library: libHist
#include "TFormula.h"

TFormula


class description - header file - source file
viewCVS header - viewCVS source

class TFormula: public TNamed

Inheritance Inherited Members Includes Libraries
Class Charts

Function Members (Methods)

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public:
TFormula()
TFormula(const TFormula& formula)
TFormula(const char* name, const char* formula)
virtual~TFormula()
voidTObject::AbstractMethod(const char* method) const
virtual voidAnalyze(const char* schain, Int_t& err, Int_t offset = 0)
virtual Bool_tAnalyzeFunction(TString& chaine, Int_t& err, Int_t offset = 0)
virtual voidTObject::AppendPad(Option_t* option = "")
virtual voidTObject::Browse(TBrowser* b)
static TClass*Class()
virtual const char*TObject::ClassName() const
virtual voidClear(Option_t* option = "")
virtual TObject*TNamed::Clone(const char* newname = "") const
virtual Int_tTNamed::Compare(const TObject* obj) const
virtual Int_tCompile(const char* expression = "")
virtual voidCopy(TObject& formula) const
virtual char*DefinedString(Int_t code)
virtual Double_tDefinedValue(Int_t code)
virtual Int_tDefinedVariable(TString& variable, Int_t& action)
virtual voidTObject::Delete(Option_t* option = "")
virtual Int_tTObject::DistancetoPrimitive(Int_t px, Int_t py)
virtual voidTObject::Draw(Option_t* option = "")
virtual voidTObject::DrawClass() const
virtual TObject*TObject::DrawClone(Option_t* option = "") const
virtual voidTObject::Dump() const
virtual voidTObject::Error(const char* method, const char* msgfmt) const
virtual Double_tEval(Double_t x, Double_t y = 0, Double_t z = 0, Double_t t = 0) const
virtual Double_tEvalPar(const Double_t* x, const Double_t* params = 0)
virtual Double_tEvalParOld(const Double_t* x, const Double_t* params = 0)
virtual voidTObject::Execute(const char* method, const char* params, Int_t* error = 0)
virtual voidTObject::Execute(TMethod* method, TObjArray* params, Int_t* error = 0)
virtual voidTObject::ExecuteEvent(Int_t event, Int_t px, Int_t py)
virtual voidTObject::Fatal(const char* method, const char* msgfmt) const
virtual voidTNamed::FillBuffer(char*& buffer)
virtual TObject*TObject::FindObject(const char* name) const
virtual TObject*TObject::FindObject(const TObject* obj) const
virtual Option_t*TObject::GetDrawOption() const
static Long_tTObject::GetDtorOnly()
virtual TStringGetExpFormula(Option_t* option = "") const
virtual const char*TObject::GetIconName() const
virtual const TObject*GetLinearPart(Int_t i)
virtual const char*TNamed::GetName() const
virtual Int_tGetNdim() const
virtual Int_tGetNpar() const
virtual Int_tGetNumber() const
virtual char*TObject::GetObjectInfo(Int_t px, Int_t py) const
static Bool_tTObject::GetObjectStat()
virtual Option_t*TObject::GetOption() const
Double_tGetParameter(Int_t ipar) const
Double_tGetParameter(const char* name) const
virtual Double_t*GetParameters() const
virtual voidGetParameters(Double_t* params)
virtual const char*GetParName(Int_t ipar) const
virtual Int_tGetParNumber(const char* name) const
virtual const char*TNamed::GetTitle() const
virtual UInt_tTObject::GetUniqueID() const
virtual Bool_tTObject::HandleTimer(TTimer* timer)
virtual ULong_tTNamed::Hash() const
virtual voidTObject::Info(const char* method, const char* msgfmt) const
virtual Bool_tTObject::InheritsFrom(const char* classname) const
virtual Bool_tTObject::InheritsFrom(const TClass* cl) const
virtual voidTObject::Inspect() const
voidTObject::InvertBit(UInt_t f)
virtual TClass*IsA() const
virtual Bool_tTObject::IsEqual(const TObject* obj) const
virtual Bool_tTObject::IsFolder() const
virtual Bool_tIsLinear()
virtual Bool_tIsNormalized()
Bool_tTObject::IsOnHeap() const
virtual Bool_tTNamed::IsSortable() const
Bool_tTObject::IsZombie() const
virtual voidTNamed::ls(Option_t* option = "") const
voidTObject::MayNotUse(const char* method) const
virtual Bool_tTObject::Notify()
static voidTObject::operator delete(void* ptr)
static voidTObject::operator delete(void* ptr, void* vp)
static voidTObject::operator delete[](void* ptr)
static voidTObject::operator delete[](void* ptr, void* vp)
void*TObject::operator new(size_t sz)
void*TObject::operator new(size_t sz, void* vp)
void*TObject::operator new[](size_t sz)
void*TObject::operator new[](size_t sz, void* vp)
TFormula&operator=(const TFormula& rhs)
voidOptimize()
virtual voidTObject::Paint(Option_t* option = "")
virtual voidTObject::Pop()
virtual voidPrint(Option_t* option = "") const
virtual voidProcessLinear(TString& replaceformula)
virtual Int_tTObject::Read(const char* name)
virtual voidTObject::RecursiveRemove(TObject* obj)
voidTObject::ResetBit(UInt_t f)
virtual voidTObject::SaveAs(const char* filename = "", Option_t* option = "") const
virtual voidTObject::SavePrimitive(ostream& out, Option_t* option = "")
voidTObject::SetBit(UInt_t f)
voidTObject::SetBit(UInt_t f, Bool_t set)
virtual voidTObject::SetDrawOption(Option_t* option = "")
static voidTObject::SetDtorOnly(void* obj)
virtual voidTNamed::SetName(const char* name)
virtual voidTNamed::SetNameTitle(const char* name, const char* title)
virtual voidSetNumber(Int_t number)
static voidTObject::SetObjectStat(Bool_t stat)
virtual voidSetParameter(const char* name, Double_t parvalue)
virtual voidSetParameter(Int_t ipar, Double_t parvalue)
virtual voidSetParameters(const Double_t* params)
virtual voidSetParameters(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 voidSetParName(Int_t ipar, const char* name)
virtual voidSetParNames(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 voidTNamed::SetTitle(const char* title = "")
virtual voidTObject::SetUniqueID(UInt_t uid)
virtual voidShowMembers(TMemberInspector& insp, char* parent)
virtual Int_tTNamed::Sizeof() const
virtual voidStreamer(TBuffer& b)
voidStreamerNVirtual(TBuffer& b)
virtual voidTObject::SysError(const char* method, const char* msgfmt) const
Bool_tTObject::TestBit(UInt_t f) const
Int_tTObject::TestBits(UInt_t f) const
virtual voidUpdate()
virtual voidTObject::UseCurrentStyle()
virtual voidTObject::Warning(const char* method, const char* msgfmt) const
virtual Int_tTObject::Write(const char* name = "0", Int_t option = 0, Int_t bufsize = 0)
virtual Int_tTObject::Write(const char* name = "0", Int_t option = 0, Int_t bufsize = 0) const
protected:
voidClearFormula(Option_t* option = "")
virtual voidConvert(UInt_t fromVersion)
virtual voidTObject::DoError(int level, const char* location, const char* fmt, va_list va) const
Double_tEvalParFast(const Double_t* x, const Double_t* params)
Double_tEvalPrimitive(const Double_t* x, const Double_t* params)
Double_tEvalPrimitive0(const Double_t* x, const Double_t* params)
Double_tEvalPrimitive1(const Double_t* x, const Double_t* params)
Double_tEvalPrimitive2(const Double_t* x, const Double_t* params)
Double_tEvalPrimitive3(const Double_t* x, const Double_t* params)
Double_tEvalPrimitive4(const Double_t* x, const Double_t* params)
Short_tGetAction(Int_t code) const
Short_tGetActionOptimized(Int_t code) const
Int_tGetActionParam(Int_t code) const
Int_tGetActionParamOptimized(Int_t code) const
Int_t*GetOper() const
Int_t*GetOperOptimized() const
virtual Bool_tIsString(Int_t oper) const
voidMakePrimitive(const char* expr, Int_t pos)
voidTObject::MakeZombie()
Int_tPreCompile()
voidSetAction(Int_t code, Int_t value, Int_t param = 0)
voidSetActionOptimized(Int_t code, Int_t value, Int_t param = 0)

Data Members

public:
enum { kEnd
kAdd
kSubstract
kMultiply
kDivide
kModulo
kcos
ksin
ktan
kacos
kasin
katan
katan2
kfmod
kpow
ksq
ksqrt
kstrstr
kmin
kmax
klog
kexp
klog10
kpi
kabs
ksign
kint
kSignInv
krndm
kAnd
kOr
kEqual
kNotEqual
kLess
kGreater
kLessThan
kGreaterThan
kNot
kcosh
ksinh
ktanh
kacosh
kasinh
katanh
kStringEqual
kStringNotEqual
kBitAnd
kBitOr
kLeftShift
kRightShift
kexpo
kxexpo
kyexpo
kzexpo
kxyexpo
kgaus
kxgaus
kygaus
kzgaus
kxygaus
klandau
kxlandau
kylandau
kzlandau
kxylandau
kpol
kxpol
kypol
kzpol
kParameter
kConstant
kBoolOptimize
kStringConst
kVariable
kFunctionCall
kData
kUnary
kBinary
kThree
kDefinedVariable
kDefinedString
kPlusD
kPlusDD
kMultD
kMultDD
kBoolOptimizeOr
kBoolOptimizeAnd
kBoolSet
kFDM
kFD0
kFD1
kFD2
kFD3
kNotGlobal
kNormalized
kLinear
};
enum TObject::EStatusBits { kCanDelete
kMustCleanup
kObjInCanvas
kIsReferenced
kHasUUID
kCannotPick
kNoContextMenu
kInvalidObject
};
enum TObject::[unnamed] { kIsOnHeap
kNotDeleted
kZombie
kBitMask
kSingleKey
kOverwrite
kWriteDelete
};
public:
G__p2memfuncfOptimal!pointer to optimal function
protected:
Int_tfNdimDimension of function (1=1-Dim, 2=2-Dim,etc)
Int_tfNparNumber of parameters
Int_tfNoperNumber of operators
Int_tfNconstNumber of constants
Int_tfNumberformula number identifier
Int_tfNvalNumber of different variables in expression
Int_tfNstringNumber 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
TObjArrayfFunctionsArray of function calls to make
TObjArrayfLinearParts! Linear parts if the formula is linear (contains '|')
TBitsfAlreadyFound! cache for information
Int_tfNOperOptimized!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
TStringTNamed::fNameobject identifier
TStringTNamed::fTitleobject title
private:
Int_t*fOper[fNoper] List of operators. (See documentation for changes made at version 7)

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()
*-*-*-*-*-*-*-*-*-*-*Formula default constructor*-*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  ============================
TFormula(const char *name,const char *expression)
*-*-*-*-*-*-*-*-*-*-*Normal Formula constructor*-*-*-*-*-*-*-*-*-*-*-*-*-*
*-*                  ==========================
TFormula(const TFormula &formula)
 Default constructor.
TFormula& operator=(const TFormula &rhs)
 Operator =
~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)
*-*-*-*-*-*-*-*-*-*-*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)
*-*-*-*-*-*-*-*-*-*-*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 *uparams)
*-*-*-*-*-*-*-*-*-*-*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(Option_t *option)
*-*-*-*-*-*-*-*-*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.
*-*
*-*  if option contains "p" the returned string will contain the formula
*-*  expression with symbolic parameters, eg [0] replaced by the actual value
*-*  of the parameter. Example:
*-*  if expression in formula is: "[0]*(x>-[1])+[2]*exp(-[3]*x)"
*-*  and parameters are 3.25,-4.01,4.44,-0.04, GetExpFormula("p") will return:
*-*   "(3.25*(x>+4.01))+(4.44*exp(+0.04*x))"
const TObject* GetLinearPart(Int_t i)
 Return linear part.
Double_t GetParameter(Int_t ipar)
return value of parameter number ipar
Double_t GetParameter(const char *parName)
return value of parameter named parName
const char * GetParName(Int_t ipar)
*-*-*-*-*-*-*-*Return name of one parameter*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
*-*            ============================
Int_t GetParNumber(const char *parName)
 return parameter number by name
Bool_t IsString(Int_t oper)
 return true if the expression at the index 'oper' is to be treated as
 as string
void Print(Option_t *)
*-*-*-*-*-*-*-*-*-*-*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 *uparams)
*-*-*-*-*-*-*-*-*-*-*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

Int_t * GetOper()
{ return fOper; }
Short_t GetAction(Int_t code)
{ return fOper[code] >> kTFOperShift; }
Int_t GetActionParam(Int_t code)
{ return fOper[code] & kTFOperMask; }
void SetAction(Int_t code, Int_t value, Int_t param = 0)
Int_t * GetOperOptimized()
{ return fOperOptimized; }
Short_t GetActionOptimized(Int_t code)
{ return fOperOptimized[code] >> kTFOperShift; }
Int_t GetActionParamOptimized(Int_t code)
{ return fOperOptimized[code] & kTFOperMask; }
void SetActionOptimized(Int_t code, Int_t value, Int_t param = 0)
Double_t EvalPar(const Double_t *x, const Double_t *params=0)
{return ((*this).*fOptimal)(x,params);}
Int_t GetNdim()
{return fNdim;}
Int_t GetNpar()
{return fNpar;}
Int_t GetNumber()
{return fNumber;}
Double_t * GetParameters()
{return fParams;}
void GetParameters(Double_t *params)
{for(Int_t i=0;i<fNpar;i++) params[i] = fParams[i];}
Bool_t IsLinear()
{return TestBit(kLinear);}
Bool_t IsNormalized()
{return TestBit(kNormalized);}
void SetNumber(Int_t number)
{fNumber = number;}
void Update()
{;}

Author: Nicolas Brun 19/08/95
Last update: root/hist:$Name: $:$Id: TFormula.cxx,v 1.128 2006/10/06 09:26:53 couet Exp $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *


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