GammaFunctionGenerator.cc

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//FAMOS headers
#include "FastSimulation/Utilities/interface/GammaFunctionGenerator.h"
#include "FastSimulation/Utilities/interface/RandomEngineAndDistribution.h"

GammaFunctionGenerator::GammaFunctionGenerator()
{
  xmax = 30.;

  for(unsigned i=1;i<=12;++i)
    {
      // For all let's put the limit at 2.*(alpha-1)      (alpha-1 is the max of the dist)
      approxLimit.push_back(2*((double)i));
      myIncompleteGamma.a().setValue((double)i);
      integralToApproxLimit.push_back(myIncompleteGamma(approxLimit[i-1]));
      theGammas.push_back(
       GammaNumericalGenerator((double)i,1.,0,approxLimit[i-1]+1.));
    }
  coreCoeff.push_back(0.);  // alpha=1 not used
  coreCoeff.push_back(1./8.24659e-01);
  coreCoeff.push_back(1./7.55976e-01);
  coreCoeff.push_back(1./7.12570e-01);
  coreCoeff.push_back(1./6.79062e-01);
  coreCoeff.push_back(1./6.65496e-01);
  coreCoeff.push_back(1./6.48736e-01);
  coreCoeff.push_back(1./6.25185e-01);
  coreCoeff.push_back(1./6.09188e-01);
  coreCoeff.push_back(1./6.06221e-01);
  coreCoeff.push_back(1./6.05057e-01);
}

GammaFunctionGenerator::~GammaFunctionGenerator() {}

double GammaFunctionGenerator::shoot(RandomEngineAndDistribution const* random) const
{
  if(alpha<0.) return -1.;
  if(badRange) return xmin/beta;
  if(alpha<12)
    {

      if (alpha == na)
    {
      return gammaInt(random)/beta;
    }
      else if (na == 0)
    {
      return gammaFrac(random)/beta;
    }
      else
    {
      double gi=gammaInt(random);
      double gf=gammaFrac(random);
      return (gi+gf)/beta;
    }
    }
  else
    {
      // an other generator has to be used in such a case
      return -1.;
    }
}

double GammaFunctionGenerator::gammaFrac(RandomEngineAndDistribution const* random) const
{
  /* This is exercise 16 from Knuth; see page 135, and the solution is
     on page 551.  */

  double p, q, x, u, v;
  p = M_E / (frac + M_E);
  do
    {
      u = random->flatShoot();
      v = random->flatShoot();

      if (u < p)
        {
          x = exp ((1 / frac) * log (v));
          q = exp (-x);
        }
      else
        {
          x = 1 - log (v);
          q = exp ((frac - 1) * log (x));
        }
    }
  while (random->flatShoot() >= q);

  return x;
}

double GammaFunctionGenerator::gammaInt(RandomEngineAndDistribution const* random) const
{
  // Exponential distribution : no approximation
  if(na==1)
    {
      return xmin-log(random->flatShoot());
    }

  unsigned gn=na-1;

  // are we sure to be in the tail 
  if(coreProba==0.)
    return xmin-coreCoeff[gn]*log(random->flatShoot());

  // core-tail interval
  if(random->flatShoot()<coreProba)
    {
      return theGammas[gn].gamma_lin(random);
    }
  //  std::cout << " Tail called " << std::endl;
  return approxLimit[gn]-coreCoeff[gn]*log(random->flatShoot());
}

void GammaFunctionGenerator::setParameters(double a,double b, double xm)
{
  //  std::cout << "Setting parameters " << std::endl;
  alpha=a;
  beta=b;
  xmin=xm*beta;
  if(xm>xmax) 
    {
      badRange=true;
      return;
    }
  badRange=false;
  na=0;
  
  if(alpha>0.&&alpha<12) 
    na=(unsigned)floor(alpha);

  frac=alpha-na;  
  // Now calculate the probability to shoot between approxLimit and xmax
  // The Incomplete gamma is normalized to 1 
  if(na<=1) return;
  
  myIncompleteGamma.a().setValue((double)na);
  
  unsigned gn=na-1;
  //  std::cout << " na " << na << " xm " << xm << " beta " << beta << " xmin " << xmin << " approxLimit " << approxLimit[gn] << std::endl;
  if(xmin>approxLimit[gn]) 
    {
      coreProba=0.;
    }
  else
    {
      double tmp=(xmin!=0.) ?myIncompleteGamma(xmin) : 0.;
      coreProba=(integralToApproxLimit[gn]-tmp)/(1.-tmp);
      theGammas[gn].setSubInterval(xmin,approxLimit[gn]);
    }
  //  std::cout << " Proba " << coreProba << std::endl;
}