Scipy interpolate.splprep错误“输入无效”
我正在尝试使用SciPy的interpolate.splprep方法将曲线插入到一组（x，y）点，使用此StackOverflow answer中的步骤。我的代码（包含数据）如下所示。 请原谅我使用这个大型数据集，因为代码在不同的数据集上运行得非常好。请滚动到底部以查看实现。
#!/usr/bin/env python3
import numpy as np
import matplotlib.pyplot as plt
from scipy import interpolate
# -----------------------------------------------------------------------------
# Data
xp=np.array([ -1.19824526e-01, -1.19795807e-01, -1.22298912e-01,
-1.24784611e-01, -1.27233423e-01, -1.27048456e-01,
-1.29424259e-01, -1.31781573e-01, -1.34102825e-01,
-1.36386619e-01, -1.41324999e-01, -1.43569618e-01,
-1.48471481e-01, -1.53300646e-01, -1.55387133e-01,
-1.57436481e-01, -1.53938796e-01, -1.58562951e-01,
-1.53139517e-01, -1.50456275e-01, -1.49637920e-01,
-1.48774455e-01, -1.47843528e-01, -1.44278335e-01,
-1.43299274e-01, -1.39716798e-01, -1.36111285e-01,
-1.32534352e-01, -1.28982866e-01, -1.25433151e-01,
-1.21912263e-01, -1.16106245e-01, -1.12701128e-01,
-1.09303316e-01, -1.05947571e-01, -1.00467194e-01,
-9.72083398e-02, -9.39822094e-02, -9.08033710e-02,
-8.96420533e-02, -8.65053261e-02, -8.34162875e-02,
-8.03788778e-02, -7.73929193e-02, -7.62032638e-02,
-7.32655732e-02, -7.03760465e-02, -6.91826390e-02,
-6.63378816e-02, -6.35537275e-02, -6.08302060e-02,
-5.96426925e-02, -5.69864087e-02, -5.43931715e-02,
-5.18641746e-02, -4.93958173e-02, -4.82415854e-02,
-4.58486281e-02, -4.35196817e-02, -4.01162919e-02,
-3.79466513e-02, -3.48161871e-02, -3.18596693e-02,
-2.90650417e-02, -2.64251761e-02, -2.31429101e-02,
-1.94312163e-02, -1.73997964e-02, -1.55068323e-02,
-1.43163160e-02, -1.31800087e-02, -1.20987991e-02,
-1.10708190e-02, -1.05380016e-02, -9.58116017e-03,
-9.06399242e-03, -8.54450012e-03, -7.67847396e-03,
-7.17608354e-03, -6.67181154e-03, -5.89474349e-03,
-5.40878144e-03, -4.92121197e-03, -4.43202070e-03,
-3.94148294e-03, -3.44986011e-03, -2.82410814e-03,
-2.35269319e-03, -1.88058008e-03, -1.47393691e-03,
-9.78376399e-04, -4.82633521e-04, 1.33099164e-05,
5.09212801e-04, 1.05098855e-03, 1.56929991e-03,
2.08706303e-03, 2.72055571e-03, 3.26012954e-03,
3.79870854e-03, 4.33573131e-03, 4.87172652e-03,
5.40640816e-03, 5.93914581e-03, 6.47004490e-03,
6.99921852e-03, 7.52610639e-03, 7.70592714e-03,
8.20559501e-03, 8.70268809e-03, 9.19766855e-03,
9.68963219e-03, 1.01781695e-02, 1.01960805e-02,
1.06577199e-02, 1.11156340e-02, 1.15703286e-02,
1.20215921e-02, 1.24693015e-02, 1.29129042e-02,
1.33526781e-02, 1.37884367e-02, 1.42204360e-02,
1.46473802e-02, 1.50699789e-02, 1.54884533e-02,
1.59020551e-02, 1.63103362e-02, 8.12110387e-02,
7.80794051e-02, 1.67140103e-02, 8.31537241e-02,
7.99472912e-02, 7.99472912e-02, 7.67983984e-02,
1.71128723e-02, 8.50656342e-02, 8.17851028e-02,
7.85638577e-02, 7.53861405e-02, 1.75061328e-02,
8.19411806e-02, 7.38391281e-02, 1.78939640e-02,
8.70866930e-02, 8.36940292e-02, 8.03586974e-02,
7.70534244e-02, 7.70534244e-02, 7.38013540e-02,
7.38013540e-02, 7.06147796e-02, 1.82766038e-02,
8.54279559e-02, 8.20231372e-02, 7.53294330e-02,
7.20765174e-02, 1.86539411e-02, 8.36524496e-02,
7.85095832e-02, 7.51592888e-02, 7.18792721e-02,
1.90250409e-02, 7.82997201e-02, 7.49183992e-02,
7.49183992e-02, 7.16144248e-02, 7.16144248e-02,
6.83771846e-02, 1.93904576e-02, 7.46192919e-02,
7.12865685e-02, 7.12865685e-02, 6.80175748e-02,
1.97501330e-02, 7.42568965e-02, 7.08996495e-02,
7.08996495e-02, 6.75887344e-02, 2.01042729e-02,
7.38173451e-02, 6.70923613e-02, 2.13903228e-02,
7.50479910e-02, 6.82108239e-02, 5.69753762e-02,
5.24303656e-02, 5.24303656e-02, 4.52683211e-02,
4.52683211e-02, 4.25493203e-02, 2.17470907e-02,
7.45062992e-02, 6.76173090e-02, 6.76173090e-02,
6.42925100e-02, 6.42925100e-02, 5.94649095e-02,
5.94649095e-02, 3.92303424e-02, 2.20977481e-02,
7.21341379e-02, 3.72338037e-02, 2.24415025e-02,
7.14448972e-02, 3.40025442e-02, 2.27777176e-02,
7.07064856e-02, 3.57533680e-02, 2.41421550e-02,
6.81719132e-02, 3.62534788e-02, 2.44798556e-02,
6.56110398e-02, 3.80586628e-02, 3.29287629e-02,
2.93070471e-02, 2.48093588e-02, 6.13326924e-02,
3.85518913e-02, 3.46206958e-02, 2.85091877e-02,
2.51312268e-02, 5.38330011e-02, 3.76841669e-02,
3.50540735e-02, 2.77018960e-02, 2.65615352e-02,
5.28838088e-02, 3.81396763e-02, 3.54777506e-02,
2.80364970e-02, 2.68822682e-02, 5.03377702e-02,
3.85814254e-02, 3.58887890e-02, 4.93316503e-02,
4.04098395e-02, 3.62892096e-02, 4.67615526e-02,
4.22828625e-02, 3.80435955e-02, 3.84376145e-02,
4.02332775e-02, 4.06156847e-02, 4.24553741e-02,
4.43352031e-02, 4.47040511e-02, 4.66233682e-02,
4.69790035e-02, 4.89341212e-02, 5.09256192e-02,
5.12584867e-02, 5.32790231e-02, 5.35890744e-02,
5.38831411e-02, 5.41625645e-02, 5.44267004e-02,
5.46700348e-02, 5.48984863e-02, 5.51117932e-02,
5.53082440e-02, 5.54849716e-02, 5.56464539e-02,
5.57928396e-02, 5.59201893e-02, 5.60294455e-02,
5.61233441e-02, 5.62020138e-02, 5.62604489e-02,
5.63017253e-02, 5.63275468e-02, 5.63341408e-02,
5.63226424e-02, 5.62957310e-02, 5.62533699e-02,
5.61937444e-02, 5.61140110e-02, 5.60191106e-02,
5.59087917e-02, 5.57801898e-02, 5.56328560e-02,
5.54704141e-02, 5.70775198e-02, 5.68728844e-02,
5.66515897e-02, 5.64149230e-02, 5.61622287e-02,
5.76630266e-02, 5.73643873e-02, 5.70502787e-02,
5.67190716e-02, 5.63668473e-02, 5.59997391e-02,
5.73489998e-02, 5.69355151e-02, 5.65029189e-02,
5.77751241e-02, 5.72977910e-02, 5.67990710e-02,
5.79863269e-02, 5.74393835e-02, 5.68773454e-02,
5.62926261e-02, 5.56922722e-02, 5.50771272e-02,
5.44454686e-02, 5.37935810e-02, 5.31273003e-02,
5.24468411e-02, 5.17483760e-02, 5.10330229e-02,
5.03036776e-02, 4.95607328e-02, 4.87997085e-02,
4.80238054e-02, 4.72347342e-02, 4.64331616e-02,
4.56132865e-02, 4.47805574e-02, 4.39358955e-02,
4.30782240e-02, 4.22044750e-02, 4.01052073e-02,
3.92354976e-02, 3.83523540e-02, 3.74567873e-02,
3.65508593e-02, 3.45751478e-02, 3.36740998e-02,
3.27625023e-02, 3.18417381e-02, 3.09129121e-02,
2.90665673e-02, 2.81454989e-02, 2.72171846e-02,
2.62807950e-02, 2.53342284e-02, 2.43816409e-02,
2.34221736e-02, 2.24541496e-02, 2.08179757e-02,
1.98678098e-02, 1.89113740e-02, 1.79488243e-02,
1.69806146e-02, 1.65158032e-02, 1.55075714e-02,
1.44932106e-02, 1.34746855e-02, 1.24525920e-02,
1.14268067e-02, 1.03968750e-02, 9.36414487e-03,
8.58823755e-03, 7.51804527e-03, 6.44485601e-03,
5.37002690e-03, 4.29398700e-03, 3.31511044e-03,
2.20302298e-03, 1.09069996e-03, -2.27320426e-05,
-1.16892664e-03, -2.31490869e-03, -3.46060569e-03,
-4.74178052e-03, -5.91852523e-03, -7.09360822e-03,
-8.26683115e-03, -9.43736653e-03, -1.06042682e-02,
-1.17686419e-02, -1.33107457e-02, -1.45010352e-02,
-1.56869180e-02, -1.68693838e-02, -1.80464175e-02,
-1.97732638e-02, -2.09722818e-02, -2.21650612e-02,
-2.40185758e-02, -2.52303300e-02, -2.71803154e-02,
-2.84115598e-02, -3.04489552e-02, -3.16936647e-02,
-3.29299358e-02, -3.50861051e-02, -3.63332401e-02,
-3.85745058e-02, -3.98348648e-02, -4.21660006e-02,
-4.34302610e-02, -4.46836493e-02, -4.59254575e-02,
-4.71530952e-02, -4.96209305e-02, -4.95594200e-02,
-5.07435074e-02, -5.19101301e-02, -5.16977894e-02,
-5.14280802e-02, -5.11057669e-02, -5.07251169e-02,
-5.16985297e-02, -5.12126585e-02, -5.06852098e-02,
-5.15589749e-02, -5.09397027e-02, -5.17615499e-02,
-5.10672514e-02, -5.18313966e-02, -5.25816754e-02,
-5.33179227e-02, -5.40360028e-02, -5.47358953e-02,
-5.54213064e-02, -5.77400978e-02, -5.84092053e-02,
-5.90603644e-02, -6.14284845e-02, -6.38379284e-02,
-6.62872262e-02, -6.69166162e-02, -6.93865431e-02,
-7.18947674e-02, -7.44284962e-02, -7.69969804e-02,
-7.96063191e-02, -8.01834105e-02, -8.28053535e-02,
-8.54623715e-02, -8.59961071e-02, -8.86660185e-02,
-8.91520913e-02, -9.18335218e-02, -9.45402708e-02,
-9.49610563e-02, -9.76401856e-02, -1.00332460e-01,
-1.03032191e-01, -1.03358935e-01, -1.06040606e-01,
-1.06322470e-01, -1.08984284e-01, -1.09195131e-01,
-1.11833426e-01, -1.11994247e-01, -1.14596404e-01,
-1.17192554e-01, -1.17248317e-01])
yp = np.array([ -3.90948536e-05, -2.12984775e-03, -4.31095583e-03,
-6.58019633e-03, -8.93758156e-03, -1.11568100e-02,
-1.36444162e-02, -1.62222092e-02, -1.88895170e-02,
-2.16446498e-02, -2.49629308e-02, -2.79508857e-02,
-3.16029501e-02, -3.54376380e-02, -3.87881494e-02,
-4.22310942e-02, -4.41873802e-02, -4.85246067e-02,
-4.68663315e-02, -4.60459599e-02, -4.86676408e-02,
-5.12750434e-02, -5.38586293e-02, -5.54310799e-02,
-5.79452426e-02, -5.93547929e-02, -6.06497762e-02,
-6.18505946e-02, -6.29584706e-02, -6.39609234e-02,
-6.48713094e-02, -6.44090476e-02, -6.51181556e-02,
-6.57260659e-02, -6.62541381e-02, -6.52943568e-02,
-6.56184758e-02, -6.58578685e-02, -6.60229010e-02,
-6.76012689e-02, -6.76366183e-02, -6.76004442e-02,
-6.74972483e-02, -6.73282385e-02, -6.86657097e-02,
-6.83738036e-02, -6.80140059e-02, -6.92366190e-02,
-6.87491258e-02, -6.82071471e-02, -6.76134579e-02,
-6.86669494e-02, -6.79695621e-02, -6.72259327e-02,
-6.64391135e-02, -6.56069234e-02, -6.64563885e-02,
-6.55361171e-02, -6.45783892e-02, -6.18312378e-02,
-6.07850085e-02, -5.80009440e-02, -5.52383021e-02,
-5.24888121e-02, -4.97523554e-02, -4.54714570e-02,
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-2.70365186e-02, -2.70739448e-02, -2.83768113e-02,
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-2.84104617e-02, -2.96993141e-02, -2.96767995e-02,
-2.96453017e-02, -3.09305120e-02, -3.08782748e-02,
-3.08172540e-02, -3.07460634e-02, -3.06652277e-02,
-3.05756546e-02, -3.04773301e-02, -3.03684498e-02,
-3.02505329e-02, -3.01240628e-02, -2.87032761e-02,
-2.85638294e-02, -2.84161924e-02, -2.82602014e-02,
-2.80957411e-02, -2.79220043e-02, -2.65224371e-02,
-2.63408455e-02, -2.61506690e-02, -2.59523304e-02,
-2.57465736e-02, -2.55333569e-02, -2.53114227e-02,
-2.50819674e-02, -2.48453976e-02, -2.46014650e-02,
-2.43490672e-02, -2.40896946e-02, -2.38232320e-02,
-2.35495727e-02, -2.32681400e-02, -1.11708561e-01,
-1.07398522e-01, -2.29799277e-02, -1.10281290e-01,
-1.06025945e-01, -1.06025945e-01, -1.01847844e-01,
-2.26850806e-02, -1.08812919e-01, -1.04614895e-01,
-1.00492396e-01, -9.64256156e-02, -2.23830803e-02,
-1.01124594e-01, -9.11212826e-02, -2.20738630e-02,
-1.03723227e-01, -9.96804013e-02, -9.57062055e-02,
-9.17682599e-02, -9.17682599e-02, -8.78935733e-02,
-8.78935733e-02, -8.40962884e-02, -2.17583603e-02,
-9.82127298e-02, -9.42965108e-02, -8.65980524e-02,
-8.28570139e-02, -2.14365508e-02, -9.28460674e-02,
-8.71354106e-02, -8.34157663e-02, -7.97743543e-02,
-2.11075333e-02, -8.39100274e-02, -8.02849723e-02,
-8.02849723e-02, -7.67428202e-02, -7.67428202e-02,
-7.32724167e-02, -2.07721464e-02, -7.72159766e-02,
-7.37663681e-02, -7.37663681e-02, -7.03828404e-02,
-2.04308432e-02, -7.42042591e-02, -7.08482147e-02,
-7.08482147e-02, -6.75385453e-02, -2.00834820e-02,
-7.12338454e-02, -6.47417418e-02, -2.06352744e-02,
-6.99333169e-02, -6.35600774e-02, -5.30876202e-02,
-4.88515872e-02, -4.88515872e-02, -4.21763073e-02,
-4.21763073e-02, -3.96425097e-02, -2.02588101e-02,
-6.70368116e-02, -6.08364913e-02, -6.08364913e-02,
-5.78440553e-02, -5.78440553e-02, -5.34994049e-02,
-5.34994049e-02, -3.52908904e-02, -1.98763502e-02,
-6.26583213e-02, -3.23368135e-02, -1.94880238e-02,
-5.99037138e-02, -2.85040222e-02, -1.90931928e-02,
-5.72132575e-02, -2.89247783e-02, -1.95297821e-02,
-5.32198482e-02, -2.82971986e-02, -1.91058177e-02,
-4.94013681e-02, -2.86515116e-02, -2.47888430e-02,
-2.20618305e-02, -1.86758942e-02, -4.45232330e-02,
-2.79827472e-02, -2.51286391e-02, -2.06919011e-02,
-1.82397645e-02, -3.76607947e-02, -2.63609122e-02,
-2.45208701e-02, -1.93767971e-02, -1.85788804e-02,
-3.56379420e-02, -2.56998805e-02, -2.39058698e-02,
-1.88908564e-02, -1.81130913e-02, -3.26595065e-02,
-2.50304222e-02, -2.32829732e-02, -3.07966353e-02,
-2.52257065e-02, -2.26527986e-02, -2.80693713e-02,
-2.53799880e-02, -2.28350066e-02, -2.21686432e-02,
-2.22782703e-02, -2.15723084e-02, -2.16081542e-02,
-2.15998200e-02, -2.08220272e-02, -2.07341864e-02,
-1.99180705e-02, -1.97463091e-02, -1.95241512e-02,
-1.86330762e-02, -1.83210810e-02, -1.73881714e-02,
-1.64501676e-02, -1.55073488e-02, -1.45603397e-02,
-1.36076891e-02, -1.26514336e-02, -1.16918550e-02,
-1.07281971e-02, -9.76103257e-03, -8.79150351e-03,
-7.81935696e-03, -6.84417527e-03, -5.86703766e-03,
-4.88857954e-03, -3.90851347e-03, -2.92690669e-03,
-1.94445885e-03, -9.62077293e-04, 2.10973681e-05,
1.00443470e-03, 1.98670872e-03, 2.96920518e-03,
3.95065293e-03, 4.93054490e-03, 5.90896238e-03,
6.88594418e-03, 7.86095305e-03, 8.83291761e-03,
9.80227952e-03, 1.11168744e-02, 1.21109612e-02,
1.31014370e-02, 1.40884671e-02, 1.50714343e-02,
1.65579859e-02, 1.75619959e-02, 1.85609524e-02,
1.95539892e-02, 2.05406220e-02, 2.15208623e-02,
2.31958067e-02, 2.41936890e-02, 2.51825785e-02,
2.69676402e-02, 2.79735240e-02, 2.89676199e-02,
3.08600313e-02, 3.18685118e-02, 3.28673845e-02,
3.38531747e-02, 3.48305552e-02, 3.57981735e-02,
3.67545357e-02, 3.76978426e-02, 3.86308181e-02,
3.95533112e-02, 4.04626970e-02, 4.13583593e-02,
4.22429533e-02, 4.31163338e-02, 4.39732984e-02,
4.48174616e-02, 4.56497573e-02, 4.64690781e-02,
4.72699006e-02, 4.80584575e-02, 4.88339015e-02,
4.95941309e-02, 5.03364921e-02, 4.95646923e-02,
5.02584615e-02, 5.09357803e-02, 5.15956682e-02,
5.22416815e-02, 5.13017754e-02, 5.18954788e-02,
5.24741267e-02, 5.30389590e-02, 5.35886852e-02,
5.24828002e-02, 5.29815950e-02, 5.34658214e-02,
5.39333680e-02, 5.43819816e-02, 5.48154596e-02,
5.52339801e-02, 5.56342267e-02, 5.42908141e-02,
5.46458325e-02, 5.49864909e-02, 5.53070690e-02,
5.56106186e-02, 5.76746395e-02, 5.79561804e-02,
5.82151857e-02, 5.84584712e-02, 5.86858866e-02,
5.88950787e-02, 5.90831689e-02, 5.92552324e-02,
6.12619766e-02, 6.14026109e-02, 6.15224608e-02,
6.16256880e-02, 6.17123394e-02, 6.36720486e-02,
6.37186812e-02, 6.37481408e-02, 6.56861133e-02,
6.56722393e-02, 6.56407664e-02, 6.55917721e-02,
6.74743714e-02, 6.73786194e-02, 6.72646677e-02,
6.71325153e-02, 6.69773741e-02, 6.68003322e-02,
6.66053297e-02, 6.83473413e-02, 6.81027202e-02,
6.78376164e-02, 6.75542903e-02, 6.72524243e-02,
6.88634515e-02, 6.85066915e-02, 6.81318613e-02,
6.96716731e-02, 6.92387957e-02, 7.07292209e-02,
7.02467261e-02, 7.16584645e-02, 7.11134550e-02,
7.05499862e-02, 7.18681370e-02, 7.12419450e-02,
7.24822144e-02, 7.17989089e-02, 7.29694293e-02,
7.22180480e-02, 7.14476517e-02, 7.06588875e-02,
6.98486903e-02, 7.08078412e-02, 6.81567317e-02,
6.72843393e-02, 6.63881936e-02, 6.37899997e-02,
6.12404950e-02, 5.87433383e-02, 5.62902969e-02,
5.53950962e-02, 5.29895052e-02, 5.06437557e-02,
4.97490264e-02, 4.74631181e-02, 4.65678359e-02,
4.43551128e-02, 4.34554011e-02, 4.25440351e-02,
4.16213883e-02, 4.06842153e-02, 3.97338457e-02,
3.87727819e-02, 3.89122376e-02, 3.78978623e-02,
3.68719281e-02, 3.68766567e-02, 3.68230044e-02,
3.67095055e-02, 3.55465346e-02, 3.53200609e-02,
3.50311849e-02, 3.46717730e-02, 3.42461153e-02,
3.37555022e-02, 3.23610029e-02, 3.17505933e-02,
3.10701527e-02, 2.95754797e-02, 2.87735213e-02,
2.72210019e-02, 2.62970023e-02, 2.52956273e-02,
2.36404433e-02, 2.25053642e-02, 2.12889860e-02,
1.99902757e-02, 1.81872330e-02, 1.67574555e-02,
1.49054892e-02, 1.33429656e-02, 1.14391250e-02,
9.74643800e-03, 7.79267351e-03, 5.96714375e-03,
4.05355227e-03, 2.00672241e-03])
# -----------------------------------------------------------------------------
# Use scipy to interpolate.
xp = np.r_[xp, xp[0]]
yp = np.r_[yp, yp[0]]
tck, u = interpolate.splprep([xp, yp], s=0, k=1, per=True)
xi, yi = interpolate.splev(np.linspace(0, 1, 1000), tck)
# -----------------------------------------------------------------------------
# Plot result
fig = plt.figure()
ax = plt.subplot(111)
ax.plot(xp, yp, '.', markersize=2)
ax.plot(xi, yi, alpha=0.5)
plt.show()
我在一台计算机上遇到以下错误（MacOS），
---> tck, u = interpolate.splprep([xp, yp], s=0, k=1, per=True)
SystemError: <built-in function _parcur> returned NULL without setting an error
这个错误在另一台机器上（Ubuntu），
----> tck, u = interpolate.splprep([xp, yp], s=0, k=1, per=True)
ValueError: Invalid inputs.
interpolate.splprep使用来自FITPACK的FORTRAN parcur例程（来自documentation）。
我的问题是 -
- 为什么代码适用于不同的数据集？例如
xp = np.array([0.1, 0.2, 0.3, 0.4]) yp = np.array([-0.1, -0.3, -0.4, 0.2])而不是这个特别的？这个错误是什么意思？ - 如何让这个工作？ （使用此方法或任何其他方法）即内插曲线或过滤异常值...
- 出于好奇，为什么错误机器（和操作系统）依赖？
这是绘制时数据的外观，我想你可以猜出我想插入哪条曲线（如果可能的话我想删除哪些异常值）
1 个答案:
答案 0 :(得分：2)
如果两个连续输入相同，Fitpack就适合。错误发生得足够深，这取决于库如何编译和链接，因此错误的分类。
例如，xp[147:149], yp[147:149]（以及其他几个）：
(array([ 0.07705342, 0.07705342]), array([-0.09176826, -0.09176826]))
没关系：
okay = np.where(np.abs(np.diff(xp)) + np.abs(np.diff(yp)) > 0)
xp = np.r_[xp[okay], xp[-1], xp[0]]
yp = np.r_[yp[okay], yp[-1], yp[0]]
# the rest of your code
我添加了最后一点，因为diff的输出总是一个元素更短，所以最后一个需要手动包含。 （然后当然，你再次将第0点作为周期性）
切断奇怪的部分
这是我试图切断数据集的奇怪挤压部分。它使用a Gaussian filter from ndimage。这次保留原点xp，yp;过滤后的是xn，yn。
jump = np.sqrt(np.diff(xp)**2 + np.diff(yp)**2)
smooth_jump = ndimage.gaussian_filter1d(jump, 5, mode='wrap') # window of size 5 is arbitrary
limit = 2*np.median(smooth_jump) # factor 2 is arbitrary
xn, yn = xp[:-1], yp[:-1]
xn = xn[(jump > 0) & (smooth_jump < limit)]
yn = yn[(jump > 0) & (smooth_jump < limit)]
因此，我们不仅删除重复点，还删除值过多跳转的点。其余的和以前一样，插值是由xn，yn构建的。我绘制原始点以与新（红色）曲线进行比较：
ax.plot(xp, yp, 'o', markersize=2)
ax.plot(xi, yi, 'r', alpha=0.5)
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