import numpy
import matplotlib.pyplot as plt
import scipy.interpolate

def f(x): return numpy.sin(x)

x5 = numpy.linspace(0, 2.*numpy.pi, 5)
fp5 = scipy.interpolate.lagrange(x5, f(x5))

x10 = numpy.linspace(0, 2.*numpy.pi, 10)
fp10 = scipy.interpolate.lagrange(x10, f(x10))

x15 = numpy.linspace(0, 2.*numpy.pi, 15)
fp15 = scipy.interpolate.lagrange(x15, f(x15))

x = numpy.linspace(0, 2.*numpy.pi, 1000)
plt.figure()
plt.plot(
    x, f(x),
    x, fp5(x), 'r',
    x, fp10(x), 'b', 
    x, fp15(x), 'g',
    x5, f(x5), 'ro',
    x10, f(x10), 'bx',
    x15, f(x15), 'g*',
    )
plt.legend(('f(x)', '5', '10', '15'))         

def g(x): return 1/(1+x*x)

x5 = numpy.linspace(-5, 5., 5)
gp5 = scipy.interpolate.lagrange(x5, g(x5))

x10 = numpy.linspace(-5, 5, 10)
gp10 = scipy.interpolate.lagrange(x10, g(x10))

x15 = numpy.linspace(-5, 5., 15)
gp15 = scipy.interpolate.lagrange(x15, g(x15))

x = numpy.linspace(-5, 5, 1000)
plt.figure()
plt.plot(
    x, g(x),
    x, gp5(x), 'r',
    x, gp10(x), 'b', 
    x, gp15(x), 'g',
    x5, g(x5), 'ro',
    x10, g(x10), 'bx',
    x15, g(x15), 'g*',
    )
plt.legend(('g(x)', '5', '10', '15'))         

def h(x): return x**-12 - x**-6

x5 = numpy.linspace(1, 5., 5)
hp5 = scipy.interpolate.lagrange(x5, h(x5))

x10 = numpy.linspace(1, 5, 10)
hp10 = scipy.interpolate.lagrange(x10, h(x10))

x15 = numpy.linspace(1, 5., 15)
hp15 = scipy.interpolate.lagrange(x15, h(x15))

x = numpy.linspace(1, 5, 1000)
plt.figure()
plt.plot(
    x, h(x),
    x, hp5(x), 'r',
    x, hp10(x), 'b', 
    x, hp15(x), 'g',
    x5, h(x5), 'ro',
    x10, h(x10), 'bx',
    x15, h(x15), 'g*',
    )
plt.legend(('h(x)', '5', '10', '15'))         

plt.show()