library: libHist #include "TFormula.h"

# TFormula

class description - source file - inheritance tree (.pdf)

## class TFormula : public TNamed

| Inheritance Chart:
`TObject`
| <- | `TNamed`
| <- | `TFormula` |
<- |
`TF1` | <- |
`TF12` |
`TF2` | <- |
`TF3` |
`TTreeFormula` |

        protected:

                    void ClearFormula(Option_t* option = "")
            virtual void Convert(UInt_t fromVersion)
                Double_t EvalParFast(const Double_t* x, const Double_t* params)
                Double_t EvalPrimitive(const Double_t* x, const Double_t* params)
                Double_t EvalPrimitive0(const Double_t* x, const Double_t* params)
                Double_t EvalPrimitive1(const Double_t* x, const Double_t* params)
                Double_t EvalPrimitive2(const Double_t* x, const Double_t* params)
                Double_t EvalPrimitive3(const Double_t* x, const Double_t* params)
                Double_t EvalPrimitive4(const Double_t* x, const Double_t* params)
                 Short_t GetAction(Int_t code) const
                 Short_t GetActionOptimized(Int_t code) const
                   Int_t GetActionParam(Int_t code) const
                   Int_t GetActionParamOptimized(Int_t code) const
                  Int_t* GetOper() const
                  Int_t* GetOperOptimized() const
          virtual Bool_t IsString(Int_t oper) const
                    void MakePrimitive(const char* expr, Int_t pos)
                   Int_t PreCompile()
                    void SetAction(Int_t code, Int_t value, Int_t param = 0)
                    void SetActionOptimized(Int_t code, Int_t value, Int_t param = 0)

        public:

                                 TFormula()
                                 TFormula(const char* name, const char* formula)
                                 TFormula(const TFormula& formula)
                         virtual ~TFormula()
                    virtual void Analyze(const char* schain, Int_t& err, Int_t offset = 0)
                  virtual Bool_t AnalyzeFunction(TString& chaine, Int_t& err, Int_t offset = 0)
                  static TClass* Class()
                    virtual void Clear(Option_t* option = "")
                   virtual Int_t Compile(const char* expression = "")
                    virtual void Copy(TObject& formula) const
                   virtual char* DefinedString(Int_t code)
                virtual Double_t DefinedValue(Int_t code)
                   virtual Int_t DefinedVariable(TString& variable, Int_t& action)
                virtual Double_t Eval(Double_t x, Double_t y = 0, Double_t z = 0, Double_t t = 0) const
                virtual Double_t EvalPar(const Double_t* x, const Double_t* params = 0)
                virtual Double_t EvalParOld(const Double_t* x, const Double_t* params = 0)
                 virtual TString GetExpFormula() const
          virtual const TObject* GetLinearPart(Int_t i) const
                   virtual Int_t GetNdim() const
                   virtual Int_t GetNpar() const
                   virtual Int_t GetNumber() const
                        Double_t GetParameter(Int_t ipar) const
                        Double_t GetParameter(const char* name) const
               virtual Double_t* GetParameters() const
                    virtual void GetParameters(Double_t* params)
             virtual const char* GetParName(Int_t ipar) const
                   virtual Int_t GetParNumber(const char* name) const
                 virtual TClass* IsA() const
                  virtual Bool_t IsLinear()
                  virtual Bool_t IsNormalized()
                       TFormula& operator=(const TFormula& rhs)
                            void Optimize()
                    virtual void Print(Option_t* option = "") const
                    virtual void ProcessLinear(TString& replaceformula)
                    virtual void SetNumber(Int_t number)
                    virtual void SetParameter(const char* name, Double_t parvalue)
                    virtual void SetParameter(Int_t ipar, Double_t parvalue)
                    virtual void SetParameters(const Double_t* params)
                    virtual 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)
                    virtual void SetParName(Int_t ipar, const char* name)
                    virtual 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")
                    virtual void ShowMembers(TMemberInspector& insp, char* parent)
                    virtual void Streamer(TBuffer& b)
                            void StreamerNVirtual(TBuffer& b)
                    virtual void Update()

### Data Members

        private:

          Int_t* fOper  [fNoper] List of operators. (See documentation for changes made at version 7)

        protected:

                        Int_t fNdim            Dimension of function (1=1-Dim, 2=2-Dim,etc)
                        Int_t fNpar            Number of parameters
                        Int_t fNoper           Number of operators
                        Int_t fNconst          Number of constants
                        Int_t fNumber          formula number identifier
                        Int_t fNval            Number of different variables in expression
                        Int_t fNstring         Number of different constants character strings
                     TString* fExpr            [fNoper] List of expressions
                    Double_t* fConst           [fNconst] Array of fNconst formula constants
                    Double_t* fParams          [fNpar] Array of fNpar parameters
                     TString* fNames           [fNpar] Array of parameter names
                    TObjArray fFunctions       Array of function calls to make
                    TObjArray fLinearParts     ! Linear parts if the formula is linear (contains '|')
                        TBits fAlreadyFound    ! cache for information
                        Int_t fNOperOptimized  !Number of operators after optimization
                     TString* fExprOptimized   ![fNOperOptimized] List of expressions
                       Int_t* fOperOptimized   ![fNOperOptimized] List of operators. (See documentation for changes made at version 7)
                 TOperOffset* fOperOffset      ![fNOperOptimized]         Offsets of operrands
          TFormulaPrimitive** fPredefined      ![fNPar] predefined function

        public:

          static const enum TFormula:: kEnd
          static const enum TFormula:: kAdd
          static const enum TFormula:: kSubstract
          static const enum TFormula:: kMultiply
          static const enum TFormula:: kDivide
          static const enum TFormula:: kModulo
          static const enum TFormula:: kcos
          static const enum TFormula:: ksin
          static const enum TFormula:: ktan
          static const enum TFormula:: kacos
          static const enum TFormula:: kasin
          static const enum TFormula:: katan
          static const enum TFormula:: katan2
          static const enum TFormula:: kfmod
          static const enum TFormula:: kpow
          static const enum TFormula:: ksq
          static const enum TFormula:: ksqrt
          static const enum TFormula:: kstrstr
          static const enum TFormula:: kmin
          static const enum TFormula:: kmax
          static const enum TFormula:: klog
          static const enum TFormula:: kexp
          static const enum TFormula:: klog10
          static const enum TFormula:: kpi
          static const enum TFormula:: kabs
          static const enum TFormula:: ksign
          static const enum TFormula:: kint
          static const enum TFormula:: kSignInv
          static const enum TFormula:: krndm
          static const enum TFormula:: kAnd
          static const enum TFormula:: kOr
          static const enum TFormula:: kEqual
          static const enum TFormula:: kNotEqual
          static const enum TFormula:: kLess
          static const enum TFormula:: kGreater
          static const enum TFormula:: kLessThan
          static const enum TFormula:: kGreaterThan
          static const enum TFormula:: kNot
          static const enum TFormula:: kcosh
          static const enum TFormula:: ksinh
          static const enum TFormula:: ktanh
          static const enum TFormula:: kacosh
          static const enum TFormula:: kasinh
          static const enum TFormula:: katanh
          static const enum TFormula:: kStringEqual
          static const enum TFormula:: kStringNotEqual
          static const enum TFormula:: kBitAnd
          static const enum TFormula:: kBitOr
          static const enum TFormula:: kLeftShift
          static const enum TFormula:: kRightShift
          static const enum TFormula:: kexpo
          static const enum TFormula:: kxexpo
          static const enum TFormula:: kyexpo
          static const enum TFormula:: kzexpo
          static const enum TFormula:: kxyexpo
          static const enum TFormula:: kgaus
          static const enum TFormula:: kxgaus
          static const enum TFormula:: kygaus
          static const enum TFormula:: kzgaus
          static const enum TFormula:: kxygaus
          static const enum TFormula:: klandau
          static const enum TFormula:: kxlandau
          static const enum TFormula:: kylandau
          static const enum TFormula:: kzlandau
          static const enum TFormula:: kxylandau
          static const enum TFormula:: kpol
          static const enum TFormula:: kxpol
          static const enum TFormula:: kypol
          static const enum TFormula:: kzpol
          static const enum TFormula:: kParameter
          static const enum TFormula:: kConstant
          static const enum TFormula:: kBoolOptimize
          static const enum TFormula:: kStringConst
          static const enum TFormula:: kVariable
          static const enum TFormula:: kFunctionCall
          static const enum TFormula:: kData
          static const enum TFormula:: kUnary
          static const enum TFormula:: kBinary
          static const enum TFormula:: kThree
          static const enum TFormula:: kDefinedVariable
          static const enum TFormula:: kDefinedString
          static const enum TFormula:: kPlusD
          static const enum TFormula:: kPlusDD
          static const enum TFormula:: kMultD
          static const enum TFormula:: kMultDD
          static const enum TFormula:: kBoolOptimizeOr
          static const enum TFormula:: kBoolOptimizeAnd
          static const enum TFormula:: kBoolSet
          static const enum TFormula:: kFDM
          static const enum TFormula:: kFD0
          static const enum TFormula:: kFD1
          static const enum TFormula:: kFD2
          static const enum TFormula:: kFD3
          static const enum TFormula:: kNotGlobal
          static const enum TFormula:: kNormalized
          static const enum TFormula:: kLinear
                          G__p2memfunc fOptimal          !pointer to optimal function

## Class Description

    *-*-*-*-*-*-*-*-*-*-*The  F O R M U L A  class*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*                  =========================
    *-*
    *-*   This class has been implemented by

Nicolas Brun

    (age 18).
    *-*   ========================================================

/* */

    *-*
    *-*  Example of valid expressions:
    *-*     -  sin(x)/x
    *-*     -  [0]*sin(x) + [1]*exp(-[2]*x)
    *-*     -  x + y**2
    *-*     -  x^2 + y^2
    *-*     -  [0]*pow([1],4)
    *-*     -  2*pi*sqrt(x/y)
    *-*     -  gaus(0)*expo(3)  + ypol3(5)*x
    *-*     -  gausn(0)*expo(3) + ypol3(5)*x
    *-*
    *-*  In the last example above:
    *-*     gaus(0) is a substitute for [0]*exp(-0.5*((x-[1])/[2])**2)
    *-*        and (0) means start numbering parameters at 0
    *-*     gausn(0) is a substitute for [0]*exp(-0.5*((x-[1])/[2])**2)/(sqrt(2*pi)*[2]))
    *-*        and (0) means start numbering parameters at 0
    *-*     expo(3) is a substitute for exp([3]+[4])*x)
    *-*     pol3(5) is a substitute for par[5]+par[6]*x+par[7]*x**2+par[8]*x**3
    *-*         (here Pol3 stands for Polynomial of degree 3)
    *-*
    *-*   TMath functions can be part of the expression, eg:
    *-*     -  TMath::Landau(x)*sin(x)
    *-*     -  TMath::Erf(x)
    *-*
    *-*   Comparisons operators are also supported (&&, ||, ==, <=, >=, !)
    *-*   Examples:
    *-*      sin(x*(x<0.5 || x>1))
    *-*   If the result of a comparison is TRUE, the result is 1, otherwise 0.
    *-*
    *-*   Already predefined names can be given. For example, if the formula
    *-*     TFormula old(sin(x*(x<0.5 || x>1))) one can assign a name to the formula. By default
    *-*     the name of the object = title = formula itself.
    *-*     old.SetName("old").
    *-*     then, old can be reused in a new expression.
    *-*     TFormula new("x*old") is equivalent to:
    *-*     TFormula new("x*sin(x*(x<0.5 || x>1))")
    *-*
    *-*   Up to 4 dimensions are supported (indicated by x, y, z, t)
    *-*   An expression may have 0 parameters or a list of parameters
    *-*   indicated by the sequence [par_number]
    *-*
    *-*   A graph showing the logic to compile and analyze a formula
    *-*   is shown in TFormula::Compile and TFormula::Analyze.
    *-*   Once a formula has been compiled, it can be evaluated for a given
    *-*   set of parameters. see graph in TFormula::EvalPar.
    *-*
    *-*   This class is the base class for the function classes TF1,TF2 and TF3.
    *-*   It is also used by the ntuple selection mechanism TNtupleFormula.
    *-*
    *-*   In version 7 of TFormula, the usage of fOper has been changed
    *-*   to improve the performance of TFormula::EvalPar.
    *-*   Conceptually, fOper was changed from a simple array of Int_t
    *-*   to an array of composite values.
    *-*   For example a 'ylandau(5)' operation used to be encoded as 4105;
    *-*   it is now encoded as (klandau >> kTFOperShit) + 5
    *-*   Any class inheriting from TFormula and using directly fOper (which
    *-*   is now a private data member), needs to be updated to take this
    *-*   in consideration.  The member functions recommended to set and
    *-*   access fOper are:  SetAction, GetAction, GetActionParam
    *-*   For more performant access to the information, see the implementation
    *-*   TFormula::EvalPar
    *-*
    *-*     WHY TFormula CANNOT ACCEPT A CLASS MEMBER FUNCTION ?
    *-*     ====================================================
    *-* This is a frequently asked question.
    *-* C++ is a strongly typed language. There is no way for TFormula (without
    *-* recompiling this class) to know about all possible user defined data types.
    *-* This also apply to the case of a static class function.
    *-* Because TMath is a special and frequent case, TFormula is aware
    *-* of all TMath functions.
    *-*
    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

TFormula(): TNamed()

    *-*-*-*-*-*-*-*-*-*-*Formula default constructor*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*                  ============================

TFormula(const char *name,const char *expression) : TNamed(name,expression)

    *-*-*-*-*-*-*-*-*-*-*Normal Formula constructor*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*                  ==========================

TFormula(const TFormula &formula) : TNamed()

~TFormula()

    *-*-*-*-*-*-*-*-*-*-*Formula default destructor*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*                  ===========================

Bool_t AnalyzeFunction(TString &chaine, Int_t &err, Int_t offset)

    *-*-*-*-*-*-*-*-*Check if the chain as function call *-*-*-*-*-*-*-*-*-*-*
    *-*              =======================================
    *-*
    *-*   If you overload this member function, you also HAVE TO
    *-*   never call the constructor:
    *-*
    *-*     TFormula::TFormula(const char *name,const char *expression)
    *-*
    *-*   and write your own constructor
    *-*
    *-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
    *-*
    *-*   which has to call the TFormula default constructor and whose implementation
    *-*   should be similar to the implementation of the normal TFormula constructor
    *-*
    *-*   This is necessary because the normal TFormula constructor call indirectly
    *-*   the virtual member functions Analyze, DefaultString, DefaultValue
    *-*   and DefaultVariable.
    *-*

void Analyze(const char *schain, Int_t &err, Int_t offset)

    *-*-*-*-*-*-*-*-*Analyze a sub-expression in one formula*-*-*-*-*-*-*-*-*-*-*
    *-*              =======================================
    *-*
    *-*   Expressions in one formula are recursively analyzed.
    *-*   Result of analysis is stored in the object tables.
    *-*
    *-*                  Table of function codes and errors
    *-*                  ==================================
    *-*
    *-*   * functions :
    *-*
    *-*     +           1                   pow          20
    *-*     -           2                   sq           21
    *-*     *           3                   sqrt         22
    *-*     /           4                   strstr       23
    *-*     %           5                   min          24
    *-*                                     max          25
    *-*                                     log          30
    *-*     cos         10                  exp          31
    *-*     sin         11                  log10        32
    *-*     tan         12
    *-*     acos        13                  abs          41
    *-*     asin        14                  sign         42
    *-*     atan        15                  int          43
    *-*     atan2       16
    *-*     fmod        17                  rndm         50
    *-*
    *-*     cosh        70                  acosh        73
    *-*     sinh        71                  asinh        74
    *-*     tanh        72                  atanh        75
    *-*
    *-*     expo       100                  gaus        110     gausn  (see note below)
    *-*     expo(0)    100 0                gaus(0)     110 0   gausn(0)
    *-*     expo(1)    100 1                gaus(1)     110 1   gausn(1)
    *-*     xexpo      100 x                xgaus       110 x   xgausn
    *-*     yexpo      101 x                ygaus       111 x   ygausn
    *-*     zexpo      102 x                zgaus       112 x   zgausn
    *-*     xyexpo     105 x                xygaus      115 x   xygausn
    *-*     yexpo(5)   102 5                ygaus(5)    111 5   ygausn(5)
    *-*     xyexpo(2)  105 2                xygaus(2)   115 2   xygausn(2)
    *-*
    *-*     landau      120 x   landaun (see note below)
    *-*     landau(0)   120 0   landaun(0)
    *-*     landau(1)   120 1   landaun(1)
    *-*     xlandau     120 x   xlandaun
    *-*     ylandau     121 x   ylandaun
    *-*     zlandau     122 x   zlandaun
    *-*     xylandau    125 x   xylandaun
    *-*     ylandau(5)  121 5   ylandaun(5)
    *-*     xylandau(2) 125 2   xylandaun(2)
    *-*
    *-*     pol0        130 x               pol1        130 1xx
    *-*     pol0(0)     130 0               pol1(0)     130 100
    *-*     pol0(1)     130 1               pol1(1)     130 101
    *-*     xpol0       130 x               xpol1       130 101
    *-*     ypol0       131 x               ypol1       131 101
    *-*     zpol0       132 x               zpol1       132 1xx
    *-*     ypol0(5)    131 5               ypol1(5)    131 105
    *-*
    *-*     pi          40
    *-*
    *-*     &&          60                  <            64
    *-*     ||          61                  >            65
    *-*     ==          62                  <=           66
    *-*     !=          63                  =>           67
    *-*     !           68
    *-*     ==(string)  76                  &            78
    *-*     !=(string)  77                  |            79
    *-*     <<(shift)   80                  >>(shift)    81
    *-*
    *-*   * constants (kConstants) :
    *-*
    *-*    c0  141 1      c1  141 2  etc..
    *-*
    *-*   * strings (kStringConst):
    *-*
    *-*    sX  143 x
    *-*
    *-*   * variables (kFormulaVar) :
    *-*
    *-*     x    144 0      y    144 1      z    144 2      t    144 3
    *-*
    *-*   * parameters :
    *-*
    *-*     [1]        140 1
    *-*     [2]        140 2
    *-*     etc.
    *-*
    *-*   special cases for normalized gaussian or landau distributions
    *-*   =============================================================
    *-*   the expression "gaus" is a substitute for
    *-*     [0]*exp(-0.5*((x-[1])/[2])**2)
    *-*   to obtain a standard normalized gaussian, use "gausn" instead of "gaus"
    *-*   the expression "gausn" is a substitute for
    *-*     [0]*exp(-0.5*((x-[1])/[2])**2)/(sqrt(2*pi)*[2]))
    *-*
    *-*   In the same way the expression "landau" is a substitute for
    *-*     [0]*TMath::Landau(x,[1],[2],kFALSE)
    *-*   to obtain a standard normalized landau, use "landaun" instead of "landau"
    *-*   the expression "landaun" is a substitute for
    *-*     [0]*TMath::Landau(x,[1],[2],kTRUE)
    *-*
    *-*   boolean optimization (kBoolOptmize) :
    *-*   =====================================
    *-*
    *-*     Those pseudo operation are used to implement lazy evaluation of
    *-*     && and ||.  When the left hand of the expression if false
    *-*     (respectively true), the evaluation of the right is entirely skipped
    *-*     (since it would not change the value of the expreession).
    *-*
    *-*     &&   142 11 (one operation on right) 142 21 (2 operations on right)
    *-*     ||   142 12 (one operation on right) 142 22 (2 operations on right)
    *-*
    *-*   * functions calls (kFunctionCall) :
    *-*
    *-*    f0 145  0  f1 145  1  etc..
    *-*
    *-*   errors :
    *-*   ========
    *-*
    *-*     1  : Division By Zero
    *-*     2  : Invalid Floating Point Operation
    *-*     4  : Empty String
    *-*     5  : invalid syntax
    *-*     6  : Too many operators
    *-*     7  : Too many parameters
    *-*    10  : z specified but not x and y
    *-*    11  : z and y specified but not x
    *-*    12  : y specified but not x
    *-*    13  : z and x specified but not y
    *-*    20  : non integer value for parameter number
    *-*    21  : atan2 requires two arguments
    *-*    22  : pow requires two arguments
    *-*    23  : degree of polynomial not specified
    *-*    24  : Degree of polynomial must be positive
    *-*    25  : Degree of polynomial must be less than 20
    *-*    26  : Unknown name
    *-*    27  : Too many constants in expression
    *-*    28  : strstr requires two arguments
    *-*    29  : interpreted or compiled function have to return a numerical type
    *-*    30  : Bad numerical expression
    *-*    31  : Part of the variable exist but some of it is not accessible or useable
    *-*    40  : '(' is expected
    *-*    41  : ')' is expected
    *-*    42  : '[' is expected
    *-*    43  : ']' is expected

/* */

    *-*
    *-*  Special functions
    *-*  -----------------
    *-*  By default, the formula is assigned fNumber=0. However, the following
    *-*  formula built with simple functions are assigned  fNumber:
    *-*    "gaus"    100  (or gausn)
    *-*    "expo"    200
    *-*    "polN"    300+N
    *-*    "landau"  400
    *-*  Note that expressions like gaus(0), expo(1) will force fNumber=0
    *-*
    *-*  Warning when deriving a class from TFormula
    *-*  -------------------------------------------
    *-*   If you overload this member function, you also HAVE TO
    *-*   never call the constructor:
    *-*
    *-*     TFormula::TFormula(const char *name,const char *expression)
    *-*
    *-*   and write your own constructor
    *-*
    *-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
    *-*
    *-*   which has to call the TFormula default constructor and whose implementation
    *-*   should be similar to the implementation of the normal TFormula constructor
    *-*
    *-*   This is necessary because the normal TFormula constructor call indirectly
    *-*   the virtual member functions Analyze, DefaultString, DefaultValue
    *-*   and DefaultVariable.
    *-*
    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

void Clear(Option_t * /*option*/ )

    *-*-*-*-*-*-*-*-*Resets the objects*-*-*-*-*-*-*-*-*-*-*
    *-*              ==================
    *-*
    *-* Resets the object to its state before compilation.
    *-*

void ClearFormula(Option_t * /*option*/ )

    *-*-*-*-*-*-*-*-*Resets the objects*-*-*-*-*-*-*-*-*-*-*
    *-*              ==================
    *-*
    *-* Resets the object to its state before compilation.
    *-*

Int_t Compile(const char *expression)

    *-*-*-*-*-*-*-*-*-*-*Compile expression already stored in fTitle*-*-*-*-*-*
    *-*                  ===========================================
    *-*
    *-*   Loop on all subexpressions of formula stored in fTitle
    *-*
    *-*   If you overload this member function, you also HAVE TO
    *-*   never call the constructor:
    *-*
    *-*     TFormula::TFormula(const char *name,const char *expression)
    *-*
    *-*   and write your own constructor
    *-*
    *-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
    *-*
    *-*   which has to call the TFormula default constructor and whose implementation
    *-*   should be similar to the implementation of the normal TFormula constructor
    *-*
    *-*   This is necessary because the normal TFormula constructor call indirectly
    *-*   the virtual member functions Analyze, DefaultString, DefaultValue
    *-*   and DefaultVariable.
    *-*

/* */

    *-*
    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

void Copy(TObject &obj) const

    *-*-*-*-*-*-*-*-*-*-*Copy this formula*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*                  =================

char* DefinedString(Int_t)

    *-*-*-*-*-*Return address of string corresponding to special code*-*-*-*-*-*
    *-*        ======================================================
    *-*
    *-*   This member function is inactive in the TFormula class.
    *-*   It may be redefined in derived classes.
    *-*
    *-*   If you overload this member function, you also HAVE TO
    *-*   never call the constructor:
    *-*
    *-*     TFormula::TFormula(const char *name,const char *expression)
    *-*
    *-*   and write your own constructor
    *-*
    *-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
    *-*
    *-*   which has to call the TFormula default constructor and whose implementation
    *-*   should be similar to the implementation of the normal TFormula constructor
    *-*
    *-*   This is necessary because the normal TFormula constructor call indirectly
    *-*   the virtual member functions Analyze, DefaultString, DefaultValue
    *-*   and DefaultVariable.
    *-*
    /*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

Double_t DefinedValue(Int_t)

    *-*-*-*-*-*Return value corresponding to special code*-*-*-*-*-*-*-*-*
    *-*        ==========================================
    *-*
    *-*   This member function is inactive in the TFormula class.
    *-*   It may be redefined in derived classes.
    *-*
    *-*   If you overload this member function, you also HAVE TO
    *-*   never call the constructor:
    *-*
    *-*     TFormula::TFormula(const char *name,const char *expression)
    *-*
    *-*   and write your own constructor
    *-*
    *-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
    *-*
    *-*   which has to call the TFormula default constructor and whose implementation
    *-*   should be similar to the implementation of the normal TFormula constructor
    *-*
    *-*   This is necessary because the normal TFormula constructor call indirectly
    *-*   the virtual member functions Analyze, DefaultString, DefaultValue
    *-*   and DefaultVariable.
    *-*
    /*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

Int_t DefinedVariable(TString &chaine,Int_t &action)

    *-*-*-*-*-*Check if expression is in the list of defined variables*-*-*-*-*
    *-*        =======================================================
    *-*
    *-*   This member function can be overloaded in derived classes
    *-*
    *-*   If you overload this member function, you also HAVE TO
    *-*   never call the constructor:
    *-*
    *-*     TFormula::TFormula(const char *name,const char *expression)
    *-*
    *-*   and write your own constructor
    *-*
    *-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
    *-*
    *-*   which has to call the TFormula default constructor and whose implementation
    *-*   should be similar to the implementation of the normal TFormula constructor
    *-*
    *-*   This is necessary because the normal TFormula constructor call indirectly
    *-*   the virtual member functions Analyze, DefaultString, DefaultValue
    *-*   and DefaultVariable.
    *-*
    *-*   The expected returns values are
    *-*     -2 :  the name has been recognized but won't be usable
    *-*     -1 :  the name has not been recognized
    *-*    >=0 :  the name has been recognized, return the action parameter.
    *-*
    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

Double_t Eval(Double_t x, Double_t y, Double_t z, Double_t t) const

    *-*-*-*-*-*-*-*-*-*-*Evaluate this formula*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*                  =====================
    *-*
    *-*   The current value of variables x,y,z,t is passed through x, y, z and t.
    *-*   The parameters used will be the ones in the array params if params is given
    *-*    otherwise parameters will be taken from the stored data members fParams
    *-*
    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

Double_t EvalParOld(const Double_t *x, const Double_t *params)

    *-*-*-*-*-*-*-*-*-*-*Evaluate this formula*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*                  =====================
    *-*
    *-*   The current value of variables x,y,z,t is passed through the pointer x.
    *-*   The parameters used will be the ones in the array params if params is given
    *-*    otherwise parameters will be taken from the stored data members fParams

/* */

    *-*
    *-*
    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

TString GetExpFormula() const

    *-*-*-*-*-*-*-*-*Reconstruct the formula expression from*-*-*-*-*-*-*-*-*-*-*
    *-*              the internal TFormula member variables
    *-*              =======================================
    *-*
    *-*   This function uses the internal member variables of TFormula to
    *-*   construct the mathematical expression associated with the TFormula
    *-*   instance. This function can be used to get an expanded version of the
    *-*   expression originally assigned to the TFormula instance, i.e. that
    *-*   the string returned by GetExpFormula() doesn't depend on other
    *-*   TFormula object names

const TObject* GetLinearPart(Int_t i)

Double_t GetParameter(Int_t ipar) const

    return value of parameter number ipar

Double_t GetParameter(const char *parName) const

    return value of parameter named parName

const char* GetParName(Int_t ipar) const

    *-*-*-*-*-*-*-*Return name of one parameter*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*            ============================

Int_t GetParNumber(const char *parName) const

     return parameter number by name

Bool_t IsString(Int_t oper) const

     return true if the expression at the index 'oper' is to be treated as
     as string

void Print(Option_t *) const

    *-*-*-*-*-*-*-*-*-*-*Dump this formula with its attributes*-*-*-*-*-*-*-*-*-*
    *-*                  =====================================

void ProcessLinear(TString &formula)

    if the formula is for linear fitting, change the title to
    normal and fill the LinearParts array

void SetParameter(const char *name, Double_t value)

    *-*-*-*-*-*-*-*Initialize parameter number ipar*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*            ================================

void SetParameter(Int_t ipar, Double_t value)

    *-*-*-*-*-*-*-*Initialize parameter number ipar*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*            ================================

void SetParameters(const Double_t *params)

     Initialize array of all parameters
     see also next function with same name

void SetParameters(Double_t p0,Double_t p1,Double_t p2,Double_t p3,Double_t p4 ,Double_t p5,Double_t p6,Double_t p7,Double_t p8,Double_t p9,Double_t p10)

     Initialize up to 10 parameters
     All arguments except THE FIRST TWO are optional
     In case of a function with only one parameter, call this function with p1=0.
     Minimum two arguments are required to differentiate this function
     from the SetParameters(cont Double_t *params)

void SetParName(Int_t ipar, const char *name)

     Set name of parameter number ipar

void SetParNames(const char*name0,const char*name1,const char*name2,const char*name3,const char*name4, const char*name5,const char*name6,const char*name7,const char*name8,const char*name9,const char*name10)

    *-*-*-*-*-*-*-*-*-*Set up to 10 parameter names*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*                ============================

void Streamer(TBuffer &b)

    *-*-*-*-*-*-*-*-*Stream a class object*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*              =========================================

void Convert(UInt_t /* fromVersion */)

     Convert the fOper of a TFormula version fromVersion to the current in memory version

void MakePrimitive(const char *expr, Int_t pos)

      MakePrimitive
      find TFormulaPrimitive replacement for some operands

void Optimize()

     MI include

     Optimize formula
     1.) Minimize the number of operands
         a.)  several operanands are glued togther
         b.)  some primitive functions glued together - exemp. (x+y) => PlusXY(x,y)
         c.)  maximize number of standard calls minimizing number of jumps in Eval cases
         d.)  variables, parameters and constants are mapped - using fOperOfssets0
              Eval procedure use direct acces to data (only one corresponding case statement in eval procedure)

              pdata[operand={Var,Par,Const}][offset]
              pdata[fOperOffsets0[i]][fOperOffset1[i+1]]
     2.) The fastest evaluation function is choosen at the end
         a.) fOptimal := pointer to the fastest function for given evaluation string
                 switch(GetActionOptimized(0)){
                   case kData : {fOptimal= (TFormulaPrimitive::TFuncG)&TFormula::EvalPrimitive0; break;}
                   case kUnary : {fOptimal= (TFormulaPrimitive::TFuncG)&TFormula::EvalPrimitive1; break;}
                   case kBinary : {fOptimal= (TFormulaPrimitive::TFuncG)&TFormula::EvalPrimitive2; break;}
                   case kThree : {fOptimal= (TFormulaPrimitive::TFuncG)&TFormula::EvalPrimitive3; break;}
                   case kFDM : {fOptimal= (TFormulaPrimitive::TFuncG)&TFormula::EvalPrimitive4; break;}
                 }
         b.) ex. fOptimal = ::EvalPrimitive0 - if it return only variable, constant or parameter
                          = ::EvalParameter1 - if only one unary operation
                          = ::EvalPrimitive2 - if only one binary operation
                            .......

Double_t EvalPrimitive(const Double_t *x, const Double_t *params)

    Evaluate primitive formula

Double_t EvalPrimitive0(const Double_t *x, const Double_t *params)

    Evaluate primitive formula

Double_t EvalPrimitive1(const Double_t *x, const Double_t *params)

    Evaluate primitive formula

Double_t EvalPrimitive2(const Double_t *x, const Double_t *params)

    Evaluate primitive formula

Double_t EvalPrimitive3(const Double_t *x, const Double_t *params)

    Evaluate primitive formula

Double_t EvalPrimitive4(const Double_t *x, const Double_t *params)

    Evaluate primitive formula

Double_t EvalParFast(const Double_t *x, const Double_t *params)

    *-*-*-*-*-*-*-*-*-*-*Evaluate this formula*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*                  =====================
    *-*
    *-*   The current value of variables x,y,z,t is passed through the pointer x.
    *-*   The parameters used will be the ones in the array params if params is given
    *-*    otherwise parameters will be taken from the stored data members fParams

/* */

    *-*
    *-*
    *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

Int_t PreCompile()

    Pre compile function

### Inline Functions

                 Int_t* GetOper() const
                Short_t GetAction(Int_t code) const
                  Int_t GetActionParam(Int_t code) const
                   void SetAction(Int_t code, Int_t value, Int_t param = 0)
                 Int_t* GetOperOptimized() const
                Short_t GetActionOptimized(Int_t code) const
                  Int_t GetActionParamOptimized(Int_t code) const
                   void SetActionOptimized(Int_t code, Int_t value, Int_t param = 0)
              TFormula& operator=(const TFormula& rhs)
               Double_t EvalPar(const Double_t* x, const Double_t* params = 0)
                  Int_t GetNdim() const
                  Int_t GetNpar() const
                  Int_t GetNumber() const
              Double_t* GetParameters() const
                   void GetParameters(Double_t* params)
                 Bool_t IsLinear()
                 Bool_t IsNormalized()
                   void SetNumber(Int_t number)
                   void Update()
                TClass* Class()
                TClass* IsA() const
                   void ShowMembers(TMemberInspector& insp, char* parent)
                   void StreamerNVirtual(TBuffer& b)

Author: Nicolas Brun 19/08/95
Last update: root/hist:$Name: $:$Id: TFormula.cxx,v 1.96 2005/05/18 12:31:09 brun Exp $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *