void StandardProfileInspectorDemo(const char* infile = "",
const char* workspaceName = "combined",
const char* modelConfigName = "ModelConfig",
const char* dataName = "obsData"){
/////////////////////////////////////////////////////////////
// First part is just to access a user-defined file
// or create the standard example file if it doesn't exist
////////////////////////////////////////////////////////////
const char* filename = "";
if (!strcmp(infile,""))
filename = "results/example_combined_GaussExample_model.root";
else
filename = infile;
// Check if example input file exists
TFile *file = TFile::Open(filename);
// if input file was specified byt not found, quit
if(!file && strcmp(infile,"")){
cout <<"file not found" << endl;
return;
}
// if default file not found, try to create it
if(!file ){
// Normally this would be run on the command line
cout <<"will run standard hist2workspace example"<<endl;
gROOT->ProcessLine(".! prepareHistFactory .");
gROOT->ProcessLine(".! hist2workspace config/example.xml");
cout <<"\n\n---------------------"<<endl;
cout <<"Done creating example input"<<endl;
cout <<"---------------------\n\n"<<endl;
}
// now try to access the file again
file = TFile::Open(filename);
if(!file){
// if it is still not there, then we can't continue
cout << "Not able to run hist2workspace to create example input" <<endl;
return;
}
/////////////////////////////////////////////////////////////
// Tutorial starts here
////////////////////////////////////////////////////////////
// get the workspace out of the file
RooWorkspace* w = (RooWorkspace*) file->Get(workspaceName);
if(!w){
cout <<"workspace not found" << endl;
return;
}
// get the modelConfig out of the file
ModelConfig* mc = (ModelConfig*) w->obj(modelConfigName);
// get the modelConfig out of the file
RooAbsData* data = w->data(dataName);
// make sure ingredients are found
if(!data || !mc){
w->Print();
cout << "data or ModelConfig was not found" <<endl;
return;
}
//////////////////////////////////////////////
// now use the profile inspector
ProfileInspector p;
TList* list = p.GetListOfProfilePlots(*data,mc);
// now make plots
TCanvas* c1 = new TCanvas("c1","ProfileInspectorDemo"); //,800,200);
c1->Divide(4,4);
// const RooArgSet* nuis_params = mc->GetNuisanceParameters();
for(int i=0; i<list->GetSize(); ++i){
c1->cd(i+1);
//RooRealVar* nuis = (RooRealVar*) nuis_params->At(i);
TGraph* graph = (TGraph*) list->At(i);
std::string y_title = graph->GetYaxis()->GetTitle();
y_title = "Profiled value of: " + y_title;
graph->GetYaxis()->SetTitle(y_title.c_str());
graph->GetYaxis()->SetTitleSize(0.05);
graph->GetYaxis()->SetTitleOffset(0.8);
//std::string poi_name = graph->GetXaxis()->GetTitle();
//graph->GetYaxis()->SetTitle(var->GetName());
graph->GetXaxis()->SetTitleSize(0.05);
graph->GetXaxis()->SetTitleOffset(0.8);
graph->Draw("al");
//list->At(i)->Draw("al");
}
c1->Print("ProfileInspector.eps");
c1->Print("ProfileInspector.pdf");
cout << endl;
}
void StandardProfileInspectorDemo(const char* infile = "",
const char* workspaceName = "combined",
const char* modelConfigName = "ModelConfig",
const char* dataName = "obsData"){
/////////////////////////////////////////////////////////////
// First part is just to access a user-defined file
// or create the standard example file if it doesn't exist
////////////////////////////////////////////////////////////
const char* filename = "";
if (!strcmp(infile,""))
filename = "results/example_combined_GaussExample_model.root";
else
filename = infile;
// Check if example input file exists
TFile *file = TFile::Open(filename);
// if input file was specified byt not found, quit
if(!file && strcmp(infile,"")){
cout <<"file not found" << endl;
return;
}
// if default file not found, try to create it
if(!file ){
// Normally this would be run on the command line
cout <<"will run standard hist2workspace example"<<endl;
gROOT->ProcessLine(".! prepareHistFactory .");
gROOT->ProcessLine(".! hist2workspace config/example.xml");
cout <<"\n\n---------------------"<<endl;
cout <<"Done creating example input"<<endl;
cout <<"---------------------\n\n"<<endl;
}
// now try to access the file again
file = TFile::Open(filename);
if(!file){
// if it is still not there, then we can't continue
cout << "Not able to run hist2workspace to create example input" <<endl;
return;
}
/////////////////////////////////////////////////////////////
// Tutorial starts here
////////////////////////////////////////////////////////////
// get the workspace out of the file
RooWorkspace* w = (RooWorkspace*) file->Get(workspaceName);
if(!w){
cout <<"workspace not found" << endl;
return;
}
// get the modelConfig out of the file
ModelConfig* mc = (ModelConfig*) w->obj(modelConfigName);
// get the modelConfig out of the file
RooAbsData* data = w->data(dataName);
// make sure ingredients are found
if(!data || !mc){
w->Print();
cout << "data or ModelConfig was not found" <<endl;
return;
}
//////////////////////////////////////////////
// now use the profile inspector
ProfileInspector p;
TList* list = p.GetListOfProfilePlots(*data,mc);
// now make plots
TCanvas* c1 = new TCanvas("c1","ProfileInspectorDemo",800,200);
c1->Divide(list->GetSize());
for(int i=0; i<list->GetSize(); ++i){
c1->cd(i+1);
list->At(i)->Draw("al");
}
// now make plots
TCanvas* c1 = new TCanvas("c1","ProfileInspectorDemo",800,200);
if(list->GetSize()>4){
double n = list->GetSize();
int nx = (int)sqrt(n) ;
int ny = TMath::CeilNint(n/nx);
nx = TMath::CeilNint( sqrt(n) );
c1->Divide(ny,nx);
} else
c1->Divide(list->GetSize());
for(int i=0; i<list->GetSize(); ++i){
c1->cd(i+1);
list->At(i)->Draw("al");
}
}
void test_counting_experiment() {
////////////////////// MODEL BUILDING /////////////////////////////////
///////////////////////////////////////////////////////////////////////////
/*
N_s = N_tot_theory(Mass,Xsec) * Acceptance_SR * Eff_AmBe_bin_i * mu
N_b = N_Co_SR_bin_i * Norm_factor
Xesec: considered 10^-40 cm^2
Norm_factor = N_Data_CR / N_Co_CR --> assuming no difference between Co and Data in CR and SR.
N_tot_theory(Mass,Xsec): for 225 livedays, 45kg and considering Xsec. It is a constant, no uncertainty at the moment.
---Costraint Signal
nuissance parameter = Acceptance_SR, Eff_AmBe_bin_i
Gauss(Acceptance_SR_obs | Acceptance_SR, err.)
Poisson(S0_i | S_tot_SR * Eff_AmBe_bin_i)
---Costraint Bkg
nuissance parameter = N_Co_SR_bin_i, Norm_factor
Gauss(Norm_factor_obs | Norm_factor, err)
Poisson(B0_i | N_Co_SR_bin_i)
---- WARNING:: convergence problems: mu_hat should always be >> 1, too small values have problem in finding minimum
because mu is set >0. ---> Try to fix Xsec in order to have mu_hat ~ 10
*/
RooWorkspace w("w");
//gROOT->ProcessLine(".L retrieve_input_from_histo_NoSys.C+");
gROOT->ProcessLine(".L retrieve_input_from_histo.C+");
retrieve_input_from_histo(w);
// Building the model
ModelConfig mc("ModelConfig",&w);
mc.SetPdf(*w.pdf("model"));
mc.SetParametersOfInterest(*w.var("mu"));
// Setting nuissance parameter
mc.SetNuisanceParameters(*w.set("nuissance_parameter"));
// need now to set the global observable
mc.SetGlobalObservables(*w.set("g_observables"));
mc.SetObservables(*w.set("observables"));
// this is needed for the hypothesis tests
mc.SetSnapshot(*w.var("mu"));
// make data set with the number of observed events
RooDataSet data("data","", *w.set("observables"));
data.add(*w.set("observables"));
// import data set in workspace and save it in a file
w.import(data);
// import model in the workspace
w.import(mc);
w.writeToFile("CountingModel.root", true);
w.Print();
data.Print();
/*
cout << w.var("S_i")->getValV() << endl;//<< " " << w.var("S_i_exp")->getValV() << endl;
///////////////////////////////////////////////////////////////////////
ProfileLikelihoodCalculator pl(data,mc);
pl.SetConfidenceLevel(0.95);
LikelihoodInterval* interval = pl.GetInterval();
// find the iterval on the first Parameter of Interest
RooRealVar* firstPOI = (RooRealVar*) mc.GetParametersOfInterest()->first();
double lowerLimit = interval->LowerLimit(*firstPOI);
double upperLimit = interval->UpperLimit(*firstPOI);
cout << "\n95% interval on " <<firstPOI->GetName()<<" is : ["<<
lowerLimit << ", "<<
upperLimit <<"] "<<endl;
LikelihoodIntervalPlot * plot = new LikelihoodIntervalPlot(interval);
// plot->SetRange(0,50); // possible eventually to change ranges
//plot->SetNPoints(50); // do not use too many points, it could become very slow for some models
plot->Draw(""); // use option TF1 if too slow (plot.Draw("tf1")
*/
////////////////////////// hypo test
// get the modelConfig (S+B) out of the file
// and create the B model from the S+B model
ModelConfig * sbModel = (ModelConfig*) mc.Clone();
sbModel->SetName("S+B Model");
RooRealVar* poi = (RooRealVar*) sbModel->GetParametersOfInterest()->first();
poi->setVal(1); // set POI snapshot in S+B model for expected significance
sbModel->SetSnapshot(*poi);
ModelConfig * bModel = (ModelConfig*) mc.Clone();
bModel->SetName("B Model");
RooRealVar* poi2 = (RooRealVar*) bModel->GetParametersOfInterest()->first();
poi2->setVal(0);
bModel->SetSnapshot( *poi2 );
//------------------Limit calculation for N_th event expected = 10
AsymptoticCalculator ac(data, *bModel, *sbModel);
//ac.SetOneSidedDiscovery(true); // for one-side discovery test
// ac.SetOneSided(true); // for one-side tests (limits)
ac.SetQTilde(true);
ac.SetPrintLevel(2); // to suppress print level
// create hypotest inverter
// passing the desired calculator
HypoTestInverter *calc = new HypoTestInverter(ac); // for asymptotic
//HypoTestInverter calc(fc); // for frequentist
calc->SetConfidenceLevel(0.90);
//calc->UseCLs(false);
calc->UseCLs(true);
int npoints = 500; // number of points to scan
//int npoints = 1000; // number of points to scan default 1000
// min and max (better to choose smaller intervals)
double poimin = poi->getMin();
double poimax = poi->getMax();
//poimin = 0; poimax=10;
std::cout << "Doing a fixed scan in interval : " << poimin << " , " << poimax << std::endl;
calc->SetFixedScan(npoints,poimin,poimax);
calc->SetVerbose(2);
HypoTestInverterResult * r = calc->GetInterval();
double upperLimit = r->UpperLimit();
std::cout << "The computed Expected upper limit is: " << r->GetExpectedUpperLimit(0) << std::endl;
//------------ Getting the interval as function of m --------------//
/* ifstream in;
in.open("integral_mass.dat");
vector <double> masses_v;
vector <double> observed_v;
vector <double> expected_v;
vector <double> expected_gaud_v;
vector <double> expected_S1_up_v;
vector <double> expected_S1_dw_v;
vector <double> expected_S2_up_v;
vector <double> expected_S2_dw_v;
double mass_itr =0.;
double Nev_exp_th_itr =0.;
double xsec_modifier = 10.;
double N_tot_theory = w.var("N_tot_theory")->getValV();
while(mass_itr <1000.){
in >> mass_itr;
in >> Nev_exp_th_itr;
xsec_modifier = Nev_exp_th_itr * 225.009 * 34.; //225.009 livedays and 34 kg and 10^-40 cm2 Xsec.
masses_v.push_back(mass_itr);
observed_v.push_back( 1.e-40 * N_tot_theory / xsec_modifier * upperLimit );
expected_v.push_back( 1.e-40 * N_tot_theory / xsec_modifier * r->GetExpectedUpperLimit(0) );
expected_gaud_v.push_back(7e-38 * 1.37590955945e-05 / Nev_exp_th_itr );
expected_S1_up_v.push_back(1.e-40 * N_tot_theory / xsec_modifier * r->GetExpectedUpperLimit(1));
expected_S2_up_v.push_back(1.e-40 * N_tot_theory / xsec_modifier * r->GetExpectedUpperLimit(2));
expected_S2_dw_v.push_back(1.e-40 * N_tot_theory / xsec_modifier * r->GetExpectedUpperLimit(-2));
expected_S1_dw_v.push_back(1.e-40 * N_tot_theory / xsec_modifier * r->GetExpectedUpperLimit(-1));
cout << "Expected median limit for mass " << mass_itr << " GeV = " << 1.e-40 * N_tot_theory / xsec_modifier * r->GetExpectedUpperLimit(0) << " cm^2 " << endl;
// observed_v.push_back( w.var("Xsec")->getValV() * w.var("K_m")->getValV()* upperLimit );
// expected_v.push_back( w.var("Xsec")->getValV() * w.var("K_m")->getValV()* r->GetExpectedUpperLimit(0) );
// expected_S1_up_v.push_back(w.var("Xsec")->getValV() * w.var("K_m")->getValV()* r->GetExpectedUpperLimit(1));
// expected_S2_up_v.push_back(w.var("Xsec")->getValV() * w.var("K_m")->getValV()* r->GetExpectedUpperLimit(2));
// expected_S2_dw_v.push_back(w.var("Xsec")->getValV() * w.var("K_m")->getValV()* r->GetExpectedUpperLimit(-2));
// expected_S1_dw_v.push_back(w.var("Xsec")->getValV() * w.var("K_m")->getValV()* r->GetExpectedUpperLimit(-1));
}
in.close();
const int n = masses_v.size();
double xe[n];
double mA[n];
double observed[n];
double expected[n];
double expected_gaudenz[n];
double exSigma1_l[n];
double exSigma1_u[n];
double exSigma2_l[n];
double exSigma2_u[n];
for(int k=0; k< n; k++){
mA[k] = masses_v[k];
observed[k] = observed_v[k];
expected[k] = expected_v[k];
expected_gaudenz[k] = expected_gaud_v[k];
exSigma1_l[k] =expected_v[k] - expected_S1_dw_v[k] ;
exSigma1_u[k] = expected_S1_up_v[k] - expected_v[k];
exSigma2_l[k] = expected_v[k] - expected_S2_dw_v[k];
exSigma2_u[k] = expected_S2_up_v[k] - expected_v[k] ;
}
TGraphErrors *obs_limits = new TGraphErrors(n, mA, observed);
TGraphErrors *Exp_limits = new TGraphErrors(n, mA, expected );
TGraphAsymmErrors *Exp_limitsS1 = new TGraphAsymmErrors(n, mA, expected ,xe, xe, exSigma1_l, exSigma1_u );
TGraphAsymmErrors *Exp_limitsS2 = new TGraphAsymmErrors(n, mA, expected ,xe, xe, exSigma2_l, exSigma2_u);
TGraphErrors *Exp_limits_gaudenz = new TGraphErrors( n, mA, expected_gaudenz);
//double expected_xmass[15] = {8e-36,7e-37, 2e-37, 1e-37, 8e-38, 6e-38, 5.5e-38, 5e-38, 4.3e-38, 5e-38, 6e-38, 7e-38, 9e-38, 1.2e-37, 1.5e-37};
//double m_xmass[15] = { 20, 30., 40., 50., 60., 70., 80., 90., 100., 200., 300., 400, 500.,700., 1000.};
TGraphErrors *Exp_limits_xmass = new TGraphErrors(16);
Exp_limits_xmass->SetPoint(0,20,8e-36);
Exp_limits_xmass->SetPointError(0,0,0);
Exp_limits_xmass->SetPoint(1,29.8071,7.162923e-37);
Exp_limits_xmass->SetPointError(1,0,0);
Exp_limits_xmass->SetPoint(2,39.90202,2.027528e-37);
Exp_limits_xmass->SetPointError(2,0,0);
Exp_limits_xmass->SetPoint(3,53.41583,9.91722e-38);
Exp_limits_xmass->SetPointError(3,0,0);
Exp_limits_xmass->SetPoint(4,62.16429,7.461589e-38);
Exp_limits_xmass->SetPointError(4,0,0);
Exp_limits_xmass->SetPoint(5,69.85718,6.3506e-38);
Exp_limits_xmass->SetPointError(5,0,0);
Exp_limits_xmass->SetPoint(6,83.21777,5.354015e-38);
Exp_limits_xmass->SetPointError(6,0,0);
Exp_limits_xmass->SetPoint(7,90,5e-38);
Exp_limits_xmass->SetPointError(7,0,0);
Exp_limits_xmass->SetPoint(8,105.0887,4.600252e-38);
Exp_limits_xmass->SetPointError(8,0,0);
Exp_limits_xmass->SetPoint(9,200,5e-38);
Exp_limits_xmass->SetPointError(9,0,0);
Exp_limits_xmass->SetPoint(10,300,6e-38);
Exp_limits_xmass->SetPointError(10,0,0);
Exp_limits_xmass->SetPoint(11,388.2045,7.252295e-38);
Exp_limits_xmass->SetPointError(11,0,0);
Exp_limits_xmass->SetPoint(12,590.8438,9.823615e-38);
Exp_limits_xmass->SetPointError(12,0,0);
Exp_limits_xmass->SetPoint(13,746.1269,1.210266e-37);
Exp_limits_xmass->SetPointError(13,0,0);
Exp_limits_xmass->SetPoint(14,1000,1.5e-37);
Exp_limits_xmass->SetPointError(14,0,0);
Exp_limits_xmass->SetPoint(15,4244.204,4.354065e-37);
Exp_limits_xmass->SetPointError(15,0,0);
TCanvas *c1 = new TCanvas("limits", "limit", 600, 600);
Exp_limitsS1->SetFillColor(3);
Exp_limitsS1->SetLineColor(3);
Exp_limitsS1->SetMarkerColor(3);
Exp_limitsS1->SetMarkerSize(0);
Exp_limitsS2->SetFillColor(5);
Exp_limitsS2->SetLineColor(5);
Exp_limitsS2->SetMarkerColor(5);
Exp_limitsS2->SetMarkerSize(0);
obs_limits->SetFillColor(0);
obs_limits->SetLineWidth(3);
obs_limits->SetMarkerSize(0);
Exp_limits->SetFillColor(0);
Exp_limits->SetMarkerSize(0);
Exp_limits->SetLineStyle(7);
Exp_limits->SetLineWidth(3);
Exp_limits_gaudenz->SetFillColor(0);
Exp_limits_gaudenz->SetMarkerSize(0);
Exp_limits_gaudenz->SetLineWidth(3);
Exp_limits_gaudenz->SetLineColor(4);
Exp_limits_xmass->SetFillColor(0);
Exp_limits_xmass->SetMarkerSize(0);
Exp_limits_xmass->SetLineWidth(3);
Exp_limits_xmass->SetLineColor(2);
//Exp_limitsS2->GetYaxis()->SetTitle("#sigma#timesBR( #phi #rightarrow #tau#tau ) [pb]");
Exp_limitsS2->GetYaxis()->SetTitle("#sigma");
Exp_limitsS2->GetXaxis()->SetTitle("M [GeV]");
Exp_limitsS2->GetXaxis()->SetLimits(9.,1000.);
Exp_limitsS2->GetYaxis()->SetRangeUser(1E-38,1E-30);
Exp_limits->GetXaxis()->SetLimits(9.,1000.);
Exp_limits->GetYaxis()->SetRangeUser(1E-38,1E-30);
Exp_limitsS2->Draw("Al3");
Exp_limitsS1->Draw("sameL3");
Exp_limits->Draw("PL");
Exp_limits_gaudenz->Draw("PC");
Exp_limits_xmass->Draw("PC");
//obs_limits->Draw("PL");
TLegend* lego = new TLegend(0.2,0.9,0.5,0.7);
lego->SetTextSize(0.033);
lego->SetFillColor(0);
lego->SetBorderSize(0);
lego->AddEntry(obs_limits,"Observed 90\% CLs limit");
lego->AddEntry(Exp_limits_gaudenz, "Expected 90\% Gaudenz");
lego->AddEntry(Exp_limits_xmass, "Expected 90\% XMASS");
lego->AddEntry(Exp_limits, "Expected 90\% CLs limit");
lego->AddEntry(Exp_limitsS1,"1 #sigma","f");
lego->AddEntry(Exp_limitsS2,"2 #sigma","f");
lego->Draw();
gPad->SetLogy();
gPad->SetLogx();
gPad->RedrawAxis("g");
myText(0.4,0.86,2,"Test");
*/
// now use the profile inspector
ProfileInspector p;
TList* list = p.GetListOfProfilePlots(data,&mc);
// now make plots
TCanvas* c1 = new TCanvas("c1","ProfileInspectorDemo",800,200);
if(list->GetSize()>4){
double n = list->GetSize();
int nx = (int)sqrt(n) ;
int ny = TMath::CeilNint(n/nx);
nx = TMath::CeilNint( sqrt(n) );
c1->Divide(ny,nx);
} else
c1->Divide(list->GetSize());
for(int i=0; i<list->GetSize(); ++i){
c1->cd(i+1);
list->At(i)->Draw("al");
}
cout << endl;
/* // plot now the result of the scan
HypoTestInverterPlot *plot = new HypoTestInverterPlot("HTI_Result_Plot","HypoTest Scan Result",r);
// plot in a new canvas with style
TCanvas * c1 = new TCanvas("HypoTestInverter Scan");
c1->SetLogy(false);
plot->Draw("2CL"); // plot also CLb and CLs+b
//plot->Draw("OBS"); // plot only observed p-value
*/
// plot also in a new canvas the test statistics distributions
// plot test statistics distributions for the two hypothesis
/* // when distribution is generated (case of FrequentistCalculators)
const int n = r->ArraySize();
if (n> 0 && r->GetResult(0)->GetNullDistribution() ) {
TCanvas * c2 = new TCanvas("Test Statistic Distributions","",2);
if (n > 1) {
int ny = TMath::CeilNint( sqrt(n) );
int nx = TMath::CeilNint(double(n)/ny);
c2->Divide( nx,ny);
}
for (int i=0; i<n; i++) {
if (n > 1) c2->cd(i+1);
SamplingDistPlot * pl = plot->MakeTestStatPlot(i);
pl->SetLogYaxis(true);
pl->Draw();
}
}
*/
}
void StandardProfileInspectorDemo(const char* infile = "",
const char* workspaceName = "combined",
const char* modelConfigName = "ModelConfig",
const char* dataName = "obsData"){
/////////////////////////////////////////////////////////////
// First part is just to access a user-defined file
// or create the standard example file if it doesn't exist
////////////////////////////////////////////////////////////
const char* filename = "";
if (!strcmp(infile,"")) {
filename = "results/example_combined_GaussExample_model.root";
bool fileExist = !gSystem->AccessPathName(filename); // note opposite return code
// if file does not exists generate with histfactory
if (!fileExist) {
#ifdef _WIN32
cout << "HistFactory file cannot be generated on Windows - exit" << endl;
return;
#endif
// Normally this would be run on the command line
cout <<"will run standard hist2workspace example"<<endl;
gROOT->ProcessLine(".! prepareHistFactory .");
gROOT->ProcessLine(".! hist2workspace config/example.xml");
cout <<"\n\n---------------------"<<endl;
cout <<"Done creating example input"<<endl;
cout <<"---------------------\n\n"<<endl;
}
}
else
filename = infile;
// Try to open the file
TFile *file = TFile::Open(filename);
// if input file was specified byt not found, quit
if(!file ){
cout <<"StandardRooStatsDemoMacro: Input file " << filename << " is not found" << endl;
return;
}
/////////////////////////////////////////////////////////////
// Tutorial starts here
////////////////////////////////////////////////////////////
// get the workspace out of the file
RooWorkspace* w = (RooWorkspace*) file->Get(workspaceName);
if(!w){
cout <<"workspace not found" << endl;
return;
}
// get the modelConfig out of the file
ModelConfig* mc = (ModelConfig*) w->obj(modelConfigName);
// get the modelConfig out of the file
RooAbsData* data = w->data(dataName);
// make sure ingredients are found
if(!data || !mc){
w->Print();
cout << "data or ModelConfig was not found" <<endl;
return;
}
//////////////////////////////////////////////
// now use the profile inspector
ProfileInspector p;
TList* list = p.GetListOfProfilePlots(*data,mc);
// now make plots
TCanvas* c1 = new TCanvas("c1","ProfileInspectorDemo",800,200);
if(list->GetSize()>4){
double n = list->GetSize();
int nx = (int)sqrt(n) ;
int ny = TMath::CeilNint(n/nx);
nx = TMath::CeilNint( sqrt(n) );
c1->Divide(ny,nx);
} else
c1->Divide(list->GetSize());
for(int i=0; i<list->GetSize(); ++i){
c1->cd(i+1);
list->At(i)->Draw("al");
}
cout << endl;
}
