Make function dynamically to pass in lmfit

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Python3.6

Hi, I need to pass a function (here is fun) to lmfit to do fitting as below:

import lmfit, Model
model = Model(fun, independent_vars=ind)

But function have to be this way because lmfit only works this way:

def fun(explicit names for all the parameters):
    return string expression of stdout

My issue is that the function parameters and the returned expression by fun must be changed dynamically in each iteration so I should be able to write a function that its parameters and returns is changing dynamically.

Even any suggestion on how to write a function from two strings (as parameter and return) would be welcomed.

I need the following function been created:

def fit_function(expr, list_var, list_para, dict_data(key_var,list_data) ) ->list_para:

What I have tried:

In fact based on a list of a string (as function parameter) and the stdout print (as return in fun), I should write the fun for each iteration. The following code shows how running lnfca() which is a sympy, symbolic string needs to be passed in fun for every iteration.

def fun_print(ff):
    return print(NumPyPrinter().doprint(ff))
fun_print(lnfca())
import contextlib
import io
captured_output = io.StringIO()
with contextlib.redirect_stdout(captured_output):
    fun_print(lnfca())

This way stdout print can be captured, but I have no idea how one can write a function this way(changing parameters and return is really crucial here) Is there any way to do it??

in summer to fit a model using lmfit it should be passed to Model as follows:

def f(x, gamma, alpha, beta, eta):
    L = x[0]
    K = x[1]
    
    return gamma - (1/eta)*np.log(alpha*L**-eta + beta*K**-eta)

fmodel = Model(f)
params = Parameters()
params.add('gamma', value = 1,    vary=True, min = 1)
params.add('alpha', value = 0.01, vary=True, max = 1, min = 0)
params.add('beta',  value = 0.98, vary=True, max = 1, min = 0)
params.add('eta',   value = 1,    vary=True, min = -1)

result = fmodel.fit(np.log(VA), params, x=(L,K))
print(result.fit_report())

Please take a look here:https://stackoverflow.com/questions/69046347/scipy-minimize-scipy-curve-fit-lmfit

But in my case I should make the f function in a dynamic way for each iteration that includes different variables and expression to create the following:

def fit_function(expr, list_var, list_para, dict_data(key_var,list_data) ) :
return expr