TGraphAsymmErrors

class TGraphAsymmErrors : public TGraph

    protected:

      virtual Double_t** Allocate(Int_t size)
                Double_t Beta_ab(double a, double b, int k, int N) const
                Double_t Betai(double a, double b, double x) const
                Double_t Brent(double ax, double bx, double cx, double tol, double* xmin) const
            virtual void CopyAndRelease(Double_t** newarrays, Int_t ibegin, Int_t iend, Int_t obegin)
          virtual Bool_t CopyPoints(Double_t** arrays, Int_t ibegin, Int_t iend, Int_t obegin)
                  Bool_t CtorAllocate()
            virtual void Efficiency(int k, int N, double conflevel, double& mode, double& low, double& high) const
            virtual void FillZero(Int_t begin, Int_t end, Bool_t from_ctor = kTRUE)
                Double_t Ibetai(double a, double b, double x) const
                Double_t Interval(double low) const
                Double_t SearchLower(double high, int k, int N, double c) const
                Double_t SearchUpper(double low, int k, int N, double c) const
            virtual void SwapPoints(Int_t pos1, Int_t pos2)

    public:

                         TGraphAsymmErrors()
                         TGraphAsymmErrors(Int_t n)
                         TGraphAsymmErrors(Int_t n, const Float_t* x, const Float_t* y, const Float_t* exl = 0, const Float_t* exh = 0, const Float_t* eyl = 0, const Float_t* eyh = 0)
                         TGraphAsymmErrors(Int_t n, const Double_t* x, const Double_t* y, const Double_t* exl = 0, const Double_t* exh = 0, const Double_t* eyl = 0, const Double_t* eyh = 0)
                         TGraphAsymmErrors(const TVector& vx, const TVector& vy, const TVector& vexl, const TVector& vexh, const TVector& veyl, const TVector& veyh)
                         TGraphAsymmErrors(const TVectorD& vx, const TVectorD& vy, const TVectorD& vexl, const TVectorD& vexh, const TVectorD& veyl, const TVectorD& veyh)
                         TGraphAsymmErrors(const TGraphAsymmErrors& gr)
                         TGraphAsymmErrors(const TH1* h)
                         TGraphAsymmErrors(const TH1* pass, const TH1* total, Option_t* option = "")
                 virtual ~TGraphAsymmErrors()
            virtual void Apply(TF1* f)
            virtual void BayesDivide(const TH1* pass, const TH1* total, Option_t* option = "")
          static TClass* Class()
            virtual void ComputeRange(Double_t& xmin, Double_t& ymin, Double_t& xmax, Double_t& ymax) const
        virtual Double_t GetErrorX(Int_t bin) const
        virtual Double_t GetErrorXhigh(Int_t i) const
        virtual Double_t GetErrorXlow(Int_t i) const
        virtual Double_t GetErrorY(Int_t bin) const
        virtual Double_t GetErrorYhigh(Int_t i) const
        virtual Double_t GetErrorYlow(Int_t i) const
       virtual Double_t* GetEXhigh() const
       virtual Double_t* GetEXlow() const
       virtual Double_t* GetEYhigh() const
       virtual Double_t* GetEYlow() const
         virtual TClass* IsA() const
      TGraphAsymmErrors& operator=(const TGraphAsymmErrors&)
            virtual void Paint(Option_t* chopt = "")
            virtual void Print(Option_t* chopt = "") const
            virtual void SavePrimitive(ofstream& out, Option_t* option)
            virtual void SetPointError(Double_t exl, Double_t exh, Double_t eyl, Double_t eyh)
            virtual void SetPointError(Int_t i, Double_t exl, Double_t exh, Double_t eyl, Double_t eyh)
            virtual void SetPointEXhigh(Int_t i, Double_t exh)
            virtual void SetPointEXlow(Int_t i, Double_t exl)
            virtual void SetPointEYhigh(Int_t i, Double_t eyh)
            virtual void SetPointEYlow(Int_t i, Double_t eyl)
            virtual void ShowMembers(TMemberInspector& insp, char* parent)
            virtual void Streamer(TBuffer& b)
                    void StreamerNVirtual(TBuffer& b)

Data Members

    protected:

      Double_t* fEXlow   [fNpoints] array of X low errors
      Double_t* fEXhigh  [fNpoints] array of X high errors
      Double_t* fEYlow   [fNpoints] array of Y low errors
      Double_t* fEYhigh  [fNpoints] array of Y high errors

Class Description

   A TGraphAsymmErrors is a TGraph with assymetric error bars.
   The various format options to draw a TGraphAsymmErrors are explained in
     TGraphAsymmErrors::Paint.

  The picture below has been generated by the following macro:
------------------------------------------------------------------------
{
   gROOT->Reset();
   c1 = new TCanvas("c1","A Simple Graph with error bars",200,10,700,500);

   c1->SetFillColor(42);
   c1->SetGrid();
   c1->GetFrame()->SetFillColor(21);
   c1->GetFrame()->SetBorderSize(12);

   Int_t n = 10;
   Double_t x[n]  = {-0.22, 0.05, 0.25, 0.35, 0.5, 0.61,0.7,0.85,0.89,0.95};
   Double_t y[n]  = {1,2.9,5.6,7.4,9,9.6,8.7,6.3,4.5,1};
   Double_t exl[n] = {.05,.1,.07,.07,.04,.05,.06,.07,.08,.05};
   Double_t eyl[n] = {.8,.7,.6,.5,.4,.4,.5,.6,.7,.8};
   Double_t exh[n] = {.02,.08,.05,.05,.03,.03,.04,.05,.06,.03};
   Double_t eyh[n] = {.6,.5,.4,.3,.2,.2,.3,.4,.5,.6};
   gr = new TGraphAsymmErrors(n,x,y,exl,exh,eyl,eyh);
   gr->SetTitle("TGraphAsymmErrors Example");
   gr->SetMarkerColor(4);
   gr->SetMarkerStyle(21);
   gr->Draw("ALP");

   c1->Update();
}

*-*-*-*-*-*-*-*-*-*-*TGraphAsymmErrors default constructor*-*-*-*-*-*-*-*-*-*-*-*
*-*                  =====================================

 TGraphAsymmErrors copy constructor

*-*-*-*-*-*-*-*-*-*-*TGraphAsymmErrors normal constructor*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  ====================================

  the arrays are preset to zero

*-*-*-*-*-*-*-*-*-*-*TGraphAsymmErrors normal constructor*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  ====================================

  if exl,h or eyl,h are null, the corresponding arrays are preset to zero

*-*-*-*-*-*-*-*-*-*-*TGraphAsymmErrors normal constructor*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  ====================================

  if exl,h or eyl,h are null, the corresponding arrays are preset to zero

 constructor with six vectors of floats in input
 A grapherrors is built with the X coordinates taken from vx and Y coord from vy
 and the errors from vectors vexl/h and veyl/h.
 The number of points in the graph is the minimum of number of points
 in vx and vy.

 constructor with six vectors of doubles in input
 A grapherrors is built with the X coordinates taken from vx and Y coord from vy
 and the errors from vectors vexl/h and veyl/h.
 The number of points in the graph is the minimum of number of points
 in vx and vy.

 TGraphAsymmErrors constructor importing its parameters from the TH1 object passed as argument
 the low and high errors are set to the bin error of the histogram.

 Creates a TGraphAsymmErrors by dividing two input TH1 histograms:
 pass/total. (see TGraphAsymmErrors::BayesDivide)

*-*-*-*-*-*-*-*-*-*-*TGraphAsymmErrors default destructor*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  ===============================

 apply a function to all data points
 y = f(x,y)

 Errors are calculated as eyh = f(x,y+eyh)-f(x,y) and
 eyl = f(x,y)-f(x,y-eyl)

 Special treatment has to be applied for the functions where the
 role of "up" and "down" is reversed.
 function suggested/implemented by Miroslav Helbich <helbich@mail.desy.de>

 Fills this TGraphAsymmErrors by dividing two input TH1 histograms pass/total.

 Andy Haas (haas@fnal.gov)
 University of Washington

 Method and code directly taken from:
 Marc Paterno (paterno@fnal.gov)
 FNAL/CD

 The input histograms must be filled with weights of 1.
 By default the function does not check this assertion.
 if option "w" is specified, the function will fail if the histograms
 have been filled with weights not equal to 1.

 The assumption is that the entries in "pass" are a
 subset of those in "total". That is, we create an "efficiency"
 graph, where each entry is between 0 and 1, inclusive.
 The resulting graph can be fit to functions, using standard methods:
 graph->Fit("erf")... for instance. (You have to define the erf
 function for yourself for now, sorry.)

 The points are assigned an x value at the center of each histogram bin.
 The y values are #pass/#total, between 0 and 1.
 The x errors span each histogram bin (lowedge->lowedge+width)
 The y errors are the fun part. :)

 The y errors are assigned based on applying Bayes theorem.
 The model is the Binomial distribution, and the "prior" is
 the flat distribution from 0 to 1.
 If there is no data in a bin of the total histogram, no information
 can be obtained for that bin, so no point is made on the graph.

 The complete method and a beautiful discussion can be found here:
 http://home.fnal.gov/~paterno/images/effic.pdf
 And more information is on these pages:
 http://home.fnal.gov/~paterno/probability/localresources.html
 A backup of the main document is here:
 http://www-clued0.fnal.gov/~haas/documents/paterno_effic.pdf

 A 68.3% Confidence Level is used to assign the errors.
 Warning! You should understand, the errors reported are the shortest
 ranges containing 68.3% of the probability distrubution. The errors are
 not exactly Gaussian! The Minuit fitting routines will assume that
 the errors are Gaussian. But this is a reasonable approximation.
 A fit using the full shape of the error distribution for each point
 would be far more difficult to perform.

 Calculates the fraction of the area under the
 curve x^k*(1-x)^(N-k) between x=a and x=b

 Calculates the incomplete beta function  I_x(a,b); this is
 the incomplete beta function divided by the complete beta function

 Calculates the incomplete beta function B_x(a,b), as defined
 in Gradshteyn and Ryzhik (4th edition) 8.391

 Implementation file for the numerical equation solver library.
 This includes root finding and minimum finding algorithms.
 Adapted from Numerical Recipes in C, 2nd edition.
 Translated to C++ by Marc Paterno

 Copy errors from fE*** to arrays[***]
 or to f*** Copy points.

 Should be called from ctors after fNpoints has been set

 Calculate the shortest central confidence interval containing the required
 probability content.
 Interval(low) returns the length of the interval starting at low
 that contains CONFLEVEL probability. We use Brent's method,
 except in two special cases: when k=0, or when k=N
 Main driver routine
 Author: Marc Paterno

 Set zero values for point arrays in the range [begin, end)

    This function is called by GraphFitChisquare.
    It returns the error along X at point i.

    This function is called by GraphFitChisquare.
    It returns the error along Y at point i.

 Return the length of the interval starting at low
 that contains CONFLEVEL of the x^GLOBAL_k*(1-x)^(GLOBAL_N-GLOBAL_k)
 distribution.
 If there is no sufficient interval starting at low, we return 2.0

 Paint this TGraphAsymmErrors with its current attributes

 by default horizonthal and vertical small lines are drawn at
 the end of the error bars. if option "z" or "Z" is specified,
 these lines are not drawn.

 if option contains ">" an arrow is drawn at the end of the error bars
 if option contains "|>" a full arrow is drawn at the end of the error bars
 the size of the arrow is set to 2/3 of the marker size.

 By default, error bars are drawn. If option "X" is specified,
 the errors are not drawn (TGraph::Paint equivalent).

 if option "[]" is specified only the end vertical/horizonthal lines
 of the error bars are drawn. This option is interesting to superimpose
 systematic errors on top of a graph with statistical errors.

 if option "2" is specified error rectangles are drawn.

 if option "3" is specified a filled area is drawn through the end points >
 the vertical error bars.

 if option "4" is specified a smoothed filled area is drawn through the end
 points of the vertical error bars.

*-*-*-*-*-*-*-*-*-*-*Print graph and errors values*-*-*-*-*-*-*-*-*-*-*-*
*-*                  =============================

 Save primitive as a C++ statement(s) on output stream out

 Integrates the binomial distribution with
 parameters k,N, and determines what is the lower edge of the
 integration region which ends at high, and which contains
 probability content c. If a lower limit is found, the value is
 returned. If no solution is found, the -1 is returned.
 check to see if there is any solution by verifying that the integral down
 to the minimum lower limit (0) is greater than c

 Integrates the binomial distribution with
 parameters k,N, and determines what is the upper edge of the
 integration region which starts at low which contains probability
 content c. If an upper limit is found, the value is returned. If no
 solution is found, -1 is returned.
 check to see if there is any solution by verifying that the integral up
 to the maximum upper limit (1) is greater than c

*-*-*-*-*-*-*Set ex and ey values for point pointed by the mouse*-*-*-*
*-*          ===================================================

*-*-*-*-*-*-*-*-*-*-*Set ex and ey values for point number i*-*-*-*-*-*-*-*
*-*                  =======================================

 Set EXlow for point i

 Set EXhigh for point i

 Set EYlow for point i

 Set EYhigh for point i

 Stream an object of class TGraphAsymmErrors.

Inline Functions

                Double_t** Allocate(Int_t size)
                 Double_t* GetEXlow() const
                 Double_t* GetEXhigh() const
                 Double_t* GetEYlow() const
                 Double_t* GetEYhigh() const
                   TClass* Class()
                   TClass* IsA() const
                      void ShowMembers(TMemberInspector& insp, char* parent)
                      void StreamerNVirtual(TBuffer& b)
        TGraphAsymmErrors& operator=(const TGraphAsymmErrors&)