"""
Compute the absolute- and relative errors for the 
approximation 

   f(x) ~= ( f(x+h) - f(x) )/h

when f(x) = sin(x), x = 1.2 and h -> 0+
"""
import matplotlib.pyplot as plt
import numpy as np
#
# Compute the finite difference for different h's
#
x0 = 1.2
f0 = np.sin(1.2)
fp_exact = np.cos(1.2)

err_abs = []
err_asym = []
h = []
for i in np.linspace(-20,0,41):
  hi = 10**i
  h.append(hi)
  fp_approx = (np.sin(x0+hi)-f0)/hi
  err_abs.append(abs(fp_exact) - fp_approx)
  err_asym.append(0.5*f0*hi)
  
plt.subplot(111)
plt.loglog(h,err_abs,'-*b',h,err_asym,'--r')
plt.show()
"""
#
# Plot the absolute error
#
loglog(h,err_abs,'-*',h,err_asym,'--')
xlabel('h')
ylabel('Absolute error')
"""