Univariate Interpolation Examples in Python (part-2)

    In this tutorial, you'll briefly learn how to use SciPy API's BarycentricInterpolator and KroghInterpolator classes in Python.  

    Interpolation is a method of estimating unknown data points in a known range to make the curve smoother. Univariate interpolation is a type of curve fitting that seeks the curve that best fits a set of two-dimensional data points. Since the data points are sampled from a single variable function, it is called univariate interpolation.  

    The tutorial covers;

1. Preparing test data
   
2. BarycentricInterpolator  method
3. KroghInterpolator method
4. Source code listing
   

    We'll start by loading the required libraries.

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

 

 

Preparing test data

 

   We'll create a simple x and y data for this tutorial. We can visualize it on a graph and apply linear interpolation. Linear interpolation in a graph is simply connecting data points linearly.

 

y = [-1, -2, 1, 3, 2, -1, -3, -1, 1, 2]
x = np.linspace(1, len(y), len(y))

plt.figure(figsize=(8, 6))
plt.plot(x, y, '.r', markersize=10)
plt.plot(x, y)
plt.grid()        
plt.show()

 

 

BarycentricInterpolator method

    BarycentricInterpolator builds a polynomial with provided set of points. It enables the evaluation of the polynomial, effective interpolation of the y values, and updates y through the addition of new x values. The below listing shows the implementation of BarycentricInterpolator method. First, we'll fit model on x and y data, then provide new x data to find out new estimated y values.

xnew = np.linspace(min(x), max(x), num=100)
bary = interpolate.BarycentricInterpolator(x, y)
yfit = bary(xnew)

plt.plot(x, y, '.')
plt.plot(xnew, yfit)
plt.grid()
plt.show() 

 

KroghInterpolator method

    KroghInterpolator evaluates the polynomial and all of its derivatives. The implementation of KroghInterpolator method is similar to above listing. We'll fit model on x and y data, then provide new x data to find out new estimated y values.

 
krogh = interpolate.KroghInterpolator(x, y)
yfit = krogh(xnew)

plt.plot(x, y, '.')
plt.plot(xnew, yfit)
plt.grid()
plt.show() 

    Now we can visualize both methods on a graph and compare each method performance with a given data. The following listing shows how to plot all in one graph.

xnew = np.linspace(min(x), max(x), num=100)  

# fit each method on x, y data 

bary = interpolate.BarycentricInterpolator(x,y)
krogh = interpolate.KroghInterpolator(x,y)

y_bary = bary(xnew)
y_krogh = krogh(xnew) 

# visualize on a graph

ig, ax = plt.subplots(2,1, figsize=(12, 8))
ax[0].plot(x, y, '.r', markersize=10)
ax[0].plot(xnew, y_bary, 'g')
ax[0].set_title("BarycentricInterpolator")
ax[0].grid()

ax[1].plot(x, y, '.r', markersize=10)
ax[1].plot(xnew, y_krogh, 'b')
ax[1].set_title("KroghInterpolator")
ax[1].grid()

plt.tight_layout()        
plt.show()

  

 

    In this tutorial, we've briefly learned how to interpolate data by using SciPy's BarycentricInterpolator and KroghInterpolator classes in Python. The full source code is listed below. 

 

 

Source code listing

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

# Preparing data 

y = [-1, -2, 1, 3, 2, -1, -3, -1, 1, 2]
x = np.linspace(1, len(y), len(y))
 

plt.figure(figsize=(8, 6))
plt.plot(x, y, '.r', markersize=10)

plt.plot(x, y)

plt.grid()        
plt.show() 

xnew = np.linspace(min(x), max(x), num=100)  
 

# fit each method on x, y data 
bary = interpolate.BarycentricInterpolator(x,y)
krogh = interpolate.KroghInterpolator(x,y)

y_bary = bary(xnew)
y_krogh = krogh(xnew)   

# visualize on a graph 

ig, ax = plt.subplots(2,1, figsize=(12, 8))
ax[0].plot(x, y, '.r', markersize=10)
ax[0].plot(xnew, y_bary, 'g')
ax[0].set_title("BarycentricInterpolator")
ax[0].grid()

ax[1].plot(x, y, '.r', markersize=10)
ax[1].plot(xnew, y_krogh, 'b')
ax[1].set_title("KroghInterpolator")
ax[1].grid()

plt.tight_layout()        
plt.show()    

 

References:

1. SciPy Interpolation