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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