I believe I know what is going on, but I don't understand why. 

The line for the first derivative that failed to coincide with the points in the plot for the cosine is actually the interpolated first derivative scaled by the factor pi/180. When I multiply the interpolated values for the first derivative by 180/pi,  the interpolated first derivative coincides with the points for the cosine as expected. 

What I don't understand is how the interpolator came up with the scale factor it did and applied it using pure numbers.

Any thoughts? 

Sam Dupree.

On 1/21/23 18:04, Samuel Dupree wrote:

I'm running SciPy ver. 1.9.3 under Python ver. 3.9.15  on a Mac Pro (2019) desktop running Mac OSX ver. 13.1 Ventura. The problem I'm having is getting scipy.interpolate.pchip_interpolate to return the first derivative of a pchip interpolation. 

The test program I'm using is given below (and attached to this note).

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

x_observed  = np.linspace(0.0, 360.0, 51)
y_observed  = np.sin(np.pi*x_observed/180)
dydx_observed = np.cos(np.pi*x_observed/180)

as a function of x in degrees. So cosine really gives you the derivative wrt. (x * pi/180),

dy / d(x_observed * np.pi/180) = np.cos(np.pi*x_observed/180).

Besides, as noted in a previous post, the interpolated derivative may not reproduces exactly the

derivative of the interpolation, but the 180/pi factor should come solely from the transformation

to/from working in degrees.

Cheers,

Derek