scipy.optimize.curve_fit 双高斯拟合失败

如何解决scipy.optimize.curve_fit 双高斯拟合失败

我正在尝试对双高斯分布进行相当直接的拟合，但我从 scipy_curvefit 得到的结果并不令人满意。我使用的代码如下所示。

counts= np.asarray([ 1.,1.,8.,6.,5.,4.,10.,25.,73.,89.,122.,119.,105.,107.,69.,74.,49.,60.,30.,37.,40.,42.,43.,34.,41.,22.,11.,7.,0.,3.,2.,0.])
bins=np.asarray([0.05112413,0.05349386,0.0558636,0.05823333,0.06060306,0.0629728,0.06534253,0.06771226,0.07008199,0.07245173,0.07482146,0.07719119,0.07956093,0.08193066,0.08430039,0.08667013,0.08903986,0.09140959,0.09377933,0.09614906,0.09851879,0.10088853,0.10325826,0.10562799,0.10799773,0.11036746,0.11273719,0.11510692,0.11747666,0.11984639,0.12221612,0.12458586,0.12695559,0.12932532,0.13169506,0.13406479,0.13643452,0.13880426,0.14117399,0.14354372,0.14591346,0.14828319,0.15065292,0.15302266,0.15539239,0.15776212,0.16013185,0.16250159,0.16487132,0.16724105])

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

def gauss(x,mu,sigma,A):
    return A*np.exp(-(x-mu)**2/2/sigma**2)

def bimodal(x,mu1,sigma1,A1,mu2,sigma2,A2):
    return gauss(x,A1)+gauss(x,A2)

plt.figure(figsize=(10,7))
expected=[0.08,0.001,120,0.11,70]

p,cov=curve_fit(bimodal,bins[6:32],counts[6:32],p0=expected)

fit_chi=chisquare(bimodal(bins[6:32],*p),f_exp=counts[6:32] )
p_man=[ 7.9441e-02 +0.002,6.127e-03 +0.0006,118,1.0068e-01+0.005,1.222e-02-0.004,4.373e+01]
man_chi=chisquare(bimodal(bins[6:32],*p_man),f_exp=counts[6:32] )

x=np.arange(0.,0.4,0.001)
plt.bar(bins,counts,bins[1]-bins[0])
plt.plot(x,bimodal(x,'-',color='r',label='model %.2f'%fit_chi[0])
plt.plot(x,color='orange',label='model manual: %.2f'%man_chi[0])
plt.ylim(1,140)
plt.yscale('log')
plt.legend()
plt.xlim(0,0.4) 
plt.savefig('DoubleGauss.png')

我知道我的分布不完全是两个高斯分布，但非常接近。这是拟合的结果，也是我手动调整双峰函数参数时的结果。

Plot with both fits

您可以看到，当我手动调整参数时，不仅我的手动数字在视觉上看起来更好，而且卡方（在标签中）也更好。我还尝试通过使用拟合参数作为下一次迭代的起始值来迭代改进拟合，但我没有得到任何改进。这对我来说似乎很奇怪。有没有人知道我可能做错了什么，或者我使用的方法不适合这项任务？