How to set double Gaussian distribution in Python?

Question

I am trying to get a double gaussian distribution for data ( link ) using Python. Raw data are of the form:

For the given data, I would like to get two Gauss profiles for the peaks shown in the figure. I tried it with the following code ( source ):

from sklearn import mixture
import matplotlib.pyplot
import matplotlib.mlab
import numpy as np
from pylab import *
data = np.genfromtxt('gaussian_fit.dat', skiprows = 1)
x = data[:, 0]
y = data[:, 1]
clf = mixture.GMM(n_components=2, covariance_type='full')
clf.fit((y, x))
m1, m2 = clf.means_
w1, w2 = clf.weights_
c1, c2 = clf.covars_
fig = plt.figure(figsize = (5, 5))
plt.subplot(111)
plotgauss1 = lambda x: plot(x,w1*matplotlib.mlab.normpdf(x,m1,np.sqrt(c1))[0], linewidth=3)
plotgauss2 = lambda x: plot(x,w2*matplotlib.mlab.normpdf(x,m2,np.sqrt(c2))[0], linewidth=3)
fig.savefig('gaussian_fit.pdf')

But I can’t get the desired result. So how can one get a double Gaussian distribution in Python?

Update

I managed to fit one Gaussian distribution with the following code:

import pylab as plb
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy import asarray as ar,exp
import numpy as np

data = np.genfromtxt('gaussian_fit.dat', skiprows = 1)
x = data[:, 0]
y = data[:, 1]
n = len(x)
mean = sum(x*y)/n
sigma = sum(y*(x-mean)**2)/n


def gaus(x,a,x0,sigma):
    return a*exp(-(x-x0)**2/(2*sigma**2))


popt,pcov = curve_fit(gaus, x, y ,p0 = [1, mean, sigma])


fig = plt.figure(figsize = (5, 5))
plt.subplot(111)
plt.plot(x, y, label='Raw')
plt.plot(x, gaus(x, *popt), 'o', markersize = 4, label='Gaussian fit')
plt.xlabel('X')
plt.ylabel('Y')
plt.legend()
fig.savefig('gaussian_fit.pdf')

Answer 1

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params = [c1, mu1, sigma1, c2, mu2, sigma2]

c1 c2 , .. , mu1 mu2 , sigma1 sigma2 , . , (= c1, c2 ) (= mu1, mu1, ), sigma1 sigma2 1.0.

from sklearn import mixture
import matplotlib.pyplot
import matplotlib.mlab
import numpy as np
from pylab import *
from scipy.optimize import leastsq

data = np.genfromtxt('gaussian_fit.dat', skiprows = 1)
x = data[:, 0]
y = data[:, 1]

def double_gaussian( x, params ):
    (c1, mu1, sigma1, c2, mu2, sigma2) = params
    res =   c1 * np.exp( - (x - mu1)**2.0 / (2.0 * sigma1**2.0) ) \
          + c2 * np.exp( - (x - mu2)**2.0 / (2.0 * sigma2**2.0) )
    return res

def double_gaussian_fit( params ):
    fit = double_gaussian( x, params )
    return (fit - y_proc)

# Remove background.
y_proc = np.copy(y)
y_proc[y_proc < 5] = 0.0

# Least squares fit. Starting values found by inspection.
fit = leastsq( double_gaussian_fit, [13.0,-13.0,1.0,60.0,3.0,1.0] )
plot( x, y, c='b' )
plot( x, double_gaussian( x, fit[0] ), c='r' )