binned_extended_logLL_fit.inl

This example show how to perform an binned extended likelihood fit. The model has three components, two Gaussians and one Exponential, \( model(x) = N_1*Gaussian_1(x) + N_2*Gaussian_2(x) + N_3*Exponential()\) The example first generating a dataset sampling the model in parallel and then fit the parameters and yields.

/*----------------------------------------------------------------------------
 *
 *   Copyright (C) 2016 - 2023 Antonio Augusto Alves Junior
 *
 *   This file is part of Hydra Data Analysis Framework.
 *
 *   Hydra is free software: you can redistribute it and/or modify
 *   it under the terms of the GNU General Public License as published by
 *   the Free Software Foundation, either version 3 of the License, or
 *   (at your option) any later version.
 *
 *   Hydra is distributed in the hope that it will be useful,
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *   GNU General Public License for more details.
 *
 *   You should have received a copy of the GNU General Public License
 *   along with Hydra.  If not, see <http://www.gnu.org/licenses/>.
 *
 *---------------------------------------------------------------------------*/

/*
 * binned_extended_logLL_fit.inl
 *
 *  Created on: 10/12/2017
 *      Author: Antonio Augusto Alves Junior
 */

#ifndef BINNED_EXTENDED_LOGLL_FIT_INL_
#define BINNED_EXTENDED_LOGLL_FIT_INL_

/**
 * \example binned_extended_logLL_fit.inl
 *
 * This example show how to perform an binned extended likelihood
 * fit. The model has three components, two Gaussians and one Exponential,
 * \f$ model(x) = N_1*Gaussian_1(x) + N_2*Gaussian_2(x) + N_3*Exponential()\f$
 * The example first generating a dataset sampling the model in parallel and
 * then fit the parameters and yields.
 */

#include <iostream>
#include <assert.h>
#include <time.h>
#include <chrono>
#include <random>
#include <algorithm>

//command line
#include <tclap/CmdLine.h>

//this lib
#include <hydra/device/System.h>
#include <hydra/Function.h>
#include <hydra/Lambda.h>
#include <hydra/Random.h>
#include <hydra/LogLikelihoodFCN.h>
#include <hydra/Parameter.h>
#include <hydra/UserParameters.h>
#include <hydra/Pdf.h>
#include <hydra/AddPdf.h>
#include <hydra/DenseHistogram.h>
#include <hydra/functions/Gaussian.h>
#include <hydra/functions/Exponential.h>
#include <hydra/RandomFill.h>

//Minuit2
#include "Minuit2/FunctionMinimum.h"
#include "Minuit2/MnUserParameterState.h"
#include "Minuit2/MnPrint.h"
#include "Minuit2/MnMigrad.h"
#include "Minuit2/MnMinimize.h"

/*-------------------------------------
 * Include classes from ROOT to fill
 * and draw histograms and plots.
 *-------------------------------------
 */
#ifdef _ROOT_AVAILABLE_

#include <TROOT.h>
#include <TH1D.h>
#include <TApplication.h>
#include <TCanvas.h>

#endif //_ROOT_AVAILABLE_


using namespace ROOT::Minuit2;
using namespace hydra::arguments;


declarg(_X, double)


int main(int argv, char** argc)
{
    size_t nentries = 0;

    try {

        TCLAP::CmdLine cmd("Command line arguments for ", '=');

        TCLAP::ValueArg<size_t> EArg("n", "number-of-events","Number of events", true, 10e6, "size_t");
        cmd.add(EArg);

        // Parse the argv array.
        cmd.parse(argv, argc);

        // Get the value parsed by each arg.
        nentries = EArg.getValue();

    }
    catch (TCLAP::ArgException &e)  {
        std::cerr << "error: " << e.error() << " for arg " << e.argId()
                                                        << std::endl;
    }

    //-----------------
    // some definitions
    double min   =  0.0;
    double max   =  10.0;

    //===========================
    //fit model
    hydra::Parameter  mean1_p  = hydra::Parameter::Create().Name("Mean_1").Value( 2.5) .Error(0.0001).Limits(0.0, 10.0);
    hydra::Parameter  sigma1_p = hydra::Parameter::Create().Name("Sigma_1").Value(0.5).Error(0.0001).Limits(0.01, 1.5);

    //gaussian function evaluating on the first argument
    auto Gauss1_PDF = hydra::make_pdf( hydra::Gaussian<_X>(mean1_p, sigma1_p),
            hydra::AnalyticalIntegral<hydra::Gaussian<_X>>(min, max));

    //-------------------------------------------

    //gaussian 2
    hydra::Parameter  mean2_p  = hydra::Parameter::Create().Name("Mean_2").Value(5.0) .Error(0.0001).Limits(0.0, 10.0);
    hydra::Parameter  sigma2_p = hydra::Parameter::Create().Name("Sigma_2").Value(0.5).Error(0.0001).Limits(0.01, 1.5);

    //gaussian function evaluating on the first argument
    auto Gauss2_PDF = hydra::make_pdf(hydra::Gaussian<_X>(mean2_p, sigma2_p),
            hydra::AnalyticalIntegral<hydra::Gaussian<_X>>(min, max));

    //--------------------------------------------

    //exponential
    //parameters
    hydra::Parameter  tau_p  = hydra::Parameter::Create().Name("Tau").Value(1.0).Error(0.0001).Limits(-2.0, 2.0);

    //gaussian function evaluating on the first argument
    auto Exp_PDF = hydra::make_pdf( hydra::Exponential<_X>(tau_p),
            hydra::AnalyticalIntegral<hydra::Exponential<_X>>(min, max));


    //------------------
    //yields
    hydra::Parameter N_Gauss_1_p("N_Gauss1" ,nentries, sqrt(nentries), nentries-nentries/2 , nentries+nentries/2) ;
    hydra::Parameter N_Gauss_2_p("N_Gauss2" ,nentries, sqrt(nentries), nentries-nentries/2 , nentries+nentries/2) ;
    hydra::Parameter     N_Exp_p("N_Exp" ,nentries, sqrt(nentries), nentries-nentries/2 , nentries+nentries/2) ;


    //make model
    auto model = hydra::add_pdfs( {N_Gauss_1_p, N_Gauss_2_p, N_Exp_p }, Gauss1_PDF, Gauss2_PDF, Exp_PDF);
    model.SetExtended(1);

    //===========================

#ifdef _ROOT_AVAILABLE_

    TH1D hist_gaussian_d("gaussian_d", "Gaussian",    100, min, max);
    TH1D hist_fitted_gaussian_d("fitted_gaussian_d", "Gaussian",    100, min, max);

#endif //_ROOT_AVAILABLE_

    //begin scope
    {

        //1D device buffer
        hydra::device::vector<double>  data_d(3*nentries);

        //-------------------------------------------------------
        // Generate data

        // gaussian1
        hydra::fill_random(data_d.begin(), data_d.begin() + nentries,
                hydra::Gaussian<_X>(mean1_p, sigma1_p) );

        // gaussian2
        hydra::fill_random(data_d.begin()+ nentries, data_d.begin() + 2*nentries,
                        hydra::Gaussian<_X>(mean2_p, sigma2_p) );


        // exponential
        hydra::fill_random(data_d.begin()+ 2*nentries, data_d.end(),
                            hydra::Exponential<_X>(tau_p) );


        std::cout<< std::endl<< "Generated data:"<< std::endl;
        for(size_t i=0; i<10; i++)
            std::cout << "[" << i << "] :" << data_d[i] << std::endl;

        hydra::DenseHistogram<double,1,  hydra::device::sys_t> Hist_Data(100, min, max);
        Hist_Data.Fill( data_d.begin(), data_d.end() );

        //make model and fcn
        auto fcn   = hydra::make_loglikehood_fcn( model, Hist_Data);

        //-------------------------------------------------------
        //fit
        ROOT::Minuit2::MnPrint::SetGlobalLevel(-1);
        hydra::Print::SetLevel(hydra::WARNING);
        //minimization strategy
        MnStrategy strategy(2);

        // create Migrad minimizer
        MnMigrad migrad_d(fcn, fcn.GetParameters().GetMnState() ,  strategy);

        std::cout<<fcn.GetParameters().GetMnState()<<std::endl;

        // ... Minimize and profile the time

        auto start_d = std::chrono::high_resolution_clock::now();
        FunctionMinimum minimum_d =  FunctionMinimum(migrad_d(std::numeric_limits<unsigned int>::max(), 1));
        auto end_d = std::chrono::high_resolution_clock::now();
        std::chrono::duration<double, std::milli> elapsed_d = end_d - start_d;

        // output
        std::cout<<"Minimum: "<< minimum_d << std::endl;

        //time
        std::cout << "-----------------------------------------"<<std::endl;
        std::cout << "| [Fit] GPU Time (ms) ="<< elapsed_d.count() <<std::endl;
        std::cout << "-----------------------------------------"<<std::endl;


#ifdef _ROOT_AVAILABLE_

        for(size_t i=0;  i<100; i++)
            hist_gaussian_d.SetBinContent(i+1, Hist_Data.GetBinContent(i));


        //draw fitted function
        hist_fitted_gaussian_d.Sumw2();
        for (size_t i=0 ; i<=100 ; i++) {
            double x = hist_fitted_gaussian_d.GetBinCenter(i);
            hist_fitted_gaussian_d.SetBinContent(i, fcn.GetPDF()(x) );
        }
        hist_fitted_gaussian_d.Scale(hist_gaussian_d.Integral()/hist_fitted_gaussian_d.Integral() );

#endif //_ROOT_AVAILABLE_

    }//end scope

#ifdef _ROOT_AVAILABLE_

    TApplication *myapp=new TApplication("myapp",0,0);

    //draw histograms
    TCanvas canvas_d("canvas_d" ,"Distributions - Device", 500, 500);
    hist_gaussian_d.Draw("hist");
    hist_fitted_gaussian_d.Draw("histsameC");
    hist_fitted_gaussian_d.SetLineColor(2);

    myapp->Run();

#endif //_ROOT_AVAILABLE_

    return 0;


}


#endif /* BINNED_EXTENDED_LOGLL_FIT_INL_ */