P

p

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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
>>> float(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)
exponent_vector = np.exp(vector)
# Add up the all the exponentials
sum_of_exponents = np.sum(exponent_vector)
# Divide every exponent by the sum of all exponents
softmax_vector = exponent_vector / sum_of_exponents
return softmax_vector
if __name__ == "__main__":
print(softmax((0,)))
```