Python-使用lmfit使高斯适应嘈杂的数据 [英] Python - Fit gaussian to noisy data with lmfit

问题描述

我正在尝试使高斯拟合此数据

I'm trying to fit a gaussian to this data

x = [4170.177259096838, 4170.377258006199, 4170.577256915561, 4170.777255824922, 4170.977254734283, 4171.177253643645, 4171.377252553006, 4171.577251462368, 4171.777250371729, 4171.977249281091, 4172.177248190453, 4172.377247099814, 4172.577246009175, 4172.777244918537, 4172.977243827898, 4173.17724273726, 4173.377241646621, 4173.577240555983, 4173.777239465344, 4173.977238374706, 4174.177237284067, 4174.377236193429, 4174.57723510279, 4174.777234012152, 4174.977232921513, 4175.177231830875, 4175.377230740236, 4175.577229649598, 4175.777228558959, 4175.977227468321, 4176.177226377682, 4176.377225287044, 4176.577224196405, 4176.777223105767, 4176.977222015128, 4177.17722092449, 4177.377219833851, 4177.577218743213, 4177.777217652574, 4177.977216561936, 4178.177215471297, 4178.377214380659, 4178.57721329002, 4178.777212199382, 4178.977211108743, 4179.177210018105, 4179.377208927466, 4179.577207836828, 4179.777206746189, 4179.977205655551, 4180.177204564912, 4180.377203474274, 4180.577202383635, 4180.777201292997, 4180.977200202357, 4181.17719911172, 4181.377198021081, 4181.577196930443, 4181.777195839804, 4181.977194749166, 4182.177193658527, 4182.377192567888, 4182.5771914772495, 4182.777190386612, 4182.9771892959725, 4183.177188205335, 4183.377187114696, 4183.577186024058, 4183.777184933419, 4183.9771838427805, 4184.177182752143, 4184.3771816615035, 4184.5771805708655, 4184.777179480228, 4184.977178389589, 4185.1771772989505, 4185.3771762083115, 4185.5771751176735, 4185.777174027035, 4185.977172936397, 4186.1771718457585, 4186.3771707551205, 4186.5771696644815, 4186.777168573843, 4186.977167483204, 4187.177166392566, 4187.377165301927, 4187.577164211289, 4187.77716312065, 4187.977162030013, 4188.177160939374, 4188.377159848735, 4188.577158758096, 4188.777157667458, 4188.977156576819, 4189.177155486181, 4189.377154395542, 4189.577153304904, 4189.777152214265, 4189.977151123627, 4190.177150032989, 4190.37714894235, 4190.577147851711, 4190.777146761073, 4190.977145670434, 4191.177144579796, 4191.377143489157, 4191.577142398519, 4191.77714130788, 4191.977140217242, 4192.177139126603, 4192.377138035965, 4192.577136945326, 4192.777135854688, 4192.977134764049, 4193.177133673411, 4193.377132582772, 4193.577131492134, 4193.777130401495, 4193.977129310857, 4194.177128220218, 4194.377127129579, 4194.577126038941, 4194.777124948303, 4194.977123857664, 4195.177122767026, 4195.377121676387, 4195.577120585749, 4195.77711949511, 4195.977118404472, 4196.177117313833, 4196.377116223195, 4196.577115132556, 4196.777114041918, 4196.977112951279, 4197.177111860641, 4197.377110770002, 4197.577109679364, 4197.777108588725, 4197.977107498087, 4198.177106407448, 4198.37710531681, 4198.577104226171, 4198.777103135533, 4198.977102044893, 4199.177100954256, 4199.377099863617, 4199.577098772979, 4199.77709768234, 4199.977096591702, 4200.177095501063, 4200.377094410424, 4200.5770933197855, 4200.777092229148, 4200.9770911385085, 4201.177090047871, 4201.377088957232, 4201.577087866594, 4201.7770867759555, 4201.9770856853165, 4202.177084594679, 4202.377083504041, 4202.5770824134015, 4202.777081322764, 4202.977080232125, 4203.1770791414865, 4203.377078050848, 4203.5770769602095, 4203.777075869571, 4203.9770747789335, 4204.1770736882945, 4204.3770725976565, 4204.5770715070175, 4204.777070416379, 4204.97706932574, 4205.177068235102, 4205.377067144463, 4205.577066053825, 4205.777064963186, 4205.977063872549, 4206.17706278191, 4206.377061691271, 4206.577060600632, 4206.777059509994, 4206.977058419355, 4207.177057328717, 4207.377056238078, 4207.57705514744, 4207.777054056801, 4207.977052966163, 4208.177051875525, 4208.377050784886, 4208.577049694247, 4208.777048603609, 4208.977047512971, 4209.177046422332, 4209.377045331693, 4209.577044241055, 4209.777043150416, 4209.977042059778, 4210.177040969139, 4210.377039878501, 4210.577038787862, 4210.777037697224, 4210.977036606585, 4211.177035515947, 4211.377034425308, 4211.57703333467, 4211.777032244031, 4211.977031153393, 4212.177030062754, 4212.377028972116, 4212.577027881477, 4212.777026790839, 4212.9770257002, 4213.177024609562, 4213.377023518923, 4213.577022428285, 4213.777021337646, 4213.977020247008, 4214.177019156369, 4214.377018065731, 4214.577016975092, 4214.777015884454, 4214.977014793814, 4215.177013703177, 4215.377012612538, 4215.5770115219, 4215.777010431261, 4215.977009340623, 4216.177008249984, 4216.377007159345, 4216.577006068707, 4216.777004978069, 4216.977003887429, 4217.177002796792, 4217.377001706153, 4217.577000615515, 4217.776999524876, 4217.976998434238, 4218.176997343599, 4218.37699625296, 4218.5769951623215, 4218.776994071684, 4218.9769929810445, 4219.176991890407, 4219.376990799769, 4219.5769897091295, 4219.7769886184915, 4219.9769875278525, 4220.176986437215, 4220.376985346577, 4220.5769842559375, 4220.7769831653, 4220.9769820746615, 4221.1769809840225, 4221.376979893384, 4221.5769788027455, 4221.776977712107, 4221.9769766214695, 4222.17697553083, 4222.3769744401925, 4222.576973349554, 4222.776972258915, 4222.976971168276, 4223.176970077638, 4223.376968986999, 4223.576967896361, 4223.776966805722, 4223.976965715085, 4224.176964624445, 4224.376963533807, 4224.576962443168, 4224.77696135253, 4224.976960261891, 4225.176959171253, 4225.376958080614, 4225.576956989976, 4225.776955899337, 4225.976954808699, 4226.17695371806, 4226.376952627422, 4226.576951536783, 4226.776950446145, 4226.976949355506, 4227.176948264868, 4227.376947174229, 4227.576946083591, 4227.776944992952, 4227.976943902314, 4228.176942811675, 4228.376941721037, 4228.576940630398, 4228.776939539759, 4228.976938449121, 4229.176937358483, 4229.376936267844, 4229.576935177205, 4229.776934086567, 4229.976932995929]
y = [1.0063203573226929, 0.9789621233940125, 0.9998905658721924, 0.9947001934051514, 1.023498773574829, 1.0001505613327026, 0.9659610986709596, 1.0141736268997192, 0.9910064339637756, 0.961456060409546, 0.9808377623558044, 0.9717124700546264, 1.0020164251327517, 0.9276596307754515, 1.0044682025909424, 0.9898168444633484, 1.0139398574829102, 1.016809344291687, 0.9985541105270386, 1.0404949188232422, 1.0104306936264038, 1.0101377964019775, 1.0228283405303955, 1.014385461807251, 0.9949180483818054, 0.9398794174194336, 1.0047662258148191, 1.0185784101486206, 0.9942153096199036, 1.0496678352355957, 0.929694890975952, 1.0259612798690796, 1.0174839496612549, 0.9557819366455078, 1.009858012199402, 1.0258405208587646, 1.0318727493286133, 0.9781686067581176, 0.9566296339035034, 0.9626089930534364, 1.040783166885376, 0.9469046592712402, 0.9732370972633362, 1.0082777738571167, 1.0438332557678225, 1.067220687866211, 1.0809389352798462, 1.0122139453887942, 0.995375156402588, 1.025692343711853, 1.0900095701217651, 1.0033329725265503, 0.9947514533996582, 0.9366152882575988, 1.0340673923492432, 1.0574461221694946, 0.9984419345855712, 0.9406535029411316, 1.0367794036865234, 1.0252420902252195, 0.9390246868133544, 1.057265043258667, 1.0652446746826172, 1.0001699924468994, 1.0561981201171875, 0.9452269077301024, 1.0119216442108154, 1.000349760055542, 0.9879921674728394, 0.9834288954734802, 0.976799249649048, 0.9408118724822998, 1.0574927330017092, 1.0466219186782837, 0.97526878118515, 0.9811903238296508, 0.9985196590423584, 0.9862677454948424, 0.964194357395172, 1.0116554498672483, 0.9122620820999146, 0.9972245693206788, 0.9447768926620485, 1.0320085287094116, 1.0034307241439822, 0.965615689754486, 1.0228805541992188, 0.9555847048759459, 1.00389301776886, 0.9856386780738832, 0.9894683361053468, 1.0711736679077148, 0.990192711353302, 1.016653060913086, 1.0263935327529907, 0.9454292058944702, 0.9236765503883362, 0.9511216878890992, 0.9773555994033812, 0.9222095608711244, 0.9599731564521791, 1.0067923069000244, 1.0022263526916504, 0.9766445159912108, 1.0026237964630127, 1.010635256767273, 0.9901092052459716, 0.9869268536567688, 1.0354781150817869, 0.9797658920288086, 0.9543874263763428, 0.9747632145881652, 0.9942164421081544, 1.008299469947815, 0.9546594023704528, 1.0318409204483032, 1.0383642911911009, 1.0332415103912354, 1.0234425067901611, 1.0186198949813845, 1.0179851055145264, 1.0760197639465332, 0.9456835985183716, 1.0079874992370603, 0.9838529229164124, 0.8951097726821899, 0.9530791640281676, 0.9732348322868348, 0.9659185409545898, 1.0089071989059448, 0.963958203792572, 1.0035384893417358, 0.9776629805564879, 0.964256465435028, 0.9468261599540709, 1.0145124197006226, 1.0375784635543823, 0.992344319820404, 0.9584225416183472, 1.0427420139312744, 0.9997742176055908, 0.9584409594535828, 1.0051720142364502, 0.9606672525405884, 0.9797580242156982, 0.9900978207588196, 0.943138301372528, 0.9368865489959716, 0.9272330403327942, 0.9655094146728516, 0.9074565172195436, 0.97406405210495, 0.8742623329162598, 0.9219859838485718, 0.9126378297805786, 0.8354664444923401, 0.9138413667678832, 0.9268960952758788, 0.8841327428817749, 0.9733222126960754, 0.8825243711471558, 0.9243521094322203, 0.9403685927391052, 0.8782523870468141, 0.9003781080245972, 0.8850597143173218, 0.9231640696525574, 0.931676983833313, 0.8601804971694946, 0.8312444686889648, 0.9361259937286376, 0.9289224147796632, 0.8919285535812378, 0.8838070034980774, 0.9187015891075134, 0.9484543204307556, 0.8572731018066406, 0.8458079099655151, 0.92625629901886, 0.9748064875602722, 0.9674397706985474, 0.9326313138008118, 0.9933922290802002, 1.0025516748428345, 0.9956294894218444, 0.8995802998542786, 0.9598655700683594, 1.0185420513153076, 0.9935647249221802, 0.9689980745315552, 0.9919951558113098, 1.0028616189956665, 1.0252325534820557, 1.0221387147903442, 1.009528875350952, 1.0272767543792725, 0.9865442514419556, 0.9821861386299132, 0.95982563495636, 0.9557262063026428, 0.9864148497581482, 1.0166704654693604, 1.0599093437194824, 1.0000406503677368, 0.9622656106948853, 1.0044697523117063, 1.0404677391052246, 1.0023702383041382, 0.9803014993667604, 1.0197279453277588, 0.9902933835983276, 0.998839259147644, 0.966608464717865, 1.0340296030044556, 0.9632315635681152, 0.9758646488189696, 0.9757773876190186, 0.9818265438079834, 1.0110433101654053, 1.0131133794784546, 1.0256367921829224, 1.0690158605575562, 0.9764784574508668, 0.9947471022605896, 0.9979920387268066, 0.9850373864173888, 0.9165602922439576, 0.9634824395179749, 1.052489995956421, 0.9370544552803041, 1.0348092317581177, 1.0473220348358154, 0.9566289782524108, 0.9579214453697203, 0.972671627998352, 0.9536439180374146, 0.9755330085754396, 0.9753606915473938, 0.9924075603485109, 0.9893715381622314, 0.9780346751213074, 1.0207450389862058, 0.9914312362670898, 0.9940584301948548, 1.0417673587799072, 0.977041721343994, 1.0113568305969238, 1.030456304550171, 1.0540854930877686, 0.9963837265968324, 1.002269268035889, 0.9528346061706544, 0.9132148027420044, 1.0386162996292114, 0.9384365677833556, 1.0175614356994631, 1.0362330675125122, 0.9502999186515808, 1.0015273094177246, 0.987025022506714, 0.9869014024734496, 0.9577396512031556, 0.9633736610412598, 1.0747206211090088, 1.1858476400375366, 0.9917531609535216, 1.0963184833526611, 0.9528627991676332, 0.9999563694000244, 1.0115929841995241, 1.0094747543334959, 0.9977090358734132, 0.9800350666046144, 1.0336441993713381, 1.0021690130233765, 0.9629588127136229, 0.9191407561302184, 0.9930744767189026, 1.0318671464920044, 0.975939691066742, 0.9548277258872986, 1.0113637447357178, 0.9920935630798341, 0.9777255654335022, 0.9780721664428712, 0.9507009387016296, 0.9387223720550536, 1.0220414400100708, 1.019809007644653, 0.9822806715965272, 1.0380866527557373, 1.0477066040039062, 1.0222935676574707, 1.0258997678756714, 1.027082443237305, 1.0487046241760254, 0.9292799830436708, 0.999277114868164, 1.044923186302185, 1.0261610746383667]
e = [3.865531107294373e-05, 3.866014958475717e-05, 3.866496626869776e-05, 3.8669764762744314e-05, 3.867453415296041e-05, 3.8679270801367245e-05, 3.8683978345943615e-05, 3.868864223477431e-05, 3.8693269743816934e-05, 3.8697849959135056e-05, 3.870237924274989e-05, 3.8706857594661415e-05, 3.871127773891203e-05, 3.871564331348054e-05, 3.871994340443053e-05, 3.872417437378317e-05, 3.8728336221538484e-05, 3.8732425309717655e-05, 3.8736438000341884e-05, 3.874037065543234e-05, 3.8744219637010247e-05, 3.874798130709678e-05, 3.8751652027713135e-05, 3.875523543683812e-05, 3.8758716982556514e-05, 3.876210394082591e-05, 3.8765389035688706e-05, 3.8768568629166105e-05, 3.87716390832793e-05, 3.877460039802827e-05, 3.877745257341303e-05, 3.878018469549716e-05, 3.8782800402259454e-05, 3.878529605572112e-05, 3.8787664379924536e-05, 3.878991265082732e-05, 3.8792029954493046e-05, 3.8794016290921725e-05, 3.879586802213453e-05, 3.8797588786110275e-05, 3.879916766891256e-05, 3.8800608308520175e-05, 3.88019070669543e-05, 3.880306030623615e-05, 3.880407166434452e-05, 3.8804930227342986e-05, 3.8805643271189176e-05, 3.880619988194667e-05, 3.880660733557306e-05, 3.8806854718131945e-05, 3.8806945667602115e-05, 3.88068801839836e-05, 3.880665099131875e-05, 3.8806265365565196e-05, 3.880571239278652e-05, 3.880499571096152e-05, 3.880410804413259e-05, 3.880305666825734e-05, 3.8801834307378165e-05, 3.8800444599473856e-05, 3.87988802685868e-05, 3.879714495269582e-05, 3.8795235013822094e-05, 3.879315045196563e-05, 3.879089126712642e-05, 3.8788453821325675e-05, 3.8785838114563376e-05, 3.878304414683953e-05, 3.8780071918154135e-05, 3.877691779052839e-05, 3.877357812598348e-05, 3.877006747643463e-05, 3.8766367651987814e-05, 3.876248956657946e-05, 3.875842594425194e-05, 3.8754180422984064e-05, 3.8749749364797026e-05, 3.874513640766963e-05, 3.8740334275644266e-05, 3.873535024467856e-05, 3.8730184314772493e-05, 3.872482920996845e-05, 3.871929220622405e-05, 3.871356602758169e-05, 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我尝试了给出的示例 Python高斯适合模拟高斯噪声数据和使用Scipy与ROOT等方法拟合(高斯)没有运气.

I have tried the examples given in Python gaussian fit on simulated gaussian noisy data, and Fitting (a gaussian) with Scipy vs. ROOT et al without luck.

我希望使用lmfit做到这一点，因为它具有多个优点.尝试是按照lmfit文档进行的，这是代码和图解

I'm looking to do this with lmfit because it has several advantages. This attempt was done following lmfit documentation, here is the code and plot

from numpy import sqrt, pi, exp
from lmfit import  Model
import matplotlib.pyplot as plt

def gaussian(x, amp, cen, wid):
    "1-d gaussian: gaussian(x, amp, cen, wid)"
    return (amp/(sqrt(2*pi)*wid)) * exp(-(x-cen)**2 /(2*wid**2))

gmodel = Model(gaussian)
result = gmodel.fit(y, x=x, amp=-0.5, cen=4200, wid=2)

plt.plot(x, y,'ro', ms=6)
plt.plot(x, result.init_fit, 'g--', lw=2)
plt.plot(x, result.best_fit, 'b-', lw=2)

因此，绿色为初始参数的拟合度，蓝色为最佳拟合度，如您所见，我的点和一条直线都偏离了高斯.

So in green is the fit with the initial parameters, and in blue is what should be the best fit, and as you can see I get a gaussian shifted from my points and a straight line.

此外，我的数据的第三行是y轴上的错误.用lmfit拟合数据时如何考虑错误?

Also, the third row of my data are the errors in the y axis. How can I take the errors into account when fitting the data with lmfit?

推荐答案

最简单的方法可能是利用

The easiest way to do this is probably to make use of the built-in models and combine the GaussianModel and ConstantModel. You can use the errors in the fitting using the keyword 'weights' as described here.

您可能想要做这样的事情:

You'll probably want to do something like this:

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

xval = np.array(x)
yval = np.array(y)
err = np.array(e)

peak = GaussianModel()
offset = ConstantModel()
model = peak + offset

pars = offset.make_params(c=np.median(y))
pars += peak.guess(yval, x=xval, amplitude=-0.5)

result = model.fit(yval, pars, x=xval, weights=1/err)
print(result.fit_report())

plt.plot(xval, yval, 'ro', ms=6)
plt.plot(xval, result.best_fit, 'b--')

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