#!/usr/bin/env python
"""Root finding using SciPy's Newton's method routines.
"""
from math import sin
from scipy.integrate import quad
from scipy.optimize import newton
# test input function
def f(t):
#@ f(t): t * sin^2(t)
return t*(sin(t))**2 #@
def g(t):
"Exact form for g by integrating f(t)"
u = 0.25
return .25*(t**2-t*sin(2*t)+(sin(t))**2)-u
def gn(t):
"g(t) obtained by numerical integration"
u = 0.25
#@ Hint: use quad, see its return value carefully.
return quad(f,0.0,t)[0] - u #@
# main
tguess = 10.0
print '"Exact" solution (knowing the analytical form of the integral)'
t0 = newton(g,tguess,f) #@
print "t0, g(t0) =",t0,g(t0)
print
print "Solution using the numerical integration technique"
t1 = newton(gn,tguess,f) #@
print "t1, g(t1) =",t1,g(t1)
print
print "To six digits, the answer in this case is t==1.06601."
