用等于 0 的 function 拟合数据，无法转换为 f(x) = x 的形式

Question

I have 2 columns and 31 rows in a pandas dataframe. I want to plot this x,y data and fit them to a complex function with 4 parameters. The function looks something like this. The function has to be 0

# Data:
T,p = df["T"], df["p"] #31 rows

# known constants: a,b,Ta,c0,x

def c(T,v,VP,a=...,b=...,Ta=...,c0=...):
     c = c0 + a*(T-Ta) + b*t_r(T)**v/(t_r(T)**v-K(T,VP))
     return c

# t_r and K are other functions

def function(p,T,p0,v,N,VP,a,b,c0,x):
    return np.log(1-p) + p + (x*c(T,v,VP))*p**2 + (p0/N)*(R-0.5*R**3) # =0

I am interested in fitting the parameters N,p0,Vp

I tried to use Lmfit and changed my function to -> function(params,T,p)

from Lmfit import minimize, Parameters

## add Parameters 
params = Parameters() ##Class with a list of parameters

# add all constant Parameters with vary = False
params.add("a", value=...,vary=False)
...

## add variables to fit with vary = True, limits with min,max 
params.add("N",value=..., vary=True,min=0,max=...)
...


output = minimize(function,params) #Fit Results
output.params.pretty_print() #Show Results

Now I acquired the parameters, but I want to check if this makes sense by plot(T,p) for a more continous array, like:

Ts = np.linspace(10,60,1000) # x-array
ps = ...    ?                # y-array
plt.plot(Ts,ps,label="Fit")  # Plot Data

How could I obtain a function to calculate p for T on each point to plot it?

Answer 1

I find an answer myself.

First I wrap my function in a way that the y-value p is the first argument. And I used lmfit parameter class as arguments. Lmfit Parameters are basically dictionaries.

p_solvable = lambda p,T,parameter : function(p,T,parameter["p0"],parameter["v"],...)

Then I solve the equation by scipy.optimize.root_scalar with the brentq method. The brentq method needs Brackets where the signs are changing. I chose 1 as lower limit so np.log(1-p > 0) is defined and just the doubled maximum as upper limit.

p_max = np.max(p)

def p(T):
   P_Init = [root_scalar(p_solvable,args=(T,parameter), method="brentq", bracket=[1,p_max*2]).root for T in T]
   return P_Init

Now I have a function where I can input f(x) = y and fit it with lmfit or scipy curve_fit