让 lmfit 模型与Integrate.quad 函数一起使用时遇到问题

Question

我定义了一个可以正常模拟某些数据的函数。 对于物理学家来说：该函数应该在 NMR 数据中生成低于超导转变的 Hebel-Slichter 相干峰。

我现在想使用 lmfit 将函数拟合到我的数据。 我收到一条错误消息，这似乎是因为我在函数的Integrate.quad 部分中使用了附加参数（参数）。我对 python 确实不太熟练。可以让它工作吗？

代码有点混乱，因为我有一个部分（已注释掉）仅用于绘制数据和模拟。代码和错误消息如下所示：

import numpy as np
import matplotlib.pyplot as plt
import scipy.integrate as integrate
#import scipy.special as special
#from scipy.optimize import curve_fit
from lmfit import Model

#The function that describes the change in the DOS around the Fermi-level as a function of temperature below Tc
def T1Tfunc(En, Temperature , Gamma0 , Nfactor, Gap2 , Tc):
    kB = 8.617E-5

    Delta0 = kB * Tc * Gap2 / 2
    
        
    Delta1 = Delta0 * np.tanh(((Tc / Temperature)-1) ** 0.5)
    Gamma1 = Gamma0 * (Temperature / Tc) ** Nfactor
    
    Enp = En + 8.974E-6
    
    EnB = En + Gamma1 * 1j
    EnBp = Enp + Gamma1 * 1j
    
    Ns = (EnB / np.sqrt(EnB * EnB - Delta1 * Delta1))
    Nsp = (EnBp / np.sqrt(EnBp * EnBp - Delta1 * Delta1))
    Ms = (Delta1 / np.sqrt(EnB * EnB - Delta1 * Delta1))
    Msp = (Delta1 / np.sqrt(EnBp * EnBp - Delta1 * Delta1))
    
    FE = 1/(1 + np.exp(En/(kB*Temperature)))
    FEp = 1/(1 + np.exp(Enp/(kB*Temperature)))
    
    func = (np.real(Ns)*np.real(Nsp)+np.real(Ms)*np.real(Msp))*FE*(1-FEp)
    return func

#The integration of the DOS, and resulting spin-lattice relaxation rate
def  T1T(Temperature , Gamma0 , Nfactor , Gap2 , Tc , Koringaa , Koringab): 
    kB = 8.61728E-5

    # Integration parameters
    aint = 0
    bint = 0.1

    I = integrate.quad(T1Tfunc, aint, bint, args=(Temperature , Gamma0 , Nfactor , Gap2 , Tc))[0]
#For Korringa
    return I*(2/(kB*Temperature)) * (Koringaa + Koringab * Temperature)
#For No-Korringa
#    return I*(2/(kB*Temperature)) * (Koringaa + Koringab * Tc)

T1T = np.vectorize(T1T)

#Some if functions for when the calculation values end up too small, and for above Tc
def T1Textended(Temperature , Gamma0 , Nfactor, Gap2 , Tc , Koringaa , Koringab): 
    if Temperature < (0.1 * Tc):
        T1Te = 0
    elif Temperature < Tc:
        T1Te = T1T(Temperature , Gamma0 , Nfactor , Gap2 , Tc , Koringaa , Koringab)
    else:
        T1Te = Koringaa + Koringab * Temperature
    return T1Te

T1Textended = np.vectorize(T1Textended)


#Importing some example data to be fitted

filename = 'Rb2CsC60.txt'
data = np.loadtxt(filename, delimiter=',')
datax = data[:, 0]
datay = data[:, 1]
dataerr = data[:, 2]
#print(data)

# #For plotting a simulation resulting from the function, on top of data

# #Parameters when simulating
# Tc = 32.2
# Gamma0 = 9.56496E-4
# #Gap2 = 4.18126
# Gap2 = 
# Nfactor = 1
# Koringaa = 0.02542
# Koringab = 4.24127E-4

# Temperature = np.arange((0.1 * Tc), (1.8 * Tc), (Tc / 100))
# DOST0p0 = T1Textended(Temperature , Gamma0 , Nfactor , Gap2 , Tc , Koringaa , Koringab)

# fig = plt.figure()
# ax = plt.axes()
# line1 = ax.plot(Temperature,DOST0p0)
# ax.scatter(datax,datay)

# #plt.ylim([0, 2])
# #plt.xlim([0, (2 * Tc)])

# plt.title(u"1/T_1T vs. Temperature \n \u0393\u2080 = {} eV, n = {}, T_c = {}".format(Gamma0, Nfactor, Tc))
# plt.xlabel("Temperature (K)")
# plt.ylabel("$1/(T_{1}T)$");

#Now attempting to fit the function to some data

#Define T1Textended as a function to be wrapped by the 'Model' fitting package of lmfit 
HSmodel = Model(T1Textended)

#Define and set the parameters for the model, to be fitted
params = Model.Parameters()
params.add('Tc', value=32.2, vary=False)
params.add('Gamma0', value=1E-3, vary=True)
params.add('Nfactor', value=1, vary=False)
params.add('Gap2', value=4.25, vary=True)
params.add('Koringaa', value=1, vary=True)
params.add('Koringab', value=0, vary=True)

#Check that it is read properly and gives all the right input parameters and variables
print(HSmodel.param_names, HSmodel.independent_vars)

错误信息：

runfile('C:/Users/Ross Colman/Qsync/Hebel-Slichter/DOS_simulation/HS_fit.py', wdir='C:/Users/Ross Colman/Qsync/Hebel-Slichter/DOS_simulation') 回溯（最近一次调用最后一次）：

文件“C:\Users\Ross Colman\Qsync\Hebel-Slichter\DOS_simulation\HS_fit.py”，第 111 行，位于 HSmodel = 模型（T1Textded）

文件“C:\ProgramData\Anaconda3\lib\site-packages\lmfit\model.py”，第 277 行，位于 init self._parse_params()

文件“C:\ProgramData\Anaconda3\lib\site-packages\lmfit\model.py”，第 489 行，在 _parse_params 中 引发 ValueError(f"不支持 varargs '*{fnam}'")

ValueError：不支持可变参数'*args'

如有任何帮助，我们将不胜感激

Answer 1

lmfit.Model()

无法包装由

numpy.vectorize()

“矢量化”的函数。