[FIXED] Numpy mean of all pairwise divisions between arrays

Issue

I have two arrays of arbitrary length:

a = [1,2,3]
b = [4,5]

I want the average of all fractions x/y where x is from a and y is from b i.e. avg(1/4 + 1/5 + 2/4 + 2/5 +...) = 0.45 in this case.

I would like to avoid using loops, and stick to numpy functions. I have found a solution using np.meshgrid:

numerator = a
denominator = 1/b

pairs = np.array(np.meshgrid(numerator, denominator)).T.reshape(-1,2)
>>> array([[1.  , 0.25],
           [1.  , 0.2 ],
           [2.  , 0.25],
           [2.  , 0.2 ],
           [3.  , 0.25],
           [3.  , 0.2 ]])

fractions = np.multiply.reduce(pairs, axis=1)
>>> array([0.25, 0.2 , 0.5 , 0.4 , 0.75, 0.6 ])

result = np.mean(fractions)
>>> 0.45 # Correct

I would like to know if there is a more elegant (mathematical?) way of achieving the result I want. Help is much appreciated.

Solution

You can first determine the sum of all items, and then divide that sum by the items in b to determine the mean:

>>> a = np.array([1,2,3])
>>> b = np.array([4,5])
>>> (a.mean() / b).mean()
0.45

The advantage of first calculating the mean of the numerators, is that this algorithm takes linear time (O(|a| + |b|)), instead of quadratic time (O(|a|×|b|)).

Answered By - Willem Van Onsem