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

# InterpolatedUnivariateSpline

x = np.arange(0, 2*np.pi+np.pi/4, 2*np.pi/8)
y = np.sin(x)
s = interpolate.InterpolatedUnivariateSpline(x, y)
xnew = np.arange(0, 2*np.pi, np.pi/50)
ynew = s(xnew)

plt.figure()
plt.plot(x, y, 'x', xnew, ynew, xnew, np.sin(xnew), x, y, 'b')
plt.legend(['Linear', 'InterpolatedUnivariateSpline', 'True'])
plt.axis([-0.05, 6.33, -1.05, 1.05])
plt.title('InterpolatedUnivariateSpline')
plt.show()

# LSQUnivarateSpline with non-uniform knots

t = [np.pi/2-.1, np.pi/2+.1, 3*np.pi/2-.1, 3*np.pi/2+.1]
s = interpolate.LSQUnivariateSpline(x, y, t, k=2)
ynew = s(xnew)

plt.figure()
plt.plot(x, y, 'x', xnew, ynew, xnew, np.sin(xnew), x, y, 'b')
plt.legend(['Linear', 'LSQUnivariateSpline', 'True'])
plt.axis([-0.05, 6.33, -1.05, 1.05])
plt.title('Spline with Specified Interior Knots')
plt.show()