n x n matrix in numpy by applying function to pairs of elements in n x 1 numpy array

Question

If I have an array in numpy a which is nx 1 . In addition, I have a function F(x,y) which takes in two values and returns a single value. I want to construct an nxn matrix b where b_ij = F(a_i, a_j) (in the array a ). Is there any way to do this without looping over both arrays?

Answer 1

Assume that your function is:

def F(a_i, a_j):
    return (a_i + a_j) if a_i % 2 == 0 else (a_i + a_j + 1)

To call it on 2 arrays in 1 go, define the vectorized version of this function:

FF = np.vectorize(F)

Then call it:

result = FF(a, a.T)

As the source array I used:

a = np.array([[1], [5], [10], [50], [80]])

so its shape is (5, 1) (a single-column array) and got:

array([[  3,   7,  12,  52,  82],
       [  7,  11,  16,  56,  86],
       [ 11,  15,  20,  60,  90],
       [ 51,  55,  60, 100, 130],
       [ 81,  85,  90, 130, 160]])