SciPy: Using interpolate.bisplev() function (3 examples)

Introduction

SciPy’s interpolate.bisplev() function is essential for those dealing with two-dimensional data that requires interpolation or smoothing. By providing an interface to bivariate spline evaluation, it offers an exquisite balance between flexibility and performance.

The interpolate.bisplev() function in SciPy is a powerful tool for bivariate spline interpolation, enabling complex data fitting and smoothing applications. This guide will explore its usage through three progressively complex examples.

Basic Use-Case: Evaluating a Simple Bivariate Spline

Before jumping into complex examples, let’s start with the basics. The following example demonstrates how to evaluate a bivariate spline at specified points.

import numpy as np
from scipy import interpolate

# Grid of points
x = np.arange(0, 5)
y = np.arange(0, 5)
x, y = np.meshgrid(x, y)

# Function values at grid points
z = np.sin(x) * np.cos(y)

# Fit spline
spline = interpolate.bisplrep(x, y, z, s=0)

# Evaluate spline
xnew, ynew = np.mgrid[0:5:20j, 0:5:20j]
# Use bisplev to evaluate the fitted spline
znew = interpolate.bisplev(xnew[:,0], ynew[0,:], spline)

print(znew)

Output:

[[-5.66384491e-17 -9.47327318e-19  3.13523075e-17  4.49652717e-17
   4.45963816e-17  3.49504533e-17  2.07323034e-17  6.64674796e-18
  -2.67192588e-18 -5.33125672e-18 -3.00051159e-18  2.41300620e-18
   9.00199332e-18  1.48591464e-17  1.80771622e-17  1.67487374e-17
   1.57696369e-17  1.57696369e-17  1.57696369e-17  1.57696369e-17]
   ....

This code snippet demonstrates how to fit a bivariate spline to a simple grid of points and evaluate it at a finer grid, visualizing the result of interpolation.

Intermediate Example: Complex Spline Fitting and Evaluation

Once comfortable with basic spline fitting and evaluation, one can explore more complex scenarios. This example illustrates a scenario involving non-uniform grids and more intricate functions.

import numpy as np
from scipy import interpolate

# Non-uniform grid
x = np.random.rand(100)*4
y = np.random.rand(100)*4

# Complex function
z = np.sin(x) * np.log(y + 1)

# Fit spline
spline = interpolate.bisplrep(x, y, z, s=1)

# Evaluate spline
xi, yi = np.mgrid[0:4:100j, 0:4:100j]
znew = interpolate.bisplev(xi[:,0], yi[0,:], spline)

# This illustrates fitting a spline to a complex, non-uniform dataset

The complexity of the function and non-uniformity of the grid in this example highlight the versatility of the interpolate.bisplev() function.

Advanced Use-Case: Incorporating Derivatives

In more sophisticated applications, one might need to evaluate derivatives of the bivariate spline. This section shows how to achieve this functionality using interpolate.bisplev().

import numpy as np
from scipy import interpolate

# Assume spline from previous examples

# Evaluate first derivative w.r.t x
zdx = interpolate.bisplev(xi[:,0], yi[0,:], spline, dx=1)

# Evaluate first derivative w.r.t y
zdy = interpolate.bisplev(xi[:,0], yi[0,:], spline, dy=1)

# This showcases how to evaluate derivatives of a fitted spline, adding to its versatility.

Evaluating derivatives of bivariate splines is crucial for applications requiring gradient information or slope analysis.

Conclusion

Throughout this guide, we’ve explored the interpolate.bisplev() function from the basic to advanced levels. With its powerful spline fitting and evaluation capabilities, including derivative calculations, SciPy’s interpolate.bisplev() becomes an indispensable tool for data scientists and engineers working with two-dimensional data. By mastering its use, you can significantly enhance the analysis and interpretation of complex datasets.