ROOT   Reference Guide
rs401d_FeldmanCousins.C File Reference

## Detailed Description

Neutrino Oscillation Example from Feldman & Cousins

This tutorial shows a more complex example using the FeldmanCousins utility to create a confidence interval for a toy neutrino oscillation experiment. The example attempts to faithfully reproduce the toy example described in Feldman & Cousins' original paper, Phys.Rev.D57:3873-3889,1998.

␛[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby␛[0m
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
generate toy data with nEvents = 692
**********
** 1 **SET PRINT 1
**********
**********
** 2 **SET NOGRAD
**********
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 deltaMSq 4.00000e+01 1.95000e+01 1.00000e+00 3.00000e+02
2 sinSq2theta 6.00000e-03 2.00000e-03 0.00000e+00 2.00000e-02
**********
** 3 **SET ERR 0.5
**********
**********
** 4 **SET PRINT 1
**********
**********
** 5 **SET STR 1
**********
NOW USING STRATEGY 1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
** 6 **MIGRAD 1000 1
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION. STRATEGY 1. CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=-1131.15 FROM MIGRAD STATUS=INITIATE 8 CALLS 9 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 deltaMSq 4.00000e+01 1.95000e+01 1.99953e-01 1.35503e+01
2 sinSq2theta 6.00000e-03 2.00000e-03 2.21072e-01 -1.80161e+00
ERR DEF= 0.5
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-1131.34 FROM MIGRAD STATUS=CONVERGED 32 CALLS 33 TOTAL
EDM=8.53319e-08 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 deltaMSq 3.75389e+01 4.12974e+00 9.32732e-04 7.25756e-03
2 sinSq2theta 6.29097e-03 8.61732e-04 2.04882e-03 6.82827e-04
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 2 ERR DEF=0.5
1.706e+01 -1.140e-03
-1.140e-03 7.447e-07
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2
1 0.31971 1.000 -0.320
2 0.31971 -0.320 1.000
**********
** 7 **SET ERR 0.5
**********
**********
** 8 **SET PRINT 1
**********
**********
** 9 **HESSE 1000
**********
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-1131.34 FROM HESSE STATUS=OK 10 CALLS 43 TOTAL
EDM=8.52815e-08 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 deltaMSq 3.75389e+01 4.12748e+00 3.73093e-05 -8.56559e-01
2 sinSq2theta 6.29097e-03 8.61259e-04 4.09765e-04 -3.79981e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 2 ERR DEF=0.5
1.705e+01 -1.133e-03
-1.133e-03 7.439e-07
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2
1 0.31815 1.000 -0.318
2 0.31815 -0.318 1.000
[#1] INFO:Minization -- p.d.f. provides expected number of events, including extended term in likelihood.
[#1] INFO:NumericIntegration -- RooRealIntegral::init(PnmuTonePrime_Int[EPrime,LPrime]) using numeric integrator RooAdaptiveIntegratorND to calculate Int(LPrime,EPrime)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(PnmuTone_Int[E,L]) using numeric integrator RooAdaptiveIntegratorND to calculate Int(L,E)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(PnmuTone_Int[L]_Norm[E,L]) using numeric integrator RooIntegrator1D to calculate Int(L)
[#1] INFO:Minization -- createNLL picked up cached consraints from workspace with 0 entries
Metropolis-Hastings progress: ....................................................................................................
[#1] INFO:Eval -- Proposal acceptance rate: 3.3%
[#1] INFO:Eval -- Number of steps in chain: 165
[#1] INFO:NumericIntegration -- RooRealIntegral::init(product_Int[deltaMSq,sinSq2theta]_Norm[deltaMSq,sinSq2theta]) using numeric integrator RooAdaptiveIntegratorND to calculate Int(deltaMSq,sinSq2theta)
[#0] WARNING:NumericIntegration -- RooAdaptiveIntegratorND::dtor(product) WARNING: Number of suppressed warningings about integral evaluations where target precision was not reached is 1
[#1] INFO:NumericIntegration -- RooRealIntegral::init(product_Int[deltaMSq,sinSq2theta]_Norm[deltaMSq,sinSq2theta]) using numeric integrator RooAdaptiveIntegratorND to calculate Int(deltaMSq,sinSq2theta)
[#1] INFO:Eval -- cutoff = 0.166573, conf = 0.904333
[#0] WARNING:NumericIntegration -- RooAdaptiveIntegratorND::dtor(product) WARNING: Number of suppressed warningings about integral evaluations where target precision was not reached is 1
[#0] WARNING:NumericIntegration -- RooAdaptiveIntegratorND::dtor(PnmuTone) WARNING: Number of suppressed warningings about integral evaluations where target precision was not reached is 628
[#0] WARNING:NumericIntegration -- RooAdaptiveIntegratorND::dtor(PnmuTonePrime) WARNING: Number of suppressed warningings about integral evaluations where target precision was not reached is 628
Real time 0:02:16, CP time 136.040
MCMC actual confidence level: 0.904333
[#1] INFO:Minization -- RooProfileLL::evaluate(nll_model_modelData_Profile[deltaMSq,sinSq2theta]) Creating instance of MINUIT
[#1] INFO:Minization -- RooProfileLL::evaluate(nll_model_modelData_Profile[deltaMSq,sinSq2theta]) determining minimum likelihood for current configurations w.r.t all observable
[#1] INFO:Minization -- RooProfileLL::evaluate(nll_model_modelData_Profile[deltaMSq,sinSq2theta]) minimum found at (deltaMSq=37.5376, sinSq2theta=0.00629099)
..[#1] INFO:Minization -- LikelihoodInterval - Finding the contour of deltaMSq ( 0 ) and sinSq2theta ( 1 )
Real time 0:02:47, CP time 167.120
#include "RooGlobalFunc.h"
#include "RooDataSet.h"
#include "RooDataHist.h"
#include "RooRealVar.h"
#include "RooConstVar.h"
#include "RooProduct.h"
#include "RooProdPdf.h"
#include "TROOT.h"
#include "RooPolynomial.h"
#include "RooRandom.h"
#include "RooNLLVar.h"
#include "RooProfileLL.h"
#include "RooPlot.h"
#include "TCanvas.h"
#include "TH1F.h"
#include "TH2F.h"
#include "TTree.h"
#include "TMarker.h"
#include "TStopwatch.h"
#include <iostream>
// PDF class created for this macro
#if !defined(__CINT__) || defined(__MAKECINT__)
#include "../tutorials/roostats/NuMuToNuE_Oscillation.h"
#include "../tutorials/roostats/NuMuToNuE_Oscillation.cxx" // so that it can be executed directly
#else
#include "../tutorials/roostats/NuMuToNuE_Oscillation.cxx+" // so that it can be executed directly
#endif
// use this order for safety on library loading
using namespace RooFit;
using namespace RooStats;
void rs401d_FeldmanCousins(bool doFeldmanCousins = false, bool doMCMC = true)
{
// to time the macro
t.Start();
// Taken from Feldman & Cousins paper, Phys.Rev.D57:3873-3889,1998.
// e-Print: physics/9711021 (see page 13.)
//
// Quantum mechanics dictates that the probability of such a transformation is given by the formula
// $P (\nu\mu \rightarrow \nu e ) = sin^2 (2\theta) sin^2 (1.27 \Delta m^2 L /E )$
// where P is the probability for a $\nu\mu$ to transform into a $\nu e$ , L is the distance in km between
// the creation of the neutrino from meson decay and its interaction in the detector, E is the
// neutrino energy in GeV, and $\Delta m^2 = |m^2 - m^2 |$ in $(eV/c^2 )^2$ .
//
// To demonstrate how this works in practice, and how it compares to alternative approaches
// that have been used, we consider a toy model of a typical neutrino oscillation experiment.
// The toy model is defined by the following parameters: Mesons are assumed to decay to
// neutrinos uniformly in a region 600 m to 1000 m from the detector. The expected background
// from conventional $\nu e$ interactions and misidentified $\nu\mu$ interactions is assumed to be 100
// events in each of 5 energy bins which span the region from 10 to 60 GeV. We assume that
// the $\nu\mu$ flux is such that if $P (\nu\mu \rightarrow \nu e ) = 0.01$ averaged over any bin, then that bin
// would
// have an expected additional contribution of 100 events due to $\nu\mu \rightarrow \nu e$ oscillations.
// Make signal model model
RooRealVar E("E", "", 15, 10, 60, "GeV");
RooRealVar L("L", "", .800, .600, 1.0, "km"); // need these units in formula
RooRealVar deltaMSq("deltaMSq", "#Delta m^{2}", 40, 1, 300, "eV/c^{2}");
RooRealVar sinSq2theta("sinSq2theta", "sin^{2}(2#theta)", .006, .0, .02);
// RooRealVar deltaMSq("deltaMSq","#Delta m^{2}",40,20,70,"eV/c^{2}");
// RooRealVar sinSq2theta("sinSq2theta","sin^{2}(2#theta)", .006,.001,.01);
// PDF for oscillation only describes deltaMSq dependence, sinSq2theta goes into sigNorm
// 1) The code for this PDF was created by issuing these commands
// root [0] RooClassFactory x
// root [1] x.makePdf("NuMuToNuE_Oscillation","L,E,deltaMSq","","pow(sin(1.27*deltaMSq*L/E),2)")
NuMuToNuE_Oscillation PnmuTone("PnmuTone", "P(#nu_{#mu} #rightarrow #nu_{e}", L, E, deltaMSq);
// only E is observable, so create the signal model by integrating out L
RooAbsPdf *sigModel = PnmuTone.createProjection(L);
// create $\int dE' dL' P(E',L' | \Delta m^2)$.
// Given RooFit will renormalize the PDF in the range of the observables,
// the average probability to oscillate in the experiment's acceptance
// needs to be incorporated into the extended term in the likelihood.
// Do this by creating a RooAbsReal representing the integral and divide by
// the area in the E-L plane.
// The integral should be over "primed" observables, so we need
// an independent copy of PnmuTone not to interfere with the original.
// Independent copy for Integral
RooRealVar EPrime("EPrime", "", 15, 10, 60, "GeV");
RooRealVar LPrime("LPrime", "", .800, .600, 1.0, "km"); // need these units in formula
NuMuToNuE_Oscillation PnmuTonePrime("PnmuTonePrime", "P(#nu_{#mu} #rightarrow #nu_{e}", LPrime, EPrime, deltaMSq);
RooAbsReal *intProbToOscInExp = PnmuTonePrime.createIntegral(RooArgSet(EPrime, LPrime));
// Getting the flux is a bit tricky. It is more clear to include a cross section term that is not
// explicitly referred to in the text, eg.
// number events in bin = flux * cross-section for nu_e interaction in E bin * average prob nu_mu osc. to nu_e in bin
// let maxEventsInBin = flux * cross-section for nu_e interaction in E bin
// maxEventsInBin * 1% chance per bin = 100 events / bin
// therefore maxEventsInBin = 10,000.
// for 5 bins, this means maxEventsTot = 50,000
RooConstVar maxEventsTot("maxEventsTot", "maximum number of sinal events", 50000);
RooConstVar inverseArea("inverseArea", "1/(#Delta E #Delta L)",
1. / (EPrime.getMax() - EPrime.getMin()) / (LPrime.getMax() - LPrime.getMin()));
// $sigNorm = maxEventsTot \cdot \int dE dL \frac{P_{oscillate\ in\ experiment}}{Area} \cdot {sin}^2(2\theta)$
RooProduct sigNorm("sigNorm", "", RooArgSet(maxEventsTot, *intProbToOscInExp, inverseArea, sinSq2theta));
// bkg = 5 bins * 100 events / bin
RooConstVar bkgNorm("bkgNorm", "normalization for background", 500);
// flat background (0th order polynomial, so no arguments for coefficients)
RooPolynomial bkgEShape("bkgEShape", "flat bkg shape", E);
// total model
RooAddPdf model("model", "", RooArgList(*sigModel, bkgEShape), RooArgList(sigNorm, bkgNorm));
// for debugging, check model tree
// model.printCompactTree();
// model.graphVizTree("model.dot");
// turn off some messages
// --------------------------------------
// n events in data to data, simply sum of sig+bkg
Int_t nEventsData = bkgNorm.getVal() + sigNorm.getVal();
cout << "generate toy data with nEvents = " << nEventsData << endl;
// adjust random seed to get a toy dataset similar to one in paper.
// Found by trial and error (3 trials, so not very "fine tuned")
// create a toy dataset
RooDataSet *data = model.generate(RooArgSet(E), nEventsData);
// --------------------------------------
// make some plots
TCanvas *dataCanvas = new TCanvas("dataCanvas");
dataCanvas->Divide(2, 2);
// plot the PDF
dataCanvas->cd(1);
TH1 *hh = PnmuTone.createHistogram("hh", E, Binning(40), YVar(L, Binning(40)), Scaling(kFALSE));
hh->SetTitle("True Signal Model");
hh->Draw("surf");
// plot the data with the best fit
dataCanvas->cd(2);
RooPlot *Eframe = E.frame();
data->plotOn(Eframe);
model.fitTo(*data, Extended());
model.plotOn(Eframe);
model.plotOn(Eframe, Components(*sigModel), LineColor(kRed));
model.plotOn(Eframe, Components(bkgEShape), LineColor(kGreen));
model.plotOn(Eframe);
Eframe->SetTitle("toy data with best fit model (and sig+bkg components)");
Eframe->Draw();
// plot the likelihood function
dataCanvas->cd(3);
RooNLLVar nll("nll", "nll", model, *data, Extended());
RooProfileLL pll("pll", "", nll, RooArgSet(deltaMSq, sinSq2theta));
// TH1* hhh = nll.createHistogram("hhh",sinSq2theta,Binning(40),YVar(deltaMSq,Binning(40))) ;
TH1 *hhh = pll.createHistogram("hhh", sinSq2theta, Binning(40), YVar(deltaMSq, Binning(40)), Scaling(kFALSE));
hhh->SetTitle("Likelihood Function");
hhh->Draw("surf");
dataCanvas->Update();
// --------------------------------------------------------------
// show use of Feldman-Cousins utility in RooStats
// set the distribution creator, which encodes the test statistic
RooArgSet parameters(deltaMSq, sinSq2theta);
ModelConfig modelConfig;
modelConfig.SetWorkspace(*w);
modelConfig.SetPdf(model);
modelConfig.SetParametersOfInterest(parameters);
RooStats::FeldmanCousins fc(*data, modelConfig);
fc.SetTestSize(.1); // set size of test
fc.SetNBins(10); // number of points to test per parameter
// use the Feldman-Cousins tool
ConfInterval *interval = 0;
if (doFeldmanCousins)
interval = fc.GetInterval();
// ---------------------------------------------------------
// show use of ProfileLikeihoodCalculator utility in RooStats
RooStats::ProfileLikelihoodCalculator plc(*data, modelConfig);
plc.SetTestSize(.1);
ConfInterval *plcInterval = plc.GetInterval();
// --------------------------------------------
// show use of MCMCCalculator utility in RooStats
MCMCInterval *mcInt = NULL;
if (doMCMC) {
// turn some messages back on
TStopwatch mcmcWatch;
mcmcWatch.Start();
RooArgList axisList(deltaMSq, sinSq2theta);
MCMCCalculator mc(*data, modelConfig);
mc.SetNumIters(5000);
mc.SetNumBurnInSteps(100);
mc.SetUseKeys(true);
mc.SetTestSize(.1);
mc.SetAxes(axisList); // set which is x and y axis in posterior histogram
// mc.SetNumBins(50);
mcInt = (MCMCInterval *)mc.GetInterval();
mcmcWatch.Stop();
mcmcWatch.Print();
}
// -------------------------------
// make plot of resulting interval
dataCanvas->cd(4);
// first plot a small dot for every point tested
if (doFeldmanCousins) {
RooDataHist *parameterScan = (RooDataHist *)fc.GetPointsToScan();
TH2F *hist = (TH2F *)parameterScan->createHistogram("sinSq2theta:deltaMSq", 30, 30);
// hist->Draw();
TH2F *forContour = (TH2F *)hist->Clone();
// now loop through the points and put a marker if it's in the interval
RooArgSet *tmpPoint;
// loop over points to test
for (Int_t i = 0; i < parameterScan->numEntries(); ++i) {
// get a parameter point from the list of points to test.
tmpPoint = (RooArgSet *)parameterScan->get(i)->clone("temp");
if (interval) {
if (interval->IsInInterval(*tmpPoint)) {
forContour->SetBinContent(
hist->FindBin(tmpPoint->getRealValue("sinSq2theta"), tmpPoint->getRealValue("deltaMSq")), 1);
} else {
forContour->SetBinContent(
hist->FindBin(tmpPoint->getRealValue("sinSq2theta"), tmpPoint->getRealValue("deltaMSq")), 0);
}
}
delete tmpPoint;
}
if (interval) {
Double_t level = 0.5;
forContour->SetContour(1, &level);
forContour->SetLineWidth(2);
forContour->SetLineColor(kRed);
forContour->Draw("cont2,same");
}
}
MCMCIntervalPlot *mcPlot = NULL;
if (mcInt) {
cout << "MCMC actual confidence level: " << mcInt->GetActualConfidenceLevel() << endl;
mcPlot = new MCMCIntervalPlot(*mcInt);
mcPlot->SetLineColor(kMagenta);
mcPlot->Draw();
}
dataCanvas->Update();
LikelihoodIntervalPlot plotInt((LikelihoodInterval *)plcInterval);
plotInt.SetTitle("90% Confidence Intervals");
if (mcInt)
plotInt.Draw("same");
else
plotInt.Draw();
dataCanvas->Update();
/// print timing info
t.Stop();
t.Print();
}
int Int_t
Definition: RtypesCore.h:43
const Bool_t kFALSE
Definition: RtypesCore.h:90
double Double_t
Definition: RtypesCore.h:57
const Bool_t kTRUE
Definition: RtypesCore.h:89
@ kRed
Definition: Rtypes.h:64
@ kGreen
Definition: Rtypes.h:64
@ kMagenta
Definition: Rtypes.h:64
@ kBlue
Definition: Rtypes.h:64
static struct mg_connection * fc(struct mg_context *ctx)
Definition: civetweb.c:3728
Double_t getRealValue(const char *name, Double_t defVal=0, Bool_t verbose=kFALSE) const
Get value of a RooAbsReal stored in set with given name.
TH1 * createHistogram(const char *name, const RooAbsRealLValue &xvar, const RooCmdArg &arg1=RooCmdArg::none(), const RooCmdArg &arg2=RooCmdArg::none(), const RooCmdArg &arg3=RooCmdArg::none(), const RooCmdArg &arg4=RooCmdArg::none(), const RooCmdArg &arg5=RooCmdArg::none(), const RooCmdArg &arg6=RooCmdArg::none(), const RooCmdArg &arg7=RooCmdArg::none(), const RooCmdArg &arg8=RooCmdArg::none()) const
Calls createHistogram(const char *name, const RooAbsRealLValue& xvar, const RooLinkedList& argList) c...
Definition: RooAbsData.cxx:628
virtual RooPlot * plotOn(RooPlot *frame, const RooCmdArg &arg1=RooCmdArg::none(), const RooCmdArg &arg2=RooCmdArg::none(), const RooCmdArg &arg3=RooCmdArg::none(), const RooCmdArg &arg4=RooCmdArg::none(), const RooCmdArg &arg5=RooCmdArg::none(), const RooCmdArg &arg6=RooCmdArg::none(), const RooCmdArg &arg7=RooCmdArg::none(), const RooCmdArg &arg8=RooCmdArg::none()) const
Calls RooPlot* plotOn(RooPlot* frame, const RooLinkedList& cmdList) const ;.
Definition: RooAbsData.cxx:546
virtual RooAbsPdf * createProjection(const RooArgSet &iset)
Return a p.d.f that represent a projection of this p.d.f integrated over given observables.
Definition: RooAbsPdf.cxx:3342
RooAbsReal is the common abstract base class for objects that represent a real value and implements f...
Definition: RooAbsReal.h:60
RooAbsReal * createIntegral(const RooArgSet &iset, const RooCmdArg &arg1, const RooCmdArg &arg2=RooCmdArg::none(), const RooCmdArg &arg3=RooCmdArg::none(), const RooCmdArg &arg4=RooCmdArg::none(), const RooCmdArg &arg5=RooCmdArg::none(), const RooCmdArg &arg6=RooCmdArg::none(), const RooCmdArg &arg7=RooCmdArg::none(), const RooCmdArg &arg8=RooCmdArg::none()) const
Create an object that represents the integral of the function over one or more observables listed in ...
Definition: RooAbsReal.cxx:560
RooAddPdf is an efficient implementation of a sum of PDFs of the form.
RooArgList is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgList.h:21
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgSet.h:28
virtual TObject * clone(const char *newname) const
Definition: RooArgSet.h:84
RooConstVar represent a constant real-valued object.
Definition: RooConstVar.h:25
The RooDataHist is a container class to hold N-dimensional binned data.
Definition: RooDataHist.h:40
virtual Int_t numEntries() const
Return the number of bins.
virtual const RooArgSet * get() const
Definition: RooDataHist.h:79
RooDataSet is a container class to hold unbinned data.
Definition: RooDataSet.h:33
void setStreamStatus(Int_t id, Bool_t active)
(De)Activate stream with given unique ID
static RooMsgService & instance()
Return reference to singleton instance.
Class RooNLLVar implements a -log(likelihood) calculation from a dataset and a PDF.
Definition: RooNLLVar.h:26
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:44
void SetTitle(const char *name)
Set the title of the RooPlot to 'title'.
Definition: RooPlot.cxx:1258
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:712
RooPolynomial implements a polynomial p.d.f of the form.
Definition: RooPolynomial.h:28
A RooProduct represents the product of a given set of RooAbsReal objects.
Definition: RooProduct.h:30
Class RooProfileLL implements the profile likelihood estimator for a given likelihood and set of para...
Definition: RooProfileLL.h:26
static TRandom * randomGenerator()
Return a pointer to a singleton random-number generator implementation.
Definition: RooRandom.cxx:53
RooRealVar represents a variable that can be changed from the outside.
Definition: RooRealVar.h:35
The FeldmanCousins class (like the Feldman-Cousins technique) is essentially a specific configuration...
The ProfileLikelihoodCalculator is a concrete implementation of CombinedCalculator (the interface cla...
The RooWorkspace is a persistable container for RooFit projects.
Definition: RooWorkspace.h:43
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
The Canvas class.
Definition: TCanvas.h:27
virtual void Update()
Update canvas pad buffers.
Definition: TCanvas.cxx:2433
Set current canvas & pad.
Definition: TCanvas.cxx:701
The TH1 histogram class.
Definition: TH1.h:56
virtual void SetTitle(const char *title)
Definition: TH1.cxx:6345
TObject * Clone(const char *newname=0) const
Make a complete copy of the underlying object.
Definition: TH1.cxx:2665
virtual void SetContour(Int_t nlevels, const Double_t *levels=0)
Set the number and values of contour levels.
Definition: TH1.cxx:7947
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition: TH1.cxx:2998
virtual Int_t FindBin(Double_t x, Double_t y=0, Double_t z=0)
Return Global bin number corresponding to x,y,z.
Definition: TH1.cxx:3596
2-D histogram with a float per channel (see TH1 documentation)}
Definition: TH2.h:251
virtual void SetBinContent(Int_t bin, Double_t content)
Set bin content.
Definition: TH2.cxx:2480
virtual void Divide(Int_t nx=1, Int_t ny=1, Float_t xmargin=0.01, Float_t ymargin=0.01, Int_t color=0)
Automatic pad generation by division.
virtual void SetSeed(ULong_t seed=0)
Set the random generator seed.
Definition: TRandom.cxx:597
Stopwatch class.
Definition: TStopwatch.h:28
void Start(Bool_t reset=kTRUE)
Start the stopwatch.
Definition: TStopwatch.cxx:58
void Stop()
Stop the stopwatch.
Definition: TStopwatch.cxx:77
void Print(Option_t *option="") const
Print the real and cpu time passed between the start and stop events.
Definition: TStopwatch.cxx:219
RooCmdArg Scaling(Bool_t flag)
RooCmdArg YVar(const RooAbsRealLValue &var, const RooCmdArg &arg=RooCmdArg::none())
RooCmdArg Extended(Bool_t flag=kTRUE)
RooCmdArg Binning(const RooAbsBinning &binning)
RooCmdArg Components(const RooArgSet &compSet)
RooCmdArg LineColor(Color_t color)
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Namespace for the RooStats classes.
Definition: Asimov.h:19
static constexpr double L
constexpr Double_t E()
Base of natural log:
Definition: TMath.h:97

Definition in file rs401d_FeldmanCousins.C.