Pass a 3D function with parameters to the minimizer

[uzair90]

Hello,

I am trying to pass a 3-D function with parameters to the minimizer. I define my 3D function like:

double MinimizeXYZROOT(double *xx, double *params){

  const Double_t x = xx[0];
  const Double_t y = xx[1];
  const Double_t z = xx[2];
  
  double *p = (double *)params;  
.............
.............
return value;
}

This is the way I am trying to do the minimisation right now:

..................................
.................................

TF3 *f3=new TF3("",MinimizeXYZROOT,-500,500,-500,500,0.00001,1000);
  
  ROOT::Math::WrappedTF3 f(f3);

  for(int ipar=0;ipar<iEnt;ipar++){
    f3->SetParameter(ipar,ParArray[ipar]);    
  }

  minimum->SetFunction(f);
.........................
.........................

Can someone please guide me on how to pass a 3D function with parameters to the minimizer?

Thanks,
Uzair

ROOT Version: 6.20/04
Platform: Ubuntu 20.04.1
Compiler: 9.3.0

---

[moneta]

Hi,

I presume you want to minimize f(x,y,z|p) given the parameters p and not finding the best values of the paramters p, given some x,y,z values.

In that case, you have two possibilities:

1. Create a TF3 class and then call TF3::GetMinimumXYZ(), see
   https://root.cern.ch/doc/v608/classTF3.html#a663ab974987bd018a8a51976cc778ade
   In this case Minuit is used by default but you can change the Minimizer by calling before,
   ROOT::Math::MinimizerOptions::SetDefaultMinimizer( minimizerName)

   Possible choices for minimizerName are:

   - Minuit, Minuit2, GSLMultiMin, GSLSimAn, Genetic 
   

   The correct way to create a TF3 is also

   TF3 *f3=new TF3("",MinimizeXYZROOT,-500,500,-500,500,0.00001,1000, npar);
   

   where npar is the number of function parameters

2. You use directly the MInimizer interface as shown in this tutorial:
   https://root.cern/doc/master/NumericalMinimization_8C.html

   In this case, it is still convenient to create a TF3 and then you pass the TF3 to the minimizer, by
   wrapping using the `ROOT::Math::WrappedMultiTF1’ class. For example doing:

   TF3 *f3=new TF3("",MinimizeXYZROOT,-500,500,-500,500,0.00001,1000, npar);
   f3->SetParameters(......)
   ROOT::Math::WrappedMultiTF1 f(*f3);
   ROOT::Math::Minimizer* minimum = ROOT::Math::Factory::CreateMinimizer(minName, algoName);
   minimum->SetFunction(f);
   // use same code as tutorial (set variables passing initial values and step sizes)
   minimum->SetVariable(0,"x",variable[0], step[0]);
   minimum->SetVariable(1,"y",variable[1], step[1]);
   minimum->SetVariable(2,"z",variable[2], step[2]);
   // minimize function
   minimum->Minimize();
   

Cheers

Lorenzo

[uzair90]

Thank you Lorenzo! The first case worked perfectly. Regarding the second case I am having a problem. When I say:

ROOT::Math::WrappedMultiTF1 f(f3);

Root says that it is not defined and there is no such class. Can you please guide me here?

Thanks,
Uzair

[moneta]

Hi

Sorry , there was an error in my code (I have updated now). The line should be:

ROOT::Math::WrappedMultiTF1 f(*f3);

Actually ROOT::Math::WrappedMultiTF1 is a typedef to ROOT::Math::WrappedMultiTF1Templ<double>, but it should be recognized by ROOT and work fine

Lorenzo