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 "TError.h"
#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)
   : fDim(0), fMinimizer(nullptr), fMinuitFCN(nullptr), fMinimum(nullptr)
{
   // Default constructor implementation depending on minimizer type
   SetMinimizerType(type);
}
 
Minuit2Minimizer::Minuit2Minimizer(const char *type) : fDim(0), fMinimizer(nullptr), fMinuitFCN(nullptr), fMinimum(nullptr)
{
   // 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" || algoname == "fumili2")
      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;
}
 
void Minuit2Minimizer::Clear()
{
   // delete the state in case of consecutive minimizations
   fState = MnUserParameterState();
   // clear also the function minimum
   if (fMinimum)
      delete fMinimum;
   fMinimum = nullptr;
}
 
// 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;
   MnPrint print("Minuit2Minimizer::SetVariable", PrintLevel());
 
   if (step <= 0) {
      print.Info("Parameter", name, "has zero or invalid step size - consider it as constant");
      fState.Add(name, val);
   } else
      fState.Add(name, val, step);
 
   unsigned int minuit2Index = fState.Index(name);
   if (minuit2Index != ivar) {
      print.Warn("Wrong index", minuit2Index, "used for the variable", name);
      ivar = minuit2Index;
      return false;
   }
   fState.RemoveLimits(ivar);
 
   return true;
}
 
/** set initial second derivatives
 */
bool Minuit2Minimizer::SetCovarianceDiag(std::span<const double> d2, unsigned int n)
{
   MnPrint print("Minuit2Minimizer::SetCovarianceDiag", PrintLevel());
 
   std::vector<double> cov(n * (n + 1) / 2);
 
   for (unsigned int i = 0; i < n; i++) {
      for (unsigned int j = i; j < n; j++)
         cov[i + j * (j + 1) / 2] = (i == j) ? d2[i] : 0.;
   }
 
   return Minuit2Minimizer::SetCovariance(cov, n);
}
 
bool Minuit2Minimizer::SetCovariance(std::span<const double> cov, unsigned int nrow)
{
   MnPrint print("Minuit2Minimizer::SetCovariance", PrintLevel());
 
   fState.AddCovariance({cov, nrow});
 
   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);
   }
   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()) {
      MnPrint print("Minuit2Minimizer", PrintLevel());
      print.Error("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()) {
      MnPrint print("Minuit2Minimizer", PrintLevel());
      print.Error("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();
   const bool hasGrad = func.HasGradient();
   if (!fUseFumili) {
      fMinuitFCN = hasGrad ? static_cast<ROOT::Minuit2::FCNBase *>(new ROOT::Minuit2::FCNGradAdapter<ROOT::Math::IMultiGradFunction>(dynamic_cast<ROOT::Math::IMultiGradFunction const&>(func), ErrorDef()))
                           : static_cast<ROOT::Minuit2::FCNBase *>(new ROOT::Minuit2::FCNAdapter<ROOT::Math::IMultiGenFunction>(func, ErrorDef()));
   } else {
      if(hasGrad) {
         // for Fumili the fit method function interface is required
         auto fcnfunc = dynamic_cast<const ROOT::Math::FitMethodGradFunction *>(&func);
         if (!fcnfunc) {
            MnPrint print("Minuit2Minimizer", PrintLevel());
            print.Error("Wrong Fit method function for Fumili");
            return;
         }
         fMinuitFCN = new ROOT::Minuit2::FumiliFCNAdapter<ROOT::Math::FitMethodGradFunction>(*fcnfunc, fDim, ErrorDef());
      } else {
         // for Fumili the fit method function interface is required
         auto fcnfunc = dynamic_cast<const ROOT::Math::FitMethodFunction *>(&func);
         if (!fcnfunc) {
            MnPrint print("Minuit2Minimizer", PrintLevel());
            print.Error("Wrong Fit method function for Fumili");
            return;
         }
         fMinuitFCN = new ROOT::Minuit2::FumiliFCNAdapter<ROOT::Math::FitMethodFunction>(*fcnfunc, fDim, ErrorDef());
      }
   }
}
 
void Minuit2Minimizer::SetHessianFunction(std::function<bool(std::span<const double>, double *)> hfunc)
{
   // for Fumili not supported for the time being
   if (fUseFumili) return;
   auto fcn = static_cast<ROOT::Minuit2::FCNGradAdapter<ROOT::Math::IMultiGradFunction> *>(fMinuitFCN);
   if (!fcn) return;
   fcn->SetHessianFunction(hfunc);
}
 
namespace {
 
ROOT::Minuit2::MnStrategy customizedStrategy(unsigned int strategyLevel, ROOT::Math::MinimizerOptions const &options)
{
   ROOT::Minuit2::MnStrategy st{strategyLevel};
   // set strategy and add extra options if needed
   const ROOT::Math::IOptions *minuit2Opt = options.ExtraOptions();
   if (!minuit2Opt) {
      minuit2Opt = ROOT::Math::MinimizerOptions::FindDefault("Minuit2");
   }
   if (!minuit2Opt) {
      return st;
   }
   auto customize = [&minuit2Opt](const char *name, auto val) {
      minuit2Opt->GetValue(name, val);
      return val;
   };
   // set extra  options
   st.SetGradientNCycles(customize("GradientNCycles", int(st.GradientNCycles())));
   st.SetHessianNCycles(customize("HessianNCycles", int(st.HessianNCycles())));
   st.SetHessianGradientNCycles(customize("HessianGradientNCycles", int(st.HessianGradientNCycles())));
 
   st.SetGradientTolerance(customize("GradientTolerance", st.GradientTolerance()));
   st.SetGradientStepTolerance(customize("GradientStepTolerance", st.GradientStepTolerance()));
   st.SetHessianStepTolerance(customize("HessianStepTolerance", st.HessianStepTolerance()));
   st.SetHessianG2Tolerance(customize("HessianG2Tolerance", st.HessianG2Tolerance()));
 
   return st;
}
 
} // namespace
 
bool Minuit2Minimizer::Minimize()
{
   // perform the minimization
   // store a copy of FunctionMinimum
 
   MnPrint print("Minuit2Minimizer::Minimize", PrintLevel());
 
   if (!fMinuitFCN) {
      print.Error("FCN function has not been set");
      return false;
   }
 
   assert(GetMinimizer() != nullptr);
 
   // delete result of previous minimization
   if (fMinimum)
      delete fMinimum;
   fMinimum = nullptr;
 
   const int maxfcn = MaxFunctionCalls();
   const double tol = Tolerance();
   const int strategyLevel = Strategy();
   fMinuitFCN->SetErrorDef(ErrorDef());
 
   const int printLevel = PrintLevel();
   if (PrintLevel() >= 1) {
      // print the real number of maxfcn used (defined in ModularFunctionMinimizer)
      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
   fMinimizer->Builder().SetPrintLevel(printLevel);
 
   // switch off Minuit2 printing
   const int prev_level = (printLevel <= 0) ? TurnOffPrintInfoLevel() : -2;
   const int prevGlobalLevel = MnPrint::SetGlobalLevel(printLevel);
 
   // set the precision if needed
   if (Precision() > 0)
      fState.SetPrecision(Precision());
 
   // add extra options if needed
   const ROOT::Math::IOptions *minuit2Opt = fOptions.ExtraOptions();
   if (!minuit2Opt) {
      minuit2Opt = ROOT::Math::MinimizerOptions::FindDefault("Minuit2");
   }
   if (minuit2Opt) {
      // set extra  options
      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 = nullptr;
#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::MnStrategy strategy = customizedStrategy(strategyLevel, fOptions);
 
   ROOT::Minuit2::FunctionMinimum min = GetMinimizer()->Minimize(*fMinuitFCN, fState, strategy, maxfcn, tol);
   fMinimum = new ROOT::Minuit2::FunctionMinimum(min);
 
   // check if Hesse needs to be run. We do it when is requested (IsValidError() == true , set by SetParabError(true) in fitConfig)
   // (IsValidError() means the flag to get correct error from the Minimizer is set (Minimizer::SetValidError())
   // AND when we have a valid minimum,
   // AND  when the the current covariance matrix is estimated using the iterative approximation (Dcovar != 0 , i.e. Hesse has not computed  before)
   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);
   MnPrint::SetGlobalLevel(prevGlobalLevel);
 
   // 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) {
 
      std::span<const 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;
   }
 
   MnPrint print("Minuit2Minimizer::Minimize", debugLevel);
   bool validMinimum = min.IsValid();
   if (validMinimum) {
      // print a warning message in case something is not ok
      // this for example is case when Covar was made posdef and fStatus=3
      if (fStatus != 0 && debugLevel > 0)
         print.Warn(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;
      }
      print.Warn("Minimization did NOT converge,", txt);
   }
 
   if (debugLevel >= 1)
      PrintResults();
 
   // set the minimum values in the fValues vector
   std::span<const MinuitParameter> paramsObj = fState.MinuitParameters();
   if (paramsObj.empty())
      return false;
   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)
   std::span<const MinuitParameter> paramsObj = fState.MinuitParameters();
   if (paramsObj.empty())
      return nullptr;
   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;
   }
 
   MnPrint print("Minuit2Minimizer::GetMinosError", PrintLevel());
 
   // 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 == nullptr) {
      print.Error("Failed - no function minimum existing");
      return false;
   }
 
   if (!fMinimum->IsValid()) {
      print.Error("Failed - 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) {
      print.Info([&](std::ostream &os) {
         os << "Found a new minimum: run again the Minimization starting from the new point";
         os << "\nFVAL  = " << fState.Fval();
         for (auto &par : fState.MinuitParameters()) {
            os << '\n' << par.Name() << "\t  = " << par.Value();
         }
      });
      // 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)
      print.Info("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)
{
 
   bool runLower = runopt != 2;
   bool runUpper = runopt != 1;
 
   const int debugLevel = PrintLevel();
   // switch off Minuit2 printing
   const int prev_level = (debugLevel <= 0) ? TurnOffPrintInfoLevel() : -2;
   const int prevGlobalLevel = MnPrint::SetGlobalLevel(debugLevel);
 
   // 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);
 
   // restore global print level
   if (prev_level > -2)
      RestoreGlobalPrintLevel(prev_level);
   MnPrint::SetGlobalLevel(prevGlobalLevel);
 
   // 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;
      }
   }
 
   MnPrint print("RunMinosError", PrintLevel());
   bool lowerInvalid = (runLower && !me.LowerValid());
   bool upperInvalid = (runUpper && !me.UpperValid());
   // print message in case of invalid error also in printLevel0
   if (lowerInvalid) {
      print.Warn("Invalid lower error for parameter", fMinimum->UserState().Name(i));
   }
   if (upperInvalid) {
      print.Warn("Invalid upper error for parameter", fMinimum->UserState().Name(i));
   }
   // print also case it is lower/upper limit
   if (me.AtLowerLimit()) {
      print.Warn("Lower error for parameter", fMinimum->UserState().Name(i), "is at the Lower limit!");
   }
   if (me.AtUpperLimit()) {
      print.Warn("Upper error for parameter", fMinimum->UserState().Name(i), "is at the Upper limit!");
   }
 
   int mstatus = 0;
   if (lowerInvalid || upperInvalid) {
      // set status according 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
 
   MnPrint print("Minuit2Minimizer::Scan", PrintLevel());
   if (!fMinuitFCN) {
      print.Error("Function must be set before using Scan");
      return false;
   }
 
   if (ipar > fState.MinuitParameters().size()) {
      print.Error("Invalid number; minimizer variables must be set before using Scan");
      return false;
   }
 
   // switch off Minuit2 printing
   const int prev_level = (PrintLevel() <= 0) ? TurnOffPrintInfoLevel() : -2;
   const int prevGlobalLevel = MnPrint::SetGlobalLevel(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);
 
   // restore global print level
   if (prev_level > -2)
      RestoreGlobalPrintLevel(prev_level);
   MnPrint::SetGlobalLevel(prevGlobalLevel);
 
   if (result.size() != nstep) {
      print.Error("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) {
      print.Info("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
 
   MnPrint print("Minuit2Minimizer::Contour", PrintLevel());
 
   if (fMinimum == nullptr) {
      print.Error("No function minimum existing; must minimize function before");
      return false;
   }
 
   if (!fMinimum->IsValid()) {
      print.Error("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());
   }
 
   print.Info("Computing contours -", ErrorDef());
 
   // switch off Minuit2 printing (for level of  0,1)
   const int prev_level = (PrintLevel() <= 1) ? TurnOffPrintInfoLevel() : -2;
   const int prevGlobalLevel = MnPrint::SetGlobalLevel(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());
 
   // restore global print level
   if (prev_level > -2)
      RestoreGlobalPrintLevel(prev_level);
   MnPrint::SetGlobalLevel(prevGlobalLevel);
 
   // compute the contour
   std::vector<std::pair<double, double>> result = contour(ipar, jpar, npoints);
   if (result.size() != npoints) {
      print.Error("Invalid result from MnContours");
      return false;
   }
   for (unsigned int i = 0; i < npoints; ++i) {
      x[i] = result[i].first;
      y[i] = result[i].second;
   }
 
   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
 
   MnPrint print("Minuit2Minimizer::Hesse", PrintLevel());
 
   if (!fMinuitFCN) {
      print.Error("FCN function has not been set");
      return false;
   }
 
   const int maxfcn = MaxFunctionCalls();
   print.Info("Using max-calls", maxfcn);
 
   // switch off Minuit2 printing
   const int prev_level = (PrintLevel() <= 0) ? TurnOffPrintInfoLevel() : -2;
   const int prevGlobalLevel = MnPrint::SetGlobalLevel(PrintLevel());
 
   // set the precision if needed
   if (Precision() > 0)
      fState.SetPrecision(Precision());
 
   ROOT::Minuit2::MnHesse hesse(customizedStrategy(Strategy(), fOptions));
 
   // 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);
   }
 
   // restore global print level
   if (prev_level > -2)
      RestoreGlobalPrintLevel(prev_level);
   MnPrint::SetGlobalLevel(prevGlobalLevel);
 
   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 (covStatus == 0)
      covStatusType = "full but not positive defined";
 
   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;
      }
 
      print.Warn("Hesse failed - matrix is", covStatusType);
      print.Warn(hstatus);
 
      fStatus += 100 * hstatus;
      return false;
   }
 
   print.Info("Hesse is valid - matrix is", covStatusType);
 
   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)
      fMinimizer->Builder().SetTraceObject(obj);
}
 
void Minuit2Minimizer::SetStorageLevel(int level)
{
   // set storage level
   if (fMinimizer)
      fMinimizer->Builder().SetStorageLevel(level);
}
 
} // end namespace Minuit2
 
} // end namespace ROOT