# Answered! Question: I need help minimizing this summation function dependent on what the values of ai are. Can someon……

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

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# 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!

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)