from numpy import linspace,abs
from sympy import Symbol,exp,atan,diff,lambdify
from matplotlib.pyplot import figure,subplot,plot,grid,title

x=Symbol('x')
# Define the function
f=exp(x)-3.0/2.0-atan(x)
# Compute its derivative
df=diff(f,x)
# Make functions
F = lambdify(x, f, modules=['numpy'])
DF = lambdify(x, df, modules=['numpy'])
X = linspace(-1,1,100)
figure(figsize(10,4))
subplot(1,2,1)
plot(X,F(X))
grid('on')
title('Function')
subplot(1,2,2)
plot(X,DF(X))
grid('on')
title('Derivative')

M = 20      # maximum iterations
x = 0.5     # initial guess
eps = 1e-15 # relative tolerance on root

f = F(x)
for i in range(M):
    df= DF(x)
    dx= -f/df
    x = x + dx
    e = abs(dx)
    f = F(x)
    print "{0:6d} {1:22.14e} {2:22.14e} {3:22.14e}".format(i,x,e,abs(f))
    if e < eps * abs(x):
        break