rf704_amplitudefit.C File Reference

Detailed Description

Speecial p.d.f.

's: using a p.d.f defined by a sum of real-valued amplitude components

 
 
␛[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
 
[#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.