My bisection code in python doesnt return the root

Question

I am trying to find a good approximation to the root of a function using a bisection algorithm, however, when I run the code it doesnt return the root (c). Here is my code.

import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-10,10,201)

def f(x): 
    return np.cos(x) 

plt.figure()
plt.plot(x,f(x),label = 'cosx')
plt.xlabel('independent variable x')
plt.ylabel('dependent variable y')
plt.title('')

plt.show()

TOL = 10**-6
a = 0
b = 1

def bisection(a,b,TOL):
    c = (a+b)/2.0  
    while (b-a)/2.0 > TOL:
        if f(c)==0:
            return c
        elif f(a)*f(c)<0:
            b = c
        else:
            a = c
    c = (a+b)/2.0
    return c

Also, it is incredibly difficult to figure out how to format multiple lines of code on this site...any help with that would be good too. I mean, I wanted to just copy my entire code with one click, but it wouldnt let me do that...very annoying. — Truxton Boyce, Sep 14 '14 at 18:42
Copy and paste the code. Then select the code, and with the code selected hit the curly-brace button `{}` or type control-K. — DSM, Sep 14 '14 at 18:44

Padraic Cunningham · Accepted Answer · 2014-09-14T19:54:39.810

0

As posted your code don't change the values of c in the loop as it is outside the while loop so the value of a and b never change causing an infinite loop:

def bisection(a,b,TOL):
    c = (a+b)/2.0  
    while (b-a)/2.0 > TOL:
        if f(c)==0:
            return c
        elif f(a)*f(c)<0:
            b = c
        else:
            a = c
        c = (a+b)/2.0 # put inside the while
    return c

To see the value of c through the loop add a print statement:

def bisection(a, b, TOL):
    c = (a + b) / 2.0
    while (b - a) / 2.0 > TOL:
        if f(c) == 0:
            return c
        elif f(a) * f(c) < 0:
            b = c
        else:
            a = c
        c = (a + b) / 2.0
        print ("Current value of c is {}".format(c)) 
    return c

edited Sep 14 '14 at 19:54

answered Sep 14 '14 at 19:17

Padraic Cunningham

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How do I put it inside of the while loop? It looks like to me it is already there? – Truxton Boyce Sep 14 '14 at 19:30
if you look at the line I commented, it is indented inside the loop where the code you posted has it outside the while loop – Padraic Cunningham Sep 14 '14 at 19:31
you are calling it using something like `print bisection(a,b,TOL)` yes? – Padraic Cunningham Sep 14 '14 at 19:43
do I have to call the function or something? – Truxton Boyce Sep 14 '14 at 19:43
O.k. yes it seems to have worked, but how can I print the output of each step instead of the final step? – Truxton Boyce Sep 14 '14 at 19:45
do you want to see the value of c each iteration? – Padraic Cunningham Sep 14 '14 at 19:45
Yes, I would like to see c at each iteration. Thank you – Truxton Boyce Sep 14 '14 at 19:52
@TruxtonBoyce, I added to the answer – Padraic Cunningham Sep 14 '14 at 19:54

My bisection code in python doesnt return the root

1 Answers1