Error in running the Elliott Fitting function

[shashisourabh]

Hi All,
I am new to the python and trying to do some curve fitting for my lab data. I have found an Elliott Fit code from Dr. Valerio D'Innocenzo's doctoral thesis and changed a bit to work for my data but it is not working. It was giving me errors like :

" RuntimeWarning: overflow encountered in cosh
return (1 / (abs(np.cosh((e-x))/ gamma)) * 2 * np.pi * np.sqrt(Eb) / (1 - np.exp(-2 * np.pi / (np.sqrt(D)))) * 1 / (1 - npc * (x - Eg))) "

My experimental data is in 2nd column and energy values in 1st column.

Can anyone help me fix it?
Thanks,
Shashi

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
# ODEpack tool for differential equation integration
from numpy.distutils.fcompiler import none
from scipy.integrate import odeint, quad
# Optimization tool
import scipy.optimize as opt
#Interpolation tool
from scipy.interpolate import interp1d

def Elliots_fit (p, a_exp , e):
    Eb, Eg, gamma, npc, k = p
    #Descrete transitions to the excitonic states
    absex = np.zeros((e.size))
    n = np.linspace(1, 500, 500)
    for i in range(0, e.size):
        expr = 4*np.pi*(Eb**(3/2)) / (n**3)*(1/(np.cosh((e[i] - Eg + Eb/n**2) / gamma)))
        S = expr.cumsum(axis=0)
        absex[i] = S[-1]

    #Band to band absorption with Sommerfeld correction
    abseh = np.zeros((e.size))

    def fun_eh(x, e, gamma, Eb, Eg, npc):
        D = (x-Eg)/Eb
        return (1 / (abs(np.cosh((e-x))/ gamma)) * 2 * np.pi * np.sqrt(Eb) / (1 - np.exp(-2 * np.pi / (np.sqrt(D)))) * 1 / (1 - npc * (x - Eg)))

    for i in range(0, e.size):
        q = quad(fun_eh, Eg, np.inf, args=(e[i], gamma, Eb, Eg, npc))
        abseh[i] = q[0]
    #Complete Abs simulation (background added)
    abs_sim = np.zeros((e.size))
    for i in range(0, e.size):
        abs_sim[i] = (e[i] / Eb**(3/2))*(absex[i] + abseh[i])
    return (abs_sim*k-abs_exp_fit)

#Data loading
data = np.loadtxt('transmission_data.txt')
# plt.plot(e, data[:,2])
e_exp = data [:,0] # concerted from nm to eV
a_exp = data[:,1] # My data
#Intial Values
Eb = 0.030 # exciton binding energy (eV)
gamma = 0.029 # inhomogeneous line broadening (eV)
Eg = 2.402 # semiconductor bandgap (eV)
npc = -0.31 # non−parabolic coefficient
k = 0.0035
#Energy axis generation
# ix0 = np.searchsorted(e_exp ,1.58862)
# ix1 = np.searchsorted(e_exp ,1.42976)
# e = np.linspace(e_exp[ix1], e_exp[ix0-1], 500) # energy axes (eV)
e = np.linspace(e_exp[len(e_exp)-1], e_exp[0], 3440) # energy axes (eV)
p0 = np.array([Eb, Eg, gamma, npc, k],dtype=np.float64 )#b = np.array([[1,2,3,4,5],[6,7,8,9,10]],dtype=np.float64)
#Fit Calling
#Interpolating the simulated abs over the exp x−axis
f = interp1d(e_exp ,a_exp)
abs_exp_fit = f(e)
opt_out = opt.leastsq(Elliots_fit ,p0, args =( abs_exp_fit , e), full_output=1)
fitted_param = opt_out[0]
#Standard error evaluation

fitting = Elliots_fit(fitted_param, abs_exp_fit, e)

plt.plot(e, abs_exp_fit)
plt.plot(e, fitting)

if (len( abs_exp_fit ) > len(p0)) and opt_out [1] is not None:
    s_sq = (( fitting-abs_exp_fit )**2).sum()((len( abs_exp_fit )-len(p0)))
    pcov = opt_out[1] * s_sq
else:
    pcov = np.inf
error = []
for i in range(len(opt_out [0])):
    try:
        error.append( np.absolute(pcov[i][i])**0.5)
    except:
        error.append( 0.00 )
pfit_leastsq = opt_out [0]
perr_leastsq = np.array(error)

[Larz60+]

Please provide the actual error traceback message verbatim.
It contains very valuable information for diagnosis of problem.
Thank You

[shashisourabh]

Error:
C:\Users\bob\AppData\Local\Programs\Python\Python37-32\python.exe "C:\Program Files\JetBrains\PyCharm Community Edition 2019.2\helpers\pydev\pydevconsole.py" --mode=client --port=52730
import sys; print('Python %s on %s' % (sys.version, sys.platform))
sys.path.extend(['F:\\Python', 'F:/Python'])
Python 3.7.4 (tags/v3.7.4:e09359112e, Jul  8 2019, 19:29:22) [MSC v.1916 32 bit (Intel)]
Type 'copyright', 'credits' or 'license' for more information
IPython 7.10.2 -- An enhanced Interactive Python. Type '?' for help.
PyDev console: using IPython 7.10.2
Python 3.7.4 (tags/v3.7.4:e09359112e, Jul  8 2019, 19:29:22) [MSC v.1916 32 bit (Intel)] on win32
runfile('C:/Users/bob/.PyCharmCE2019.2/config/scratches/ElliottFitting.py', wdir='C:/Users/bob/.PyCharmCE2019.2/config/scratches')
Backend TkAgg is interactive backend. Turning interactive mode on.
C:/Users/bob/.PyCharmCE2019.2/config/scratches/ElliottFitting.py:27: RuntimeWarning: overflow encountered in cosh
  return (1 / (abs(np.cosh((e-x))/ gamma)) * 2 * np.pi * np.sqrt(Eb) / (1 - np.exp(-2 * np.pi / (np.sqrt(D)))) * 1 / (1 - npc * (x - Eg)))
C:/Users/bob/.PyCharmCE2019.2/config/scratches/ElliottFitting.py:18: RuntimeWarning: invalid value encountered in double_scalars
  expr = 4*np.pi*(Eb**(3/2)) / (n**3)*(1/(np.cosh((e[i] - Eg + Eb/n**2) / gamma)))
C:/Users/bob/.PyCharmCE2019.2/config/scratches/ElliottFitting.py:30: IntegrationWarning: The occurrence of roundoff error is detected, which prevents 
  the requested tolerance from being achieved.  The error may be 
  underestimated.
  q = quad(fun_eh, Eg, np.inf, args=(e[i], gamma, Eb, Eg, npc))
C:/Users/bob/.PyCharmCE2019.2/config/scratches/ElliottFitting.py:35: RuntimeWarning: invalid value encountered in double_scalars
  abs_sim[i] = (e[i] / Eb**(3/2))*(absex[i] + abseh[i])
C:/Users/bob/.PyCharmCE2019.2/config/scratches/ElliottFitting.py:30: IntegrationWarning: The algorithm does not converge.  Roundoff error is detected
  in the extrapolation table.  It is assumed that the requested tolerance
  cannot be achieved, and that the returned result (if full_output = 1) is 
  the best which can be obtained.
  q = quad(fun_eh, Eg, np.inf, args=(e[i], gamma, Eb, Eg, npc))
C:/Users/bob/.PyCharmCE2019.2/config/scratches/ElliottFitting.py:30: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.
  If increasing the limit yields no improvement it is advised to analyze 
  the integrand in order to determine the difficulties.  If the position of a 
  local difficulty can be determined (singularity, discontinuity) one will 
  probably gain from splitting up the interval and calling the integrator 
  on the subranges.  Perhaps a special-purpose integrator should be used.
  q = quad(fun_eh, Eg, np.inf, args=(e[i], gamma, Eb, Eg, npc))
C:/Users/bob/.PyCharmCE2019.2/config/scratches/ElliottFitting.py:30: IntegrationWarning: The integral is probably divergent, or slowly convergent.
  q = quad(fun_eh, Eg, np.inf, args=(e[i], gamma, Eb, Eg, npc))
Traceback (most recent call last):
  File "C:\Users\bob\AppData\Local\Programs\Python\Python37-32\lib\site-packages\IPython\core\interactiveshell.py", line 3319, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "<ipython-input-2-e821db8486f9>", line 1, in <module>
    runfile('C:/Users/bob/.PyCharmCE2019.2/config/scratches/ElliottFitting.py', wdir='C:/Users/bob/.PyCharmCE2019.2/config/scratches')
  File "C:\Program Files\JetBrains\PyCharm Community Edition 2019.2\helpers\pydev\_pydev_bundle\pydev_umd.py", line 197, in runfile
    pydev_imports.execfile(filename, global_vars, local_vars)  # execute the script
  File "C:\Program Files\JetBrains\PyCharm Community Edition 2019.2\helpers\pydev\_pydev_imps\_pydev_execfile.py", line 18, in execfile
    exec(compile(contents+"\n", file, 'exec'), glob, loc)
  File "C:/Users/bob/.PyCharmCE2019.2/config/scratches/ElliottFitting.py", line 69, in <module>
    s_sq = (( fitting-abs_exp_fit )**2).sum()((len( abs_exp_fit )-len(p0)))
TypeError: 'numpy.float64' object is not callable
plt.plot(e, abs_exp_fit)
plt.plot(e, fitting)
Out[3]: [<matplotlib.lines.Line2D at 0x2854030>]

[shashisourabh]

Can anyone tell me how to fix this code?

[Larz60+]

Something doesn't look quite right with line 69.
It looks like perhaps parenthesis are in the wrong positions.
Do you have a link to the original D'Innocenzo's thesis?

[scidam]

I think, you missed arithmetical symbol in (( fitting-abs_exp_fit )**2).sum()((len( abs_exp_fit )-len(p0))).

( fitting-abs_exp_fit )**2).sum() -- This is a numpy array. Further, you've used parenthesis: ( fitting-abs_exp_fit )**2).sum()(...).
That means you tried to call a numpy array.

You need to change your code to

s_sq = (( fitting-abs_exp_fit )**2).sum()<some symbol here>((len( abs_exp_fit )-len(p0)))

where <some symbol here> is either "/", "*", etc (or something else).

[shashisourabh]

Something doesn't look quite right with line 69.
It looks like perhaps parenthesis are in the wrong positions.
Do you have a link to the original D'Innocenzo's thesis?

Here is the link to his thesis: https://www.politesi.polimi.it/bitstream...zo.pdf.pdf

[shashisourabh]

I fixed line 69 but still getting error with "cosh" function. Also, if anyone who is an expert in fitting can help figure out why the author(D'Innocenzo) has used "a_exp" at line 12 although he has not used the variable in the function definition.

[Larz60+]

still getting error

still need to see error trace

[osvan]

Have you had any success with Elliott fitting?