Getting a pure function from a model fit

Question

I am looking for defining a function returning a function. This function must return a polynomial fit. I managed to pass the function to fit as argument but i stuggle with the returned value of the function.

With the code below I get fit but this do not seem to be a pure function. This is a problem because the code after needs pure functions.

GetFitProba[f_Symbol, T_, V_, eta_, cut_, t_] := (
  data = Transpose[
    List[Table[i, {i, IntegerPart[cut], V}], 
     f[#, T, V, eta, t] & /@ Table[i, {i, IntegerPart[cut], V}]]];
  fit = LinearModelFit[
    data, {1, x, x^2, x^3, x^4, x^5, x^6, x^8, x^9, x^10, x^11, x^12},
     x];
  fit[x]
  )

Then I call it like that:

h[x_] := GetFitProba[f, T, V, eta, cut, t];

(where f, t, V, eta, cut, and t are well defined)

I think the problem come from the objet returned by LinearModelFit (which is a FittedModel) but I do not understand how I am supposed to managed it. I tried to return Normal[fit] and things like that but it didn't work.

Thank you for your help !

Answer 1

I am going to boldly plunge ahead despite being unable to test directly, because why not. As you may have noticed, fit returns a FittedModel object. Most such objects have a bunch of properties that you can find by passing them a string argument; you can get a list of all such properties with fit["Properties"]. In this case, you want fit["Function"].

ClearAll[GetFitProba];
GetFitProba[f_, T_, V_, eta_, cut_, t_] :=
 Module[{data = 
    Transpose[
     List[Table[i, {i, IntegerPart[cut], V}], 
      f[#, T, V, eta, t] & /@ Table[i, {i, IntegerPart[cut], V}]]],
   fit},

  fit = LinearModelFit[
    data, {1, x, x^2, x^3, x^4, x^5, x^6, x^8, x^9, x^10, x^11, x^12},
     x];

  fit["Function"]];

Just as an aside, I ditched the requirement that f have head Symbol, since you might want use a pure function (with head Function), or even perhaps a curried "operator form" of a function like Lookup. Also, I went ahead used Module to make the fit and data variables local, which is good practice.

Now that you have a pure function, you can just assign it to h directly:

ClearAll[h]; 
h = GetFitProba[f, T, V, eta, cut, t];