无法使用 lmfit 拟合自定义 model - ValueError：model function 生成的 NaN 值和拟合中止

Question

I have this data:

y=[2.103402,2.426855,1.011672,1.595371,1.861879,2.492542,2.567561,4.685010,4.452643,5.321630,6.637233,
6.109260,6.220958,5.928408,5.654726,5.498096,5.468448,6.128418,6.071376,6.487270,6.609533,6.907320,
7.626838,8.432065,9.749410,8.976752,8.742036,8.779956,8.212357,8.578200,9.170012,9.134267,9.199465,
9.094945,9.342948,9.802524,10.959913,10.488497,10.892593,10.673570,10.608582,10.036824,9.741473]

x=[300,400,500,600,700,800,900,1000,1100,1200,1300,1400,1500,1600,1700,1800,1900,2000,2100,2200,2300,
2400,2500,2600,2700,2800,2900,3000,3100,3200,3300,3400,3500,3600,3700,3800,3900,4000,4100,4200,4300,4400,4500]

data looks like this, the fit is manually adjusted:

I want to fit this custom log function:

def log_n_func(x, a, b, c, n):
    return a*(np.log(b+x)/np.log(n))+c

I tried two approaches:

import lmfit

def log_n_func(x, a, b, c, n):
    return a*(np.log(b+x)/np.log(n))+c

regressor = lmfit.Model(log_n_func)                  
initial_guess = dict(a=3.61, b=443.86, c=-34, n=2)                
results = regressor.fit(data=y, x=x, **initial_guess)
y_fit = results.best_fit

and

from lmfit import Model, Parameters

model = Model(log_n_func, independent_vars=['x'], param_names=["a", "b", "c", "n"])  
params = Parameters()
params.add("a", value=3.6)
params.add("b", value=440)
params.add("c", value=-34)
params.add("n", value=2)
result = model.fit(data=y, params=params, x=x)

but both lead to the same error: ValueError: The model function generated NaN values and the fit aborted. Please check your model function and/or set boundaries on parameters where applicable, In cases like this. using "nan_policy='omit'" will probably not work. ValueError: The model function generated NaN values and the fit aborted. Please check your model function and/or set boundaries on parameters where applicable, In cases like this. using "nan_policy='omit'" will probably not work.

What did I do wrong?

Answer 1

logarithms are not defined values equal to or below 0, so that numpy log(x) will sensibly give NaN for np.log(x) for x<0 .

When doing a fit, the parameter values can take any values unless you explicitly restrict the range of values.

Neither your b variable or your n variable are bounded at all. n could certainly go below zero during the fit. If b goes below -1000, then some values of b+x will also be below 0. Either one will cause a nan value in your model and the fit will stop immediately.

That is why the message says "Please check your model function and/or set boundaries on parameters where applicable". You will need to set bounds to prevent the argument of log() from being 0 or negative.