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"""

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,)))