Python: While loop - how do I avoid division by zero?

Question

I am writing code for summing the Fourier Series that ranges from [-n,n]. However, I'm having trouble with it iterating when it gets to n = 0. I wrote an 'if' statement inside my while loop so it can ignore it, but it seems like it isn't. Here's my code:

from __future__ import division
import numpy as np
import math
import matplotlib.pyplot as plt


#initial values 
ni = -10
nf = 10
ti = -3
tf = 3
dt = 0.01
yi = 0 #initial f(t) value
j = complex(0,1)

#initialization
tarray = [ti]
yarray = [yi]
t = ti
n = ni
y = yi


cn = 1/(8*(np.pi)**3*n**3*j**3)*(j*4*np.pi*n) #part (b)


#iterating loop
while t<tf:
    n = ni 
    y = yi 
    while n<nf:
        if n == 0: 
            cn = 1/6
            y += cn
            n += 1
        else: 
            y +=  cn*np.exp(j*np.pi*n*t)  
            n += 1

    yarray.append(y)
    t+=dt
    tarray.append(t)

#converting list-array
tarray = np.array(tarray)
yarray = np.array(yarray)

#plotting
plt.plot(tarray,yarray, linewidth = 1)
plt.axis("tight")
plt.xlabel('t')
plt.ylabel('f(t) upto n partial sums')
plt.title('Fourier Series for n terms')
plt.legend()
plt.show()

I want it to iterate and create an array of y-values for n ranging from some negative number to some positive number (say for n from [-10,10]), but as soon as it hits n = 0 it seems to be plugging that in into the 'else' clause even though I want it to use what's in the 'if' clause, giving me a "ZeroDivisionError: complex division by zero". How do I fix this?

Edit: Put the entire code block here so you can see the context.

It would probably be helpful if you included all the code necessary to make the snippet actually run and produce the divide by zero error you are seeing. — d512, Mar 31 '16 at 03:16
it seems like `t` is going from `-3` to `3` and will also be zero at some point — jack3694078, Mar 31 '16 at 03:30
The only way I can see to reproduce your error is to move `cn = 1/(8*(np.pi)**3*n**3*j**3)*(j*4*np.pi*n)` inside the loop. In your code there does not seem to be any risk of division by 0? am I missing something here? — user5219763, Mar 31 '16 at 03:40
I'm not able to reproduce issue you mentioned. Is there any special condition to get one? — Saleem, Mar 31 '16 at 03:50

score 0 · Accepted Answer · answered Mar 31 '16 at 03:36

This is not the most elegant way at all but try this:

while t<tf:
n = ni 
y = yi 
while n<nf:
    try:
        1/n
        cn = 1/6
        y += cn
        n += 1

     except ZeroDivisionError: 
        y +=  cn*np.exp(j*np.pi*n*t)  #1/n*np.sin(n*t)
        n += 1

yarray.append(y)
t+=dt
tarray.append(t)

ptrj · Answer 2 · 2016-03-31T16:19:05.157

The coefficient cn is a function of n and should be updated in every loop. You made it constant (and even equal to 1/6 for positive n).

The inner loop could look like

y = 1/6                                        # starting with n = 0
for n in range(1,nf):
    y -= 1/(2*np.pi*n)**2 * np.sin(np.pi*n*t)   # see below

Corresponding coefficients for positive and negative n's are equal and exp(ix) - exp(-ix) = 2i sin(x), so it nicely reduces. (Double check the calculation.)

Python: While loop - how do I avoid division by zero?

2 Answers2