DoubleCrystalBallGenerator.cc

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//FAMOS headers
#include "FastSimulation/Utilities/interface/DoubleCrystalBallGenerator.h"
#include "FastSimulation/Utilities/interface/RandomEngineAndDistribution.h"
 
//ROOT headers
#include "TMath.h"
#include <iostream>
 
using namespace TMath;
 
double DoubleCrystalBallGenerator::shoot(
    double mu, double sigma, double aL, double nL, double aR, double nR, RandomEngineAndDistribution const* random) {
  if (nL <= 1 || nR <= 1)
    return 0;  //n>1 required
 
  double dL = nL / aL;
  double dR = nR / aR;
  double N = 1 / (sigma * (nL / aL * 1 / (nL - 1) * Exp(-aL * aL / 2) +
                           Sqrt(Pi() / 2) * (Erf(aL / Sqrt(2)) + Erf(aR / Sqrt(2))) +
                           nR / aR * 1 / (nR - 1) * Exp(-aR * aR / 2)));
 
  //start x as NaN
  double x = 0. / 0.;
  while (!Finite(x)) {
    //shoot a flat random number
    double y = random->flatShoot();
 
    //check range
    //crystal ball CDF changes at (x-mu)/sigma = -aL && (x-mu)/sigma = aR
    //compute this in pieces because it is awful
    double AL = dL / (nL - 1) * Exp(-aL * aL / 2);
    double CL = Sqrt(Pi() / 2) * Erf(aL / Sqrt(2));
    double CR = Sqrt(Pi() / 2) * Erf(aR / Sqrt(2));
    if (y < sigma * N * AL) {  //below lower boundary, use inverted power law CDF (left side)
      double BL = dL / (nL - 1) * Exp(-aL * aL / 2);
      x = mu + sigma * (-dL * Power(y / (sigma * N * BL), 1 / (-nL + 1)) - aL + dL);
    } else if (y > sigma * N * (AL + CL + CR)) {  //above lower boundary, use inverted power law CDF (right side)
      double AR = dR / (nR - 1) * Exp(-aR * aR / 2);
      double BR = dR / (1 - nR) * Exp(-aR * aR / 2);
      double D = (y / (sigma * N) - AL - CL - CR - AR) / BR;
      x = mu + sigma * (dR * Power(D, 1 / (-nR + 1)) + aR - dR);
    } else {  //between boundaries, use gaussian CDF with proper normalization (in terms of erfc)
      double D = 1 - Sqrt(2 / Pi()) * (y / (sigma * N) - AL - CL);
      x = mu + sigma * Sqrt(2) * ErfcInverse(D);
    }
  }
  return x;
}