Minuit2Minimizer.cxx

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// @(#)root/minuit2:$Id$
// Author: L. Moneta Wed Oct 18 11:48:00 2006
 
/**********************************************************************
 *                                                                    *
 * Copyright (c) 2006  LCG ROOT Math Team, CERN/PH-SFT                *
 *                                                                    *
 *                                                                    *
 **********************************************************************/
 
// Implementation file for class Minuit2Minimizer
 
#include "Minuit2/Minuit2Minimizer.h"
 
#include "Math/IFunction.h"
#include "Math/IOptions.h"
 
#include "Fit/ParameterSettings.h"
 
#include "Minuit2/FCNAdapter.h"
#include "Minuit2/FumiliFCNAdapter.h"
#include "Minuit2/FCNGradAdapter.h"
#include "Minuit2/FunctionMinimum.h"
#include "Minuit2/MnMigrad.h"
#include "Minuit2/MnMinos.h"
#include "Minuit2/MinosError.h"
#include "Minuit2/MnHesse.h"
#include "Minuit2/MinuitParameter.h"
#include "Minuit2/MnUserFcn.h"
#include "Minuit2/MnPrint.h"
#include "Minuit2/VariableMetricMinimizer.h"
#include "Minuit2/SimplexMinimizer.h"
#include "Minuit2/CombinedMinimizer.h"
#include "Minuit2/ScanMinimizer.h"
#include "Minuit2/FumiliMinimizer.h"
#include "Minuit2/MnParameterScan.h"
#include "Minuit2/MnContours.h"
#include "Minuit2/MnTraceObject.h"
#include "Minuit2/MinimumBuilder.h"
 
#include <cassert>
#include <iostream>
#include <algorithm>
#include <functional>
 
#ifdef USE_ROOT_ERROR
#include "TROOT.h"
#include "TMinuit2TraceObject.h"
#endif
 
namespace ROOT {
 
namespace Minuit2 {
 
 
   // functions needed to control siwthc off of Minuit2 printing level
#ifdef USE_ROOT_ERROR
   int TurnOffPrintInfoLevel() {
   // switch off Minuit2 printing of INFO message (cut off is 1001)
   int prevErrorIgnoreLevel = gErrorIgnoreLevel;
   if (prevErrorIgnoreLevel < 1001) {
      gErrorIgnoreLevel = 1001;
      return prevErrorIgnoreLevel;
   }
   return -2;  // no op in this case
}
 
void RestoreGlobalPrintLevel(int value) {
      gErrorIgnoreLevel = value;
}
#else
   // dummy functions
   int TurnOffPrintInfoLevel() { return -1; }
   int ControlPrintLevel( ) { return -1;}
   void RestoreGlobalPrintLevel(int ) {}
#endif
 
 
 
 
Minuit2Minimizer::Minuit2Minimizer(ROOT::Minuit2::EMinimizerType type ) :
   Minimizer(),
   fDim(0),
   fMinimizer(0),
   fMinuitFCN(0),
   fMinimum(0)
{
   // Default constructor implementation depending on minimizer type
   SetMinimizerType(type);
}
 
Minuit2Minimizer::Minuit2Minimizer(const char *  type ) :
   Minimizer(),
   fDim(0),
   fMinimizer(0),
   fMinuitFCN(0),
   fMinimum(0)
{
   // constructor from a string
 
   std::string algoname(type);
   // tolower() is not an  std function (Windows)
   std::transform(algoname.begin(), algoname.end(), algoname.begin(), (int(*)(int)) tolower );
 
   EMinimizerType algoType = kMigrad;
   if (algoname == "simplex")   algoType = kSimplex;
   if (algoname == "minimize" ) algoType = kCombined;
   if (algoname == "scan" )     algoType = kScan;
   if (algoname == "fumili" )   algoType = kFumili;
   if (algoname == "bfgs" )     algoType = kMigradBFGS;
 
   SetMinimizerType(algoType);
}
 
void Minuit2Minimizer::SetMinimizerType(ROOT::Minuit2::EMinimizerType type) {
   // Set  minimizer algorithm type
   fUseFumili = false;
   switch (type) {
   case ROOT::Minuit2::kMigrad:
      //std::cout << "Minuit2Minimizer: minimize using MIGRAD " << std::endl;
      SetMinimizer( new ROOT::Minuit2::VariableMetricMinimizer() );
      return;
   case ROOT::Minuit2::kMigradBFGS:
      //std::cout << "Minuit2Minimizer: minimize using MIGRAD " << std::endl;
      SetMinimizer( new ROOT::Minuit2::VariableMetricMinimizer(VariableMetricMinimizer::BFGSType()) );
      return;
   case ROOT::Minuit2::kSimplex:
      //std::cout << "Minuit2Minimizer: minimize using SIMPLEX " << std::endl;
      SetMinimizer( new ROOT::Minuit2::SimplexMinimizer() );
      return;
   case ROOT::Minuit2::kCombined:
      SetMinimizer( new ROOT::Minuit2::CombinedMinimizer() );
      return;
   case ROOT::Minuit2::kScan:
      SetMinimizer( new ROOT::Minuit2::ScanMinimizer() );
      return;
   case ROOT::Minuit2::kFumili:
      SetMinimizer( new ROOT::Minuit2::FumiliMinimizer() );
      fUseFumili = true;
      return;
   default:
      //migrad minimizer
      SetMinimizer( new ROOT::Minuit2::VariableMetricMinimizer() );
 
   }
}
 
 
Minuit2Minimizer::~Minuit2Minimizer()
{
   // Destructor implementation.
   if (fMinimizer) delete fMinimizer;
   if (fMinuitFCN) delete fMinuitFCN;
   if (fMinimum)   delete fMinimum;
}
 
Minuit2Minimizer::Minuit2Minimizer(const Minuit2Minimizer &) :
   ROOT::Math::Minimizer()
{
   // Implementation of copy constructor.
}
 
Minuit2Minimizer & Minuit2Minimizer::operator = (const Minuit2Minimizer &rhs)
{
   // Implementation of assignment operator.
   if (this == &rhs) return *this;  // time saving self-test
   return *this;
}
 
 
void Minuit2Minimizer::Clear() {
   // delete the state in case of consecutive minimizations
   fState = MnUserParameterState();
   // clear also the function minimum
   if (fMinimum) delete fMinimum;
   fMinimum = 0;
}
 
 
// set variables
 
bool Minuit2Minimizer::SetVariable(unsigned int ivar, const std::string & name, double val, double step) {
   // set a free variable.
   // Add the variable if not existing otherwise  set value if exists already
   // this is implemented in MnUserParameterState::Add
   // if index is wrong (i.e. variable already exists but with a different index return false) but
   // value is set for corresponding variable name
 
//    std::cout << " add parameter " << name << "  " <<  val << " step " << step << std::endl;
 
   if (step <= 0) {
      std::string txtmsg = "Parameter " + name + "  has zero or invalid step size - consider it as constant ";
      MN_INFO_MSG2("Minuit2Minimizer::SetVariable",txtmsg);
      fState.Add(name.c_str(), val);
   }
   else
      fState.Add(name.c_str(), val, step);
 
   unsigned int minuit2Index = fState.Index(name.c_str() );
   if ( minuit2Index != ivar) {
      std::string txtmsg("Wrong index used for the variable " + name);
      MN_INFO_MSG2("Minuit2Minimizer::SetVariable",txtmsg);
      MN_INFO_VAL2("Minuit2Minimizer::SetVariable",minuit2Index);
      ivar = minuit2Index;
      return false;
   }
   fState.RemoveLimits(ivar);
 
   return true;
}
 
bool Minuit2Minimizer::SetLowerLimitedVariable(unsigned int ivar , const std::string & name , double val , double step , double lower ) {
   // add a lower bounded variable
   if (!SetVariable(ivar, name, val, step) ) return false;
   fState.SetLowerLimit(ivar, lower);
   return true;
}
 
bool Minuit2Minimizer::SetUpperLimitedVariable(unsigned int ivar , const std::string & name , double val , double step , double upper ) {
   // add a upper bounded variable
   if (!SetVariable(ivar, name, val, step) ) return false;
   fState.SetUpperLimit(ivar, upper);
   return true;
}
 
 
 
bool Minuit2Minimizer::SetLimitedVariable(unsigned int ivar , const std::string & name , double val , double step , double lower , double upper) {
   // add a double bound variable
   if (!SetVariable(ivar, name, val, step) ) return false;
   fState.SetLimits(ivar, lower, upper);
   return true;
}
 
bool Minuit2Minimizer::SetFixedVariable(unsigned int ivar , const std::string & name , double val ) {
   // add a fixed variable
   // need a step size otherwise treated as a constant
   // use 10%
   double step = ( val != 0) ? 0.1 * std::abs(val) : 0.1;
   if (!SetVariable(ivar, name, val, step ) ) {
      ivar = fState.Index(name.c_str() );
   }
   fState.Fix(ivar);
   return true;
}
 
std::string Minuit2Minimizer::VariableName(unsigned int ivar) const {
   // return the variable name
   if (ivar >= fState.MinuitParameters().size() ) return std::string();
   return fState.GetName(ivar);
}
 
 
int Minuit2Minimizer::VariableIndex(const std::string & name) const {
   // return the variable index
   // check if variable exist
   return fState.Trafo().FindIndex(name);
}
 
 
bool Minuit2Minimizer::SetVariableValue(unsigned int ivar, double val) {
   // set value for variable ivar (only for existing parameters)
   if (ivar >= fState.MinuitParameters().size() ) return false;
   fState.SetValue(ivar, val);
   return true;
}
 
bool Minuit2Minimizer::SetVariableValues(const double * x)  {
   // set value for variable ivar (only for existing parameters)
   unsigned int n =  fState.MinuitParameters().size();
   if (n== 0) return false;
   for (unsigned int ivar = 0; ivar < n; ++ivar)
      fState.SetValue(ivar, x[ivar]);
   return true;
}
 
bool Minuit2Minimizer::SetVariableStepSize(unsigned int ivar, double step) {
   // set the step-size of an existing variable
   // parameter must exist or return false
   if (ivar >= fState.MinuitParameters().size() ) return false;
   fState.SetError(ivar, step);
   return true;
}
 
bool Minuit2Minimizer::SetVariableLowerLimit(unsigned int ivar, double lower) {
   // set the limits of an existing variable
   // parameter must exist or return false
   if (ivar >= fState.MinuitParameters().size() ) return false;
   fState.SetLowerLimit(ivar, lower);
   return true;
}
bool Minuit2Minimizer::SetVariableUpperLimit(unsigned int ivar, double upper ) {
   // set the limits of an existing variable
   // parameter must exist or return false
   if (ivar >= fState.MinuitParameters().size() ) return false;
   fState.SetUpperLimit(ivar, upper);
   return true;
}
 
bool Minuit2Minimizer::SetVariableLimits(unsigned int ivar, double lower, double upper) {
   // set the limits of an existing variable
   // parameter must exist or return false
   if (ivar >= fState.MinuitParameters().size() ) return false;
   fState.SetLimits(ivar, lower,upper);
   return true;
}
 
bool Minuit2Minimizer::FixVariable(unsigned int ivar) {
   // Fix an existing variable
   if (ivar >= fState.MinuitParameters().size() ) return false;
   fState.Fix(ivar);
   return true;
}
 
bool Minuit2Minimizer::ReleaseVariable(unsigned int ivar) {
   // Release an existing variable
   if (ivar >= fState.MinuitParameters().size() ) return false;
   fState.Release(ivar);
   return true;
}
 
bool Minuit2Minimizer::IsFixedVariable(unsigned int ivar) const {
   // query if variable is fixed
   if (ivar >= fState.MinuitParameters().size() ) {
      MN_ERROR_MSG2("Minuit2Minimizer","wrong variable index");
      return false;
   }
   return (fState.Parameter(ivar).IsFixed() || fState.Parameter(ivar).IsConst() );
}
 
bool Minuit2Minimizer::GetVariableSettings(unsigned int ivar, ROOT::Fit::ParameterSettings & varObj) const {
   // retrieve variable settings (all set info on the variable)
   if (ivar >= fState.MinuitParameters().size() ) {
      MN_ERROR_MSG2("Minuit2Minimizer","wrong variable index");
      return false;
   }
   const MinuitParameter & par = fState.Parameter(ivar);
   varObj.Set( par.Name(), par.Value(), par.Error() );
   if (par.HasLowerLimit() ) {
     if (par.HasUpperLimit() ) {
       varObj.SetLimits(par.LowerLimit(), par.UpperLimit() );
     } else {
       varObj.SetLowerLimit(par.LowerLimit() );
     }
   } else if (par.HasUpperLimit() ) {
     varObj.SetUpperLimit(par.UpperLimit() );
   }
   if (par.IsConst() || par.IsFixed() ) varObj.Fix();
   return true;
}
 
 
 
void Minuit2Minimizer::SetFunction(const  ROOT::Math::IMultiGenFunction & func) {
   // set function to be minimized
   if (fMinuitFCN) delete fMinuitFCN;
   fDim = func.NDim();
   if (!fUseFumili) {
      fMinuitFCN = new ROOT::Minuit2::FCNAdapter<ROOT::Math::IMultiGenFunction> (func, ErrorDef() );
   }
   else {
      // for Fumili the fit method function interface is required
      const ROOT::Math::FitMethodFunction * fcnfunc = dynamic_cast<const ROOT::Math::FitMethodFunction *>(&func);
      if (!fcnfunc) {
         MN_ERROR_MSG("Minuit2Minimizer: Wrong Fit method function for Fumili");
         return;
      }
      fMinuitFCN = new ROOT::Minuit2::FumiliFCNAdapter<ROOT::Math::FitMethodFunction> (*fcnfunc, fDim, ErrorDef() );
   }
}
 
void Minuit2Minimizer::SetFunction(const  ROOT::Math::IMultiGradFunction & func) {
   // set function to be minimized
   fDim = func.NDim();
   if (fMinuitFCN) delete fMinuitFCN;
   if (!fUseFumili) {
      fMinuitFCN = new ROOT::Minuit2::FCNGradAdapter<ROOT::Math::IMultiGradFunction> (func, ErrorDef() );
   }
   else {
      // for Fumili the fit method function interface is required
      const ROOT::Math::FitMethodGradFunction * fcnfunc = dynamic_cast<const ROOT::Math::FitMethodGradFunction*>(&func);
      if (!fcnfunc) {
         MN_ERROR_MSG("Minuit2Minimizer: Wrong Fit method function for Fumili");
         return;
      }
      fMinuitFCN = new ROOT::Minuit2::FumiliFCNAdapter<ROOT::Math::FitMethodGradFunction> (*fcnfunc, fDim, ErrorDef() );
   }
}
 
bool Minuit2Minimizer::Minimize() {
   // perform the minimization
   // store a copy of FunctionMinimum
   if (!fMinuitFCN) {
      MN_ERROR_MSG2("Minuit2Minimizer::Minimize","FCN function has not been set");
      return false;
  }
 
   assert(GetMinimizer() != 0 );
 
   // delete result of previous minimization
   if (fMinimum) delete fMinimum;
   fMinimum = 0;
 
 
   int maxfcn = MaxFunctionCalls();
   double tol = Tolerance();
   int strategyLevel = Strategy();
   fMinuitFCN->SetErrorDef(ErrorDef() );
 
   int printLevel = PrintLevel();
   if (printLevel >=1) {
      // print the real number of maxfcn used (defined in ModularFuncitonMinimizer)
      int maxfcn_used = maxfcn;
      if (maxfcn_used == 0) {
         int nvar = fState.VariableParameters();
         maxfcn_used = 200 + 100*nvar + 5*nvar*nvar;
      }
      std::cout << "Minuit2Minimizer: Minimize with max-calls " << maxfcn_used
                << " convergence for edm < " << tol << " strategy "
                << strategyLevel << std::endl;
   }
 
   // internal minuit messages
   MnPrint::SetLevel(printLevel );
   fMinimizer->Builder().SetPrintLevel(printLevel);
 
   // switch off Minuit2 printing
   int prev_level = (printLevel <= 0 ) ?   TurnOffPrintInfoLevel() : -2;
 
   // set the precision if needed
   if (Precision() > 0) fState.SetPrecision(Precision());
 
   // set strategy and add extra options if needed
   ROOT::Minuit2::MnStrategy strategy(strategyLevel);
   ROOT::Math::IOptions * minuit2Opt = ROOT::Math::MinimizerOptions::FindDefault("Minuit2");
   if (minuit2Opt) {
      // set extra  options
      int nGradCycles = strategy.GradientNCycles();
      int nHessCycles = strategy.HessianNCycles();
      int nHessGradCycles = strategy.HessianGradientNCycles();
 
      double gradTol =  strategy.GradientTolerance();
      double gradStepTol = strategy.GradientStepTolerance();
      double hessStepTol = strategy.HessianStepTolerance();
      double hessG2Tol = strategy.HessianG2Tolerance();
 
      minuit2Opt->GetValue("GradientNCycles",nGradCycles);
      minuit2Opt->GetValue("HessianNCycles",nHessCycles);
      minuit2Opt->GetValue("HessianGradientNCycles",nHessGradCycles);
 
      minuit2Opt->GetValue("GradientTolerance",gradTol);
      minuit2Opt->GetValue("GradientStepTolerance",gradStepTol);
      minuit2Opt->GetValue("HessianStepTolerance",hessStepTol);
      minuit2Opt->GetValue("HessianG2Tolerance",hessG2Tol);
 
      strategy.SetGradientNCycles(nGradCycles);
      strategy.SetHessianNCycles(nHessCycles);
      strategy.SetHessianGradientNCycles(nHessGradCycles);
 
      strategy.SetGradientTolerance(gradTol);
      strategy.SetGradientStepTolerance(gradStepTol);
      strategy.SetHessianStepTolerance(hessStepTol);
      strategy.SetHessianG2Tolerance(hessStepTol);
 
      int storageLevel = 1;
      bool ret = minuit2Opt->GetValue("StorageLevel",storageLevel);
      if (ret) SetStorageLevel(storageLevel);
 
      if (printLevel > 0) {
         std::cout << "Minuit2Minimizer::Minuit  - Changing default options" << std::endl;
         minuit2Opt->Print();
      }
 
 
   }
 
   // set a minimizer tracer object (default for printlevel=10, from gROOT for printLevel=11)
   // use some special print levels
   MnTraceObject * traceObj = 0;
#ifdef USE_ROOT_ERROR
   if (printLevel == 10 && gROOT) {
      TObject * obj = gROOT->FindObject("Minuit2TraceObject");
      traceObj = dynamic_cast<ROOT::Minuit2::MnTraceObject*>(obj);
      if (traceObj) {
         // need to remove from the list
         gROOT->Remove(obj);
      }
   }
   if (printLevel == 20 || printLevel == 30 || printLevel == 40 || (printLevel >= 20000 && printLevel < 30000) ) {
      int parNumber = printLevel-20000;
      if (printLevel == 20) parNumber = -1;
      if (printLevel == 30) parNumber = -2;
      if (printLevel == 40) parNumber = 0;
      traceObj = new TMinuit2TraceObject(parNumber);
   }
#endif
   if (printLevel == 100 || (printLevel >= 10000 && printLevel < 20000)) {
      int parNumber = printLevel-10000;
      traceObj = new MnTraceObject(parNumber);
   }
   if (traceObj) {
      traceObj->Init(fState);
      SetTraceObject(*traceObj);
   }
 
   const ROOT::Minuit2::FCNGradientBase * gradFCN = dynamic_cast<const ROOT::Minuit2::FCNGradientBase *>( fMinuitFCN );
   if ( gradFCN != 0) {
      // use gradient
      //SetPrintLevel(3);
      ROOT::Minuit2::FunctionMinimum min =  GetMinimizer()->Minimize(*gradFCN, fState, strategy, maxfcn, tol);
      fMinimum = new ROOT::Minuit2::FunctionMinimum (min);
   }
   else {
      ROOT::Minuit2::FunctionMinimum min = GetMinimizer()->Minimize(*GetFCN(), fState, strategy, maxfcn, tol);
      fMinimum = new ROOT::Minuit2::FunctionMinimum (min);
   }
 
   // check if Hesse needs to be run
   if (fMinimum->IsValid() && IsValidError() && fMinimum->State().Error().Dcovar() != 0 ) {
      // run Hesse (Hesse will add results in the last state of fMinimum
      ROOT::Minuit2::MnHesse hesse(strategy );
      hesse( *fMinuitFCN, *fMinimum, maxfcn);
   }
 
   // -2 is the highest low invalid value for gErrorIgnoreLevel
   if (prev_level > -2) RestoreGlobalPrintLevel(prev_level);
 
   // copy minimum state (parameter values and errors)
   fState = fMinimum->UserState();
   bool ok =  ExamineMinimum(*fMinimum);
   //fMinimum = 0;
 
   // delete trace object if it was constructed
   if (traceObj) {       delete traceObj;   }
   return ok;
}
 
bool  Minuit2Minimizer::ExamineMinimum(const ROOT::Minuit2::FunctionMinimum & min) {
   /// study the function minimum
 
   // debug ( print all the states)
   int debugLevel = PrintLevel();
   if (debugLevel >= 3) {
 
      const std::vector<ROOT::Minuit2::MinimumState>& iterationStates = min.States();
      std::cout << "Number of iterations " << iterationStates.size() << std::endl;
      for (unsigned int i = 0; i <  iterationStates.size(); ++i) {
         //std::cout << iterationStates[i] << std::endl;
         const ROOT::Minuit2::MinimumState & st =  iterationStates[i];
         std::cout << "----------> Iteration " << i << std::endl;
         int pr = std::cout.precision(12);
         std::cout << "            FVAL = " << st.Fval() << " Edm = " << st.Edm() << " Nfcn = " << st.NFcn() << std::endl;
         std::cout.precision(pr);
         if (st.HasCovariance() )
             std::cout << "            Error matrix change = " << st.Error().Dcovar() << std::endl;
         if (st.HasParameters() ) {
            std::cout << "            Parameters : ";
            // need to transform from internal to external
            for (int j = 0; j < st.size() ; ++j) std::cout << " p" << j << " = " << fState.Int2ext( j, st.Vec()(j) );
            std::cout << std::endl;
         }
      }
   }
 
   fStatus = 0;
   std::string txt;
   if (!min.HasPosDefCovar() ) {
      // this happens normally when Hesse failed
      // it can happen in case MnSeed failed (see ROOT-9522)
      txt = "Covar is not pos def";
      fStatus = 5;
   }
   if (min.HasMadePosDefCovar() ) {
      txt = "Covar was made pos def";
      fStatus = 1;
   }
   if (min.HesseFailed() ) {
      txt = "Hesse is not valid";
      fStatus = 2;
   }
   if (min.IsAboveMaxEdm() ) {
      txt = "Edm is above max";
      fStatus = 3;
   }
   if (min.HasReachedCallLimit() ) {
      txt = "Reached call limit";
      fStatus = 4;
   }
 
 
   bool validMinimum = min.IsValid();
   if (validMinimum) {
      // print a warning message in case something is not ok
      if (fStatus != 0 && debugLevel > 0)  MN_INFO_MSG2("Minuit2Minimizer::Minimize",txt);
   }
   else {
      // minimum is not valid when state is not valid and edm is over max or has passed call limits
      if (fStatus == 0) {
         // this should not happen
         txt = "unknown failure";
         fStatus = 6;
      }
      std::string msg = "Minimization did NOT converge, " + txt;
      MN_INFO_MSG2("Minuit2Minimizer::Minimize",msg);
   }
 
   if (debugLevel >= 1) PrintResults();
 
   // set the minimum values in the fValues vector
   const std::vector<MinuitParameter> & paramsObj = fState.MinuitParameters();
   if (paramsObj.size() == 0) return 0;
   assert(fDim == paramsObj.size());
   // re-size vector if it has changed after a new minimization
   if (fValues.size() != fDim) fValues.resize(fDim);
   for (unsigned int i = 0; i < fDim; ++i) {
      fValues[i] = paramsObj[i].Value();
   }
 
   return validMinimum;
}
 
 
void Minuit2Minimizer::PrintResults() {
   // print results of minimization
   if (!fMinimum) return;
   if (fMinimum->IsValid() ) {
      // valid minimum
      std::cout << "Minuit2Minimizer : Valid minimum - status = " << fStatus  << std::endl;
      int pr = std::cout.precision(18);
      std::cout << "FVAL  = " << fState.Fval() << std::endl;
      std::cout << "Edm   = " << fState.Edm() << std::endl;
      std::cout.precision(pr);
      std::cout << "Nfcn  = " << fState.NFcn() << std::endl;
      for (unsigned int i = 0; i < fState.MinuitParameters().size(); ++i) {
         const MinuitParameter & par = fState.Parameter(i);
         std::cout << par.Name() << "\t  = " << par.Value() << "\t ";
         if (par.IsFixed() )      std::cout << "(fixed)" << std::endl;
         else if (par.IsConst() ) std::cout << "(const)" << std::endl;
         else if (par.HasLimits() )
            std::cout << "+/-  " << par.Error() << "\t(limited)"<< std::endl;
         else
            std::cout << "+/-  " << par.Error() << std::endl;
      }
   }
   else {
      std::cout << "Minuit2Minimizer : Invalid Minimum - status = " << fStatus << std::endl;
      std::cout << "FVAL  = " << fState.Fval() << std::endl;
      std::cout << "Edm   = " << fState.Edm() << std::endl;
      std::cout << "Nfcn  = " << fState.NFcn() << std::endl;
   }
}
 
const double * Minuit2Minimizer::Errors() const {
   // return error at minimum (set to zero for fixed and constant params)
   const std::vector<MinuitParameter> & paramsObj = fState.MinuitParameters();
   if (paramsObj.size() == 0) return 0;
   assert(fDim == paramsObj.size());
   // be careful for multiple calls of this function. I will redo an allocation here
   // only when size of vectors has changed (e.g. after a new minimization)
   if (fErrors.size() != fDim)   fErrors.resize( fDim );
   for (unsigned int i = 0; i < fDim; ++i) {
      const MinuitParameter & par = paramsObj[i];
      if (par.IsFixed() || par.IsConst() )
         fErrors[i] = 0;
      else
         fErrors[i] = par.Error();
   }
 
   return  &fErrors.front();
}
 
 
double Minuit2Minimizer::CovMatrix(unsigned int i, unsigned int j) const {
   // get value of covariance matrices (transform from external to internal indices)
   if ( i >= fDim || j >= fDim) return 0;
   if (  !fState.HasCovariance()    ) return 0; // no info available when minimization has failed
   if (fState.Parameter(i).IsFixed() || fState.Parameter(i).IsConst() ) return 0;
   if (fState.Parameter(j).IsFixed() || fState.Parameter(j).IsConst() ) return 0;
   unsigned int k = fState.IntOfExt(i);
   unsigned int l = fState.IntOfExt(j);
   return fState.Covariance()(k,l);
}
 
bool Minuit2Minimizer::GetCovMatrix(double * cov) const {
   // get value of covariance matrices
   if ( !fState.HasCovariance()    ) return false; // no info available when minimization has failed
   for (unsigned int i = 0; i < fDim; ++i) {
      if (fState.Parameter(i).IsFixed() || fState.Parameter(i).IsConst() ) {
         for (unsigned int j = 0; j < fDim; ++j) { cov[i*fDim + j] = 0; }
      }
      else
      {
         unsigned int l = fState.IntOfExt(i);
         for (unsigned int j = 0; j < fDim; ++j) {
            // could probably speed up this loop (if needed)
            int k = i*fDim + j;
            if (fState.Parameter(j).IsFixed() || fState.Parameter(j).IsConst() )
               cov[k] = 0;
            else {
            // need to transform from external to internal indices)
            // for taking care of the removed fixed row/columns in the Minuit2 representation
               unsigned int m = fState.IntOfExt(j);
               cov[k] =  fState.Covariance()(l,m);
            }
         }
      }
   }
   return true;
}
 
bool Minuit2Minimizer::GetHessianMatrix(double * hess) const {
   // get value of Hessian matrix
   // this is the second derivative matrices
   if (  !fState.HasCovariance()    ) return false; // no info available when minimization has failed
   for (unsigned int i = 0; i < fDim; ++i) {
      if (fState.Parameter(i).IsFixed() || fState.Parameter(i).IsConst() ) {
         for (unsigned int j = 0; j < fDim; ++j) { hess[i*fDim + j] = 0; }
      }
      else {
         unsigned int l = fState.IntOfExt(i);
         for (unsigned int j = 0; j < fDim; ++j) {
            // could probably speed up this loop (if needed)
            int k = i*fDim + j;
            if (fState.Parameter(j).IsFixed() || fState.Parameter(j).IsConst() )
               hess[k] = 0;
            else {
               // need to transform from external to internal indices)
               // for taking care of the removed fixed row/columns in the Minuit2 representation
               unsigned int m = fState.IntOfExt(j);
               hess[k] =  fState.Hessian()(l,m);
            }
         }
      }
   }
 
   return true;
}
 
 
double Minuit2Minimizer::Correlation(unsigned int i, unsigned int j) const {
   // get correlation between parameter i and j
   if ( i >= fDim || j >= fDim) return 0;
   if (  !fState.HasCovariance()    ) return 0; // no info available when minimization has failed
   if (fState.Parameter(i).IsFixed() || fState.Parameter(i).IsConst() ) return 0;
   if (fState.Parameter(j).IsFixed() || fState.Parameter(j).IsConst() ) return 0;
   unsigned int k = fState.IntOfExt(i);
   unsigned int l = fState.IntOfExt(j);
   double cij =  fState.IntCovariance()(k,l);
   double tmp =  std::sqrt( std::abs ( fState.IntCovariance()(k,k) * fState.IntCovariance()(l,l) ) );
   if (tmp > 0 ) return cij/tmp;
   return 0;
}
 
double Minuit2Minimizer::GlobalCC(unsigned int i) const {
   // get global correlation coefficient for the parameter i. This is a number between zero and one which gives
   // the correlation between the i-th parameter  and that linear combination of all other parameters which
   // is most strongly correlated with i.
 
   if ( i >= fDim ) return 0;
    // no info available when minimization has failed or has some problems
   if ( !fState.HasGlobalCC()    ) return 0;
   if (fState.Parameter(i).IsFixed() || fState.Parameter(i).IsConst() ) return 0;
   unsigned int k = fState.IntOfExt(i);
   return fState.GlobalCC().GlobalCC()[k];
}
 
 
bool Minuit2Minimizer::GetMinosError(unsigned int i, double & errLow, double & errUp, int runopt) {
   // return the minos error for parameter i
   // if a minimum does not exist an error is returned
   // runopt is a flag which specifies if only lower or upper error needs to be run
   // if runopt = 0 both, = 1 only lower, + 2 only upper errors
   errLow = 0; errUp = 0;
   
 
   assert( fMinuitFCN );
 
   // need to know if parameter is const or fixed
   if ( fState.Parameter(i).IsConst() || fState.Parameter(i).IsFixed() ) {
      return false;
   }
 
 
   // to run minos I need function minimum class
   // redo minimization from current state
//    ROOT::Minuit2::FunctionMinimum min =
//       GetMinimizer()->Minimize(*GetFCN(),fState, ROOT::Minuit2::MnStrategy(strategy), MaxFunctionCalls(), Tolerance());
//    fState = min.UserState();
   if (fMinimum == 0) {
      MN_ERROR_MSG("Minuit2Minimizer::GetMinosErrors:  failed - no function minimum existing");
      return false;
   }
 
   if (!fMinimum->IsValid() ) {
      MN_ERROR_MSG("Minuit2Minimizer::MINOS failed due to invalid function minimum");
      return false;
   }
 
   fMinuitFCN->SetErrorDef(ErrorDef() );
   // if error def has been changed update it in FunctionMinimum
   if (ErrorDef() != fMinimum->Up() )
      fMinimum->SetErrorDef(ErrorDef() );
 
   int mstatus = RunMinosError(i,errLow, errUp, runopt);
 
   // run again the Minimization in case of a new minimum
   // bit 8 is set
   if ((mstatus & 8) != 0) {
     
      MN_INFO_MSG2("Minuit2Minimizer::GetMinosError",
                   "Found a new minimum: run again the Minimization  starting from the new  point ");
      if (PrintLevel() > 1) {
         std::cout << "New minimum point found by MINOS: " << std::endl;
         std::cout << "FVAL  = " << fState.Fval() << std::endl;
         for (auto & par : fState.MinuitParameters() ) {
            std::cout << par.Name() << "\t  = " << par.Value() << std::endl;
         }
      }
      // release parameter that was fixed in the returned state from Minos
      ReleaseVariable(i);
      bool ok = Minimize();
      if (!ok)  return false;
      // run again Minos from new Minimum (also lower error needs to be re-computed)
      MN_INFO_MSG2("Minuit2Minimizer::GetMinosError", "Run now again Minos from the new found Minimum");
      mstatus = RunMinosError(i, errLow, errUp, runopt);
 
      // do not reset new minimum bit to flag for other parameters
      mstatus |= 8; 
   }
 
   fStatus += 10*mstatus;
   fMinosStatus = mstatus; 
 
   bool isValid =  ((mstatus & 1) == 0) && ((mstatus & 2) == 0);    
   return isValid;
}
 
 
int Minuit2Minimizer::RunMinosError(unsigned int i, double & errLow, double & errUp, int runopt) {
   // switch off Minuit2 printing
 
   bool runLower = runopt != 2;
   bool runUpper = runopt != 1;
 
   int debugLevel = PrintLevel();
   // internal minuit messages
   MnPrint::SetLevel( debugLevel );
 
   int prev_level = (PrintLevel() <= 0 ) ?   TurnOffPrintInfoLevel() : -2;
 
   // set the precision if needed
   if (Precision() > 0) fState.SetPrecision(Precision());
 
 
   ROOT::Minuit2::MnMinos minos( *fMinuitFCN, *fMinimum);
 
   // run MnCross
   MnCross low;
   MnCross up;
   int maxfcn = MaxFunctionCalls();
   double tol = Tolerance();
 
   const char * par_name = fState.Name(i);
 
   // now input tolerance for migrad calls inside Minos (MnFunctionCross)
   // before it was fixed to 0.05
   // cut off too small tolerance (they are not needed)
   tol = std::max(tol, 0.01);
 
   
   // get the real number of maxfcn used (defined in MnMinos) to be printed 
   int maxfcn_used = maxfcn;
   if (maxfcn_used == 0) {
      int nvar = fState.VariableParameters();
      maxfcn_used = 2*(nvar+1)*(200 + 100*nvar + 5*nvar*nvar);
   }
 
   if (runLower) {
      if (debugLevel >=1) {
         std::cout << "******************************************************************************************************\n";
         std::cout << "Minuit2Minimizer::GetMinosError - Run MINOS LOWER error for parameter #" << i << " : " << par_name
                << " using max-calls " << maxfcn_used << ", tolerance " << tol << std::endl;
      }
      low = minos.Loval(i, maxfcn, tol);
   }
   if (runUpper) {
      if (debugLevel >=1) {
         std::cout << "******************************************************************************************************\n";
         std::cout << "Minuit2Minimizer::GetMinosError - Run MINOS UPPER error for parameter #" << i << " : " << par_name
                << " using max-calls " << maxfcn_used << ", tolerance " << tol << std::endl;
      }
      up  = minos.Upval(i,maxfcn,tol);
   }
 
   ROOT::Minuit2::MinosError me(i, fMinimum->UserState().Value(i),low, up);
 
   if (prev_level > -2) RestoreGlobalPrintLevel(prev_level);
 
   // debug result of Minos
   // print error message in Minos
   // Note that the only invalid condition can happen when the (npar-1) minimization fails
   // The error is also invalid when the maximum number of calls is reached or a new function minimum is found
   // in case of the parameter at the limit the error is not invalid.
   // When the error is invalid the returned error is the Hessian error.
 
   if (debugLevel > 0) {
      if (runLower) {
         if (!me.LowerValid() )
            std::cout << "Minos:  Invalid lower error for parameter " << par_name << std::endl;
         if(me.AtLowerLimit())
            std::cout << "Minos:  Parameter : " << par_name << "  is at Lower limit; error is " << me.Lower()
                      << std::endl;
         if(me.AtLowerMaxFcn())
            std::cout << "Minos:  Maximum number of function calls exceeded when running for lower error for parameter " << par_name << std::endl;
         if(me.LowerNewMin() )
            std::cout << "Minos:  New Minimum found while running Minos for lower error for parameter " << par_name << std::endl;
 
         if (debugLevel >= 1 && me.LowerValid())
            std::cout << "Minos: Lower error for parameter " << par_name << "  :  " << me.Lower() << std::endl;
      }
      if (runUpper) {
         if (!me.UpperValid() )
            std::cout << "Minos:  Invalid upper error for parameter " << par_name << std::endl;
         if(me.AtUpperLimit())
            std::cout << "Minos:  Parameter " << par_name << " is at Upper limit; error is "<< me.Upper() << std::endl;
         if(me.AtUpperMaxFcn())
            std::cout << "Minos:  Maximum number of function calls exceeded when running for upper error for parameter " << par_name << std::endl;
         if(me.UpperNewMin() )
            std::cout << "Minos:  New Minimum found while running Minos for upper error for parameter " << par_name << std::endl;
 
         if (debugLevel >= 1 && me.UpperValid())
            std::cout << "Minos: Upper error for parameter " << par_name << "  :  " << me.Upper() << std::endl;
      }
   }
 
   bool lowerInvalid =  (runLower && !me.LowerValid() );
   bool upperInvalid =  (runUpper && !me.UpperValid() );
   // print message in case of invalid error also in printLevel0
   if (lowerInvalid) {
      std::string msg_txt = std::string("Invalid lower error for parameter ") + std::string(fMinimum->UserState().Name(i));
      MN_INFO_MSG2("Minuit2Minimizer::GetMinosErrors", msg_txt);
   }
   if (upperInvalid) {
      std::string msg_txt = std::string("Invalid upper error for parameter ") + std::string(fMinimum->UserState().Name(i));
      MN_INFO_MSG2("Minuit2Minimizer::GetMinosErrors", msg_txt);
   }
   // print also case it is lower/upper limit
   if (me.AtLowerLimit()) {
      std::string msg_txt = std::string("Lower error for parameter ") + std::string(fMinimum->UserState().Name(i)) +
                            std::string(" is at the Lower limit !");
      MN_INFO_MSG2("Minuit2Minimizer::GetMinosErrors", msg_txt);
   }
   if (me.AtUpperLimit()) {
      std::string msg_txt = std::string("Upper error for parameter ") + std::string(fMinimum->UserState().Name(i)) +
                            std::string(" is at the Upper limit !");
      MN_INFO_MSG2("Minuit2Minimizer::GetMinosErrors", msg_txt);
   }
 
   int mstatus = 0;
   if (lowerInvalid || upperInvalid ) {
      // set status accroding to bit
      // bit 1:  lower invalid Minos errors
      // bit 2:  upper invalid Minos error
      // bit 3:   invalid because max FCN
      // bit 4 : invalid because a new minimum has been found
      if (lowerInvalid) {
         mstatus |= 1;
         if (me.AtLowerMaxFcn() ) mstatus |= 4;
         if (me.LowerNewMin() ) mstatus |= 8;
      }
      if(upperInvalid) {
         mstatus |= 2;
         if (me.AtUpperMaxFcn() ) mstatus |= 4;
         if (me.UpperNewMin() ) mstatus |= 8;
      }
   }
   // case upper/lower limit
   if (me.AtUpperLimit() || me.AtLowerLimit())
      mstatus |= 16; 
 
   
 
   if (runLower) errLow = me.Lower();
   if (runUpper) errUp = me.Upper();
 
   // in case of new minimum found update also the  minimum state
   if (  ( runLower && me.LowerNewMin()) && (runUpper && me.UpperNewMin() ) ) {
      // take state with lower function value
      fState = (low.State().Fval() < up.State().Fval()) ? low.State() : up.State();
   } else if ( runLower && me.LowerNewMin() ) {
      fState = low.State();
   } else if ( runUpper && me.UpperNewMin() ) {
      fState = up.State();
   }
 
   return mstatus;
 
}
 
 
bool Minuit2Minimizer::Scan(unsigned int ipar, unsigned int & nstep, double * x, double * y, double xmin, double xmax) {
   // scan a parameter (variable) around the minimum value
   // the parameters must have been set before
   // if xmin=0 && xmax == 0  by default scan around 2 sigma of the error
   // if the errors  are also zero then scan from min and max of parameter range
 
   if (!fMinuitFCN) {
      MN_ERROR_MSG2("Minuit2Minimizer::Scan"," Function must be set before using Scan");
      return false;
   }
 
   if ( ipar > fState.MinuitParameters().size() ) {
      MN_ERROR_MSG2("Minuit2Minimizer::Scan"," Invalid number. Minimizer variables must be set before using Scan");
      return false;
   }
 
   // switch off Minuit2 printing
   int prev_level = (PrintLevel() <= 0 ) ?   TurnOffPrintInfoLevel() : -2;
 
   MnPrint::SetLevel( PrintLevel() );
 
 
   // set the precision if needed
   if (Precision() > 0) fState.SetPrecision(Precision());
 
   MnParameterScan scan( *fMinuitFCN, fState.Parameters() );
   double amin = scan.Fval(); // fcn value of the function before scan
 
   // first value is param value
   std::vector<std::pair<double, double> > result = scan(ipar, nstep-1, xmin, xmax);
 
   if (prev_level > -2) RestoreGlobalPrintLevel(prev_level);
 
   if (result.size() != nstep) {
      MN_ERROR_MSG2("Minuit2Minimizer::Scan"," Invalid result from MnParameterScan");
      return false;
   }
   // sort also the returned points in x
   std::sort(result.begin(), result.end() );
 
 
   for (unsigned int i = 0; i < nstep; ++i ) {
      x[i] = result[i].first;
      y[i] = result[i].second;
   }
 
   // what to do if a new minimum has been found ?
   // use that as new minimum
   if (scan.Fval() < amin ) {
      MN_INFO_MSG2("Minuit2Minimizer::Scan","A new minimum has been found");
      fState.SetValue(ipar, scan.Parameters().Value(ipar) );
 
   }
 
 
   return true;
}
 
bool Minuit2Minimizer::Contour(unsigned int ipar, unsigned int jpar, unsigned int & npoints, double * x, double * y) {
   // contour plot for parameter i and j
   // need a valid FunctionMinimum otherwise exits
   if (fMinimum == 0) {
      MN_ERROR_MSG2("Minuit2Minimizer::Contour"," no function minimum existing. Must minimize function before");
      return false;
   }
 
   if (!fMinimum->IsValid() ) {
      MN_ERROR_MSG2("Minuit2Minimizer::Contour","Invalid function minimum");
      return false;
   }
   assert(fMinuitFCN);
 
   fMinuitFCN->SetErrorDef(ErrorDef() );
   // if error def has been changed update it in FunctionMinimum
   if (ErrorDef() != fMinimum->Up() ) {
      fMinimum->SetErrorDef(ErrorDef() );
   }
 
   if ( PrintLevel() >= 1 )
      MN_INFO_VAL2("Minuit2Minimizer::Contour - computing contours - ",ErrorDef());
 
   // switch off Minuit2 printing (for level of  0,1)
   int prev_level = (PrintLevel() <= 1 ) ?   TurnOffPrintInfoLevel() : -2;
 
   // decrease print-level to have too many messages
   MnPrint::SetLevel( PrintLevel() -1 );
 
   // set the precision if needed
   if (Precision() > 0) fState.SetPrecision(Precision());
 
   // eventually one should specify tolerance in contours
   MnContours contour(*fMinuitFCN, *fMinimum, Strategy() );
 
   if (prev_level > -2) RestoreGlobalPrintLevel(prev_level);
 
   // compute the contour
   std::vector<std::pair<double,double> >  result = contour(ipar,jpar, npoints);
   if (result.size() != npoints) {
      MN_ERROR_MSG2("Minuit2Minimizer::Contour"," Invalid result from MnContours");
      return false;
   }
   for (unsigned int i = 0; i < npoints; ++i ) {
      x[i] = result[i].first;
      y[i] = result[i].second;
   }
 
   // restore print level
   MnPrint::SetLevel( PrintLevel() );
 
 
   return true;
 
 
}
 
bool Minuit2Minimizer::Hesse( ) {
    // find Hessian (full second derivative calculations)
   // the contained state will be updated with the Hessian result
   // in case a function minimum exists and is valid the result will be
   // appended in the function minimum
 
   if (!fMinuitFCN) {
      MN_ERROR_MSG2("Minuit2Minimizer::Hesse","FCN function has not been set");
      return false;
   }
 
   int strategy = Strategy();
   int maxfcn = MaxFunctionCalls();
 
   // switch off Minuit2 printing
   int prev_level = (PrintLevel() <= 0 ) ?   TurnOffPrintInfoLevel() : -2;
 
   MnPrint::SetLevel( PrintLevel() );
 
   // set the precision if needed
   if (Precision() > 0) fState.SetPrecision(Precision());
 
   ROOT::Minuit2::MnHesse hesse( strategy );
 
   if (PrintLevel() >= 1)
      std::cout << "Minuit2Minimizer::Hesse using max-calls " << maxfcn << std::endl;
 
   // case when function minimum exists
   if (fMinimum) {
 
      // if (PrintLevel() >= 3) {
      //    std::cout << "Minuit2Minimizer::Hesse  - State before running Hesse " << std::endl;
      //    std::cout << fState << std::endl;
      // }
 
      // run hesse and function minimum will be updated with Hesse result
      hesse( *fMinuitFCN, *fMinimum, maxfcn );
      // update user state
      fState = fMinimum->UserState();
   }
 
   else {
      // run Hesse on point stored in current state (independent of function minimum validity)
      // (x == 0)
      fState = hesse( *fMinuitFCN, fState, maxfcn);
   }
 
   if (prev_level > -2) RestoreGlobalPrintLevel(prev_level);
 
   if (PrintLevel() >= 3) {
      std::cout << "Minuit2Minimizer::Hesse  - State returned from Hesse " << std::endl;
      std::cout << fState << std::endl;
   }
 
   int covStatus = fState.CovarianceStatus();
   std::string covStatusType = "not valid";
   if (covStatus == 1) covStatusType = "approximate";
   if (covStatus == 2) covStatusType = "full but made positive defined";
   if (covStatus == 3) covStatusType = "accurate";
 
   if (!fState.HasCovariance() ) {
      // if false means error is not valid and this is due to a failure in Hesse
      // update minimizer error status
      int hstatus = 4;
      // information on error state can be retrieved only if fMinimum is available
      if (fMinimum) {
         if (fMinimum->Error().HesseFailed() ) hstatus = 1;
         if (fMinimum->Error().InvertFailed() ) hstatus = 2;
         else if (!(fMinimum->Error().IsPosDef()) ) hstatus = 3;
      }
      if (PrintLevel() > 0) {
         std::string msg = "Hesse failed - matrix is " + covStatusType;
         MN_INFO_MSG2("Minuit2Minimizer::Hesse",msg);
         MN_INFO_VAL2("MInuit2Minimizer::Hesse",hstatus);
      }
      fStatus += 100*hstatus;
      return false;
   }
   if (PrintLevel() > 0) {
      std::string msg = "Hesse is valid - matrix is " + covStatusType;
      MN_INFO_MSG2("Minuit2Minimizer::Hesse",msg);
   }
 
   return true;
}
 
int Minuit2Minimizer::CovMatrixStatus() const {
   // return status of covariance matrix
   //-1 - not available (inversion failed or Hesse failed)
   // 0 - available but not positive defined
   // 1 - covariance only approximate
   // 2 full matrix but forced pos def
   // 3 full accurate matrix
 
   if (fMinimum) {
      // case a function minimum  is available
      if (fMinimum->HasAccurateCovar() ) return 3;
      else if (fMinimum->HasMadePosDefCovar() ) return 2;
      else if (fMinimum->HasValidCovariance() ) return 1;
      else if (fMinimum->HasCovariance() ) return 0;
      return -1;
   }
   else {
      // case fMinimum is not available - use state information
      return fState.CovarianceStatus();
   }
   return 0;
}
 
void Minuit2Minimizer::SetTraceObject(MnTraceObject & obj) {
   // set trace object
   if (!fMinimizer) return;
   fMinimizer->Builder().SetTraceObject(obj);
}
 
void Minuit2Minimizer::SetStorageLevel(int level) {
   // set storage level
   if (!fMinimizer) return;
   fMinimizer->Builder().SetStorageLevel(level);
 }
 
} // end namespace Minuit2
 
} // end namespace ROOT