newtonRaphson method

newton.py

## module error
''' err(string).
Prints 'string' and terminates program.
'''
import sys
def err(string):
    print string
    raw_input('Press return to exit')
    sys.exit()

## module newtonRaphson
''' root = newtonRaphson(f,df,a,b,tol=1.0e-9).
    Finds a root of f(x) = 0 by combining the Newton-Raphson
    method with bisection. The root must be bracketed in (a,b).
    Calls user-supplied functions f(x) and its derivative df(x).  
'''   
def newtonRaphson(f, df, a, b, tol=1.0e-9):
    # import error
    fa = f(a)
    if fa == 0.0: return a
    fb = f(b)
    if fb == 0.0: return b
    if fa * fb > 0.0: err('Root is not bracketed')
    x = 0.5 * (a + b)                   
    for i in range(30):
        fx = f(x)
        if abs(fx) < tol: return x
      # Tighten the brackets on the root
        if fa * fx < 0.0:
            b = x 
        else:                 
            a = x
      # Try a Newton-Raphson step   
        dfx = df(x)
      # If division by zero, push x out of bounds
        try: dx = -fx / dfx
        except ZeroDivisionError: dx = b - a
        x = x + dx
      # If the result is outside the brackets, use bisection 
        if (b - x) * (x - a) < 0.0: 
            dx = 0.5 * (b - a)                     
            x = a + dx
      # Check for convergence    
        if abs(dx) < tol * max(abs(b), 1.0): return x
    print 'Too many iterations in Newton-Raphson'


def f(x):
    return x**3 - 10*x**2 + 5
    
def df(x):
    return 3*x - 20*x

solution = newtonRaphson(f, df, 0.1, 1, tol=1e-11)

print solution