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Reference Guide
BreitWigner.C File Reference

Detailed Description

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Tutorial illustrating how to create a plot comparing a Breit Wigner to a Relativistic Breit Wigner

can be run with:

root[0] .x BreitWigner.C
#include "TMath.h"
#include <limits>
#include <string>
#include "TAxis.h"
#include "TGraph.h"
#include "TCanvas.h"
#include "TLatex.h"
#include "TLegend.h"
#include "TStyle.h" //For gStyle to remove stat box.
void plotTwoTGraphs(Double_t x[], Double_t y1[], Double_t y2[], const Int_t nPoints
, Double_t lowerXLimit, Double_t upperXLimit
, Double_t lowerYLimit, Double_t upperYLimit
, std::string legend1, std::string legend2
, std::string plotTitle1, std::string plotTitle2, std::string plotTitle3
, std::string pdfTitle){
///////////////////////////////////////////////////////
//Define variables for plot aesthetics and positioning
Double_t legendXPos = 0.63; Double_t legendYPos = 0.85;
Double_t legendXWidth = 0.29; Double_t legendYHeight = 0.1;
Double_t plotTitleXPos = 0.23; Double_t plotTitleYPos = 0.25;
Double_t fontSize = 0.04;
Double_t lineWidth = 2;
bool setLimitPlotLogScale = true;
std::string xAxisTitle = "E [GeV]"; std::string yAxisTitle = "Events";
Double_t xAxisTitleOffset = 1; Double_t yAxisTitleOffset = 1.3;
///////////////////////////////////////////////////////
// Initialize TGraphs
TGraph* gr1 = new TGraph(nPoints,x,y1);
TGraph* gr2 = new TGraph(nPoints,x,y2);
gr1->SetLineWidth(lineWidth);
gr2->SetLineWidth(lineWidth);
/////////////////////////////////////////////////////////
// Initialize canvas
TCanvas* c1 = new TCanvas("c1","transparent pad",200,10,600,600);
c1->SetLogy(setLimitPlotLogScale);
c1->SetTicks(1,1);
c1->SetRightMargin(0.02);
c1->SetTopMargin(0.02);
///////////////////////////////////////////////////////
//Make just a basic invisible TGraph just for the axes
const Double_t axis_x[2] = {lowerXLimit,upperXLimit};
const Double_t axis_y[2] = {lowerYLimit,upperYLimit};
TGraph* grAxis = new TGraph(2, axis_x, axis_y);
grAxis->SetTitle("");
grAxis->GetYaxis()->SetTitle(yAxisTitle.c_str());
grAxis->GetXaxis()->SetTitle(xAxisTitle.c_str());
grAxis->GetXaxis()->SetRangeUser(lowerXLimit,upperXLimit);
grAxis->GetYaxis()->SetRangeUser(lowerYLimit,upperYLimit);
grAxis->GetXaxis()->SetLabelSize(fontSize);
grAxis->GetYaxis()->SetLabelSize(fontSize);
grAxis->GetXaxis()->SetTitleSize(fontSize);
grAxis->GetYaxis()->SetTitleSize(fontSize);
grAxis->GetXaxis()->SetTitleOffset(xAxisTitleOffset);
grAxis->GetYaxis()->SetTitleOffset(yAxisTitleOffset);
grAxis->SetLineWidth(0);//So invisible
///////////////////////////////////////////////////////////
// Make legend and set aesthetics
auto legend = new TLegend(legendXPos,legendYPos,legendXPos+legendXWidth,legendYPos+legendYHeight);
legend->SetFillStyle(0);
legend->SetBorderSize(0);
legend->SetTextSize(fontSize);
legend->AddEntry(gr1,legend1.c_str(),"L");
legend->AddEntry(gr2,legend2.c_str(),"L");
/////////////////////////////////////////////////////////////
// Add plot title to plot. Make in three lines so not crowded.
// Shift each line down by shiftY
float shiftY{0.037};
TLatex* tex_Title = new TLatex(plotTitleXPos,plotTitleYPos-0*shiftY,plotTitle1.c_str());
tex_Title->SetNDC();
tex_Title->SetTextFont(42);
tex_Title->SetTextSize(fontSize);
tex_Title->SetLineWidth(lineWidth);
TLatex* tex_Title2 = new TLatex(plotTitleXPos,plotTitleYPos-1*shiftY,plotTitle2.c_str());
tex_Title2->SetNDC();
tex_Title2->SetTextFont(42);
tex_Title2->SetTextSize(fontSize);
tex_Title2->SetLineWidth(lineWidth);
TLatex* tex_Title3 = new TLatex(plotTitleXPos,plotTitleYPos-2*shiftY,plotTitle3.c_str());
tex_Title3->SetNDC();
tex_Title3->SetTextFont(42);
tex_Title3->SetTextSize(fontSize);
tex_Title3->SetLineWidth(lineWidth);
/////////////////////////////////////
// Draw everything
grAxis->Draw("AL");
gr1->Draw("L same");
gr2->Draw("L same");
legend->Draw();
tex_Title->Draw();
tex_Title2->Draw();
tex_Title3->Draw();
c1->RedrawAxis(); //Be sure to redraw axis AFTER plotting TGraphs otherwise TGraphs will be on top of tick marks and axis borders.
gPad->Print(pdfTitle.c_str());
}
void BreitWigner(){
/////////////////////////////////////////////////////////
// Define x axis limits and steps for each plotted point
const Int_t nPoints = 1000;
Double_t xMinimum = 0; Double_t xMaximum = 13000;
Double_t xStepSize = (xMaximum-xMinimum)/nPoints;
///////////////////////////////////////////////////////
// Define arrays of (x,y) points.
Double_t x[nPoints];
Double_t y_nonRelBW[nPoints], y_relBW[nPoints];
//////////////////////////////////
// Define Breit-Wigner parameters
Double_t width = 1350;
Double_t sigma = 269.7899;
Double_t median = 9000;
///////////////////////////////////////////////////
// Loop over x axis range, filling in (x,y) points,
// and finding y minimums and maximums for axis limit.
Double_t yMinimum = std::numeric_limits<Double_t>::max();
Double_t yMaximum = TMath::BreitWignerRelativistic(median,median,width); //y maximum is at x=median (and non relativistic = relativistic at median so choice of function does not matter).
for (Int_t i=0;i<nPoints;i++) {
Double_t currentX = xMinimum+i*xStepSize;
x[i] = currentX;
y_nonRelBW[i] = TMath::BreitWigner(currentX,median,width);
y_relBW[i] = TMath::BreitWignerRelativistic(currentX,median,width);
if (y_nonRelBW[i]<yMinimum){yMinimum = y_nonRelBW[i];}
if (y_relBW[i]<yMinimum){yMinimum = y_relBW[i];}
}
plotTwoTGraphs(x, y_nonRelBW, y_relBW, nPoints
, xMinimum, xMaximum //xAxis limits
, yMinimum/4, yMaximum*4 //yAxis limits, expand for aesthetics.
,"NonRel BW", "Rel BW" //Legend entries
, "Comparing BW", "M = " + std::to_string(int(round(median))) + " GeV", "#Gamma = " + std::to_string(int(round(width))) + " GeV" //Plot Title entry (three lines)
, "BW_M"+std::to_string(int(round(median)))+"_Gamma" + std::to_string(int(round(width))) +".pdf)" //PDF file title.
);
}
int Int_t
Definition: RtypesCore.h:45
double Double_t
Definition: RtypesCore.h:59
@ kBlack
Definition: Rtypes.h:65
@ kBlue
Definition: Rtypes.h:66
Option_t Option_t TPoint TPoint const char y2
Option_t Option_t width
Option_t Option_t TPoint TPoint const char y1
R__EXTERN TStyle * gStyle
Definition: TStyle.h:414
#define gPad
Definition: TVirtualPad.h:288
virtual void SetTitleOffset(Float_t offset=1)
Set distance between the axis and the axis title.
Definition: TAttAxis.cxx:301
virtual void SetLabelSize(Float_t size=0.04)
Set size of axis labels.
Definition: TAttAxis.cxx:206
virtual void SetTitleSize(Float_t size=0.04)
Set size of axis title.
Definition: TAttAxis.cxx:312
virtual void SetLineWidth(Width_t lwidth)
Set the line width.
Definition: TAttLine.h:43
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition: TAttLine.h:40
virtual void SetTextFont(Font_t tfont=62)
Set the text font.
Definition: TAttText.h:46
virtual void SetTextSize(Float_t tsize=1)
Set the text size.
Definition: TAttText.h:47
virtual void SetRangeUser(Double_t ufirst, Double_t ulast)
Set the viewing range for the axis from ufirst to ulast (in user coordinates, that is,...
Definition: TAxis.cxx:978
The Canvas class.
Definition: TCanvas.h:23
A TGraph is an object made of two arrays X and Y with npoints each.
Definition: TGraph.h:41
void Draw(Option_t *chopt="") override
Draw this graph with its current attributes.
Definition: TGraph.cxx:808
TAxis * GetXaxis() const
Get x axis of the graph.
Definition: TGraph.cxx:1553
TAxis * GetYaxis() const
Get y axis of the graph.
Definition: TGraph.cxx:1563
void SetTitle(const char *title="") override
Change (i.e.
Definition: TGraph.cxx:2338
To draw Mathematical Formula.
Definition: TLatex.h:18
This class displays a legend box (TPaveText) containing several legend entries.
Definition: TLegend.h:23
virtual void SetTitle(const char *title="")
Set the title of the TNamed.
Definition: TNamed.cxx:164
virtual void Draw(Option_t *option="")
Default Draw method for all objects.
Definition: TObject.cxx:274
void SetOptStat(Int_t stat=1)
The type of information printed in the histogram statistics box can be selected via the parameter mod...
Definition: TStyle.cxx:1589
virtual void SetNDC(Bool_t isNDC=kTRUE)
Set NDC mode on if isNDC = kTRUE, off otherwise.
Definition: TText.cxx:813
RVec< PromoteType< T > > round(const RVec< T > &v)
Definition: RVec.hxx:1815
const Double_t sigma
return c1
Definition: legend1.C:41
Double_t x[n]
Definition: legend1.C:17
Double_t BreitWigner(Double_t x, Double_t mean=0, Double_t gamma=1)
Calculates a Breit Wigner function with mean and gamma.
Definition: TMath.cxx:442
Double_t BreitWignerRelativistic(Double_t x, Double_t median=0, Double_t gamma=1)
Calculates a Relativistic Breit Wigner function with median and gamma.
Definition: TMath.cxx:452
Author
Jack Lindon

Definition in file BreitWigner.C.