Derivative of manipulated spline

Question

I am using the InterpolatedUnivariateSpline function from the scipy.interpolate library. I know that there exists a function the evaluate the derivative of the resulting spline. What I am interested in is the derivative of the log of the spline. Is there a way to calculate this directly?

Answer 1

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import InterpolatedUnivariateSpline
x = np.arange(1, 9)
y = np.sqrt(x)                                  # something to use as y-values
spl = InterpolatedUnivariateSpline(x, y)

logder = lambda x: spl.derivative()(x)/spl(x)   # derivative of log of spline

t = np.linspace(x.min(), x.max())
plt.plot(t, logder(t))
plt.show()

Constructing a spline based on the logarithm of data is also a reasonable approach, but it is not the same thing as the logarithm of the original spline.

if you can define a function, depending on a spline, which can be differentiated by python (analytically)

Differentiating an arbitrary function analytically is out of scope for SciPy. In the above example, I had to know that the derivative of log(x) is 1/x; SciPy does not know that. SymPy is a library for symbolic math operations such as derivatives.

It's possible to use SymPy to find the derivative of a function symbolically and then turn it, using lambdify, into a callable function that SciPy or matplotlib, etc can use.

One can also work with splines in an entirely symbolic way using SymPy but it's slow.