cfitdescription and tutorial

Jordi Garra Ticó

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git clone http://git.cern.ch/pub/tutcfit

Preliminary work

● Checkout the tutorial git repository

● Run the installation script

sh bin/installpkg.sh

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introduction

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Introduction

● In minuit, a fit is accomplished as the minimization of a function.

● Examples:● 2

●

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2 fit

● Example: linear regression:

DIY

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2 fit

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fit

● Example: Gaussian

DIY

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fit

It is fundamental that the pdf is normalized.

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Yield problem

● Try to fit the yield of this pdf:

DIY

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Yield problem

Well, we did not build the likelihood as a product of normalized pdfs.

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Yield problem● To solve this problem, the likelihood must

contain the pdf of the number of events, which is assumed to be Poisson distributed.

● Defining Expression of pdfspdf

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Yield problem

● Again, try to fit the yield of this pdf:

DIY

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Yield problem

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compilation

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compilation of c++ code

● c++ code contains:● header files (.hh,.h,.hpp)

– They declare functions and objects.

● source files (.cc,.cpp)– They implement the functions and the objects behavior.

● A program may be implemented in one or more source files.

● A typical standalone compilation command is

g++ ­std=c++0x ­o program main.cc

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compilation of c++ code

● Compilation has 2 steps:● Compilation

– Produces object files (.o) from source files.

– It requires all the headers each source file depends on.● Including external packages.

– Header paths are specified after the ­I argument.

– Compiler is invoked with ­c option.

g++ ­std=c++0x ­c ­o main.o main.cc ­I include

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compilation of c++ code

● Compilation has 2 steps:● Linking

– Produces executables from object files.– It requires all the libraries each source file depends on.– Libraries (.so, .a) are also the result of a linking step, and

they do not require other libraries.– Library paths are specified with ­L, and each library that

the executable depends on is specified with ­l.

g++ ­std=c++0x ­o prog main.o ­L path ­lcfit

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compilation of c++ code

● EXERCISE● The cfit tutorial repository contains a compile directory.● The sha.cc file uses the openssl package.

● You can use the pkg­config command to figure out which libraries and headers must be specified.

● The hist.cc file uses root's TH1D and TCanvas.

● You can use the root­config to figure out which libraries and headers must be specified.

DIY

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compilation of c++ code

● It is not necessary to specify header or library paths in certain conditions. The compiler automatically looks for● headers in:

– /usr/include, /usr/local/include, and others.

– All paths in CPLUS_INCLUDE_PATH.

● libraries in:– /usr/lib, /usr/lib64, /lib, and others.

– All paths in LIBRARY_PATH.

● This saves us from typing ­I or ­L paths, but not ­l library lists.

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compilation of c++ code

● The cfit tutorial repository contains a script that sets up the CPLUS_INCLUDE_PATH, LIBRARY_PATH and LD_LIBRARY_PATH.

source bin/libs

● Very useful in our case:● Use libraries that are not installed in the

system.

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compilation of c++ code

● Sourcing the bin/libs script does several things:● Reads the cfg/versions file to figure out which

package versions to use.– Very useful to keep track of all the versions used, just by

having the cfg/versions file under version control (git).

● Runs LbLogin if needed.

● Runs SetupProject for the required project (libs sets up the root project).

● Sets up the CPLUS_INCLUDE_PATH, LIBRARY_PATH and LD_LIBRARY_PATH variables.

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compilation of c++ code

● If you install the proposed libraries in the default directory, you can do either of these 2 options:● Option A:

– Add the following line to your ~/.bashrc

– Run source bin/libs every time you want to work on a project that uses these packages.

● Option B:– Add to your ~/.bashrc the lines advised after the

execution of the bin/installpkg.sh script.

– Manually keep track of the package versions you use.

export pkgdir=${HOME}/pkg DIY

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cfit

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Description

● A simple and easy-to-use object-oriented c++ library to fit complex pdfs to datasets.

● Interface to Minuit. It produces a Minuit object of class FCNBase.

● Code clarity is a priority.● Implements MPI parallelization of the evaluation

of the minimizer (2 or NLL)

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What cfit is not

● A graphics library.● A configuration file reader.● An interface to root objects.● However:

● There are tools available to do these tasks (atools).

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Library classes

PdfModel

Gauss

Argus

CrystalBall

......

PdfExpr

Variable Parameter

FCNBase

Chi2

Nll

MinimizerExpr

Dataset

ParameterExpr

Fit recipe:● Fill a dataset● Define the variables (dataset columns to be used)● Define the parameters● Define the pdf (either as a model or expression)● Feed the dataset and pdf to the minimizer● Minimize

Minimizer

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Library classes

● PdfModel represents normalized pdf models.

● PdfExpr represents an expression of models, and may not be normalized.

● Inconsistent expressions are forbidden.● Multiplying 2 pdfs that depend on the same

variables.● Adding or subtracting 2 pdfs that don't depend on

the same variables.● Dividing 2 pdfs.● ......

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Dataset data;

std::ifstream input( “data.dat” );while ( input >> value1 >> value2 ){  data.push( “x”, value1 ); // Optional error  data.push( “y”, value2 );}input.close();

Variable x( “x” );Variable y( “y” );

Parameter area ( “area” , 2.0e5, 300.0 );Parameter mu   ( “mu”   , 1.0  ,   0.1 );Parameter sigma( “sigma”, 2.0  ,   0.1 );

Gauss gaussian( x, mu, sigma );

Chi2 chi2( area * gaussian, y, data );

const FunctionMinimum& min = chi2.minimize();

Fill a dataset

Define the variables

Define the parameters

Define the pdf

Feed the pdf and dataset to minimizer

Minimize

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Variable x( “x” );Variable y( “y” );

Parameter area  ( “area”  ,  2.0e5, 300.0   );Parameter mu    ( “mu”    ,  1.0  ,   0.003 );Parameter sigma ( “sigma” ,  2.0  ,   0.003 );

Gauss g ( x, mu , sigma  );

Chi2 chi2( area * g, y, data );

const FunctionMinimum& min = chi2.minimize();

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Variable x( “x” );Variable y( “y” );

Parameter area1 ( "area1" ,  1.0e5, 300.0   );Parameter area2 ( "area2" ,  1.0e5, 300.0   );Parameter mu1   ( "mu1"   , ­1.0  ,   0.003 );Parameter mu2   ( "mu2"   ,  2.0  ,   0.003 );Parameter sigma1( "sigma1",  2.0  ,   0.003 );Parameter sigma2( "sigma2",  1.0  ,   0.003 );

Gauss g1( x, mu1, sigma1 );Gauss g2( x, mu2, sigma2 );

PdfExpr total = area1 * g1 + area2 * g2;

Chi2 chi2( total, y, data );

const FunctionMinimum& min = chi2.minimize();

Expressions of pdfs simplify the clarity of the code

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Variable x( “x” );Variable y( “y” );

Parameter area  ( "area"  ,  2.0e5, 300.0   );Parameter phi   ( "phi"   ,  0.5  ,   0.1   );Parameter mu1   ( "mu1"   , ­1.0  ,   0.003 );Parameter mu2   ( "mu2"   ,  2.0  ,   0.003 );Parameter sigma1( "sigma1",  2.0  ,   0.003 );Parameter sigma2( "sigma2",  1.0  ,   0.003 );

Gauss g1( x, mu1, sigma1 );Gauss g2( x, mu2, sigma2 );

PdfExpr total = area  * ( pow( sin( phi ), 2 ) * g1 +                          pow( cos( phi ), 2 ) * g2 );

Chi2 chi2( total, y, data );

const FunctionMinimum& min = chi2.minimize();

Just writenormally

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Simple example

● The cfit tutorial repository contains a gauss directory● It generates 10000 normal events and fits a

Gaussian to them● What would be the command to compile it?● Run the source bin/libs command and

examine the variables CPLUS_INCLUDE_PATH, LIBRARY_PATH and LD_LIBRARY_PATH.

● Adapt it to use a sum of 2 Gaussians as pdf, where one of the 2 Gaussians has twice as much yield as the other. DIY

DIY

DIY

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Working with amplitudes

● is the phase of the Vub

element of the CKM matrix.

● In B DK decays, the D meson is not a flavor eigenstate, but a combination of both.

Important LHCb example:

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Dealing with amplitudes

Time-dependent amplitude (used in D mixing)

Amplitude for mixture state from B+ D K+

Defining

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Dealing with amplitudes

Coef

CoefExpr

DecayModel

Decay3Body

DecayMixing3Body

......

PdfExprPdfModel

Resonance Amplitude

RelBreitWigner

GounarisSakurai

gLASS

......

PhaseSpace

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Dealing with amplitudes

● The same amplitude can be useful for several decay models.● Amplitude in Decay3Body produces a squared

amplitude (useful for analysis).

● Amplitude in DecayMixing3Body produces a lifetime dependent pdf (shown a few slides above).

● These decay models are pdf models and, therefore, are normalized.

● The limits of the decay model pdf are determined by PhaseSpace objects.

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Parameter mKst( "mKst", 0.8937010, 0.1 ); // MassesParameter mRho( "mRho", 0.7758000, 0.1 ); //Parameter wKst( "wKst", 0.0467401, 0.1 ); // WidthsParameter wRho( "wRho", 0.1464000, 0.1 ); //Parameter rBW ( "rBW" , 1.5      , 0.5 ); // Blatt­Weisskopf radius.

Parameter reCoefKstm( "reCoefKstm", ­1.196090, 0.005755 );Parameter reCoefRho ( "reCoefRho" ,  1.0     , 0.1      );Parameter imCoefKstm( "imCoefKstm",  1.256890, 0.006278 );Parameter imCoefRho ( "imCoefRho" ,  0.0     , 0.1      );

Coef coefKstm( reCoefKstm, imCoefKstm );Coef coefRho ( reCoefRho , imCoefRho  );

RelBreitWigner  propKstm( 1, 3, mKst, wKst, rBW, 1 );GounarisSakurai propRho ( 2, 3, mRho, wRho, rBW, 1 );

Amplitude amp;

amp += coefKstm * propKstm;amp += coefRho  * propRho;

PhaseSpace ps( mD0, mKs, mPi, mPi );

Decay3Body decayModel( mSq12, mSq13, mSq23, amp, ps );

Resonance parameters

Resonance coefficients

Propagators

Amplitude(propagator expression)

Resonant pair Angular momentum

Pdf model

Pdf limits

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Dealing with amplitudes● In the tutorial, you will be able to fit the resonance

coefficients and produce these plots.

● Compile and run the project in the model directory.

DIY

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Simultaneous fits

● What is a simultaneous fit?● What exactly is simultaneous in a simultaneous fit?

DIY

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Simultaneous fits

● What is a simultaneous fit?● What exactly is simultaneous in a simultaneous fit?

● Consider:● Several different data sets (e.g. different decays).● Several pdfs to describe these datasets, but with

some common parameters.

● What we need to minimize is the sum of all the minimizers involved (either 2 or ).

DIY

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Simultaneous fits● Recall the design of the minimizers.

FCNBase

Chi2

Nll

MinimizerExprMinimizer

MinimizerExpr minimizer = nll1 + nll2;minimizer += nll3;min = minimizer.minimize();

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Model design

● Constructor must push(...) all variables and parameters.● It makes cfit aware of them.

● Mandatory definition of

● For pdfs of 1 variable, good practice to define

const double evaluate( const std::vector< double >& pars ) const throw( PdfException )

const double evaluate( const double& pars ) const throw( PdfException )

NewModel* copy() const { return new NewModel( *this ); }

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Model design

● Voluntary functionsconst double evaluate( const std::vector< double >&                 pars  ,                       const std::vector< double >&                 cacheR,                       const std::vector< std::complex< double > >& cacheC )                                        const throw( PdfException )

void cache()

const std::map< std::string, double > generate() const throw( PdfException )

const double area( const double& min, const double& max ) const throw( PdfException )

● The cfit tutorial repository contains a newmodel directory that implements a simple new model.● Check the implementation and try to design a new

model for a pdf of your choice. DIY