Getting scipy.interpolate.pchip_interpolate to return the first derivative of a pchip interpolation
Samuel Dupree <[email protected]> Mon, 23 Jan 2023 00:42:22 -0500
| Newsgroups | gmane.comp.python.scientific.user |
|---|---|
| Organization | XayDeltaOne |
| Message-ID | <[email protected]> |
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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.
Upon closer inspection, 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
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<p><font face="Verdana">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. <br>
</font></p>
<p><font face="Verdana">The test program I'm using is given below
(and attached to this note).</font></p>
<p><br>
<font face="Monaco">import numpy as np<br>
import matplotlib.pyplot as plt<br>
from scipy.interpolate import pchip_interpolate<br>
<br>
x_observed = np.linspace(0.0, 360.0, 51)<br>
y_observed = np.sin(np.pi*x_observed/180)<br>
dydx_observed = np.cos(np.pi*x_observed/180)<br>
<br>
x = np.linspace(min(x_observed), max(x_observed), num=100)<br>
y = pchip_interpolate(x_observed, y_observed, x, der=0,
axis=0)<br>
dydx = pchip_interpolate(x_observed, y_observed, x, der=1,
axis=0)<br>
<br>
plt.plot(x_observed, y_observed, "bo" , label="observation
funct")<br>
plt.plot(x_observed, dydx_observed, "rx" , label="observation
deriv")<br>
plt.plot(x , y , "c-", label="pchip
interpolation funct")<br>
plt.plot(x , dydx , "k-", label="pchip
interpolation deriv")<br>
plt.legend()<br>
plt.savefig("pchip_example_01.png")<br>
plt.show()</font><br>
</p>
<p><font face="Verdana"><br>
</font></p>
<p><font face="Verdana">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.</font></p>
<p><font face="Verdana">Upon closer inspection, I believe I know
what is going on, but I don't understand why.</font></p>
<font face="Verdana">
</font>
<p><font face="Verdana">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.</font></p>
<font face="Verdana">
</font>
<p><font face="Verdana">What I don't understand is how the
interpolator came up with the scale factor it did and applied it
using pure numbers.</font></p>
<font face="Verdana">
</font>
<p><font face="Verdana">Any thoughts?</font></p>
<p><font face="Verdana">Sam Dupree<br>
</font></p>
<p><font face="monospace"><font face="Verdana"></font></font></p>
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