cavata_prescription.cpp

//Created by KVClassFactory on Fri Jan 15 18:14:06 2010
//Author: John Frankland,,,
 
#include "cavata_prescription.h"
 
ClassImp(KVImpactParameters::cavata_prescription)
 
 
 
namespace KVImpactParameters {
   cavata_prescription::cavata_prescription(TH1* h, Option_t* evol)
   {
      fData = h;
      fEvol = evol;
      fIPScale = nullptr;
      fObsTransform = nullptr;
      Bmax = 1.0;
   }
 
 
 
 
   cavata_prescription::~cavata_prescription()
   {
      // Destructor
      SafeDelete(fIPScale);
      SafeDelete(fXSecScale);
      SafeDelete(fObsTransform);
   }
 
 
 
 
   void cavata_prescription::MakeScale(Int_t npoints, Double_t bmax)
   {
      // Calculate the relationship between the impact parameter and the observable
      // whose distribution is contained in the histogram given to the constructor.
      //
      // \param[in] npoints number of points to use to calculate scale (points in generated TGraph).
      // The greater the number of points, the more accurate the results.
      // Default value is 100. Maximum value is number of bins in histogram of observable, fData.
      // \param[in] bmax the maximum reduced impact parameter for the data
      //
      // For a given value \f$X\f$ of the observable \f$x\f$, the reduced impact parameter
      // \f$\hat{b}\f$ is calculated from the distribution of \f$x\f$, \f$Y(x)\f$, using the following formula:
      //\f[
      //\hat{b}^{2} = \frac{\int^{\infty}_{x=X} Y(x) dx}{\int_{0}^{\infty} Y(x) dx}
      //\f]
      //
      // \remark To obtain absolute values of impact parameter/cross-section use MakeAbsoluteScale().
 
      if (bmax > 1.0) {
         KVError::Warning(this, "MakeScale", "called with bmax>1.0 - calling MakeAbsoluteScale for absolute impact parameters");
         MakeAbsoluteScale(npoints, bmax);
         return;
      }
      Bmax = bmax;
      Smax = pow(bmax, 2.); //total reduced X-section
      make_scale(npoints);
   }
 
 
 
 
   void cavata_prescription::make_scale(Int_t npoints)
   {
      std::unique_ptr<TH1> cumul(HM.CumulatedHisto(fData, fEvol.Data(), -1, -1, "max"));
      Int_t nbins = cumul->GetNbinsX();
      Int_t first_bin = 1;
      Int_t last_bin = nbins;
      npoints = TMath::Min(nbins, npoints);
      fIPScale = new TGraph(npoints);
      fXSecScale = new TGraph(npoints);
      Double_t delta_bin = 1.*(last_bin - first_bin) / (npoints - 1.);
      Int_t bin;
      for (int i = 0; i < npoints; i++) {
         bin = first_bin + i * delta_bin;
         Double_t et12 = cumul->GetBinCenter(bin);
         Double_t b = Bmax * sqrt(cumul->GetBinContent(bin));
         Double_t sigma = Smax * cumul->GetBinContent(bin);
         fIPScale->SetPoint(i, et12, b);
         fXSecScale->SetPoint(i, et12, sigma);
      }
 
      fObsTransform = new TF1("fObsTransform", this, &cavata_prescription::BTransform,
                              fData->GetXaxis()->GetXmin(), fData->GetXaxis()->GetXmax(), 0, "KVImpactParameter", "BTransform");
      fObsTransformXSec = new TF1("fObsTransformXSec", this, &cavata_prescription::XTransform,
                                  fData->GetXaxis()->GetXmin(), fData->GetXaxis()->GetXmax(), 0, "KVImpactParameter", "XTransform");
   }
 
 
 
 
   void cavata_prescription::MakeAbsoluteScale(Int_t npoints, Double_t bmax)
   {
      // Calculate the relationship between the impact parameter and the observable
      // whose distribution is contained in the histogram given to the constructor.
      //
      // \param[in] npoints number of points to use to calculate scale (points in generated TGraph).
      // The greater the number of points, the more accurate the results.
      // Default value is 100. Maximum value is number of bins in histogram of observable, fData.
      // \param[in] bmax the maximum absolute impact parameter for the data in [fm]
      //
      // For a given value \f$X\f$ of the observable \f$x\f$, the reduced impact parameter
      // \f$\hat{b}\f$ is calculated from the distribution of \f$x\f$, \f$Y(x)\f$, using the following formula:
      //\f[
      //\hat{b}^{2} = \frac{\int^{\infty}_{x=X} Y(x) dx}{\int_{0}^{\infty} Y(x) dx}
      //\f]
      //
      // \remark To obtain reduced values of impact parameter/cross-section use MakeScale().
 
      Bmax = bmax;
      Smax = GetXSecFromIP(bmax); //total X-section in [mb]
      make_scale(npoints);
   }
 
 
 
 
   Double_t cavata_prescription::BTransform(Double_t* x, Double_t*)
   {
      // Function using the TGraph calculated with MakeScale() or MakeAbsoluteScale() in order to
      // transform distributions of the observable histogrammed in fData
      // into distributions of the impact parameter.
      //
      // This function is used to generate the TF1 fObsTransform
      //
      // \param[in] x[0] value of observable
 
      return fIPScale->Eval(*x);
   }
 
 
 
 
   Double_t cavata_prescription::XTransform(Double_t* x, Double_t*)
   {
      // Function using the TGraph calculated with MakeScale() or MakeAbsoluteScale() in order to
      // transform distributions of the observable histogrammed in fData
      // into distributions of cross-section.
      //
      // This function is used to generate the TF1 fObsTransformXsec
      //
      // \param[in] x[0] value of observable
 
      return fXSecScale->Eval(*x);
   }
 
 
 
 
   TH1* cavata_prescription::GetIPDistribution(TH1* obs, Int_t nbinx, Option_t* norm)
   {
      // Transform the distribution of the observable contained in the histogram 'obs'
      // into a distribution of the impact parameter.
      //
      // \param[in] obs pointer to histogram containing observable distribution for some selected events
      // \param[in] nbinx number of bins in created impact parameter histo (default = 100)
      // \param[in] norm
      // \parblock
      // - norm = "" (default)
      //   no adjustment is made for the change in bin width due to the transformation
      // - norm = "width"
      //   bin contents are adjusted for width change, so that the integral of the histogram
      //   contents taking into account the bin width (i.e. TH1::Integral("width")) is the same.
      // \endparblock
      // \return pointer to histogram filled with impact parameter distribution
 
      if (!fObsTransform) {
         KVError::Error(this, "GetIPDistribution", "Call MakeScale first to calculate correspondance observable<->i.p.");
         return 0;
      }
      return HM.ScaleHisto(obs, fObsTransform, 0, nbinx, -1, 0., Bmax, -1, -1, norm);
   }
 
 
 
 
   TGraph* cavata_prescription::GetIPEvolution(TH2* obscor, TString moment, TString axis)
   {
      // Draw evolution of any observable as function of impact parameter
      //
      // \param[in] obscor pointer to histogram containing bidim correlating some observable on Y axis with
      // the observable used to calculate the impact parameter on the X axis
      // \param[in] moment give moment of Y to use for evolution ("GetMean", "GetRMS", "GetKurtosis", etc. methods of TH1)
      // \param[in] axis
      // \parblock
      // - if the impact parameter observable is on the Y-axis of obscor, use axis="X"
      // - by default axis="Y", i.e. we assume that the I.P. observable is on the X axis)
      //\endparblock
      // \return pointer to TGraph giving evolution of given moment of Y as a function
      // of the impact parameter
 
      if (!fObsTransform) {
         KVError::Error(this, "GetIPEvolution", "Call MakeScale first to calculate correspondance observable<->i.p.");
         return 0;
      }
      TGraphErrors* gre = HM.GetMomentEvolution(obscor, moment, "", axis);
      TGraph* gr = HM.ScaleGraph(gre, fObsTransform, 0);
      delete gre;
      return gr;
   }
 
 
 
 
 
   TH1* cavata_prescription::GetXSecDistribution(TH1* obs, Int_t nbinx, Option_t* norm)
   {
      // Transform the distribution of the observable contained in the histogram obs
      // into a distribution of cross-section
      //
      // \param[in] obs pointer to histogram containing observable distribution for some selected events
      // \param[in] nbinx number of bins in created impact parameter histo (default = 100)
      // \param[in] norm
      // \parblock
      // - norm = "" (default)
      //   no adjustment is made for the change in bin width due to the transformation
      // - norm = "width"
      //   bin contents are adjusted for width change, so that the integral of the histogram
      //   contents taking into account the bin width (i.e. TH1::Integral("width")) is the same.
      // \endparblock
      // \return pointer to histogram filled with cross-section distribution
 
      if (!fObsTransformXSec) {
         KVError::Error(this, "GetXSecDistribution", "Call MakeScale first to calculate correspondance observable<->i.p.");
         return 0;
      }
      return HM.ScaleHisto(obs, fObsTransformXSec, 0, nbinx, -1, 0., Smax, -1, -1, norm);
   }
 
 
 
 
   TGraph* cavata_prescription::GetXSecEvolution(TH2* obscor, TString moment, TString axis)
   {
      // Draw evolution of any observable as function of cross-section
      //
      // \param[in] obscor pointer to histogram containing bidim correlating some observable on Y axis with
      // the observable used to calculate the impact parameter on the X axis
      // \param[in] moment give moment of Y to use for evolution ("GetMean", "GetRMS", "GetKurtosis", etc. methods of TH1)
      // \param[in] axis
      // \parblock
      // - if the impact parameter observable is on the Y-axis of obscor, use axis="X"
      // - by default axis="Y", i.e. we assume that the I.P. observable is on the X axis)
      //\endparblock
      // \return pointer to TGraph giving evolution of given moment of Y as a function
      // of cross-section
 
 
      if (!fObsTransformXSec) {
         KVError::Error(this, "GetXSecEvolution", "Call MakeScale first to calculate correspondance observable<->i.p.");
         return 0;
      }
      TGraphErrors* gre = HM.GetMomentEvolution(obscor, moment, "", axis);
      TGraph* gr = HM.ScaleGraph(gre, fObsTransformXSec, 0);
      delete gre;
      return gr;
   }
 
 
 
 
   std::vector<Double_t> cavata_prescription::SliceXSec(Int_t nslices, Double_t totXsec)
   {
      // Generate vector of observable values which can be used to select nslices
      // of constant cross-section.
      //
      // \note the vector will contain (nslices-1) values
      //
      // \param[in] nslices number of slices to generates
      // \param[in] totXsec total cross-section to slice
      // \returns vector containing (nslices-1) values of the observable to make cuts
      //
      // Example:
      //~~~~~~~~~~~~{.cpp}
      //     KVImpactParameter ip(data);    // histo containing observable distribution
      //     ip.MakeAbsoluteScale(100,ip.GetIPFromXSec(data->Integral()))
      //     std::vector<Double_t> slices = ip.SliceXSec(5, Xsec);
      //     if(obs > slices[0]){
      //            // most central events (observable increases when b decreases)
      //            // with cross-section Xsec/5
      //     } else if(obs > slices[1]){
      //            // next most central events, cross-section=Xsec/5
      //     }
      //      ...
      //     } else if(obs > slices[3]){
      //            // next-to-most-peripheral events
      //     } else {
      //            // most peripheral events (obs < slices[3])
      //     }
      //~~~~~~~~~~~~
 
      Double_t xsecSlice = totXsec / double(nslices);
      std::vector<Double_t> slices(nslices - 1);
      for (int i = 0; i < nslices - 1; ++i) {
         slices[i] = GetObservableXSec((i + 1) * xsecSlice);
      }
      return slices;
   }
 
 
 
 
   double cavata_prescription::GetMeanBForSCA(double bmin, double bmax) const
   {
      // Calculate the mean impact parameter for b in [bmin,bmax]
      // in sharp cut-off approximation i.e. assuming a triangular distribution:
      //\f[
      //\bar{b} = \frac{2(b^3_{max}-b^3_{min})}{3(b^2_{max}-b^2_{min})}
      //\f]
 
      return (2. / 3.) * (pow(bmax, 3) - pow(bmin, 3)) / (pow(bmax, 2) - pow(bmin, 2));
   }
 
 
 
 
   double cavata_prescription::GetSigmaBForSCA(double bmin, double bmax) const
   {
      // Calculate the standard deviation of impact parameter for b in [bmin,bmax]
      // in sharp cut-off approximation i.e. assuming a triangular distribution:
      //\f[
      //\sigma^2_b = \frac{(b^4_{max}-b^4_{min})}{2(b^2_{max}-b^2_{min})} - \bar{b}^2
      //\f]
 
      return sqrt(0.5 * (pow(bmax, 4) - pow(bmin, 4)) / (pow(bmax, 2) - pow(bmin, 2)) - pow(GetMeanBForSCA(bmin, bmax), 2));
   }
 
 
}