RooMinimizer.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                 *
 *   AL, Alfio Lazzaro,   INFN Milan,        alfio.lazzaro@mi.infn.it        *
 *                                                                           *
 * 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 RooMinimizer.cxx
\class RooMinimizer
\ingroup Roofitcore
 
RooMinimizer is a wrapper class around ROOT::Fit:Fitter that
provides a seamless interface between the minimizer functionality
and the native RooFit interface.
By default the Minimizer is MINUIT.
RooMinimizer can minimize any RooAbsReal function with respect to
its parameters. Usual choices for minimization are RooNLLVar
and RooChi2Var
RooMinimizer has methods corresponding to MINUIT functions like
hesse(), migrad(), minos() etc. In each of these function calls
the state of the MINUIT engine is synchronized with the state
of the RooFit variables: any change in variables, change
in the constant status etc is forwarded to MINUIT prior to
execution of the MINUIT call. Afterwards the RooFit objects
are resynchronized with the output state of MINUIT: changes
parameter values, errors are propagated.
Various methods are available to control verbosity, profiling,
automatic PDF optimization.
**/
 
#ifndef __ROOFIT_NOROOMINIMIZER
 
#include "RooFit.h"
 
#include "TClass.h"
 
#include <iostream>
#include <fstream>
 
#include "TH2.h"
#include "TMarker.h"
#include "TGraph.h"
#include "Fit/FitConfig.h"
#include "TStopwatch.h"
#include "TMatrixDSym.h"
 
#include "RooArgSet.h"
#include "RooArgList.h"
#include "RooAbsReal.h"
#include "RooAbsRealLValue.h"
#include "RooRealVar.h"
#include "RooAbsPdf.h"
#include "RooSentinel.h"
#include "RooMsgService.h"
#include "RooPlot.h"
 
 
#include "RooMinimizer.h"
#include "RooFitResult.h"
 
#include "Math/Minimizer.h"
 
#if (__GNUC__==3&&__GNUC_MINOR__==2&&__GNUC_PATCHLEVEL__==3)
char* operator+( streampos&, char* );
#endif
 
using namespace std;
 
ClassImp(RooMinimizer);
;
 
ROOT::Fit::Fitter *RooMinimizer::_theFitter = 0 ;
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Cleanup method called by atexit handler installed by RooSentinel
/// to delete all global heap objects when the program is terminated
 
void RooMinimizer::cleanup()
{
  if (_theFitter) {
    delete _theFitter ;
    _theFitter =0 ;
  }
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Construct MINUIT interface to given function. Function can be anything,
/// but is typically a -log(likelihood) implemented by RooNLLVar or a chi^2
/// (implemented by RooChi2Var). Other frequent use cases are a RooAddition
/// of a RooNLLVar plus a penalty or constraint term. This class propagates
/// all RooFit information (floating parameters, their values and errors)
/// to MINUIT before each MINUIT call and propagates all MINUIT information
/// back to the RooFit object at the end of each call (updated parameter
/// values, their (asymmetric errors) etc. The default MINUIT error level
/// for HESSE and MINOS error analysis is taken from the defaultErrorLevel()
/// value of the input function.
 
RooMinimizer::RooMinimizer(RooAbsReal& function)
{
  RooSentinel::activate() ;
 
  // Store function reference
  _extV = 0 ;
  _func = &function ;
  _optConst = kFALSE ;
  _verbose = kFALSE ;
  _profile = kFALSE ;
  _profileStart = kFALSE ;
  _printLevel = 1 ;
  _minimizerType = "Minuit"; // default minimizer
 
  if (_theFitter) delete _theFitter ;
  _theFitter = new ROOT::Fit::Fitter;
  _fcn = new RooMinimizerFcn(_func,this,_verbose);
  _theFitter->Config().SetMinimizer(_minimizerType.c_str());
  setEps(1.0); // default tolerance
  // default max number of calls
  _theFitter->Config().MinimizerOptions().SetMaxIterations(500*_fcn->NDim());
  _theFitter->Config().MinimizerOptions().SetMaxFunctionCalls(500*_fcn->NDim());
 
  // Shut up for now
  setPrintLevel(-1) ;
 
  // Use +0.5 for 1-sigma errors
  setErrorLevel(_func->defaultErrorLevel()) ;
 
  // Declare our parameters to MINUIT
  _fcn->Synchronize(_theFitter->Config().ParamsSettings(),
          _optConst,_verbose) ;
 
  // Now set default verbosity
  if (RooMsgService::instance().silentMode()) {
    setPrintLevel(-1) ;
  } else {
    setPrintLevel(1) ;
  }
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Destructor
 
RooMinimizer::~RooMinimizer()
{
  if (_extV) {
    delete _extV ;
  }
 
  if (_fcn) {
    delete _fcn;
  }
 
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Change MINUIT strategy to istrat. Accepted codes
/// are 0,1,2 and represent MINUIT strategies for dealing
/// most efficiently with fast FCNs (0), expensive FCNs (2)
/// and 'intermediate' FCNs (1)
 
void RooMinimizer::setStrategy(Int_t istrat)
{
  _theFitter->Config().MinimizerOptions().SetStrategy(istrat);
 
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Change maximum number of MINUIT iterations 
/// (RooMinimizer default 500 * #parameters)
 
void RooMinimizer::setMaxIterations(Int_t n) 
{
  _theFitter->Config().MinimizerOptions().SetMaxIterations(n);
}
 
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Change maximum number of likelihood function calss from MINUIT
/// (RooMinimizer default 500 * #parameters)
 
void RooMinimizer::setMaxFunctionCalls(Int_t n) 
{
  _theFitter->Config().MinimizerOptions().SetMaxFunctionCalls(n);
}
 
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Set the level for MINUIT error analysis to the given
/// value. This function overrides the default value
/// that is taken in the RooMinimizer constructor from
/// the defaultErrorLevel() method of the input function
 
void RooMinimizer::setErrorLevel(Double_t level)
{
  _theFitter->Config().MinimizerOptions().SetErrorDef(level);
 
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Change MINUIT epsilon
 
void RooMinimizer::setEps(Double_t eps)
{
  _theFitter->Config().MinimizerOptions().SetTolerance(eps);
 
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Enable internal likelihood offsetting for enhanced numeric precision
 
void RooMinimizer::setOffsetting(Bool_t flag) 
{
  _func->enableOffsetting(flag) ; 
}
 
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Choose the minimiser algorithm.
void RooMinimizer::setMinimizerType(const char* type)
{
  _minimizerType = type;
}
 
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Return underlying ROOT fitter object 
 
ROOT::Fit::Fitter* RooMinimizer::fitter()
{
  return _theFitter ;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Return underlying ROOT fitter object 
 
const ROOT::Fit::Fitter* RooMinimizer::fitter() const 
{
  return _theFitter ;
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Parse traditional RooAbsPdf::fitTo driver options
///
///  m - Run Migrad only
///  h - Run Hesse to estimate errors
///  v - Verbose mode
///  l - Log parameters after each Minuit steps to file
///  t - Activate profile timer
///  r - Save fit result
///  0 - Run Migrad with strategy 0
 
RooFitResult* RooMinimizer::fit(const char* options)
{
  TString opts(options) ;
  opts.ToLower() ;
 
  // Initial configuration
  if (opts.Contains("v")) setVerbose(1) ;
  if (opts.Contains("t")) setProfile(1) ;
  if (opts.Contains("l")) setLogFile(Form("%s.log",_func->GetName())) ;
  if (opts.Contains("c")) optimizeConst(1) ;
 
  // Fitting steps
  if (opts.Contains("0")) setStrategy(0) ;
  migrad() ;
  if (opts.Contains("0")) setStrategy(1) ;
  if (opts.Contains("h")||!opts.Contains("m")) hesse() ;
  if (!opts.Contains("m")) minos() ;
 
  return (opts.Contains("r")) ? save() : 0 ;
}
 
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Minimise the function passed in the constructor.
/// \param[in] type Type of fitter to use, e.g. "Minuit" "Minuit2".
/// \attention This overrides the default fitter of this RooMinimizer.
/// \param[in] alg  Fit algorithm to use. (Optional)
Int_t RooMinimizer::minimize(const char* type, const char* alg)
{
  _fcn->Synchronize(_theFitter->Config().ParamsSettings(),
          _optConst,_verbose) ;
 
  _minimizerType = type;
  _theFitter->Config().SetMinimizer(type,alg);
 
  profileStart() ;
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::CollectErrors) ;
  RooAbsReal::clearEvalErrorLog() ;
 
  bool ret = _theFitter->FitFCN(*_fcn);
  _status = ((ret) ? _theFitter->Result().Status() : -1);
 
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::PrintErrors) ;
  profileStop() ;
  _fcn->BackProp(_theFitter->Result());
 
  saveStatus("MINIMIZE",_status) ;
 
  return _status ;
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Execute MIGRAD. Changes in parameter values
/// and calculated errors are automatically
/// propagated back the RooRealVars representing
/// the floating parameters in the MINUIT operation.
 
Int_t RooMinimizer::migrad()
{
  _fcn->Synchronize(_theFitter->Config().ParamsSettings(),
          _optConst,_verbose) ;
  profileStart() ;
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::CollectErrors) ;
  RooAbsReal::clearEvalErrorLog() ;
 
  _theFitter->Config().SetMinimizer(_minimizerType.c_str(),"migrad");
  bool ret = _theFitter->FitFCN(*_fcn);
  _status = ((ret) ? _theFitter->Result().Status() : -1);
 
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::PrintErrors) ;
  profileStop() ;
  _fcn->BackProp(_theFitter->Result());
 
  saveStatus("MIGRAD",_status) ;
 
  return _status ;
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Execute HESSE. Changes in parameter values
/// and calculated errors are automatically
/// propagated back the RooRealVars representing
/// the floating parameters in the MINUIT operation.
 
Int_t RooMinimizer::hesse()
{
  if (_theFitter->GetMinimizer()==0) {
    coutW(Minimization) << "RooMinimizer::hesse: Error, run Migrad before Hesse!"
         << endl ;
    _status = -1;
  }
  else {
 
    _fcn->Synchronize(_theFitter->Config().ParamsSettings(),
          _optConst,_verbose) ;
    profileStart() ;
    RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::CollectErrors) ;
    RooAbsReal::clearEvalErrorLog() ;
 
    _theFitter->Config().SetMinimizer(_minimizerType.c_str());
    bool ret = _theFitter->CalculateHessErrors();
    _status = ((ret) ? _theFitter->Result().Status() : -1);
 
    RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::PrintErrors) ;
    profileStop() ;
    _fcn->BackProp(_theFitter->Result());
 
    saveStatus("HESSE",_status) ;
  
  }
 
  return _status ;
 
}
 
////////////////////////////////////////////////////////////////////////////////
/// Execute MINOS. Changes in parameter values
/// and calculated errors are automatically
/// propagated back the RooRealVars representing
/// the floating parameters in the MINUIT operation.
 
Int_t RooMinimizer::minos()
{
  if (_theFitter->GetMinimizer()==0) {
    coutW(Minimization) << "RooMinimizer::minos: Error, run Migrad before Minos!"
         << endl ;
    _status = -1;
  }
  else {
 
    _fcn->Synchronize(_theFitter->Config().ParamsSettings(),
            _optConst,_verbose) ;
    profileStart() ;
    RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::CollectErrors) ;
    RooAbsReal::clearEvalErrorLog() ;
 
    _theFitter->Config().SetMinimizer(_minimizerType.c_str());
    bool ret = _theFitter->CalculateMinosErrors();
    _status = ((ret) ? _theFitter->Result().Status() : -1);
 
    RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::PrintErrors) ;
    profileStop() ;
    _fcn->BackProp(_theFitter->Result());
 
    saveStatus("MINOS",_status) ;
 
  }
 
  return _status ;
 
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Execute MINOS for given list of parameters. Changes in parameter values
/// and calculated errors are automatically
/// propagated back the RooRealVars representing
/// the floating parameters in the MINUIT operation.
 
Int_t RooMinimizer::minos(const RooArgSet& minosParamList)
{
  if (_theFitter->GetMinimizer()==0) {
    coutW(Minimization) << "RooMinimizer::minos: Error, run Migrad before Minos!"
         << endl ;
    _status = -1;
  }
  else if (minosParamList.getSize()>0) {
 
    _fcn->Synchronize(_theFitter->Config().ParamsSettings(),
            _optConst,_verbose) ;
    profileStart() ;
    RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::CollectErrors) ;
    RooAbsReal::clearEvalErrorLog() ;
 
    // get list of parameters for Minos
    TIterator* aIter = minosParamList.createIterator() ;
    RooAbsArg* arg ;
    std::vector<unsigned int> paramInd;
    while((arg=(RooAbsArg*)aIter->Next())) {
      RooAbsArg* par = _fcn->GetFloatParamList()->find(arg->GetName());
      if (par && !par->isConstant()) {
   Int_t index = _fcn->GetFloatParamList()->index(par);
   paramInd.push_back(index);
      }
    }
    delete aIter ;
 
    if (paramInd.size()) {
      // set the parameter indeces
      _theFitter->Config().SetMinosErrors(paramInd);
 
      _theFitter->Config().SetMinimizer(_minimizerType.c_str());
      bool ret = _theFitter->CalculateMinosErrors();
      _status = ((ret) ? _theFitter->Result().Status() : -1);
      // to avoid that following minimization computes automatically the Minos errors
      _theFitter->Config().SetMinosErrors(kFALSE);
 
    }
 
    RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::PrintErrors) ;
    profileStop() ;
    _fcn->BackProp(_theFitter->Result());
 
    saveStatus("MINOS",_status) ;
 
  }
 
  return _status ;
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Execute SEEK. Changes in parameter values
/// and calculated errors are automatically
/// propagated back the RooRealVars representing
/// the floating parameters in the MINUIT operation.
 
Int_t RooMinimizer::seek()
{
  _fcn->Synchronize(_theFitter->Config().ParamsSettings(),
          _optConst,_verbose) ;
  profileStart() ;
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::CollectErrors) ;
  RooAbsReal::clearEvalErrorLog() ;
 
  _theFitter->Config().SetMinimizer(_minimizerType.c_str(),"seek");
  bool ret = _theFitter->FitFCN(*_fcn);
  _status = ((ret) ? _theFitter->Result().Status() : -1);
 
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::PrintErrors) ;
  profileStop() ;
  _fcn->BackProp(_theFitter->Result());
 
  saveStatus("SEEK",_status) ;
 
  return _status ;
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Execute SIMPLEX. Changes in parameter values
/// and calculated errors are automatically
/// propagated back the RooRealVars representing
/// the floating parameters in the MINUIT operation.
 
Int_t RooMinimizer::simplex()
{
  _fcn->Synchronize(_theFitter->Config().ParamsSettings(),
          _optConst,_verbose) ;
  profileStart() ;
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::CollectErrors) ;
  RooAbsReal::clearEvalErrorLog() ;
 
  _theFitter->Config().SetMinimizer(_minimizerType.c_str(),"simplex");
  bool ret = _theFitter->FitFCN(*_fcn);
  _status = ((ret) ? _theFitter->Result().Status() : -1);
 
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::PrintErrors) ;
  profileStop() ;
  _fcn->BackProp(_theFitter->Result());
 
  saveStatus("SEEK",_status) ;
    
  return _status ;
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Execute IMPROVE. Changes in parameter values
/// and calculated errors are automatically
/// propagated back the RooRealVars representing
/// the floating parameters in the MINUIT operation.
 
Int_t RooMinimizer::improve()
{
  _fcn->Synchronize(_theFitter->Config().ParamsSettings(),
          _optConst,_verbose) ;
  profileStart() ;
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::CollectErrors) ;
  RooAbsReal::clearEvalErrorLog() ;
 
  _theFitter->Config().SetMinimizer(_minimizerType.c_str(),"migradimproved");
  bool ret = _theFitter->FitFCN(*_fcn);
  _status = ((ret) ? _theFitter->Result().Status() : -1);
 
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::PrintErrors) ;
  profileStop() ;
  _fcn->BackProp(_theFitter->Result());
 
  saveStatus("IMPROVE",_status) ;
 
  return _status ;
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Change the MINUIT internal printing level
 
Int_t RooMinimizer::setPrintLevel(Int_t newLevel)
{
  Int_t ret = _printLevel ;
  _theFitter->Config().MinimizerOptions().SetPrintLevel(newLevel+1);
  _printLevel = newLevel+1 ;
  return ret ;
}
 
////////////////////////////////////////////////////////////////////////////////
/// If flag is true, perform constant term optimization on
/// function being minimized.
 
void RooMinimizer::optimizeConst(Int_t flag)
{
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::CollectErrors) ;
 
  if (_optConst && !flag){
    if (_printLevel>-1) coutI(Minimization) << "RooMinimizer::optimizeConst: deactivating const optimization" << endl ;
    _func->constOptimizeTestStatistic(RooAbsArg::DeActivate) ;
    _optConst = flag ;
  } else if (!_optConst && flag) {
    if (_printLevel>-1) coutI(Minimization) << "RooMinimizer::optimizeConst: activating const optimization" << endl ;
    _func->constOptimizeTestStatistic(RooAbsArg::Activate,flag>1) ;
    _optConst = flag ;
  } else if (_optConst && flag) {
    if (_printLevel>-1) coutI(Minimization) << "RooMinimizer::optimizeConst: const optimization already active" << endl ;
  } else {
    if (_printLevel>-1) coutI(Minimization) << "RooMinimizer::optimizeConst: const optimization wasn't active" << endl ;
  }
 
  RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::PrintErrors) ;
 
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Save and return a RooFitResult snapshot of current minimizer status.
/// This snapshot contains the values of all constant parameters,
/// the value of all floating parameters at RooMinimizer construction and
/// after the last MINUIT operation, the MINUIT status, variance quality,
/// EDM setting, number of calls with evaluation problems, the minimized
/// function value and the full correlation matrix.
 
RooFitResult* RooMinimizer::save(const char* userName, const char* userTitle)
{
  if (_theFitter->GetMinimizer()==0) {
    coutW(Minimization) << "RooMinimizer::save: Error, run minimization before!"
         << endl ;
    return 0;
  }
 
  TString name,title ;
  name = userName ? userName : Form("%s", _func->GetName()) ;
  title = userTitle ? userTitle : Form("%s", _func->GetTitle()) ;
  RooFitResult* fitRes = new RooFitResult(name,title) ;
 
  // Move eventual fixed parameters in floatList to constList
  Int_t i ;
  RooArgList saveConstList(*(_fcn->GetConstParamList())) ;
  RooArgList saveFloatInitList(*(_fcn->GetInitFloatParamList())) ;
  RooArgList saveFloatFinalList(*(_fcn->GetFloatParamList())) ;
  for (i=0 ; i<_fcn->GetFloatParamList()->getSize() ; i++) {
    RooAbsArg* par = _fcn->GetFloatParamList()->at(i) ;
    if (par->isConstant()) {
      saveFloatInitList.remove(*saveFloatInitList.find(par->GetName()),kTRUE) ;
      saveFloatFinalList.remove(*par) ;
      saveConstList.add(*par) ;
    }
  }
  saveConstList.sort() ;
 
  fitRes->setConstParList(saveConstList) ;
  fitRes->setInitParList(saveFloatInitList) ;
 
  // The fitter often clones the function. We therefore have to ask it for its copy.
  const auto fitFcn = dynamic_cast<const RooMinimizerFcn*>(_theFitter->GetFCN());
  double removeOffset = 0.;
  if (fitFcn) {
    fitRes->setNumInvalidNLL(fitFcn->GetNumInvalidNLL());
    removeOffset = - fitFcn->getOffset();
  }
 
  fitRes->setStatus(_status) ;
  fitRes->setCovQual(_theFitter->GetMinimizer()->CovMatrixStatus()) ;
  fitRes->setMinNLL(_theFitter->Result().MinFcnValue() + removeOffset);
  fitRes->setEDM(_theFitter->Result().Edm()) ;
  fitRes->setFinalParList(saveFloatFinalList) ;
  if (!_extV) {
    std::vector<double> globalCC;
    TMatrixDSym corrs(_theFitter->Result().Parameters().size()) ;
    TMatrixDSym covs(_theFitter->Result().Parameters().size()) ;
    for (UInt_t ic=0; ic<_theFitter->Result().Parameters().size(); ic++) {
      globalCC.push_back(_theFitter->Result().GlobalCC(ic));
      for (UInt_t ii=0; ii<_theFitter->Result().Parameters().size(); ii++) {
   corrs(ic,ii) = _theFitter->Result().Correlation(ic,ii);
   covs(ic,ii) = _theFitter->Result().CovMatrix(ic,ii);
      }
    }
    fitRes->fillCorrMatrix(globalCC,corrs,covs) ;
  } else {
    fitRes->setCovarianceMatrix(*_extV) ;
  }
 
  fitRes->setStatusHistory(_statusHistory) ;
 
  return fitRes ;
 
}
 
////////////////////////////////////////////////////////////////////////////////
/// Create and draw a TH2 with the error contours in the parameters `var1` and `var2`.
/// \param[in] var1 The first parameter (x axis).
/// \param[in] var2 The second parameter (y axis).
/// \param[in] n1 First contour.
/// \param[in] n2 Optional contour. 0 means don't draw.
/// \param[in] n3 Optional contour. 0 means don't draw.
/// \param[in] n4 Optional contour. 0 means don't draw.
/// \param[in] n5 Optional contour. 0 means don't draw.
/// \param[in] n6 Optional contour. 0 means don't draw.
/// \param[in] npoints Number of points for evaluating the contour.
///
/// Up to six contours can be drawn using the arguments `n1` to `n6` to request the desired
/// coverage in units of \f$ \sigma = n^2 \cdot \mathrm{ErrorDef} \f$.
/// See ROOT::Math::Minimizer::ErrorDef().
 
RooPlot* RooMinimizer::contour(RooRealVar& var1, RooRealVar& var2,
                Double_t n1, Double_t n2, Double_t n3,
                Double_t n4, Double_t n5, Double_t n6, unsigned int npoints)
{
 
 
  RooArgList* params = _fcn->GetFloatParamList() ;
  RooArgList* paramSave = (RooArgList*) params->snapshot() ;
 
  // Verify that both variables are floating parameters of PDF
  Int_t index1= _fcn->GetFloatParamList()->index(&var1);
  if(index1 < 0) {
    coutE(Minimization) << "RooMinimizer::contour(" << GetName()
         << ") ERROR: " << var1.GetName()
         << " is not a floating parameter of "
         << _func->GetName() << endl ;
    return 0;
  }
 
  Int_t index2= _fcn->GetFloatParamList()->index(&var2);
  if(index2 < 0) {
    coutE(Minimization) << "RooMinimizer::contour(" << GetName()
         << ") ERROR: " << var2.GetName()
         << " is not a floating parameter of PDF "
         << _func->GetName() << endl ;
    return 0;
  }
 
  // create and draw a frame
  RooPlot* frame = new RooPlot(var1,var2) ;
 
  // draw a point at the current parameter values
  TMarker *point= new TMarker(var1.getVal(), var2.getVal(), 8);
  frame->addObject(point) ;
 
  // check first if a inimizer is available. If not means
  // the minimization is not done , so do it 
  if (_theFitter->GetMinimizer()==0) {
     coutW(Minimization) << "RooMinimizer::contour: Error, run Migrad before contours!"
                         << endl ;
     return frame;
  }
 
  
  // remember our original value of ERRDEF  
  Double_t errdef= _theFitter->GetMinimizer()->ErrorDef();
 
  Double_t n[6] ;
  n[0] = n1 ; n[1] = n2 ; n[2] = n3 ; n[3] = n4 ; n[4] = n5 ; n[5] = n6 ;
 
  for (Int_t ic = 0 ; ic<6 ; ic++) {
    if(n[ic] > 0) {
 
       // set the value corresponding to an n1-sigma contour
       _theFitter->GetMinimizer()->SetErrorDef(n[ic]*n[ic]*errdef);
 
      // calculate and draw the contour
      Double_t *xcoor = new Double_t[npoints+1];
      Double_t *ycoor = new Double_t[npoints+1];
      bool ret = _theFitter->GetMinimizer()->Contour(index1,index2,npoints,xcoor,ycoor);
 
      if (!ret) {
   coutE(Minimization) << "RooMinimizer::contour("
             << GetName()
             << ") ERROR: MINUIT did not return a contour graph for n="
             << n[ic] << endl ;
      } else {
   xcoor[npoints] = xcoor[0];
   ycoor[npoints] = ycoor[0];
   TGraph* graph = new TGraph(npoints+1,xcoor,ycoor);
 
   graph->SetName(Form("contour_%s_n%f",_func->GetName(),n[ic])) ;
   graph->SetLineStyle(ic+1) ;
   graph->SetLineWidth(2) ;
   graph->SetLineColor(kBlue) ;
   frame->addObject(graph,"L") ;
      }
 
      delete [] xcoor;
      delete [] ycoor;
    }
  }
 
 
  // restore the original ERRDEF
  _theFitter->Config().MinimizerOptions().SetErrorDef(errdef);
 
  // restore parameter values
  *params = *paramSave ;
  delete paramSave ;
 
  return frame ;
 
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Start profiling timer
 
void RooMinimizer::profileStart()
{
  if (_profile) {
    _timer.Start() ;
    _cumulTimer.Start(_profileStart?kFALSE:kTRUE) ;
    _profileStart = kTRUE ;
  }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Stop profiling timer and report results of last session
 
void RooMinimizer::profileStop()
{
  if (_profile) {
    _timer.Stop() ;
    _cumulTimer.Stop() ;
    coutI(Minimization) << "Command timer: " ; _timer.Print() ;
    coutI(Minimization) << "Session timer: " ; _cumulTimer.Print() ;
  }
}
 
 
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Apply results of given external covariance matrix. i.e. propagate its errors
/// to all RRV parameter representations and give this matrix instead of the
/// HESSE matrix at the next save() call
 
void RooMinimizer::applyCovarianceMatrix(TMatrixDSym& V)
{
  _extV = (TMatrixDSym*) V.Clone() ;
  _fcn->ApplyCovarianceMatrix(*_extV);
 
}
 
 
 
RooFitResult* RooMinimizer::lastMinuitFit(const RooArgList& varList)
{
  // Import the results of the last fit performed, interpreting
  // the fit parameters as the given varList of parameters.
 
  if (_theFitter==0 || _theFitter->GetMinimizer()==0) {
    oocoutE((TObject*)0,InputArguments) << "RooMinimizer::save: Error, run minimization before!"
               << endl ;
    return 0;
  }
 
  // Verify length of supplied varList
  if (varList.getSize()>0 && varList.getSize()!=Int_t(_theFitter->Result().NTotalParameters())) {
    oocoutE((TObject*)0,InputArguments)
      << "RooMinimizer::lastMinuitFit: ERROR: supplied variable list must be either empty " << endl
      << "                             or match the number of variables of the last fit ("
      << _theFitter->Result().NTotalParameters() << ")" << endl ;
    return 0 ;
  }
 
 
  // Verify that all members of varList are of type RooRealVar
  TIterator* iter = varList.createIterator() ;
  RooAbsArg* arg  ;
  while((arg=(RooAbsArg*)iter->Next())) {
    if (!dynamic_cast<RooRealVar*>(arg)) {
      oocoutE((TObject*)0,InputArguments) << "RooMinimizer::lastMinuitFit: ERROR: variable '"
                 << arg->GetName() << "' is not of type RooRealVar" << endl ;
      return 0 ;
    }
  }
  delete iter ;
 
  RooFitResult* res = new RooFitResult("lastMinuitFit","Last MINUIT fit") ;
 
  // Extract names of fit parameters
  // and construct corresponding RooRealVars
  RooArgList constPars("constPars") ;
  RooArgList floatPars("floatPars") ;
 
  UInt_t i ;
  for (i = 0; i < _theFitter->Result().NTotalParameters(); ++i) {
 
    TString varName(_theFitter->Result().GetParameterName(i));
    Bool_t isConst(_theFitter->Result().IsParameterFixed(i)) ;
 
    Double_t xlo = _theFitter->Config().ParSettings(i).LowerLimit();
    Double_t xhi = _theFitter->Config().ParSettings(i).UpperLimit();
    Double_t xerr = _theFitter->Result().Error(i);
    Double_t xval = _theFitter->Result().Value(i);
 
    RooRealVar* var ;
    if (varList.getSize()==0) {
 
      if ((xlo<xhi) && !isConst) {
        var = new RooRealVar(varName,varName,xval,xlo,xhi) ;
      } else {
        var = new RooRealVar(varName,varName,xval) ;
      }
      var->setConstant(isConst) ;
    } else {
 
      var = (RooRealVar*) varList.at(i)->Clone() ;
      var->setConstant(isConst) ;
      var->setVal(xval) ;
      if (xlo<xhi) {
        var->setRange(xlo,xhi) ;
      }
 
      if (varName.CompareTo(var->GetName())) {
   oocoutI((TObject*)0,Eval)  << "RooMinimizer::lastMinuitFit: fit parameter '" << varName
               << "' stored in variable '" << var->GetName() << "'" << endl ;
      }
 
    }
 
    if (isConst) {
      constPars.addOwned(*var) ;
    } else {
      var->setError(xerr) ;
      floatPars.addOwned(*var) ;
    }
  }
 
  res->setConstParList(constPars) ;
  res->setInitParList(floatPars) ;
  res->setFinalParList(floatPars) ;
  res->setMinNLL(_theFitter->Result().MinFcnValue()) ;
  res->setEDM(_theFitter->Result().Edm()) ;
  res->setCovQual(_theFitter->GetMinimizer()->CovMatrixStatus()) ;
  res->setStatus(_theFitter->Result().Status()) ;
  std::vector<double> globalCC;
  TMatrixDSym corrs(_theFitter->Result().Parameters().size()) ;
  TMatrixDSym covs(_theFitter->Result().Parameters().size()) ;
  for (UInt_t ic=0; ic<_theFitter->Result().Parameters().size(); ic++) {
    globalCC.push_back(_theFitter->Result().GlobalCC(ic));
    for (UInt_t ii=0; ii<_theFitter->Result().Parameters().size(); ii++) {
      corrs(ic,ii) = _theFitter->Result().Correlation(ic,ii);
      covs(ic,ii) = _theFitter->Result().CovMatrix(ic,ii);
    }
  }
  res->fillCorrMatrix(globalCC,corrs,covs) ;
 
  return res;
 
}
 
#endif