rf315_projectpdf.C File Reference

Detailed Description

Multidimensional models: marginizalization of multi-dimensional p.d.f.s through integration

 
 
␛[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([gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[y]) using numeric integrator RooIntegrator1D to calculate Int(y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[y]) using numeric integrator RooIntegrator1D to calculate Int(y)
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
[#1] INFO:Minization --  The following expressions will be evaluated in cache-and-track mode: (gaussx)
[#0] WARNING:Minization -- RooMinimizerFcn::synchronize: WARNING: no initial error estimate available for a1: using 0.4
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 a1          -1.50000e+00  4.00000e-01   -3.00000e+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         500           1
 **********
 FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
 
prevFCN = 1900.156536   START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
a1=-1.491, 
prevFCN = 1900.000822  a1=-1.509, 
prevFCN = 1900.423606  a1=-1.499, 
prevFCN = 1900.135899  a1=-1.501, 
prevFCN = 1900.178287   FCN=1900.16 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  a1          -1.50000e+00   4.00000e-01   2.08372e-01  -4.77802e+01
                               ERR DEF= 0.5
a1=-1.484, 
prevFCN = 1899.958651  a1=-1.483, 
prevFCN = 1899.959675  a1=-1.484, 
prevFCN = 1899.958586  a1=-1.484, 
prevFCN = 1899.958497  a1=-1.483, 
prevFCN = 1899.958935  a1=-1.485, 
prevFCN = 1899.958964   MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
a1=-1.484, 
prevFCN = 1899.958497  a1=-1.483, 
prevFCN = 1899.958935  a1=-1.485, 
prevFCN = 1899.958964  a1=-1.484, 
prevFCN = 1899.958512  a1=-1.484, 
prevFCN = 1899.958518   COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=1899.96 FROM MIGRAD    STATUS=CONVERGED      15 CALLS          16 TOTAL
                     EDM=2.41873e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  a1          -1.48409e+00   2.51054e-02   3.89173e-04  -3.80132e-02
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  1    ERR DEF=0.5
  6.303e-04 
a1=-1.484,  **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE         500
 **********
 
prevFCN = 1899.958497  a1=-1.484, 
prevFCN = 1899.958512  a1=-1.484, 
prevFCN = 1899.958518  a1=-1.484, 
prevFCN = 1899.958497  a1=-1.484, 
prevFCN = 1899.958498   COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=1899.96 FROM HESSE     STATUS=OK              5 CALLS          21 TOTAL
                     EDM=2.42353e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  a1          -1.48409e+00   2.51054e-02   7.78346e-05  -2.44471e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  1    ERR DEF=0.5
  6.303e-04 
a1=-1.484, [#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
[#1] INFO:NumericIntegration -- RooRealIntegral::init([gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[y]) using numeric integrator RooIntegrator1D to calculate Int(y)

 
#include "RooRealVar.h"
#include "RooDataHist.h"
#include "RooGaussian.h"
#include "RooProdPdf.h"
#include "RooPolyVar.h"
#include "TH1.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "RooNumIntConfig.h"
#include "RooConstVar.h"
using namespace RooFit;
 
void rf315_projectpdf()
{
   // C r e a t e   p d f   m ( x , y )  =  g x ( x | y ) * g ( y )
   // --------------------------------------------------------------
 
   // Increase default precision of numeric integration
   // as this exercise has high sensitivity to numeric integration precision
   RooAbsPdf::defaultIntegratorConfig()->setEpsRel(1e-8);
   RooAbsPdf::defaultIntegratorConfig()->setEpsAbs(1e-8);
 
   // Create observables
   RooRealVar x("x", "x", -5, 5);
   RooRealVar y("y", "y", -2, 2);
 
   // Create function f(y) = a0 + a1*y
   RooRealVar a0("a0", "a0", 0);
   RooRealVar a1("a1", "a1", -1.5, -3, 1);
   RooPolyVar fy("fy", "fy", y, RooArgSet(a0, a1));
 
   // Create gaussx(x,f(y),sx)
   RooRealVar sigmax("sigmax", "width of gaussian", 0.5);
   RooGaussian gaussx("gaussx", "Gaussian in x with shifting mean in y", x, fy, sigmax);
 
   // Create gaussy(y,0,2)
   RooGaussian gaussy("gaussy", "Gaussian in y", y, RooConst(0), RooConst(2));
 
   // Create gaussx(x,sx|y) * gaussy(y)
   RooProdPdf model("model", "gaussx(x|y)*gaussy(y)", gaussy, Conditional(gaussx, x));
 
   // M a r g i n a l i z e   m ( x , y )   t o   m ( x )
   // ----------------------------------------------------
 
   // modelx(x) = Int model(x,y) dy
   RooAbsPdf *modelx = model.createProjection(y);
 
   // U s e   m a r g i n a l i z e d   p . d . f .   a s   r e g u l a r   1 - D   p . d . f .
   // ------------------------------------------------------------------------------------------
 
   // Sample 1000 events from modelx
   RooAbsData *data = modelx->generateBinned(x, 1000);
 
   // Fit modelx to toy data
   modelx->fitTo(*data, Verbose());
 
   // Plot modelx over data
   RooPlot *frame = x.frame(40);
   data->plotOn(frame);
   modelx->plotOn(frame);
 
   // Make 2D histogram of model(x,y)
   TH1 *hh = model.createHistogram("x,y");
   hh->SetLineColor(kBlue);
 
   TCanvas *c = new TCanvas("rf315_projectpdf", "rf315_projectpdf", 800, 400);
   c->Divide(2);
   c->cd(1);
   gPad->SetLeftMargin(0.15);
   frame->GetYaxis()->SetTitleOffset(1.4);
   frame->Draw();
   c->cd(2);
   gPad->SetLeftMargin(0.20);
   hh->GetZaxis()->SetTitleOffset(2.5);
   hh->Draw("surf");
}

Author

07/2008 - Wouter Verkerke

Definition in file rf315_projectpdf.C.