问题
I am trying to interpolate a curve to a set of (x,y) points using SciPy's interpolate.splprep method, using the procedure followed in this StackOverflow answer. My code (with the data) is given below. Please excuse me for using this large dataset, as the code works perfectly fine on a different dataset. Kindly scroll to the bottom to see the implemetation.
#!/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,
-3.98863362e-02, -3.73592876e-02, -3.48720213e-02,
-3.37707235e-02, -3.26655171e-02, -3.15625118e-02,
-3.04616664e-02, -3.06508019e-02, -2.95344258e-02,
-2.96968330e-02, -2.98505905e-02, -2.87101259e-02,
-2.88391064e-02, -2.89597166e-02, -2.77967360e-02,
-2.78958771e-02, -2.79854740e-02, -2.80670276e-02,
-2.81405467e-02, -2.82051366e-02, -2.69913041e-02,
-2.70365186e-02, -2.70739448e-02, -2.83768113e-02,
-2.83979671e-02, -2.84108899e-02, -2.84155794e-02,
-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()
I get the following error on one machine (MacOS),
---> tck, u = interpolate.splprep([xp, yp], s=0, k=1, per=True)
SystemError: <built-in function _parcur> returned NULL without setting an error
And this error on another machine (Ubuntu),
----> tck, u = interpolate.splprep([xp, yp], s=0, k=1, per=True)
ValueError: Invalid inputs.
interpolate.splprep uses the FORTRAN parcur routine from FITPACK (from the documentation).
My questions are -
- Why does the code work for different datasets? e.g.
xp = np.array([0.1, 0.2, 0.3, 0.4]) yp = np.array([-0.1, -0.3, -0.4, 0.2])and not for this particular one? What does the error mean? - How can I get this to work? (Using this method or any other method) i.e. either interpolate a curve or filter the outliers ...
- Out of curiosity, why is the error machine (and OS) dependent?
This is how the data looks when plotted, I think you can guess which curve I'd like to interpolate to (and which outliers I'd like to remove, if possible)
回答1:
Fitpack has a fit if it two consecutive inputs are identical. The error happens deep enough that it depends on how the libraries were compiled and linked, hence the assortment of errors.
For example, xp[147:149], yp[147:149] (and several others):
(array([ 0.07705342, 0.07705342]), array([-0.09176826, -0.09176826]))
These are okay:
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
I add the last point back because the output of diff is always one element shorter, so the last one needs to be included manually. (And then of course, you put the 0th point again for periodicity)
Cutting off the weird part
This is my attempt to cut off the weird extruding part of the dataset. It uses a Gaussian filter from ndimage. The original points xp, yp are kept this time; the filtered ones are 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)]
So, we remove not only duplicate points but also the points where the values jump around too much. The rest goes as before, interpolation is built out of xn, yn now. I plot original points for comparison with the new (red) curve):
ax.plot(xp, yp, 'o', markersize=2)
ax.plot(xi, yi, 'r', alpha=0.5)
来源：https://stackoverflow.com/questions/47948453/scipy-interpolate-splprep-error-invalid-inputs