rf103_interprfuncs.C File Reference

Detailed Description

Basic functionality: interpreted functions and p.d.f.s

 
 
␛[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(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 alpha        5.00000e+00  9.90000e-01    1.00000e-01  1.00000e+01
 **********
 **    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         500           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=35708.9 FROM MIGRAD    STATUS=INITIATE        4 CALLS           5 TOTAL
                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX       
  EXT PARAMETER               CURRENT GUESS       STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  alpha        5.00000e+00   9.90000e-01   2.01369e-01   1.02940e+02
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=35708.6 FROM MIGRAD    STATUS=CONVERGED      12 CALLS          13 TOTAL
                     EDM=1.24247e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  alpha        4.96355e+00   4.16961e-02   1.10376e-03  -4.18389e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  1    ERR DEF=0.5
  1.739e-03 
 **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE         500
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=35708.6 FROM HESSE     STATUS=OK              5 CALLS          18 TOTAL
                     EDM=1.24183e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  alpha        4.96355e+00   4.16961e-02   2.20752e-04  -1.74664e-02
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  1    ERR DEF=0.5
  1.739e-03 
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
[#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 mean2        1.00000e+01  5.00000e+00    0.00000e+00  2.00000e+02
     2 sigma        3.00000e+00  9.90000e-01    1.00000e-01  1.00000e+01
 **********
 **    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=5148.93 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  mean2        1.00000e+01   5.00000e+00   1.18625e-01  -5.23438e+03
   2  sigma        3.00000e+00   9.90000e-01   2.22742e-01  -7.90389e+03
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=2551.39 FROM MIGRAD    STATUS=CONVERGED      59 CALLS          60 TOTAL
                     EDM=8.7852e-06    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  mean2        1.00100e+02   1.98019e+00   6.89576e-04   4.58015e-02
   2  sigma        3.11719e+00   7.12427e-02   5.29831e-04   1.79331e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  3.922e+00  2.826e-03 
  2.826e-03  5.076e-03 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.02003   1.000  0.020
        2  0.02003   0.020  1.000
 **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        1000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=2551.39 FROM HESSE     STATUS=OK             10 CALLS          70 TOTAL
                     EDM=8.78617e-06    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  mean2        1.00100e+02   1.98016e+00   1.37915e-04   1.00004e-03
   2  sigma        3.11719e+00   7.12418e-02   1.05966e-04  -4.01138e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  3.922e+00  2.730e-03 
  2.730e-03  5.076e-03 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.01935   1.000  0.019
        2  0.01935   0.019  1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
 
  RooFitResult: minimized FCN value: 2551.39, estimated distance to minimum: 8.78617e-06
                covariance matrix quality: Full, accurate covariance matrix
                Status : MINIMIZE=0 HESSE=0 
 
    Floating Parameter    FinalValue +/-  Error   
  --------------------  --------------------------
                 mean2    1.0010e+02 +/-  1.98e+00
                 sigma    3.1172e+00 +/-  7.12e-02
 

 
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "RooFitResult.h"
#include "RooGenericPdf.h"
#include "RooConstVar.h"
 
using namespace RooFit;
 
void rf103_interprfuncs()
{
   // ----------------------------------------------------
   // G e n e r i c   i n t e r p r e t e d   p . d . f .
   // ====================================================
 
   // Declare observable x
   RooRealVar x("x", "x", -20, 20);
 
   // C o n s t r u c t   g e n e r i c   p d f   f r o m   i n t e r p r e t e d   e x p r e s s i o n
   // -------------------------------------------------------------------------------------------------
 
   // To construct a proper p.d.f, the formula expression is explicitly normalized internally by dividing
   // it by a numeric integral of the expression over x in the range [-20,20]
   //
   RooRealVar alpha("alpha", "alpha", 5, 0.1, 10);
   RooGenericPdf genpdf("genpdf", "genpdf", "(1+0.1*abs(x)+sin(sqrt(abs(x*alpha+0.1))))", RooArgSet(x, alpha));
 
   // S a m p l e ,   f i t   a n d   p l o t   g e n e r i c   p d f
   // ---------------------------------------------------------------
 
   // Generate a toy dataset from the interpreted p.d.f
   RooDataSet *data = genpdf.generate(x, 10000);
 
   // Fit the interpreted p.d.f to the generated data
   genpdf.fitTo(*data);
 
   // Make a plot of the data and the p.d.f overlaid
   RooPlot *xframe = x.frame(Title("Interpreted expression pdf"));
   data->plotOn(xframe);
   genpdf.plotOn(xframe);
 
   // -----------------------------------------------------------------------------------------------------------
   // S t a n d a r d   p . d . f   a d j u s t   w i t h   i n t e r p r e t e d   h e l p e r   f u n c t i o n
   // ==========================================================================================================
   // Make a gauss(x,sqrt(mean2),sigma) from a standard RooGaussian
 
   // C o n s t r u c t   s t a n d a r d   p d f  w i t h   f o r m u l a   r e p l a c i n g   p a r a m e t e r
   // ------------------------------------------------------------------------------------------------------------
 
   // Construct parameter mean2 and sigma
   RooRealVar mean2("mean2", "mean^2", 10, 0, 200);
   RooRealVar sigma("sigma", "sigma", 3, 0.1, 10);
 
   // Construct interpreted function mean = sqrt(mean^2)
   RooFormulaVar mean("mean", "mean", "sqrt(mean2)", mean2);
 
   // Construct a gaussian g2(x,sqrt(mean2),sigma) ;
   RooGaussian g2("g2", "h2", x, mean, sigma);
 
   // G e n e r a t e   t o y   d a t a
   // ---------------------------------
 
   // Construct a separate gaussian g1(x,10,3) to generate a toy Gaussian dataset with mean 10 and width 3
   RooGaussian g1("g1", "g1", x, RooConst(10), RooConst(3));
   RooDataSet *data2 = g1.generate(x, 1000);
 
   // F i t   a n d   p l o t   t a i l o r e d   s t a n d a r d   p d f
   // -------------------------------------------------------------------
 
   // Fit g2 to data from g1
   RooFitResult *r = g2.fitTo(*data2, Save());
   r->Print();
 
   // Plot data on frame and overlay projection of g2
   RooPlot *xframe2 = x.frame(Title("Tailored Gaussian pdf"));
   data2->plotOn(xframe2);
   g2.plotOn(xframe2);
 
   // Draw all frames on a canvas
   TCanvas *c = new TCanvas("rf103_interprfuncs", "rf103_interprfuncs", 800, 400);
   c->Divide(2);
   c->cd(1);
   gPad->SetLeftMargin(0.15);
   xframe->GetYaxis()->SetTitleOffset(1.4);
   xframe->Draw();
   c->cd(2);
   gPad->SetLeftMargin(0.15);
   xframe2->GetYaxis()->SetTitleOffset(1.4);
   xframe2->Draw();
}

Author

07/2008 - Wouter Verkerke

Definition in file rf103_interprfuncs.C.