用 curve_fit 限制高斯拟合
Confine a gaussian fit with curve_fit
在我的学士论文框架内，我需要用python评估我的数据。不幸的是，我的同学们还没有合适的脚本，而且我对编程还很陌生。
我有这个数据集，我正在尝试使用 scipy.optimize.curve_fit 对其进行高斯拟合。由于有很多无法使用的计数，尤其是在轴的末端，我想限制要安装的部分。
图片raw data
这是我目前所拥有的：
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 我找到了关于 curve_fit
的一般描述
如果我尝试使用
bounds=([2400,-np.inf, -np.inf],[2600, np.inf, np.inf]),
我收到 ValueError：x0 不可行。这里有什么问题？
我也试过用
popt,pcov = curve_fit(Gauss, x[2400:2600], y[2400:2600], p0=[max(y), mean, sigma], maxfev=360000)
正如对此问题的评论中所建议的： "Error when obtaining gaussian fit for graph" at Whosebug
在这种情况下，我只能得到一条直线。
图片：Confinement with x[2400:2600],y[2400:2600] as arguments of curve_fit
我真的希望你能帮我解决这个问题。我只需要一种方法来适应我的一小部分数据。提前致谢！
有趣的数据：
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])
您可能会发现 lmfit 模块 (https://lmfit.github.io/lmfit-py/) 对此很有用。它旨在使曲线拟合变得非常容易，具有内置的常见峰模型（如高斯），并具有许多有用的功能，例如允许您设置参数范围。使用 lmfit 拟合您的数据可能如下所示：
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()
这将打印出来
[[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
然后画这样的图：
在我的学士论文框架内，我需要用python评估我的数据。不幸的是，我的同学们还没有合适的脚本，而且我对编程还很陌生。
我有这个数据集，我正在尝试使用 scipy.optimize.curve_fit 对其进行高斯拟合。由于有很多无法使用的计数，尤其是在轴的末端，我想限制要安装的部分。
图片raw data
这是我目前所拥有的：
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 我找到了关于 curve_fit
的一般描述如果我尝试使用
bounds=([2400,-np.inf, -np.inf],[2600, np.inf, np.inf]),
我收到 ValueError：x0 不可行。这里有什么问题？
我也试过用
popt,pcov = curve_fit(Gauss, x[2400:2600], y[2400:2600], p0=[max(y), mean, sigma], maxfev=360000)
正如对此问题的评论中所建议的： "Error when obtaining gaussian fit for graph" at Whosebug
在这种情况下，我只能得到一条直线。
图片：Confinement with x[2400:2600],y[2400:2600] as arguments of curve_fit
我真的希望你能帮我解决这个问题。我只需要一种方法来适应我的一小部分数据。提前致谢！
有趣的数据：
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])
您可能会发现 lmfit 模块 (https://lmfit.github.io/lmfit-py/) 对此很有用。它旨在使曲线拟合变得非常容易，具有内置的常见峰模型（如高斯），并具有许多有用的功能，例如允许您设置参数范围。使用 lmfit 拟合您的数据可能如下所示：
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()
这将打印出来
[[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
然后画这样的图：