Notebook

Integration¶

Numerical integration using R passing the function from ROOT

Author:
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, March 28, 2023 at 09:54 AM.

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%%cpp -d
#include<TMath.h>
#include<TRInterface.h>
#include<Math/Integrator.h>
#include<TF1.h>

To integrate using R the function must be vectorized The idea is just to receive a vector like an argument,to evaluate every element saving the result in another vector and return the resultant vector.

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%%cpp -d
std::vector<Double_t>  BreitWignerVectorized(std::vector<Double_t> xx)
{
   std::vector<Double_t> result(xx.size());
   for(Int_t i=0;i<xx.size();i++)
   {
      result[i]=TMath::BreitWigner(xx[i]);
   }
   return result;
}

Definition of a helper function:

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%%cpp -d
double BreitWignerWrap( double x){
   return TMath::BreitWigner(x);
}

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ROOT::R::TRInterface &r=ROOT::R::TRInterface::Instance();

r["BreitWigner"]=ROOT::R::TRFunctionExport(BreitWignerVectorized);

Double_t value=r.Eval("integrate(BreitWigner, lower = -2, upper = 2)$value");

std::cout.precision(18);
std::cout<<"Integral of the BreitWigner Function in the interval [-2, 2] R        = "<<value<<std::endl;


ROOT::Math::WrappedFunction<> wf(BreitWignerWrap);
ROOT::Math::Integrator i(wf);
value=i.Integral(-2,2);
std::cout<<"Integral of the BreitWigner Function in the interval [-2, 2] MathMore = "<<value<<std::endl;


TF1 f1("BreitWigner","BreitWignerWrap(x)");
value=f1.Integral(-2,2);
std::cout<<"Integral of the BreitWigner Function in the interval [-2, 2] TF1      = "<<value<<std::endl;

infinite limits

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value=r.Eval("integrate(BreitWigner, lower = -Inf, upper = Inf)$value");
std::cout<<"Integral of BreitWigner Function in the interval [-Inf, Inf] R    = "<<value<<std::endl;