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exampleFit3D¶

example of fitting a 3D function Typical multidimensional parametric regression where the predictor depends on 3 variables

In the case of 1 or 2D one can use the TGraph classes but since no TGraph3D class exists this tutorial provide an example of fitting 3D points

Author: Lorenzo Moneta
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, March 27, 2023 at 09:47 AM.

In [1]:

const int n = 1000;
double x[n], y[n], z[n], v[n];
double ev = 0.1;

generate the data

In [2]:

TRandom2 r;
for (int i = 0; i < n; ++i) {
   x[i] = r.Uniform(0,10);
   y[i] = r.Uniform(0,10);
   z[i] = r.Uniform(0,10);
   v[i] = sin(x[i] ) + cos(y[i]) + z[i] + r.Gaus(0,ev);
}

create a 3d binned data structure

In [3]:

ROOT::Fit::BinData data(n,3);
double xx[3];
for(int i = 0; i < n; ++i) {
   xx[0] = x[i];
   xx[1] = y[i];
   xx[2] = z[i];
   // add the 3d-data coordinate, the predictor value (v[i])  and its errors
   data.Add(xx, v[i], ev);
}

TF3 * f3 = new TF3("f3","[0] * sin(x) + [1] * cos(y) + [2] * z",0,10,0,10,0,10);
f3->SetParameters(2,2,2);
ROOT::Fit::Fitter fitter;

input_line_53:2:2: warning: 'data' shadows a declaration with the same name in the 'std' namespace; use '::data' to reference this declaration
 ROOT::Fit::BinData data(n,3);
 ^

wrapped the TF1 in a IParamMultiFunction interface for the Fitter class

In [4]:

ROOT::Math::WrappedMultiTF1 wf(*f3,3);
fitter.SetFunction(wf);

In [5]:

bool ret = fitter.Fit(data);
if (ret) {
   const ROOT::Fit::FitResult & res = fitter.Result();
   // print result (should be around 1)
   res.Print(std::cout);
   // copy all fit result info (values, chi2, etc..) in TF3
   f3->SetFitResult(res);
   // test fit p-value (chi2 probability)
   double prob = res.Prob();
   if (prob < 1.E-2)
      Error("exampleFit3D","Bad data fit - fit p-value is %f",prob);
   else
      std::cout << "Good fit : p-value  = " << prob << std::endl;

}
else
   Error("exampleFit3D","3D fit failed");

input_line_58:2:24: error: reference to 'data' is ambiguous
 bool ret = fitter.Fit(data);
                       ^
input_line_53:2:21: note: candidate found by name lookup is 'data'
 ROOT::Fit::BinData data(n,3);
                    ^
/usr/include/c++/9/bits/range_access.h:318:5: note: candidate found by name lookup is 'std::data'
    data(initializer_list<_Tp> __il) noexcept
    ^
/usr/include/c++/9/bits/range_access.h:289:5: note: candidate found by name lookup is 'std::data'
    data(_Container& __cont) noexcept(noexcept(__cont.data()))
    ^
/usr/include/c++/9/bits/range_access.h:299:5: note: candidate found by name lookup is 'std::data'
    data(const _Container& __cont) noexcept(noexcept(__cont.data()))
    ^
/usr/include/c++/9/bits/range_access.h:309:5: note: candidate found by name lookup is 'std::data'
    data(_Tp (&__array)[_Nm]) noexcept
    ^