ErrorIntegral.C

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/// \file
/// \ingroup tutorial_fit
/// \notebook -js
/// Estimate the error in the integral of a fitted function
/// taking into account the errors in the parameters resulting from the fit.
/// The error is estimated also using the correlations values obtained from
/// the fit
///
/// run the macro doing:
///
/// ~~~{.cpp}
///  .x ErrorIntegral.C
/// ~~~
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \author Lorenzo Moneta

#include "TF1.h"
#include "TH1D.h"
#include "TVirtualFitter.h"
#include "TMath.h"
#include <assert.h>
#include <iostream>
#include <cmath>

TF1 * fitFunc;  // fit function pointer

const int NPAR = 2; // number of function parameters;

//____________________________________________________________________
double f(double * x, double * p) {
   // function used to fit the data
   return p[1]*TMath::Sin( p[0] * x[0] );
}

//____________________________________________________________________
void ErrorIntegral() {
   fitFunc = new TF1("f",f,0,1,NPAR);
   TH1D * h1     = new TH1D("h1","h1",50,0,1);

   double  par[NPAR] = { 3.14, 1.};
   fitFunc->SetParameters(par);

   h1->FillRandom("f",1000); // fill histogram sampling fitFunc
   fitFunc->SetParameter(0,3.);  // vary a little the parameters
   h1->Fit(fitFunc);             // fit the histogram

   h1->Draw();

   /* calculate the integral*/
   double integral = fitFunc->Integral(0,1);

   TVirtualFitter * fitter = TVirtualFitter::GetFitter();
   assert(fitter != 0);
   double * covMatrix = fitter->GetCovarianceMatrix();

   /* using new function in TF1 (from 12/6/2007)*/
   double sigma_integral = fitFunc->IntegralError(0,1);

   std::cout << "Integral = " << integral << " +/- " << sigma_integral
             << std::endl;

   // estimated integral  and error analytically

   double * p = fitFunc->GetParameters();
   double ic  = p[1]* (1-std::cos(p[0]) )/p[0];
   double c0c = p[1] * (std::cos(p[0]) + p[0]*std::sin(p[0]) -1.)/p[0]/p[0];
   double c1c = (1-std::cos(p[0]) )/p[0];

   // estimated error with correlations
   double sic = std::sqrt( c0c*c0c * covMatrix[0] + c1c*c1c * covMatrix[3]
      + 2.* c0c*c1c * covMatrix[1]);

   if ( std::fabs(sigma_integral-sic) > 1.E-6*sic )
      std::cout << " ERROR: test failed : different analytical  integral : "
                << ic << " +/- " << sic << std::endl;
}