ROOT   Reference Guide
rf608_fitresultaspdf.C File Reference

## Detailed Description

Likelihood and minimization: representing the parabolic approximation of the fit as a multi-variate Gaussian on the parameters of the fitted pdf

␛[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
[#0] WARNING:InputArguments -- The parameter 'sigma_g1' with range [-1e+30, 1e+30] of the RooGaussian 'g1' exceeds the safe range of (0, inf). Advise to limit its range.
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
[#1] INFO:Minization -- The following expressions will be evaluated in cache-and-track mode: (g1,g2)
**********
** 1 **SET PRINT 1
**********
**********
** 2 **SET NOGRAD
**********
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 frac 5.00000e-01 1.00000e-01 0.00000e+00 1.00000e+00
2 mean 0.00000e+00 2.00000e-01 -1.00000e+00 1.00000e+00
3 sigma_g2 4.00000e+00 2.00000e-01 3.00000e+00 5.00000e+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=2523.5 FROM MIGRAD STATUS=INITIATE 10 CALLS 11 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac 5.00000e-01 1.00000e-01 2.01358e-01 -1.31418e+01
2 mean 0.00000e+00 2.00000e-01 2.01358e-01 4.68351e+00
3 sigma_g2 4.00000e+00 2.00000e-01 2.01358e-01 5.45887e+00
ERR DEF= 0.5
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=2522.85 FROM MIGRAD STATUS=CONVERGED 50 CALLS 51 TOTAL
EDM=4.43971e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac 5.43820e-01 5.60284e-02 2.70800e-03 8.34315e-02
2 mean -4.18828e-02 9.05559e-02 3.14649e-03 -5.37978e-03
3 sigma_g2 4.01280e+00 2.08953e-01 4.84455e-03 -4.10552e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 3 ERR DEF=0.5
3.153e-03 -3.621e-04 8.647e-03
-3.621e-04 8.223e-03 -1.611e-03
8.647e-03 -1.611e-03 4.431e-02
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3
1 0.73165 1.000 -0.071 0.732
2 0.08551 -0.071 1.000 -0.084
3 0.73231 0.732 -0.084 1.000
**********
** 7 **SET ERR 0.5
**********
**********
** 8 **SET PRINT 1
**********
**********
** 9 **HESSE 1500
**********
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=2522.85 FROM HESSE STATUS=OK 16 CALLS 67 TOTAL
EDM=4.43683e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 frac 5.43820e-01 5.60802e-02 5.41601e-04 8.77525e-02
2 mean -4.18828e-02 9.05561e-02 6.29298e-04 -4.18951e-02
3 sigma_g2 4.01280e+00 2.09149e-01 9.68910e-04 1.27960e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 3 ERR DEF=0.5
3.158e-03 -3.614e-04 8.670e-03
-3.614e-04 8.223e-03 -1.615e-03
8.670e-03 -1.615e-03 4.440e-02
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3
1 0.73224 1.000 -0.071 0.732
2 0.08555 -0.071 1.000 -0.085
3 0.73291 0.732 -0.085 1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooAddPdf.h"
#include "RooChebychev.h"
#include "RooFitResult.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "TFile.h"
#include "TStyle.h"
#include "TH2.h"
#include "TH3.h"
using namespace RooFit;
{
// C r e a t e m o d e l a n d d a t a s e t
// -----------------------------------------------
// Observable
RooRealVar x("x", "x", -20, 20);
// Model (intentional strong correlations)
RooRealVar mean("mean", "mean of g1 and g2", 0, -1, 1);
RooRealVar sigma_g1("sigma_g1", "width of g1", 2);
RooGaussian g1("g1", "g1", x, mean, sigma_g1);
RooRealVar sigma_g2("sigma_g2", "width of g2", 4, 3.0, 5.0);
RooGaussian g2("g2", "g2", x, mean, sigma_g2);
RooRealVar frac("frac", "frac", 0.5, 0.0, 1.0);
RooAddPdf model("model", "model", RooArgList(g1, g2), frac);
// Generate 1000 events
RooDataSet *data = model.generate(x, 1000);
// F i t m o d e l t o d a t a
// ----------------------------------
RooFitResult *r = model.fitTo(*data, Save());
// C r e a t e M V G a u s s i a n p d f o f f i t t e d p a r a m e t e r s
// ------------------------------------------------------------------------------------
RooAbsPdf *parabPdf = r->createHessePdf(RooArgSet(frac, mean, sigma_g2));
// S o m e e x e c e r c i s e s w i t h t h e p a r a m e t e r p d f
// -----------------------------------------------------------------------------
// Generate 100K points in the parameter space, sampled from the MVGaussian pdf
RooDataSet *d = parabPdf->generate(RooArgSet(mean, sigma_g2, frac), 100000);
// Sample a 3-D histogram of the pdf to be visualized as an error ellipsoid using the GLISO draw option
TH3 *hh_3d = (TH3 *)parabPdf->createHistogram("mean,sigma_g2,frac", 25, 25, 25);
// Project 3D parameter pdf down to 3 permutations of two-dimensional pdfs
// The integrations corresponding to these projections are performed analytically
// by the MV Gaussian pdf
RooAbsPdf *pdf_sigmag2_frac = parabPdf->createProjection(mean);
RooAbsPdf *pdf_mean_frac = parabPdf->createProjection(sigma_g2);
RooAbsPdf *pdf_mean_sigmag2 = parabPdf->createProjection(frac);
// Make 2D plots of the 3 two-dimensional pdf projections
TH2 *hh_sigmag2_frac = (TH2 *)pdf_sigmag2_frac->createHistogram("sigma_g2,frac", 50, 50);
TH2 *hh_mean_frac = (TH2 *)pdf_mean_frac->createHistogram("mean,frac", 50, 50);
TH2 *hh_mean_sigmag2 = (TH2 *)pdf_mean_sigmag2->createHistogram("mean,sigma_g2", 50, 50);
hh_mean_frac->SetLineColor(kBlue);
hh_sigmag2_frac->SetLineColor(kBlue);
hh_mean_sigmag2->SetLineColor(kBlue);
// Draw the 'sigar'
new TCanvas("rf608_fitresultaspdf_1", "rf608_fitresultaspdf_1", 600, 600);
hh_3d->Draw("iso");
// Draw the 2D projections of the 3D pdf
TCanvas *c2 = new TCanvas("rf608_fitresultaspdf_2", "rf608_fitresultaspdf_2", 900, 600);
c2->Divide(3, 2);
c2->cd(1);
gPad->SetLeftMargin(0.15);
hh_mean_sigmag2->GetZaxis()->SetTitleOffset(1.4);
hh_mean_sigmag2->Draw("surf3");
c2->cd(2);
gPad->SetLeftMargin(0.15);
hh_sigmag2_frac->GetZaxis()->SetTitleOffset(1.4);
hh_sigmag2_frac->Draw("surf3");
c2->cd(3);
gPad->SetLeftMargin(0.15);
hh_mean_frac->GetZaxis()->SetTitleOffset(1.4);
hh_mean_frac->Draw("surf3");
// Draw the distributions of parameter points sampled from the pdf
TH1 *tmp1 = d->createHistogram("mean,sigma_g2", 50, 50);
TH1 *tmp2 = d->createHistogram("sigma_g2,frac", 50, 50);
TH1 *tmp3 = d->createHistogram("mean,frac", 50, 50);
c2->cd(4);
gPad->SetLeftMargin(0.15);
tmp1->GetZaxis()->SetTitleOffset(1.4);
tmp1->Draw("lego3");
c2->cd(5);
gPad->SetLeftMargin(0.15);
tmp2->GetZaxis()->SetTitleOffset(1.4);
tmp2->Draw("lego3");
c2->cd(6);
gPad->SetLeftMargin(0.15);
tmp3->GetZaxis()->SetTitleOffset(1.4);
tmp3->Draw("lego3");
}
ROOT::R::TRInterface & r
Definition: Object.C:4
#define d(i)
Definition: RSha256.hxx:102
@ kBlue
Definition: Rtypes.h:66
#define gPad
Definition: TVirtualPad.h:287
RooDataSet * generate(const RooArgSet &whatVars, Int_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())
See RooAbsPdf::generate(const RooArgSet&,const RooCmdArg&,const RooCmdArg&,const RooCmdArg&,...
Definition: RooAbsPdf.h:58
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:3378
TH1 * createHistogram(const char *varNameList, Int_t xbins=0, Int_t ybins=0, Int_t zbins=0) const
Create and fill a ROOT histogram TH1, TH2 or TH3 with the values of this function for the variables w...
RooAddPdf is an efficient implementation of a sum of PDFs of the form.
Definition: RooAddPdf.h:32
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:29
RooDataSet is a container class to hold unbinned data.
Definition: RooDataSet.h:33
RooFitResult is a container class to hold the input and output of a PDF fit to a dataset.
Definition: RooFitResult.h:40
Plain Gaussian p.d.f.
Definition: RooGaussian.h:24
RooRealVar represents a variable that can be changed from the outside.
Definition: RooRealVar.h:39
virtual void SetTitleOffset(Float_t offset=1)
Set distance between the axis and the axis title.
Definition: TAttAxis.cxx:293
virtual void SetFillColor(Color_t fcolor)
Set the fill area color.
Definition: TAttFill.h:37
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition: TAttLine.h:40
The Canvas class.
Definition: TCanvas.h:23
TH1 is the base class of all histogram classes in ROOT.
Definition: TH1.h:58
TAxis * GetZaxis()
Definition: TH1.h:322
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition: TH1.cxx:3073
Service class for 2-Dim histogram classes.
Definition: TH2.h:30
The 3-D histogram classes derived from the 1-D histogram classes.
Definition: TH3.h:31
RooCmdArg Save(Bool_t flag=kTRUE)
Double_t x[n]
Definition: legend1.C:17
return c2
Definition: legend2.C:14
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Date
July 2008

Definition in file rf608_fitresultaspdf.C.