Fitting Multiple Lorentzians To Brillouin Spectrum Using Scipy In Python 3

I am trying to fit Brillouin Spectra (with several peaks) using scipy.optimize.curve_fit. I have have multiple spectra with several peaks and I am trying to fit them with lorentzi

Solution 1:

With some small modifications the code of the OP runs just fine. Now it looks like:

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import leastsq
from scipy.signal import find_peaks

def lorentzian( x, x0, a, gam ):
    return a * gam**2 / ( gam**2 + ( x - x0 )**2 )

def multi_lorentz( x, params ):
    off = params[0]
    paramsRest = params[1:]
    assert not ( len( paramsRest ) % 3 )
    return off + sum( [ lorentzian( x, *paramsRest[ i : i+3 ] ) for i in range( 0, len( paramsRest ), 3 ) ] )

def res_multi_lorentz( params, xData, yData ):
    diff = [ multi_lorentz( x, params ) - y for x, y in zip( xData, yData ) ]
    return diff

y0 = np.loadtxt( 'y_peo.tsv' )
yData = np.loadtxt( 'y_peo.tsv' )
xData = np.arange( len( yData ) )

yGround = min( yData )
yData = yData - yGround
yAmp = max( yData )
yData = yData / yAmp 

#initial properties of peaks 
pk, properties = find_peaks( yData, height = .05, width = 3 )#, prominence=0.1 )
#extract peak heights and fwhm 
I = properties [ 'peak_heights' ]
fwhm = properties[ 'widths' ]

guess = [0]
for i in range( len( pk ) ): 
    guess.append( pk[i] )
    guess.append( I[i] )
    guess.append( fwhm[i] ) 

guess=np.array( guess )

popt, pcov = leastsq( res_multi_lorentz, x0=guess, args=( xData, yData ) )
print( popt )


testData = [ multi_lorentz( x, popt ) for x in xData ]
fitData = [ yGround + yAmp * multi_lorentz( x, popt ) for x in xData ]

fig= plt.figure( figsize=( 10, 5 ) )
ax= fig.add_subplot( 2, 1, 1 )
bx= fig.add_subplot( 2, 1, 2 )
ax.plot( pk, yData[pk], 'o', ms=5 )
ax.plot( xData, yData, 'ok', ms=1 )
ax.plot( xData, testData , 'r--', lw=0.5 )
bx.plot( xData, y0, ls='', marker='o', markersize=1 )
bx.plot( xData, fitData )
plt.show()

giving

[9.39456104e-03 6.55864388e+01 5.73522507e-02 5.46727721e+00
 1.21329586e+02 2.97187567e-01 2.12738107e+00 1.76823266e+02
 1.57244131e-01 4.55424037e+00 3.51556692e+02 3.08959955e-01
 4.39114581e+00 4.02954496e+02 9.02677035e-01 2.27647259e+00
 4.53994668e+02 3.74379310e-01 4.02432791e+00 6.15694190e+02
 4.51943494e-01 4.06522919e+00 6.63307635e+02 1.05793098e+00
 2.32168786e+00 7.10644233e+02 4.33194434e-01 4.17050014e+00
 8.61276198e+02 1.79240633e-01 4.26617114e+00 9.06211127e+02
 5.03070470e-01 2.10563379e+00 9.50973864e+02 1.78487912e-01
 4.01254815e+00]

and