Fitting a multi-peak function to a DataSet using LMFIT

问题

I'm trying to make a multi-lorentzian fitting using the LMFIT library, but it's not working and I even understand that the syntax of what I made is completelly wrong, but I don't have any new ideas.

My problem is this: I have a very long spectra with multiple sets of peaks, but the number of peaks is not constant in these sets, so sometimes I will have just 1 peak, but sometimes I might have 8 or even 20.

#function definition:

def Lorentzian(x, amp, cen, wid, n):
    f = 0
    for i in range( int(n) ):
        "lorentzian function: wid = half-width at half-max"
        f += (amp[i]/(1 + ((x-cen[i])/wid[i])**2))
    return f

#library import and model definition:

import lmfit as lf

lmodel = lf.Model(Lorentzian)

#The initial parameters for the model:
peaks_in_interval = np.array([2378, 2493, 2525, 2630, 2769])

number_of_peaks = len(peaks_in_interval)         
amplitude = width = np.zeros( number_of_peaks ) + 1
center = x[peaks_in_interval]

params = lmodel.make_params(x = x, amp = amplitude, cen = center, wid = width, n = number_of_peaks)

#This is the line that doesn't work:                        
result = lmodel.fit( y, params, x = x )

I've started trying to make a generic function that returns a multi-Lorentzian, but I'm struggling in how to make that work...

I'm also sending the data for x, y arrays.

DataSet for x and y

This is what the DataSet of x and y looks like.

回答1:

You should be able to make use of the built-in models and using prefixes as described in the manual. In addition, there was a recent discussion about a very similar topic on the mailinglist.

You can do something as shown below. It doesn't fit the last peak very well yet, but you can probably fiddle around a bit with the starting values and such. Moreover, since your baseline isn't completely flat it might improve when you use a LinearModel insteadd of a ConstantModel, but I haven't tried.

from lmfit.models import LorentzianModel, ConstantModel
import numpy as np
import matplotlib.pyplot as plt

x, y = np.loadtxt('Peaks.txt', unpack=True)

peaks_in_interval = np.array([43, 159, 191, 296, 435, 544])
number_of_peaks = len(peaks_in_interval)
amplitude = y[peaks_in_interval] / 5
width = np.zeros(number_of_peaks) + 0.1
center = x[peaks_in_interval]

def make_model(num):
    pref = "f{0}_".format(num)
    model = LorentzianModel(prefix = pref)
    model.set_param_hint(pref+'amplitude', value=amplitude[num], min=0, max=5*amplitude[num])
    model.set_param_hint(pref+'center', value=center[num], min=center[num]-0.5, max=center[num]+0.5)
    model.set_param_hint(pref+'sigma', value=width[num], min=0, max=2)
    return model

mod = None
for i in range(len(peaks_in_interval)):
    this_mod = make_model(i)
    if mod is None:
        mod = this_mod
    else:
        mod = mod + this_mod

offset = ConstantModel()
offset.set_param_hint('c', value=np.average(y[-75:]))
mod = mod + offset

out=mod.fit(y, x=x, method='nelder')
plt.interactive(True)
print(out.fit_report())
plt.plot(x, y)
plt.plot(x, out.best_fit, label='best fit')
plt.plot(x, out.init_fit, 'r--', label='fit with initial values')
plt.show()

来源：https://stackoverflow.com/questions/46684859/fitting-a-multi-peak-function-to-a-dataset-using-lmfit

标签

python

lmfit