Python/maths/softmax.py

"""
This script demonstrates the implementation of the Softmax function.

Its a function that takes as input a vector of K real numbers, and normalizes
it into a probability distribution consisting of K probabilities proportional
to the exponentials of the input numbers. After softmax, the elements of the
vector always sum up to 1.

Script inspired from its corresponding Wikipedia article
https://en.wikipedia.org/wiki/Softmax_function
"""

import numpy as np


def softmax(vector):
    """
        Implements the softmax function

        Parameters:
            vector (np.array,list,tuple): A  numpy array of shape (1,n)
            consisting of real values or a similar list,tuple


        Returns:
            softmax_vec (np.array): The input numpy array  after applying
            softmax.

        The softmax vector adds up to one. We need to ceil to mitigate for
        precision
        >>> np.ceil(np.sum(softmax([1,2,3,4])))
        1.0

        >>> vec = np.array([5,5])
        >>> softmax(vec)
        array([0.5, 0.5])

        >>> softmax([0])
        array([1.])
    """

    # Calculate e^x for each x in your vector where e is Euler's
    # number (approximately 2.718)
    exponentVector = np.exp(vector)

    # Add up the all the exponentials
    sumOfExponents = np.sum(exponentVector)

    # Divide every exponent by the sum of all exponents
    softmax_vector = exponentVector / sumOfExponents

    return softmax_vector


if __name__ == "__main__":
    print(softmax((0,)))