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rf705_linearmorph.C File Reference

Detailed Description

View in nbviewer Open in SWAN Special pdf's: linear interpolation between pdf shapes using the 'Alex Read' algorithm

RooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby
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 0x563faabac850 with pdf g1_MORPH_g2_CACHE_Obs[x] for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563faabac850 with pdf g1_MORPH_g2_CACHE_Obs[x] for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563faabac850 with pdf g1_MORPH_g2_CACHE_Obs[x] for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563faabac850 with pdf g1_MORPH_g2_CACHE_Obs[x] for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563faabac850 with pdf g1_MORPH_g2_CACHE_Obs[x] for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563faabac850 with pdf g1_MORPH_g2_CACHE_Obs[x] for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563faabac850 with pdf g1_MORPH_g2_CACHE_Obs[x] for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563faabac850 with pdf g1_MORPH_g2_CACHE_Obs[x] for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563fab543bd0 with pdf g1_MORPH_g2_CACHE_Obs[x] for nset (x,alpha) with code 0 from preexisting content.
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563faabac850 with pdf g1_MORPH_g2_CACHE_Obs[x] for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563fab543bd0 with pdf g1_MORPH_g2_CACHE_Obs[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 0x563fab543bd0 with pdf g1_MORPH_g2_CACHE_Obs[alpha,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 0x563fab543bd0 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x] for nset (x) with code 0 from preexisting content.
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563fab543bd0 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x] for nset (x) with code 0 from preexisting content.
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563fab485a40 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x] for nset (x) with code 0 from preexisting content.
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x563fab485a40 with pdf g1_MORPH_g2_CACHE_Obs[alpha,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 "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)));
// 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.

c
#define c(i)
Definition: RSha256.hxx:101
RooPlot::Draw
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:691
kTRUE
const Bool_t kTRUE
Definition: RtypesCore.h:91
RooFit::Bins
RooCmdArg Bins(Int_t nbin)
Definition: RooGlobalFunc.cxx:177
RooIntegralMorph.h
RooGaussian.h
RooFit::ShiftToZero
RooCmdArg ShiftToZero()
Definition: RooGlobalFunc.cxx:51
x
Double_t x[n]
Definition: legend1.C:17
RooGaussian
Plain Gaussian p.d.f.
Definition: RooGaussian.h:24
TAttLine::SetLineColor
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition: TAttLine.h:40
TCanvas.h
RooFit::YVar
RooCmdArg YVar(const RooAbsRealLValue &var, const RooCmdArg &arg=RooCmdArg::none())
Definition: RooGlobalFunc.cxx:246
RooFit::Binning
RooCmdArg Binning(const RooAbsBinning &binning)
Definition: RooGlobalFunc.cxx:83
TH1::GetZaxis
TAxis * GetZaxis()
Definition: TH1.h:322
RooDataSet.h
RooNLLVar.h
RooPolynomial.h
RooPlot::frame
static RooPlot * frame(const RooAbsRealLValue &var, Double_t xmin, Double_t xmax, Int_t nBins)
Create a new frame for a given variable in x.
Definition: RooPlot.cxx:249
RooFit
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Definition: RooCFunction1Binding.h:29
RooPolynomial
RooPolynomial implements a polynomial p.d.f of the form.
Definition: RooPolynomial.h:28
RooAbsData::plotOn
virtual RooPlot * plotOn(RooPlot *frame, const RooCmdArg &arg1=RooCmdArg::none(), const RooCmdArg &arg2=RooCmdArg::none(), const RooCmdArg &arg3=RooCmdArg::none(), const RooCmdArg &arg4=RooCmdArg::none(), const RooCmdArg &arg5=RooCmdArg::none(), const RooCmdArg &arg6=RooCmdArg::none(), const RooCmdArg &arg7=RooCmdArg::none(), const RooCmdArg &arg8=RooCmdArg::none()) const
Definition: RooAbsData.cxx:547
RooFit::Verbose
RooCmdArg Verbose(Bool_t flag=kTRUE)
Definition: RooGlobalFunc.cxx:189
kFALSE
const Bool_t kFALSE
Definition: RtypesCore.h:92
RooNLLVar
Class RooNLLVar implements a -log(likelihood) calculation from a dataset and a PDF.
Definition: RooNLLVar.h:30
RooPlot.h
RooPlot::GetYaxis
TAxis * GetYaxis() const
Definition: RooPlot.cxx:1258
RooPlot
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:44
RooRealVar.h
kRed
@ kRed
Definition: Rtypes.h:66
RooConstVar.h
RooAbsReal::plotOn
virtual RooPlot * plotOn(RooPlot *frame, const RooCmdArg &arg1=RooCmdArg(), const RooCmdArg &arg2=RooCmdArg(), const RooCmdArg &arg3=RooCmdArg(), const RooCmdArg &arg4=RooCmdArg(), const RooCmdArg &arg5=RooCmdArg(), const RooCmdArg &arg6=RooCmdArg(), const RooCmdArg &arg7=RooCmdArg(), const RooCmdArg &arg8=RooCmdArg(), const RooCmdArg &arg9=RooCmdArg(), const RooCmdArg &arg10=RooCmdArg()) const
Plot (project) PDF on specified frame.
Definition: RooAbsReal.cxx:1730
RooFit::LineColor
RooCmdArg LineColor(Color_t color)
Definition: RooGlobalFunc.cxx:57
TCanvas
The Canvas class.
Definition: TCanvas.h:23
TAxis.h
TH1
TH1 is the base class of all histogramm classes in ROOT.
Definition: TH1.h:58
RooFit::Range
RooCmdArg Range(const char *rangeName, Bool_t adjustNorm=kTRUE)
Definition: RooGlobalFunc.cxx:53
kBlue
@ kBlue
Definition: Rtypes.h:66
gPad
#define gPad
Definition: TVirtualPad.h:287
RooDataSet
RooDataSet is a container class to hold unbinned data.
Definition: RooDataSet.h:33
TAttAxis::SetTitleOffset
virtual void SetTitleOffset(Float_t offset=1)
Set distance between the axis and the axis title.
Definition: TAttAxis.cxx:293
RooRealVar
RooRealVar represents a variable that can be changed from the outside.
Definition: RooRealVar.h:37
TH1.h
RooArgSet
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgSet.h:29
RooIntegralMorph
Class RooIntegralMorph is an implementation of the histogram interpolation technique described by Ale...
Definition: RooIntegralMorph.h:26
TH1::Draw
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition: TH1.cxx:3050
RooFit::RooConst
RooConstVar & RooConst(Double_t val)
Definition: RooGlobalFunc.cxx:347