// @(#)root/graf:$Name: $:$Id: TGraphAsymmErrors.cxx,v 1.52 2005/09/05 07:25:22 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 "TBox.h"
#include "TVirtualPad.h"
#include "TF1.h"
#include "TH1.h"
#include "TVector.h"
#include "TVectorD.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
if (!CtorAllocate()) return;
Int_t n = fNpoints*sizeof(Double_t);
memcpy(fEXlow, gr.fEXlow, n);
memcpy(fEYlow, gr.fEYlow, n);
memcpy(fEXhigh, gr.fEXhigh, n);
memcpy(fEYhigh, gr.fEYhigh, n);
}
//______________________________________________________________________________
TGraphAsymmErrors::TGraphAsymmErrors(Int_t n)
: TGraph(n)
{
//*-*-*-*-*-*-*-*-*-*-*TGraphAsymmErrors normal constructor*-*-*-*-*-*-*-*-*-*-*-*-*
//*-* ====================================
//
// the arrays are preset to zero
if (!CtorAllocate()) return;
FillZero(0, fNpoints);
}
//______________________________________________________________________________
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 (!CtorAllocate()) return;
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 (!CtorAllocate()) return;
n = fNpoints*sizeof(Double_t);
if(exl) { memcpy(fEXlow, exl, n);
} else { memset(fEXlow, 0, n); }
if(exh) { memcpy(fEXhigh, exh, n);
} else { memset(fEXhigh, 0, n); }
if(eyl) { memcpy(fEYlow, eyl, n);
} else { memset(fEYlow, 0, n); }
if(eyh) { memcpy(fEYhigh, eyh, n);
} else { memset(fEYhigh, 0, n); }
}
//______________________________________________________________________________
TGraphAsymmErrors::TGraphAsymmErrors(const TVector &vx, const TVector &vy, const TVector &vexl, const TVector &vexh, const TVector &veyl, const TVector &veyh)
:TGraph()
{
// 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.
fNpoints = TMath::Min(vx.GetNrows(), vy.GetNrows());
if (!TGraph::CtorAllocate()) return;
if (!CtorAllocate()) return;
for (Int_t i=0; i < fNpoints; i++) {
fX[i] = vx(i);
fY[i] = vy(i);
fEXlow[i] = vexl(i);
fEYlow[i] = veyl(i);
fEXhigh[i] = vexh(i);
fEYhigh[i] = veyh(i);
}
}
//______________________________________________________________________________
TGraphAsymmErrors::TGraphAsymmErrors(const TVectorD &vx, const TVectorD &vy, const TVectorD &vexl, const TVectorD &vexh, const TVectorD &veyl, const TVectorD &veyh)
:TGraph()
{
// 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.
fNpoints = TMath::Min(vx.GetNrows(), vy.GetNrows());
if (!TGraph::CtorAllocate()) return;
if (!CtorAllocate()) return;
for (Int_t i=0; i < fNpoints; i++) {
fX[i] = vx(i);
fY[i] = vy(i);
fEXlow[i] = vexl(i);
fEYlow[i] = veyl(i);
fEXhigh[i] = vexh(i);
fEYhigh[i] = veyh(i);
}
}
//______________________________________________________________________________
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 (!CtorAllocate()) return;
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)
CtorAllocate();
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=GetErrorXlow(i);
exh=GetErrorXhigh(i);
eyl=GetErrorYlow(i);
eyh=GetErrorYhigh(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 = TMath::Min(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 = TMath::Min(ymin,fY[i]/3);
} else {
ymin = fY[i]-fEYlow[i];
}
}
if (fY[i] +fEYhigh[i] > ymax) ymax = fY[i]+fEYhigh[i];
}
}
//______________________________________________________________________________
void TGraphAsymmErrors::CopyAndRelease(Double_t **newarrays,
Int_t ibegin, Int_t iend, Int_t obegin)
{
CopyPoints(newarrays, ibegin, iend, obegin);
if (newarrays) {
delete[] fEXlow;
fEXlow = newarrays[0];
delete[] fEXhigh;
fEXhigh = newarrays[1];
delete[] fEYlow;
fEYlow = newarrays[2];
delete[] fEYhigh;
fEYhigh = newarrays[3];
delete[] fX;
fX = newarrays[4];
delete[] fY;
fY = newarrays[5];
delete[] newarrays;
}
}
//______________________________________________________________________________
Bool_t TGraphAsymmErrors::CopyPoints(Double_t **arrays,
Int_t ibegin, Int_t iend, Int_t obegin)
{
// Copy errors from fE*** to arrays[***]
// or to f*** Copy points.
if (TGraph::CopyPoints(arrays ? arrays+4 : 0, ibegin, iend, obegin)) {
Int_t n = (iend - ibegin)*sizeof(Double_t);
if (arrays) {
memmove(&arrays[0][obegin], &fEXlow[ibegin], n);
memmove(&arrays[1][obegin], &fEXhigh[ibegin], n);
memmove(&arrays[2][obegin], &fEYlow[ibegin], n);
memmove(&arrays[3][obegin], &fEYhigh[ibegin], n);
} else {
memmove(&fEXlow[obegin], &fEXlow[ibegin], n);
memmove(&fEXhigh[obegin], &fEXhigh[ibegin], n);
memmove(&fEYlow[obegin], &fEYlow[ibegin], n);
memmove(&fEYhigh[obegin], &fEYhigh[ibegin], n);
}
return kTRUE;
} else {
return kFALSE;
}
}
//______________________________________________________________________________
Bool_t TGraphAsymmErrors::CtorAllocate(void)
{
// Should be called from ctors after fNpoints has been set
if (!fNpoints) {
fEXlow = fEYlow = fEXhigh = fEYhigh = 0;
return kFALSE;
}
fEXlow = new Double_t[fMaxSize];
fEYlow = new Double_t[fMaxSize];
fEXhigh = new Double_t[fMaxSize];
fEYhigh = new Double_t[fMaxSize];
return kTRUE;
}
//______________________________________________________________________________
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;
}
//______________________________________________________________________________
void TGraphAsymmErrors::FillZero(Int_t begin, Int_t end,
Bool_t from_ctor)
{
// Set zero values for point arrays in the range [begin, end)
if (!from_ctor) {
TGraph::FillZero(begin, end, from_ctor);
}
Int_t n = (end - begin)*sizeof(Double_t);
memset(fEXlow + begin, 0, n);
memset(fEXhigh + begin, 0, n);
memset(fEYlow + begin, 0, n);
memset(fEYhigh + begin, 0, n);
}
//______________________________________________________________________________
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));
}
//______________________________________________________________________________
Double_t TGraphAsymmErrors::GetErrorXhigh(Int_t i) const
{
if (i<0 || i>fNpoints) return -1;
if (fEXhigh) return fEXhigh[i];
return -1;
}
//______________________________________________________________________________
Double_t TGraphAsymmErrors::GetErrorXlow(Int_t i) const
{
if (i<0 || i>fNpoints) return -1;
if (fEXlow) return fEXlow[i];
return -1;
}
//______________________________________________________________________________
Double_t TGraphAsymmErrors::GetErrorYhigh(Int_t i) const
{
if (i<0 || i>fNpoints) return -1;
if (fEYhigh) return fEYhigh[i];
return -1;
}
//______________________________________________________________________________
Double_t TGraphAsymmErrors::GetErrorYlow(Int_t i) const
{
if (i<0 || i>fNpoints) return -1;
if (fEYlow) return fEYlow[i];
return -1;
}
//______________________________________________________________________________
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.
//
// 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.
Double_t *xline = 0;
Double_t *yline = 0;
Int_t if1 = 0;
Int_t if2 = 0;
const Int_t kBASEMARKER=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);
Bool_t option2 = kFALSE;
Bool_t option3 = kFALSE;
Bool_t option4 = kFALSE;
if (strchr(option,'2')) option2 = kTRUE;
if (strchr(option,'3')) option3 = kTRUE;
if (strchr(option,'4')) {option3 = kTRUE; option4 = kTRUE;}
if (option3) {
xline = new Double_t[2*fNpoints];
yline = new Double_t[2*fNpoints];
if (!xline || !yline) {
Error("Paint", "too many points, out of memory");
return;
}
if1 = 1;
if2 = 2*fNpoints;
}
TAttLine::Modify();
TArrow arrow;
arrow.SetLineWidth(GetLineWidth());
arrow.SetLineColor(GetLineColor());
arrow.SetFillColor(GetFillColor());
TBox box;
box.SetLineWidth(GetLineWidth());
box.SetLineColor(GetLineColor());
box.SetFillColor(GetFillColor());
symbolsize = GetMarkerSize();
sbase = symbolsize*kBASEMARKER;
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*kBASEMARKER/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]);
// draw the error rectangles
if (option2) {
box.PaintBox(gPad->XtoPad(fX[i] - fEXlow[i]),
gPad->YtoPad(fY[i] - fEYlow[i]),
gPad->XtoPad(fX[i] + fEXhigh[i]),
gPad->YtoPad(fY[i] + fEYhigh[i]));
continue;
}
// keep points for fill area drawing
if (option3) {
xline[if1-1] = x;
xline[if2-1] = x;
yline[if1-1] = gPad->YtoPad(fY[i] + fEYhigh[i]);
yline[if2-1] = gPad->YtoPad(fY[i] - fEYlow[i]);
if1++;
if2--;
continue;
}
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);
if (option3) {
Int_t logx = gPad->GetLogx();
Int_t logy = gPad->GetLogy();
gPad->SetLogx(0);
gPad->SetLogy(0);
if (option4) PaintGraph(2*fNpoints, xline, yline,"FC");
else PaintGraph(2*fNpoints, xline, yline,"F");
gPad->SetLogx(logx);
gPad->SetLogy(logy);
delete [] xline;
delete [] yline;
}
}
//______________________________________________________________________________
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]);
}
}
//______________________________________________________________________________
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::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);
}
ROOT page - Class index - Class Hierarchy - Top of the page
This page has been automatically generated. If you have any comments or suggestions about the page layout send a mail to ROOT support, or contact the developers with any questions or problems regarding ROOT.