TFormula.h

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// @(#)root/hist:$Id$
// Author: Maciej Zimnoch   30/09/2013
 
/*************************************************************************
 * Copyright (C) 1995-2013, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
#ifndef ROOT_TFormula
#define ROOT_TFormula
 
 
#include "TNamed.h"
#include "TBits.h"
#include "TInterpreter.h"
#include <cassert>
#include <vector>
#include <list>
#include <map>
#include <string>
#include <atomic>
#include <Math/Types.h>
 
class TMethodCall;
 
 
class TFormulaFunction
{
public:
   TString  fName;
   TString  fBody;
   Int_t    fNargs;
   Bool_t   fFound;
   Bool_t   fFuncCall;
   const char *  GetName() const    { return fName.Data(); }
   const char *  GetBody() const    { return fBody.Data(); }
   Int_t    GetNargs() const   { return fNargs;}
   Bool_t   IsFuncCall() const { return fFuncCall;}
   TFormulaFunction(){}
   TFormulaFunction(const TString &name, const TString &body, int numArgs)
      : fName(name),fBody(body),fNargs(numArgs),fFound(false),fFuncCall(true) {}
   TFormulaFunction(const TString& name)
   : fName(name),fBody(""),fNargs(0),fFound(false),fFuncCall(false){}
   Bool_t operator<(const TFormulaFunction &rhv) const
   {
      // order by length - first the longer ones to avoid replacing wrong functions
      if ( fName.Length() < rhv.fName.Length() )
         return true;
      else if ( fName.Length() > rhv.fName.Length() )
         return false;
      // case of equal length
      return fName < rhv.fName && fBody < rhv.fBody;
   }
   Bool_t operator==(const TFormulaFunction &rhv) const
   {
      return fName == rhv.fName && fBody == rhv.fBody && fNargs == rhv.fNargs;
   }
};
 
class TFormulaVariable
{
public:
   TString fName;
   Double_t fValue;
   Int_t fArrayPos;
   Bool_t fFound;
   const char * GetName() const     { return fName.Data(); }
   Double_t GetInitialValue() const    { return fValue; }
   Int_t    GetArrayPos() const { return fArrayPos; }
   TFormulaVariable():fName(""),fValue(-1),fArrayPos(-1),fFound(false){}
   TFormulaVariable(const TString &name, Double_t value, Int_t pos)
   : fName(name), fValue(value), fArrayPos(pos),fFound(false) {}
   Bool_t operator<(const TFormulaVariable &rhv) const
   {
      return fName < rhv.fName;
   }
};
 
struct TFormulaParamOrder {
   bool operator() (const TString& a, const TString& b) const;
};
 
 
class TFormula : public TNamed
{
private:
 
   // All data members are transient apart from the string defining the formula and the parameter values
 
   TString           fClingInput;           //! input function passed to Cling
   std::vector<Double_t>  fClingVariables;       //!  cached variables
   std::vector<Double_t>  fClingParameters;      //  parameter values
   Bool_t            fReadyToExecute;       //! trasient to force initialization
   std::atomic<Bool_t>  fClingInitialized;  //!  transient to force re-initialization
   Bool_t            fAllParametersSetted;    // flag to control if all parameters are setted
   Bool_t            fLazyInitialization = kFALSE;  //! transient flag to control lazy initialization (needed for reading from files)
   std::unique_ptr<TMethodCall> fMethod; //! pointer to methodcall
   std::unique_ptr<TMethodCall> fGradMethod; //! pointer to a methodcall
   TString           fClingName;     //! unique name passed to Cling to define the function ( double clingName(double*x, double*p) )
   std::string       fSavedInputFormula;  //! unique name used to defined the function and used in the global map (need to be saved in case of lazy initialization)
 
   using CallFuncSignature = TInterpreter::CallFuncIFacePtr_t::Generic_t;
   std::string       fGradGenerationInput; //! input query to clad to generate a gradient
   CallFuncSignature fFuncPtr = nullptr; //!  function pointer, owned by the JIT.
   CallFuncSignature fGradFuncPtr = nullptr; //!  function pointer, owned by the JIT.
   void *   fLambdaPtr = nullptr;            //!  pointer to the lambda function
   static bool       fIsCladRuntimeIncluded;
 
   void     InputFormulaIntoCling();
   Bool_t   PrepareEvalMethod();
   void     FillDefaults();
   void     HandlePolN(TString &formula);
   void     HandleParametrizedFunctions(TString &formula);
   void HandleParamRanges(TString &formula);
   void HandleFunctionArguments(TString &formula);
   void     HandleExponentiation(TString &formula);
   void     HandleLinear(TString &formula);
   Bool_t   InitLambdaExpression(const char * formula);
   static Bool_t   IsDefaultVariableName(const TString &name);
   void ReplaceAllNames(TString &formula, std::map<TString, TString> &substitutions);
   void FillParametrizedFunctions(std::map<std::pair<TString, Int_t>, std::pair<TString, TString>> &functions);
   void FillVecFunctionsShurtCuts();
   void ReInitializeEvalMethod();
   std::string GetGradientFuncName() const {
      assert(fClingName.Length() && "TFormula is not initialized yet!");
      return std::string(fClingName.Data()) + "_grad";
   }
   bool HasGradientGenerationFailed() const {
      return !fGradMethod && !fGradGenerationInput.empty();
   }
 
protected:
 
   std::list<TFormulaFunction>         fFuncs;    //!
   std::map<TString,TFormulaVariable>  fVars;     //!  list of  variable names
   std::map<TString,Int_t,TFormulaParamOrder>   fParams;   //|| list of  parameter names
   std::map<TString,Double_t>          fConsts;   //!
   std::map<TString,TString>           fFunctionsShortcuts;  //!
   TString                             fFormula;  // string representing the formula expression
   Int_t                               fNdim;  //   Dimension - needed for lambda expressions
   Int_t                               fNpar;  //!  Number of parameter (transient since we save the vector)
   Int_t                               fNumber;  //!
   std::vector<TObject*>               fLinearParts;  // vector of linear functions
   Bool_t                              fVectorized = false;      // whether we should use vectorized or regular variables
   // (we default to false since a lot of functions still cannot be expressed in vectorized form)
 
   static Bool_t IsOperator(const char c);
   static Bool_t IsBracket(const char c);
   static Bool_t IsFunctionNameChar(const char c);
   static Bool_t IsScientificNotation(const TString & formula, int ipos);
   static Bool_t IsHexadecimal(const TString & formula, int ipos);
   static Bool_t IsAParameterName(const TString & formula, int ipos);
   void   ExtractFunctors(TString &formula);
   void   PreProcessFormula(TString &formula);
   void   ProcessFormula(TString &formula);
   Bool_t PrepareFormula(TString &formula);
   void   ReplaceParamName(TString &formula, const TString & oldname, const TString & name);
   void   DoAddParameter(const TString &name, Double_t value, bool processFormula);
   void   DoSetParameters(const Double_t * p, Int_t size);
   void   SetPredefinedParamNames();
 
   Double_t       DoEval(const Double_t * x, const Double_t * p = nullptr) const;
#ifdef R__HAS_VECCORE
   ROOT::Double_v DoEvalVec(const ROOT::Double_v *x, const Double_t *p = nullptr) const;
#endif
 
public:
 
   enum EStatusBits {
      kNotGlobal     = BIT(10),    // don't store in gROOT->GetListOfFunction (it should be protected)
      kNormalized    = BIT(14),    // set to true if the TFormula (ex gausn) is normalized
      kLinear        = BIT(16),    //set to true if the TFormula is for linear fitting
      kLambda        = BIT(17)     // set to true if TFormula has been build with a lambda
   };
   using GradientStorage = std::vector<Double_t>;
 
                  TFormula();
   virtual        ~TFormula();
   TFormula&      operator=(const TFormula &rhs);
   TFormula(const char *name, const char * formula = "", bool addToGlobList = true, bool vectorize = false);
   TFormula(const char *name, const char * formula, int ndim, int npar, bool addToGlobList = true);
                  TFormula(const TFormula &formula);
   //               TFormula(const char *name, Int_t nparams, Int_t ndims);
 
   void           AddParameter(const TString &name, Double_t value = 0) { DoAddParameter(name,value,true); }
   void           AddVariable(const TString &name, Double_t value = 0);
   void           AddVariables(const TString *vars, const Int_t size);
   Int_t          Compile(const char *expression="");
   virtual void   Copy(TObject &f1) const;
   virtual void   Clear(Option_t * option="");
   Double_t       Eval(Double_t x) const;
   Double_t       Eval(Double_t x, Double_t y) const;
   Double_t       Eval(Double_t x, Double_t y , Double_t z) const;
   Double_t       Eval(Double_t x, Double_t y , Double_t z , Double_t t ) const;
   Double_t       EvalPar(const Double_t *x, const Double_t *params=0) const;
 
   /// Generate gradient computation routine with respect to the parameters.
   /// \returns true if a gradient was generated and GradientPar can be called.
   bool GenerateGradientPar();
 
   /// Compute the gradient employing automatic differentiation.
   ///
   /// \param[in] x - The given variables, if nullptr the already stored
   ///                variables are used.
   /// \param[out] result - The result of the computation wrt each direction.
   void GradientPar(const Double_t *x, TFormula::GradientStorage& result);
 
   void GradientPar(const Double_t *x, Double_t *result);
 
   // query if TFormula provides gradient computation using AD (CLAD)
   bool HasGeneratedGradient() const {
      return fGradMethod != nullptr;
   }
 
   // template <class T>
   // T Eval(T x, T y = 0, T z = 0, T t = 0) const;
   template <class T>
   T EvalPar(const T *x, const Double_t *params = 0) const {
      return  EvalParVec(x, params);
   }
#ifdef R__HAS_VECCORE
   ROOT::Double_v EvalParVec(const ROOT::Double_v *x, const Double_t *params = 0) const;
#endif
   TString        GetExpFormula(Option_t *option="") const;
   TString        GetGradientFormula() const;
   const TObject *GetLinearPart(Int_t i) const;
   Int_t          GetNdim() const {return fNdim;}
   Int_t          GetNpar() const {return fNpar;}
   Int_t          GetNumber() const { return fNumber; }
   const char *   GetParName(Int_t ipar) const;
   Int_t          GetParNumber(const char * name) const;
   Double_t       GetParameter(const char * name) const;
   Double_t       GetParameter(Int_t param) const;
   Double_t*      GetParameters() const;
   void           GetParameters(Double_t *params) const;
   Double_t       GetVariable(const char *name) const;
   Int_t          GetVarNumber(const char *name) const;
   TString        GetVarName(Int_t ivar) const;
   Bool_t         IsValid() const { return fReadyToExecute && fClingInitialized; }
   Bool_t IsVectorized() const { return fVectorized; }
   Bool_t         IsLinear() const { return TestBit(kLinear); }
   void           Print(Option_t *option = "") const;
   void           SetName(const char* name);
   void           SetParameter(const char* name, Double_t value);
   void           SetParameter(Int_t param, Double_t value);
   void           SetParameters(const Double_t *params);
   //void           SetParameters(const pair<TString,Double_t> *params, const Int_t size);
   void           SetParameters(Double_t p0,Double_t p1,Double_t p2=0,Double_t p3=0,Double_t p4=0,
                                     Double_t p5=0,Double_t p6=0,Double_t p7=0,Double_t p8=0,
                                     Double_t p9=0,Double_t p10=0); // *MENU*
   void           SetParName(Int_t ipar, const char *name);
   void           SetParNames(const char *name0="p0",const char *name1="p1",const char
                             *name2="p2",const char *name3="p3",const char
                             *name4="p4", const char *name5="p5",const char *name6="p6",const char *name7="p7",const char
                             *name8="p8",const char *name9="p9",const char *name10="p10"); // *MENU*
   void           SetVariable(const TString &name, Double_t value);
   void           SetVariables(const std::pair<TString,Double_t> *vars, const Int_t size);
   void SetVectorized(Bool_t vectorized);
 
   ClassDef(TFormula,13)
};
#endif