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rf303_conditional.C File Reference
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View in nbviewer Open in SWAN 'MULTIDIMENSIONAL MODELS' RooFit tutorial macro #303

Use of tailored p.d.f as conditional p.d.fs.s

pdf = gauss(x,f(y),sx | y ) with f(y) = a0 + a1*y

␛[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby␛[0m
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
All rights reserved, please read http://roofit.sourceforge.net/license.txt
RooDataSet::modelData[x,y] = 6850 entries
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
**********
** 1 **SET PRINT 1
**********
**********
** 2 **SET NOGRAD
**********
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 a0 -5.00000e-01 1.00000e+00 -5.00000e+00 5.00000e+00
2 a1 -5.00000e-01 2.00000e-01 -1.00000e+00 1.00000e+00
3 sigma 5.00000e-01 1.90000e-01 1.00000e-01 2.00000e+00
**********
** 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 1500 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=421420 FROM MIGRAD STATUS=INITIATE 12 CALLS 13 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 a0 -5.00000e-01 1.00000e+00 2.02430e-01 -7.46265e+04
2 a1 -5.00000e-01 2.00000e-01 2.35352e-01 -6.95347e+05
3 sigma 5.00000e-01 1.90000e-01 2.52163e-01 -1.29056e+06
ERR DEF= 0.5
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=9659.64 FROM MIGRAD STATUS=CONVERGED 101 CALLS 102 TOTAL
EDM=8.18253e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 a0 9.03100e-03 1.19768e-02 1.62548e-04 -2.31829e+00
2 a1 5.02815e-01 2.21631e-03 1.74026e-04 -2.33580e+00
3 sigma 9.91234e-01 8.46817e-03 6.05957e-04 -4.27913e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 3 ERR DEF=0.5
1.434e-04 1.880e-07 4.948e-08
1.880e-07 4.912e-06 8.995e-09
4.948e-08 8.995e-09 7.171e-05
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3
1 0.00710 1.000 0.007 0.000
2 0.00710 0.007 1.000 0.000
3 0.00068 0.000 0.000 1.000
**********
** 7 **SET ERR 0.5
**********
**********
** 8 **SET PRINT 1
**********
**********
** 9 **HESSE 1500
**********
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=9659.64 FROM HESSE STATUS=OK 16 CALLS 118 TOTAL
EDM=8.17764e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 a0 9.03100e-03 1.19768e-02 3.25095e-05 1.80620e-03
2 a1 5.02815e-01 2.21631e-03 3.48052e-05 2.61474e+00
3 sigma 9.91234e-01 8.46818e-03 1.21191e-04 -6.18987e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 3 ERR DEF=0.5
1.434e-04 1.880e-07 2.151e-09
1.880e-07 4.912e-06 2.334e-10
2.151e-09 2.334e-10 7.171e-05
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3
1 0.00708 1.000 0.007 0.000
2 0.00708 0.007 1.000 0.000
3 0.00002 0.000 0.000 1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on x averages using data variables (y)
[#1] INFO:Plotting -- RooDataWeightedAverage::ctor(modelDataWgtAvg) constructing data weighted average of function model_Norm[x] over 6850 data points of (y) with a total weight of 6850
.........................................................................................................................................................................................................
[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on x averages using data variables (y)
[#1] INFO:Plotting -- RooDataWeightedAverage::ctor(modelDataWgtAvg) constructing data weighted average of function model_Norm[x] over 100 data points of (y) with a total weight of 6850
.........................................................................................................................................................................................................
[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on x averages using data variables (y)
[#1] INFO:Plotting -- RooDataWeightedAverage::ctor(modelDataWgtAvg) constructing data weighted average of function model_Norm[x] over 5 data points of (y) with a total weight of 6850
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#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooDataHist.h"
#include "RooGaussian.h"
#include "RooPolyVar.h"
#include "RooProdPdf.h"
#include "RooPlot.h"
#include "TRandom.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"
using namespace RooFit;
RooDataSet* makeFakeDataXY() ;
void rf303_conditional()
{
// S e t u p c o m p o s e d m o d e l g a u s s ( x , m ( y ) , s )
// -----------------------------------------------------------------------
// Create observables
RooRealVar x("x","x",-10,10) ;
RooRealVar y("y","y",-10,10) ;
// Create function f(y) = a0 + a1*y
RooRealVar a0("a0","a0",-0.5,-5,5) ;
RooRealVar a1("a1","a1",-0.5,-1,1) ;
RooPolyVar fy("fy","fy",y,RooArgSet(a0,a1)) ;
// Create gauss(x,f(y),s)
RooRealVar sigma("sigma","width of gaussian",0.5,0.1,2.0) ;
RooGaussian model("model","Gaussian with shifting mean",x,fy,sigma) ;
// Obtain fake external experimental dataset with values for x and y
RooDataSet* expDataXY = makeFakeDataXY() ;
// G e n e r a t e d a t a f r o m c o n d i t i o n a l p . d . f m o d e l ( x | y )
// ---------------------------------------------------------------------------------------------
// Make subset of experimental data with only y values
RooDataSet* expDataY= (RooDataSet*) expDataXY->reduce(y) ;
// Generate 10000 events in x obtained from _conditional_ model(x|y) with y values taken from experimental data
RooDataSet *data = model.generate(x,ProtoData(*expDataY)) ;
data->Print() ;
// F i t c o n d i t i o n a l p . d . f m o d e l ( x | y ) t o d a t a
// ---------------------------------------------------------------------------------------------
model.fitTo(*expDataXY,ConditionalObservables(y)) ;
// P r o j e c t c o n d i t i o n a l p . d . f o n x a n d y d i m e n s i o n s
// ---------------------------------------------------------------------------------------------
// Plot x distribution of data and projection of model on x = 1/Ndata sum(data(y_i)) model(x;y_i)
RooPlot* xframe = x.frame() ;
expDataXY->plotOn(xframe) ;
model.plotOn(xframe,ProjWData(*expDataY)) ;
// Speed up (and approximate) projection by using binned clone of data for projection
RooAbsData* binnedDataY = expDataY->binnedClone() ;
model.plotOn(xframe,ProjWData(*binnedDataY),LineColor(kCyan),LineStyle(kDotted)) ;
// Show effect of projection with too coarse binning
((RooRealVar*)expDataY->get()->find("y"))->setBins(5) ;
RooAbsData* binnedDataY2 = expDataY->binnedClone() ;
model.plotOn(xframe,ProjWData(*binnedDataY2),LineColor(kRed)) ;
// Make canvas and draw RooPlots
new TCanvas("rf303_conditional","rf303_conditional",600, 460);
gPad->SetLeftMargin(0.15) ; xframe->GetYaxis()->SetTitleOffset(1.2) ; xframe->Draw() ;
}
RooDataSet* makeFakeDataXY()
{
RooRealVar x("x","x",-10,10) ;
RooRealVar y("y","y",-10,10) ;
RooArgSet coord(x,y) ;
RooDataSet* d = new RooDataSet("d","d",RooArgSet(x,y)) ;
for (int i=0 ; i<10000 ; i++) {
Double_t tmpy = gRandom->Gaus(0,10) ;
Double_t tmpx = gRandom->Gaus(0.5*tmpy,1) ;
if (fabs(tmpy)<10 && fabs(tmpx)<10) {
x = tmpx ;
y = tmpy ;
d->add(coord) ;
}
}
return d ;
}
d
#define d(i)
Definition: RSha256.hxx:102
Double_t
double Double_t
Definition: RtypesCore.h:55
kRed
@ kRed
Definition: Rtypes.h:63
kCyan
@ kCyan
Definition: Rtypes.h:63
kDotted
@ kDotted
Definition: TAttLine.h:48
gRandom
R__EXTERN TRandom * gRandom
Definition: TRandom.h:62
gPad
#define gPad
Definition: TVirtualPad.h:286
RooAbsCollection::find
RooAbsArg * find(const char *name) const
Find object with given name in list.
Definition: RooAbsCollection.cxx:811
RooAbsData
RooAbsData is the common abstract base class for binned and unbinned datasets.
Definition: RooAbsData.h:37
RooAbsData::reduce
RooAbsData * reduce(const RooCmdArg &arg1, const RooCmdArg &arg2=RooCmdArg(), const RooCmdArg &arg3=RooCmdArg(), const RooCmdArg &arg4=RooCmdArg(), const RooCmdArg &arg5=RooCmdArg(), const RooCmdArg &arg6=RooCmdArg(), const RooCmdArg &arg7=RooCmdArg(), const RooCmdArg &arg8=RooCmdArg())
Create a reduced copy of this dataset.
Definition: RooAbsData.cxx:360
RooAbsData::plotOn
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:531
RooArgSet
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgSet.h:28
RooDataSet
RooDataSet is a container class to hold unbinned data.
Definition: RooDataSet.h:31
RooDataSet::get
virtual const RooArgSet * get(Int_t index) const
Return RooArgSet with coordinates of event 'index'.
Definition: RooDataSet.cxx:995
RooDataSet::binnedClone
RooDataHist * binnedClone(const char *newName=0, const char *newTitle=0) const
Return binned clone of this dataset.
Definition: RooDataSet.cxx:933
RooGaussian
Plain Gaussian p.d.f.
Definition: RooGaussian.h:25
RooPlot
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:41
RooPlot::GetYaxis
TAxis * GetYaxis() const
Definition: RooPlot.cxx:1123
RooPlot::Draw
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:558
RooPolyVar
Class RooPolyVar is a RooAbsReal implementing a polynomial in terms of a list of RooAbsReal coefficie...
Definition: RooPolyVar.h:28
RooRealVar
RooRealVar represents a fundamental (non-derived) real valued object.
Definition: RooRealVar.h:36
TAttAxis::SetTitleOffset
virtual void SetTitleOffset(Float_t offset=1)
Set distance between the axis and the axis title Offset is a correction factor with respect to the "s...
Definition: TAttAxis.cxx:294
TCanvas
The Canvas class.
Definition: TCanvas.h:31
TRandom::Gaus
virtual Double_t Gaus(Double_t mean=0, Double_t sigma=1)
Samples a random number from the standard Normal (Gaussian) Distribution with the given mean and sigm...
Definition: TRandom.cxx:256
sigma
const Double_t sigma
Definition: h1analysisProxy.h:11
y
Double_t y[n]
Definition: legend1.C:17
x
Double_t x[n]
Definition: legend1.C:17
ROOT::Math::fabs
VecExpr< UnaryOp< Fabs< T >, VecExpr< A, T, D >, T >, T, D > fabs(const VecExpr< A, T, D > &rhs)
Definition: UnaryOperators.h:131
RooFit::ProjWData
RooCmdArg ProjWData(const RooAbsData &projData, Bool_t binData=kFALSE)
Definition: RooGlobalFunc.cxx:45
RooFit::ProtoData
RooCmdArg ProtoData(const RooDataSet &protoData, Bool_t randomizeOrder=kFALSE, Bool_t resample=kFALSE)
Definition: RooGlobalFunc.cxx:224
RooFit::ConditionalObservables
RooCmdArg ConditionalObservables(const RooArgSet &set)
Definition: RooGlobalFunc.cxx:193
RooFit::LineColor
RooCmdArg LineColor(Color_t color)
Definition: RooGlobalFunc.cxx:55
RooFit::LineStyle
RooCmdArg LineStyle(Style_t style)
Definition: RooGlobalFunc.cxx:56
Author
07/2008 - Wouter Verkerke

Definition in file rf303_conditional.C.