限制高斯適合在我的本科論文的框架curve_fit

Question

，我需要用Python來評估我的數據。不幸的是，我的同學還沒有適合的腳本，而且我對編程還很陌生。

我有這樣的數據集，我試圖通過使用scipy.optimize.curve_fit高斯，以適應它。由於有很多不可用的計數，特別是在軸末端，我想限制要安裝的部分。

圖片raw data

這是我到目前爲止有：

import numpy as np 
import matplotlib.pyplot as plt 
from scipy.optimize import curve_fit 

x=np.arange(5120) 
y=array([ 0.81434599, 1.17054264, 0.85279188, ..., 1.  , 
    1.  , 13.56291391]) #most of the data isn't interesting 
#to me, part of interest see below 

def Gauss(x, a, x0, sigma): 
    return a * np.exp(-(x - x0)**2/(2 * sigma**2)) 

mean = sum(x * y)/sum(y) 
sigma = np.sqrt(sum(y * (x - mean)**2)/sum(y)) 

popt,pcov = curve_fit(Gauss, x, y, p0=[max(y), mean, sigma], 
maxfev=360000) 

plt.plot(x,y,label='data') 
plt.plot(x,Gauss(x, *popt), 'r-',label='fit') 

在docs.scipy.org我發現約curve_fit

的一般性描述，如果我嘗試使用 bounds=([2400,-np.inf, -np.inf],[2600, np.inf, np.inf]) ， 我得到ValueError：x0是不可行的。這裏有什麼問題？在計算器 「獲得高斯適合圖形時出錯」在這種情況下，我只得到一條直線，但：

我也試圖與 popt,pcov = curve_fit(Gauss, x[2400:2600], y[2400:2600], p0=[max(y), mean, sigma], maxfev=360000) 來限制它作爲在這個問題上意見建議。

圖片：Confinement with x[2400:2600],y[2400:2600] as arguments of curve_fit

我真的希望你能幫助我在這裏。我只需要一種方法來適應我的一小部分數據。提前致謝！

有趣的數據：

y=array([ 0.93396226, 1.00884956, 1.15457413, 1.07590759, 
0.88915094, 1.07142857, 1.10714286, 1.14171123, 1.06666667, 
0.84975369, 0.95480226, 0.99388379, 1.01675978, 0.83967391, 
0.9771987 , 1.02402402, 1.04531722, 1.07492795, 0.97135417, 
0.99714286, 1.0248139 , 1.26223776, 1.1533101 , 0.99099099, 
1.18867925, 1.15772871, 0.95076923, 1.03313253, 1.02278481, 
0.93265993, 1.06705539, 1.00265252, 1.02023121, 0.92076503, 
0.99728997, 1.03353659, 1.15116279, 1.04336043, 0.95076923, 
1.05515588, 0.92571429, 0.93448276, 1.02702703, 0.90056818, 
0.96068796, 1.08493151, 1.13584906, 1.1212938 , 1.0739645 , 
0.98972603, 0.94594595, 1.07913669, 0.98425197, 0.87762238, 
0.96811594, 1.02710843, 0.99392097, 0.91384615, 1.09809264, 
1.00630915, 0.93175074, 0.87572254, 1.00651466, 0.78772379, 
1.12244898, 1.2248062 , 0.97109827, 0.94607843, 0.97900262, 
0.97527473, 1.01212121, 1.16422287, 1.20634921, 0.97275204, 
1.01090909, 0.99404762, 1.00561798, 1.01146132, 1.08695652, 
0.97214485, 1.03525641, 0.99096386, 1.05135952, 1.16451613, 
0.90462428, 0.76876877, 0.47701149, 0.27607362, 0.21580547, 
0.20598007, 0.16766467, 0.15533981, 0.19745223, 0.15407855, 
0.18925831, 0.26997245, 0.47603834, 0.596875 , 0.85126582, 0.96  
, 1.06578947, 1.08761329, 0.89548023, 0.99705882, 1.07142857, 
0.95677233, 0.86119874, 1.02857143, 0.98250729, 0.94214876, 
1.04166667, 0.96024465, 1.07022472, 1.10344828, 1.04859335, 
0.96655518, 1.06424581, 1.01754386, 1.03492063, 1.18627451, 
0.91036415, 1.03355705, 1.09116809, 0.96083551, 1.01298701, 
1.03691275, 1.02923977, 1.11612903, 1.01457726, 1.06285714, 
0.98186528, 1.16470588, 0.86645963, 1.07317073, 1.09615385, 
1.21192053, 0.94385027, 0.94244604, 0.88390501, 0.95718654, 
0.9691358 , 1.01729107, 1.01119403, 1.20350877, 1.12890625, 
1.06940063, 0.90410959, 1.14662757, 0.97093023, 1.03021148, 
1.10629921, 0.97118156, 1.10693642, 1.07917889, 0.9484127 , 
1.07581227, 0.98006645, 0.98986486, 0.90066225, 0.90066225, 
0.86779661, 0.86779661, 0.96996997, 1.01438849, 0.91186441, 
0.91290323, 1.03745318, 1.0615942 , 0.97202797, 1.16608997, 
0.94182825, 1.08333333, 0.9076087 , 1.18181818, 1.20618557, 
1.01273885, 0.93606138, 0.87457627, 0.90575916, 1.09756098, 
0.99115044, 1.13380282, 1.04333333, 1.04026846, 1.0297619 , 
1.04334365, 1.03395062, 0.92553191, 0.98198198, 1.  , 
0.9439528 , 1.02684564, 1.1372549 , 0.96676737, 0.99649123, 
1.07051282, 1.10367893, 1.0866426 , 1.15384615, 0.99667774]) 

Answer 1

您可能會發現lmfit模塊（https://lmfit.github.io/lmfit-py/）對這項有益的。它的目的是使曲線擬合很容易，有像高斯共有峯內置機型，並有許多有用的功能，如允許您在參數設置範圍。一件合身與lmfit您的數據可能是這樣的：

import numpy as np 
import matplotlib.pyplot as plt 

from lmfit.models import GaussianModel, ConstantModel 

y = np.array([.....]) # uses your shorter data range 
x = np.arange(len(y)) 

# make a model that is a Gaussian + a constant: 
model = GaussianModel(prefix='peak_') + ConstantModel() 

# make parameters with starting values: 
params = model.make_params(c=1.0, peak_center=90, 
          peak_sigma=5, peak_amplitude=-5) 

# it's not really needed for this data, but you can put bounds on 
# parameters like this (or set .vary=False to fix a parameter) 
params['peak_sigma'].min = 0   # sigma > 0 
params['peak_amplitude'].max = 0  # amplitude < 0 
params['peak_center'].min = 80 
params['peak_center'].max = 100 

# run fit 
result = model.fit(y, params, x=x) 

# print, plot results 
print(result.fit_report()) 
plt.plot(x, y) 
plt.plot(x, result.best_fit) 
plt.show() 

這將打印出

[[Model]] 
    (Model(gaussian, prefix='peak_') + Model(constant)) 
[[Fit Statistics]] 
    # function evals = 54 
    # data points  = 200 
    # variables  = 4 
    chi-square   = 1.616 
    reduced chi-square = 0.008 
    Akaike info crit = -955.625 
    Bayesian info crit = -942.432 
[[Variables]] 
    peak_sigma:  4.03660814 +/- 0.204240 (5.06%) (init= 5) 
    peak_center:  91.2246614 +/- 0.200267 (0.22%) (init= 90) 
    peak_amplitude: -9.79111362 +/- 0.445273 (4.55%) (init=-5) 
    c:    1.02138228 +/- 0.006796 (0.67%) (init= 1) 
    peak_fwhm:  9.50548558 +/- 0.480950 (5.06%) == '2.3548200*peak_sigma' 
    peak_height:  -0.96766623 +/- 0.041854 (4.33%) == '0.3989423*peak_amplitude/max(1.e-15, peak_sigma)' 
[[Correlations]] (unreported correlations are < 0.100) 
    C(peak_sigma, peak_amplitude) = -0.599 
    C(peak_amplitude, c)   = -0.328 
    C(peak_sigma, c)    = 0.196 

，讓這樣一個情節：