题

下面是一个图表$y$及其衍生物$dy/dx$使用 python 计算numpy.gradient，它使用中心方案逼近具有有限差分的导数。显然存在一个问题，即结果中引入了非物理的扭结。

由于微分会放大原始数据中的任何高频内容，因此数值微分总是很棘手，尽管在这里我的数据相对平滑且无噪声。有没有人认识到这种类型的行为以及可以做些什么来获得适当的衍生物？

关于数据的一些信息：

$y$是从计算网格中采样的数据，具有更多的小样本点$x$, 越来越粗糙$x$增加。您看到绘制的数据是通过对统一数量的数据点进行线性插值得到的。然而，由于不均匀的间距，我不得不使用大量的点，以便数据点很小$x$实际上是“真实”数据值，但在高$x$在“真实”点之间有很多点只是线性插值，没有向图中添加任何真实信息。起初我以为可能有一些浮点舍入问题导致

编辑：MCVE

为了说明问题，这里使用一小部分数据来生成此图：

import numpy as np
import matplotlib.pyplot as plt

# Subset of data such that
# sub_data = data[50:150,:]

sub_data = np.asarray([[1.700089160294737667e-05, 9.632603526115417480e-01],
[1.733388671709690243e-05, 9.813255667686462402e-01],
[1.766688365023583174e-05, 9.993913173675537109e-01],
[1.799987876438535750e-05, 1.017457604408264160e+00],
[1.833267015172168612e-05, 1.035513401031494141e+00],
[1.866566708486061543e-05, 1.053580760955810547e+00],
[1.899866219901014119e-05, 1.071648478507995605e+00],
[1.933165913214907050e-05, 1.089716911315917969e+00],
[1.966444870049599558e-05, 1.107774615287780762e+00],
[2.000245694944169372e-05, 1.126114964485168457e+00],
[2.033545388258062303e-05, 1.144184470176696777e+00],
[2.066844899673014879e-05, 1.162254691123962402e+00],
[2.100123856507707387e-05, 1.180314183235168457e+00],
[2.133423549821600318e-05, 1.198385119438171387e+00],
[2.166586818930227309e-05, 1.216382265090942383e+00],
[2.199886512244120240e-05, 1.234277606010437012e+00],
[2.233165650977753103e-05, 1.251089692115783691e+00],
[2.266465162392705679e-05, 1.267913579940795898e+00],
[2.299764855706598610e-05, 1.284739017486572266e+00],
[2.333043812541291118e-05, 1.301555633544921875e+00],
[2.366844637435860932e-05, 1.318636536598205566e+00],
[2.400144148850813508e-05, 1.335466384887695312e+00],
[2.433443842164706439e-05, 1.352297544479370117e+00],
[2.466722798999398947e-05, 1.369119763374328613e+00],
[2.500022492313291878e-05, 1.385953545570373535e+00],
[2.533322003728244454e-05, 1.402788400650024414e+00],
[2.566621697042137384e-05, 1.419624686241149902e+00],
[2.599900835775770247e-05, 1.436451792716979980e+00],
[2.633200347190722823e-05, 1.453290104866027832e+00],
[2.666500040504615754e-05, 1.470129728317260742e+00],
[2.699799551919568330e-05, 1.486970305442810059e+00],
[2.733579822233878076e-05, 1.504054188728332520e+00],
[2.766743091342505068e-05, 1.520827651023864746e+00],
[2.800042602757457644e-05, 1.537671327590942383e+00],
[2.833321741491090506e-05, 1.554505705833435059e+00],
[2.866621252906043082e-05, 1.571351289749145508e+00],
[2.899920946219936013e-05, 1.588197588920593262e+00],
[2.933220639533828944e-05, 1.605044960975646973e+00],
[2.966499596368521452e-05, 1.621882915496826172e+00],
[2.999799289682414383e-05, 1.638731956481933594e+00],
[3.033098801097366959e-05, 1.655581831932067871e+00],
[3.066398494411259890e-05, 1.672432422637939453e+00],
[3.100178582826629281e-05, 1.689526319503784180e+00],
[3.133478094241581857e-05, 1.706378579139709473e+00],
[3.166777969454415143e-05, 1.723231554031372070e+00],
[3.200077480869367719e-05, 1.740085244178771973e+00],
[3.233356619603000581e-05, 1.756929397583007812e+00],
[3.266656131017953157e-05, 1.773784637451171875e+00],
[3.299955642432905734e-05, 1.790640354156494141e+00],
[3.333234781166538596e-05, 1.806897401809692383e+00],
[3.366534292581491172e-05, 1.822490572929382324e+00],
[3.399697743589058518e-05, 1.838021636009216309e+00],
[3.433498568483628333e-05, 1.853852272033691406e+00],
[3.466777343419380486e-05, 1.869441509246826172e+00],
[3.500077218632213771e-05, 1.885041832923889160e+00],
[3.533376730047166348e-05, 1.900644183158874512e+00],
[3.566676605259999633e-05, 1.916247844696044922e+00],
[3.599955380195751786e-05, 1.931843996047973633e+00],
[3.633255255408585072e-05, 1.947450876235961914e+00],
[3.666554766823537648e-05, 1.963059425354003906e+00],
[3.699854278238490224e-05, 1.978669643402099609e+00],
[3.733133416972123086e-05, 1.994271874427795410e+00],
[3.766432928387075663e-05, 2.009885072708129883e+00],
[3.800233753281645477e-05, 2.025733470916748047e+00],
[3.833533264696598053e-05, 2.041349411010742188e+00],
[3.866812403430230916e-05, 2.056957483291625977e+00],
[3.900111914845183492e-05, 2.072576045989990234e+00],
[3.933411426260136068e-05, 2.088196039199829102e+00],
[3.966690564993768930e-05, 2.103807926177978516e+00],
[3.999854016001336277e-05, 2.119366645812988281e+00],
[4.033153527416288853e-05, 2.134990215301513672e+00],
[4.066453038831241429e-05, 2.150615453720092773e+00],
[4.099732177564874291e-05, 2.166232347488403320e+00],
[4.133032052777707577e-05, 2.181859731674194336e+00],
[4.166832513874396682e-05, 2.197722673416137695e+00],
[4.200132389087229967e-05, 2.213352441787719727e+00],
[4.233411164022982121e-05, 2.228973865509033203e+00],
[4.266711039235815406e-05, 2.244606018066406250e+00],
[4.300010550650767982e-05, 2.260239124298095703e+00],
[4.333310062065720558e-05, 2.275873422622680664e+00],
[4.366589200799353421e-05, 2.291499376296997070e+00],
[4.399888712214305997e-05, 2.307135581970214844e+00],
[4.433188223629258573e-05, 2.322772979736328125e+00],
[4.466467362362891436e-05, 2.338401794433593750e+00],
[4.499766873777844012e-05, 2.352876663208007812e+00],
[4.533567698672413826e-05, 2.367459297180175781e+00],
[4.566867210087366402e-05, 2.381829023361206055e+00],
[4.600146712618879974e-05, 2.396192073822021484e+00],
[4.633309799828566611e-05, 2.410506963729858398e+00],
[4.666609311243519187e-05, 2.424882888793945312e+00],
[4.699908822658471763e-05, 2.439260959625244141e+00],
[4.733187961392104626e-05, 2.453632116317749023e+00],
[4.766487472807057202e-05, 2.468014001846313477e+00],
[4.799787348019890487e-05, 2.482398033142089844e+00],
[4.833086859434843063e-05, 2.496783494949340820e+00],
[4.866365998168475926e-05, 2.511162519454956055e+00],
[4.900166459265165031e-05, 2.525767564773559570e+00],
[4.933466334477998316e-05, 2.540158748626708984e+00],
[4.966766209690831602e-05, 2.554551839828491211e+00],
[5.000044984626583755e-05, 2.568938016891479492e+00]])


x = sub_data[:,0]
y = sub_data[:,1]
dx = x[1]-x[0]

dydx = np.gradient(y,dx)

plt.figure()
fig, ax1 = plt.subplots(figsize=(8,4))
ax2 = ax1.twinx()

ax1.plot(x,y,'k-')
ax2.plot(x,dydx, 'r-')
plt.show()