I need help minimizing this summation function dependent on what the values of ai are. Can someone help me write a code (in Python 2.7.12) that chooses ai values such that Fmin is minimized? I have a script now, but the problem is that it asks me to input values of ai and then it spits out a value for Fmin. I want a script that selects ai such that Fmin is smallest. Anyways, here's my (wrong) script:

import math m = 11 first = 0 second = 0 pi = math.pi

# delare an empty list to hold values of a a = []

# getting input from user for i in range(0,m): a.append( float(input('Enter a value of a[' + str(i) + ']: ')) )

# calculation for summation # in function range(1,m), 1 is included and m is excluded. So effectively we go from 1 to m-1. first = 0.0 second = 0.0 for j in range(1, m): temporary_sum_first = 0.0 temporary_sum_second = 0.0 for i in range(0, m): # this is the summation inside the square brackets temporary_sum_first += (a[i] * math.cos(2*pi*i*j/m)) temporary_sum_second += ((-a[i])*i* math.sin(2*pi*i*j/m))

# now square it and sum it first = first + math.pow(temporary_sum_first, 2) second = second + math.pow(temporary_sum_second, 2) # at this point, we have finished summing i=0 to i=m-1 for one value of p, we continue this for m-1 values of j.

Fmin=first+second print("Summation value:") print(Fmin)

And then at some point I'm going to want to plot this function out as well. I appreciate the help!