Efficient evaluation of a function at every cell of a NumPy array

Given a NumPy array A, what is the fastest/most efficient way to apply the same function, f, to every cell?

1. Suppose that we will assign to A(i,j) the f(A(i,j)).

2. The function, f, doesn't have a binary output, thus the mask(ing) operations won't help.

Is the "obvious" double loop iteration (through every cell) the optimal solution?

You could just vectorize the function and then apply it directly to a Numpy array each time you need it:

import numpy as np

def f(x):
    return x * x + 3 * x - 2 if x > 0 else x * 5 + 8

f = np.vectorize(f)  # or use a different name if you want to keep the original f

result_array = f(A)  # if A is your Numpy array

It's probably better to specify an explicit output type directly when vectorizing:

f = np.vectorize(f, otypes=[np.float])

A similar question is: Mapping a NumPy array in place. If you can find a ufunc for your f(), then you should use the out parameter.