include/root/TF1.h

0001 // @(#)root/hist:$Id$
0002 // Author: Rene Brun   18/08/95
0003
0004 /*************************************************************************
0005  * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
0006  * All rights reserved.                                                  *
0007  *                                                                       *
0008  * For the licensing terms see $ROOTSYS/LICENSE.                         *
0009  * For the list of contributors see $ROOTSYS/README/CREDITS.             *
0010  *************************************************************************/
0011 // ---------------------------------- F1.h
0012
0013 #ifndef ROOT_TF1
0014 #define ROOT_TF1
0015
0016 //////////////////////////////////////////////////////////////////////////
0017 //                                                                      //
0018 // TF1                                                                  //
0019 //                                                                      //
0020 // The Parametric 1-D function                                          //
0021 //                                                                      //
0022 //////////////////////////////////////////////////////////////////////////
0023
0024 #include "RConfigure.h"
0025 #include <functional>
0026 #include <cassert>
0027 #include <memory>
0028 #include <string>
0029 #include <vector>
0030 #include "TFormula.h"
0031 #include "TMethodCall.h"
0032 #include "TAttLine.h"
0033 #include "TAttFill.h"
0034 #include "TAttMarker.h"
0035 #include "TF1AbsComposition.h"
0036 #include "TMath.h"
0037 #include "TMatrixDSymfwd.h"
0038 #include "Math/Types.h"
0039 #include "Math/ParamFunctor.h"
0040
0041 #include <string>
0042
0043 class TF1;
0044 class TH1;
0045 class TAxis;
0046 class TRandom;
0047
0048 namespace ROOT {
0049    namespace Fit {
0050       class FitResult;
0051    }
0052 }
0053
0054 class TF1Parameters {
0055 public:
0056    TF1Parameters() {} // needed for the I/O
0057    TF1Parameters(Int_t npar) :
0058       fParameters(std::vector<Double_t>(npar)),
0059       fParNames(std::vector<std::string>(npar))
0060    {
0061       for (int i = 0; i < npar; ++i) {
0062          fParNames[i] = std::string(TString::Format("p%d", i).Data());
0063       }
0064    }
0065    // copy constructor
0066    TF1Parameters(const TF1Parameters &rhs) :
0067       fParameters(rhs.fParameters),
0068       fParNames(rhs.fParNames)
0069    {}
0070    // assignment
0071    TF1Parameters &operator=(const TF1Parameters &rhs)
0072    {
0073       if (&rhs == this) return *this;
0074       fParameters = rhs.fParameters;
0075       fParNames = rhs.fParNames;
0076       return *this;
0077    }
0078    virtual ~TF1Parameters() {}
0079
0080    // getter methods
0081    Double_t GetParameter(Int_t iparam) const
0082    {
0083       return (CheckIndex(iparam)) ? fParameters[iparam] : 0;
0084    }
0085    Double_t GetParameter(const char *name) const
0086    {
0087       return GetParameter(GetParNumber(name));
0088    }
0089    const Double_t *GetParameters() const
0090    {
0091       return fParameters.data();
0092    }
0093    const std::vector<double> &ParamsVec() const
0094    {
0095       return fParameters;
0096    }
0097
0098    Int_t GetParNumber(const char *name) const;
0099
0100    const char *GetParName(Int_t iparam) const
0101    {
0102       return (CheckIndex(iparam)) ? fParNames[iparam].c_str() : "";
0103    }
0104
0105
0106    // setter methods
0107    void   SetParameter(Int_t iparam, Double_t value)
0108    {
0109       if (!CheckIndex(iparam)) return;
0110       fParameters[iparam] = value;
0111    }
0112    void  SetParameters(const Double_t *params)
0113    {
0114       std::copy(params, params + fParameters.size(), fParameters.begin());
0115    }
0116    template <typename... Args>
0117    void   SetParameters(Double_t arg1, Args &&... args);
0118
0119    void   SetParameter(const char *name, Double_t value)
0120    {
0121       SetParameter(GetParNumber(name), value);
0122    }
0123    void   SetParName(Int_t iparam, const char *name)
0124    {
0125       if (!CheckIndex(iparam)) return;
0126       fParNames[iparam] = std::string(name);
0127    }
0128    template <typename... Args>
0129    void   SetParNames(Args &&... args);
0130
0131    ClassDef(TF1Parameters, 1)  // The Parameters of a parameteric function
0132 private:
0133
0134    bool CheckIndex(Int_t i) const
0135    {
0136       return (i >= 0 && i < int(fParameters.size()));
0137    }
0138
0139    std::vector<Double_t> fParameters;    // parameter values
0140    std::vector<std::string> fParNames;   // parameter names
0141 };
0142
0143 /// Set parameter values.
0144 /// NaN values will be skipped, meaning that the corresponding parameters will not be changed.
0145 template <typename... Args>
0146 void TF1Parameters::SetParameters(Double_t arg1, Args &&...args)
0147 {
0148    int i = 0;
0149    for (double val : {arg1, static_cast<Double_t>(args)...}) {
0150       if(!TMath::IsNaN(val)) SetParameter(i++, val);
0151    }
0152 }
0153
0154 /// Set parameter names.
0155 /// Empty strings will be skipped, meaning that the corresponding name will not be changed.
0156 template <typename... Args>
0157 void TF1Parameters::SetParNames(Args &&...args)
0158 {
0159    int i = 0;
0160    for (auto name : {static_cast<std::string const&>(args)...}) {
0161       if(!name.empty()) SetParName(i++, name.c_str());
0162    }
0163 }
0164
0165 namespace ROOT {
0166    namespace Internal {
0167       /// %Internal class used by TF1 for defining
0168       /// template specialization for different TF1 constructors
0169       template<class Func>
0170       struct TF1Builder {
0171          static void Build(TF1 *f, Func func);
0172       };
0173
0174       template<class Func>
0175       struct TF1Builder<Func *> {
0176          static void Build(TF1 *f, Func *func);
0177       };
0178
0179       /// %Internal class used by TF1 for obtaining the type from a functor
0180       /// out of the set of valid operator() signatures.
0181       template<typename T>
0182       struct GetFunctorType {
0183       };
0184
0185       template<typename F, typename T>
0186       struct GetFunctorType<T(F::*)(const T *, const double *)> {
0187          using type = T;
0188       };
0189
0190       template<typename F, typename T>
0191       struct GetFunctorType<T(F::*)(const T *, const double *) const> {
0192          using type = T;
0193       };
0194
0195       template<typename F, typename T>
0196       struct GetFunctorType<T(F::*)(T *, double *)> {
0197          using type = T;
0198       };
0199
0200       template<typename F, typename T>
0201       struct GetFunctorType<T(F::*)(T *, double *) const> {
0202          using type = T;
0203       };
0204
0205       /// %Internal class used by TF1 to get the right operator() signature
0206       /// from a Functor with several ones.
0207       template<typename T, typename F>
0208       auto GetTheRightOp(T(F::*opPtr)(const T *, const double *)) -> decltype(opPtr)
0209       {
0210          return opPtr;
0211       }
0212
0213       template<typename T, typename F>
0214       auto GetTheRightOp(T(F::*opPtr)(const T *, const double *) const) -> decltype(opPtr)
0215       {
0216          return opPtr;
0217       }
0218
0219       template<typename T, typename F>
0220       auto GetTheRightOp(T(F::*opPtr)(T *, double *)) -> decltype(opPtr)
0221       {
0222          return opPtr;
0223       }
0224
0225       template<typename T, typename F>
0226       auto GetTheRightOp(T(F::*opPtr)(T *, double *) const) -> decltype(opPtr)
0227       {
0228          return opPtr;
0229       }
0230    }
0231 }
0232
0233
0234 class TF1 : public TNamed, public TAttLine, public TAttFill, public TAttMarker {
0235
0236    template<class Func>
0237    friend struct ROOT::Internal::TF1Builder;
0238
0239 public:
0240    /// Add to list behavior
0241    enum class EAddToList {
0242       kDefault,
0243       kAdd,
0244       kNo
0245    };
0246
0247
0248    struct TF1FunctorPointer {
0249       virtual  ~TF1FunctorPointer() {}
0250       virtual  TF1FunctorPointer * Clone() const = 0;
0251    };
0252
0253 protected:
0254
0255    enum EFType {
0256       kFormula = 0,      ///< Formula functions which can be stored,
0257       kPtrScalarFreeFcn, ///< Pointer to scalar free function,
0258       kInterpreted,      ///< Interpreted functions constructed by name,
0259       kTemplVec,         ///< Vectorized free functions or TemplScalar functors evaluating on vectorized parameters,
0260       kTemplScalar,      ///< TemplScalar functors evaluating on scalar parameters
0261       kCompositionFcn
0262    }; // formula based on composition class (e.g. NSUM, CONV)
0263
0264    Double_t    fXmin{-1111};                        ///<  Lower bounds for the range
0265    Double_t    fXmax{-1111};                        ///<  Upper bounds for the range
0266    Int_t       fNpar{};                             ///<  Number of parameters
0267    Int_t       fNdim{};                             ///<  Function dimension
0268    Int_t       fNpx{100};                           ///<  Number of points used for the graphical representation
0269    EFType      fType{EFType::kTemplScalar};
0270    Int_t       fNpfits{};                           ///<  Number of points used in the fit
0271    Int_t       fNDF{};                              ///<  Number of degrees of freedom in the fit
0272    Double_t    fChisquare{};                        ///<  Function fit chisquare
0273    Double_t    fMinimum{-1111};                     ///<  Minimum value for plotting
0274    Double_t    fMaximum{-1111};                     ///<  Maximum value for plotting
0275    std::vector<Double_t>    fParErrors;             ///<  Array of errors of the fNpar parameters
0276    std::vector<Double_t>    fParMin;                ///<  Array of lower limits of the fNpar parameters
0277    std::vector<Double_t>    fParMax;                ///<  Array of upper limits of the fNpar parameters
0278    std::vector<Double_t>    fSave;                  ///<  Array of fNsave function values
0279    std::vector<Double_t>    fIntegral;              ///<! Integral of function binned on fNpx bins
0280    std::vector<Double_t>    fAlpha;                 ///<! Array alpha. for each bin in x the deconvolution r of fIntegral
0281    std::vector<Double_t>    fBeta;                  ///<! Array beta.  is approximated by x = alpha +beta*r *gamma*r**2
0282    std::vector<Double_t>    fGamma;                 ///<! Array gamma.
0283    TObject     *fParent{nullptr};                   ///<! Parent object hooking this function (if one)
0284    TH1         *fHistogram{nullptr};                ///<! Pointer to histogram used for visualisation
0285    std::unique_ptr<TMethodCall> fMethodCall;        ///<! Pointer to MethodCall in case of interpreted function
0286    Bool_t      fNormalized{false};                  ///<  Normalization option (false by default)
0287    Double_t    fNormIntegral{};                     ///<  Integral of the function before being normalized
0288    std::unique_ptr<TF1FunctorPointer>  fFunctor;    ///<! Functor object to wrap any C++ callable object
0289    std::unique_ptr<TFormula>   fFormula;            ///<  Pointer to TFormula in case when user define formula
0290    std::unique_ptr<TF1Parameters> fParams;          ///<  Pointer to Function parameters object (exists only for not-formula functions)
0291    std::unique_ptr<TF1AbsComposition> fComposition; ///<  Pointer to composition (NSUM or CONV)
0292
0293    /// General constructor for TF1. Most of the other constructors delegate on it
0294    TF1(EFType functionType, const char *name, Double_t xmin, Double_t xmax, Int_t npar, Int_t ndim, EAddToList addToGlobList, TF1Parameters *params = nullptr, TF1FunctorPointer * functor = nullptr):
0295       TNamed(name, name), TAttLine(), TAttFill(), TAttMarker(), fXmin(xmin), fXmax(xmax), fNpar(npar), fNdim(ndim),
0296       fType(functionType), fParErrors(npar), fParMin(npar), fParMax(npar)
0297    {
0298       fParams.reset(params);
0299       fFunctor.reset(functor);
0300       DoInitialize(addToGlobList);
0301    }
0302
0303 private:
0304    // NSUM parsing helper functions
0305    void DefineNSUMTerm(TObjArray *newFuncs, TObjArray *coeffNames,
0306                TString &fullFormula,
0307                TString &formula, int termStart, int termEnd,
0308                Double_t xmin, Double_t xmax);
0309    int TermCoeffLength(TString &term);
0310
0311 protected:
0312
0313    template <class T>
0314    struct TF1FunctorPointerImpl: TF1FunctorPointer {
0315       TF1FunctorPointerImpl(const ROOT::Math::ParamFunctorTempl<T> &func): fImpl(func) {};
0316       TF1FunctorPointerImpl(const std::function<T(const T *f, const Double_t *param)> &func) : fImpl(func){};
0317       ~TF1FunctorPointerImpl() override {}
0318        TF1FunctorPointer * Clone() const override { return new TF1FunctorPointerImpl<T>(fImpl); }
0319       ROOT::Math::ParamFunctorTempl<T> fImpl;
0320    };
0321
0322
0323
0324
0325    static std::atomic<Bool_t> fgAbsValue;  //use absolute value of function when computing integral
0326    static Bool_t fgRejectPoint;  //True if point must be rejected in a fit
0327    static std::atomic<Bool_t> fgAddToGlobList; //True if we want to register the function in the global list
0328    static TF1   *fgCurrent;   //pointer to current function being processed
0329
0330
0331    //void CreateFromFunctor(const char *name, Int_t npar, Int_t ndim = 1);
0332    void DoInitialize(EAddToList addToGlobList);
0333
0334    void IntegrateForNormalization();
0335    // tabulate the cumulative function integral at  fNpx points. Used by GetRandom
0336    Bool_t ComputeCdfTable(Option_t * opt);
0337
0338    virtual Double_t GetMinMaxNDim(Double_t *x , Bool_t findmax, Double_t epsilon = 0, Int_t maxiter = 0) const;
0339    virtual void GetRange(Double_t *xmin, Double_t *xmax) const;
0340    virtual TH1 *DoCreateHistogram(Double_t xmin, Double_t xmax, Bool_t recreate = kFALSE);
0341
0342    TString ProvideSaveName(Option_t *option);
0343
0344 public:
0345
0346    // TF1 status bits
0347    enum EStatusBits {
0348       kNotGlobal   = BIT(10),  // don't register in global list of functions
0349       kNotDraw     = BIT(9)  // don't draw the function when in a TH1
0350    };
0351
0352    TF1();
0353    TF1(const char *name, const char *formula, Double_t xmin = 0, Double_t xmax = 1, EAddToList addToGlobList = EAddToList::kDefault, bool vectorize = false);
0354    TF1(const char *name, const char *formula, Double_t xmin, Double_t xmax, Option_t * option);  // same as above but using a string for option
0355    TF1(const char *name, Double_t xmin, Double_t xmax, Int_t npar, Int_t ndim = 1, EAddToList addToGlobList = EAddToList::kDefault);
0356    TF1(const char *name, Double_t (*fcn)(Double_t *, Double_t *), Double_t xmin = 0, Double_t xmax = 1, Int_t npar = 0, Int_t ndim = 1, EAddToList addToGlobList = EAddToList::kDefault);
0357    TF1(const char *name, Double_t (*fcn)(const Double_t *, const Double_t *), Double_t xmin = 0, Double_t xmax = 1, Int_t npar = 0, Int_t ndim = 1, EAddToList addToGlobList = EAddToList::kDefault);
0358
0359    template <class T>
0360    TF1(const char *name, std::function<T(const T *data, const Double_t *param)> &fcn, Double_t xmin = 0, Double_t xmax = 1, Int_t npar = 0, Int_t ndim = 1, EAddToList addToGlobList = EAddToList::kDefault):
0361       TF1(EFType::kTemplScalar, name, xmin, xmax, npar, ndim, addToGlobList, new TF1Parameters(npar), new TF1FunctorPointerImpl<T>(fcn))
0362    {
0363       fType = std::is_same<T, double>::value ? TF1::EFType::kTemplScalar : TF1::EFType::kTemplVec;
0364    }
0365
0366    ////////////////////////////////////////////////////////////////////////////////
0367    /// Constructor using a pointer to function.
0368    ///
0369    /// \param[in] name object name
0370    /// \param[in] fcn pointer to function
0371    /// \param[in] xmin,xmax x axis limits
0372    /// \param[in] npar is the number of free parameters used by the function
0373    /// \param[in] ndim number of dimensions
0374    /// \param[in] addToGlobList boolean marking if it should be added to global list
0375    ///
0376    /// This constructor creates a function of type C when invoked
0377    /// with the normal C++ compiler.
0378    ///
0379    ///
0380    /// \warning A function created with this constructor cannot be Cloned
0381
0382
0383    template <class T>
0384    TF1(const char *name, T(*fcn)(const T *, const Double_t *), Double_t xmin = 0, Double_t xmax = 1, Int_t npar = 0, Int_t ndim = 1, EAddToList addToGlobList = EAddToList::kDefault):
0385       TF1(EFType::kTemplVec, name, xmin, xmax, npar, ndim, addToGlobList, new TF1Parameters(npar), new TF1FunctorPointerImpl<T>(fcn))
0386    {}
0387
0388    // Constructors using functors (compiled mode only)
0389    TF1(const char *name, ROOT::Math::ParamFunctor f, Double_t xmin = 0, Double_t xmax = 1, Int_t npar = 0, Int_t ndim = 1, EAddToList addToGlobList = EAddToList::kDefault);
0390
0391    // Template constructors from any  C++ callable object,  defining  the operator() (double * , double *)
0392    // and returning a double.
0393    // The class name is not needed when using compile code, while it is required when using
0394    // interpreted code via the specialized constructor with void *.
0395    // An instance of the C++ function class or its pointer can both be used. The former is reccomended when using
0396    // C++ compiled code, but if CINT compatibility is needed, then a pointer to the function class must be used.
0397    // xmin and xmax specify the plotting range,  npar is the number of parameters.
0398    // See the tutorial math/exampleFunctor.C for an example of using this constructor
0399    template <typename Func>
0400    TF1(const char *name, Func f, Double_t xmin, Double_t xmax, Int_t npar, Int_t ndim = 1, EAddToList addToGlobList = EAddToList::kDefault) :
0401       TF1(EFType::kTemplScalar, name, xmin, xmax, npar, ndim, addToGlobList)
0402    {
0403       //actual fType set in TF1Builder
0404       ROOT::Internal::TF1Builder<Func>::Build(this, f);
0405    }
0406
0407    // backward compatible interface
0408    template <typename Func>
0409    TF1(const char *name, Func f, Double_t xmin, Double_t xmax, Int_t npar, const char *, EAddToList addToGlobList = EAddToList::kDefault) :
0410       TF1(EFType::kTemplScalar, name, xmin, xmax, npar, 1, addToGlobList, new TF1Parameters(npar))
0411    {
0412       ROOT::Internal::TF1Builder<Func>::Build(this, f);
0413    }
0414
0415
0416    // Template constructors from a pointer to any C++ class of type PtrObj with a specific member function of type
0417    // MemFn.
0418    // The member function must have the signature of  (double * , double *) and returning a double.
0419    // The class name and the method name are not needed when using compile code
0420    // (the member function pointer is used in this case), while they are required when using interpreted
0421    // code via the specialized constructor with void *.
0422    // xmin and xmax specify the plotting range,  npar is the number of parameters.
0423    // See the tutorial math/exampleFunctor.C for an example of using this constructor
0424    template <class PtrObj, typename MemFn>
0425    TF1(const char *name, const  PtrObj &p, MemFn memFn, Double_t xmin, Double_t xmax, Int_t npar, Int_t ndim = 1, EAddToList addToGlobList = EAddToList::kDefault) :
0426       TF1(EFType::kTemplScalar, name, xmin, xmax, npar, ndim, addToGlobList, new TF1Parameters(npar), new TF1FunctorPointerImpl<double>(ROOT::Math::ParamFunctor(p, memFn)))
0427    {}
0428
0429    // backward compatible interface
0430    template <class PtrObj, typename MemFn>
0431    TF1(const char *name, const  PtrObj &p, MemFn memFn, Double_t xmin, Double_t xmax, Int_t npar, const char *, const char *, EAddToList addToGlobList = EAddToList::kDefault) :
0432       TF1(EFType::kTemplScalar, name, xmin, xmax, npar, 1, addToGlobList, new TF1Parameters(npar), new TF1FunctorPointerImpl<double>(ROOT::Math::ParamFunctor(p, memFn)))
0433    {}
0434
0435    TF1(const TF1 &f1);
0436    TF1 &operator=(const TF1 &rhs);
0437      ~TF1() override;
0438    virtual void     AddParameter(const TString &name, Double_t value)
0439    {
0440       if (fFormula) fFormula->AddParameter(name, value);
0441    }
0442    // virtual void     AddParameters(const pair<TString,Double_t> *pairs, Int_t size) { fFormula->AddParameters(pairs,size); }
0443    // virtual void     AddVariable(const TString &name, Double_t value = 0) { if (fFormula) fFormula->AddVariable(name,value); }
0444    // virtual void     AddVariables(const TString *vars, Int_t size) { if (fFormula) fFormula->AddVariables(vars,size); }
0445    virtual Bool_t   AddToGlobalList(Bool_t on = kTRUE);
0446    static  Bool_t   DefaultAddToGlobalList(Bool_t on = kTRUE);
0447    void     Browse(TBrowser *b) override;
0448    void     Copy(TObject &f1) const override;
0449    TObject         *Clone(const char *newname = nullptr) const override;
0450    virtual Double_t Derivative(Double_t x, Double_t *params = nullptr, Double_t epsilon = 0.001) const;
0451    virtual Double_t Derivative2(Double_t x, Double_t *params = nullptr, Double_t epsilon = 0.001) const;
0452    virtual Double_t Derivative3(Double_t x, Double_t *params = nullptr, Double_t epsilon = 0.001) const;
0453    static  Double_t DerivativeError();
0454    Int_t    DistancetoPrimitive(Int_t px, Int_t py) override;
0455    void     Draw(Option_t *option = "") override;
0456    virtual TF1     *DrawCopy(Option_t *option = "") const;
0457    virtual TObject *DrawDerivative(Option_t *option = "al"); // *MENU*
0458    virtual TObject *DrawIntegral(Option_t *option = "al"); // *MENU*
0459    virtual void     DrawF1(Double_t xmin, Double_t xmax, Option_t *option = "");
0460    virtual Double_t Eval(Double_t x, Double_t y = 0, Double_t z = 0, Double_t t = 0) const;
0461    //template <class T> T Eval(T x, T y = 0, T z = 0, T t = 0) const;
0462    virtual Double_t EvalPar(const Double_t *x, const Double_t *params = nullptr);
0463    template <class T> T EvalPar(const T *x, const Double_t *params = nullptr);
0464    virtual Double_t operator()(Double_t x, Double_t y = 0, Double_t z = 0, Double_t t = 0) const;
0465    template <class T> T operator()(const T *x, const Double_t *params = nullptr);
0466    Double_t EvalUncertainty(Double_t x, const TMatrixDSym *covMatrix = nullptr) const;
0467    void     ExecuteEvent(Int_t event, Int_t px, Int_t py) override;
0468    virtual void     FixParameter(Int_t ipar, Double_t value);
0469    /// Return true if function has data in fSave buffer
0470    Bool_t HasSave() const { return !fSave.empty(); }
0471    bool IsVectorized()
0472    {
0473       return (fType == EFType::kTemplVec) || (fType == EFType::kFormula && fFormula && fFormula->IsVectorized());
0474    }
0475    /// Return the Chisquare after fitting. See ROOT::Fit::FitResult::Chi2()
0476    Double_t     GetChisquare() const
0477    {
0478       return fChisquare;
0479    }
0480    virtual TH1     *GetHistogram() const;
0481    virtual TH1     *CreateHistogram()
0482    {
0483       return DoCreateHistogram(fXmin, fXmax);
0484    }
0485    virtual TFormula *GetFormula()
0486    {
0487       return fFormula.get();
0488    }
0489    virtual const TFormula *GetFormula() const
0490    {
0491       return fFormula.get();
0492    }
0493    virtual TString  GetExpFormula(Option_t *option = "") const
0494    {
0495       return (fFormula) ? fFormula->GetExpFormula(option) : TString();
0496    }
0497    virtual const TObject *GetLinearPart(Int_t i) const
0498    {
0499       return (fFormula) ? fFormula->GetLinearPart(i) : nullptr;
0500    }
0501    virtual Double_t GetMaximum(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.E-10, Int_t maxiter = 100, Bool_t logx = false) const;
0502    virtual Double_t GetMinimum(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.E-10, Int_t maxiter = 100, Bool_t logx = false) const;
0503    virtual Double_t GetMaximumX(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.E-10, Int_t maxiter = 100, Bool_t logx = false) const;
0504    virtual Double_t GetMinimumX(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.E-10, Int_t maxiter = 100, Bool_t logx = false) const;
0505    virtual Double_t GetMaximumStored() const
0506    {
0507       return fMaximum;
0508    }
0509    virtual Double_t GetMinimumStored() const
0510    {
0511       return fMinimum;
0512    }
0513    virtual Int_t    GetNpar() const
0514    {
0515       return fNpar;
0516    }
0517    virtual Int_t    GetNdim() const
0518    {
0519       return fNdim;
0520    }
0521    virtual Int_t    GetNDF() const;
0522    virtual Int_t    GetNpx() const
0523    {
0524       return fNpx;
0525    }
0526    TMethodCall    *GetMethodCall() const
0527    {
0528       return fMethodCall.get();
0529    }
0530    virtual Int_t    GetNumber() const
0531    {
0532       return (fFormula) ? fFormula->GetNumber() : 0;
0533    }
0534    virtual Int_t    GetNumberFreeParameters() const;
0535    virtual Int_t    GetNumberFitPoints() const
0536    {
0537       return fNpfits;
0538    }
0539    char    *GetObjectInfo(Int_t px, Int_t py) const override;
0540    TObject    *GetParent() const
0541    {
0542       return fParent;
0543    }
0544    virtual Double_t GetParameter(Int_t ipar) const
0545    {
0546       return (fFormula) ? fFormula->GetParameter(ipar) : fParams->GetParameter(ipar);
0547    }
0548    virtual Double_t GetParameter(const TString &name)  const
0549    {
0550       return (fFormula) ? fFormula->GetParameter(name) : fParams->GetParameter(name);
0551    }
0552    virtual Double_t *GetParameters() const
0553    {
0554       return (fFormula) ? fFormula->GetParameters() : const_cast<Double_t *>(fParams->GetParameters());
0555    }
0556    virtual void     GetParameters(Double_t *params)
0557    {
0558       if (fFormula) fFormula->GetParameters(params);
0559       else std::copy(fParams->ParamsVec().begin(), fParams->ParamsVec().end(), params);
0560    }
0561    virtual const char *GetParName(Int_t ipar) const
0562    {
0563       return (fFormula) ? fFormula->GetParName(ipar) : fParams->GetParName(ipar);
0564    }
0565    virtual Int_t    GetParNumber(const char *name) const
0566    {
0567       return (fFormula) ? fFormula->GetParNumber(name) : fParams->GetParNumber(name);
0568    }
0569    virtual Double_t GetParError(Int_t ipar) const;
0570    virtual Double_t GetParError(const char *name) const
0571    {
0572       return GetParError(GetParNumber(name));
0573    }
0574    virtual const Double_t *GetParErrors() const
0575    {
0576       return fParErrors.data();
0577    }
0578    virtual void     GetParLimits(Int_t ipar, Double_t &parmin, Double_t &parmax) const;
0579    virtual Double_t GetProb() const;
0580    virtual Int_t    GetQuantiles(Int_t n, Double_t *xp, const Double_t *p);
0581    virtual Double_t GetRandom(TRandom * rng = nullptr, Option_t * opt = nullptr);
0582    virtual Double_t GetRandom(Double_t xmin, Double_t xmax, TRandom * rng = nullptr, Option_t * opt = nullptr);
0583    virtual void     GetRange(Double_t &xmin, Double_t &xmax) const;
0584    virtual void     GetRange(Double_t &xmin, Double_t &ymin, Double_t &xmax, Double_t &ymax) const;
0585    virtual void     GetRange(Double_t &xmin, Double_t &ymin, Double_t &zmin, Double_t &xmax, Double_t &ymax, Double_t &zmax) const;
0586    virtual Double_t GetSave(const Double_t *x);
0587    virtual Double_t GetX(Double_t y, Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.E-10, Int_t maxiter = 100, Bool_t logx = false) const;
0588    virtual Double_t GetXmin() const
0589    {
0590       return fXmin;
0591    }
0592    virtual Double_t GetXmax() const
0593    {
0594       return fXmax;
0595    }
0596    TAxis           *GetXaxis() const ;
0597    TAxis           *GetYaxis() const ;
0598    TAxis           *GetZaxis() const ;
0599    virtual Double_t GetVariable(const TString &name)
0600    {
0601       return (fFormula) ? fFormula->GetVariable(name) : 0;
0602    }
0603    virtual Double_t GradientPar(Int_t ipar, const Double_t *x, Double_t eps = 0.01) const;
0604    template <class T>
0605    T GradientPar(Int_t ipar, const T *x, Double_t eps = 0.01) const;
0606    template <class T>
0607    T GradientParTempl(Int_t ipar, const T *x, Double_t eps = 0.01) const;
0608
0609    virtual void     GradientPar(const Double_t *x, Double_t *grad, Double_t eps = 0.01) const;
0610    template <class T>
0611    void GradientPar(const T *x, T *grad, Double_t eps = 0.01) const;
0612    template <class T>
0613    void GradientParTempl(const T *x, T *grad, Double_t eps = 0.01) const;
0614
0615    virtual void     InitArgs(const Double_t *x, const Double_t *params);
0616    static  void     InitStandardFunctions();
0617    virtual Double_t Integral(Double_t a, Double_t b, Double_t epsrel = 1.e-12);
0618    virtual Double_t IntegralOneDim(Double_t a, Double_t b, Double_t epsrel, Double_t epsabs, Double_t &err);
0619    virtual Double_t IntegralError(Double_t a, Double_t b, const Double_t *params = nullptr, const Double_t *covmat = nullptr, Double_t epsilon = 1.E-2);
0620    virtual Double_t IntegralError(Int_t n, const Double_t *a, const Double_t *b, const Double_t *params = nullptr, const Double_t *covmat = nullptr, Double_t epsilon = 1.E-2);
0621    // virtual Double_t IntegralFast(const TGraph *g, Double_t a, Double_t b, Double_t *params = nullptr);
0622    virtual Double_t IntegralFast(Int_t num, Double_t *x, Double_t *w, Double_t a, Double_t b, Double_t *params = nullptr, Double_t epsilon = 1e-12);
0623    virtual Double_t IntegralMultiple(Int_t n, const Double_t *a, const Double_t *b, Int_t maxpts, Double_t epsrel, Double_t epsabs , Double_t &relerr, Int_t &nfnevl, Int_t &ifail);
0624    virtual Double_t IntegralMultiple(Int_t n, const Double_t *a, const Double_t *b, Int_t /*minpts*/, Int_t maxpts, Double_t epsrel, Double_t &relerr, Int_t &nfnevl, Int_t &ifail)
0625    {
0626       return  IntegralMultiple(n, a, b, maxpts, epsrel, epsrel, relerr, nfnevl, ifail);
0627    }
0628    virtual Double_t IntegralMultiple(Int_t n, const Double_t *a, const Double_t *b, Double_t epsrel, Double_t &relerr);
0629    virtual Bool_t   IsEvalNormalized() const
0630    {
0631       return fNormalized;
0632    }
0633    /// return kTRUE if the point is inside the function range
0634    virtual Bool_t   IsInside(const Double_t *x) const
0635    {
0636       return !((x[0] < fXmin) || (x[0] > fXmax));
0637    }
0638    virtual Bool_t   IsLinear() const
0639    {
0640       return (fFormula) ? fFormula->IsLinear() : false;
0641    }
0642    virtual Bool_t   IsValid() const;
0643    void     Print(Option_t *option = "") const override;
0644    void     Paint(Option_t *option = "") override;
0645    virtual void     ReleaseParameter(Int_t ipar);
0646    virtual void     Save(Double_t xmin, Double_t xmax, Double_t ymin, Double_t ymax, Double_t zmin, Double_t zmax);
0647    void     SavePrimitive(std::ostream &out, Option_t *option = "") override;
0648    virtual void     SetChisquare(Double_t chi2)
0649    {
0650       fChisquare = chi2;
0651    }
0652    virtual void     SetFitResult(const ROOT::Fit::FitResult &result, const Int_t *indpar = nullptr);
0653    template <class PtrObj, typename MemFn>
0654    void SetFunction(PtrObj &p, MemFn memFn);
0655    template <typename Func>
0656    void SetFunction(Func f);
0657    virtual void     SetMaximum(Double_t maximum = -1111); // *MENU*
0658    virtual void     SetMinimum(Double_t minimum = -1111); // *MENU*
0659    virtual void     SetNDF(Int_t ndf);
0660    virtual void     SetNumberFitPoints(Int_t npfits)
0661    {
0662       fNpfits = npfits;
0663    }
0664    virtual void     SetNormalized(Bool_t flag)
0665    {
0666       fNormalized = flag;
0667       Update();
0668    }
0669    inline void SetNdim(Int_t ndim)
0670    {
0671       fNdim = ndim;
0672       Update();
0673    }
0674    virtual void     SetNpx(Int_t npx = 100); // *MENU*
0675    virtual void     SetParameter(Int_t param, Double_t value)
0676    {
0677       (fFormula) ? fFormula->SetParameter(param, value) : fParams->SetParameter(param, value);
0678       Update();
0679    }
0680    virtual void     SetParameter(const TString &name, Double_t value)
0681    {
0682       (fFormula) ? fFormula->SetParameter(name, value) : fParams->SetParameter(name, value);
0683       Update();
0684    }
0685    virtual void     SetParameters(const Double_t *params)
0686    {
0687       (fFormula) ? fFormula->SetParameters(params) : fParams->SetParameters(params);
0688       Update();
0689    }
0690    /// Set parameter values.
0691    /// NaN values will be skipped, meaning that the corresponding parameters will not be changed.
0692    virtual void SetParameters(double p0, double p1 = TMath::QuietNaN(), double p2 = TMath::QuietNaN(),
0693                               double p3 = TMath::QuietNaN(), double p4 = TMath::QuietNaN(), double p5 = TMath::QuietNaN(),
0694                               double p6 = TMath::QuietNaN(), double p7 = TMath::QuietNaN(), double p8 = TMath::QuietNaN(),
0695                               double p9 = TMath::QuietNaN(), double p10 = TMath::QuietNaN())
0696    {
0697       // Note: this is not made a variadic template method because it would
0698       // presumably break the context menu in the TBrowser. Also, probably this
0699       // method should not be virtual, because if the user wants to change
0700       // parameter setting behavior, the SetParameter() method can be
0701       // overridden.
0702       if (fFormula) fFormula->SetParameters(p0, p1, p2, p3, p4, p5, p6, p7, p8, p9, p10);
0703       else          fParams->SetParameters(p0, p1, p2, p3, p4, p5, p6, p7, p8, p9, p10);
0704       Update();
0705    } // *MENU*
0706    virtual void     SetParName(Int_t ipar, const char *name);
0707    virtual void     SetParNames(const char *name0 = "", const char *name1 = "", const char *name2 = "",
0708                                 const char *name3 = "", const char *name4 = "", const char *name5 = "",
0709                                 const char *name6 = "", const char *name7 = "", const char *name8 = "",
0710                                 const char *name9 = "", const char *name10 = ""); // *MENU*
0711    virtual void     SetParError(Int_t ipar, Double_t error);
0712    virtual void     SetParErrors(const Double_t *errors);
0713    virtual void     SetParLimits(Int_t ipar, Double_t parmin, Double_t parmax);
0714    virtual void     SetParent(TObject *p = nullptr)
0715    {
0716       fParent = p;
0717    }
0718    virtual void     SetRange(Double_t xmin, Double_t xmax); // *MENU*
0719    virtual void     SetRange(Double_t xmin, Double_t ymin,  Double_t xmax, Double_t ymax);
0720    virtual void     SetRange(Double_t xmin, Double_t ymin, Double_t zmin,  Double_t xmax, Double_t ymax, Double_t zmax);
0721    virtual void     SetSavedPoint(Int_t point, Double_t value);
0722    void     SetTitle(const char *title = "") override; // *MENU*
0723    virtual void     SetVectorized(Bool_t vectorized)
0724    {
0725       if (fType == EFType::kFormula && fFormula)
0726          fFormula->SetVectorized(vectorized);
0727       else
0728          Warning("SetVectorized", "Can only set vectorized flag on formula-based TF1");
0729    }
0730    virtual void     Update();
0731
0732    static  TF1     *GetCurrent();
0733    static  void     AbsValue(Bool_t reject = kTRUE);
0734    static  void     RejectPoint(Bool_t reject = kTRUE);
0735    static  Bool_t   RejectedPoint();
0736    static  void     SetCurrent(TF1 *f1);
0737
0738    //Moments
0739    virtual Double_t Moment(Double_t n, Double_t a, Double_t b, const Double_t *params = nullptr, Double_t epsilon = 0.000001);
0740    virtual Double_t CentralMoment(Double_t n, Double_t a, Double_t b, const Double_t *params = nullptr, Double_t epsilon = 0.000001);
0741    virtual Double_t Mean(Double_t a, Double_t b, const Double_t *params = nullptr, Double_t epsilon = 0.000001)
0742    {
0743       return Moment(1, a, b, params, epsilon);
0744    }
0745    virtual Double_t Variance(Double_t a, Double_t b, const Double_t *params = nullptr, Double_t epsilon = 0.000001)
0746    {
0747       return CentralMoment(2, a, b, params, epsilon);
0748    }
0749
0750    //some useful static utility functions to compute sampling points for Integral
0751    //static  void     CalcGaussLegendreSamplingPoints(TGraph *g, Double_t eps=3.0e-11);
0752    //static  TGraph  *CalcGaussLegendreSamplingPoints(Int_t num=21, Double_t eps=3.0e-11);
0753    static  void     CalcGaussLegendreSamplingPoints(Int_t num, Double_t *x, Double_t *w, Double_t eps = 3.0e-11);
0754
0755 private:
0756    template <class T>
0757    T EvalParTempl(const T *data, const Double_t *params = nullptr);
0758
0759 #ifdef R__HAS_VECCORE
0760    inline double EvalParVec(const Double_t *data, const Double_t *params);
0761 #endif
0762
0763    ClassDefOverride(TF1, 12) // The Parametric 1-D function
0764 };
0765
0766 namespace ROOT {
0767    namespace Internal {
0768
0769       template<class Func>
0770       void TF1Builder<Func>::Build(TF1 *f, Func func)
0771       {
0772          using Fnc_t = typename ROOT::Internal::GetFunctorType<decltype(ROOT::Internal::GetTheRightOp(&Func::operator()))>::type;
0773          f->fType = std::is_same<Fnc_t, double>::value? TF1::EFType::kTemplScalar : TF1::EFType::kTemplVec;
0774          f->fFunctor.reset(new TF1::TF1FunctorPointerImpl<Fnc_t>(ROOT::Math::ParamFunctorTempl<Fnc_t>(func)));
0775          f->fParams = std::make_unique<TF1Parameters>(f->fNpar);
0776       }
0777
0778       template<class Func>
0779       void TF1Builder<Func *>::Build(TF1 *f, Func *func)
0780       {
0781          using Fnc_t = typename ROOT::Internal::GetFunctorType<decltype(ROOT::Internal::GetTheRightOp(&Func::operator()))>::type;
0782          f->fType = std::is_same<Fnc_t, double>::value? TF1::EFType::kTemplScalar : TF1::EFType::kTemplVec;
0783          f->fFunctor.reset(new TF1::TF1FunctorPointerImpl<Fnc_t>(ROOT::Math::ParamFunctorTempl<Fnc_t>(func)));
0784          f->fParams = std::make_unique<TF1Parameters>(f->fNpar);
0785       }
0786
0787       /// TF1 building from a string
0788       /// used to build a TFormula based on a lambda function
0789       template<>
0790       struct TF1Builder<const char *> {
0791          static void Build(TF1 *f, const char *formula)
0792          {
0793             f->fType = TF1::EFType::kFormula;
0794             f->fFormula = std::make_unique<TFormula>("tf1lambda", formula, f->fNdim, f->fNpar, false);
0795             TString formulaExpression(formula);
0796             Ssiz_t first = formulaExpression.Index("return") + 7;
0797             Ssiz_t last  = formulaExpression.Last(';');
0798             TString title = formulaExpression(first, last - first);
0799             f->SetTitle(title);
0800          }
0801       };
0802
0803       inline void
0804       EvalParMultiDim(TF1 *func, Double_t *out, const Double_t *x, std::size_t size, std::size_t rows, Double_t *params)
0805       {
0806          for (size_t i = 0; i < rows; i++) {
0807             out[i] = func->EvalPar(x + i * size, params);
0808          }
0809       }
0810    }
0811 }
0812
0813 inline Double_t TF1::operator()(Double_t x, Double_t y, Double_t z, Double_t t) const
0814 {
0815    return Eval(x, y, z, t);
0816 }
0817
0818 template <class T>
0819 inline T TF1::operator()(const T *x, const Double_t *params)
0820 {
0821    return EvalPar(x, params);
0822 }
0823
0824 ////////////////////////////////////////////////////////////////////////////////
0825 ///   EvalPar for vectorized
0826 template <class T>
0827 T TF1::EvalPar(const T *x, const Double_t *params)
0828 {
0829   if (fType == EFType::kTemplVec || fType == EFType::kTemplScalar) {
0830      return EvalParTempl(x, params);
0831   } else if (fType == EFType::kFormula) {
0832      return fFormula->EvalPar(x, params);
0833   } else
0834      return TF1::EvalPar((double *)x, params);
0835 }
0836
0837 ////////////////////////////////////////////////////////////////////////////////
0838 ///   Eval for vectorized functions
0839 // template <class T>
0840 // T TF1::Eval(T x, T y, T z, T t) const
0841 // {
0842 //    if (fType == EFType::kFormula)
0843 //       return fFormula->Eval(x, y, z, t);
0844
0845 //    T xx[] = {x, y, z, t};
0846 //    Double_t *pp = (Double_t *)fParams->GetParameters();
0847 //    return ((TF1 *)this)->EvalPar(xx, pp);
0848 // }
0849
0850 // Internal to TF1. Evaluates Templated interfaces
0851 template <class T>
0852 inline T TF1::EvalParTempl(const T *data, const Double_t *params)
0853 {
0854    assert(fType == EFType::kTemplScalar || fType == EFType::kTemplVec);
0855    if (!params) params = (Double_t *)fParams->GetParameters();
0856    if (fFunctor)
0857       return ((TF1FunctorPointerImpl<T> *)fFunctor.get())->fImpl(data, params);
0858
0859    // this should throw an error
0860    // we nned to implement a vectorized GetSave(x)
0861    return TMath::SignalingNaN();
0862 }
0863
0864 #ifdef R__HAS_VECCORE
0865 // Internal to TF1. Evaluates Vectorized TF1 on data of type Double_v
0866 inline double TF1::EvalParVec(const Double_t *data, const Double_t *params)
0867 {
0868    assert(fType == EFType::kTemplVec);
0869    std::vector<ROOT::Double_v> d(fNdim);
0870    ROOT::Double_v res;
0871
0872    for(auto i=0; i<fNdim; i++) {
0873       d[i] = ROOT::Double_v(data[i]);
0874    }
0875
0876    if (fFunctor) {
0877       res = ((TF1FunctorPointerImpl<ROOT::Double_v> *) fFunctor.get())->fImpl(d.data(), params);
0878    } else {
0879       //    res = GetSave(x);
0880       return TMath::SignalingNaN();
0881    }
0882    return vecCore::Get<ROOT::Double_v>(res, 0);
0883 }
0884 #endif
0885
0886 inline void TF1::SetRange(Double_t xmin, Double_t,  Double_t xmax, Double_t)
0887 {
0888    TF1::SetRange(xmin, xmax);
0889 }
0890 inline void TF1::SetRange(Double_t xmin, Double_t, Double_t,  Double_t xmax, Double_t, Double_t)
0891 {
0892    TF1::SetRange(xmin, xmax);
0893 }
0894
0895 template <typename Func>
0896 void TF1::SetFunction(Func f)
0897 {
0898    // set function from a generic C++ callable object
0899    fType = EFType::kPtrScalarFreeFcn;
0900    fFunctor = std::make_unique<TF1::TF1FunctorPointerImpl<double>>(ROOT::Math::ParamFunctor(f));
0901 }
0902 template <class PtrObj, typename MemFn>
0903 void TF1::SetFunction(PtrObj &p, MemFn memFn)
0904 {
0905    // set from a pointer to a member function
0906    fType = EFType::kPtrScalarFreeFcn;
0907    fFunctor = std::make_unique<TF1::TF1FunctorPointerImpl<double>>(ROOT::Math::ParamFunctor(p, memFn));
0908 }
0909
0910 template <class T>
0911 inline T TF1::GradientPar(Int_t ipar, const T *x, Double_t eps) const
0912 {
0913    if (fType == EFType::kTemplVec || fType == EFType::kTemplScalar) {
0914       return GradientParTempl<T>(ipar, x, eps);
0915    } else
0916       return GradientParTempl<Double_t>(ipar, (const Double_t *)x, eps);
0917 }
0918
0919 template <class T>
0920 inline T TF1::GradientParTempl(Int_t ipar, const T *x, Double_t eps) const
0921 {
0922    if (GetNpar() == 0)
0923       return 0;
0924
0925    if (eps < 1e-10 || eps > 1) {
0926       Warning("Derivative", "parameter esp=%g out of allowed range[1e-10,1], reset to 0.01", eps);
0927       eps = 0.01;
0928    }
0929    Double_t h;
0930    TF1 *func = (TF1 *)this;
0931    Double_t *parameters = GetParameters();
0932
0933    // Copy parameters for thread safety
0934    std::vector<Double_t> parametersCopy(parameters, parameters + GetNpar());
0935    parameters = parametersCopy.data();
0936
0937    Double_t al, bl, h2;
0938    T f1, f2, g1, g2, d0, d2;
0939
0940    ((TF1 *)this)->GetParLimits(ipar, al, bl);
0941    if (al * bl != 0 && al >= bl) {
0942       // this parameter is fixed
0943       return 0;
0944    }
0945
0946    // check if error has been computer (is not zero)
0947    if (func->GetParError(ipar) != 0)
0948       h = eps * func->GetParError(ipar);
0949    else
0950       h = eps;
0951
0952    // save original parameters
0953    Double_t par0 = parameters[ipar];
0954
0955    parameters[ipar] = par0 + h;
0956    f1 = func->EvalPar(x, parameters);
0957    parameters[ipar] = par0 - h;
0958    f2 = func->EvalPar(x, parameters);
0959    parameters[ipar] = par0 + h / 2;
0960    g1 = func->EvalPar(x, parameters);
0961    parameters[ipar] = par0 - h / 2;
0962    g2 = func->EvalPar(x, parameters);
0963
0964    // compute the central differences
0965    h2 = 1 / (2. * h);
0966    d0 = f1 - f2;
0967    d2 = 2 * (g1 - g2);
0968
0969    T grad = h2 * (4 * d2 - d0) / 3.;
0970
0971    // restore original value
0972    parameters[ipar] = par0;
0973
0974    return grad;
0975 }
0976
0977 template <class T>
0978 inline void TF1::GradientPar(const T *x, T *grad, Double_t eps) const
0979 {
0980    if (fType == EFType::kTemplVec || fType == EFType::kTemplScalar) {
0981       GradientParTempl<T>(x, grad, eps);
0982    } else
0983       GradientParTempl<Double_t>((const Double_t *)x, (Double_t *)grad, eps);
0984 }
0985
0986 template <class T>
0987 inline void TF1::GradientParTempl(const T *x, T *grad, Double_t eps) const
0988 {
0989    if (eps < 1e-10 || eps > 1) {
0990       Warning("Derivative", "parameter esp=%g out of allowed range[1e-10,1], reset to 0.01", eps);
0991       eps = 0.01;
0992    }
0993
0994    for (Int_t ipar = 0; ipar < GetNpar(); ipar++) {
0995       grad[ipar] = GradientParTempl<T>(ipar, x, eps);
0996    }
0997 }
0998
0999 #endif