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

As a reference, the following code:

#pythran export mb_r(float64[], float64[])
import numpy as np

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

Runs at the following speed on pure CPython:

% python -m perf timeit -s 'import numpy as np; x = np.random.rand(400); y = np.random.rand(400); from mbr import mb_r' 'mb_r(x, y)' 
.....................
Mean +- std dev: 730 us +- 35 us

And when compiled with Pythran I get

% pythran -march=native -DUSE_BOOST_SIMD mbr.py
% python -m perf timeit -s 'import numpy as np; x = np.random.rand(400); y = np.random.rand(400); from mbr import mb_r' 'mb_r(x, y)'
.....................
Mean +- std dev: 65.8 us +- 1.7 us

So roughly a x10 speedup, on a single core with AVX extension.