使用python分离曲线的高斯分量 [英] Separating gaussian components of a curve using python
问题描述
我正在尝试低分辨率光谱的发射线,以便获得高斯分量。此图表示我正在使用的数据类型:
I am trying to deblend the emission lines of low resolution spectrum in order to get the gaussian components. This plot represents the kind of data I am using:
经过一番搜索,我发现的唯一选择是从kmpfit包中应用gauest函数(< a href = http://www.astro.rug.nl/software/kapteyn/kmpfittutorial.html#gauest rel = nofollow noreferrer> http://www.astro.rug.nl/software/kapteyn/kmpfittutorial .html#gauest )。我已经复制了他们的示例,但我无法使它正常工作。
After searching a bit, the only option I found was the application of the gauest function from the kmpfit package (http://www.astro.rug.nl/software/kapteyn/kmpfittutorial.html#gauest). I have copied their example but I cannot make it work.
我想知道是否有人可以提供任何替代方法,或者如何纠正我的代码:
I wonder if anyone could please offer me any alternative to do this or how to correct my code:
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()
推荐答案
一种典型的简单拟合方法:
A typical simplistic way to fit:
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)),'-')
其中p0是您最初的猜测。从外观上看,您可能想使用Lorentzian函数...
Where p0 is your initial guess. By the looks of things, you might want to use Lorentzian functions...
如果使用full_output = True,则会获得有关拟合的所有信息。还要在scipy.optimize中检出curve_fit和fmin *函数。周围有很多包装纸,但是通常,像这里一样,直接使用它们比较容易。
If you use full_output=True, you get all kind of info about the fitting. Also check out curve_fit and the fmin* functions in scipy.optimize. There are plenty of wrappers around these around, but often, like here, it's easier to use them directly.
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