Python - 剪切数据以适合配置文件

Question

我有几组数据，我试图适应不同的配置文件。在其中一个最小区域的中心，有污染阻止我做得很好，如图所示：

考虑到尖峰并不总是处于相同的位置，我如何在数据底部剪掉那些尖峰？或者您将如何处理这样的数据？我使用lmfit来拟合轮廓，在这种情况下是Lorentzian和Gaussian。这是一个最小的工作示例，我使用初始值来更紧密地拟合数据：

import numpy as np
import matplotlib.pyplot as plt
from lmfit import Model
from lmfit.models import GaussianModel, ConstantModel, LorentzianModel

x = np.array([4085.18084467,  4085.38084374,  4085.5808428 , 4085.78084186, 4085.98084092,  4086.18083999,  4086.38083905,  4086.58083811, 4086.78083717,  4086.98083623,  4087.1808353 ,  4087.38083436, 4087.58083342,  4087.78083248,  4087.98083155,  4088.18083061, 4088.38082967,  4088.58082873,  4088.78082779,  4088.98082686, 4089.18082592,  4089.38082498,  4089.58082404,  4089.78082311, 4089.98082217,  4090.18082123,  4090.38082029,  4090.58081935, 4090.78081842,  4090.98081748,  4091.18081654,  4091.3808156 , 4091.58081466,  4091.78081373,  4091.98081279,  4092.18081185, 4092.38081091,  4092.58080998,  4092.78080904,  4092.9808081 , 4093.18080716,  4093.38080622,  4093.58080529,  4093.78080435, 4093.98080341,  4094.18080247,  4094.38080154,  4094.5808006 , 4094.78079966,  4094.98079872,  4095.18079778,  4095.38079685, 4095.58079591,  4095.78079497,  4095.98079403,  4096.1807931 , 4096.38079216,  4096.58079122,  4096.78079028,  4096.98078934, 4097.18078841,  4097.38078747,  4097.58078653,  4097.78078559,4097.98078466,  4098.18078372,  4098.38078278,  4098.58078184, 4098.7807809 ,  4098.98077997,  4099.18077903,  4099.38077809, 4099.58077715,  4099.78077622,  4099.98077528,  4100.18077434, 4100.3807734 ,  4100.58077246,  4100.78077153,  4100.98077059, 4101.18076965,  4101.38076871,  4101.58076778,  4101.78076684, 4101.9807659 ,  4102.18076496,  4102.38076402,  4102.58076309, 4102.78076215,  4102.98076121,  4103.18076027,  4103.38075934, 4103.5807584 ,  4103.78075746,  4103.98075652,  4104.18075558, 4104.38075465,  4104.58075371,  4104.78075277,  4104.98075183, 4105.1807509 ,  4105.38074996,  4105.58074902,  4105.78074808, 4105.98074714,  4106.18074621,  4106.38074527,  4106.58074433, 4106.78074339,  4106.98074246,  4107.18074152,  4107.38074058, 4107.58073964,  4107.7807387 ,  4107.98073777,  4108.18073683, 4108.38073589,  4108.58073495,  4108.78073401,  4108.98073308, 4109.18073214,  4109.3807312 ,  4109.58073026,  4109.78072933, 4109.98072839,  4110.18072745,  4110.38072651,  4110.58072557, 4110.78072464,  4110.9807237 ,  4111.18072276,  4111.38072182, 4111.58072089,  4111.78071995,  4111.98071901,  4112.18071807, 4112.38071713,  4112.5807162 ,  4112.78071526,  4112.98071432, 4113.18071338,  4113.38071245,  4113.58071151,  4113.78071057, 4113.98070963,  4114.18070869,  4114.38070776,  4114.58070682, 4114.78070588,  4114.98070494,  4115.18070401,  4115.38070307, 4115.58070213,  4115.78070119,  4115.98070025,  4116.18069932, 4116.38069838,  4116.58069744,  4116.7806965 ,  4116.98069557, 4117.18069463,  4117.38069369,  4117.58069275,  4117.78069181, 4117.98069088,  4118.18068994,  4118.380689  ,  4118.58068806, 4118.78068713,  4118.98068619,  4119.18068525,  4119.38068431, 4119.58068337,  4119.78068244,  4119.9806815 ,  4120.18068056, 4120.38067962,  4120.58067869,  4120.78067775,  4120.98067681, 4121.18067587,  4121.38067493,  4121.580674  ,  4121.78067306, 4121.98067212,  4122.18067118,  4122.38067025,  4122.58066931, 4122.78066837,  4122.98066743,  4123.18066649,  4123.38066556, 4123.58066462,  4123.78066368,  4123.98066274,  4124.1806618 , 4124.38066087,  4124.58065993,  4124.78065899,  4124.98065805, 4125.18065712,  4125.38065618,  4125.58065524,  4125.7806543 , 4125.98065336,  4126.18065243,  4126.38065149,  4126.58065055, 4126.78064961,  4126.98064868,  4127.18064774,  4127.3806468 , 4127.58064586,  4127.78064492,  4127.98064399,  4128.18064305, 4128.38064211,  4128.58064117,  4128.78064024,  4128.9806393 , 4129.18063836,  4129.38063742,  4129.58063648,  4129.78063555, 4129.98063461,  4130.18063367,  4130.38063273,  4130.5806318 , 4130.78063086,  4130.98062992,  4131.18062898,  4131.38062804, 4131.58062711,  4131.78062617,  4131.98062523,  4132.18062429, 4132.38062336,  4132.58062242,  4132.78062148,  4132.98062054, 4133.1806196 ,  4133.38061867,  4133.58061773,  4133.78061679, 4133.98061585,  4134.18061492,  4134.38061398,  4134.58061304, 4134.7806121 ,  4134.98061116])
y = np.array([0.90312759,  1.00923175,  0.94618369,  0.98284045,  0.91510612,        0.96737804,  0.97690214,  0.94363369,  1.00887784,  1.00110387,        0.91647096,  0.97943202,  1.00672907,  1.01552094,  1.01089407,        0.96914584,  0.9908419 ,  1.0176613 ,  0.97032148,  0.96003562,        0.9702355 ,  0.93684173,  0.94652734,  0.94895018,  1.01214356,        0.85777678,  0.89308203,  0.9789272 ,  0.93901884,  0.9684622 ,        0.96969321,  0.86326307,  0.89607392,  0.92459571,  1.00454429,        1.06019733,  0.97291196,  0.95646497,  0.95899707,  1.02830351,        0.94938178,  0.91481128,  0.92606219,  0.97085631,  0.93597434,        0.91316857,  0.90644542,  0.91726926,  0.91686184,  0.96445563,        0.92166362,  0.95831572,  0.93859066,  0.85285273,  0.89944073,        0.91812428,  0.94265677,  0.88281406,  0.9470601 ,  0.94921529,        0.97289222,  0.94632251,  0.96633195,  0.94096512,  0.95324803,        0.90920845,  0.92100257,  0.91181745,  0.95715298,  0.91715382,        0.90219214,  0.87585035,  0.86592191,  0.89335902,  0.85536392,        0.89619274,  0.9450366 ,  0.82780137,  0.81214176,  0.83461329,        0.82858317,  0.80851704,  0.79253546,  0.85440086,  0.81679169,        0.80579976,  0.72312218,  0.75583125,  0.75204599,  0.84519188,        0.68686821,  0.71472154,  0.71706318,  0.72640234,  0.70526356,        0.68295282,  0.66795774,  0.65004383,  0.68096834,  0.72697547,        0.72436393,  0.77128385,  0.79666758,  0.67349101,  0.61479406,        0.57046337,  0.51614312,  0.52945366,  0.53112169,  0.53757761,        0.56680358,  0.63839684,  0.60704329,  0.62377533,  0.67862515,        0.64587581,  0.71316115,  0.76309798,  0.72217569,  0.7477785 ,        0.79731849,  0.76934137,  0.77063868,  0.77871584,  0.77688526,        0.84342722,  0.85382332,  0.88700466,  0.85837992,  0.79589266,        0.83798993,  0.79835529,  0.84612746,  0.83214907,  0.86373676,        0.90729115,  0.82111605,  0.86165685,  0.84090099,  0.90389133,        0.89554032,  0.90792356,  0.92798016,  0.95588479,  0.95019718,        0.95447497,  0.89845759,  0.91638311,  0.99263342,  0.97477606,        0.95482538,  0.94489498,  0.94344967,  0.90526465,  0.92538486,        0.96279787,  0.94005143,  0.96842454,  0.92296494,  0.89954172,        0.8684367 ,  0.95039002,  0.95229769,  0.93752274,  0.94741173,        0.96704449,  1.01130839,  0.95499414,  0.99596569,  0.95130622,        1.00014723,  1.00252218,  0.95130331,  1.0022896 ,  0.99851989,        0.94405282,  0.95814021,  0.94851972,  1.01302067,  1.01400272,        0.97960083,  0.97070283,  1.01312797,  0.9842154 ,  1.01147273,       0.97331853,  0.91403182,  0.96813051,  0.92319169,  0.9294103 ,        0.96960715,  0.94811518,  0.97115083,  0.84687543,  0.90725159,        0.88061293,  0.87319615,  0.85331661,  0.89775082,  0.90956716,        0.83174505,  0.89753388,  0.89554364,  0.95329739,  0.87687031,        0.93883127,  0.97433899,  0.99515225,  0.97519981,  0.91956466,        0.97977674,  0.93582089,  1.00662722,  0.90157277,  1.02887754,        0.9777419 ,  0.94257094,  1.02359615,  0.98968414,  1.00075502,        1.03230265,  1.05904074,  1.00488442,  1.05507886,  1.05085518,        1.02561781,  1.05896008,  0.98024381,  1.08005691,  0.94528977,        1.03853637,  1.02064405,  1.0467137 ,  1.05375156,  1.12907949,        0.99295611,  1.06601022,  1.02846374,  0.98006807,  0.96446772,        0.97702428,  0.97788589,  0.93889781,  0.96366778,  0.96645265,        0.95857242,  1.05796304,  0.99441763,  1.00573183,  1.05001927])
e = np.array([0.0647344 ,  0.04583914,  0.05665552,  0.04447208,  0.05644753,        0.03968611,  0.05985188,  0.04252311,  0.03366922,  0.04237672,        0.03765898,  0.03290132,  0.04626836,  0.05106203,  0.03619188,        0.03944098,  0.08115469,  0.05859644,  0.06091101,  0.05170821,        0.0427244 ,  0.06804469,  0.06708318,  0.03369381,  0.04160575,        0.08007032,  0.09292148,  0.04378329,  0.08216214,  0.06087074,        0.05375458,  0.06185891,  0.06385766,  0.08084546,  0.04864063,        0.06400878,  0.04988693,  0.06689165,  0.05989534,  0.08010138,        0.0681177 ,  0.04478208,  0.03876582,  0.05977015,  0.06610619,        0.05020086,  0.07244604,  0.0445143 ,  0.06970626,  0.04423994,        0.0414573 ,  0.06892836,  0.05715395,  0.04014724,  0.07908425,        0.06082051,  0.08380691,  0.08576757,  0.06571406,  0.04842625,        0.05298355,  0.05271857,  0.06340425,  0.10849621,  0.0811072 ,        0.03642638,  0.10614094,  0.09865099,  0.06711037,  0.10244762,        0.11843505,  0.1092357 ,  0.09748241,  0.09657009,  0.09970179,        0.10203563,  0.18494082,  0.14097796,  0.1151294 ,  0.16172895,        0.17611204,  0.16226913,  0.2295418 ,  0.17795924,  0.1253298 ,        0.1771586 ,  0.15139061,  0.14739618,  0.1620105 ,  0.19158538,        0.21431605,  0.19292715,  0.23308884,  0.30519423,  0.31401994,        0.30569885,  0.31216375,  0.35147676,  0.25016472,  0.16232236,        0.09058787,  0.0604483 ,  0.05168302,  0.21432774,  0.38149791,        0.5061975 ,  0.44281541,  0.50646427,  0.43761581,  0.44989111,        0.47778238,  0.39944325,  0.32462726,  0.34560857,  0.3175776 ,        0.30253441,  0.23059451,  0.24516185,  0.20708065,  0.26429751,        0.1830661 ,  0.15155041,  0.16497299,  0.15794139,  0.13626666,        0.17839823,  0.13502886,  0.14148522,  0.10869864,  0.11723602,        0.09074029,  0.06922157,  0.07719777,  0.13181317,  0.11441895,        0.10655855,  0.12073767,  0.0846133 ,  0.07974657,  0.06538693,        0.0573741 ,  0.07864047,  0.08351471,  0.08130351,  0.0768824 ,        0.07951992,  0.04478989,  0.0765122 ,  0.04842814,  0.04355571,        0.05138656,  0.07215294,  0.04681987,  0.05790133,  0.06163808,        0.082449  ,  0.06127927,  0.04971221,  0.05107901,  0.04493687,        0.06072161,  0.06094332,  0.03630467,  0.04162285,  0.04058228,        0.04526251,  0.06191432,  0.04901982,  0.0454908 ,  0.06186274,        0.0407017 ,  0.03865571,  0.04353665,  0.03898987,  0.04666321,        0.05856035,  0.04225933,  0.04797901,  0.03523971,  0.04728414,        0.05494382,  0.04773011,  0.03210954,  0.05651663,  0.03625933,        0.03596701,  0.03800191,  0.06267668,  0.06431192,  0.0602614 ,        0.05139896,  0.04571979,  0.04375182,  0.0576867 ,  0.07491418,        0.05339972,  0.07619115,  0.11569378,  0.07087871,  0.09076518,        0.13554717,  0.07811761,  0.07180695,  0.05831886,  0.06042863,        0.08759576,  0.06650081,  0.08420164,  0.08185432,  0.04338836,        0.04970979,  0.04008252,  0.03605485,  0.03456321,  0.05594584,        0.03856822,  0.03576337,  0.03118799,  0.0441686 ,  0.0469118 ,        0.03591666,  0.03562582,  0.04934832,  0.03280972,  0.03201576,        0.04338048,  0.07443531,  0.04121059,  0.03774147,  0.03717577,        0.03354207,  0.03806978,  0.0319364 ,  0.03715712,  0.0379478 ,        0.04867626,  0.0304592 ,  0.03393844,  0.034518  ,  0.04293514,        0.05177898,  0.05332907,  0.0352937 ,  0.03359781,  0.04625272,        0.03733088,  0.03501259,  0.03346308,  0.04333749,  0.05741173])

cont = ConstantModel(prefix='cte_')
pars = cont.guess(y, x=x)

gauss = GaussianModel(prefix='g_')
pars.update( gauss.make_params())    
pars['cte_c'].set(1)
pars['g_center'].set(4125, min=4120, max=4130)
pars['g_sigma'].set(1, min=0.5)
pars['g_amplitude'].set(-0.2, min=-0.5)

loren = LorentzianModel(prefix='l_')
pars.update( loren.make_params())    
pars['l_center'].set(4106, min=4095, max=4115)
pars['l_sigma'].set(4, max=6)
pars['l_amplitude'].set(-6., max=-4.)

model = gauss + loren + cont

init = model.eval(pars, x=x)
result = model.fit(y, pars, x=x, weights=1/e)

#print(result.fit_report(min_correl=0.5))

fig, ax = plt.subplots(figsize=(8,6))

ax.plot(x, y, 'k-', lw=2) # data in red
ax.plot(x, init, 'g--', lw=2) # initial guess 
ax.plot(x, result.best_fit, 'r-', lw=2) # best fit
ax.set(xlim=(4085,4135), ylim=(0.4,1.14))

Answer 1

如果坏点总是处于相同的x值，您可以从数据中删除该点，可能是这样的：

import numpy as np
def index_nearest(array, value):
    """index of array nearest to value"""
    return np.abs(array-value).argmin()

ybad = index_nearest(x, 4150)
y[ybad] = x[ybad] = np.nan
x = x[np.where(np.isfinite(y))]
y = y[np.where(np.isfinite(y))]

然后将模型与那些删除了坏点的数据相匹配。

但是，还有：如果不显然是错误的点并且数据“只是”嘈杂，那么删除看起来像坏点的东西可能没有任何优势。你的数据对我来说很吵，但很难看出系统性的坏点。如果你要删除一个点，请记住你断言这个测量不仅仅受到正常噪声的影响，而且是错误的。

最后：另一种处理噪声数据的方法可能是尝试平滑数据，比如使用Savitzky-Golay滤波器。使用这种方法总是存在使特征平滑的危险，但是适度的S-G滤波器通常有助于清除足以检测特征的噪声数据。当然，如果对过滤数据的拟合与未过滤数据的拟合产生显着不同的结果，您可能需要理解为什么会这样。