Python lmfit: voigt setting - difference between out.best_fit and out.best_values

Question

I'm struggling to write code to fit my Voigt profile to experimental data. At the moment, I sometimes get a reasonable function, but I need to do automatic about 1000 attacks. This means that this is not an option if every second landing is disabled.

I tried two different ways to build the plot function, and I unexpectedly got different results. First, I built the fit function using out.best_fit, and I tried this by providing the optimal parameters for my Voigt function using out.best_values.param.

As you can see here:

Here is the relevant part of my code:

import matplotlib.pyplot as plt
import numpy as np
from lmfit import Model



absPlot = np.genfromtxt('absPlot.txt')


def Gaussian(x, *p):
    A, x0, sigma, zerolevel = p
    return A*(np.sqrt(2*np.pi*sigma))*np.exp(-(x-x0)**2/(2*sigma**2))+zerolevel

def Lorentzian(x, *p):
    A, x0, gamma, zerolevel = p
    return A/np.pi*gamma/((x-x0)**2+gamma**2)+zerolevel

def VoigtConv(x, A, x0, sigma, gamma):
    G = np.fft.fft(Gaussian(x,1,x0,sigma,0))
    L = np.fft.fft(Lorentzian(x,1,x0,gamma,0))
    V = A*np.real(np.fft.fftshift(np.fft.ifft(G*L)))
    return V



vModel = Model(VoigtConv)
vModel.set_param_hint('A', value = 111, min=100, max=2*10**4)
vModel.set_param_hint('x0', value = 1.22*10**9, min=1.20*10**9, max=1.23*10**9)
vModel.set_param_hint('sigma', value = 4*10**8, min=3.2*10**8, max=4.4*10**8)
vModel.set_param_hint('gamma', value = 0, min=10**4, max=1.02*10**8)

result = vModel.fit(absPlot[50:170,1], x=absPlot[50:170,0], method='nelder')

#calculate y-values of fit function using out.best_values.get
yValTest = VoigtConv(absPlot[:,0], result.best_values.get('A'),  result.best_values.get('x0'), result.best_values.get('sigma'), result.best_values.get('gamma'),)

plt.figure(1)
plt.plot(absPlot[50:170, 0],absPlot[50:170, 1], '.k',  label='Measured Data')
plt.plot(absPlot[50:170, 0], result.best_fit, linewidth=1.2, label='Voigt Fit')
plt.plot(absPlot[50:170, 0], yValTest[50:170], linewidth=1.2, label='Voigt Fit Calc')
legend = plt.legend(loc='upper right', fontsize=14)
plt.show()

edit: . ,

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Answer 1

, , , :

yValTest = VoigtConv(absPlot[:,0], result.best_values.get('A'),  result.best_values.get('x0'), result.best_values.get('sigma'), result.best_values.get('gamma'),)

( )

yValTest = VoigtConv(absPlot[50:170, 0], result.best_values.get('A'),  result.best_values.get('x0'), result.best_values.get('sigma'), result.best_values.get('gamma'),)

plt.plot(absPlot[50:170, 0], yValTest[50:170], linewidth=1.2, label='Voigt Fit Calc')

( )

plt.plot(absPlot[50:170, 0], yValTest, linewidth=1.2, label='Voigt Fit Calc')

, . , ( , ):

:

np.array_equal(result.best_fit, yValTest)

True, , .

( pandas, ):

import matplotlib.pyplot as plt
import numpy as np
from lmfit import Model
import pandas as pd


absPlot = pd.read_csv('lmfit_voigt.csv', index_col=None).values


def Gaussian(x, *p):
    A, x0, sigma, zerolevel = p
    return A*(np.sqrt(2*np.pi*sigma))*np.exp(-(x-x0)**2/(2*sigma**2))+zerolevel

def Lorentzian(x, *p):
    A, x0, gamma, zerolevel = p
    return A/np.pi*gamma/((x-x0)**2+gamma**2)+zerolevel

def VoigtConv(x, A, x0, sigma, gamma):
    G = np.fft.fft(Gaussian(x,1,x0,sigma,0))
    L = np.fft.fft(Lorentzian(x,1,x0,gamma,0))
    V = A*np.real(np.fft.fftshift(np.fft.ifft(G*L)))
    return V


vModel = Model(VoigtConv)
vModel.set_param_hint('A', value = 111, min=100, max=2*10**4)
vModel.set_param_hint('x0', value = 1.22*10**9, min=1.20*10**9, max=1.23*10**9)
vModel.set_param_hint('sigma', value = 4*10**8, min=3.2*10**8, max=4.4*10**8)
vModel.set_param_hint('gamma', value = 0, min=10**4, max=1.02*10**8)

result = vModel.fit(absPlot[50:170,1], x=absPlot[50:170,0], method='nelder')

#calculate y-values of fit function using out.best_values.get
yValTest = VoigtConv(absPlot[50:170, 0], result.best_values.get('A'),  result.best_values.get('x0'), result.best_values.get('sigma'), result.best_values.get('gamma'),)

plt.figure(1)
plt.plot(absPlot[50:170, 0], absPlot[50:170, 1], '.k',  label='Measured Data')
plt.plot(absPlot[50:170, 0], result.best_fit, linewidth=1.2, label='Voigt Fit')
plt.plot(absPlot[50:170, 0], yValTest, linewidth=1.2, label='Voigt Fit Calc')
legend = plt.legend(loc='upper right', fontsize=14)
plt.show()