_______________________________________________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)
x = np.linspace(min(x_observed), max(x_observed), num=100)
y = pchip_interpolate(x_observed, y_observed, x, der=0, axis=0)
dydx = pchip_interpolate(x_observed, y_observed, x, der=1, axis=0)
plt.plot(x_observed, y_observed, "bo" , label="observation funct")
plt.plot(x_observed, dydx_observed, "rx" , label="observation deriv")
plt.plot(x , y , "c-", label="pchip interpolation funct")
plt.plot(x , dydx , "k-", label="pchip interpolation deriv")
plt.legend()
plt.savefig("pchip_example_01.png")
plt.show()
The program generates values of the sine function (y_observed) over the range of 0 to 360 degrees. (x_observed). In a similar fashion, the cosine function (first derivative of the sine function) is generated over the same range (dydx_observed). pchip_interpolate is used to perform the interpolation over a specified range for the function and its first derivative. A composite plot is generated showing the points for the function (the sine) and its first derivative (cosine). The interpolated points overlay the function (sine) as expected. However, the first derivative returned fails to overlay the cosine function. The plot is attached to this note.
Any thoughts or suggestions?
Sam Dupree
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