TFractionFitter

class TFractionFitter : public TObject

    private:

      void CheckConsistency()
      void CheckParNo(Int_t parm) const
      void ComputeChisquareLambda()
      void ComputeFCN(Int_t& npar, Double_t* gin, Double_t& f, Double_t* par, Int_t flag)
      void FindPrediction(int bin, double* fractions, double& Ti, int& k0, double& Aki) const
      void GetRanges(Int_t& minX, Int_t& maxX, Int_t& minY, Int_t& maxY, Int_t& minZ, Int_t& maxZ) const

    public:

                      TFractionFitter()
                      TFractionFitter(TH1* data, TObjArray* MCs)
              virtual ~TFractionFitter()
       static TClass* Class()
                 void Constrain(Int_t parm, Double_t low, Double_t high)
                 void ErrorAnalysis(Double_t UP)
                Int_t Fit()
             Double_t GetChisquare() const
      TVirtualFitter* GetFitter() const
                 TH1* GetMCPrediction(Int_t parm) const
                Int_t GetNDF() const
                 TH1* GetPlot()
             Double_t GetProb() const
                 void GetResult(Int_t parm, Double_t& value, Double_t& error) const
      virtual TClass* IsA() const
                 void ReleaseRangeX()
                 void ReleaseRangeY()
                 void ReleaseRangeZ()
                 void SetData(TH1* data)
                 void SetMC(Int_t parm, TH1* MC)
                 void SetRangeX(Int_t low, Int_t high)
                 void SetRangeY(Int_t low, Int_t high)
                 void SetRangeZ(Int_t low, Int_t high)
                 void SetWeight(Int_t parm, TH1* weight)
         virtual void ShowMembers(TMemberInspector& insp, char* parent)
         virtual void Streamer(TBuffer& b)
                 void StreamerNVirtual(TBuffer& b)
                 void UnConstrain(Int_t parm)

Data Members

    protected:

         Bool_t fFitDone       flags whether a valid fit has been performed
          Int_t fLowLimitX     first bin in X dimension
          Int_t fHighLimitX    last  bin in X dimension
          Int_t fLowLimitY     first bin in Y dimension
          Int_t fHighLimitY    last  bin in Y dimension
          Int_t fLowLimitZ     first bin in Z dimension
          Int_t fHighLimitZ    last  bin in Z dimension
          Int_t fNpfits        Number of points used in the fit
          Int_t fNDF           Number of degrees of freedom in the fit
       Double_t fChisquare     Template fit chisquare
      TObjArray fAji           array of pointers to predictions of real template distributions
           TH1* fData          pointer to the "data" histogram to be fitted to
      TObjArray fMCs           array of pointers to template histograms
      TObjArray fWeights       array of pointers to corresponding weight factors (may be null)
       Double_t fIntegralData  "data" histogram content integral over allowed fit range
      Double_t* fIntegralMCs   same for template histograms (weights not taken into account)
      Double_t* fFractions     template fractions scaled to the "data" histogram statistics
           TH1* fPlot          pointer to histogram containing summed template predictions
          Int_t fNpar          number of fit parameters

Class Description

 Fits MC fractions to data histogram (a la HMCMLL, see R. Barlow and C. Beeston,
 Comp. Phys. Comm. 77 (1993) 219-228, and http://www.hep.man.ac.uk/~roger/hfrac.f).

 The virtue of this fit is that it takes into account both data and Monte Carlo
 statistical uncertainties. The way in which this is done is through a standard
 likelihood fit using Poisson statistics; however, the template (MC) predictions
 are also varied within statistics, leading to additional contributions to the
 overall likelihood. This leads to many more fit parameters (one per bin per
 template), but the minimisation with respect to these additional parameters is
 done analytically rather than introducing them as formal fit parameters. Some
 special care needs to be taken in the case of bins with zero content. For more
 details please see the original publication cited above.

 An example application of this fit is given below. For a TH1* histogram
 ("data") fitted as the sum of three Monte Carlo sources ("mc"):

 {
   TH1F *data;                              //data histogram
   TH1F *mc0;                               // first MC histogram
   TH1F *mc1;                               // second MC histogram
   TH1F *mc2;                               // third MC histogram
   ....                                     // retrieve histograms
   TObjArray *mc = new TObjArray(3);        // MC histograms are put in this array
   mc->Add(mc0);
   mc->Add(mc1);
   mc->Add(mc2);
   TFractionFitter* fit = new TFractionFitter(data, mc); // initialise
   fit->Constrain(1,0.0,1.0);               // constrain fraction 1 to be between 0 and 1
   fit->SetRangeX(1,15);                    // use only the first 15 bins in the fit
   Int_t status = fit->Fit();               // perform the fit
   cout << "fit status: " << status << endl;
   if (status == 0) {                       // check on fit status
     TH1F* prediction = (TH1F*) fit->GetPlot();
     data->Draw("Ep");
     result->Draw("same");
   }
 }


 Instantiation
 =============
 A fit object is instantiated through
     TFractionFitter* fit = new TFractionFitter(data, mc);
 A number of basic checks (intended to ensure that the template histograms
 represent the same "kind" of distribution as the data one) are carried out.
 The TVirtualFitter object is then addressed and all fit parameters (the
 template fractions) declared (initially unbounded).

 Applying constraints
 ====================
 Fit parameters can be constrained through
     fit->Constrain(parameter #, lower bound, upper bound);
 Setting lower bound = upper bound = 0 removes the constraint (a la Minuit);
 however, a function
     fit->Unconstrain(parameter #)
 is also provided to simplify this.

 Setting parameter values
 ========================
 The function
     TVirtualFitter* vFit = fit->GetFitter();
 is provided for direct access to the TVirtualFitter object. This allows to
 set and fix parameter values, and set step sizes directly.

 Restricting the fit range
 =========================
 The fit range can be restricted through
     fit->SetRangeX(first bin #, last bin #);
 and freed using
     fit->ReleaseRangeX();
 For 2D histograms the Y range can be similarly restricted using
     fit->SetRangeY(first bin #, last bin #);
     fit->ReleaseRangeY();
 and for 3D histograms also
     fit->SetRangeZ(first bin #, last bin #);
     fit->ReleaseRangeZ();

 Weights histograms
 ==================
 Weights histograms (for a motivation see the above publication) can be specified
 for the individual MC sources through
     fit->SetWeight(parameter #, pointer to weights histogram);
 and unset by specifying a null pointer.

 Obtaining fit results
 =====================
 The fit is carried out through
     Int_t status = fit->Fit();
 where  status  is the code returned from the "MINIMIZE" command. For fits
 that converged, parameter values and errors can be obtained through
     fit->GetResult(parameter #, value, error);
 and the histogram corresponding to the total Monte Carlo prediction (which
 is not the same as a simple weighted sum of the input Monte Carlo distributions)
 can be obtained by
     TH1* result = fit->GetPlot();

 Using different histograms
 ==========================
 It is possible to change the histogram being fitted through
     fit->SetData(TH1* data);
 and to change the template histogram for a given parameter number through
     fit->SetMC(parameter #, TH1* MC);
 This can speed up code in case of multiple data or template histograms;
 however, it should be done with care as any settings are taken over from
 the previous fit. In addition, neither the dimensionality nor the numbers of
 bins of the histograms should change (in that case it is better to instantiate
 a new TFractionFitter object).

 Errors
 ======
 Any serious inconsistency results in an error.

 TFractionFitter default constructor.

 TFractionFitter constructor. Does a complete initialisation (including
 consistency checks, default fit range as the whole histogram but without
 under- and overflows, and declaration of the fit parameters). Note that
 the histograms are not copied, only references are used.
 Arguments:
     data: histogram to be fitted
     MCs:  array of TH1* corresponding template distributions

 TFractionFitter default destructor

 Change the histogram to be fitted to. Notes:
 - Parameter constraints and settings are retained from a possible previous fit.
 - Modifying the dimension or number of bins results in an error (in this case
   rather instantiate a new TFractionFitter object)

 Change the histogram for template number <parm>. Notes:
 - Parameter constraints and settings are retained from a possible previous fit.
 - Modifying the dimension or number of bins results in an error (in this case
   rather instantiate a new TFractionFitter object)

 Set bin by bin weights for template number <parm> (the parameter numbering
 follows that of the input template vector).
 Weights can be "unset" by passing a null pointer.
 Consistency of the weights histogram with the data histogram is checked at
 this point, and an error in case of problems.

 Give direct access to the underlying minimisation class. This can be
 used e.g. to modify parameter values or step sizes.

 Function for internal use, checking parameter validity
 An invalid parameter results in an error.

 Set the X range of the histogram to be used in the fit.
 Use ReleaseRangeX() to go back to fitting the full histogram.
 The consistency check ensures that no empty fit range occurs (and also
 recomputes the bin content integrals).
 Arguments:
     low:  lower X bin number
     high: upper X bin number

 Release restrictions on the X range of the histogram to be used in the fit.

 Set the Y range of the histogram to be used in the fit (2D or 3D histograms only).
 Use ReleaseRangeY() to go back to fitting the full histogram.
 The consistency check ensures that no empty fit range occurs (and also
 recomputes the bin content integrals).
 Arguments:
     low:  lower Y bin number
     high: upper Y bin number

 Release restrictions on the Y range of the histogram to be used in the fit.

 Set the Z range of the histogram to be used in the fit (3D histograms only).
 Use ReleaseRangeY() to go back to fitting the full histogram.
 The consistency check ensures that no empty fit range occurs (and also
 recomputes the bin content integrals).
 Arguments:
     low:  lower Y bin number
     high: upper Y bin number

 Release restrictions on the Z range of the histogram to be used in the fit.

 Constrain the values of parameter number <parm> (the parameter numbering
 follows that of the input template vector).
 Use UnConstrain() to remove this constraint.

 Remove the constraints on the possible values of parameter <parm>.

 Function used internally to check the consistency between the
 various histograms. Checks are performed on nonexistent or empty
 histograms, the precise histogram class, and the number of bins.
 In addition, integrals over the "allowed" bin ranges are computed.
 Any inconsistency results in a error.

 Perform the fit with the default UP value.
 The value returned is the minimisation status.

 Set UP to the given value (see class TMinuit), and perform a MINOS minimisation.

 Obtain the fit result for parameter <parm> (the parameter numbering
 follows that of the input template vector).

 Return the "template prediction" corresponding to the fit result (this is not
 the same as the weighted sum of template distributions, as template statistical
 uncertainties are taken into account).
 Note that the name of this histogram will simply be the same as that of the
 "data" histogram, prefixed with the string "Fraction fit to hist: ".

 Used internally to obtain the bin ranges according to the dimensionality of
 the histogram and the limits set by hand.

 Used internally to compute the likelihood value.

 Function used internally to obtain the template prediction in the individual bins

 Return the likelihood ratio Chi-squared (chi2) for the fit.
 The value is computed when the fit is executed successfully.
 Chi2 calculation is based on the "likelihood ratio" lambda,
 lambda = L(y;n) / L(m;n),
 where L(y;n) is the likelihood of the fit result <y> describing the data <n>
 and L(m;n) is the likelihood of an unknown "true" underlying distribution
 <m> describing the data <n>. Since <m> is unknown, the data distribution is
 used instead,
 lambda = L(y;n) / L(n;n).
 Note that this ratio is 1 if the fit is perfect. The chi2 value is then
 computed according to
 chi2 = -2*ln(lambda).
 This parameter can be shown to follow a Chi-square distribution. See for
 example S. Baker and R. Cousins, "Clarification of the use of chi-square
 and likelihood functions in fits to histograms", Nucl. Instr. Meth. A221,
 pp. 437-442 (1984)

 return the number of degrees of freedom in the fit
 the fNDF parameter has been previously computed during a fit.
 The number of degrees of freedom corresponds to the number of points
 used in the fit minus the number of templates.

 return the fit probability

 Method used internally to compute the likelihood ratio chi2
 See the function GetChisquare() for details

 Return the adjusted MC template (Aji) for template (parm).
 Note that the (Aji) times fractions only sum to the total prediction
 of the fit if all weights are 1.

Inline Functions

            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void Streamer(TBuffer& b)
               void StreamerNVirtual(TBuffer& b)