(1000)]
actual2 = np.array(actual)
desired2 = np.array(desired)
if __name__ == "__main__":
    print(timeit.timeit('cost(actual,desired)','from __main__ import cost,actual,desired',number=10))
    # 0.00271458847557
    print(timeit.timeit('cost2(actual2,desired2)','from __main__ import cost2,actual2,desired2',number=10))
    # 0.000187942916669

looks faster ... assuming its already a numpy array ... it will probably take longer if you have to convert it to a numpy array

the bigger the list size the greater your gains will be