In [1]:

from __future__ import division

import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as pt

In [28]:

#nodes = [0, 0.3]
nodes = [0, 0.3, 0.8]
#nodes = [0, 0.3, 0.8, 2, 3]

In [23]:

def lagrange_basis_func(j, x):
    ...            
    return result

(Edit cell for solution)

In [24]:

mesh = np.linspace(-0.5, 3.5, 100)

In [26]:

pt.axhline(0, color="black")
pt.axhline(1, linestyle="--", color="black", alpha=0.3)
for node in nodes:
    pt.axvline(node, linestyle="--", color="black", alpha=0.3)

for i in range(len(nodes)):
    pt.plot(mesh, lagrange_basis_func(i, mesh))
    
pt.ylim([-2,2])

Out[26]:

$$\begin{pmatrix}-2, & 2\end{pmatrix}$$

Questions:

How many interpolating polynomials are there?
Is interpolation any good outside of the interval?

In [36]:

nodes = [0, 0.5, 2, 2.5]
values = np.random.randn(4)

def f(x):
    # Make f interpolate 'values' at 'nodes'
    return (
        ...
        )

(Edit this cell for solution.)

In [37]:

pt.plot(nodes, values, "o")
pt.plot(mesh, f(mesh))

Out[37]:

[<matplotlib.lines.Line2D at 0x496bdd0>]

In []: