TFormula

class TFormula : public TNamed

    public:

                 TFormula TFormula(const char* name, const char* formula)
                 TFormula TFormula()
                 TFormula TFormula(const TFormula& formula)
             virtual void ~TFormula()
             virtual void Analyze(const char* schain, Int_t& err)
                  TClass* Class()
            virtual Int_t Compile(const char* expression)
             virtual void Copy(TObject& formula)
            virtual char* DefinedString(Int_t code)
         virtual Double_t DefinedValue(Int_t code)
            virtual Int_t DefinedVariable(TString& variable)
         virtual Double_t Eval(Double_t x, Double_t y = 0, Double_t z = 0)
         virtual Double_t EvalPar(Double_t* x, Double_t* params = 0)
                    Int_t GetNdim()
                    Int_t GetNpar()
                    Int_t GetNumber()
                 Double_t GetParameter(Int_t ipar)
             virtual void GetParameters(Double_t* params)
      virtual const char* GetParName(Int_t ipar) const
          virtual TClass* IsA() const
             virtual void Print(Option_t* option)
             virtual void SetNumber(Int_t number)
             virtual void SetParameter(Int_t ipar, Double_t parvalue)
             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)
             virtual void SetParameters(Double_t* params)
             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)
             virtual void ShowMembers(TMemberInspector& insp, char* parent)
             virtual void Streamer(TBuffer& b)
             virtual void Update()

  Data Members

    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     List of expressions
         Int_t* fOper     List of operators
      Double_t* fConst    Array of fNconst formula constants
      Double_t* fParams   Array of fNpar parameters
       TString* fNames    Array of parameter names

See also

TF1

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
*-*
*-*  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
*-*     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)
*-*
*-*   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 3 dimensions are supported (indicated by x, y, z)
*-*   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.
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

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

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

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

*-*-*-*-*-*-*-*-*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
*-*                                     log          30
*-*     cos         10                  exp          31
*-*     sin         11                  log10        32
*-*     tan         12
*-*     acos        13                  abs          41
*-*     asin        14                  sign         42
*-*     atan        15
*-*     atan2       16                  rndm         50
*-*
*-*     cosh        70                  acosh        73
*-*     sinh        71                  asinh        74
*-*     tanh        72                  atanh        75
*-*
*-*     expo      10xx                  gaus       20xx
*-*     expo(0)   1000                  gaus(0)    2000
*-*     expo(1)   1001                  gaus(1)    2001
*-*     xexpo     10xx                  xgaus      20xx
*-*     yexpo     11xx                  ygaus      21xx
*-*     zexpo     12xx                  zgaus      22xx
*-*     xyexpo    15xx                  xygaus     25xx
*-*     yexpo(5)  1105                  ygaus(5)   2105
*-*     xyexpo(2) 1502                  xygaus(2)  2502
*-*
*-*     landau      40xx
*-*     landau(0)   4000
*-*     landau(1)   4001
*-*     xlandau     40xx
*-*     ylandau     41xx
*-*     zlandau     42xx
*-*     xylandau    45xx
*-*     ylandau(5)  4105
*-*     xylandau(2) 4502
*-*
*-*     pol0      100xx                 pol1      101xx
*-*     pol0(0)   10000                 pol1(0)   10100
*-*     pol0(1)   10001                 pol1(1)   10101
*-*     xpol0     100xx                 xpol1     101xx
*-*     ypol0     200xx                 ypol1     201xx
*-*     zpol0     300xx                 zpol1     301xx
*-*     ypol0(5)  20005                 ypol1(5)  20105
*-*
*-*     pi          40
*-*
*-*     &&          60                  <            64
*-*     ||          61                  >            65
*-*     ==          62                  <=           66
*-*     !=          63                  =>           67
*-*     !           68
*-*     ==(string)  76                  &            78
*-*     !=(string)  77                  |            79
*-*
*-*   * constants :
*-*
*-*    c0  50000      c1  50001  etc..
*-*
*-*   * strings :
*-*
*-*    s0  80000      s1  80001  etc..
*-*
*-*   * variables :
*-*
*-*     x    100000     y    100001     z    100002     t    100003
*-*
*-*   * parameters :
*-*
*-*     [1]        101
*-*     [2]        102
*-*     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
*-*    40  : '(' is expected
*-*    41  : ')' is expected
*-*    42  : '[' is expected
*-*    43  : ']' is expected

/*

*/

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

*-*-*-*-*-*-*-*-*-*-*Compile expression already stored in fTitle*-*-*-*-*-*
*-*                  ===========================================
*-*
*-*   Loop on all subexpressions of formula stored in fTitle
*-*

/*

*/

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

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

*-*-*-*-*-*Return address of string corresponding to special code*-*-*-*-*-*
*-*        ======================================================
*-*
*-*   This member function is inactive in the TFormula class.
*-*   It may be redefined in derived classes.
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*Return value corresponding to special code*-*-*-*-*-*-*-*-*
*-*        ==========================================
*-*
*-*   This member function is inactive in the TFormula class.
*-*   It may be redefined in derived classes.
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*Check if expression is in the list of defined variables*-*-*-*-*
*-*        =======================================================
*-*
*-*   This member function can be overloaded in derived classes
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*-*-*-*-*Evaluate this formula*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  =====================
*-*
*-*   The current value of variables x,y,z is passed through x, y and z.
*-*   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
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*-*-*-*-*Evaluate this formula*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  =====================
*-*
*-*   The current value of variables x,y,z 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

/*

*/

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

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

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

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

*-*-*-*-*-*-*-*Initialize array of all parameters*-*-*-*-*-*-*-*-*-*-*-*-*
*-*            ==================================

*-*-*-*-*-*-*-*Initialize up to 10 parameters*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
*-*            ==============================

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

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

Inline Functions

              Int_t GetNdim()
              Int_t GetNpar()
              Int_t GetNumber()
           Double_t GetParameter(Int_t ipar)
               void GetParameters(Double_t* params)
               void SetNumber(Int_t number)
               void SetParName(Int_t ipar, const char* name)
               void Update()
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)