Use Python lmfit with a variable number of parameters in function

Question

I am trying to deconvolve complex gas chromatogram signals into individual gaussian signals. Here is an example, where the dotted line represents the signal I am trying to deconvolve.

I was able to write the code to do this using scipy.optimize.curve_fit; however, once applied to real data the results were unreliable. I believe being able to set bounds to my parameters will improve my results, so I am attempting to use lmfit, which allows this. I am having a problem getting lmfit to work with a variable number of parameters. The signals I am working with may have an arbitrary number of underlying gaussian components, so the number of parameters I need will vary. I found some hints here, but still can't figure it out...

Creating a python lmfit Model with arbitrary number of parameters

Here is the code I am currently working with. The code will run, but the parameter estimates do not change when the model is fit. Does anyone know how I can get my model to work?

import numpy as np
from collections import OrderedDict
from scipy.stats import norm
from lmfit import Parameters, Model

def add_peaks(x_range, *pars):
    y = np.zeros(len(x_range))
    for i in np.arange(0, len(pars), 3):
        curve = norm.pdf(x_range, pars[i], pars[i+1]) * pars[i+2]
        y = y + curve
    return(y)

# generate some fake data
x_range = np.linspace(0, 100, 1000)
peaks = [50., 40., 60.]
a = norm.pdf(x_range, peaks[0], 5) * 2
b = norm.pdf(x_range, peaks[1], 1) * 0.1
c = norm.pdf(x_range, peaks[2], 1) * 0.1
fake = a + b + c

param_dict = OrderedDict()

for i in range(0, len(peaks)):
    param_dict['pk' + str(i)] = peaks[i]
    param_dict['wid' + str(i)] = 1.
    param_dict['mult' + str(i)] = 1.

# In case, you'd like to see the plot of fake data
#y = add_peaks(x_range, *param_dict.values())
#plt.plot(x_range, y)
#plt.show()

# Initialize the model and fit
pmodel = Model(add_peaks)

params = pmodel.make_params()
for i in param_dict.keys():
    params.add(i, value=param_dict[i])

result = pmodel.fit(fake, params=params, x_range=x_range)
print(result.fit_report())

Coxswain

Answer 1

I was able to find a solution here:

https://lmfit.github.io/lmfit-py/builtin_models.html#example-3-fitting-multiple-peaks-and-using-prefixes

Building on the code above, the following accomplishes what I was trying to do...

from lmfit.models import GaussianModel

gauss1 = GaussianModel(prefix='g1_')
gauss2 = GaussianModel(prefix='g2_')
gauss3 = GaussianModel(prefix='g3_')
gauss4 = GaussianModel(prefix='g4_')
gauss5 = GaussianModel(prefix='g5_')

gauss = [gauss1, gauss2, gauss3, gauss4, gauss5]
prefixes = ['g1_', 'g2_', 'g3_', 'g4_', 'g5_']

mod = np.sum(gauss[0:len(peaks)])
pars = mod.make_params()

for i, prefix in zip(range(0, len(peaks)), prefixes[0:len(peaks)]):
    pars[prefix + 'center'].set(peaks[i])

init = mod.eval(pars, x=x_range)
out = mod.fit(fake, pars, x=x_range)
print(out.fit_report(min_correl=0.5))
out.plot_fit()
plt.show()

Coxswain

Answer 2

I think you would be better off using lmfits ability to build composite model.
That is, with a single peak defined with

from scipy.stats import norm
def peak(x, amp, center, sigma):
    return amp * norm.pdf(x, center, sigma)

(see also lmfit.models.GaussianModel), you can build a model with many peaks:

npeaks = 3
model = Model(peak, prefix='p1_')
for i in range(1, npeaks):
     model = model + Model(peak, prefix='p%d_' % (i+1))

params = model.make_params()

Now model will be a sum of 3 Gaussian functions, and the params created for that model will have names like p1_amp, p1_center, p2_amp, ..., which you can add sensible initial values and/or bounds and/or constraints.

Given your example data, you could pass in initial values to make_params like

params = model.make_params(p1_amp=2.0, p1_center=50., p1_sigma=2, 
                           p2_amp=0.2, p2_center=40., p2_sigma=2, 
                           p3_amp=0.2, p3_center=60., p3_sigma=2)

result = model.fit(fake, params, x=x_range)

Upthrust