Yesterday I showed you [how to fit a single Gaussian in some data]. Today lets deal with the case of two Gaussians. This came about due to some students trying to fit two Gaussian's to a shell star as the spectral line was altered from a simple Gaussian, actually there is a nice P-Cygni dip in there data so you should be able to recover the absorption line by this kind of fitting. Anyway, fitting 2 Gaussian's is basically the same thing as fitting one in python but with the added function. I'm thinking I'll work up how to deal with a whole spectrum including source finding. In this case what you have to deal with is that there are two sources and so a rough estimation of the peak position of both is crucial to the fit (well in the way it is implemented).
You basically want to end up with something like this:
Where the green points are the data, the blue dashed line the fit and the red line where the maximum is in the array. The fitting is done via a least-squares fitting routine.
In this example we will first start by generating some data, skipping the input from a file (but you can use the code from the 1 Gaussian example).
import scipy, numpy, pylab, asciidata from numpy import * from pylab import * from scipy import * from scipy.optimize import leastsq#generate some data
gaussian = lambda x: 3*exp(-(10-x)**2/10.) + 1*exp(-(30-x)**2/10.)#change the parameters as you see fit
y_power = gaussian(arange(100))
x_pos = arange(100)gauss_fit = lambda p, x: p[0]*(1/sqrt(2*pi*(p[2]**2)))*exp(-(x-p[1])**2/(2*p[2]**2))+p[3]*(1/sqrt(2*pi*(p[5]**2)))*exp(-(x-p[4])**2/(2*p[5]**2)) #1d Gaussian func
e_gauss_fit = lambda p, x, y: (gauss_fit(p,x) -y) #1d Gaussian fit
v0= [1,10,1,1,30,1] #inital guesses for Gaussian Fit. - just do it around the peaks
out = leastsq(e_gauss_fit, v0[:], args=(x_pos, y_power), maxfev=100000, full_output=1) #Gauss Fit
v = out[0] #fit parameters out
covar = out[1] #covariance matrix output
xxx = arange(min(x_pos),max(x_pos),x_pos[1]-x_pos[0])
ccc = gauss_fit(v,xxx) # this will only work if the units are pixel and not wavelengthfig = figure(figsize=(9, 9)) #make a plot
ax1 = fig.add_subplot(111)
ax1.plot(x_pos,y_power,'gs') #spectrum
ax1.plot(xxx,ccc,'b--') #fitted spectrum
ax1.axvline(x=xxx[where(ccc == max(ccc))[0]][0],color='r') #max position in data
setp(gca(), ylabel="power", xlabel="pixel position")
pylab.savefig("plotfitting.png")print "p[0], a1: ", v[0]
print "p[1], mu1: ", v[1]
print "p[2], sigma1: ", v[2]
print "p[3], a2: ", v[0]
print "p[4], mu2: ", v[1]
print "p[5], sigma2: ", v[2]
The full detailed listing is given in [multiplegaussfit.py]
