"""
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,)))