How to compute efficiently in python, the weighted point average (centroid) for each pair of points across two arrays

# Table with weight 2/3
a = np.array(
    [[0, 0],
     [12, 12]]
)

# Table with weight 1/3
b = np.array(
    [[12, 6],
     [9, 3]]
)

# Returned table
c = np.array(
    [[4, 2],
     [11, 9]]
)

I have a, b (each holding some points) and I want to compute efficiently given their weights, matrix c holding the pairwise point averages. Something like their weighted centroid.

How can I do that?
Thanks

>Solution :

You can use simple basic numpy matrix operations:

c = a * weight_a + b * weight_b

# With your example : 
c = a * 2 / 3 + b * 1 / 3
# array([[ 4.,  2.],
#       [11.,  9.]])