两分量高斯拟合无法正常工作

如何解决两分量高斯拟合无法正常工作

我正在尝试使用以下代码进行两分量高斯拟合：

def double_gaussian(velo_peak,a1,mu1,sigma1,a2,mu2,sigma2):
                      
            
            res_two = a1 * np.exp(-(velo_peak - mu1)**2/(2 * sigma1**2))  \
                      + a2 * np.exp(-(velo_peak - mu2)**2/(2 * sigma2**2))

            return res_two
#Guess parameters:
guess = [5,115.2,0.7,4,115.7,0.7]
popt,pcov = curve_fit(double_gaussian,velo_peak,spec_peak,guess)
plt.plot(velo_peak*1e-9,double_gaussian(velo_peak,*popt),'r-',label='fit')

我用两个分量定义了方程，然后输入了猜测值并尝试绘制，但出现以下错误： warnings.warn('Covariance of the parameters could not be estimated', 因此，我得到了一条适合的直线。 我会说我觉得代码合乎逻辑，但当然，有一些问题。提供任何帮助将不胜感激。

解决方法

问题似乎出在最初的猜测上：

import matplotlib.pyplot as plt  # type: ignore
import numpy as np  # type: ignore
from scipy.optimize import curve_fit  # type: ignore

def double_gaussian(velo_peak,a1,mu1,sigma1,a2,mu2,sigma2):
    g1 = a1 * np.exp(-((velo_peak - mu1) ** 2) / (2 * sigma1 ** 2))
    g2 = a2 * np.exp(-((velo_peak - mu2) ** 2) / (2 * sigma2 ** 2))
    return g1 + g2

xdata = np.linspace(100,120,1000)
y = double_gaussian(xdata,5,115.2,0.7,4,105.7,0.7)
np.random.seed(1729)
y_noise = 0.2 * np.random.normal(size=xdata.size)
ydata = y + y_noise
plt.plot(xdata,ydata,"b-",label="data")

# Guess parameters:
# guess = [5,0.7]  # ok (duh)
# guess = [1,100,1,1]  # fails 10k
# guess = [5,115,105,1]  # ok
# guess = [5,5]  # warn
# guess = [5,2,2]  # ok
# guess = [1,3,3]  # ok
# guess = [1,110,3]  # only one found
# guess = [1,3]  # only one found
guess = [1,118,102,3]  # ok
popt,pcov = curve_fit(double_gaussian,xdata,guess,maxfev=10000)
plt.plot(xdata,double_gaussian(xdata,*popt),"r-",label="fit")

plt.show()

无法访问数据就很难提供帮助。您可能想尝试某种方法来找到峰值位置，并将其用作 mu1/2 值，它会有所帮助。或者在起始参数空间上进行某种网格搜索，评估模型和数据之间的误差。

编辑：

我尝试增加优化器调用 maxfev=100_000_000 的迭代次数，并得到以下结果：

# guess = [1,1]  # bad 100kk
# guess = [1,1]  # ok 100kk
# guess = [1,111,109,1]  # bad 100kk
guess = [1,112,108,1]  # ok 100kk

同样，起始 mu 值似乎非常重要。

干杯！