How to calculate a logistic sigmoid function in Python?

Question

This is a logistic sigmoid function:

I know x. How can I calculate F(x

Answer 1

Here's how you would implement the logistic sigmoid in a numerically stable way (as described here):

def sigmoid(x):
    "Numerically-stable sigmoid function."
    if x >= 0:
        z = exp(-x)
        return 1 / (1 + z)
    else:
        z = exp(x)
        return z / (1 + z)

Or perhaps this is more accurate:

import numpy as np

def sigmoid(x):  
    return math.exp(-np.logaddexp(0, -x))

Internally, it implements the same condition as above, but then uses log1p.

In general, the multinomial logistic sigmoid is:

def nat_to_exp(q):
    max_q = max(0.0, np.max(q))
    rebased_q = q - max_q
    return np.exp(rebased_q - np.logaddexp(-max_q, np.logaddexp.reduce(rebased_q)))

(However, logaddexp.reduce could be more accurate.)