The PCHIP algorithm is written out in the SciPy API documentation: https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.Pchip... In general, there is no guarantee that if you tabulate and interpolate, the derivative matches the derivative of the underlying function. On Sun, Jan 22, 2023 at 12:51 PM Samuel Dupree <sdupree@speakeasy.net> wrote:
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)
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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