使用来自scipy和python 3.x的*** curve_fit ***改进高斯拟合

Question

I believe I am successfully implementing gaussian fitting using curve fit from scipy. But the problem that I am running into is that... the fit isn't so great, because the optimized parameter is changing the centroid.

    data =np.loadtxt('mock.txt')
    my_x=data[:,0]
    my_y=data[:,1]

    def gauss(x,mu,sigma,A):
        return A*np.exp(-(x-mu)**2/2/sigma**2)
    def trimodal_gauss(x,mu1,sigma1,A1,mu2,sigma2,A2,mu3,sigma3,A3):
        return gauss(x,mu1,sigma1,A1)+gauss(x,mu2,sigma2,A2)+gauss(x,mu3,sigma3,A3)



    """""
    Gaussian fitting parameters recognized in each file
    """""
    first_centroid=(10180.4*2+9)/9
    second_centroid=(10180.4*2+(58.6934*1)+7)/9
    third_centroid=(10180.4*2+(58.6934*2)+5)/9
    centroid=[]
    centroid+=(first_centroid,second_centroid,third_centroid)

    apparent_resolving_power=1200
    sigma=[]
    for i in range(len(centroid)):
        sigma.append(centroid[i]/((apparent_resolving_power)*2.355))

    height=[1,1,1]

    p=[]    

    p = np.array([list(t) for t in zip(centroid, sigma, height)]).flatten() 


    popt, pcov = curve_fit(trimodal_gauss,my_x,my_y,p0=p) 

output:

I understand that there are a lot of peaks here but I really need it to fit only three Gaussians but at the right centroid(given in my initial guess). In other words, I really don't hope that the centroid I give is not changing. Has anyone encountered a challenge as such? and could please help me what I could do to make it happen?

Answer 1

You should define three separate functions with fixed values for the centers. Then you fit the sum function of these functions for only the leftover parameters.

Simply put, your trimodal_gauss() should not take mu s but only A s and sigma s. The mu s should be constants.

A trivial (but not very general) way of doing this is:

def trimodal_gauss(x, sigma1, A1, sigma2, A2, sigma3, A3):
    mu1 = 1234 # put your mu's here
    mu2 = 2345
    mu3 = 3456
    g1 = gauss(x, mu1, sigma1, A1)
    g2 = gauss(x, mu2, sigma2, A2)
    g3 = gauss(x, mu3, sigma3, A3)
    return g1 + g2 + g3

From this one can generalize the idea by a "generator" for trimodal_gauss functions that takes the three (or n?) mu s and creates the function of the other parameters. Like so:

def make_trimodal_gauss(mu1, mu2, mu3):
    def result_function(x, sigma1, A1, sigma2, A2, sigma3, A3):
        g1 = gauss(x, mu1, sigma1, A1)
        g2 = gauss(x, mu2, sigma2, A2)
        g3 = gauss(x, mu3, sigma3, A3)
        return g1 + g2 + g3
    return result_function


mu1 = 1234 # put your mu's here
mu2 = 2345
mu3 = 3456

trimodal_gauss = make_trimodal_gauss(mu1, mu2, mu3)

#usage like this: trimodal_gauss(x, sigma1, A1, sigma2, A2, sigma3, A3)

Answer 2

If you use the lmfit module ( https://github.com/lmfit/lmfit-py ), you can easily put bounds on the centroids of your Gaussian functions, or even fix them. Lmfit also makes it easy to build up multi-peak models.

You didn't give a complete example or link to your data, but a fit with lmfit to your data might look like this:

import numpy as np
from lmfit import GaussianModel
data =np.loadtxt('mock.txt')
my_x=data[:,0]
my_y=data[:,1]

model = ( GaussianModel(prefix='p1_') +
          GaussianModel(prefix='p2_') +
          GaussianModel(prefix='p3_') )

params = model.make_params(p1_amplitude=100, p1_sigma=2, p1_center=2262,
                           p2_amplitude=100, p2_sigma=2, p2_center=2269,
                           p3_amplitude=100, p3_sigma=2, p3_center=2276,
                       )

# set boundaries on the Gaussian Centers:
params['p1_center'].min = 2260
params['p1_center'].max = 2264

params['p2_center'].min = 2267
params['p2_center'].max = 2273

params['p3_center'].min = 2274
params['p3_center'].max = 2279

# or you could just fix one of the centroids like this:
params['p3_center'].vary = False

# if needed, you could force all the sigmas to be the same value
# or related by simple mathematical expressions
params['p2_sigma'].expr = 'p1_sigma'
params['p3_sigma'].expr = '2*p1_sigma'

# fit this model to data:
result  = model.fit(my_y, params, x=my_x)

# print results
print(result.fit_report())

# evaluate individual gaussian components:
peaks = model.eval_components(params=result.params, x=my_x)

# plot results:
plt.plot(my_x, my_y, label='data')
plt.plot(my_x, result.best_fit, label='best fit')
plt.plot(my_x, peaks['p1_'])
plt.plot(my_x, peaks['p2_'])
plt.plot(my_x, peaks['p3_'])
plt.show()