RooPoisson.cxx

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 /*****************************************************************************
  * Project: RooFit                                                           *
  *                                                                           *
  * Simple Poisson PDF
  * author: Kyle Cranmer <cranmer@cern.ch>
  *                                                                           *
  *****************************************************************************/
 
/** \class RooPoisson
    \ingroup Roofit
 
Poisson pdf
**/
 
#include "RooPoisson.h"
 
#include "RooAbsReal.h"
#include "RooAbsCategory.h"
 
#include "RooRandom.h"
#include "RooMath.h"
#include "TMath.h"
#include "Math/ProbFuncMathCore.h"
 
#include "TError.h"
 
#include <limits>
 
using namespace std;
 
ClassImp(RooPoisson);
 
////////////////////////////////////////////////////////////////////////////////
/// Constructor
 
RooPoisson::RooPoisson(const char *name, const char *title,
             RooAbsReal& _x,
             RooAbsReal& _mean,
             Bool_t noRounding) :
  RooAbsPdf(name,title),
  x("x","x",this,_x),
  mean("mean","mean",this,_mean),
  _noRounding(noRounding),
  _protectNegative(false)
{
}
 
////////////////////////////////////////////////////////////////////////////////
/// Copy constructor
 
 RooPoisson::RooPoisson(const RooPoisson& other, const char* name) :
   RooAbsPdf(other,name),
   x("x",this,other.x),
   mean("mean",this,other.mean),
   _noRounding(other._noRounding),
   _protectNegative(other._protectNegative)
{
}
 
////////////////////////////////////////////////////////////////////////////////
/// Implementation in terms of the TMath Poisson function
 
Double_t RooPoisson::evaluate() const
{
  Double_t k = _noRounding ? x : floor(x);
  if(_protectNegative && mean<0)
    return 1e-3;
  return TMath::Poisson(k,mean) ;
}
 
////////////////////////////////////////////////////////////////////////////////
/// calculate and return the negative log-likelihood of the Poisson
 
Double_t RooPoisson::getLogVal(const RooArgSet* s) const
{
  return RooAbsPdf::getLogVal(s) ;
//   Double_t prob = getVal(s) ;
//   return prob ;
 
  // Make inputs to naming conventions of RooAbsPdf::extendedTerm
  Double_t expected=mean ;
  Double_t observed=x ;
 
  // Explicitly handle case Nobs=Nexp=0
  if (fabs(expected)<1e-10 && fabs(observed)<1e-10) {
    return 0 ;
  }
 
  // Explicitly handle case Nexp=0
  if (fabs(observed)<1e-10) {
    return -1*expected;
  }
 
  // Michaels code for log(poisson) in RooAbsPdf::extendedTer with an approximated log(observed!) term
  Double_t extra=0;
  if(observed<1000000) {
    extra = -observed*log(expected)+expected+TMath::LnGamma(observed+1.);
  } else {
    //if many observed events, use Gauss approximation
    Double_t sigma_square=expected;
    Double_t diff=observed-expected;
    extra=-log(sigma_square)/2 + (diff*diff)/(2*sigma_square);
  }
 
//   if (fabs(extra)>100 || log(prob)>100) {
//     cout << "RooPoisson::getLogVal(" << GetName() << ") mu=" << expected << " x = " << x << " -log(P) = " << extra << " log(evaluate()) = " << log(prob) << endl ;
//   }
 
//   if (fabs(extra+log(prob))>1) {
//     cout << "RooPoisson::getLogVal(" << GetName() << ") WARNING mu=" << expected << " x = " << x << " -log(P) = " << extra << " log(evaluate()) = " << log(prob) << endl ;
//   }
 
  //return log(prob);
  return -extra-analyticalIntegral(1,0) ; //log(prob);
 
}
 
////////////////////////////////////////////////////////////////////////////////
 
Int_t RooPoisson::getAnalyticalIntegral(RooArgSet& allVars, RooArgSet& analVars, const char* /*rangeName*/) const
{
  if (matchArgs(allVars,analVars,x)) return 1 ;
  if (matchArgs(allVars, analVars, mean)) return 2;
  return 0 ;
}
 
////////////////////////////////////////////////////////////////////////////////
 
Double_t RooPoisson::analyticalIntegral(Int_t code, const char* rangeName) const
{
  R__ASSERT(code == 1 || code == 2) ;
 
  if(_protectNegative && mean<0)
    return exp(-2*mean); // make it fall quickly
 
  if (code == 1) {
    // Implement integral over x as summation. Add special handling in case
    // range boundaries are not on integer values of x
    const double xmin = std::max(0., x.min(rangeName));
    const double xmax = x.max(rangeName);
 
    if (xmax < 0. || xmax < xmin) {
      return 0.;
    }
    if (!x.hasMax() || RooNumber::isInfinite(xmax)) {
      //Integrating the full Poisson distribution here 
      return 1.;
    }
 
    // The range as integers. ixmin is included, ixmax outside.
    const unsigned int ixmin = xmin;
    const unsigned int ixmax = std::min(xmax + 1.,
                                        (double)std::numeric_limits<unsigned int>::max());
    
    // Sum from 0 to just before the bin outside of the range.
    if (ixmin == 0) {
      return ROOT::Math::poisson_cdf(ixmax - 1, mean);
    }
    else {
      // If necessary, subtract from 0 to the beginning of the range
      if (ixmin <= mean) {
        return ROOT::Math::poisson_cdf(ixmax - 1, mean) - ROOT::Math::poisson_cdf(ixmin - 1, mean);
      }
      else {
        //Avoid catastrophic cancellation in the high tails:
        return ROOT::Math::poisson_cdf_c(ixmin - 1, mean) - ROOT::Math::poisson_cdf_c(ixmax - 1, mean);
      }
 
    }
 
  } else if(code == 2) {
 
    // the integral with respect to the mean is the integral of a gamma distribution
    Double_t mean_min = mean.min(rangeName);
    Double_t mean_max = mean.max(rangeName);
 
    Double_t ix;
    if(_noRounding) ix = x + 1;
    else ix = Int_t(TMath::Floor(x)) + 1.0; // negative ix does not need protection (gamma returns 0.0)
 
    return ROOT::Math::gamma_cdf(mean_max, ix, 1.0) - ROOT::Math::gamma_cdf(mean_min, ix, 1.0);
  }
 
  return 0;
 
}
 
////////////////////////////////////////////////////////////////////////////////
/// Advertise internal generator in x
 
Int_t RooPoisson::getGenerator(const RooArgSet& directVars, RooArgSet &generateVars, Bool_t /*staticInitOK*/) const
{
  if (matchArgs(directVars,generateVars,x)) return 1 ;
  return 0 ;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Implement internal generator using TRandom::Poisson
 
void RooPoisson::generateEvent(Int_t code)
{
  R__ASSERT(code==1) ;
  Double_t xgen ;
  while(1) {
    xgen = RooRandom::randomGenerator()->Poisson(mean);
    if (xgen<=x.max() && xgen>=x.min()) {
      x = xgen ;
      break;
    }
  }
  return;
}