Hello lmfit community, how do i set the initial condition of amplitude in modeling a continuum normalized absorption line to start from 1(continuum) not 0? I have attached the weird one i'm getting which i want to correct, thank you.

[ZIHABAKE Daniel]

[Matt Newville]

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[ZIHABAKE Daniel]

Sorry for not clarifying the problem, i'm a masters student not experienced in programming.

My question is " i want to fit multi-Gaussian components to my continuum normalized data with picks at 5875, 5890, and 5896 angstrom where sigma of 5890 and 5896 has to be the same.

By setting initial parameter of amplitude and fit i get output amplitude which is measured from 0 not from 1(continuum level),  i would like to know how i can fix the amplitude to be measured from 1. The attached is data.

thank you.

import matplotlib.pyplot as plt
from numpy import exp, loadtxt, pi, sqrt
from lmfit import Model, Parameters
data = loadtxt('Data.txt')
x = data[:, 0]
y = data[:, 1]

#selected region for fitting
mask = (x>= 5875) & (x <= 5910)
mask = (x>= 5850) & (x <= 5950)
xarray, yarray = x[mask], y[mask]
x=xarray
y=yarray

#defining a multi-Gaussian components function 
def gaussian(x, amp1, cen1, wid1, amp2, cen2, wid2, amp3, cen3, wid3):
    g1=(amp1 / (sqrt(2*pi) * wid1)) * exp(-(x-cen1)**2 / (2*wid2**2))
    g2=(amp2 / (sqrt(2*pi) * wid2)) * exp(-(x-cen2)**2 / (2*wid2**2))
    g3=(amp3 / (sqrt(2*pi) * wid3)) * exp(-(x-cen3)**2 / (2*wid3**2))
    return g1+g2+g3
gmodel = Model(gaussian)

params = Parameters()
params.add('amp1', vale=0.8, min=0.7, max=0.3)
params.add('cen1', vale=5890, min=5887, max=5894)
params.add('wid1', vale=3.0 , min=1, max=4)
params.add('amp2', vale=0.9, min=1, max=0.7)
params.add('cen2', vale=5896, min=5891, max=5902)
params.add('wid2', vale=3.0 , min=2, max=4)
params.add('amp3', vale=1.06, min=1, max=1.7)
params.add('cen3', vale=5875, min=5870, max=5890)
params.add('wid3', vale=3.0 , min=2, max=4)


result = gmodel.fit(y, params, x=x)
print(result.fit_report())
plt.plot(x, y, 'b', label='observed')
plt.ylim(ymin=-1, ymax=1.5)
plt.plot(x, result.best_fit, 'r-', label='best fit')
plt.xlabel('wavelength[$\AA$]')
plt.ylabel('flux[erg cm-2 s-1 $\AA$ -1]')

plt.legend(loc='best')
plt.savefig('NaID-He.pdf')
plt.show()

[Matt Newville]

On Sat, Jun 4, 2022 at 6:52 AM ZIHABAKE Daniel <dziha...@gmail.com> wrote:

Sorry for not clarifying the problem, i'm a masters student not experienced in programming.

My question is " i want to fit multi-Gaussian components to my continuum normalized data with picks at 5875, 5890, and 5896 angstrom where sigma of 5890 and 5896 has to be the same.

By setting initial parameter of amplitude and fit i get output amplitude which is measured from 0 not from 1(continuum level),  i would like to know how i can fix the amplitude to be measured from 1. The attached is data.

thank you.

I think the problems are basically:

1. with 

    params.add('amp1', vale=0.8, min=0.7, max=0.3)

You want 'value' not 'vale', and 'min' needs to be less than max.  More importantly, don't set bounds to be too small.

2.  Your data is not represented well by 3 Gaussians.  You need some offset (I guess linear) too.  Also, the Gaussians will have negative amplitudes (see point 1).   

Try this (you can probably improve the plot):

###

from numpy import loadtxt

import matplotlib.pyplot as plt
from lmfit import Parameters
from lmfit.models import GaussianModel, LinearModel

data = loadtxt('Data.txt')
x = data[:, 0]
y = data[:, 1]

#selected region for fitting
mask = (x>= 5875) & (x <= 5910)
mask = (x>= 5850) & (x <= 5950)
xarray, yarray = x[mask], y[mask]
x=xarray
y=yarray

#  Note: use builtin models
gmodel = ( GaussianModel(prefix='p1_') +  GaussianModel(prefix='p2_') +
                   GaussianModel(prefix='p3_') +   LinearModel(prefix='off_'))

#  Note: many fewer bounds:
params = Parameters()
params.add('off_intercept', value=1)
params.add('off_slope', value=0)
params.add('p1_amplitude', value=-7)
params.add('p1_center', value=5890, min=5887, max=5894)
params.add('p1_sigma', value=3.0 , min=0)
params.add('p2_amplitude', value=-1)
params.add('p2_center', value=5896, min=5891, max=5902)
params.add('p2_sigma', value=3.0 , min=0)
params.add('p3_amplitude', value=0.5)
params.add('p3_center', value=5875, min=5870, max=5890)
params.add('p3_sigma', value=3.0 , min=0)

result = gmodel.fit(y, params, x=x)
print(result.fit_report())

comps = result.eval_components(x=x)

plt.plot(x, y, 'b', label='observed')
plt.ylim(ymin=-1, ymax=1.5)

plt.plot(x, result.best_fit, 'r--', label='best fit')
plt.plot(x, comps['p1_']+comps['off_'], 'b-', label='p1')
plt.plot(x, comps['p2_']+comps['off_'], 'g-', label='p3')
plt.plot(x, comps['p3_']+comps['off_'], 'k-', label='p2')
plt.plot(x, comps['off_'], 'k-', label='offset')

plt.xlabel(r'wavelength [$\rm \AA$]')
plt.ylabel(r'flux [$\rm erg / (cm^{2} \, s \, \AA)]')

plt.legend(loc='best')
plt.savefig('NaID-He.pdf')
plt.show()

###

--Matt 

[ZIHABAKE Daniel]

Thank you very much, let me try it.

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