How to optimize a nested for loop in Python

Question

So I am trying to write a python function to return a metric called the Mielke-Berry R value. The metric is calculated like so:

The current code I have written works, b

Answer 1

Here's one vectorized way to leverage broadcasting to get total -

np.abs(forecasted_array[:,None] - observed_array).sum()

To accept both lists and arrays alike, we can use NumPy builtin for the outer subtraction, like so -

np.abs(np.subtract.outer(forecasted_array, observed_array)).sum()

We can also make use of numexpr module for faster absolute computations and perform summation-reductions in one single numexpr evaluate call and as such would be much more memory efficient, like so -

import numexpr as ne

forecasted_array2D = forecasted_array[:,None]
total = ne.evaluate('sum(abs(forecasted_array2D - observed_array))')