rf705_linearmorph.C File Reference

Detailed Description

Special pdf's: linear interpolation between pdf shapes using the 'Alex Read' algorithm

 
 
␛[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:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bdf699c0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bdf699c0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bdf699c0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bdf699c0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bdf699c0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bdf699c0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bdf699c0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bdf699c0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bdf699c0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x_alpha for nset (x,alpha) with code 0 from preexisting content.
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bdf699c0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bc36c6f0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0 from preexisting content.
[#0] PROGRESS:Eval -- RooIntegralMorph::fillCacheObject(lmorph) filling multi-dimensional cache..................................................
 
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bc36c6f0 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x]_NORM_x for nset (x) with code 0
[#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: (g1,g2)
[#0] WARNING:Minimization -- RooAbsMinimizerFcn::synchronize: WARNING: no initial error estimate available for alpha: using 0.1
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 alpha        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         500           1
 **********
 FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
 
prevFCN = 2639.749221   START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
alpha=0.8026, 
prevFCN = 2639.409749  alpha=0.7974, 
prevFCN = 2640.17258  alpha=0.8003, 
prevFCN = 2639.703144  alpha=0.7997, 
prevFCN = 2639.796557   FCN=2639.75 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        8.00000e-01   1.00000e-01   2.57889e-01  -5.89245e+01
                               ERR DEF= 0.5
alpha=0.8116, 
prevFCN = 2638.919064  alpha=0.8119, 
prevFCN = 2638.930985  alpha=0.8113, 
prevFCN = 2638.908768  alpha=0.8094, 
prevFCN = 2638.901287  alpha=0.8102, 
prevFCN = 2638.885143  alpha=0.8103, 
prevFCN = 2638.886672  alpha=0.8101, 
prevFCN = 2638.883909  alpha=0.8095, 
prevFCN = 2638.898442  alpha=0.8098, 
prevFCN = 2638.889204  alpha=0.8099, 
prevFCN = 2638.884962  alpha=0.8104, 
prevFCN = 2638.887231  alpha=0.8098, 
prevFCN = 2638.888592  alpha=0.8102, 
prevFCN = 2638.885076  alpha=0.81, 
prevFCN = 2638.883889  alpha=0.8098, 
prevFCN = 2638.888745  alpha=0.81, 
prevFCN = 2638.883589  alpha=0.81, 
prevFCN = 2638.883345  alpha=0.8095, 
prevFCN = 2638.898453  alpha=0.8098, 
prevFCN = 2638.89011  alpha=0.8099, 
prevFCN = 2638.886243  alpha=0.81, 
prevFCN = 2638.884385  alpha=0.81, 
prevFCN = 2638.883475  alpha=0.8101, 
prevFCN = 2638.884457  alpha=0.8099, 
prevFCN = 2638.885715  alpha=0.8101, 
prevFCN = 2638.883988  alpha=0.81, 
prevFCN = 2638.884446  alpha=0.81, 
prevFCN = 2638.883552  alpha=0.81, 
prevFCN = 2638.883372  alpha=0.81, 
prevFCN = 2638.883349  alpha=0.81, 
prevFCN = 2638.883345   MIGRAD FAILS TO FIND IMPROVEMENT
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
alpha=0.81, 
prevFCN = 2638.883345  alpha=0.8101, 
prevFCN = 2638.883988  alpha=0.81, 
prevFCN = 2638.884446  alpha=0.81, 
prevFCN = 2638.883467  alpha=0.81, 
prevFCN = 2638.883226  alpha=0.81, 
prevFCN = 2638.883369  alpha=0.81, 
prevFCN = 2638.883321   COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=2638.88 FROM MIGRAD    STATUS=CONVERGED      41 CALLS          42 TOTAL
                     EDM=0.000209046    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  alpha        8.10021e-01   1.63457e-03   1.74006e-04   3.46989e+00
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  1    ERR DEF=0.5
  2.672e-06 
alpha=0.81,  **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE         500
 **********
 
prevFCN = 2638.883345  alpha=0.81, 
prevFCN = 2638.883369  alpha=0.81, 
prevFCN = 2638.883321  alpha=0.8103, 
prevFCN = 2638.886457  alpha=0.8097, 
prevFCN = 2638.89054  alpha=0.8131, 
prevFCN = 2638.992315  alpha=0.8069, 
prevFCN = 2639.023618  alpha=0.8171, 
prevFCN = 2639.367946  alpha=0.8029, 
prevFCN = 2639.374671  alpha=0.8102, 
prevFCN = 2638.885206  alpha=0.8098, 
prevFCN = 2638.887615  alpha=0.8101, 
prevFCN = 2638.883674  alpha=0.81, 
prevFCN = 2638.883555   COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=2638.88 FROM HESSE     STATUS=OK             13 CALLS          55 TOTAL
                     EDM=0.00230644    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  alpha        8.10021e-01   7.16762e-03   1.80513e-02   6.68797e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  1    ERR DEF=0.5
  5.138e-05 
alpha=0.81, [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bc36c6f0 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x]_NORM_x for nset (x) with code 0 from preexisting content.
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644bc36c6f0 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x]_NORM_x for nset (x) with code 0 from preexisting content.
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644be9b9a30 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x]_NORM_x for nset (x) with code 0 from preexisting content.
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x5644be9b9a30 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x]_NORM_x for nset (x) with code 0 from preexisting content.

 
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooPolynomial.h"
#include "RooIntegralMorph.h"
#include "RooNLLVar.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "TH1.h"
using namespace RooFit;
 
void rf705_linearmorph()
{
   // C r e a t e   e n d   p o i n t   p d f   s h a p e s
   // ------------------------------------------------------
 
   // Observable
   RooRealVar x("x", "x", -20, 20);
 
   // Lower end point shape: a Gaussian
   RooRealVar g1mean("g1mean", "g1mean", -10);
   RooGaussian g1("g1", "g1", x, g1mean, RooConst(2));
 
   // Upper end point shape: a Polynomial
   RooPolynomial g2("g2", "g2", x, RooArgSet(-0.03, -0.001));
 
   // C r e a t e   i n t e r p o l a t i n g   p d f
   // -----------------------------------------------
 
   // Create interpolation variable
   RooRealVar alpha("alpha", "alpha", 0, 1.0);
 
   // Specify sampling density on observable and interpolation variable
   x.setBins(1000, "cache");
   alpha.setBins(50, "cache");
 
   // Construct interpolating pdf in (x,a) represent g1(x) at a=a_min
   // and g2(x) at a=a_max
   RooIntegralMorph lmorph("lmorph", "lmorph", g1, g2, x, alpha);
 
   // P l o t   i n t e r p o l a t i n g   p d f   a t   v a r i o u s   a l p h a
   // -----------------------------------------------------------------------------
 
   // Show end points as blue curves
   RooPlot *frame1 = x.frame();
   g1.plotOn(frame1);
   g2.plotOn(frame1);
 
   // Show interpolated shapes in red
   alpha.setVal(0.125);
   lmorph.plotOn(frame1, LineColor(kRed));
   alpha.setVal(0.25);
   lmorph.plotOn(frame1, LineColor(kRed));
   alpha.setVal(0.375);
   lmorph.plotOn(frame1, LineColor(kRed));
   alpha.setVal(0.50);
   lmorph.plotOn(frame1, LineColor(kRed));
   alpha.setVal(0.625);
   lmorph.plotOn(frame1, LineColor(kRed));
   alpha.setVal(0.75);
   lmorph.plotOn(frame1, LineColor(kRed));
   alpha.setVal(0.875);
   lmorph.plotOn(frame1, LineColor(kRed));
   alpha.setVal(0.95);
   lmorph.plotOn(frame1, LineColor(kRed));
 
   // S h o w   2 D   d i s t r i b u t i o n   o f   p d f ( x , a l p h a )
   // -----------------------------------------------------------------------
 
   // Create 2D histogram
   TH1 *hh = lmorph.createHistogram("hh", x, Binning(40), YVar(alpha, Binning(40)));
   hh->SetLineColor(kBlue);
 
   // F i t   p d f   t o   d a t a s e t   w i t h   a l p h a = 0 . 8
   // -----------------------------------------------------------------
 
   // Generate a toy dataset at alpha = 0.8
   alpha = 0.8;
   RooDataSet *data = lmorph.generate(x, 1000);
 
   // Fit pdf to toy data
   lmorph.setCacheAlpha(kTRUE);
   lmorph.fitTo(*data, Verbose(kTRUE));
 
   // Plot fitted pdf and data overlaid
   RooPlot *frame2 = x.frame(Bins(100));
   data->plotOn(frame2);
   lmorph.plotOn(frame2);
 
   // S c a n   - l o g ( L )   v s   a l p h a
   // -----------------------------------------
 
   // Show scan -log(L) of dataset w.r.t alpha
   RooPlot *frame3 = alpha.frame(Bins(100), Range(0.1, 0.9));
 
   // Make 2D pdf of histogram
   RooNLLVar nll("nll", "nll", lmorph, *data);
   nll.plotOn(frame3, ShiftToZero());
 
   lmorph.setCacheAlpha(kFALSE);
 
   TCanvas *c = new TCanvas("rf705_linearmorph", "rf705_linearmorph", 800, 800);
   c->Divide(2, 2);
   c->cd(1);
   gPad->SetLeftMargin(0.15);
   frame1->GetYaxis()->SetTitleOffset(1.6);
   frame1->Draw();
   c->cd(2);
   gPad->SetLeftMargin(0.20);
   hh->GetZaxis()->SetTitleOffset(2.5);
   hh->Draw("surf");
   c->cd(3);
   gPad->SetLeftMargin(0.15);
   frame3->GetYaxis()->SetTitleOffset(1.4);
   frame3->Draw();
   c->cd(4);
   gPad->SetLeftMargin(0.15);
   frame2->GetYaxis()->SetTitleOffset(1.4);
   frame2->Draw();
 
   return;
}

Date

July 2008

Author

Wouter Verkerke

Definition in file rf705_linearmorph.C.