newton

import numpy as np
from pylab import *

def f(x):
    return (x+1)**4+4*sin(x)
def d2f(x):
    return (12*(x+1)**(2))-4*sin(x)
def df(x):
    return 4*cos(x)+4*(x+1)**3
x=linspace(-3,1,100)
plot(x, f(x), 'c-')
grid()
show()

def N(x,eps,MI=20):
    if f(x)*d2f(x)<0:
        print 'Newtonova metoda ne konvergira.'
    else:
        print '0. iteracija: %s' % x
        i=1
        while i<=MI:
            if abs(df(x))<eps:
                print 'Horizontalna tangenta'
                break
            dx=f(x)/df(x)
            x=x-dx
            print '%s. iteracija: %s' % (i,x)
            if abs(dx)<eps:
                return x,i
            else:
                i=i+1
        print 'Rjesenje nije nadjeno u zadanom broju iteracija.'
xn,i=N(-2.5,1.e-15)
print 'Rjesenje1:'
print 'x%s=%s' % (i,xn)
print '\n'
xm,j=N(0.,1.e-15)
print 'Rjesenje2:'
print 'x%s=%s' % (j,xm)
print '\n'

x=linspace(-3,1,100)
plot(x, f(x), 'r-',xn,f(xn),'m^',xm,f(xm),'m^')
grid()
show()