Some numerical methods in python.

num.py

"""
Bisection, Secant & Newton Raphson Method.
"""

import math
"""
* Variable Description:
*
* f			:	Given function
* f_		:	Derivative of f
* [a, b]	:	End point values
* TOL		:	Tolerance
* NMAX		:	Max number of iterations
"""


def bisection(f, a, b, TOL=0.001, NMAX=100):
	"""
	Takes a function f, start values [a,b], tolerance value(optional) TOL and
	max number of iterations(optional) NMAX and returns the root of the equation
	using the bisection method.
	"""
	n=1
	while n<=NMAX:
		c = (a+b)/2.0
		print "a=%s\tb=%s\tc=%s\tf(c)=%s"%(a,b,c,f(c))
		if f(c)==0 or (b-a)/2.0 < TOL:
			return c
		else:
			n = n+1
			if f(c)*f(a) > 0:
				a=c
			else:
				b=c
	return False

def secant(f,x0,x1, TOL=0.001, NMAX=100):
	"""
	Takes a function f, start values [x0,x1], tolerance value(optional) TOL and
	max number of iterations(optional) NMAX and returns the root of the equation
	using the secant method.
	"""
	n=1
	while n<=NMAX:
		x2 = x1 - f(x1)*((x1-x0)/(f(x1)-f(x0)))
		if x2-x1 < TOL:
			return x2
		else:
			x0 = x1
			x1 = x2
	return False

def newtonraphson(f, f_, x0, TOL=0.001, NMAX=100):
	"""
	Takes a function f, its derivative f_, initial value x0, tolerance value(optional) TOL and
	max number of iterations(optional) NMAX and returns the root of the equation
	using the newton-raphson method.
	"""
	n=1
	while n<=NMAX:
		x1 = x0 - (f(x0)/f_(x0))
		if x1 - x0 < TOL:
			return x1
		else:
			x0 = x1
	return False

if __name__ == "__main__":
	
	def func(x):
	"""
	Function x^3 - x -2
	We will calculate the root of this function using different methods.
	"""
		return math.pow(x,3) - x -2

	def func_(x):
	"""
	Derivate of the function f(x) = x^3 - x -2
	This will be used in Newton-Rahson method.
	"""
		return 3*math.pow(x,2)-1
	
	#Invoking Bisection Method
	res = bisection(func,1,2).
	print res
	
	#Invoking Secant Method
	res = bisection(func,1,2).
	print res
	
	#Invoking Newton Raphson Method
	res = newtonraphson(func,func_,1)
	print res

It looks like the lines that compare with the tolerance are wrong.

For example:

    if x2-x1 < TOL

should be:

    if abs(x2-x1) < TOL

otherwise, it will incorrectly return early anytime x1 is larger than x2.

If you are looking for libraries that already implement these functions, look here:
http://docs.scipy.org/doc/scipy/reference/optimize.html

I guess it missed "n += 1" in the while loop.
When the Newton and the secant don't converge, it becomes endless loop(死循环).

Yep, I was looking for a secant method function online out of laziness. Need to use abs() when you check if guesses are below the tolerance in newton and secant methods.

In your main function, you have used bisection in place of secant!