adding softmax function (#1267)

* adding softmax function

* wraped lines as asked

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,)))