#!/usr/bin/env python
# coding: utf-8

# # p09: Polynomial interpolation in equispaced and chebyshev points

# In[1]:


get_ipython().run_line_magic('matplotlib', 'inline')
get_ipython().run_line_magic('config', "InlineBackend.figure_format='svg'")
from numpy import pi,inf,linspace,arange,cos,polyval,polyfit
from numpy.linalg import norm
from matplotlib.pyplot import figure,subplot,plot,axis,title,text


# In[2]:


N = 16
xx = linspace(-1.01,1.01,400,True)
figure(figsize=(10,5))
for i in range(2):
    if i==0:
        s = 'equispaced points'; x = -1.0 + 2.0*arange(0,N+1)/N
    if i==1:
        s = 'Chebyshev points'; x = cos(pi*arange(0,N+1)/N)
    subplot(1,2,i+1)
    u = 1.0/(1.0 + 16.0*x**2)
    uu = 1.0/(1.0 + 16.0*xx**2)
    p = polyfit(x,u,N)
    pp= polyval(p,xx)
    plot(x,u,'o',xx,pp)
    axis([-1.1, 1.1, -1.0, 1.5])
    title(s)
    error = norm(uu-pp, inf)
    text(-0.6,-0.5,'max error='+str(error))