多指数衰减的 lmfit 模型

问题描述

我正在尝试使用 lmfit 包 对我的数据进行拟合。但是我找不到任何用于多指数衰减的内置模型。我试图创建自己的函数，然后适应它。 我的代码如下：

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    if (session != null) {
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出现错误但无法识别问题。

import os
import time
import numpy as np
import pandas as pd
import lmfit
from lmfit.models import ExponentialModel,LinearModel
from lmfit import Model,Parameter,report_fit

def MultiExpDecay(tiempo,C1,tau1,C2,tau2):
    return C1*np.exp(-tiempo/tau1)+C2*np.exp(-tiempo/tau2)

def MultiExpDecay_fit():
    C1s = []
    C1s_error = []
    C2s = []
    C2s_error = []
    tau1s = []
    tau1s_error = []
    tau2s = []
    tau2s_error = []
    Fit_MultiExpDecays = []
    model = Model(MultiExpDecay,independent_vars=['tiempo'])
    for c in range(len(V_APD.columns)):
        xdat = tiempo.iloc[:,c]
        ydat = V_APD.iloc[:,c]
        pars = model.guess(ydat,x=xdat)
        fit = model.fit(ydat,pars,x=xdat)
        fit_values = model.eval(pars,x=xdat)
        Fit_MultiExpDecays.append(fit_values)
        for key in fit.params:
            if key == 'C1':
                #print(key,"=",out.params[key].value,"+/-",out.params[key].stderr)
                C1s.append(fit.params[key].value)
                C1s_error.append(fit.params[key].stderr)
            elif key == 'C2':
                C2s.append(fit.params[key].value)
                C2s_error.append(fit.params[key].stderr)
            elif key == 'tau1':
                tau1s.append(fit.params[key].value)
                tau1s_error.append(fit.params[key].stderr)
            elif key == 'tau2':
                tau2s.append(fit.params[key].value)
                tau2s_error.append(fit.params[key].stderr)
    Fit_MultiExpDecays = np.transpose(pd.DataFrame(Fit_MultiExpDecays,index=labels))
    C1 = np.transpose(pd.DataFrame(C1s,index = labels,columns = ['C1']))
    C2 = np.transpose(pd.DataFrame(C2s,index=labels,columns=['C2']))
    tau1 = np.transpose(pd.DataFrame(tau1s,columns=['tau1']))
    tau2 = np.transpose(pd.DataFrame(tau2s,columns=['tau2']))
    C1_error = np.transpose(pd.DataFrame(C1s_error,columns=['C1 error']))
    C2_error = np.transpose(pd.DataFrame(C2s_error,columns=['C2 error']))
    tau1_error = np.transpose(pd.DataFrame(tau1s_error,columns=['tau1 error']))
    tau2_error = np.transpose(pd.DataFrame(tau2s_error,columns=['tau2 error']))
    C1 = pd.concat([C1,C1_error])
    C2 = pd.concat([C2,C2_error])
    tau1 = pd.concat([tau1,tau1_error])
    tau2 = pd.concat([tau2,tau2_error])
    return C1,tau2,Fit_MultiExpDecays

C1,Fit_MultiExpDecays = MultiExpDEcay_fit():

解决方法

我支持@mikuszefski 的回答。您也可以使用两个 --allow-unrelated-histories，就像

lmfit.ExponentialModel

但@mikuszefski 的回答大致相同。

对于实际问题：正如异常所说，import numpy as np from lmfit.models import ExponentialModel def dblexp( x,c1,l1,c2,l2 ): return c1 * np.exp( -x / l1 ) + c2 * np.exp( -x / l2 ) xl = np.linspace(0,10,101) yl = dblexp(xl,32.44,0.81,11.51,9.22 ) + np.random.normal(0,0.2,xl.size) mymodel = ExponentialModel(prefix='e1_') + ExponentialModel(prefix='e2_') params = mymodel.make_params(e1_amplitude=10,e1_decay=10,e2_amplitude=25,e2_decay=0.50) result = mymodel.fit(yl,params,x=xl) print( result.fit_report() ) 不知道如何为任意用户定义的模型函数猜测合理的参数值 - Model 方法默认引发此异常，并且必须被每个子类覆盖。 Model.guess() 为所提供的子模型（包括 lmfit）提供了此方法，但每个子模型都是在理解这些特定模型的情况下进行编码的。

最后：众所周知，拟合双指数衰减容易出错并且对于最小二乘法（或至少 Levenberg-Marquardt 实现）来说很困难。对于更实际的情况，我建议将数据的对数与双指数衰减的对数进行拟合。

,

我错了还是你让你的生活太复杂了。虽然我自己不使用 lmfit，但我认为它的设计使您不必完成您在此处完成的所有编程。我认为它应该看起来像：

import matplotlib.pyplot as plt
from numpy import linspace
from numpy import fromiter
from numpy import exp
from numpy.random import normal
from lmfit import Model


def dblexp( x,l2 ):
    return c1 * exp( -x / l1 ) + c2 * exp( -x / l2 )
    
xl = linspace(0,101)
yl = dblexp( xl,9.22 ) + normal(0,xl.size)


mymodel = Model( dblexp ) 

### need some good guesses to start with
params = mymodel.make_params(c1=30,l1=1,c2=5,l2 =10)

result = mymodel.fit(yl,x=xl)
print( result.fit_report() )

fig = plt.figure()
ax = fig.add_subplot( 1,1,1 )
ax.scatter( xl,yl )
ax.plot( xl,result.best_fit,'r-' )
plt.show()

提供：

[[Model]]
    Model(dblexp)
[[Fit Statistics]]
    # fitting method   = leastsq
    # function evals   = 26
    # data points      = 101
    # variables        = 4
    chi-square         = 4.77426620
    reduced chi-square = 0.04921924
    Akaike info crit   = -300.239903
    Bayesian info crit = -289.779421
[[Variables]]
    c1:  32.5481660 +/- 0.18540661 (0.57%) (init = 30)
    l1:  0.79183180 +/- 0.00931390 (1.18%) (init = 1)
    c2:  11.6241194 +/- 0.16669056 (1.43%) (init = 5)
    l2:  9.11790608 +/- 0.19623957 (2.15%) (init = 10)
[[Correlations]] (unreported correlations are < 0.100)
    C(c2,l2) = -0.949
    C(l1,c2) = -0.822
    C(l1,l2) =  0.733
    C(c1,c2) = -0.652
    C(c1,l2) =  0.645
    C(c1,l1) =  0.251

和