TFormula

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

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

 Default constructor.

 Operator =

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

*-*-*-*-*-*-*-*-*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.
*-*

*-*-*-*-*-*-*-*-*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.
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*-*-*-*-*-*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.
*-*

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

*-*-*-*-*-*-*-*-*-*-*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.
*-*
*-*   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.
*-*
/*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*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.
*-*
/*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

*-*-*-*-*-*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.
*-*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

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

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

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

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

 Return linear part.

return value of parameter number ipar

return value of parameter named parName

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

 return parameter number by name

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

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

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

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

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

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

 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)

 Set name of parameter number ipar

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

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

  MakePrimitive
  find TFormulaPrimitive replacement for some operands

 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
                        .......

Evaluate primitive formula

Evaluate primitive formula

Evaluate primitive formula

Evaluate primitive formula

Evaluate primitive formula

Evaluate primitive formula

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

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

Pre compile function