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
#!/Users/user/opt/anaconda3/bin/python3
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()
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