# (Solved Homework): I am trying to plot a function in python 2.7.12 and keep getting a syntax error at xd3.append(0). I'm basing the script

I am trying to plot a function in python 2.7.12 and keep getting a syntax error at xd3.append(0). I’m basing the script off of another script through which my function was derived, which I will attach as well. Can someone help me revise my script so that I can actually plot it out? Thanks so much!

My Script:

import math
from numpy import matrix
from numpy import linalg
import numpy
import matplotlib.pyplot as plt
import sys
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 function I want to plot
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.

#Final Summation Value
Fmin=first+second
print(“Summation value:”)
print(Fmin)
#If you comment out/ delete everything after this point, you can sub in values for ai
# and find the value of the minimization function
#Now I want to plot out what it looks like
def f(theta,x,m):

for j in range(1, m):
temporary_sum_first = 0.0
temporary_sum_second = 0.0
#This is where I think I went wrong somehow
fsum = temportary_sum_first + temporary_sum_second
for i in range(0, m):
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))
return fsum

mhalf = m/2
offt = pi/8
t_min = – offt
t_max = 2*pi +offt
Npts = 500
dt = (t_max – t_min)/Npts

Xv = []
Yv = []
Zv = []
for i in range(Npts):
Xv.append(t_min + dt*i)
Yv.append(f(Xv[i],x,m))
Zv.append(0.0)

Xd = []
Yd = []
Xd2 = []
Yd2 = []
Xd3 = []
Yd3 = []
for i in range(mhalf):
Xd.append(2*(i+1)*pi/m)
Yd.append(0)
Xd2.append(2*(i+mhalf +1)*pi/m
Xd3.append(0)
Xd3.append(2*pi)
Yd3.append(1)
Yd3.append(1)

p1 = plt.subplot(111)
p1.plot(Xv, Yv, color=’red’, lw=2)
p1.plot(Xv, Zv, color=’blue’, lw=2)
p1.scatter(Xd, Yd, color=’black’, marker=’o’, facecolors=’none’, edgecolors=’k’, s=200, lw=2)
p1.scatter(Xd2, Yd2, color=’yellow’, marker=’o’, facecolors=’none’, edgecolors=’y’, s=200, lw=2)
p1.scatter(Xd3, Yd3, color=’black’, marker=’o’, s=200, lw=2)
p1.set_xlim([t_min,t_max])
p1.set_xlabel(r’\$theta\$’,size=28)
p1.set_ylabel(r’\$f(theta)\$’,size=28)
title = r”\$m = %2.0f\$” % m
p1.set_title(title,fontsize=32,color=’black’)

figFile = ‘fig_’+str(m)+’_0.eps’
#plt.savefig(figFile,format=’eps’)
plt.show()

Reference Script:

from numpy import matrix
from numpy import linalg
import numpy
import matplotlib.pyplot as plt
from math import *
import sys

def f(theta,x,Nd):
fsum = 0.0
for i in range(Nd):
fsum = fsum + x[i]*cos(i*theta)
return fsum
Nd=11
#Nd = int(sys.argv[1]) # Command-line arg: kicking frequency
Ndhalf = Nd/2
offt = pi/8
t_min = -offt
t_max = 2*pi + offt
Npts = 500
dt = (t_max – t_min)/Npts

# Solution
x = []
x.append(1.0/Nd)
for i in range(Nd-1):
x.append(2*(Nd-i-1)/(Nd**2.0))
print i, x[i]

Xv = []
Yv = []
Zv = []
for i in range(Npts):
Xv.append(t_min + dt*i)
Yv.append(f(Xv[i],x,Nd))
Zv.append(0.0)

Xd = []
Yd = []
Xd2 = []
Yd2 = []
Xd3 = []
Yd3 = []
for i in range(Ndhalf):
Xd.append(2*(i+1)*pi/Nd)
Yd.append(0)
Xd2.append(2*(i+Ndhalf+1)*pi/Nd)
Yd2.append(0)
Xd3.append(0)
Xd3.append(2*pi)
Yd3.append(1)
Yd3.append(1)

p1 = plt.subplot(111)
p1.plot(Xv, Yv, color=’red’, lw=2)
p1.plot(Xv, Zv, color=’blue’, lw=2)
p1.scatter(Xd, Yd, color=’black’, marker=’o’, facecolors=’none’, edgecolors=’k’, s=200, lw=2)
p1.scatter(Xd2, Yd2, color=’yellow’, marker=’o’, facecolors=’none’, edgecolors=’y’, s=200, lw=2)
p1.scatter(Xd3, Yd3, color=’black’, marker=’o’, s=200, lw=2)
p1.set_xlim([t_min,t_max])
p1.set_xlabel(r’\$theta\$’,size=28)
p1.set_ylabel(r’\$f(theta)\$’,size=28)
title = r”\$m = %2.0f\$” % Nd
p1.set_title(title,fontsize=32,color=’black’)

figFile = ‘fig_’+str(Nd)+’_0.eps’
#plt.savefig(figFile,format=’eps’)
plt.show()

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