RooMCIntegrator.cxx

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/*****************************************************************************
 * Project: RooFit                                                           *
 * Package: RooFitCore                                                       *
 * @(#)root/roofitcore:$Id$
 * Authors:                                                                  *
 *   WV, Wouter Verkerke, UC Santa Barbara, verkerke@slac.stanford.edu       *
 *   DK, David Kirkby,    UC Irvine,         dkirkby@uci.edu                 *
 *                                                                           *
 * Copyright (c) 2000-2005, Regents of the University of California          *
 *                          and Stanford University. All rights reserved.    *
 *                                                                           *
 * Redistribution and use in source and binary forms,                        *
 * with or without modification, are permitted according to the terms        *
 * listed in LICENSE (http://roofit.sourceforge.net/license.txt)             *
 *****************************************************************************/
 
/**
\file RooMCIntegrator.cxx
\class RooMCIntegrator
\ingroup Roofitcore
 
Implements an adaptive multi-dimensional Monte Carlo
numerical integration, following the VEGAS algorithm originally described
in G. P. Lepage, J. Comp. Phys. 27, 192(1978). This implementation is
based on a C version from the 0.9 beta release of the GNU scientific library.
**/
 
#include "Riostream.h"
 
#include "TMath.h"
#include "RooMCIntegrator.h"
#include "RooArgSet.h"
#include "RooNumber.h"
#include "RooNumIntFactory.h"
#include "RooRealVar.h"
#include "RooCategory.h"
#include "RooMsgService.h"
 
#include <cmath>
 
 
using std::endl;
 
 
// Register this class with RooNumIntFactory
 
 
////////////////////////////////////////////////////////////////////////////////
/// This function registers class RooMCIntegrator, its configuration options
/// and its capabilities with RooNumIntFactory
 
void RooMCIntegrator::registerIntegrator(RooNumIntFactory& fact)
{
  RooCategory samplingMode("samplingMode","Sampling Mode") ;
  samplingMode.defineType("Importance",RooMCIntegrator::Importance) ;
  samplingMode.defineType("ImportanceOnly",RooMCIntegrator::ImportanceOnly) ;
  samplingMode.defineType("Stratified",RooMCIntegrator::Stratified) ;
  samplingMode.setIndex(RooMCIntegrator::Importance) ;
 
  RooCategory genType("genType","Generator Type") ;
  genType.defineType("QuasiRandom",RooMCIntegrator::QuasiRandom) ;
  genType.defineType("PseudoRandom",RooMCIntegrator::PseudoRandom) ;
  genType.setIndex(RooMCIntegrator::QuasiRandom) ;
 
  RooCategory verbose("verbose","Verbose flag") ;
  verbose.defineType("true",1) ;
  verbose.defineType("false",0) ;
  verbose.setIndex(0) ;
 
  RooRealVar alpha("alpha","Grid structure constant",1.5) ;
  RooRealVar nRefineIter("nRefineIter","Number of refining iterations",5) ;
  RooRealVar nRefinePerDim("nRefinePerDim","Number of refining samples (per dimension)",1000) ;
  RooRealVar nIntPerDim("nIntPerDim","Number of integration samples (per dimension)",5000) ;
 
  // Create prototype integrator
  auto creator = [](const RooAbsFunc& function, const RooNumIntConfig& config) {
    return std::make_unique<RooMCIntegrator>(function,config);
  };
 
  // Register prototype and default config with factory
  std::string name = "RooMCIntegrator";
  fact.registerPlugin(name, creator, {samplingMode,genType,verbose,alpha,nRefineIter,nRefinePerDim,nIntPerDim},
                    /*canIntegrate1D=*/true,
                    /*canIntegrate2D=*/true,
                    /*canIntegrateND=*/true,
                    /*canIntegrateOpenEnded=*/false);
 
  // Make this method the default for all N>2-dim integrals
  RooNumIntConfig::defaultConfig().methodND().setLabel(name) ;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Construct an integrator over 'function' with given sampling mode
/// and generator type.  The sampling mode can be 'Importance'
/// (default), 'ImportanceOnly' and 'Stratified'. The generator type
/// can be 'QuasiRandom' (default) and 'PseudoRandom'. Consult the original
/// VEGAS documentation on details of the mode and type parameters.
 
RooMCIntegrator::RooMCIntegrator(const RooAbsFunc& function, SamplingMode mode,
             GeneratorType genType, bool verbose) :
  RooAbsIntegrator(function), _grid(function), _verbose(verbose),
  _alpha(1.5),  _mode(mode), _genType(genType),
  _nRefineIter(5),_nRefinePerDim(1000),_nIntegratePerDim(5000)
{
  // coverity[UNINIT_CTOR]
  if(!(_valid= _grid.isValid())) return;
  if(_verbose) _grid.print(std::cout);
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Construct an integrator over 'function' where the configuration details
/// are taken from 'config'
 
RooMCIntegrator::RooMCIntegrator(const RooAbsFunc& function, const RooNumIntConfig& config) :
  RooAbsIntegrator(function), _grid(function)
{
  const RooArgSet& configSet = config.getConfigSection("RooMCIntegrator") ;
  _verbose = (bool) configSet.getCatIndex("verbose",0) ;
  _alpha = configSet.getRealValue("alpha",1.5) ;
  _mode = (SamplingMode) configSet.getCatIndex("samplingMode",Importance) ;
  _genType = (GeneratorType) configSet.getCatIndex("genType",QuasiRandom) ;
  _nRefineIter = (Int_t) configSet.getRealValue("nRefineIter",5) ;
  _nRefinePerDim = (Int_t) configSet.getRealValue("nRefinePerDim",1000) ;
  _nIntegratePerDim = (Int_t) configSet.getRealValue("nIntPerDim",5000) ;
 
  // check that our grid initialized without errors
  if(!(_valid= _grid.isValid())) return;
  if(_verbose) _grid.print(std::cout);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Check if we can integrate over the current domain. If return value
/// is true we cannot handle the current limits (e.g. where the domain
/// of one or more observables is open ended.
 
bool RooMCIntegrator::checkLimits() const
{
  return _grid.initialize(*integrand());
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Evaluate the integral using a fixed number of calls to evaluate the integrand
/// equal to about 10k per dimension. Use the first 5k calls to refine the grid
/// over 5 iterations of 1k calls each, and the remaining 5k calls for a single
/// high statistics integration.
 
double RooMCIntegrator::integral(const double* /*yvec*/)
{
  _timer.Start(true);
  vegas(AllStages,_nRefinePerDim*_grid.getDimension(),_nRefineIter);
  double ret = vegas(ReuseGrid,_nIntegratePerDim*_grid.getDimension(),1);
  return ret ;
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Perform one step of Monte Carlo integration using the specified number of iterations
/// with (approximately) the specified number of integrand evaluation calls per iteration.
/// Use the VEGAS algorithm, starting from the specified stage. Returns the best estimate
/// of the integral. Also sets *absError to the estimated absolute error of the integral
/// estimate if absError is non-zero.
 
double RooMCIntegrator::vegas(Stage stage, UInt_t calls, UInt_t iterations, double *absError)
{
  //cout << "VEGAS stage = " << stage << " calls = " << calls << " iterations = " << iterations << endl ;
 
  // reset the grid to its initial state if we are starting from scratch
  if(stage == AllStages) _grid.initialize(*_function);
 
  // reset the results of previous calculations on this grid, but reuse the grid itself.
  if(stage <= ReuseGrid) {
    _wtd_int_sum = 0;
    _sum_wgts = 0;
    _chi_sum = 0;
    _it_num = 1;
    _samples = 0;
  }
 
  // refine the results of previous calculations on the current grid.
  if(stage <= RefineGrid) {
    UInt_t bins = RooGrid::maxBins;
    UInt_t boxes = 1;
    UInt_t dim(_grid.getDimension());
 
    // select the sampling mode for the next step
    if(_mode != ImportanceOnly) {
      // calculate the largest number of equal subdivisions ("boxes") along each
      // axis that results in an average of no more than 2 integrand calls per cell
      boxes = (UInt_t)floor(std::pow(calls/2.0,1.0/dim));
      // use stratified sampling if we are allowed enough calls (or equivalently,
      // if the dimension is low enough)
      _mode = Importance;
      if (2*boxes >= RooGrid::maxBins) {
   _mode = Stratified;
   // adjust the number of bins and boxes to give an integral number >= 1 of boxes per bin
   Int_t box_per_bin= (boxes > RooGrid::maxBins) ? boxes/RooGrid::maxBins : 1;
   bins= boxes/box_per_bin;
   if(bins > RooGrid::maxBins) bins= RooGrid::maxBins;
   boxes = box_per_bin * bins;
   oocxcoutD((TObject*)nullptr,Integration) << "RooMCIntegrator: using stratified sampling with " << bins << " bins and "
                << box_per_bin << " boxes/bin" << endl;
      }
      else {
   oocxcoutD((TObject*)nullptr,Integration) << "RooMCIntegrator: using importance sampling with " << bins << " bins and "
                << boxes << " boxes" << endl;
      }
    }
 
    // calculate the total number of n-dim boxes for this step
    double tot_boxes = std::pow((double)boxes,(double)dim);
 
    // increase the total number of calls to get at least 2 calls per box, if necessary
    _calls_per_box = (UInt_t)(calls/tot_boxes);
    if(_calls_per_box < 2) _calls_per_box= 2;
    calls= (UInt_t)(_calls_per_box*tot_boxes);
 
    // calculate the Jacobean factor: volume/(avg # of calls/bin)
    _jac = _grid.getVolume()*std::pow((double)bins,(double)dim)/calls;
 
    // setup our grid to use the calculated number of boxes and bins
    _grid.setNBoxes(boxes);
    if(bins != _grid.getNBins()) _grid.resize(bins);
  }
 
  // allocate memory for some book-keeping arrays
  std::vector<UInt_t> box(_grid.getDimension());
  std::vector<UInt_t> bin(_grid.getDimension());
  std::vector<double> x(_grid.getDimension());
 
 
  // loop over iterations for this step
  double cum_int(0);
  double cum_sig(0);
  _it_start = _it_num;
  _chisq = 0.0;
  for (UInt_t it = 0; it < iterations; it++) {
    double intgrl(0);
    double intgrl_sq(0);
    double sig(0);
    double jacbin(_jac);
 
    _it_num = _it_start + it;
 
    // reset the values associated with each grid cell
    _grid.resetValues();
 
    // loop over grid boxes
    _grid.firstBox(box.data());
    do {
      double m(0);
      double q(0);
      // loop over integrand evaluations within this grid box
      for(UInt_t k = 0; k < _calls_per_box; k++) {
        // generate a random point in this box
        double bin_vol(0);
        _grid.generatePoint(box.data(), x.data(), bin.data(), bin_vol, _genType == QuasiRandom ? true : false);
        // evaluate the integrand at the generated point
        double fval= jacbin*bin_vol*integrand(x.data());
        // update mean and variance calculations
        double d = fval - m;
        m+= d / (k + 1.0);
        q+= d * d * (k / (k + 1.0));
        // accumulate the results of this evaluation (importance sampling only)
        if (_mode != Stratified) _grid.accumulate(bin.data(), fval*fval);
      }
      intgrl += m * _calls_per_box;
      double f_sq_sum = q * _calls_per_box ;
      sig += f_sq_sum ;
 
      // accumulate the results for this grid box (stratified sampling only)
      if (_mode == Stratified) _grid.accumulate(bin.data(), f_sq_sum);
 
      // print occasional progress messages
      if(_timer.RealTime() > 30) {
        std::size_t index = 0;
        std::size_t sizeOfDim = 1;
 
        for (unsigned int i=0; i < _grid.getDimension(); ++i) {
          index += box[i] * sizeOfDim;
          sizeOfDim *= _grid.getNBoxes();
        }
        oocoutP(nullptr, Integration) << "RooMCIntegrator: still working ... iteration "
            << it << '/' << iterations << "  box " << index << "/"<< std::pow(_grid.getNBoxes(), _grid.getDimension()) << endl;
        _timer.Start(true);
      }
      else {
        _timer.Start(false);
      }
 
    } while(_grid.nextBox(box.data()));
 
    // compute final results for this iteration
    double wgt;
    sig = sig / (_calls_per_box - 1.0)  ;
    if (sig > 0) {
      wgt = 1.0 / sig;
    }
    else if (_sum_wgts > 0) {
      wgt = _sum_wgts / _samples;
    }
    else {
      wgt = 0.0;
    }
    intgrl_sq = intgrl * intgrl;
    _result = intgrl;
    _sigma  = sqrt(sig);
 
    if (wgt > 0.0) {
      _samples++ ;
      _sum_wgts += wgt;
      _wtd_int_sum += intgrl * wgt;
      _chi_sum += intgrl_sq * wgt;
 
      cum_int = _wtd_int_sum / _sum_wgts;
      cum_sig = sqrt (1 / _sum_wgts);
 
      if (_samples > 1) {
   _chisq = (_chi_sum - _wtd_int_sum * cum_int)/(_samples - 1.0);
      }
    }
    else {
      cum_int += (intgrl - cum_int) / (it + 1.0);
      cum_sig = 0.0;
    }
    oocxcoutD((TObject*)nullptr,Integration) << "=== Iteration " << _it_num << " : I = " << intgrl << " +/- " << sqrt(sig) << endl
                 << "    Cumulative : I = " << cum_int << " +/- " << cum_sig << "( chi2 = " << _chisq
                 << ")" << endl;
    // print the grid after the final iteration
    if (oodologD((TObject*)nullptr,Integration)) {
      if(it + 1 == iterations) _grid.print(std::cout, true);
    }
    _grid.refine(_alpha);
  }
 
  if(absError) *absError = cum_sig;
  return cum_int;
}