ZeroDivisionError: float division

Question

I have got this code to solve Newton's method. But it gives a zero division error. I cannot figure out what is wrong. Thank you.

import copy

tlist = [0.0, 0.12, 0.16, 0.2, 0.31, 0.34] # list of start time for the phonemes

w = w1 = w2 = w3 = w = 5

def time() :
    frame = 0.04
    for i, start_time in enumerate(tlist) :
        end_time = tlist[i]
        frame = frame * (i + 1)
        poly = poly_coeff(start_time, end_time, frame)
        Newton(poly) 

def poly_coeff(stime, etime, f) :
    """The equation is k6 * u^3 + k5 * u^2 + k4 * u + k0 = 0. Computing the coefficients for this polynomial."""
    """Substituting the required values we get the coefficients."""
    t_u = f
    t0 = stime
    t3 = etime
    t1 = t2 = (stime + etime) / 2
    w0 = w1 = w2 = w3 = w
    k0 = w0 * (t_u - t0)
    k1 = w1 * (t_u - t1)
    k2 = w2 * (t_u - t2)
    k3 = w3 * (t_u - t3)
    k4 = 3 * (k1 - k0)
    k5 = 3 * (k2 - 2 * k1 + k0)
    k6 = k3 - 3 * k2 + 3 * k1 -k0 

    return [[k6,3], [k5,2], [k4,1], [k0,0]]

def poly_differentiate(poly):
    """ Differentiate polynomial. """
    newlist = copy.deepcopy(poly)

    for term in newlist:
        term[0] *= term[1]
        term[1] -= 1

    return newlist

def poly_substitute(poly, x):
    """ Apply value to polynomial. """
    sum = 0.0 

    for term in poly:
        sum += term[0] * (x ** term[1])
    return sum

def Newton(poly):
    """ Returns a root of the polynomial"""
    poly_diff = poly_differentiate(poly) 
    counter = 0
    epsilon = 0.000000000001

    x = float(raw_input("Enter initial guess:"))

    while True:
        x_n = x - (float(poly_substitute(poly, x)) / poly_substitute(poly_diff, x))
        counter += 1
        if abs(x_n - x) < epsilon :
            break
        x = x_n
    print "Number of iterations:", counter
    print "The actual root is:", x_n
    return x_n

if __name__ == "__main__" :
    time()

Enter initial guess:0.5
Traceback (most recent call last):
  File "newton.py", line 79, in <module>
    time()
  File "newton.py", line 18, in time
    Newton(poly) 
  File "newton.py", line 67, in Newton
    x_n = x - (float(poly_substitute(poly, x)) / poly_substitute(poly_diff, x))
ZeroDivisionError: float division

Answer 1

You have a basic bug here:

for i, start_time in enumerate(tlist):
    end_time = tlist[i]

Because of the nature of enumerate, start_time and end_time have the same value. This means that poly_coeff will return [[0,3], [0,2], [0,1], [0,0]] every time. When this result is passed (through Newton) into poly_differentiate, the result will be [[0,2], [0,1], [0,0], [0,-1]].

This result, passed into poly_substitute will yield a sum of ZERO, because you multiply all list entries by term[0] (which happens to be zero) before summing them. Then, you divide - by zero.

SOLUTION (edited per your comment):

Use the correct start_time and end_time values. It looks like you want end_time = tlist[i+1]. The edge condition of this is to break out without evaluating the final list entry. What you really want is this:

for i, start_time in enumerate(tlist[:-1]):
    end_time = tlist[i+1]