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On Sat, Jan 21, 2023 at 4:08 PM Samuel Dupree <sdup...@speakeasy.net> 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)
>
> 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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