# Choice of Nodes for Polynomial Interpolation¶

In [10]:
%matplotlib qt5

In [11]:
import numpy as np
import numpy.linalg as la

from matplotlib.pyplot import (
clf, plot, show, xlim, ylim,
get_current_fig_manager, gca, draw, connect)


Choose a function below:

In [12]:
func = "runge"

if func == "sin":
def f(x):
return np.sin(5*x)
elif func == "jump":
def f(x):
result = 0*x
result.fill(-1)
result[x > 0] = 1
return result
elif func == "runge":
def f(x):
return 1/(1+25*x**2)
else:
raise RuntimeError("unknown function '%s'" % func)


Run this cell to play with the node placement toy:

In [13]:
#keep
x_points = []
y_points = []
deg = [1]

def update_plot():
clf()
xlim([-1, 1])
ylim([-1.5, 1.5])
gca().set_autoscale_on(False)
plot(x_points, y_points, 'o')

x = np.linspace(-1, 1, 500)
plot(x, f(x), "--")

if len(x_points) >= deg[0]+1:
eval_points = np.linspace(-1, 1, 500)
poly = np.poly1d(np.polyfit(
np.array(x_points),
np.array(y_points), deg[0]))
plot(eval_points, poly(eval_points), "-")

def click(event):
"""If the left mouse button is pressed: draw a little square. """
tb = get_current_fig_manager().toolbar
if event.button == 1 and event.inaxes and tb.mode == '':
x_points.append(event.xdata)
x_ary = np.array([event.xdata])
y_ary = f(x_ary)
y_points.append(y_ary[0])

if event.button == 3 and event.inaxes and tb.mode == '':
if len(x_points) >= deg[0]+2:
deg[0] += 1

update_plot()
draw()

update_plot()
connect('button_press_event', click)
show()