rf201_composite.C File Reference

Detailed Description

Addition and convolution: composite pdf with signal and background component

pdf = f_bkg * bkg(x,a0,a1) + (1-fbkg) * (f_sig1 * sig1(x,m,s1 + (1-f_sig1) * sig2(x,m,s2)))

 
[#0] WARNING:InputArguments -- The parameter 'sigma1' with range [-inf, inf] of the RooGaussian 'sig1' exceeds the safe range of (0, inf). Advise to limit its range.
[#0] WARNING:InputArguments -- The parameter 'sigma2' with range [-inf, inf] of the RooGaussian 'sig2' exceeds the safe range of (0, inf). Advise to limit its range.
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
[#1] INFO:Minimization --  The following expressions have been identified as constant and will be precalculated and cached: (sig1,sig2)
[#1] INFO:Minimization --  The following expressions will be evaluated in cache-and-track mode: (bkg)
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 a0           5.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
     2 a1           2.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
     3 bkgfrac      5.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
     4 sig1frac     8.00000e-01  1.00000e-01    0.00000e+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
 **********
 **    6 **MIGRAD        2000           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=1962.68 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  a0           5.00000e-01   1.00000e-01   2.01358e-01   5.55984e+00
   2  a1           2.00000e-01   1.00000e-01   2.57889e-01  -1.57464e+00
   3  bkgfrac      5.00000e-01   1.00000e-01   2.01358e-01   1.16417e+00
   4  sig1frac     8.00000e-01   1.00000e-01   2.57889e-01  -2.02114e+00
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=1962.27 FROM MIGRAD    STATUS=CONVERGED      77 CALLS          78 TOTAL
                     EDM=2.21873e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  a0           4.41621e-01   7.31971e-02   4.49448e-03  -2.95364e-02
   2  a1           2.01070e-01   1.18164e-01   5.76018e-03   4.48544e-03
   3  bkgfrac      5.04184e-01   3.60469e-02   1.24368e-03  -2.15278e-02
   4  sig1frac     8.37334e-01   1.17186e-01   6.00443e-03   1.16304e-03
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=0.5
  5.397e-03  1.212e-03 -3.088e-04 -1.017e-03 
  1.212e-03  1.439e-02 -3.249e-03 -9.741e-03 
 -3.088e-04 -3.249e-03  1.302e-03  3.287e-03 
 -1.017e-03 -9.741e-03  3.287e-03  1.422e-02 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2      3      4
        1  0.14102   1.000  0.138 -0.117 -0.116
        2  0.77022   0.138  1.000 -0.751 -0.681
        3  0.82636  -0.117 -0.751  1.000  0.764
        4  0.78133  -0.116 -0.681  0.764  1.000
 **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        2000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=1962.27 FROM HESSE     STATUS=OK             23 CALLS         101 TOTAL
                     EDM=2.21633e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  a0           4.41621e-01   7.31875e-02   8.98897e-04  -1.17025e-01
   2  a1           2.01070e-01   1.17637e-01   2.30407e-04  -6.40829e-01
   3  bkgfrac      5.04184e-01   3.59091e-02   2.48735e-04   8.36870e-03
   4  sig1frac     8.37334e-01   1.16852e-01   2.40177e-04   7.40515e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=0.5
  5.396e-03  1.199e-03 -3.049e-04 -1.005e-03 
  1.199e-03  1.426e-02 -3.211e-03 -9.629e-03 
 -3.049e-04 -3.211e-03  1.292e-03  3.259e-03 
 -1.005e-03 -9.629e-03  3.259e-03  1.414e-02 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2      3      4
        1  0.14012   1.000  0.137 -0.116 -0.115
        2  0.76777   0.137  1.000 -0.748 -0.678
        3  0.82488  -0.116 -0.748  1.000  0.763
        4  0.77985  -0.115 -0.678  0.763  1.000
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg,sig2)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: (sig)
0x7ffd4becddd0 RooAddPdf::model = 0.898624/1 [Auto,Clean] 
  0x7ffd4becd4b8/V- RooChebychev::bkg = 0.79893 [Auto,Dirty] 
    0x7ffd4becd9e8/V- RooRealVar::x = 5
    0x7ffd4becb4b8/V- RooRealVar::a0 = 0.441621 +/- 0.0731875
    0x7ffd4becb8a0/V- RooRealVar::a1 = 0.20107 +/- 0.117637
  0x7ffd4beccb78/V- RooRealVar::bkgfrac = 0.504184 +/- 0.0359091
  0x7ffd4becbc88/V- RooAddPdf::sig = 1/1 [Auto,Clean] 
    0x7ffd4beca790/V- RooGaussian::sig1 = 1 [Auto,Dirty] 
      0x7ffd4becd9e8/V- RooRealVar::x = 5
      0x7ffd4becc3a8/V- RooRealVar::mean = 5
      0x7ffd4becace8/V- RooRealVar::sigma1 = 0.5
    0x7ffd4becc790/V- RooRealVar::sig1frac = 0.837334 +/- 0.116852
    0x7ffd4beccf60/V- RooGaussian::sig2 = 1 [Auto,Dirty] 
      0x7ffd4becd9e8/V- RooRealVar::x = 5
      0x7ffd4becc3a8/V- RooRealVar::mean = 5
      0x7ffd4becb0d0/V- RooRealVar::sigma2 = 1
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg,sig2)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()
0x7ffd4bece640 RooAddPdf::model = 0.898624/1 [Auto,Clean] 
  0x7ffd4becd4b8/V- RooChebychev::bkg = 0.79893 [Auto,Dirty] 
    0x7ffd4becd9e8/V- RooRealVar::x = 5
    0x7ffd4becb4b8/V- RooRealVar::a0 = 0.441621 +/- 0.0731875
    0x7ffd4becb8a0/V- RooRealVar::a1 = 0.20107 +/- 0.117637
  0x7ffd4beccb78/V- RooRealVar::bkgfrac = 0.504184 +/- 0.0359091
  0x7ffd4beca790/V- RooGaussian::sig1 = 1 [Auto,Dirty] 
    0x7ffd4becd9e8/V- RooRealVar::x = 5
    0x7ffd4becc3a8/V- RooRealVar::mean = 5
    0x7ffd4becace8/V- RooRealVar::sigma1 = 0.5
  0x564c14ba8f90/V- RooRecursiveFraction::model_recursive_fraction_sig1_2 = 0.415163 [Auto,Clean] 
    0x7ffd4becc790/V- RooRealVar::sig1frac = 0.837334 +/- 0.116852
    0x7ffd4beccb78/V- RooRealVar::bkgfrac = 0.504184 +/- 0.0359091
  0x7ffd4beccf60/V- RooGaussian::sig2 = 1 [Auto,Dirty] 
    0x7ffd4becd9e8/V- RooRealVar::x = 5
    0x7ffd4becc3a8/V- RooRealVar::mean = 5
    0x7ffd4becb0d0/V- RooRealVar::sigma2 = 1
  0x564c0fe7b960/V- RooRecursiveFraction::model_recursive_fraction_sig2_3 = 0.0806524 [Auto,Clean] 
    0x564c1009a490/V- RooConstVar::1 = 1
    0x7ffd4becc790/V- RooRealVar::sig1frac = 0.837334 +/- 0.116852
    0x7ffd4beccb78/V- RooRealVar::bkgfrac = 0.504184 +/- 0.0359091

 
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooChebychev.h"
#include "RooAddPdf.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit;
 
void rf201_composite()
{
   // S e t u p   c o m p o n e n t   p d f s
   // ---------------------------------------
 
   // Declare observable x
   RooRealVar x("x", "x", 0, 10);
 
   // Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters
   RooRealVar mean("mean", "mean of gaussians", 5);
   RooRealVar sigma1("sigma1", "width of gaussians", 0.5);
   RooRealVar sigma2("sigma2", "width of gaussians", 1);
 
   RooGaussian sig1("sig1", "Signal component 1", x, mean, sigma1);
   RooGaussian sig2("sig2", "Signal component 2", x, mean, sigma2);
 
   // Build Chebychev polynomial pdf
   RooRealVar a0("a0", "a0", 0.5, 0., 1.);
   RooRealVar a1("a1", "a1", 0.2, 0., 1.);
   RooChebychev bkg("bkg", "Background", x, RooArgSet(a0, a1));
 
   // ---------------------------------------------
   // M E T H O D   1 - T w o   R o o A d d P d f s
   // =============================================
 
   // A d d   s i g n a l   c o m p o n e n t s
   // ------------------------------------------
 
   // Sum the signal components into a composite signal pdf
   RooRealVar sig1frac("sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.);
   RooAddPdf sig("sig", "Signal", RooArgList(sig1, sig2), sig1frac);
 
   // A d d  s i g n a l   a n d   b a c k g r o u n d
   // ------------------------------------------------
 
   // Sum the composite signal and background
   RooRealVar bkgfrac("bkgfrac", "fraction of background", 0.5, 0., 1.);
   RooAddPdf model("model", "g1+g2+a", RooArgList(bkg, sig), bkgfrac);
 
   // S a m p l e ,   f i t   a n d   p l o t   m o d e l
   // ---------------------------------------------------
 
   // Generate a data sample of 1000 events in x from model
   RooDataSet *data = model.generate(x, 1000);
 
   // Fit model to data
   model.fitTo(*data);
 
   // Plot data and PDF overlaid
   RooPlot *xframe = x.frame(Title("Example of composite pdf=(sig1+sig2)+bkg"));
   data->plotOn(xframe);
   model.plotOn(xframe);
 
   // Overlay the background component of model with a dashed line
   model.plotOn(xframe, Components(bkg), LineStyle(kDashed));
 
   // Overlay the background+sig2 components of model with a dotted line
   model.plotOn(xframe, Components(RooArgSet(bkg, sig2)), LineStyle(kDotted));
 
   // Print structure of composite pdf
   model.Print("t");
 
   // ---------------------------------------------------------------------------------------------
   // M E T H O D   2 - O n e   R o o A d d P d f   w i t h   r e c u r s i v e   f r a c t i o n s
   // =============================================================================================
 
   // Construct sum of models on one go using recursive fraction interpretations
   //
   //   model2 = bkg + (sig1 + sig2)
   //
   RooAddPdf model2("model", "g1+g2+a", RooArgList(bkg, sig1, sig2), RooArgList(bkgfrac, sig1frac), true);
 
   // NB: Each coefficient is interpreted as the fraction of the
   // left-hand component of the i-th recursive sum, i.e.
   //
   //   sum4 = A + ( B + ( C + D)  with fraction fA, fB and fC expands to
   //
   //   sum4 = fA*A + (1-fA)*(fB*B + (1-fB)*(fC*C + (1-fC)*D))
 
   // P l o t   r e c u r s i v e   a d d i t i o n   m o d e l
   // ---------------------------------------------------------
   model2.plotOn(xframe, LineColor(kRed), LineStyle(kDashed));
   model2.plotOn(xframe, Components(RooArgSet(bkg, sig2)), LineColor(kRed), LineStyle(kDashed));
   model2.Print("t");
 
   // Draw the frame on the canvas
   new TCanvas("rf201_composite", "rf201_composite", 600, 600);
   gPad->SetLeftMargin(0.15);
   xframe->GetYaxis()->SetTitleOffset(1.4);
   xframe->Draw();
}

Date

July 2008

Author

Wouter Verkerke

Definition in file rf201_composite.C.