scipy.interpolate.cubichermitespline

cubichermitespline is a function from the SciPy library that returns a cubic Hermite spline interpolation function for a given set of data points.

A cubic Hermite spline is a piecewise function defined by cubic polynomials that interpolate the data points and their derivatives. This type of spline is useful for applications where a smooth interpolation is desired while maintaining control over the derivatives.

The function takes in a set of x and y values and, optionally, their corresponding first derivatives. If the derivatives are not provided, they are estimated using a finite difference method. The resulting interpolation function can be evaluated at any point within the range of the input data.

Here is an example usage of cubichermitespline:

import numpy as np
from scipy.interpolate import cubichermitespline

# generate some data
x = np.linspace(0, 10, 11)
y = np.sin(x)

# interpolate using a cubic Hermite spline
f = cubichermitespline(x, y)

# evaluate the interpolation function at some points
x_new = np.linspace(0, 10, 101)
y_new = f(x_new)

# plot the original data and the interpolated function
import matplotlib.pyplot as plt
plt.plot(x, y, 'o', label='data')
plt.plot(x_new, y_new, label='interpolation')
plt.legend()
plt.show()

This will generate a plot of the original data points and the cubic Hermite spline interpolation function evaluated at 101 points between 0 and 10.