NumericalOptimization/univariate/root-finding/newton.py

numerical_optimization_univariate_root-finding_newton.py

#-*- coding: utf-8 -*-
def _verbose(param, score):
    print 'x=%.5f, f(x)=%.5f'%(param, score)

def root_finding(function, derivate, x, epsilon=1e-5, verbose=False):
    score, delta = 1, 1
    while (abs(score) > epsilon) and (abs(delta) > epsilon):
        score = function(x)
        delta = score / derivate(x)
        if verbose: _verbose(x, score)
        x = x - delta
    return x + delta

numerical_optimization_univariate_root-finding_newton_execute.py

>>> root_finding( lambda x: x**3-x-2, lambda x: 3*(x**2)-1, 1.0 )
1.521379709733148
>>> root_finding( lambda x: x**3-x-2, lambda x: 3*(x**2)-1, 1.0, epsilon=1e-5, verbose=True )
x=1.00000, f(x)=-2.00000
x=2.00000, f(x)=4.00000
x=1.63636, f(x)=0.74530
x=1.53039, f(x)=0.05394
x=1.52144, f(x)=0.00037
x=1.52138, f(x)=0.00000
1.521379709733148