ROOT   Reference Guide
rf315_projectpdf.C File Reference

## Detailed Description

Multidimensional models: marginizalization of multi-dimensional p.d.f.s through integration

␛[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby␛[0m
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
[#1] INFO:NumericIntegration -- RooRealIntegral::init([gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[y]) using numeric integrator RooIntegrator1D to calculate Int(y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[y]) using numeric integrator RooIntegrator1D to calculate Int(y)
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
[#1] INFO:Minization -- The following expressions will be evaluated in cache-and-track mode: (gaussx)
[#0] WARNING:Minization -- RooMinimizerFcn::synchronize: WARNING: no initial error estimate available for a1: using 0.4
**********
** 1 **SET PRINT 1
**********
**********
**********
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 a1 -1.50000e+00 4.00000e-01 -3.00000e+00 1.00000e+00
**********
** 3 **SET ERR 0.5
**********
**********
** 4 **SET PRINT 1
**********
**********
** 5 **SET STR 1
**********
NOW USING STRATEGY 1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
prevFCN = 1900.156536 START MIGRAD MINIMIZATION. STRATEGY 1. CONVERGENCE WHEN EDM .LT. 1.00e-03
a1=-1.491,
prevFCN = 1900.000822 a1=-1.509,
prevFCN = 1900.423606 a1=-1.499,
prevFCN = 1900.135899 a1=-1.501,
prevFCN = 1900.178287 FCN=1900.16 FROM MIGRAD STATUS=INITIATE 4 CALLS 5 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 a1 -1.50000e+00 4.00000e-01 2.08372e-01 -4.77802e+01
ERR DEF= 0.5
a1=-1.484,
prevFCN = 1899.958651 a1=-1.483,
prevFCN = 1899.959675 a1=-1.484,
prevFCN = 1899.958586 a1=-1.484,
prevFCN = 1899.958497 a1=-1.483,
prevFCN = 1899.958935 a1=-1.485,
prevFCN = 1899.958964 MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
a1=-1.484,
prevFCN = 1899.958497 a1=-1.483,
prevFCN = 1899.958935 a1=-1.485,
prevFCN = 1899.958964 a1=-1.484,
prevFCN = 1899.958512 a1=-1.484,
prevFCN = 1899.958518 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=1899.96 FROM MIGRAD STATUS=CONVERGED 15 CALLS 16 TOTAL
EDM=2.41873e-07 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 a1 -1.48409e+00 2.51054e-02 3.89173e-04 -3.80132e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 1 ERR DEF=0.5
6.303e-04
a1=-1.484, **********
** 7 **SET ERR 0.5
**********
**********
** 8 **SET PRINT 1
**********
**********
** 9 **HESSE 500
**********
prevFCN = 1899.958497 a1=-1.484,
prevFCN = 1899.958512 a1=-1.484,
prevFCN = 1899.958518 a1=-1.484,
prevFCN = 1899.958497 a1=-1.484,
prevFCN = 1899.958498 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=1899.96 FROM HESSE STATUS=OK 5 CALLS 21 TOTAL
EDM=2.42353e-07 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 a1 -1.48409e+00 2.51054e-02 7.78346e-05 -2.44471e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 1 ERR DEF=0.5
6.303e-04
a1=-1.484, [#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
[#1] INFO:NumericIntegration -- RooRealIntegral::init([gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[y]) using numeric integrator RooIntegrator1D to calculate Int(y)
#include "RooRealVar.h"
#include "RooDataHist.h"
#include "RooGaussian.h"
#include "RooProdPdf.h"
#include "RooPolyVar.h"
#include "TH1.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "RooConstVar.h"
using namespace RooFit;
{
// C r e a t e p d f m ( x , y ) = g x ( x | y ) * g ( y )
// --------------------------------------------------------------
// Increase default precision of numeric integration
// as this exercise has high sensitivity to numeric integration precision
// Create observables
RooRealVar x("x", "x", -5, 5);
RooRealVar y("y", "y", -2, 2);
// Create function f(y) = a0 + a1*y
RooRealVar a0("a0", "a0", 0);
RooRealVar a1("a1", "a1", -1.5, -3, 1);
RooPolyVar fy("fy", "fy", y, RooArgSet(a0, a1));
// Create gaussx(x,f(y),sx)
RooRealVar sigmax("sigmax", "width of gaussian", 0.5);
RooGaussian gaussx("gaussx", "Gaussian in x with shifting mean in y", x, fy, sigmax);
// Create gaussy(y,0,2)
RooGaussian gaussy("gaussy", "Gaussian in y", y, RooConst(0), RooConst(2));
// Create gaussx(x,sx|y) * gaussy(y)
RooProdPdf model("model", "gaussx(x|y)*gaussy(y)", gaussy, Conditional(gaussx, x));
// M a r g i n a l i z e m ( x , y ) t o m ( x )
// ----------------------------------------------------
// modelx(x) = Int model(x,y) dy
RooAbsPdf *modelx = model.createProjection(y);
// U s e m a r g i n a l i z e d p . d . f . a s r e g u l a r 1 - D p . d . f .
// ------------------------------------------------------------------------------------------
// Sample 1000 events from modelx
RooAbsData *data = modelx->generateBinned(x, 1000);
// Fit modelx to toy data
modelx->fitTo(*data, Verbose());
// Plot modelx over data
RooPlot *frame = x.frame(40);
data->plotOn(frame);
modelx->plotOn(frame);
// Make 2D histogram of model(x,y)
TH1 *hh = model.createHistogram("x,y");
TCanvas *c = new TCanvas("rf315_projectpdf", "rf315_projectpdf", 800, 400);
c->Divide(2);
c->cd(1);
frame->GetYaxis()->SetTitleOffset(1.4);
frame->Draw();
c->cd(2);
hh->GetZaxis()->SetTitleOffset(2.5);
hh->Draw("surf");
}
#define c(i)
Definition: RSha256.hxx:101
#define e(i)
Definition: RSha256.hxx:103
@ kBlue
Definition: Rtypes.h:64
RooAbsData is the common abstract base class for binned and unbinned datasets.
Definition: RooAbsData.h:44
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 RooDataHist * generateBinned(const RooArgSet &whatVars, Double_t nEvents, const RooCmdArg &arg1, const RooCmdArg &arg2=RooCmdArg::none(), const RooCmdArg &arg3=RooCmdArg::none(), const RooCmdArg &arg4=RooCmdArg::none(), const RooCmdArg &arg5=RooCmdArg::none()) const
As RooAbsPdf::generateBinned(const RooArgSet&, const RooCmdArg&,const RooCmdArg&, const RooCmdArg&,...
Definition: RooAbsPdf.h:104
virtual RooFitResult * fitTo(RooAbsData &data, 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())
Fit PDF to given dataset.
Definition: RooAbsPdf.cxx:1254
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
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 RooCmdArg &arg9=RooCmdArg::none(), const RooCmdArg &arg10=RooCmdArg::none()) const
Definition: RooAbsPdf.h:118
static RooNumIntConfig * defaultIntegratorConfig()
Returns the default numeric integration configuration for all RooAbsReals.
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgSet.h:28
Plain Gaussian p.d.f.
Definition: RooGaussian.h:25
void setEpsAbs(Double_t newEpsAbs)
Set absolute convergence criteria (convergence if abs(Err)<newEpsAbs)
void setEpsRel(Double_t newEpsRel)
Set relative convergence criteria (convergence if abs(Err)/abs(Int)<newEpsRel)
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:44
TAxis * GetYaxis() const
Definition: RooPlot.cxx:1277
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:712
Class RooPolyVar is a RooAbsReal implementing a polynomial in terms of a list of RooAbsReal coefficie...
Definition: RooPolyVar.h:28
RooProdPdf is an efficient implementation of a product of PDFs of the form.
Definition: RooProdPdf.h:31
RooRealVar represents a variable that can be changed from the outside.
Definition: RooRealVar.h:35
virtual void SetTitleOffset(Float_t offset=1)
Set distance between the axis and the axis title.
Definition: TAttAxis.cxx:294
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition: TAttLine.h:40
The Canvas class.
Definition: TCanvas.h:27
The TH1 histogram class.
Definition: TH1.h:56
TAxis * GetZaxis()
Definition: TH1.h:318
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition: TH1.cxx:2998
RooConstVar & RooConst(Double_t val)
RooCmdArg Conditional(const RooArgSet &pdfSet, const RooArgSet &depSet, Bool_t depsAreCond=kFALSE)
RooCmdArg Verbose(Bool_t flag=kTRUE)
Double_t y[n]
Definition: legend1.C:17
Double_t x[n]
Definition: legend1.C:17
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Date
07/2008

Definition in file rf315_projectpdf.C.