    // @(#)root/graf:$Name:  $:$Id: TGraphAsymmErrors.cxx,v 1.40 2004/07/06 14:55:04 brun Exp $

    // Author: Rene Brun   03/03/99

    /*************************************************************************
     * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
     * All rights reserved.                                                  *
     *                                                                       *
     * For the licensing terms see $ROOTSYS/LICENSE.                         *
     * For the list of contributors see $ROOTSYS/README/CREDITS.             *
     *************************************************************************/

    #include <string.h>

    #include "Riostream.h"
    #include "TROOT.h"
    #include "TGraphAsymmErrors.h"
    #include "TStyle.h"
    #include "TMath.h"
    #include "TArrow.h"
    #include "TVirtualPad.h"
    #include "TF1.h"
    #include "TH1.h"

    ClassImp(TGraphAsymmErrors)

    namespace {
      unsigned long GLOBAL_k;   // used to pass k[i] into equations
      unsigned long GLOBAL_N;   // used to pass N[i] into equations
      double        CONFLEVEL;  // confidence level for the interval
    }

    //______________________________________________________________________________

    //

    //   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::TGraphAsymmErrors(): TGraph() { //*-*-*-*-*-*-*-*-*-*-*TGraphAsymmErrors default constructor*-*-*-*-*-*-*-*-*-*-*-* //*-* ===================================== fEXlow = 0; fEYlow = 0; fEXhigh = 0; fEYhigh = 0; } //______________________________________________________________________________ TGraphAsymmErrors::TGraphAsymmErrors(const TGraphAsymmErrors &gr) : TGraph(gr) { // TGraphAsymmErrors copy constructor fEXlow = fEYlow = fEXhigh = fEYhigh = 0; if (fNpoints == 0) return; fEXlow = new Double_t[fNpoints]; fEYlow = new Double_t[fNpoints]; fEXhigh = new Double_t[fNpoints]; fEYhigh = new Double_t[fNpoints]; for (Int_t i=0;i<fNpoints;i++) { fEXlow[i] = gr.fEXlow[i]; fEYlow[i] = gr.fEYlow[i]; fEXhigh[i] = gr.fEXhigh[i]; fEYhigh[i] = gr.fEYhigh[i]; } } //______________________________________________________________________________ TGraphAsymmErrors::TGraphAsymmErrors(Int_t n) : TGraph(n) { //*-*-*-*-*-*-*-*-*-*-*TGraphAsymmErrors normal constructor*-*-*-*-*-*-*-*-*-*-*-*-* //*-* ==================================== // // the arrays are preset to zero if (n <= 0) { Error("TGraphAsymmErrors", "illegal number of points (%d)", n); return; } fEXlow = new Double_t[n]; fEYlow = new Double_t[n]; fEXhigh = new Double_t[n]; fEYhigh = new Double_t[n]; for (Int_t i=0;i<n;i++) { fEXlow[i] = 0; fEXhigh[i] = 0; fEYlow[i] = 0; fEYhigh[i] = 0; } } //______________________________________________________________________________ TGraphAsymmErrors::TGraphAsymmErrors(Int_t n, const Float_t *x, const Float_t *y, const Float_t *exl, const Float_t *exh, const Float_t *eyl, const Float_t *eyh) : TGraph(n,x,y) { //*-*-*-*-*-*-*-*-*-*-*TGraphAsymmErrors normal constructor*-*-*-*-*-*-*-*-*-*-*-*-* //*-* ==================================== // // if exl,h or eyl,h are null, the corresponding arrays are preset to zero if (n <= 0) { Error("TGraphAsymmErrors", "illegal number of points (%d)", n); return; } fEXlow = new Double_t[n]; fEYlow = new Double_t[n]; fEXhigh = new Double_t[n]; fEYhigh = new Double_t[n]; for (Int_t i=0;i<n;i++) { if (exl) fEXlow[i] = exl[i]; else fEXlow[i] = 0; if (exh) fEXhigh[i] = exh[i]; else fEXhigh[i] = 0; if (eyl) fEYlow[i] = eyl[i]; else fEYlow[i] = 0; if (eyh) fEYhigh[i] = eyh[i]; else fEYhigh[i] = 0; } } //______________________________________________________________________________ TGraphAsymmErrors::TGraphAsymmErrors(Int_t n, const Double_t *x, const Double_t *y, const Double_t *exl, const Double_t *exh, const Double_t *eyl, const Double_t *eyh) : TGraph(n,x,y) { //*-*-*-*-*-*-*-*-*-*-*TGraphAsymmErrors normal constructor*-*-*-*-*-*-*-*-*-*-*-*-* //*-* ==================================== // // if exl,h or eyl,h are null, the corresponding arrays are preset to zero if (n <= 0) { Error("TGraphAsymmErrors", "illegal number of points (%d)", n); return; } fEXlow = new Double_t[n]; fEYlow = new Double_t[n]; fEXhigh = new Double_t[n]; fEYhigh = new Double_t[n]; for (Int_t i=0;i<n;i++) { if (exl) fEXlow[i] = exl[i]; else fEXlow[i] = 0; if (exh) fEXhigh[i] = exh[i]; else fEXhigh[i] = 0; if (eyl) fEYlow[i] = eyl[i]; else fEYlow[i] = 0; if (eyh) fEYhigh[i] = eyh[i]; else fEYhigh[i] = 0; } } //______________________________________________________________________________ TGraphAsymmErrors::TGraphAsymmErrors(const TH1 *h) : TGraph(h) { // 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. if (fNpoints <= 0) return; fEXlow = new Double_t[fNpoints]; fEYlow = new Double_t[fNpoints]; fEXhigh = new Double_t[fNpoints]; fEYhigh = new Double_t[fNpoints]; for (Int_t i=0;i<fNpoints;i++) { fEXlow[i] = h->GetBinWidth(i+1)*gStyle->GetErrorX(); fEXhigh[i] = fEXlow[i]; fEYlow[i] = h->GetBinError(i+1); fEYhigh[i] = fEYlow[i]; } } //______________________________________________________________________________ TGraphAsymmErrors::TGraphAsymmErrors(const TH1 *pass, const TH1 *total, Option_t *option) : TGraph() { // Creates a TGraphAsymmErrors by dividing two input TH1 histograms: // pass/total. (see TGraphAsymmErrors::BayesDivide) BayesDivide(pass, total, option); } //______________________________________________________________________________ TGraphAsymmErrors::~TGraphAsymmErrors() { //*-*-*-*-*-*-*-*-*-*-*TGraphAsymmErrors default destructor*-*-*-*-*-*-*-*-*-*-*-*-* //*-* =============================== delete [] fEXlow; delete [] fEXhigh; delete [] fEYlow; delete [] fEYhigh; } //______________________________________________________________________________ void TGraphAsymmErrors::Apply(TF1 *f) { // 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> Double_t x,y,exl,exh,eyl,eyh,eyl_new,eyh_new,fxy; for (Int_t i=0;i<GetN();i++) { GetPoint(i,x,y); exl=GetEXlow()[i]; exh=GetEXhigh()[i]; eyl=GetEYlow()[i]; eyh=GetEYhigh()[i]; fxy = f->Eval(x,y); SetPoint(i,x,fxy); // in the case of the functions like y-> -1*y the roles of the // upper and lower error bars is reversed if (f->Eval(x,y-eyl)<f->Eval(x,y+eyh)) { eyl_new = TMath::Abs(fxy - f->Eval(x,y-eyl)); eyh_new = TMath::Abs(f->Eval(x,y+eyh) - fxy); } else { eyh_new = TMath::Abs(fxy - f->Eval(x,y-eyl)); eyl_new = TMath::Abs(f->Eval(x,y+eyh) - fxy); } //error on x doesn't change SetPointError(i,exl,exh,eyl_new,eyh_new); } } //______________________________________________________________________________ void TGraphAsymmErrors::BayesDivide(const TH1 *pass, const TH1 *total, Option_t *option) { // 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. TString opt = option; opt.ToLower(); Int_t nbins = pass->GetNbinsX(); if (nbins != total->GetNbinsX()){ Error("BayesDivide","Histograms must have the same number of X bins"); return; } if (opt.Contains("w")) { //compare sum of weights with sum of squares of weights Double_t stats[10]; pass->GetStats(stats); if (TMath::Abs(stats[0] -stats[1]) > 1e-6) { Error("BayesDivide","Pass histogram has not been filled with weights = 1"); return; } total->GetStats(stats); if (TMath::Abs(stats[0] -stats[1]) > 1e-6) { Error("BayesDivide","Total histogram has not been filled with weights = 1"); return; } } //Set the graph to have a number of points equal to the number of histogram bins Set(nbins); // Ok, now set the points for each bin // (Note: the TH1 bin content is shifted to the right by one: // bin=0 is underflow, bin=nbins+1 is overflow.) double mode, low, high; //these will hold the result of the Bayes calculation int npoint=0;//this keeps track of the number of points added to the graph for (int b=1; b<=nbins; ++b) { // loop through the bins int t = (int)total->GetBinContent(b); if (!t) continue; //don't add points for bins with no information int p = (int)pass->GetBinContent(b); if (p>t) { Warning("BayesDivide","Histogram bin %d in pass has more entries than corresponding bin in total! (%d>%d)",b,p,t); continue; //we may as well go on... } //This is the Bayes calculation... Efficiency(p,t,0.683,mode,low,high); //These are the low and high error bars low = mode-low; high = high-mode; //If either of the errors are 0, set them to 1/10 of the other error //so that the fitters don't get confused. if (low==0.0) low=high/10.; if (high==0.0) high=low/10.; //Set the point center and its errors SetPoint(npoint,pass->GetBinCenter(b),mode); SetPointError(npoint, pass->GetBinCenter(b)-pass->GetBinLowEdge(b), pass->GetBinLowEdge(b)-pass->GetBinCenter(b)+pass->GetBinWidth(b), low,high); npoint++;//we have added a point to the graph } Set(npoint);//tell the graph how many points we've really added if (opt.Contains("debug")) { printf("BayesDivide: made a graph with %d points from %d bins\n",npoint,nbins); Print();//The debug prints out what we get for each point } } //______________________________________________________________________________ double TGraphAsymmErrors::Beta_ab(double a, double b, int k, int N) const { // Calculates the fraction of the area under the // curve x^k*(1-x)^(N-k) between x=a and x=b if (a == b) return 0; // don't bother integrating over zero range int c1 = k+1; int c2 = N-k+1; return Ibetai(c1,c2,b)-Ibetai(c1,c2,a); } //______________________________________________________________________________ double TGraphAsymmErrors::Ibetai(double a, double b, double x) const { // Calculates the incomplete beta function I_x(a,b); this is // the incomplete beta function divided by the complete beta function double bt; if (x < 0.0 || x > 1.0) { Error("Ibetai","Illegal x in routine Ibetai: x = %g",x); return 0; } if (x == 0.0 || x == 1.0) bt=0.0; else bt=TMath::Exp(TMath::LnGamma(a+b)-TMath::LnGamma(a)-TMath::LnGamma(b)+a*log(x)+b*log(1.0-x)); if (x < (a+1.0)/(a+b+2.0)) return bt*TMath::BetaCf(x,a,b)/a; else return 1.0-bt*TMath::BetaCf(1-x,b,a)/b; } //______________________________________________________________________________ double TGraphAsymmErrors::Betai(double a, double b, double x) const { // Calculates the incomplete beta function B_x(a,b), as defined // in Gradshteyn and Ryzhik (4th edition) 8.391 // calculates the complete beta function double beta = TMath::Exp(TMath::LnGamma(a)+TMath::LnGamma(b)-TMath::LnGamma(a+b)); return Ibetai(a,b,x)*beta; } //______________________________________________________________________________ double TGraphAsymmErrors::Brent(double ax, double bx, double cx, double tol, double *xmin) const { // 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 const int kITMAX = 100; const double kCGOLD = 0.3819660; const double kZEPS = 1.0e-10; int iter; double a,b,d=0.,etemp,fu,fv,fw,fx,p,q,r,tol1,tol2,u,v,w,x,xm; double e=0.0; a=(ax < cx ? ax : cx); b=(ax > cx ? ax : cx); x=w=v=bx; fw=fv=fx=Interval(x); for (iter=1;iter<=kITMAX;iter++) { xm=0.5*(a+b); tol2=2.0*(tol1=tol*TMath::Abs(x)+kZEPS); if (TMath::Abs(x-xm) <= (tol2-0.5*(b-a))) { *xmin=x; return fx; } if (TMath::Abs(e) > tol1) { r=(x-w)*(fx-fv); q=(x-v)*(fx-fw); p=(x-v)*q-(x-w)*r; q=2.0*(q-r); if (q > 0.0) p = -p; q=TMath::Abs(q); etemp=e; e=d; if (TMath::Abs(p) >= TMath::Abs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) d=kCGOLD*(e=(x >= xm ? a-x : b-x)); else { d=p/q; u=x+d; if (u-a < tol2 || b-u < tol2) d=TMath::Sign(tol1,xm-x); } } else { d=kCGOLD*(e=(x >= xm ? a-x : b-x)); } u=(TMath::Abs(d) >= tol1 ? x+d : x+TMath::Sign(tol1,d)); fu=Interval(u); if (fu <= fx) { if (u >= x) a=x; else b=x; v = w; w = x; x = u; fv = fw; fw = fx; fx = fu; } else { if (u < x) a=u; else b=u; if (fu <= fw || w == x) { v=w; w=u; fv=fw; fw=fu; } else if (fu <= fv || v == x || v == w) { v=u; fv=fu; } } } Error("Brent","Too many interations"); *xmin=x; return fx; } //______________________________________________________________________________ void TGraphAsymmErrors::ComputeRange(Double_t &xmin, Double_t &ymin, Double_t &xmax, Double_t &ymax) const { for (Int_t i=0;i<fNpoints;i++) { if (fX[i] -fEXlow[i] < xmin) { if (gPad && gPad->GetLogx()) { if (fEXlow[i] < fX[i]) xmin = fX[i]-fEXlow[i]; else xmin = fX[i]/3; } else { xmin = fX[i]-fEXlow[i]; } } if (fX[i] +fEXhigh[i] > xmax) xmax = fX[i]+fEXhigh[i]; if (fY[i] -fEYlow[i] < ymin) { if (gPad && gPad->GetLogy()) { if (fEYlow[i] < fY[i]) ymin = fY[i]-fEYlow[i]; else ymin = fY[i]/3; } else { ymin = fY[i]-fEYlow[i]; } } if (fY[i] +fEYhigh[i] > ymax) ymax = fY[i]+fEYhigh[i]; } } //______________________________________________________________________________ void TGraphAsymmErrors::Efficiency(int k, int N, double conflevel, double& mode, double& low, double& high) const { // 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 //If there are no entries, then we know nothing, thus return the prior... if (0==N) { mode = .5; low = 0.0; high = 1.0; return; } // Calculate the most probable value for the posterior cross section. // This is easy, 'cause it is just k/N double efficiency = (double)k/N; double low_edge; double high_edge; if (k == 0) { low_edge = 0.0; high_edge = SearchUpper(low_edge, k, N, conflevel); } else if (k == N) { high_edge = 1.0; low_edge = SearchLower(high_edge, k, N, conflevel); } else { GLOBAL_k = k; GLOBAL_N = N; CONFLEVEL = conflevel; Brent(0.0, 0.5, 1.0, 1.0e-9, &low_edge); high_edge = low_edge + Interval(low_edge); } // return output mode = efficiency; low = low_edge; high = high_edge; } //______________________________________________________________________________ Double_t TGraphAsymmErrors::GetErrorX(Int_t i) const { // This function is called by GraphFitChisquare. // It returns the error along X at point i. if (i < 0 || i >= fNpoints) return -1; if (!fEXlow && !fEXhigh) return -1; Double_t elow=0, ehigh=0; if (fEXlow) elow = fEXlow[i]; if (fEXhigh) ehigh = fEXhigh[i]; return TMath::Sqrt(0.5*(elow*elow + ehigh*ehigh)); } //______________________________________________________________________________ Double_t TGraphAsymmErrors::GetErrorY(Int_t i) const { // This function is called by GraphFitChisquare. // It returns the error along Y at point i. if (i < 0 || i >= fNpoints) return -1; if (!fEYlow && !fEYhigh) return -1; Double_t elow=0, ehigh=0; if (fEYlow) elow = fEYlow[i]; if (fEYhigh) ehigh = fEYhigh[i]; return TMath::Sqrt(0.5*(elow*elow + ehigh*ehigh)); } //______________________________________________________________________________ Int_t TGraphAsymmErrors::InsertPoint() { // Insert a new point at the mouse position Int_t ipoint = TGraph::InsertPoint(); Double_t *newEXlow = new Double_t[fNpoints]; Double_t *newEYlow = new Double_t[fNpoints]; Double_t *newEXhigh = new Double_t[fNpoints]; Double_t *newEYhigh = new Double_t[fNpoints]; Int_t i; for (i=0;i<ipoint;i++) { newEXlow[i] = fEXlow[i]; newEYlow[i] = fEYlow[i]; newEXhigh[i] = fEXhigh[i]; newEYhigh[i] = fEYhigh[i]; } newEXlow[ipoint] = 0; newEYlow[ipoint] = 0; newEXhigh[ipoint] = 0; newEYhigh[ipoint] = 0; for (i=ipoint+1;i<fNpoints;i++) { newEXlow[i] = fEXlow[i-1]; newEYlow[i] = fEYlow[i-1]; newEXhigh[i] = fEXhigh[i-1]; newEYhigh[i] = fEYhigh[i-1]; } delete [] fEXlow; delete [] fEYlow; delete [] fEXhigh; delete [] fEYhigh; fEXlow = newEXlow; fEYlow = newEYlow; fEXhigh = newEXhigh; fEYhigh = newEYhigh; return ipoint; } //______________________________________________________________________________ double TGraphAsymmErrors::Interval(double low) const { // 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 double high = SearchUpper(low, GLOBAL_k, GLOBAL_N, CONFLEVEL); if (high == -1.0) return 2.0; // so that this won't be the shortest interval return (high - low); } //______________________________________________________________________________ void TGraphAsymmErrors::Paint(Option_t *option) { // 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. const Int_t BASEMARKER=8; Double_t s2x, s2y, symbolsize, sbase; Double_t x, y, xl1, xl2, xr1, xr2, yup1, yup2, ylow1, ylow2, tx, ty; static Float_t cxx[11] = {1,1,0.6,0.6,1,1,0.6,0.5,1,0.6,0.6}; static Float_t cyy[11] = {1,1,1,1,1,1,1,1,1,0.5,0.6}; if (strchr(option,'X') || strchr(option,'x')) {TGraph::Paint(option); return;} Bool_t brackets = kFALSE; if (strstr(option,"[]")) brackets = kTRUE; Bool_t endLines = kTRUE; if (strchr(option,'z')) endLines = kFALSE; if (strchr(option,'Z')) endLines = kFALSE; const char *arrowOpt = 0; if (strchr(option,'>')) arrowOpt = ">"; if (strstr(option,"|>")) arrowOpt = "|>"; Bool_t axis = kFALSE; if (strchr(option,'a')) axis = kTRUE; if (strchr(option,'A')) axis = kTRUE; if (axis) TGraph::Paint(option); TAttLine::Modify(); TArrow arrow; arrow.SetLineWidth(GetLineWidth()); arrow.SetLineColor(GetLineColor()); arrow.SetFillColor(GetFillColor()); symbolsize = GetMarkerSize(); sbase = symbolsize*BASEMARKER; Int_t mark = GetMarkerStyle(); Double_t cx = 0; Double_t cy = 0; if (mark >= 20 && mark < 31) { cx = cxx[mark-20]; cy = cyy[mark-20]; } //*-*- define the offset of the error bars due to the symbol size s2x = gPad->PixeltoX(Int_t(0.5*sbase)) - gPad->PixeltoX(0); s2y =-gPad->PixeltoY(Int_t(0.5*sbase)) + gPad->PixeltoY(0); Int_t dxend = Int_t(gStyle->GetEndErrorSize()); tx = gPad->PixeltoX(dxend) - gPad->PixeltoX(0); ty =-gPad->PixeltoY(dxend) + gPad->PixeltoY(0); Float_t asize = 0.6*symbolsize*BASEMARKER/gPad->GetWh(); gPad->SetBit(kClipFrame, TestBit(kClipFrame)); for (Int_t i=0;i<fNpoints;i++) { x = gPad->XtoPad(fX[i]); y = gPad->YtoPad(fY[i]); if (x < gPad->GetUxmin()) continue; if (x > gPad->GetUxmax()) continue; if (y < gPad->GetUymin()) continue; if (y > gPad->GetUymax()) continue; xl1 = x - s2x*cx; xl2 = gPad->XtoPad(fX[i] - fEXlow[i]); if (xl1 > xl2) { if (arrowOpt) { arrow.PaintArrow(xl1,y,xl2,y,asize,arrowOpt); } else { if (!brackets) gPad->PaintLine(xl1,y,xl2,y); if (endLines) gPad->PaintLine(xl2,y-ty,xl2,y+ty); } } xr1 = x + s2x*cx; xr2 = gPad->XtoPad(fX[i] + fEXhigh[i]); if (xr1 < xr2) { if (arrowOpt) { arrow.PaintArrow(xr1,y,xr2,y,asize,arrowOpt); } else { if (!brackets) gPad->PaintLine(xr1,y,xr2,y); if (endLines) gPad->PaintLine(xr2,y-ty,xr2,y+ty); } } yup1 = y + s2y*cy; yup2 = gPad->YtoPad(fY[i] + fEYhigh[i]); if (yup2 > gPad->GetUymax()) yup2 = gPad->GetUymax(); if (yup2 > yup1) { if (arrowOpt) { arrow.PaintArrow(x,yup1,x,yup2,asize,arrowOpt); } else { if (!brackets) gPad->PaintLine(x,yup1,x,yup2); if (endLines) gPad->PaintLine(x-tx,yup2,x+tx,yup2); } } ylow1 = y - s2y*cy; ylow2 = gPad->YtoPad(fY[i] - fEYlow[i]); if (ylow2 < gPad->GetUymin()) ylow2 = gPad->GetUymin(); if (ylow2 < ylow1) { if (arrowOpt) { arrow.PaintArrow(x,ylow1,x,ylow2,asize,arrowOpt); } else { if (!brackets) gPad->PaintLine(x,ylow1,x,ylow2); if (endLines) gPad->PaintLine(x-tx,ylow2,x+tx,ylow2); } } } if (!brackets && !axis) TGraph::Paint(option); gPad->ResetBit(kClipFrame); } //______________________________________________________________________________ void TGraphAsymmErrors::Print(Option_t *) const { //*-*-*-*-*-*-*-*-*-*-*Print graph and errors values*-*-*-*-*-*-*-*-*-*-*-* //*-* ============================= // for (Int_t i=0;i<fNpoints;i++) { printf("x[%d]=%g, y[%d]=%g, exl[%d]=%g, exh[%d]=%g, eyl[%d]=%g, eyh[%d]=%g\n" ,i,fX[i],i,fY[i],i,fEXlow[i],i,fEXhigh[i],i,fEYlow[i],i,fEYhigh[i]); } } //______________________________________________________________________________ Int_t TGraphAsymmErrors::RemovePoint() { // Delete point close to the mouse position Int_t ipoint = TGraph::RemovePoint(); if (ipoint < 0) return ipoint; Double_t *newEXlow = new Double_t[fNpoints]; Double_t *newEYlow = new Double_t[fNpoints]; Double_t *newEXhigh = new Double_t[fNpoints]; Double_t *newEYhigh = new Double_t[fNpoints]; Int_t i, j = -1; for (i=0;i<fNpoints+1;i++) { if (i == ipoint) continue; j++; newEXlow[j] = fEXlow[i]; newEYlow[j] = fEYlow[i]; newEXhigh[j] = fEXhigh[i]; newEYhigh[j] = fEYhigh[i]; } delete [] fEXlow; delete [] fEYlow; delete [] fEXhigh; delete [] fEYhigh; fEXlow = newEXlow; fEYlow = newEYlow; fEXhigh = newEXhigh; fEYhigh = newEYhigh; return ipoint; } //______________________________________________________________________________ Int_t TGraphAsymmErrors::RemovePoint(Int_t ipnt) { // Delete point number ipnt Int_t ipoint = TGraph::RemovePoint(ipnt); if (ipoint < 0) return ipoint; Double_t *newEXlow = new Double_t[fNpoints]; Double_t *newEYlow = new Double_t[fNpoints]; Double_t *newEXhigh = new Double_t[fNpoints]; Double_t *newEYhigh = new Double_t[fNpoints]; Int_t i, j = -1; for (i=0;i<fNpoints+1;i++) { if (i == ipoint) continue; j++; newEXlow[j] = fEXlow[i]; newEYlow[j] = fEYlow[i]; newEXhigh[j] = fEXhigh[i]; newEYhigh[j] = fEYhigh[i]; } delete [] fEXlow; delete [] fEYlow; delete [] fEXhigh; delete [] fEYhigh; fEXlow = newEXlow; fEYlow = newEYlow; fEXhigh = newEXhigh; fEYhigh = newEYhigh; return ipoint; } //______________________________________________________________________________ void TGraphAsymmErrors::SavePrimitive(ofstream &out, Option_t *option) { // Save primitive as a C++ statement(s) on output stream out char quote = '"'; out<<" "<<endl; if (gROOT->ClassSaved(TGraphAsymmErrors::Class())) { out<<" "; } else { out<<" TGraphAsymmErrors *"; } out<<"grae = new TGraphAsymmErrors("<<fNpoints<<");"<<endl; out<<" grae->SetName("<<quote<<GetName()<<quote<<");"<<endl; out<<" grae->SetTitle("<<quote<<GetTitle()<<quote<<");"<<endl; SaveFillAttributes(out,"grae",0,1001); SaveLineAttributes(out,"grae",1,1,1); SaveMarkerAttributes(out,"grae",1,1,1); for (Int_t i=0;i<fNpoints;i++) { out<<" grae->SetPoint("<<i<<","<<fX[i]<<","<<fY[i]<<");"<<endl; out<<" grae->SetPointError("<<i<<","<<fEXlow[i]<<","<<fEXhigh[i]<<","<<fEYlow[i]<<","<<fEYhigh[i]<<");"<<endl; } static Int_t frameNumber = 0; if (fHistogram) { frameNumber++; TString hname = fHistogram->GetName(); hname += frameNumber; fHistogram->SetName(hname.Data()); fHistogram->SavePrimitive(out,"nodraw"); out<<" grae->SetHistogram("<<fHistogram->GetName()<<");"<<endl; out<<" "<<endl; } // save list of functions TIter next(fFunctions); TObject *obj; while ((obj=next())) { obj->SavePrimitive(out,"nodraw"); out<<" grae->GetListOfFunctions()->Add("<<obj->GetName()<<");"<<endl; if (obj->InheritsFrom("TPaveStats")) { out<<" ptstats->SetParent(grae->GetListOfFunctions());"<<endl; } } if (strstr(option,"multigraph")) { out<<" multigraph->Add(grae);"<<endl; return; } out<<" grae->Draw(" <<quote<<option<<quote<<");"<<endl; } //______________________________________________________________________________ double TGraphAsymmErrors::SearchLower(double high, int k, int N, double c) const { // 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 double integral = Beta_ab(0.0, high, k, N); if (integral == c) return 0.0; // lucky -- this is the solution if (integral < c) return -1.0; // no solution exists double too_low = 0.0; // lower edge estimate double too_high = high; double test; // use a bracket-and-bisect search // now we loop 20 times, to end with a root guaranteed accurate to better // than 0.1% for (int loop=0; loop<20; loop++) { test = 0.5*(too_high + too_low); integral = Beta_ab(test, high, k, N); if (integral > c) too_low = test; else too_high = test; } return test; } //______________________________________________________________________________ double TGraphAsymmErrors::SearchUpper(double low, int k, int N, double c) const { // 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 double integral = Beta_ab(low, 1.0, k, N); if (integral == c) return 1.0; // lucky -- this is the solution if (integral < c) return -1.0; // no solution exists double too_high = 1.0; // upper edge estimate double too_low = low; double test; // use a bracket-and-bisect search // now we loop 20 times, to end with a root guaranteed accurate to better // than 0.1% for (int loop=0; loop<20; loop++) { test = 0.5*(too_low + too_high); integral = Beta_ab(low, test, k, N); if (integral > c) too_high = test; else too_low = test; } return test; } //______________________________________________________________________________ void TGraphAsymmErrors::Set(Int_t n) { // Set number of points in the graph // Existing coordinates are preserved // New coordinates and errors above fNpoints are preset to 0. if (n < 0) n = 0; if (n == fNpoints) return; TGraph::Set(n); Double_t *exh=0, *exl=0, *eyh=0, *eyl=0; if (n > 0) { exh = new Double_t[n]; exl = new Double_t[n]; eyh = new Double_t[n]; eyl = new Double_t[n]; } Int_t i; for (i=0; i<fNpoints && i<n;i++) { if (fEXlow) exl[i] = fEXlow[i]; if (fEXhigh) exh[i] = fEXhigh[i]; if (fEYlow) eyl[i] = fEYlow[i]; if (fEYhigh) eyh[i] = fEYhigh[i]; } for (i=fNpoints; i<n;i++) { exh[i] = 0; exl[i] = 0; eyh[i] = 0; eyl[i] = 0; } delete [] fEXlow; delete [] fEXhigh; delete [] fEYlow; delete [] fEYhigh; fEXhigh = exh; fEXlow = exl; fEYhigh = eyh; fEYlow = eyl; } //______________________________________________________________________________ void TGraphAsymmErrors::SetPoint(Int_t i, Double_t x, Double_t y) { //*-*-*-*-*-*-*-*-*-*-*Set x and y values for point number i*-*-*-*-*-*-*-*-* //*-* ===================================== if (i < 0) return; if (i >= fNpoints) { // re-allocate the object Double_t *savex = new Double_t[i+1]; Double_t *savey = new Double_t[i+1]; Double_t *saveexl = new Double_t[i+1]; Double_t *saveeyl = new Double_t[i+1]; Double_t *saveexh = new Double_t[i+1]; Double_t *saveeyh = new Double_t[i+1]; if (fNpoints > 0) { memcpy(savex, fX, fNpoints*sizeof(Double_t)); memcpy(savey, fY, fNpoints*sizeof(Double_t)); memcpy(saveexl,fEXlow, fNpoints*sizeof(Double_t)); memcpy(saveeyl,fEYlow, fNpoints*sizeof(Double_t)); memcpy(saveexh,fEXhigh,fNpoints*sizeof(Double_t)); memcpy(saveeyh,fEYhigh,fNpoints*sizeof(Double_t)); } if (fX) delete [] fX; if (fY) delete [] fY; if (fEXlow) delete [] fEXlow; if (fEYlow) delete [] fEYlow; if (fEXhigh) delete [] fEXhigh; if (fEYhigh) delete [] fEYhigh; fX = savex; fY = savey; fEXlow = saveexl; fEYlow = saveeyl; fEXhigh = saveexh; fEYhigh = saveeyh; fNpoints = i+1; } fX[i] = x; fY[i] = y; if (fHistogram) { delete fHistogram; fHistogram = 0; } } //______________________________________________________________________________ void TGraphAsymmErrors::SetPointError(Double_t exl, Double_t exh, Double_t eyl, Double_t eyh) { //*-*-*-*-*-*-*Set ex and ey values for point pointed by the mouse*-*-*-* //*-* =================================================== Int_t px = gPad->GetEventX(); Int_t py = gPad->GetEventY(); //localize point to be deleted Int_t ipoint = -2; Int_t i; // start with a small window (in case the mouse is very close to one point) for (i=0;i<fNpoints;i++) { Int_t dpx = px - gPad->XtoAbsPixel(gPad->XtoPad(fX[i])); Int_t dpy = py - gPad->YtoAbsPixel(gPad->YtoPad(fY[i])); if (dpx*dpx+dpy*dpy < 25) {ipoint = i; break;} } if (ipoint == -2) return; fEXlow[ipoint] = exl; fEYlow[ipoint] = eyl; fEXhigh[ipoint] = exh; fEYhigh[ipoint] = eyh; gPad->Modified(); } //______________________________________________________________________________ void TGraphAsymmErrors::SetPointError(Int_t i, Double_t exl, Double_t exh, Double_t eyl, Double_t eyh) { //*-*-*-*-*-*-*-*-*-*-*Set ex and ey values for point number i*-*-*-*-*-*-*-* //*-* ======================================= if (i < 0) return; if (i >= fNpoints) { // re-allocate the object TGraphAsymmErrors::SetPoint(i,0,0); } fEXlow[i] = exl; fEYlow[i] = eyl; fEXhigh[i] = exh; fEYhigh[i] = eyh; } //______________________________________________________________________________ void TGraphAsymmErrors::SetPointEXlow(Int_t i, Double_t exl) { // Set EXlow for point i if (i < 0) return; if (i >= fNpoints) { // re-allocate the object TGraphAsymmErrors::SetPoint(i,0,0); } fEXlow[i] = exl; } //______________________________________________________________________________ void TGraphAsymmErrors::SetPointEXhigh(Int_t i, Double_t exh) { // Set EXhigh for point i if (i < 0) return; if (i >= fNpoints) { // re-allocate the object TGraphAsymmErrors::SetPoint(i,0,0); } fEXhigh[i] = exh; } //______________________________________________________________________________ void TGraphAsymmErrors::SetPointEYlow(Int_t i, Double_t eyl) { // Set EYlow for point i if (i < 0) return; if (i >= fNpoints) { // re-allocate the object TGraphAsymmErrors::SetPoint(i,0,0); } fEYlow[i] = eyl; } //______________________________________________________________________________ void TGraphAsymmErrors::SetPointEYhigh(Int_t i, Double_t eyh) { // Set EYhigh for point i if (i < 0) return; if (i >= fNpoints) { // re-allocate the object TGraphAsymmErrors::SetPoint(i,0,0); } fEYhigh[i] = eyh; } //______________________________________________________________________________ void TGraphAsymmErrors::Streamer(TBuffer &b) { // Stream an object of class TGraphAsymmErrors. if (b.IsReading()) { UInt_t R__s, R__c; Version_t R__v = b.ReadVersion(&R__s, &R__c); if (R__v > 2) { TGraphAsymmErrors::Class()->ReadBuffer(b, this, R__v, R__s, R__c); return; } //====process old versions before automatic schema evolution TGraph::Streamer(b); fEXlow = new Double_t[fNpoints]; fEYlow = new Double_t[fNpoints]; fEXhigh = new Double_t[fNpoints]; fEYhigh = new Double_t[fNpoints]; if (R__v < 2) { Float_t *exlow = new Float_t[fNpoints]; Float_t *eylow = new Float_t[fNpoints]; Float_t *exhigh = new Float_t[fNpoints]; Float_t *eyhigh = new Float_t[fNpoints]; b.ReadFastArray(exlow,fNpoints); b.ReadFastArray(eylow,fNpoints); b.ReadFastArray(exhigh,fNpoints); b.ReadFastArray(eyhigh,fNpoints); for (Int_t i=0;i<fNpoints;i++) { fEXlow[i] = exlow[i]; fEYlow[i] = eylow[i]; fEXhigh[i] = exhigh[i]; fEYhigh[i] = eyhigh[i]; } delete [] eylow; delete [] exlow; delete [] eyhigh; delete [] exhigh; } else { b.ReadFastArray(fEXlow,fNpoints); b.ReadFastArray(fEYlow,fNpoints); b.ReadFastArray(fEXhigh,fNpoints); b.ReadFastArray(fEYhigh,fNpoints); } b.CheckByteCount(R__s, R__c, TGraphAsymmErrors::IsA()); //====end of old versions } else { TGraphAsymmErrors::Class()->WriteBuffer(b,this); } } //______________________________________________________________________________ void TGraphAsymmErrors::SwapPoints(Int_t pos1, Int_t pos2) { SwapValues(fEXlow, pos1, pos2); SwapValues(fEXhigh, pos1, pos2); SwapValues(fEYlow, pos1, pos2); SwapValues(fEYhigh, pos1, pos2); TGraph::SwapPoints(pos1, pos2); }