diff --git a/maths/softmax.py b/maths/softmax.py new file mode 100644 index 000000000..92ff4ca27 --- /dev/null +++ b/maths/softmax.py @@ -0,0 +1,56 @@ +""" +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,)))