Set of root finders for AP155 - Functions and Roots Exercise

root.py

#!/usr/bin/env python

import numpy as np
import matplotlib.pyplot as plt
from scipy.misc import *
import time

def func(x):
	return x*x - 4*x*np.sin(x) +(2*np.sin(x))**2
	
def deriv(x):
    return 2**x - 4*np.sin(x) - 4*x*np.cos(x) + 2*(2*np.sin(x))*(2*np.cos(x))
	
	
def bisection(f, a, c):
	print "routine start"; old = 0
	while True:
		b = (a + c)/2.
		if f(a)*f(b) < 0:	c = b
		else:	a = b
		ans = f(b)
		if old == ans:	break
		old = ans
		return ans
	
	
def newton_raphson(func,start):
	x = [-10, start]
	while abs(x[1] - x[0]) > 1e-8:
		x[0] = x[1]
		x[1] = x[0] - func(x[0])/deriv(x[0])
	return x[1]
	
def secant(func,start):
	x = [-10, start, -20]
	while abs(x[2] - x[0]) > 1e-8:
		x[2] = x[1] - func(x[1])*(x[1] - x[0])/(func(x[1]) - func(x[0]))
		x[0], x[1] = x[1], x[2]
	return x[1]
	
def hybrid(func, a, c):
	x = [a, (a+c)/2., c]
	while abs(func(x[1])) > 1e-8:
		delta = func(x[1])/deriv(x[1])
		if (x[1] - delta) > x[0] and (x[1] - delta) < x[2]:
			x[1] = x[1] - delta
		else:
			x[1] = (x[0] + x[2])/2.
			if func(x[0])*func(x[1]) < 0:	x[2] = x[1]
			else:	x[0] = x[1]
	return x[1]