使用python分离曲线的高斯分量

Question

我试图对低分辨率光谱的发射线进行分离以获得高斯分量。此图表示我正在使用的数据类型：

在搜索了一下之后，我发现的唯一选择是应用kmpfit包中的gauest函数（http://www.astro.rug.nl/software/kapteyn/kmpfittutorial.html#gauest）。我复制了他们的例子，但我无法使其发挥作用。

我想知道是否有人可以为我提供任何替代方法来执行此操作或如何更正我的代码：

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

def CurveData():
    x = np.array([3963.67285156,  3964.49560547,  3965.31835938,  3966.14111328,  3966.96362305,
         3967.78637695,  3968.60913086,  3969.43188477,  3970.25463867,  3971.07714844,
         3971.89990234,  3972.72265625,  3973.54541016,  3974.36791992,  3975.19067383])
    y = np.array([1.75001533e-16,   2.15520995e-16,   2.85030769e-16,   4.10072843e-16, 7.17558032e-16,
         1.27759917e-15,   1.57074192e-15,   1.40802933e-15, 1.45038722e-15,  1.55195653e-15,
         1.09280316e-15,   4.96611341e-16, 2.68777266e-16,  1.87075114e-16,   1.64335999e-16])
    return x, y

def FindMaxima(xval, yval):
    xval = np.asarray(xval)
    yval = np.asarray(yval)

    sort_idx = np.argsort(xval)
    yval = yval[sort_idx]
    gradient = np.diff(yval)
    maxima = np.diff((gradient > 0).view(np.int8))
    ListIndeces = np.concatenate((([0],) if gradient[0] < 0 else ()) + (np.where(maxima == -1)[0] + 1,) + (([len(yval)-1],) if gradient[-1] > 0 else ()))
    X_Maxima, Y_Maxima = [], []

    for index in ListIndeces:
        X_Maxima.append(xval[index])
        Y_Maxima.append(yval[index])

    return X_Maxima, Y_Maxima

def GaussianMixture_Model(p, x, ZeroLevel):
    y = 0.0
    N_Comps = int(len(p) / 3)
    for i in range(N_Comps):
        A, mu, sigma = p[i*3:(i+1)*3]
        y += A * np.exp(-(x-mu)*(x-mu)/(2.0*sigma*sigma))
    Output =  y + ZeroLevel
    return Output

def Residuals_GaussianMixture(p, x, y, ZeroLevel):    
    return GaussianMixture_Model(p, x, ZeroLevel) - y

Wave, Flux  = CurveData()

Wave_Maxima, Flux_Maxima = FindMaxima(Wave, Flux)

EmLines_Number = len(Wave_Maxima)

ContinuumLevel = 1.64191e-16

# Define initial values
p_0 = []
for i in range(EmLines_Number):
    p_0.append(Flux_Maxima[i])
    p_0.append(Wave_Maxima[i])
    p_0.append(2.0)

p1, conv = optimize.leastsq(Residuals_GaussianMixture, p_0[:],args=(Wave, Flux, ContinuumLevel))

Fig    = plt.figure(figsize = (16, 10))  
Axis1  = Fig.add_subplot(111) 

Axis1.plot(Wave, Flux, label='Emission line')
Axis1.plot(Wave, GaussianMixture_Model(p1, Wave, ContinuumLevel), 'r', label='Fit with optimize.leastsq')
print p1
Axis1.plot(Wave, GaussianMixture_Model([p1[0],p1[1],p1[2]], Wave, ContinuumLevel), 'g:', label='Gaussian components')
Axis1.plot(Wave, GaussianMixture_Model([p1[3],p1[4],p1[5]], Wave, ContinuumLevel), 'g:')

Axis1.set_xlabel( r'Wavelength $(\AA)$',)
Axis1.set_ylabel('Flux' + r'$(erg\,cm^{-2} s^{-1} \AA^{-1})$')
plt.legend()

plt.show()   

Answer 1

一种典型的简单方式：

def model(p,x):
    A,x1,sig1,B,x2,sig2 = p
    return A*np.exp(-(x-x1)**2/sig1**2) + B*np.exp(-(x-x2)**2/sig2**2)

def res(p,x,y):
    return model(p,x) - y

from scipy import optimize

p0 = [1e-15,3968,2,1e-15,3972,2]
p1,conv = optimize.leastsq(res,p0[:],args=(x,y))

plot(x,y,'+') # data
#fitted function
plot(arange(3962,3976,0.1),model(p1,arange(3962,3976,0.1)),'-')

p0是你最初的猜测。根据事物的外观，你可能想要使用洛伦兹函数......

如果您使用full_output = True，您将获得有关拟合的所有信息。还可以在scipy.optimize中查看curve_fit和fmin *函数。周围有很多包装器，但通常，就像这里一样，它更容易直接使用它们。