How Can I Fit A Good Lorentzian On Python Using Scipy.optimize.curve_fit?
I'm trying to fit a Lorentzian function with more than one absorption peak (Mössbauer spectra), but the curve_fit function it not working properly, fitting just few peaks. How can
Solution 1:
This code uses leastsq
instead of curve_fit
as the latter one requires a fixed number of parameters. Here I do not want this as I let the code "decide" how many peaks are there. Note that I scaled the data to simplify the fit. The true fitting parameters are calculated easily be scaling back ( and standard error propagation )
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import leastsq
deflorentzian( x, x0, a, gam ):
return a * gam**2 / ( gam**2 + ( x - x0 )**2)
defmulti_lorentz( x, params ):
off = params[0]
paramsRest = params[1:]
assertnot ( len( paramsRest ) % 3 )
return off + sum( [ lorentzian( x, *paramsRest[ i : i+3 ] ) for i inrange( 0, len( paramsRest ), 3 ) ] )
defres_multi_lorentz( params, xData, yData ):
diff = [ multi_lorentz( x, params ) - y for x, y inzip( xData, yData ) ]
return diff
xData, yData = np.loadtxt('HEMAT_1.dat', unpack=True )
yData = yData / max(yData)
generalWidth = 1
yDataLoc = yData
startValues = [ max( yData ) ]
counter = 0whilemax( yDataLoc ) - min( yDataLoc ) > .1:
counter += 1if counter > 20: ### max 20 peak...emergency break to avoid infinite loopbreak
minP = np.argmin( yDataLoc )
minY = yData[ minP ]
x0 = xData[ minP ]
startValues += [ x0, minY - max( yDataLoc ), generalWidth ]
popt, ier = leastsq( res_multi_lorentz, startValues, args=( xData, yData ) )
yDataLoc = [ y - multi_lorentz( x, popt ) for x,y inzip( xData, yData ) ]
print popt
testData = [ multi_lorentz(x, popt ) for x in xData ]
fig = plt.figure()
ax = fig.add_subplot( 1, 1, 1 )
ax.plot( xData, yData )
ax.plot( xData, testData )
plt.show()
Providing
[ 9.96855817e-01 4.94106598e+02 -2.82103813e-01 4.66272773e+00
2.80688160e+01 -2.72449246e-01 4.71728295e+00 1.31577189e+02
-2.29698620e-01 4.20685229e+00 4.01421993e+02 -1.85917255e-01
5.57859380e+00 2.29704607e+02 -1.47193792e-01 3.91112196e+00
3.03387957e+02 -1.37127711e-01 4.39571905e+00]
and
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