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 0x55cc9b951560 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 0x55cc9b951560 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 0x55cc9b951560 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 0x55cc9b951560 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 0x55cc9b951560 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 0x55cc9b951560 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 0x55cc9b951560 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 0x55cc9b951560 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 0x55cc9b940750 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 0x55cc9b951560 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 0x55cc9b940750 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 0x55cc9b940750 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x]_NORM_x for nset (x) with code 0
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
[#1] INFO:Minization --  The following expressions have been identified as constant and will be precalculated and cached: (g1,g2)
[#0] WARNING:Minization -- RooMinimizerFcn::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 = 2639.71348   START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
alpha=0.8026, 
prevFCN = 2639.370838  alpha=0.7974, 
prevFCN = 2640.13986  alpha=0.8003, 
prevFCN = 2639.666981  alpha=0.7997, 
prevFCN = 2639.761239   FCN=2639.71 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  -5.94047e+01
                               ERR DEF= 0.5
alpha=0.8117, 
prevFCN = 2638.871739  alpha=0.812, 
prevFCN = 2638.883686  alpha=0.8114, 
prevFCN = 2638.861418  alpha=0.8095, 
prevFCN = 2638.85007  alpha=0.8102, 
prevFCN = 2638.83663  alpha=0.8104, 
prevFCN = 2638.838462  alpha=0.8105, 
prevFCN = 2638.840038  alpha=0.8099, 
prevFCN = 2638.836678  alpha=0.8104, 
prevFCN = 2638.838537  alpha=0.81, 
prevFCN = 2638.835179  alpha=0.8105, 
prevFCN = 2638.840049  alpha=0.8099, 
prevFCN = 2638.836701  alpha=0.8099, 
prevFCN = 2638.837868  alpha=0.8101, 
prevFCN = 2638.835736  alpha=0.8101, 
prevFCN = 2638.835493  alpha=0.8096, 
prevFCN = 2638.847089  alpha=0.8098, 
prevFCN = 2638.839436  alpha=0.81, 
prevFCN = 2638.835865  alpha=0.81, 
prevFCN = 2638.835182  alpha=0.81, 
prevFCN = 2638.835414  alpha=0.81, 
prevFCN = 2638.835066  alpha=0.8102, 
prevFCN = 2638.83647  alpha=0.8099, 
prevFCN = 2638.838806  alpha=0.8101, 
prevFCN = 2638.835704  alpha=0.8099, 
prevFCN = 2638.836348  alpha=0.8101, 
prevFCN = 2638.835616  alpha=0.81, 
prevFCN = 2638.835153  alpha=0.81, 
prevFCN = 2638.835081  alpha=0.81, 
prevFCN = 2638.835068  alpha=0.81, 
prevFCN = 2638.835066   MIGRAD FAILS TO FIND IMPROVEMENT
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
alpha=0.81, 
prevFCN = 2638.835066  alpha=0.8101, 
prevFCN = 2638.835704  alpha=0.8099, 
prevFCN = 2638.836348  alpha=0.81, 
prevFCN = 2638.835184  alpha=0.81, 
prevFCN = 2638.834951  alpha=0.81, 
prevFCN = 2638.835089  alpha=0.81, 
prevFCN = 2638.835043   COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=2638.84 FROM MIGRAD    STATUS=CONVERGED      41 CALLS          42 TOTAL
                     EDM=0.00017663    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  alpha        8.10030e-01   1.85998e-03   2.07772e-04   2.80295e+00
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  1    ERR DEF=0.5
  3.460e-06 
alpha=0.81,  **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE         500
 **********
 
prevFCN = 2638.835066  alpha=0.81, 
prevFCN = 2638.835089  alpha=0.81, 
prevFCN = 2638.835043  alpha=0.8104, 
prevFCN = 2638.838366  alpha=0.8097, 
prevFCN = 2638.844002  alpha=0.8134, 
prevFCN = 2638.957145  alpha=0.8066, 
prevFCN = 2638.998648  alpha=0.8172, 
prevFCN = 2639.32881  alpha=0.8027, 
prevFCN = 2639.353813  alpha=0.8102, 
prevFCN = 2638.83663  alpha=0.8098, 
prevFCN = 2638.839285  alpha=0.8101, 
prevFCN = 2638.835335  alpha=0.81, 
prevFCN = 2638.835043   COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=2638.84 FROM HESSE     STATUS=OK             13 CALLS          55 TOTAL
                     EDM=0.0028007    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  alpha        8.10030e-01   7.20341e-03   1.84784e-02   6.68818e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  1    ERR DEF=0.5
  5.190e-05 
alpha=0.81, [#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x55cc9b7dc370 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 0x55cc9b7dc370 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 0x55cc9c0b22e0 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 0x55cc9c0b22e0 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 "RooConstVar.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(RooConst(-0.03), RooConst(-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.