gistfile1.txt

f2 = lambda x : 1/(1+x**2)
lam_cheb = []
lam_unif = []

ns = range(5,45,5)

for n in ns:
  x_unif = [5*(-1 + 2*i/n) for i in range(n+1)]
  x_cheb = chebyshev(-5, 5, n)
  y_unif = [f2(x) for x in x_unif]
  y_cheb = [f2(x) for x in x_cheb]

  lin = np.linspace(-5,5,n*3)
  pyplot.plot(lin, [interp(x_cheb, y_cheb, x) for x in lin], label='Chebyshev')
  pyplot.plot(lin, [interp(x_unif, y_unif, x) for x in lin], label='Uniform')
  pyplot.ylim((-1.5, 1.5))
  pyplot.legend()
  pyplot.show()

  def lam (xs, at):
    return sum([abs(interp(xs, [1 if j == i else 0 for j in range(n+1)], at)) for i in range(n+1)])

  lam_cheb.append(max([lam(x_cheb, at) for at in lin]))
  lam_unif.append(max([lam(x_unif, at) for at in lin]))

pyplot.semilogy(ns, lam_unif, label='Lambda Uniform')
pyplot.semilogy(ns, lam_cheb, label='Lambda Chebyshev')
pyplot.legend()
pyplot.show()