rf704_amplitudefit.C File Reference

Detailed Description

'SPECIAL PDFS' RooFit tutorial macro #704

Using a p.d.f defined by a sum of real-valued amplitude components

Processing /mnt/build/workspace/root-makedoc-v612/rootspi/rdoc/src/v6-12-00-patches/tutorials/roofit/rf704_amplitudefit.C...

RooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby 
                Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
                All rights reserved, please read http://roofit.sourceforge.net/license.txt

[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_coshGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_sinhGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_coshGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_sinhGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_coshGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_sinhGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
[#1] INFO:Minization --  The following expressions have been identified as constant and will be precalculated and cached: (ampl1,ampl2)
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 f1           1.00000e+00  2.00000e-01    0.00000e+00  2.00000e+00
     2 f2           5.00000e-01  2.00000e-01    0.00000e+00  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        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=24323.4 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  f1           1.00000e+00   2.00000e-01   2.01358e-01   2.36561e+01
   2  f2           5.00000e-01   2.00000e-01   2.35352e-01  -4.09909e+01
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=24323.1 FROM MIGRAD    STATUS=CONVERGED      33 CALLS          34 TOTAL
                     EDM=1.04489e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  f1           9.85261e-01   4.18474e-01   3.64059e-03  -9.57093e-03
   2  f2           5.07031e-01   2.19792e-01   2.15145e-03   1.61567e-02
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  1.864e-01  9.565e-02 
  9.565e-02  4.937e-02 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.99694   1.000  0.997
        2  0.99694   0.997  1.000
 **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        1000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=24323.1 FROM HESSE     STATUS=OK             10 CALLS          44 TOTAL
                     EDM=1.04101e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  f1           9.85261e-01   1.40907e+00   1.45624e-04  -1.47397e-02
   2  f2           5.07031e-01   1.24234e+00   8.60579e-05  -5.15499e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  4.590e+00  2.362e+00 
  2.362e+00  1.215e+00 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.99988   1.000  1.000
        2  0.99988   1.000  1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
[#0] WARNING:InputArguments -- RooAbsReal::createHistogram(ampl1) WARNING extended mode requested for a non-pdf object, ignored
[#0] WARNING:InputArguments -- RooAbsReal::createHistogram(ampl2) WARNING extended mode requested for a non-pdf object, ignored
[#1] INFO:Plotting -- RooAbsReal::plotOn(pdf) plot on t integrates over variables (cosa)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_coshGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_sinhGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(pdf) directly selected PDF components: (ampl1)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(pdf) indirectly selected PDF components: (poly1,tm_conv_coshGBasis_[t],coshGBasis)
[#1] INFO:Plotting -- RooAbsReal::plotOn(pdf) plot on t integrates over variables (cosa)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_coshGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_sinhGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(pdf) directly selected PDF components: (ampl2)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(pdf) indirectly selected PDF components: (poly2,tm_conv_sinhGBasis_[t],sinhGBasis)
[#1] INFO:Plotting -- RooAbsReal::plotOn(pdf) plot on t integrates over variables (cosa)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_coshGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_sinhGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:Plotting -- RooAbsReal::plotOn(pdf) plot on cosa integrates over variables (t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_coshGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_sinhGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_coshGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_sinhGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(pdf) directly selected PDF components: (ampl1)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(pdf) indirectly selected PDF components: (poly1,tm_conv_coshGBasis_[t],coshGBasis)
[#1] INFO:Plotting -- RooAbsReal::plotOn(pdf) plot on cosa integrates over variables (t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_coshGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_sinhGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_coshGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(pdf) directly selected PDF components: (ampl2)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(pdf) indirectly selected PDF components: (poly2,tm_conv_sinhGBasis_[t],sinhGBasis)
[#1] INFO:Plotting -- RooAbsReal::plotOn(pdf) plot on cosa integrates over variables (t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_coshGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_sinhGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(tm_conv_sinhGBasis_[t]_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)

#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooTruthModel.h"
#include "RooFormulaVar.h"
#include "RooRealSumPdf.h"
#include "RooPolyVar.h"
#include "RooProduct.h"
#include "TH1.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;


void rf704_amplitudefit()
{
   // S e t u p   2 D   a m p l i t u d e   f u n c t i o n s
   // -------------------------------------------------------

   // Observables
   RooRealVar t("t","time",-1.,15.);
   RooRealVar cosa("cosa","cos(alpha)",-1.,1.);

   // Use RooTruthModel to obtain compiled implementation of sinh/cosh modulated decay functions
   RooRealVar tau("tau","#tau",1.5);  
   RooRealVar deltaGamma("deltaGamma","deltaGamma", 0.3);
   RooTruthModel truthModel("tm","tm",t) ;
   RooFormulaVar coshGBasis("coshGBasis","exp(-@0/ @1)*cosh(@0*@2/2)",RooArgList(t,tau,deltaGamma));
   RooFormulaVar sinhGBasis("sinhGBasis","exp(-@0/ @1)*sinh(@0*@2/2)",RooArgList(t,tau,deltaGamma));
   RooAbsReal* coshGConv = truthModel.convolution(&coshGBasis,&t);
   RooAbsReal* sinhGConv = truthModel.convolution(&sinhGBasis,&t);
      
   // Construct polynomial amplitudes in cos(a) 
   RooPolyVar poly1("poly1","poly1",cosa,RooArgList(RooConst(0.5),RooConst(0.2),RooConst(0.2)),0);
   RooPolyVar poly2("poly2","poly2",cosa,RooArgList(RooConst(1),RooConst(-0.2),RooConst(3)),0);

   // Construct 2D amplitude as uncorrelated product of amp(t)*amp(cosa)
   RooProduct  ampl1("ampl1","amplitude 1",RooArgSet(poly1,*coshGConv));
   RooProduct  ampl2("ampl2","amplitude 2",RooArgSet(poly2,*sinhGConv));



   // C o n s t r u c t   a m p l i t u d e   s u m   p d f 
   // -----------------------------------------------------

   // Amplitude strengths
   RooRealVar f1("f1","f1",1,0,2) ;
   RooRealVar f2("f2","f2",0.5,0,2) ;
   
   // Construct pdf
   RooRealSumPdf pdf("pdf","pdf",RooArgList(ampl1,ampl2),RooArgList(f1,f2)) ;

   // Generate some toy data from pdf
   RooDataSet* data = pdf.generate(RooArgSet(t,cosa),10000);

   // Fit pdf to toy data with only amplitude strength floating
   pdf.fitTo(*data) ;



   // P l o t   a m p l i t u d e   s u m   p d f 
   // -------------------------------------------

   // Make 2D plots of amplitudes
   TH1* hh_cos = ampl1.createHistogram("hh_cos",t,Binning(50),YVar(cosa,Binning(50))) ;
   TH1* hh_sin = ampl2.createHistogram("hh_sin",t,Binning(50),YVar(cosa,Binning(50))) ;
   hh_cos->SetLineColor(kBlue) ;
   hh_sin->SetLineColor(kRed) ;

   
   // Make projection on t, plot data, pdf and its components
   // Note component projections may be larger than sum because amplitudes can be negative
   RooPlot* frame1 = t.frame();
   data->plotOn(frame1);
   pdf.plotOn(frame1);
   pdf.plotOn(frame1,Components(ampl1),LineStyle(kDashed));
   pdf.plotOn(frame1,Components(ampl2),LineStyle(kDashed),LineColor(kRed));
   
   // Make projection on cosa, plot data, pdf and its components
   // Note that components projection may be larger than sum because amplitudes can be negative
   RooPlot* frame2 = cosa.frame();
   data->plotOn(frame2);
   pdf.plotOn(frame2);
   pdf.plotOn(frame2,Components(ampl1),LineStyle(kDashed));
   pdf.plotOn(frame2,Components(ampl2),LineStyle(kDashed),LineColor(kRed));
   

   
   TCanvas* c = new TCanvas("rf704_amplitudefit","rf704_amplitudefit",800,800) ;
   c->Divide(2,2) ;
   c->cd(1) ; gPad->SetLeftMargin(0.15) ; frame1->GetYaxis()->SetTitleOffset(1.4) ; frame1->Draw();
   c->cd(2) ; gPad->SetLeftMargin(0.15) ; frame2->GetYaxis()->SetTitleOffset(1.4) ; frame2->Draw();
   c->cd(3) ; gPad->SetLeftMargin(0.20) ; hh_cos->GetZaxis()->SetTitleOffset(2.3) ; hh_cos->Draw("surf") ;
   c->cd(4) ; gPad->SetLeftMargin(0.20) ; hh_sin->GetZaxis()->SetTitleOffset(2.3) ; hh_sin->Draw("surf") ;
  
  
}

Author

07/2008 - Wouter Verkerke

Definition in file rf704_amplitudefit.C.