Spline Interpolation- Scipy

 #Spline interpolation using Scipy.

from scipy.interpolate import CubicSpline

import numpy as np

import matplotlib.pyplot as plt

x = [1, 2, 3]

y = [-8, -1, 18]

f = CubicSpline(x, y, bc_type='natural')

x_new = np.linspace(1, 3, 100)

y_new = f(x_new)

print(f(2.5))

plt.plot(x_new, y_new, 'b')

plt.plot(x, y, 'ro')

plt.title('Cubic Spline Interpolation')

plt.xlabel('x')

plt.ylabel('y')

plt.show()

Output Screen:

7.375

Plotting the solution of example 5.3  using pylab

#Example 5.1,5.3 SS Satry

from pylab import* 

x = [1,2,3]

y = [-8,-1,18]

x1=linspace(1,2,100)

y1=3*(x1-1)**3-8*(2-x1)-4*(x1-1) #cubic spline

y2=7*x1-15   #linear

y5=x1**3-9  #actual function

x2=linspace(2,3,100)

y4=3*(3-x2)**3+22*x2-48  #cubic spline

y3=19*x2-39   #linear

y6=x2**3-9  #actual function

plot(x, y, 'o','data')

plot(x1,y1,'b-')

plot(x2,y4,'b-') #cubic spline -blue

plot(x1,y2,'r--')

plot(x2,y3,'r--') #linear -red

plot(x1,y5,'g-')

plot(x2,y6,'g-')   #actual function - green

show()

Output Screen

Another Example:

 

from scipy.interpolate import interp1d

import numpy as np

x =[0,1,2,3]

y =[2,-6,-8,2]

f = interp1d(x, y)

f2 = interp1d(x, y, kind='cubic')

xnew =np.linspace(0,3,100)

import matplotlib.pyplot as plt

plt.plot(x, y, 'o', xnew, f(xnew), '-', xnew, f2(xnew), '--')

plt.legend(['data', 'linear', 'cubic'], loc='best')

plt.show()

Output: