Question

Write a function softMax(x) to return a 1darray of softmax function values ??=???−?∑?−1?=0???−?fi=exi−m∑j=0K−1exj−m for ?=0,2,⋯,?−1i=0,2,⋯,K−1, where ?x is a 1darray of ?K floats, ??xi is the (?+1)(i+1)-th element of array ?x, and ?m is the largest element in array ?x. Sample: if z = np.array([10, 5, 8]), then softMax(z) returns array([0.876, 0.006, 0.118]).

in python program and the output should be array([0.876, 0.006, 0.118])

Answer 1

• Below is the detailed implementation of the above mentioned problem in python with code and it's output.
• For better understanding read the comments mentioned in the code.
• If x is our 1d numpy array then softmax(x[i]) is simply exponential of this x[i] divided by sum of exponentials of all x[i] where 1<=i<=n, where n is size of given 1-D numpy array.
• If we represent softmax(x[i]) as S(x[i]) then .
• CODE:

#import numpy module
import numpy as np
#function which computes softmax function values for the given 1-d numpy array z.
def softMax(z):
#computing using softmax function formula
return np.exp(z) / np.sum(np.exp(z), axis=0)

#test input
#1-d numpy array
z = np.array([10, 5, 8])
#call softMax() and get the result
vec=softMax(z)
#Now vec contains the result but as expected in the problem the result should be rounded till 3 decimal places
vec=np.around(vec, decimals=3)
#after rounding print
print(vec)

• OUTPUT:

  [0.876 0.006 0.118]

• For clarity and better understanding , below are the screenshot of the code and output attached.

CODE and OUTPUT

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