在 python 中使用 lmfit 库进行多峰曲线拟合

Question

I have a datafile where the first column is x-value, second column is y-value and third column is y-error. I would like to fit the data. I am following the example from here and my code is-

import matplotlib.pyplot as plt
import numpy as np

from lmfit.models import ExponentialModel, GaussianModel


file='sample-data.txt'
dat = np.loadtxt(file)
x = dat[:, 0]
y = dat[:, 1]



exp_mod = ExponentialModel(prefix='exp_')
pars = exp_mod.guess(y, x=x)

gauss1 = GaussianModel(prefix='g1_')
pars.update(gauss1.make_params())

pars['g1_center'].set(value=105000, min=75000, max=125000)
pars['g1_sigma'].set(value=150000, min=30000)
pars['g1_amplitude'].set(value=2000000, min=100000)

gauss2 = GaussianModel(prefix='g2_')
pars.update(gauss2.make_params())

pars['g2_center'].set(value=155000, min=125000, max=175000)
pars['g2_sigma'].set(value=150000, min=30000)
pars['g2_amplitude'].set(value=2000000, min=100000)

mod = gauss1 + gauss2 + exp_mod

init = mod.eval(pars, x=x)
out = mod.fit(y, pars, x=x)

print(out.fit_report(min_correl=0.5))

fig, axes = plt.subplots(1, 2, figsize=(12.8, 4.8))
axes[0].plot(x, y, 'b')
axes[0].plot(x, init, 'k--', label='initial fit')
axes[0].plot(x, out.best_fit, 'r-', label='best fit')
axes[0].legend(loc='best')

comps = out.eval_components(x=x)
axes[1].plot(x, y, 'b')
axes[1].plot(x, comps['g1_'], 'g--', label='Gaussian component 1')
axes[1].plot(x, comps['g2_'], 'm--', label='Gaussian component 2')
axes[1].plot(x, comps['exp_'], 'k--', label='Exponential component')
axes[1].legend(loc='best')

plt.show()

This code is giving me following plot (the fit is not working)-

I am expecting something like this-

1. Can anyone help me fitting the data in the plot?
2. Also in the example value, min, max for center, sigma, and amplitude were defined manually. Is there any way to get/ calculate those values from the data file?

Update

I tried using find_peaks suggested by @mikuszefski in the comment. But it is also picking up all the small peaks (noises) as the image shows.

Is there a way to choose the values only for the larger peaks?

Answer 1

You really have to ("must", "are required to", "definitely under all circumstances") provide reasonable , finite, and plausible initial values for all the parameters.

When you say

pars['g1_center'].set(value=105000, min=75000, max=125000)
pars['g1_sigma'].set(value=150000, min=30000)
pars['g1_amplitude'].set(value=2000000, min=100000)

gauss2 = GaussianModel(prefix='g2_')
pars.update(gauss2.make_params())

pars['g2_center'].set(value=155000, min=125000, max=175000)
pars['g2_sigma'].set(value=150000, min=30000)
pars['g2_amplitude'].set(value=2000000, min=100000)

You are (literally "literally") telling the program that Gaussian #1 should start with a center value of 105000, and cannot under any circumstance go beyond [75000, 125000].

The data you provided and the plot shows that the two peaks you are interested in occur at x values of around 1.4 and 1.5.

So, the value for the center is around 1 and you told it the value was around 10^5 and could not go below 75,000. That is the best fit under those constraints. The program worked without error or problem, and you got exactly what you asked for.

Again, for non-linear least-squares problems and curve-fitting, initial values always matter. There are no situations in which they do not matter.

That said, using a peak-finding algorithm as mikuszefski suggests is a fine choice.

Aside: Bounds should be used primarily to constrain the logic/physics. It might be reasonable to say the amplitude should be positive, for example. There is nothing intrinsic about Gaussians in general (or, probably, your data) that demands that a centroid value of 74999 is non-sensical. So, do not start with such bounds. Start without bounds and as simply as possible. Add such complexity only when it is needed.