Fitter.h

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// @(#)root/mathcore:$Id$
// Author: L. Moneta Wed Aug 30 11:05:19 2006
 
/**********************************************************************
 *                                                                    *
 * Copyright (c) 2006  LCG ROOT Math Team, CERN/PH-SFT                *
 *                                                                    *
 *                                                                    *
 **********************************************************************/
 
#ifndef ROOT_Fit_Fitter
#define ROOT_Fit_Fitter
 
/**
@defgroup Fit Fitting and Parameter Estimation
 
Classes used for fitting (regression analysis) and estimation of parameter values given a data sample.
 
@ingroup MathCore
 
@see ROOT::Math::MinimizerOptions::SetDefaultMinimizer
 
*/
 
#include "Fit/BinData.h"
#include "Fit/FitConfig.h"
#include "Fit/FitResult.h"
#include "Fit/UnBinData.h"
#include "Math/IParamFunction.h"
#include "Math/WrappedFunction.h"
#include "ROOT/EExecutionPolicy.hxx"
 
#include <memory>
 
namespace ROOT::Math {
 
class Minimizer;
 
// should maybe put this in a FitMethodFunctionfwd file
template <class FunctionType>
class BasicFitMethodFunction;
 
// define the normal and gradient function
typedef BasicFitMethodFunction<ROOT::Math::IMultiGenFunction> FitMethodFunction;
typedef BasicFitMethodFunction<ROOT::Math::IMultiGradFunction> FitMethodGradFunction;
 
} // namespace ROOT::Math
 
   /**
      Namespace for the fitting classes
      @ingroup Fit
    */
 
namespace ROOT::Fit {
 
/**
   @defgroup FitMain User Fitting classes
 
   Main Classes used for fitting a given data set
   @ingroup Fit
*/
 
 
//___________________________________________________________________________________
/**
   Fitter class, entry point for performing all type of fits.
   Fits are performed using the generic ROOT::Fit::Fitter::Fit method.
   The inputs are the data points and a model function (using a ROOT::Math::IParamFunction)
   The result of the fit is returned and kept internally in the  ROOT::Fit::FitResult class.
   The configuration of the fit (parameters, options, etc...) are specified in the
   ROOT::Math::FitConfig class.
   After fitting the config of the fit will be modified to have the new values the resulting
   parameter of the fit with step sizes equal to the errors. FitConfig can be preserved with
   initial parameters by calling FitConfig.SetUpdateAfterFit(false);
 
   @ingroup FitMain
*/
class Fitter {
 
public:
 
   typedef ROOT::Math::IParamMultiFunction                 IModelFunction;
   template <class T>
   using IModelFunctionTempl =                             ROOT::Math::IParamMultiFunctionTempl<T>;
#ifdef R__HAS_STD_EXPERIMENTAL_SIMD
   typedef ROOT::Math::IParametricFunctionMultiDimTempl<ROOT::Double_v>  IModelFunction_v;
   typedef ROOT::Math::IParamMultiGradFunctionTempl<ROOT::Double_v> IGradModelFunction_v;
#else
   typedef ROOT::Math::IParamMultiFunction                 IModelFunction_v;
   typedef ROOT::Math::IParamMultiGradFunction IGradModelFunction_v;
#endif
   typedef ROOT::Math::IParamMultiGradFunction             IGradModelFunction;
   typedef ROOT::Math::IParamFunction                      IModel1DFunction;
   typedef ROOT::Math::IParamGradFunction                  IGradModel1DFunction;
 
   typedef ROOT::Math::IMultiGenFunction BaseFunc;
   typedef ROOT::Math::IMultiGradFunction BaseGradFunc;
 
 
   /**
      Default constructor
   */
   Fitter () {}
 
   /**
      Constructor from a result
   */
   Fitter (const std::shared_ptr<FitResult> & result);
 
 
   /**
      Destructor.
      Make it virtual in case users derive from Fitter class to extend it by adding new methods.
      This is needed to avoid a warning seen when doing from Python
      (see ROOT issue [#12391](https://github.com/root-project/root/issues/12391) ).
      Note that the Fitter class does not provide virtual functions to be re-implemented by derived classes.
   */
   virtual ~Fitter () {}
 
   /**
      Copy constructor (disabled, class is not copyable)
   */
   Fitter(const Fitter &) = delete;
 
   /**
      Assignment operator (disabled, class is not copyable)
   */
   Fitter & operator = (const Fitter &) = delete;
 
 
public:
 
   /**
       fit a data set using any  generic model  function
       If data set is binned a least square fit is performed
       If data set is unbinned a maximum likelihood fit (not extended) is done
       Pre-requisite on the function:
       it must implement the 1D or multidimensional parametric function interface.
       Note that both the input data and the function object are copied by the Fitter.
   */
   template <class Data, class Function,
             class cond = typename std::enable_if<!(std::is_same<Function, ROOT::EExecutionPolicy>::value ||
                                                    std::is_same<Function, int>::value),
                                                  Function>::type>
   bool Fit(const Data &data, const Function &func,
            const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential)
   {
      SetFunction(func);
      return Fit(data, executionPolicy);
   }
 
   /**
      Fit a binned data set using a least square fit.
      Note that the provided input data are copied in the Fitter class.
      Use the next function (passing a `shared_ptr` to the BinData class if you want to avoid
      copying.
   */
   bool Fit(const BinData & data, const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential) {
      return LeastSquareFit(data, executionPolicy);
   }
 
   /**
      Fit a binned data set using a least square fit.
      Pass the input data using a `shared_ptr` for NOT copying the input data.
   */
   bool Fit(const std::shared_ptr<BinData> & data, const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential) {
      return LeastSquareFit(data, executionPolicy);
   }
 
   /**
       Fit a binned data set using a least square fit copying the input data.
   */
   bool LeastSquareFit(const BinData & data, const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential) {
      SetData(data);
      return DoLeastSquareFit(executionPolicy);
   }
   /**
       Fit a binned data set using a least square fit NOT copying the input data.
   */
   bool LeastSquareFit(const std::shared_ptr<BinData> & data, const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential) {
      SetData(data);
      return DoLeastSquareFit(executionPolicy);
   }
 
   /**
       Fit an un-binned data set using the negative log-likelihood method.
       This function copies the input data.
   */
   bool Fit(const UnBinData & data, bool extended = false, const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential) {
      return LikelihoodFit(data, extended, executionPolicy);
   }
   /**
       Fit an un-binned data set using the negative log-likelihood method.
       This function uses a `shared_ptr` to avoid copying the input data.
   */
   bool Fit(const std::shared_ptr<UnBinData> & data, bool extended = false, const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential) {
      return LikelihoodFit(data, extended, executionPolicy);
   }
 
   /**
      Binned Likelihood fit copying the input data.
      Default is extended.
    */
   bool LikelihoodFit(const BinData &data, bool extended = true,
                      const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential) {
      SetData(data);
      return DoBinnedLikelihoodFit(extended, executionPolicy);
   }
   /**
      Binned Likelihood fit using a `shared_ptr` for NOT copying the input data.
      Default is extended.
    */
   bool LikelihoodFit(const std::shared_ptr<BinData> &data, bool extended = true,
                      const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential) {
      SetData(data);
      return DoBinnedLikelihoodFit(extended, executionPolicy);
   }
   /**
      Un-binned Likelihood fit copying the input data
      Default is NOT extended
    */
   bool LikelihoodFit(const UnBinData & data, bool extended = false, const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential) {
      SetData(data);
      return DoUnbinnedLikelihoodFit(extended, executionPolicy);
   }
   /**
      Un-binned Likelihood fit using a `shared_ptr` for NOT copying the input data.
      Default is NOT extended
    */
   bool LikelihoodFit(const std::shared_ptr<UnBinData> & data, bool extended = false, const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential) {
      SetData(data);
      return DoUnbinnedLikelihoodFit(extended, executionPolicy);
   }
 
   /**
      Likelihood fit given a data set (Binned or Un-binned) using any  generic model  function.
      This interface copies the input data and the model function object
   */
   template < class Data , class Function>
   bool LikelihoodFit( const Data & data, const Function & func, bool extended) {
      SetFunction(func);
      return LikelihoodFit(data, extended);
   }
 
   /**
      Do a linear fit copying the input data
    */
   bool LinearFit(const BinData & data) {
      SetData(data);
      return DoLinearFit();
   }
   /**
      Do a linear fit using a `shared_ptr` for NOT copying the input data
    */
   bool LinearFit(const std::shared_ptr<BinData> & data) {
      SetData(data);
      return DoLinearFit();
   }
 
   /**
      Fit using the a generic FCN function as a C++ callable object implementing
      double () (const double *)
      Note that the function dimension (i.e. the number of parameter) is needed in this case
      For the options see documentation for following methods FitFCN(IMultiGenFunction & fcn,..)
    */
   template <class Function>
   bool FitFCN(unsigned int npar, Function  & fcn, const double * params = nullptr, unsigned int dataSize = 0, int fitType = 0) {
      return DoSetFCN(false, ROOT::Math::WrappedMultiFunction<Function &>{fcn, npar}, params, dataSize, fitType) ? FitFCN() : false;
   }
 
   /**
      Set a generic FCN function as a C++ callable object implementing
      double () (const double *)
      Note that the function dimension (i.e. the number of parameter) is needed in this case
      For the options see documentation for following methods FitFCN(IMultiGenFunction & fcn,..)
    */
   template <class Function>
   bool SetFCN(unsigned int npar, Function  & fcn, const double * params = nullptr, unsigned int dataSize = 0, int fitType = 0) {
      return DoSetFCN(false, ROOT::Math::WrappedMultiFunction<Function &>{fcn, npar}, params, dataSize, fitType);
   }
 
   /**
      Fit using the given FCN function represented by a multi-dimensional function interface
      (ROOT::Math::IMultiGenFunction).
      Give optionally the initial parameter values, data size to have the fit Ndf correctly
      set in the FitResult and flag specifying the type of fit. The fitType can be:
      0 undefined, 1 least square fit, 2 unbinned likelihood fit, 3 binned likelihood fit
      Note that if the parameters values are not given (params=0) the
      current parameter settings are used. The parameter settings can be created before
      by using the FitConfig::SetParamsSetting. If they have not been created they are created
      automatically when the params pointer is not zero.
      Note that passing a params != 0 will set the parameter settings to the new value AND also the
      step sizes to some pre-defined value (stepsize = 0.3 * abs(parameter_value) )
    */
   bool FitFCN(const ROOT::Math::IMultiGenFunction &fcn, const double *params = nullptr, unsigned int dataSize = 0, int fitType = 0);
 
   /**
       Fit using a FitMethodFunction interface. Same as method above, but now extra information
       can be taken from the function class
   */
   bool FitFCN(const ROOT::Math::FitMethodFunction & fcn, const double *params = nullptr);
 
   /**
      Set the FCN function represented by a multi-dimensional function interface
      (ROOT::Math::IMultiGenFunction) and optionally the initial parameters
      See also note above for the initial parameters for FitFCN
    */
   bool SetFCN(const ROOT::Math::IMultiGenFunction &fcn, const double *params = nullptr, unsigned int dataSize = 0, int fitType = 0);
 
   /**
      Set the FCN function represented by a multi-dimensional function interface
     (ROOT::Math::IMultiGenFunction) and optionally the initial parameters
      See also note above for the initial parameters for FitFCN
      With this interface we pass in addition a ModelFunction that will be attached to the FitResult and
      used to compute confidence interval of the fit
   */
   bool SetFCN(const ROOT::Math::IMultiGenFunction &fcn, const IModelFunction & func, const double *params = nullptr,
               unsigned int dataSize = 0, int fitType = 0);
 
   /**
       Set the objective function (FCN)  using a FitMethodFunction interface.
       Same as method above, but now extra information can be taken from the function class
   */
   bool SetFCN(const ROOT::Math::FitMethodFunction & fcn, const double *params = nullptr);
 
   /**
       Fit using a FitMethodGradFunction interface. Same as method above, but now extra information
       can be taken from the function class
   */
   bool FitFCN(const ROOT::Math::FitMethodGradFunction & fcn, const double *params = nullptr);
 
   /**
       Set the objective function (FCN)  using a FitMethodGradFunction interface.
       Same as method above, but now extra information can be taken from the function class
   */
   bool SetFCN(const ROOT::Math::FitMethodGradFunction & fcn, const double *params = nullptr);
 
 
   /**
      fit using user provided FCN with Minuit-like interface
      If npar = 0 it is assumed that the parameters are specified in the parameter settings created before
      For the options same consideration as in the previous method
    */
   typedef  void (* MinuitFCN_t )(int &npar, double *gin, double &f, double *u, int flag);
   bool FitFCN( MinuitFCN_t fcn, int npar = 0, const double *params = nullptr, unsigned int dataSize = 0, int fitType = 0);
 
   /**
      set objective function using user provided FCN with Minuit-like interface
      If npar = 0 it is assumed that the parameters are specified in the parameter settings created before
      For the options same consideration as in the previous method
    */
   bool SetFCN( MinuitFCN_t fcn, int npar = 0, const double *params = nullptr, unsigned int dataSize = 0, int fitType = 0);
 
   /**
      Perform a fit with the previously set FCN function. Require SetFCN before
    */
   bool FitFCN();
 
   /**
      Perform a simple FCN evaluation. FitResult will be modified and contain  the value of the FCN
    */
   bool EvalFCN();
 
 
 
   /**
       Set the fitted function (model function) from a parametric function interface.
       @param useGradient if true, the minimizer uses the gradient information provided by the user, otherwise a numerical gradient is computed and used.
   */
   void  SetFunction(const IModelFunction & func, bool useGradient = false);
 
   /**
       Set the fitted function (model function) from a vectorized parametric function interface
   */
#ifdef R__HAS_STD_EXPERIMENTAL_SIMD
   template <class NotCompileIfScalarBackend = std::enable_if<!(std::is_same<double, ROOT::Double_v>::value)>>
   void SetFunction(const IModelFunction_v &func, bool useGradient = false);
 
   template <class NotCompileIfScalarBackend = std::enable_if<!(std::is_same<double, ROOT::Double_v>::value)>>
   void SetFunction(const IGradModelFunction_v &func, bool useGradient = true);
#endif
   /**
      Set the fitted function from a parametric 1D function interface
    */
   void  SetFunction(const IModel1DFunction & func, bool useGradient = false);
 
   /**
       Set the fitted function (model function) from a parametric gradient function interface
   */
   void  SetFunction(const IGradModelFunction & func, bool useGradient = true);
   /**
      Set the fitted function from 1D gradient parametric function interface
    */
   void  SetFunction(const IGradModel1DFunction & func, bool useGradient = true);
 
 
   /**
      get fit result
   */
   const FitResult & Result() const {
      assert( fResult.get() );
      return *fResult;
   }
 
 
   /**
      perform an error analysis on the result using the Hessian
      Errors are obtained from the inverse of the Hessian matrix
      To be called only after fitting and when a minimizer supporting the Hessian calculations is used
      otherwise an error (false) is returned.
      A new  FitResult with the Hessian result will be produced
    */
   bool CalculateHessErrors();
 
   /**
      perform an error analysis on the result using MINOS
      To be called only after fitting and when a minimizer supporting MINOS is used
      otherwise an error (false) is returned.
      The result will be appended in the fit result class
      Optionally a vector of parameter indices can be passed for selecting
      the parameters to analyse using FitConfig::SetMinosErrors
    */
   bool CalculateMinosErrors();
 
   /**
      access to the fit configuration (const method)
   */
   const FitConfig & Config() const { return fConfig; }
 
   /**
      access to the configuration (non const method)
   */
   FitConfig & Config() { return fConfig; }
 
   /**
      query if fit is binned. In cse of false the fit can be unbinned
      or is not defined (like in case of fitting through a ROOT::Fit::Fitter::FitFCN)
    */
   bool IsBinFit() const { return fBinFit; }
 
   /**
      return pointer to last used minimizer
      (is NULL in case fit is not yet done)
      This pointer is guaranteed to be valid as far as the fitter class is valid and a new fit is not redone.
      To be used only after fitting.
      The pointer should not be stored and will be invalided after performing a new fitting.
      In this case a new instance of ROOT::Math::Minimizer will be re-created and can be
      obtained calling again GetMinimizer()
    */
   ROOT::Math::Minimizer * GetMinimizer() const { return fMinimizer.get(); }
 
   /**
      return pointer to last used objective function
      (is NULL in case fit is not yet done)
      This pointer will be valid as far as the fitter class
      has not been deleted. To be used after the fitting.
      The pointer should not be stored and will be invalided after performing a new fitting.
      In this case a new instance of the function pointer will be re-created and can be
      obtained calling again GetFCN()
    */
   ROOT::Math::IMultiGenFunction * GetFCN() const {
      return fObjFunction.get();
    }
 
 
   /**
      apply correction in the error matrix for the weights for likelihood fits
      This method can be called only after a fit. The
      passed function (loglw2) is a log-likelihood function implemented using the
      sum of weight squared
      When using FitConfig.SetWeightCorrection() this correction is applied
      automatically when doing a likelihood fit (binned or unbinned)
   */
   bool ApplyWeightCorrection(const ROOT::Math::IMultiGenFunction & loglw2, bool minimizeW2L=false);
 
   /// Set number of fit points when using an external FCN function
   /// This function can be called after Fit to set the correct number of Ndf in FitResult
   void SetNumberOfFitPoints(unsigned int npoints) {
      if (fExtObjFunction) fDataSize = npoints;
      if (!fResult->IsEmpty()) fResult->SetChi2AndNdf(-1,npoints);
   }
 
   /// Set the type of fit when using an external FCN
   /// possible types are : 1 (least-square), 2 (unbinned-likelihood), 3 (binned-likelihood)
   /// Note that in case of binned likelihood fit the chi2 will be computed as 2 * MinFCN()
   /// Note this function should be called before fitting to have effect on th FitResult
   void SetFitType(int type) {
      if (fExtObjFunction) fFitType = type;
   }
 
 
protected:
 
 
   /// least square fit
   bool DoLeastSquareFit(const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential);
   /// binned likelihood fit
   bool DoBinnedLikelihoodFit(bool extended = true, const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential);
   /// un-binned likelihood fit
   bool DoUnbinnedLikelihoodFit( bool extended = false, const ROOT::EExecutionPolicy &executionPolicy = ROOT::EExecutionPolicy::kSequential);
   /// linear least square fit
   bool DoLinearFit();
   /// Set Objective function
   bool DoSetFCN(bool useExtFCN, const ROOT::Math::IMultiGenFunction &fcn, const double *params, unsigned int dataSize,
                 int fitType);
 
   // initialize the minimizer
   bool DoInitMinimizer();
   /// do minimization
   template<class ObjFunc_t>
   bool DoMinimization(std::unique_ptr<ObjFunc_t> f, const ROOT::Math::IMultiGenFunction * chifunc = nullptr);
   // do minimization for weighted likelihood fits
   template<class ObjFunc_t>
   bool DoWeightMinimization(std::unique_ptr<ObjFunc_t> f, const ROOT::Math::IMultiGenFunction * chifunc = nullptr);
   // do minimization after having set the objective function
   bool DoMinimization(const ROOT::Math::IMultiGenFunction * chifunc = nullptr);
   // update config after fit
   void DoUpdateFitConfig();
   // update minimizer options for re-fitting
   bool DoUpdateMinimizerOptions(bool canDifferentMinim = true);
   // get function calls from the FCN
   int GetNCallsFromFCN();
 
   /// Set the input data for the fit using a shared ptr (No Copying)
   template <class Data>
   void SetData(const std::shared_ptr<Data> & data) {
      fData = std::static_pointer_cast<Data>(data);
   }
 
   /// Set the input data for the fit (Copying the given data object)
   template <class Data>
   void SetData(const Data & data) {
      SetData(std::make_shared<Data>(data));
   }
 
   /// internal functions to get data set and model function from FCN
   /// useful for fits done with customized FCN classes
   template <class ObjFuncType>
   bool GetDataFromFCN() {
      if (const ObjFuncType *objfunc = dynamic_cast<const ObjFuncType *>(ObjFunction())) {
         fFunc = objfunc->ModelFunctionPtr();
         fData = objfunc->DataPtr();
         return true;
      }
      return false;
   }
 
   /// Return pointer to the used objective function for fitting.
   /// If using an external function (e.g. given in SetFCN), return the cached pointer,
   /// otherwise use the one stored as shared ptr and managed by the Fitter class
   const ROOT::Math::IBaseFunctionMultiDimTempl<double> * ObjFunction() const {
      // need to specify here full return type since when using the typedef (IMultiGenFunction)
      // there is an error when using the class in Python (see issue #12391)
      return fExtObjFunction ? fExtObjFunction : fObjFunction.get();
   }
 
private:
 
   bool fUseGradient = false; ///< flag to indicate if using gradient or not
   bool fBinFit = false;      ///< flag to indicate if fit is binned
                              ///< in case of false the fit is unbinned or undefined)
                              ///< flag it is used to compute chi2 for binned likelihood fit
   int fFitType = 0;          ///< type of fit   (0 undefined, 1 least square, 2 likelihood, 3 binned likelihood)
   int fDataSize = 0;         ///< size of data sets (need for Fumili or LM fitters)
   FitConfig fConfig;         ///< fitter configuration (options and parameter settings)
   std::shared_ptr<IModelFunction_v> fFunc_v;     ///<! copy of the fitted  function containing on output the fit result
   std::shared_ptr<IModelFunction> fFunc;         ///<! copy of the fitted  function containing on output the fit result
   std::shared_ptr<ROOT::Fit::FitResult> fResult; ///<! pointer to the object containing the result of the fit
   std::shared_ptr<ROOT::Math::Minimizer> fMinimizer;           ///<! pointer to used minimizer
   std::shared_ptr<ROOT::Fit::FitData> fData;                   ///<! pointer to the fit data (binned or unbinned data)
   std::shared_ptr<ROOT::Math::IMultiGenFunction> fObjFunction; ///<! pointer to used objective function
   const ROOT::Math::IMultiGenFunction *fExtObjFunction = nullptr; ///<! pointer to an external FCN
};
 
#ifdef R__HAS_STD_EXPERIMENTAL_SIMD
template <class NotCompileIfScalarBackend>
void Fitter::SetFunction(const IModelFunction_v &func, bool useGradient)
{
   fUseGradient = useGradient;
   if (fUseGradient) {
      const IGradModelFunction_v *gradFunc = dynamic_cast<const IGradModelFunction_v *>(&func);
      if (gradFunc) {
         SetFunction(*gradFunc, true);
         return;
      } else {
         MATH_WARN_MSG("Fitter::SetFunction",
                       "Requested function does not provide gradient - use it as non-gradient function ");
      }
   }
 
   //  set the fit model function (clone the given one and keep a copy )
   //  std::cout << "set a non-grad function" << std::endl;
   fUseGradient = false;
   fFunc_v = std::shared_ptr<IModelFunction_v>(dynamic_cast<IModelFunction_v *>(func.Clone()));
   assert(fFunc_v);
 
   // creates the parameter  settings
   fConfig.CreateParamsSettings(*fFunc_v);
   fFunc.reset();
}
 
template <class NotCompileIfScalarBackend>
void Fitter::SetFunction(const IGradModelFunction_v &func, bool useGradient)
{
   fUseGradient = useGradient;
 
   //  set the fit model function (clone the given one and keep a copy )
   fFunc_v = std::shared_ptr<IModelFunction_v>(dynamic_cast<IGradModelFunction_v *>(func.Clone()));
   assert(fFunc_v);
 
   // creates the parameter  settings
   fConfig.CreateParamsSettings(*fFunc_v);
   fFunc.reset();
}
#endif
 
} // namespace ROOT::Fit
 
#endif /* ROOT_Fit_Fitter */