RooCBShape.cxx

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/*****************************************************************************
 * Project: RooFit                                                           *
 * Package: RooFitModels                                                     *
 * @(#)root/roofit:$Id$
 * Authors:                                                                  *
 *   WV, Wouter Verkerke, UC Santa Barbara, verkerke@slac.stanford.edu       *
 *   DK, David Kirkby,    UC Irvine,         dkirkby@uci.edu                 *
 *                                                                           *
 * Copyright (c) 2000-2005, Regents of the University of California          *
 *                          and Stanford University. All rights reserved.    *
 *                                                                           *
 * Redistribution and use in source and binary forms,                        *
 * with or without modification, are permitted according to the terms        *
 * listed in LICENSE (http://roofit.sourceforge.net/license.txt)             *
 *****************************************************************************/
 
/** \class RooCBShape
    \ingroup Roofit
 
PDF implementing the Crystal Ball line shape.
**/
 
#include "RooCBShape.h"
 
#include "RooAbsReal.h"
#include "RooRealVar.h"
#include "RooMath.h"
#include "RooBatchCompute.h"
 
#include "TMath.h"
 
#include <cmath>
 
using namespace std;
 
ClassImp(RooCBShape);
 
////////////////////////////////////////////////////////////////////////////////
 
Double_t RooCBShape::ApproxErf(Double_t arg) const
{
  static const double erflim = 5.0;
  if( arg > erflim )
    return 1.0;
  if( arg < -erflim )
    return -1.0;
 
  return RooMath::erf(arg);
}
 
////////////////////////////////////////////////////////////////////////////////
 
RooCBShape::RooCBShape(const char *name, const char *title,
             RooAbsReal& _m, RooAbsReal& _m0, RooAbsReal& _sigma,
             RooAbsReal& _alpha, RooAbsReal& _n) :
  RooAbsPdf(name, title),
  m("m", "Dependent", this, _m),
  m0("m0", "M0", this, _m0),
  sigma("sigma", "Sigma", this, _sigma),
  alpha("alpha", "Alpha", this, _alpha),
  n("n", "Order", this, _n)
{
}
 
////////////////////////////////////////////////////////////////////////////////
 
RooCBShape::RooCBShape(const RooCBShape& other, const char* name) :
  RooAbsPdf(other, name), m("m", this, other.m), m0("m0", this, other.m0),
  sigma("sigma", this, other.sigma), alpha("alpha", this, other.alpha),
  n("n", this, other.n)
{
}
 
////////////////////////////////////////////////////////////////////////////////
 
Double_t RooCBShape::evaluate() const {
  Double_t t = (m-m0)/sigma;
  if (alpha < 0) t = -t;
 
  Double_t absAlpha = fabs((Double_t)alpha);
 
  if (t >= -absAlpha) {
    return exp(-0.5*t*t);
  }
  else {
    Double_t a =  TMath::Power(n/absAlpha,n)*exp(-0.5*absAlpha*absAlpha);
    Double_t b= n/absAlpha - absAlpha;
 
    return a/TMath::Power(b - t, n);
  }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute multiple values of Crystal ball Shape distribution.  
RooSpan<double> RooCBShape::evaluateSpan(RooBatchCompute::RunContext& evalData, const RooArgSet* normSet) const {
  return RooBatchCompute::dispatch->computeCBShape(this, evalData, m->getValues(evalData, normSet), m0->getValues(evalData, normSet), sigma->getValues(evalData, normSet), alpha->getValues(evalData, normSet), n->getValues(evalData, normSet));
}
 
////////////////////////////////////////////////////////////////////////////////
 
Int_t RooCBShape::getAnalyticalIntegral(RooArgSet& allVars, RooArgSet& analVars, const char* /*rangeName*/) const
{
  if( matchArgs(allVars,analVars,m) )
    return 1 ;
 
  return 0;
}
 
////////////////////////////////////////////////////////////////////////////////
 
Double_t RooCBShape::analyticalIntegral(Int_t code, const char* rangeName) const
{
  static const double sqrtPiOver2 = 1.2533141373;
  static const double sqrt2 = 1.4142135624;
 
  R__ASSERT(code==1);
  double result = 0.0;
  bool useLog = false;
 
  if( fabs(n-1.0) < 1.0e-05 )
    useLog = true;
 
  double sig = fabs((Double_t)sigma);
 
  double tmin = (m.min(rangeName)-m0)/sig;
  double tmax = (m.max(rangeName)-m0)/sig;
 
  if(alpha < 0) {
    double tmp = tmin;
    tmin = -tmax;
    tmax = -tmp;
  }
 
  double absAlpha = fabs((Double_t)alpha);
 
  if( tmin >= -absAlpha ) {
    result += sig*sqrtPiOver2*(   ApproxErf(tmax/sqrt2)
                                - ApproxErf(tmin/sqrt2) );
  }
  else if( tmax <= -absAlpha ) {
    double a = TMath::Power(n/absAlpha,n)*exp(-0.5*absAlpha*absAlpha);
    double b = n/absAlpha - absAlpha;
 
    if(useLog) {
      result += a*sig*( log(b-tmin) - log(b-tmax) );
    }
    else {
      result += a*sig/(1.0-n)*(   1.0/(TMath::Power(b-tmin,n-1.0))
                                - 1.0/(TMath::Power(b-tmax,n-1.0)) );
    }
  }
  else {
    double a = TMath::Power(n/absAlpha,n)*exp(-0.5*absAlpha*absAlpha);
    double b = n/absAlpha - absAlpha;
 
    double term1 = 0.0;
    if(useLog) {
      term1 = a*sig*(  log(b-tmin) - log(n/absAlpha));
    }
    else {
      term1 = a*sig/(1.0-n)*(   1.0/(TMath::Power(b-tmin,n-1.0))
                              - 1.0/(TMath::Power(n/absAlpha,n-1.0)) );
    }
 
    double term2 = sig*sqrtPiOver2*(   ApproxErf(tmax/sqrt2)
                                     - ApproxErf(-absAlpha/sqrt2) );
 
 
    result += term1 + term2;
  }
 
  return result != 0. ? result : 1.E-300;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Advertise that we know the maximum of self for given (m0,alpha,n,sigma)
 
Int_t RooCBShape::getMaxVal(const RooArgSet& vars) const
{
   RooArgSet dummy ;
 
  if (matchArgs(vars,dummy,m)) {
     return 1 ;
   }
  return 0 ;
}
 
////////////////////////////////////////////////////////////////////////////////
 
Double_t RooCBShape::maxVal(Int_t code) const
{
  R__ASSERT(code==1) ;
 
  // The maximum value for given (m0,alpha,n,sigma)
  // is 1./ Integral in the variable range
  return 1.0/analyticalIntegral(1) ;
}