Solve simultaneous equations using the Newton-Raphson method in Python
''' soln = newtonRaphson2(f,x,tol=1.0e-9).
Solves the simultaneous equations f(x) = 0 by
the Newton-Raphson method using {x} as the initial
guess. Note that {f} and {x} are vectors.
'''
from numpy import zeros,dot
from gaussPivot import *
from math import sqrt
def newtonRaphson2(f,x,tol=1.0e-9):
def jacobian(f,x):
h = 1.0e-4
n = len(x)
jac = zeros((n,n))
f0 = f(x)
for i in range(n):
temp = x[i]
x[i] = temp + h
f1 = f(x)
x[i] = temp
jac[:,i] = (f1 - f0)/h
return jac,f0
for i in range(30):
jac,f0 = jacobian(f,x)
if sqrt(dot(f0,f0)/len(x)) < tol: return x
dx = gaussPivot(jac,-f0)
x = x + dx
if sqrt(dot(dx,dx)) < tol*max(max(abs(x)),1.0): return x
print 'Too many iterations'
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