rf609_xychi2fit.C File Reference

Detailed Description

Likelihood and minimization: setting up a chi^2 fit to an unbinned dataset with X,Y,err(Y) values (and optionally err(X) values)

 
 
␛[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:Minization -- RooMinimizer::optimizeConst: activating const optimization
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 a            0.00000e+00  2.00000e+00   -1.00000e+01  1.00000e+01
     2 b            0.00000e+00  2.00000e+01   -1.00000e+02  1.00000e+02
 **********
 **    3 **SET ERR           1
 **********
 **********
 **    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=2.04222 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  a            0.00000e+00   2.00000e+00   2.01358e-01   1.35235e+01
   2  b            0.00000e+00   2.00000e+01   2.01358e-01  -3.08578e+02
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=1.43197 FROM MIGRAD    STATUS=CONVERGED      32 CALLS          33 TOTAL
                     EDM=3.23329e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  a           -1.60654e-01   5.24023e-01   3.93124e-05   1.09375e-01
   2  b            3.34226e-01   4.91235e-01   3.85614e-06  -1.06196e+00
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=1
  2.749e-01 -1.964e-02 
 -1.964e-02  2.413e-01 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.07625   1.000 -0.076
        2  0.07625  -0.076  1.000
 **********
 **    7 **SET ERR           1
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        1000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=1.43197 FROM HESSE     STATUS=OK             10 CALLS          43 TOTAL
                     EDM=3.23291e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  a           -1.60654e-01   5.24019e-01   7.86248e-06  -1.60660e-02
   2  b            3.34226e-01   4.91231e-01   7.71228e-07   3.34226e-03
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=1
  2.748e-01 -1.961e-02 
 -1.961e-02  2.413e-01 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.07614   1.000 -0.076
        2  0.07614  -0.076  1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
 **********
 **   10 **SET PRINT           1
 **********
 **********
 **   11 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 a           -1.60654e-01  5.24019e-01   -1.00000e+01  1.00000e+01
     2 b            3.34226e-01  4.91231e-01   -1.00000e+02  1.00000e+02
 **********
 **   12 **SET ERR           1
 **********
 **********
 **   13 **SET PRINT           1
 **********
 **********
 **   14 **SET STR           1
 **********
 NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
 **********
 **   15 **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=176984 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  a           -1.60654e-01   5.24019e-01   5.24327e-02  -8.81282e+03
   2  b            3.34226e-01   4.91231e-01   4.91235e-03   2.93731e+07
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=76478.7 FROM MIGRAD    STATUS=CONVERGED      30 CALLS          31 TOTAL
                     EDM=2.56889e-08    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  a           -5.61220e-02   1.57588e-02   2.12800e-04  -1.43819e-01
   2  b           -3.49788e-01   2.15812e-03   2.91421e-06  -1.32588e-01
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=1
  2.483e-04  3.343e-08 
  3.343e-08  4.657e-06 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.00098   1.000  0.001
        2  0.00098   0.001  1.000
 **********
 **   16 **SET ERR           1
 **********
 **********
 **   17 **SET PRINT           1
 **********
 **********
 **   18 **HESSE        1000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=76478.7 FROM HESSE     STATUS=OK             10 CALLS          41 TOTAL
                     EDM=2.56903e-08    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  a           -5.61220e-02   1.57588e-02   4.25601e-05  -5.61223e-03
   2  b           -3.49788e-01   2.15812e-03   5.82843e-07  -3.49789e-03
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=1
  2.483e-04  3.343e-08 
  3.343e-08  4.657e-06 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.00098   1.000  0.001
        2  0.00098   0.001  1.000

 
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooPolyVar.h"
#include "RooConstVar.h"
#include "RooChi2Var.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "TRandom.h"
 
using namespace RooFit;
 
void rf609_xychi2fit()
{
   // C r e a t e   d a t a s e t   w i t h   X   a n d   Y   v a l u e s
   // -------------------------------------------------------------------
 
   // Make weighted XY dataset with asymmetric errors stored
   // The StoreError() argument is essential as it makes
   // the dataset store the error in addition to the values
   // of the observables. If errors on one or more observables
   // are asymmetric, one can store the asymmetric error
   // using the StoreAsymError() argument
 
   RooRealVar x("x", "x", -11, 11);
   RooRealVar y("y", "y", -10, 200);
   RooDataSet dxy("dxy", "dxy", RooArgSet(x, y), StoreError(RooArgSet(x, y)));
 
   // Fill an example dataset with X,err(X),Y,err(Y) values
   for (int i = 0; i <= 10; i++) {
 
      // Set X value and error
      x = -10 + 2 * i;
      x.setError(i < 5 ? 0.5 / 1. : 1.0 / 1.);
 
      // Set Y value and error
      y = x.getVal() * x.getVal() + 4 * fabs(gRandom->Gaus());
      y.setError(sqrt(y.getVal()));
 
      dxy.add(RooArgSet(x, y));
   }
 
   // P e r f o r m   c h i 2   f i t   t o   X + / - d x   a n d   Y + / - d Y   v a l u e s
   // ---------------------------------------------------------------------------------------
 
   // Make fit function
   RooRealVar a("a", "a", 0.0, -10, 10);
   RooRealVar b("b", "b", 0.0, -100, 100);
   RooPolyVar f("f", "f", x, RooArgList(b, a, RooConst(1)));
 
   // Plot dataset in X-Y interpretation
   RooPlot *frame = x.frame(Title("Chi^2 fit of function set of (X#pmdX,Y#pmdY) values"));
   dxy.plotOnXY(frame, YVar(y));
 
   // Fit chi^2 using X and Y errors
   f.chi2FitTo(dxy, YVar(y));
 
   // Overlay fitted function
   f.plotOn(frame);
 
   // Alternative: fit chi^2 integrating f(x) over ranges defined by X errors, rather
   // than taking point at center of bin
   f.chi2FitTo(dxy, YVar(y), Integrate(kTRUE));
 
   // Overlay alternate fit result
   f.plotOn(frame, LineStyle(kDashed), LineColor(kRed));
 
   // Draw the plot on a canvas
   new TCanvas("rf609_xychi2fit", "rf609_xychi2fit", 600, 600);
   gPad->SetLeftMargin(0.15);
   frame->GetYaxis()->SetTitleOffset(1.4);
   frame->Draw();
}

Date

July 2008

Author

Wouter Verkerke

Definition in file rf609_xychi2fit.C.