// test_integrator_limits.cpp
//
// Author : Jeromy Tompkins
// Date   : 8/6/2012
//
// Purpose: Investigate the effect that the abs and rel tolerance
//    parameters have on the precision of the result generated by 
//    the VEGAS MC integrator.


#include "Math/IntegratorMultiDim.h"
#include "Math/WrappedFunction.h"
#include "TMath.h"
#include "TGraph.h"
#include <iostream>
#include <iomanip>

Double_t func(const Double_t* x)
{
  return TMath::Sin(x[0])*TMath::Sin(x[0])*x[1]*x[1];
}


int main()
{
  Double_t abs_tolerance = 1.0e-8;
  Double_t rel_tolerance = 1.0e-10;

  ROOT::Math::IntegratorMultiDim integ(ROOT::Math::IntegrationMultiDim::kVEGAS, 
				       abs_tolerance, 
				       rel_tolerance);

  ROOT::Math::WrappedMultiFunction<> f(&::func, 2);

  Double_t xlow[] = {-1.0, 1.0};
  Double_t xhi[]  = {   0, 5.0};

  std::cout << std::fixed << std::setprecision(15);
      
  UInt_t npoints = 100;
  TGraph* gr = new TGraph(npoints);
  
  for (UInt_t i=0; i<npoints; i++)
    {

      Double_t res = integ.Integral(f,xlow,xhi);
      std::cout << "\n" << std::setw(4) << i << std::setw(25) << res;

      gr->SetPoint(i,i,res);
    }

  std::cout << "\n-------------------------------------------" << std::endl;
  std::cout << std::scientific << std::setprecision(3);
  std::cout << "\nAbsTol = " << std::setw(12) << abs_tolerance;
  std::cout << "\nRelTol = " << std::setw(12) << rel_tolerance;
  std::cout << "\nMean   = " << std::setw(12) << gr->GetMean(2);
  std::cout << "\nRMS    = " << std::setw(12) << gr->GetRMS(2);
  std::cout << "\n" << std::endl;

  delete gr;
  return 0;
}