interpolate, derivate and integrate a function -- some math fun-CodePudding

I have a problem. I have three lists. The list_umf are the x values and list list_kf are the y values, while list_kfm are y values, too. kfm is the integral of kf. The values are the output of my code.

To show that kfm is the integral of kf, I want to calculate the derivative of kfm, which shuold be the same as kf. But the re calculated kfm (list_kf_re) is just 101.0 every time.

Whats wrong with my code?

import numpy as np
from scipy import integrate, interpolate
from scipy.misc import derivative as deriv
import matplotlib.pyplot as plt

list_kfm = [15.348748494618041, 26.240336614039776, 37.76846357985518, 49.80068952374503, 62.25356792292074, 75.0692188764684, 88.20491343740369, 101.6276911997135,
    115.31128207665246, 129.2342114999071, 143.37856687640036, 157.72915825067278, 172.27292637703843, 186.9985127198004, 201.89593919604192, 216.95636451973587]
list_kf = [168.08871431597626, 179.78615963605742, 188.728883379148, 196.0371678709251, 202.25334207341422, 207.68364358717665, 212.51893919883966, 216.88670040685466,
    220.87653440371076, 224.55397301446894, 227.96847485999652, 231.15833919688876, 234.1538643061246, 236.97945558527186, 239.65507793294745, 242.19728380107006]
list_umf = [0.1, 0.15000000000000002, 0.20000000000000004, 0.25000000000000006, 0.30000000000000004, 0.3500000000000001, 0.40000000000000013, 0.45000000000000007,
    0.5000000000000001, 0.5500000000000002, 0.6000000000000002, 0.6500000000000001, 0.7000000000000002, 0.7500000000000002, 0.8000000000000002, 0.8500000000000002]

f = interpolate.interp1d(
    list_umf, list_kfm, bounds_error=False, fill_value=(15, 217))

list_kf_re = [deriv(f, x) for x in list_umf]

plt.plot(list_umf, list_kfm, label='kfm')
plt.plot(list_umf, list_kf, label='kf')
plt.plot(list_umf, list_kf_re, label='kfre')

print(list_kf_re)
print(list_kf)

CodePudding user response：

Use UnivariateSpline to create an interpolator that you can later apply integral or derivative functions (see this post)

Sample:

import numpy as np
#from scipy import integrate, interpolate
from scipy.interpolate import UnivariateSpline as US, InterpolatedUnivariateSpline as IUS
#from scipy.misc import derivative as deriv
import matplotlib.pyplot as plt

list_kfm = [15.348748494618041, 26.240336614039776, 37.76846357985518, 49.80068952374503, 62.25356792292074, 75.0692188764684, 88.20491343740369, 101.6276911997135,
    115.31128207665246, 129.2342114999071, 143.37856687640036, 157.72915825067278, 172.27292637703843, 186.9985127198004, 201.89593919604192, 216.95636451973587]
list_kf = [168.08871431597626, 179.78615963605742, 188.728883379148, 196.0371678709251, 202.25334207341422, 207.68364358717665, 212.51893919883966, 216.88670040685466,
    220.87653440371076, 224.55397301446894, 227.96847485999652, 231.15833919688876, 234.1538643061246, 236.97945558527186, 239.65507793294745, 242.19728380107006]
list_umf = [0.1, 0.15000000000000002, 0.20000000000000004, 0.25000000000000006, 0.30000000000000004, 0.3500000000000001, 0.40000000000000013, 0.45000000000000007,
    0.5000000000000001, 0.5500000000000002, 0.6000000000000002, 0.6500000000000001, 0.7000000000000002, 0.7500000000000002, 0.8000000000000002, 0.8500000000000002]


f = US(list_umf, list_kfm)

list_kf_re = [f.derivative()(x) for x in list_umf]

plt.plot(list_umf, list_kfm, label='kfm')
plt.plot(list_umf, list_kf, label='kf')
plt.plot(list_umf, list_kf_re, label='kfre')
plt.plot(list_umf, list_kf, 'o', label='kfre_2')


print(list_kf_re)
print(list_kf)