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rf903_numintcache.C File Reference
RooFit Tutorials

Detailed Description

'NUMERIC ALGORITHM TUNING' RooFit tutorial macro #903

Caching of slow numeric integrals and parameterization of slow numeric integrals

pict1_rf903_numintcache.C.png
Processing /builddir/build/BUILD/root-6.10.00/tutorials/roofit/rf903_numintcache.C...
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:ObjectHandling -- RooWorkspace::exportToCint(w) INFO: references to all objects in this workspace will be created in CINT in 'namespace w'
[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y,z]) using numeric integrator RooAdaptiveIntegratorND to calculate Int(x,y,z)
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
[#0] WARNING:Minization -- RooMinimizerFcn::synchronize: WARNING: no initial error estimate available for a: using 1
**********
** 1 **SET PRINT 1
**********
**********
** 2 **SET NOGRAD
**********
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 a 0.00000e+00 1.00000e+00 -5.00000e+00 5.00000e+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 = 1659.930708 START MIGRAD MINIMIZATION. STRATEGY 1. CONVERGENCE WHEN EDM .LT. 1.00e-03
a=0.02003, [#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y,z]) using numeric integrator RooAdaptiveIntegratorND to calculate Int(x,y,z)
prevFCN = 1668.090831 a=-0.02003,
prevFCN = 1666.341378 a=0.002003,
prevFCN = 1660.094465 a=-0.002003,
prevFCN = 1659.913535 FCN=1659.93 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 a 0.00000e+00 1.00000e+00 2.01358e-01 2.25805e+02
ERR DEF= 0.5
a=-0.001236,
prevFCN = 1659.902781 a=-0.001036,
prevFCN = 1659.903514 a=-0.001437,
prevFCN = 1659.903515 a=-0.001089,
prevFCN = 1659.903177 a=-0.001383,
prevFCN = 1659.903178 MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
a=-0.001236,
prevFCN = 1659.902781 a=-0.001089,
prevFCN = 1659.903177 a=-0.001383,
prevFCN = 1659.903178 a=-0.001207,
prevFCN = 1659.902797 a=-0.001266,
prevFCN = 1659.902797 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=1659.9 FROM MIGRAD STATUS=CONVERGED 14 CALLS 15 TOTAL
EDM=2.26681e-10 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 a -1.23627e-03 5.23021e-03 2.94345e-05 -1.43932e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 1 ERR DEF=0.5
2.736e-05
[#1] INFO:Minization -- Command timer: Real time 0:00:16, CP time 16.670
[#1] INFO:Minization -- Session timer: Real time 0:00:16, CP time 16.670
a=-0.001236, **********
** 7 **SET ERR 0.5
**********
**********
** 8 **SET PRINT 1
**********
**********
** 9 **HESSE 500
**********
prevFCN = 1659.902781 a=-0.001207,
prevFCN = 1659.902797 a=-0.001266,
prevFCN = 1659.902797 a=-0.00123,
prevFCN = 1659.902782 a=-0.001242,
prevFCN = 1659.902782 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=1659.9 FROM HESSE STATUS=OK 5 CALLS 20 TOTAL
EDM=2.26436e-10 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 a -1.23627e-03 5.23023e-03 5.88690e-06 -2.47254e-04
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 1 ERR DEF=0.5
2.736e-05
[#1] INFO:Minization -- Command timer: Real time 0:00:05, CP time 5.930
[#1] INFO:Minization -- Session timer: Real time 0:00:22, CP time 22.600, 2 slices
a=-0.001236, [#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
[#0] WARNING:NumericIntegration -- RooAdaptiveIntegratorND::dtor(model) WARNING: Number of suppressed warningings about integral evaluations where target precision was not reached is 20
[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on x integrates over variables (y,z)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[y,z]_Norm[x,y,z]) using numeric integrator RooAdaptiveIntegratorND to calculate Int(y,z)
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooDataHist.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "RooWorkspace.h"
#include "RooExpensiveObjectCache.h"
#include "TFile.h"
#include "TH1.h"
using namespace RooFit;
RooWorkspace* getWorkspace(Int_t mode) ;
void rf903_numintcache(Int_t mode=0)
{
// Mode = 0 : Run plain fit (slow)
// Mode = 1 : Generate workspace with pre-calculated integral and store it on file (prepare for accelerated running)
// Mode = 2 : Run fit from previously stored workspace including cached integrals (fast, requires run in mode=1 first)
// C r e a t e , s a v e o r l o a d w o r k s p a c e w i t h p . d . f .
// -----------------------------------------------------------------------------------
// Make/load workspace, exit here in mode 1
RooWorkspace* w1 = getWorkspace(mode) ;
if (mode==1) {
// Show workspace that was created
w1->Print() ;
// Show plot of cached integral values
RooDataHist* hhcache = (RooDataHist*) w1->expensiveObjectCache().getObj(1) ;
if (hhcache) {
new TCanvas("rf903_numintcache","rf903_numintcache",600,600) ;
hhcache->createHistogram("a")->Draw() ;
}
else {
Error("rf903_numintcache","Cached histogram is not existing in workspace");
}
return ;
}
// U s e p . d . f . f r o m w o r k s p a c e f o r g e n e r a t i o n a n d f i t t i n g
// -----------------------------------------------------------------------------------
// This is always slow (need to find maximum function value empirically in 3D space)
RooDataSet* d = w1->pdf("model")->generate(RooArgSet(*w1->var("x"),*w1->var("y"),*w1->var("z")),1000) ;
// This is slow in mode 0, but fast in mode 1
w1->pdf("model")->fitTo(*d,Verbose(kTRUE),Timer(kTRUE)) ;
// Projection on x (always slow as 2D integral over Y,Z at fitted value of a is not cached)
RooPlot* framex = w1->var("x")->frame(Title("Projection of 3D model on X")) ;
d->plotOn(framex) ;
w1->pdf("model")->plotOn(framex) ;
// Draw x projection on canvas
new TCanvas("rf903_numintcache","rf903_numintcache",600,600) ;
framex->Draw() ;
// Make workspace available on command line after macro finishes
gDirectory->Add(w1) ;
return ;
}
RooWorkspace* getWorkspace(Int_t mode)
{
// C r e a t e , s a v e o r l o a d w o r k s p a c e w i t h p . d . f .
// -----------------------------------------------------------------------------------
//
// Mode = 0 : Create workspace for plain running (no integral caching)
// Mode = 1 : Generate workspace with pre-calculated integral and store it on file
// Mode = 2 : Load previously stored workspace from file
RooWorkspace* w(0) ;
if (mode!=2) {
// Create empty workspace workspace
w = new RooWorkspace("w",1) ;
// Make a difficult to normalize p.d.f. in 3 dimensions that is integrated numerically.
w->factory("EXPR::model('1/((x-a)*(x-a)+0.01)+1/((y-a)*(y-a)+0.01)+1/((z-a)*(z-a)+0.01)',x[-1,1],y[-1,1],z[-1,1],a[-5,5])") ;
}
if (mode==1) {
// Instruct model to pre-calculate normalization integral that integrate at least
// two dimensions numerically. In this specific case the integral value for
// all values of parameter 'a' are stored in a histogram and available for use
// in subsequent fitting and plotting operations (interpolation is applied)
// w->pdf("model")->setNormValueCaching(3) ;
w->pdf("model")->setStringAttribute("CACHEPARMINT","x:y:z");
// Evaluate p.d.f. once to trigger filling of cache
RooArgSet normSet(*w->var("x"),*w->var("y"),*w->var("z")) ;
w->pdf("model")->getVal(&normSet) ;
w->writeToFile("rf903_numintcache.root") ;
}
if (mode==2) {
// Load preexisting workspace from file in mode==2
TFile* f = new TFile("rf903_numintcache.root") ;
w = (RooWorkspace*) f->Get("w") ;
}
// Return created or loaded workspace
return w ;
}
Author
07/2008 - Wouter Verkerke

Definition in file rf903_numintcache.C.