ParallelTest.cxx

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// @(#)root/minuit2:$Id$
// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei   2003-2005

/**********************************************************************
 *                                                                    *
 * Copyright (c) 2005 LCG ROOT Math team,  CERN/PH-SFT                *
 *                                                                    *
 **********************************************************************/


#include "GaussRandomGen.h"
#include "Minuit2/FunctionMinimum.h"
#include "Minuit2/MnUserParameterState.h"
#include "Minuit2/MnPrint.h"
#include "Minuit2/MnMigrad.h"
#include "Minuit2/MnMinos.h"
#include "Minuit2/MnPlot.h"
#include "Minuit2/MinosError.h"
#include "Minuit2/FCNBase.h"
#include <cmath>
#include <iostream>

// example of a multi dimensional fit where parallelization can be used
// to speed up the result
// define the environment variable OMP_NUM_THREADS to the number of desired threads
// By default it will have thenumber of core of the machine
// The default number of dimension is 20 (fit in 40 parameters) on 1000 data events.
// One can change the dimension and the number of events by doing:
// ./test_Minuit2_Parallel    ndim  nevents

using namespace ROOT::Minuit2;

const int default_ndim = 20;
const int default_ndata = 1000;


double GaussPdf(double x, double x0, double sigma) {
   double tmp = (x-x0)/sigma;
   return (1.0/(std::sqrt(2 * M_PI) * std::fabs(sigma))) * std::exp(-tmp*tmp/2);
}

double LogMultiGaussPdf(const std::vector<double> & x, const std::vector<double> & p) {
   double f = 0;
   int ndim = x.size();
   for (int k = 0; k < ndim; ++k) {
      double y =  GaussPdf( x[k], p[ 2*k], p[2*k + 1] );
      //std::cout << " k " << k << "  " << y << "  " << p[2*k] << "  " << p[2*k+1] << std::endl;
      y = std::max(y, 1.E-300);
      double lgaus = std::log( y );
      f += lgaus;
   }
   return f;
}

typedef std::vector< std::vector< double> > Data;

struct LogLikeFCN  : public FCNBase {

   LogLikeFCN( const Data & data) : fData(data) {}

   double operator() (const std::vector<double> & p ) const {
      double logl = 0;
      int ndata = fData.size();
      for (int i = 0; i < ndata; ++i) {
         logl -= LogMultiGaussPdf(fData[i], p);
      }
      return logl;
   }
   double Up() const { return 0.5; }
   const Data & fData;
};

int doFit(int ndim, int ndata) {

  // generate the data (1000 data points) in 100 dimension

  Data data(ndata);
  std::vector< double> event(ndim);

  std::vector<double> mean(ndim);
  std::vector<double> sigma(ndim);
  for (int k = 0; k < ndim; ++k) {
     mean[k] = -double(ndim)/2 + k;
     sigma[k] = 1. + 0.1*k;
  }

  // generate the data
  for (int i = 0; i < ndata; ++i) {
     for (int k = 0; k < ndim;++k) {
        GaussRandomGen rgaus(mean[k],sigma[k] );
        event[k] = rgaus();
     }
    data[i] = event;
  }

  // create FCN function
  LogLikeFCN fcn(data);

  // create initial starting values for parameters
  std::vector<double> init_par(2*ndim);
  for (int k = 0; k < ndim; ++k) {
     init_par[2*k] = 0;
     init_par[2*k+1] = 1;
  }

  std::vector<double> init_err(2*ndim);
  for (int k = 0; k < 2*ndim; ++k) {
     init_err[k] = 0.1;
  }
  // create minimizer (default constructor)
  VariableMetricMinimizer fMinimizer;

  // Minimize
  FunctionMinimum min = fMinimizer.Minimize(fcn, init_par, init_err);

  // output
  std::cout<<"minimum: "<<min<<std::endl;


//     // create MINOS Error factory
//     MnMinos Minos(fFCN, min);

//     {
//       // 3-sigma MINOS errors (minimal interface)
//       fFCN.SetErrorDef(9.);
//       std::pair<double,double> e0 = Minos(0);
//       std::pair<double,double> e1 = Minos(1);
//       std::pair<double,double> e2 = Minos(2);


//       // output
//       std::cout<<"3-sigma Minos errors with limits: "<<std::endl;
//       std::cout.precision(16);
//       std::cout<<"par0: "<<min.UserState().Value("mean")<<" "<<e0.first<<" "<<e0.second<<std::endl;
//       std::cout<<"par1: "<<min.UserState().Value(1)<<" "<<e1.first<<" "<<e1.second<<std::endl;
//       std::cout<<"par2: "<<min.UserState().Value("area")<<" "<<e2.first<<" "<<e2.second<<std::endl;


//     }

//   }


  return 0;
}

int main(int argc, char **argv) {
   int ndim = default_ndim;
   int ndata = default_ndata;
   if (argc > 1) {
      ndim = atoi(argv[1] );
   }
   if (argc > 2) {
      ndata = atoi(argv[2] );
   }
   std::cout << "do fit of " << ndim << " dimensional data on " << ndata << " events " << std::endl;
   doFit(ndim,ndata);
}