The Formula class.

This is a new version of the TFormula class based on Cling. This class is not 100% backward compatible with the old TFormula class, which is still available in ROOT as ROOT::v5::TFormula. Some of the TFormula member functions available in version 5, such as Analyze and AnalyzeFunction are not available in the new TFormula. On the other hand formula expressions which were valid in version 5 are still valid in TFormula version 6

This class has been implemented during Google Summer of Code 2013 by Maciej Zimnoch.

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
gaus(x, [0..2]) + expo(y, [3..4])

In the last examples 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 (PolN stands for Polynomial of degree N)
gaus(x, [0..2]) is a more explicit way of writing gaus(0)
expo(y, [3..4]) is a substitute for exp([3]+[4]*y)

TMath functions can be part of the expression, eg:

TMath::Landau(x)*sin(x)
TMath::Erf(x)

Formula may contain constants, eg:

sqrt2
e
pi
ln10
infinity

and more.

Formulas may also contain other user-defined ROOT functions defined with a TFormula, eg, where f1 is defined on one x-dimension and 2 parameters:

f1(x, [omega], [phi])
f1([0..1])
f1([1], [0])
f1(y)

To replace only parameter names, the dimension variable can be dropped. Alternatively, to change only the dimension variable, the parameters can be dropped. Note that if a parameter is dropped or keeps its old name, its old value will be copied to the new function. The syntax used in the examples above also applies to the predefined parametrized functions like gaus and expo.

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("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.

TFormula new("new","x*old")

is equivalent to:

TFormula new("new","x*sin(x*(x<0.5 || x>1))")

The class supports unlimited number of variables and parameters. By default the names which can be used for the variables are x,y,z,t or x[0],x[1],x[2],x[3],....x[N] for N-dimensional formulas.

This class is not anymore the base class for the function classes TF1, but it has now a data member of TF1 which can be accessed via TF1::GetFormula.

An expanded note on variables and parameters

In a TFormula, a variable is a defined by a name x, y, z or t or an index like x[0], x[1], x[2]; that is x[N] where N is an integer.

TFormula("", "x[0] * x[1] + 10")

TFormula::TFormula

TFormula()

Definition: TFormula.cxx:386

Parameters are similar and can take any name. It is specified using brackets e.g. [expected_mass] or [0].

TFormula("", "exp([expected_mass])-1")

Variables and parameters can be combined in the same TFormula. Here we consider a very simple case where we have an exponential decay after some time t and a number of events with timestamps for which we want to evaluate this function.

TFormula tf ("", "[0]*exp(-[1]*t)");
tf.SetParameter(0, 1);
tf.SetParameter(1, 0.5);
 
for (auto & event : events) {
   tf.Eval(event.t);
}

The distinction between variables and parameters arose from the TFormula's application in fitting. There parameters are fitted to the data provided through variables. In other applications this distinction can go away.

Parameter values can be provided dynamically using TFormula::EvalPar instead of TFormula::Eval. In this way parameters can be used identically to variables. See below for an example that uses only parameters to model a function.

Int_t params[2] = {1, 2}; // {vel_x, vel_y}
TFormula tf ("", "[vel_x]/sqrt(([vel_x + vel_y])**2)");
 
tf.EvalPar(nullptr, params);

A note on operators

All operators of C/C++ are allowed in a TFormula with a few caveats.

The operators |, &, % can be used but will raise an error if used in conjunction with a variable or a parameter. Variables and parameters are treated as doubles internally for which these operators are not defined. This means the following command will run successfully root -l -q -e TFormula("", "x+(10%3)").Eval(0) but not root -l -q -e TFormula("", "x%10").Eval(0).

The operator ^ is defined to mean exponentiation instead of the C/C++ interpretaion xor. ** is added, also meaning exponentiation.

The operators ++ and @ are added, and are shorthand for the a linear function. That means the expression x@2 will be expanded to [n]*x + [n+1]*2 where n is the first previously unused parameter number.

Definition at line 83 of file TFormula.h.

Public Types
enum	EStatusBits { kNotGlobal = BIT(10) , kNormalized = BIT(14) , kLinear = BIT(16) , kLambda = BIT(17) }

using	GradientStorage = std::vector< Double_t >

Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff }

enum	{ kSingleKey = BIT(0) , kOverwrite = BIT(1) , kWriteDelete = BIT(2) }

enum	EDeprecatedStatusBits { kObjInCanvas = BIT(3) }

enum	EStatusBits { kCanDelete = BIT(0) , kMustCleanup = BIT(3) , kIsReferenced = BIT(4) , kHasUUID = BIT(5) , kCannotPick = BIT(6) , kNoContextMenu = BIT(8) , kInvalidObject = BIT(13) }

Public Member Functions
	TFormula ()

	TFormula (const char name, const char formula, int ndim, int npar, bool addToGlobList=true)
	Constructor from a full compile-able C++ expression. More...

	TFormula (const char name, const char formula="", bool addToGlobList=true, bool vectorize=false)

	TFormula (const TFormula &formula)

virtual	~TFormula ()

void	AddParameter (const TString &name, Double_t value=0)

void	AddVariable (const TString &name, Double_t value=0)
	Adds variable to known variables, and reprocess formula. More...

void	AddVariables (const TString *vars, const Int_t size)
	Adds multiple variables. More...

virtual void	Clear (Option_t *option="")
	Clear the formula setting expression to empty and reset the variables and parameters containers. More...

Int_t	Compile (const char *expression="")
	Compile the given expression with Cling backward compatibility method to be used in combination with the empty constructor if no expression is given , the current stored formula (retrieved with GetExpFormula()) or the title is used. More...

virtual void	Copy (TObject &f1) const
	Copy this to obj. More...

Double_t	Eval (Double_t x) const
	Sets first variable (e.g. x) and evaluate formula. More...

Double_t	Eval (Double_t x, Double_t y) const
	Sets first 2 variables (e.g. x and y) and evaluate formula. More...

Double_t	Eval (Double_t x, Double_t y, Double_t z) const
	Sets first 3 variables (e.g. x, y, z) and evaluate formula. More...

Double_t	Eval (Double_t x, Double_t y, Double_t z, Double_t t) const
	Sets first 4 variables (e.g. x, y, z, t) and evaluate formula. More...

Double_t	EvalPar (const Double_t x, const Double_t params=0) const

template<class T >
T	EvalPar (const T x, const Double_t params=0) const

bool	GenerateGradientPar ()
	Generate gradient computation routine with respect to the parameters. More...

TString	GetExpFormula (Option_t *option="") const
	Return the expression formula. More...

TString	GetGradientFormula () const

const TObject *	GetLinearPart (Int_t i) const
	Return linear part. More...

Int_t	GetNdim () const

Int_t	GetNpar () const

Int_t	GetNumber () const

Double_t	GetParameter (const char *name) const
	Returns parameter value given by string. More...

Double_t	GetParameter (Int_t param) const
	Return parameter value given by integer. More...

Double_t *	GetParameters () const

void	GetParameters (Double_t *params) const

const char *	GetParName (Int_t ipar) const
	Return parameter name given by integer. More...

Int_t	GetParNumber (const char *name) const
	Return parameter index given a name (return -1 for not existing parameters) non need to print an error. More...

Double_t	GetVariable (const char *name) const
	Returns variable value. More...

TString	GetVarName (Int_t ivar) const
	Returns variable name given its position in the array. More...

Int_t	GetVarNumber (const char *name) const
	Returns variable number (positon in array) given its name. More...

void	GradientPar (const Double_t x, Double_t result)

void	GradientPar (const Double_t *x, TFormula::GradientStorage &result)
	Compute the gradient employing automatic differentiation. More...

Bool_t	IsLinear () const

Bool_t	IsValid () const

Bool_t	IsVectorized () const

TFormula &	operator= (const TFormula &rhs)
	= operator. More...

void	Print (Option_t *option="") const
	Print the formula and its attributes. More...

void	SetName (const char *name)
	Set the name of the formula. More...

void	SetParameter (const char *name, Double_t value)
	Sets parameter value. More...

void	SetParameter (Int_t param, Double_t value)
	Set a parameter given a parameter index The parameter index is by default the alphabetic order given to the parameters apart if the users has defined explicitly the parameter names. More...

void	SetParameters (const Double_t *params)
	Set a vector of parameters value. More...

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)
	Set a list of parameters. More...

void	SetParName (Int_t ipar, const char *name)

void	SetParNames (const char name0="p0", const char name1="p1", const char name2="p2", const char name3="p3", const char name4="p4", const char name5="p5", const char name6="p6", const char name7="p7", const char name8="p8", const char name9="p9", const char *name10="p10")

void	SetVariable (const TString &name, Double_t value)
	Sets variable value. More...

void	SetVariables (const std::pair< TString, Double_t > *vars, const Int_t size)
	Sets multiple variables. More...

void	SetVectorized (Bool_t vectorized)

Public Member Functions inherited from TNamed
	TNamed ()

	TNamed (const char name, const char title)

	TNamed (const TNamed &named)
	TNamed copy ctor. More...

	TNamed (const TString &name, const TString &title)

virtual	~TNamed ()
	TNamed destructor. More...

virtual void	Clear (Option_t *option="")
	Set name and title to empty strings (""). More...

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...

virtual Int_t	Compare (const TObject *obj) const
	Compare two TNamed objects. More...

virtual void	Copy (TObject &named) const
	Copy this to obj. More...

virtual void	FillBuffer (char *&buffer)
	Encode TNamed into output buffer. More...

virtual const char *	GetName () const
	Returns name of object. More...

virtual const char *	GetTitle () const
	Returns title of object. More...

virtual ULong_t	Hash () const
	Return hash value for this object. More...

virtual Bool_t	IsSortable () const

virtual void	ls (Option_t *option="") const
	List TNamed name and title. More...

TNamed &	operator= (const TNamed &rhs)
	TNamed assignment operator. More...

virtual void	Print (Option_t *option="") const
	Print TNamed name and title. More...

virtual void	SetName (const char *name)
	Set the name of the TNamed. More...

virtual void	SetNameTitle (const char name, const char title)
	Set all the TNamed parameters (name and title). More...

virtual void	SetTitle (const char *title="")
	Set the title of the TNamed. More...

virtual Int_t	Sizeof () const
	Return size of the TNamed part of the TObject. More...

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor. More...

	TObject (const TObject &object)
	TObject copy ctor. More...

virtual	~TObject ()
	TObject destructor. More...

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action. More...

ULong_t	CheckedHash ()
	Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object. More...

virtual const char *	ClassName () const
	Returns name of class to which the object belongs. More...

virtual void	Clear (Option_t *="")

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...

virtual Int_t	Compare (const TObject *obj) const
	Compare abstract method. More...

virtual void	Copy (TObject &object) const
	Copy this to obj. More...

virtual void	Delete (Option_t *option="")
	Delete this object. More...

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object. More...

virtual void	Draw (Option_t *option="")
	Default Draw method for all objects. More...

virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs. More...

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad for instance with: `gROOT->SetSelectedPad(gPad)`. More...

virtual void	Dump () const
	Dump contents of object on stdout. More...

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message. More...

virtual void	Execute (const char method, const char params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g. More...

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray. More...

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py). More...

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message. More...

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...

virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes. More...

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object. More...

virtual const char *	GetIconName () const
	Returns mime type name of object. More...

virtual const char *	GetName () const
	Returns name of object. More...

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...

virtual Option_t *	GetOption () const

virtual const char *	GetTitle () const
	Returns title of object. More...

virtual UInt_t	GetUniqueID () const
	Return the unique object id. More...

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out. More...

virtual ULong_t	Hash () const
	Return hash value for this object. More...

Bool_t	HasInconsistentHash () const
	Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e. More...

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message. More...

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname". More...

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl. More...

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas. More...

void	InvertBit (UInt_t f)

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory). More...

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...

R__ALWAYS_INLINE Bool_t	IsOnHeap () const

virtual Bool_t	IsSortable () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

virtual void	ls (Option_t *option="") const
	The ls function lists the contents of a class on stdout. More...

void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More...

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. More...

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete. More...

void	operator delete (void *ptr)
	Operator delete. More...

void	operator delete[] (void *ptr)
	Operator delete []. More...

void *	operator new (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz)

void *	operator new[] (size_t sz, void *vp)

TObject &	operator= (const TObject &rhs)
	TObject assignment operator. More...

virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself. More...

virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list. More...

virtual void	Print (Option_t *option="") const
	This method must be overridden when a class wants to print itself. More...

virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory. More...

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list. More...

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename. More...

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out". More...

void	SetBit (UInt_t f)

void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f. More...

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object. More...

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id. More...

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message. More...

R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More...

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory. More...

Protected Member Functions
void	DoAddParameter (const TString &name, Double_t value, bool processFormula)
	Adds parameter to known parameters. More...

Double_t	DoEval (const Double_t x, const Double_t p=nullptr) const
	Evaluate formula. More...

void	DoSetParameters (const Double_t *p, Int_t size)

void	ExtractFunctors (TString &formula)
	Extracts functors from formula, and put them in fFuncs. More...

Bool_t	PrepareFormula (TString &formula)
	prepare the formula to be executed normally is called with fFormula More...

void	PreProcessFormula (TString &formula)
	Preprocessing of formula Replace all ** by ^, and removes spaces. More...

void	ProcessFormula (TString &formula)
	Iterates through functors in fFuncs and performs the appropriate action. More...

void	ReplaceParamName (TString &formula, const TString &oldname, const TString &name)
	Replace in Formula expression the parameter name. More...

void	SetPredefinedParamNames ()
	Set parameter names only in case of pre-defined functions. More...

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

void	MakeZombie ()

Static Protected Member Functions
static Bool_t	IsAParameterName (const TString &formula, int ipos)

static Bool_t	IsBracket (const char c)

static Bool_t	IsFunctionNameChar (const char c)

static Bool_t	IsHexadecimal (const TString &formula, int ipos)

static Bool_t	IsOperator (const char c)

static Bool_t	IsScientificNotation (const TString &formula, int ipos)

Protected Attributes
std::map< TString, Double_t >	fConsts

TString	fFormula

std::list< TFormulaFunction >	fFuncs

std::map< TString, TString >	fFunctionsShortcuts

std::vector< TObject * >	fLinearParts

Int_t	fNdim

Int_t	fNpar

Int_t	fNumber
	Number of parameter (transient since we save the vector) More...

std::map< TString, Int_t, TFormulaParamOrder >	fParams
	list of variable names More...

std::map< TString, TFormulaVariable >	fVars

Bool_t	fVectorized = false

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

Private Types
using	CallFuncSignature = TInterpreter::CallFuncIFacePtr_t::Generic_t
	unique name used to defined the function and used in the global map (need to be saved in case of lazy initialization) More...

Private Member Functions
void	FillDefaults ()
	Fill structures with default variables, constants and function shortcuts. More...

void	FillParametrizedFunctions (std::map< std::pair< TString, Int_t >, std::pair< TString, TString > > &functions)
	Fill map with parametrized functions. More...

void	FillVecFunctionsShurtCuts ()
	Fill the shortcuts for vectorized functions We will replace for example sin with vecCore::Mat::Sin. More...

std::string	GetGradientFuncName () const

void	HandleExponentiation (TString &formula)
	Handling exponentiation Can handle multiple carets, eg. More...

void	HandleFunctionArguments (TString &formula)
	Handling user functions (and parametrized functions) to take variables and optionally parameters as arguments. More...

void	HandleLinear (TString &formula)
	Handle linear functions defined with the operator ++. More...

void	HandleParametrizedFunctions (TString &formula)
	Handling parametrized functions Function can be normalized, and have different variable then x. More...

void	HandleParamRanges (TString &formula)
	Handling parameter ranges, in the form of [1..5]. More...

void	HandlePolN (TString &formula)
	Handling polN If before 'pol' exist any name, this name will be treated as variable used in polynomial eg. More...

bool	HasGradientGenerationFailed () const

Bool_t	InitLambdaExpression (const char *formula)

void	InputFormulaIntoCling ()
	Inputs formula, transfered to C++ code into Cling. More...

Bool_t	PrepareEvalMethod ()
	Sets TMethodCall to function inside Cling environment. More...

void	ReInitializeEvalMethod ()
	Re-initialize eval method. More...

void	ReplaceAllNames (TString &formula, std::map< TString, TString > &substitutions)

Static Private Member Functions
static Bool_t	IsDefaultVariableName (const TString &name)

Private Attributes
Bool_t	fAllParametersSetted
	transient to force re-initialization More...

Bool_t	fClingInitialized
	trasient to force initialization More...

TString	fClingInput

TString	fClingName
	pointer to a methodcall More...

std::vector< Double_t >	fClingParameters
	cached variables More...

std::vector< Double_t >	fClingVariables
	input function passed to Cling More...

CallFuncSignature	fFuncPtr = nullptr
	input query to clad to generate a gradient More...

CallFuncSignature	fGradFuncPtr = nullptr
	function pointer, owned by the JIT. More...

std::string	fGradGenerationInput

std::unique_ptr< TMethodCall >	fGradMethod
	pointer to methodcall More...

void *	fLambdaPtr = nullptr
	function pointer, owned by the JIT. More...

Bool_t	fLazyInitialization = kFALSE

TMethodCall *	fMethod
	transient flag to control lazy initialization (needed for reading from files) More...

Bool_t	fReadyToExecute

std::string	fSavedInputFormula
	unique name passed to Cling to define the function ( double clingName(doublex, doublep) ) More...

Static Private Attributes
static bool	fIsCladRuntimeIncluded = false
	pointer to the lambda function More...

Additional Inherited Members
Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...

static Bool_t	GetObjectStat ()
	Get status of object stat flag. More...

static void	SetDtorOnly (void *obj)
	Set destructor only flag. More...

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable. More...

#include "inc/TFormula.h"

Inheritance diagram for TFormula:

[legend]

Member Typedef Documentation

◆ CallFuncSignature

using TFormula::CallFuncSignature = TInterpreter::CallFuncIFacePtr_t::Generic_t

private

unique name used to defined the function and used in the global map (need to be saved in case of lazy initialization)

Definition at line 101 of file TFormula.h.

◆ GradientStorage

using TFormula::GradientStorage = std::vector<Double_t>

Definition at line 174 of file TFormula.h.

Member Enumeration Documentation

◆ EStatusBits

enum TFormula::EStatusBits

Enumerator
kNotGlobal
kNormalized
kLinear
kLambda

Definition at line 168 of file TFormula.h.

Constructor & Destructor Documentation

◆ TFormula() [1/4]

TFormula::TFormula ( )

Definition at line 386 of file TFormula.cxx.

◆ ~TFormula()

TFormula::~TFormula ( )

virtual

Definition at line 413 of file TFormula.cxx.

◆ TFormula() [2/4]

TFormula::TFormula	(	const char *	name,
		const char *	formula = `""`,
		bool	addToGlobList = `true`,
		bool	vectorize = `false`
	)

Definition at line 433 of file TFormula.cxx.

◆ TFormula() [3/4]

TFormula::TFormula	(	const char *	name,
		const char *	formula,
		int	ndim,
		int	npar,
		bool	addToGlobList = `true`
	)

Constructor from a full compile-able C++ expression.

Definition at line 480 of file TFormula.cxx.

◆ TFormula() [4/4]

TFormula::TFormula ( const TFormula & formula )

Definition at line 527 of file TFormula.cxx.

Member Function Documentation

◆ AddParameter()

void TFormula::AddParameter	(	const TString &	name,
		Double_t	value = `0`
	)

inline

Definition at line 184 of file TFormula.h.

◆ AddVariable()

void TFormula::AddVariable	(	const TString &	name,
		Double_t	value = `0`
	)

Adds variable to known variables, and reprocess formula.

Definition at line 2541 of file TFormula.cxx.

◆ AddVariables()

void TFormula::AddVariables	(	const TString *	vars,
		const Int_t	size
	)

Adds multiple variables.

First argument is an array of pairs<TString,Double>, where first argument is name of variable, second argument represents value. size - number of variables passed in first argument

Definition at line 2574 of file TFormula.cxx.

◆ Clear()

void TFormula::Clear ( Option_t * option = "" )

virtual

Clear the formula setting expression to empty and reset the variables and parameters containers.

Reimplemented from TNamed.

Definition at line 726 of file TFormula.cxx.

◆ Compile()

Int_t TFormula::Compile ( const char * expression = "" )

Compile the given expression with Cling backward compatibility method to be used in combination with the empty constructor if no expression is given , the current stored formula (retrieved with GetExpFormula()) or the title is used.

return 0 if the formula compilation is successful

Definition at line 604 of file TFormula.cxx.

◆ Copy()

void TFormula::Copy ( TObject & named ) const

virtual

Copy this to obj.

Reimplemented from TNamed.

Definition at line 638 of file TFormula.cxx.

◆ DoAddParameter()

void TFormula::DoAddParameter	(	const TString &	name,
		Double_t	value,
		bool	processFormula
	)

protected

Adds parameter to known parameters.

User should use SetParameter, because parameters are added during initialization part, and after that adding new will be pointless.

Definition at line 2715 of file TFormula.cxx.

◆ DoEval()

Double_t TFormula::DoEval	(	const Double_t *	x,
		const Double_t *	p = `nullptr`
	)		const

protected

Evaluate formula.

If formula is not ready to execute(missing parameters/variables), print these which are not known. If parameter has default value, and has not been set, appropriate warning is shown.

Definition at line 3330 of file TFormula.cxx.

◆ DoSetParameters()

void TFormula::DoSetParameters	(	const Double_t *	p,
		Int_t	size
	)

protected

Definition at line 2921 of file TFormula.cxx.

◆ Eval() [1/4]

Double_t TFormula::Eval ( Double_t x ) const

Sets first variable (e.g. x) and evaluate formula.

Definition at line 3318 of file TFormula.cxx.

◆ Eval() [2/4]

Double_t TFormula::Eval	(	Double_t	x,
		Double_t	y
	)		const

Sets first 2 variables (e.g. x and y) and evaluate formula.

Definition at line 3309 of file TFormula.cxx.

◆ Eval() [3/4]

Double_t TFormula::Eval	(	Double_t	x,
		Double_t	y,
		Double_t	z
	)		const

Sets first 3 variables (e.g. x, y, z) and evaluate formula.

Definition at line 3300 of file TFormula.cxx.

◆ Eval() [4/4]

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

Sets first 4 variables (e.g. x, y, z, t) and evaluate formula.

Definition at line 3291 of file TFormula.cxx.

◆ EvalPar() [1/2]

Double_t TFormula::EvalPar	(	const Double_t *	x,
		const Double_t *	params = `0`
	)		const

Definition at line 3102 of file TFormula.cxx.

◆ EvalPar() [2/2]

template<class T >

T TFormula::EvalPar	(	const T *	x,
		const Double_t *	params = `0`
	)		const

inline

Definition at line 212 of file TFormula.h.

◆ ExtractFunctors()

void TFormula::ExtractFunctors ( TString & formula )

protected

Extracts functors from formula, and put them in fFuncs.

Simple grammar:

<function> := name(arg1,arg2...)
<variable> := name
<parameter> := [number]
<name> := String containing lower and upper letters, numbers, underscores
<number> := Integer number Operators are omitted.

Definition at line 1804 of file TFormula.cxx.

◆ FillDefaults()

void TFormula::FillDefaults ( )

private

Fill structures with default variables, constants and function shortcuts.

Definition at line 862 of file TFormula.cxx.

◆ FillParametrizedFunctions()

void TFormula::FillParametrizedFunctions ( std::map< std::pair< TString, Int_t >, std::pair< TString, TString > > & functions )

private

Fill map with parametrized functions.

Definition at line 2389 of file TFormula.cxx.

◆ FillVecFunctionsShurtCuts()

void TFormula::FillVecFunctionsShurtCuts ( )

private

Fill the shortcuts for vectorized functions We will replace for example sin with vecCore::Mat::Sin.

Definition at line 930 of file TFormula.cxx.

◆ GenerateGradientPar()

bool TFormula::GenerateGradientPar ( )

Generate gradient computation routine with respect to the parameters.

returns true on success.

Returns: true if a gradient was generated and GradientPar can be called.

Definition at line 3152 of file TFormula.cxx.

◆ GetExpFormula()

TString TFormula::GetExpFormula ( Option_t * option = "" ) const

Return the expression formula.

If option = "P" replace the parameter names with their values
If option = "CLING" return the actual expression used to build the function passed to cling
If option = "CLINGP" replace in the CLING expression the parameter with their values

Definition at line 3486 of file TFormula.cxx.

◆ GetGradientFormula()

TString TFormula::GetGradientFormula ( ) const

Definition at line 3556 of file TFormula.cxx.

◆ GetGradientFuncName()

std::string TFormula::GetGradientFuncName ( ) const

inlineprivate

Definition at line 123 of file TFormula.h.

◆ GetLinearPart()

const TObject * TFormula::GetLinearPart ( Int_t i ) const

Return linear part.

Definition at line 2525 of file TFormula.cxx.

◆ GetNdim()

Int_t TFormula::GetNdim ( ) const

inline

Definition at line 221 of file TFormula.h.

◆ GetNpar()

Int_t TFormula::GetNpar ( ) const

inline

Definition at line 222 of file TFormula.h.

◆ GetNumber()

Int_t TFormula::GetNumber ( ) const

inline

Definition at line 223 of file TFormula.h.

◆ GetParameter() [1/2]

Double_t TFormula::GetParameter ( const char * name ) const

Returns parameter value given by string.

Definition at line 2805 of file TFormula.cxx.

◆ GetParameter() [2/2]

Double_t TFormula::GetParameter ( Int_t param ) const

Return parameter value given by integer.

Definition at line 2819 of file TFormula.cxx.

◆ GetParameters() [1/2]

Double_t * TFormula::GetParameters ( ) const

Definition at line 2845 of file TFormula.cxx.

◆ GetParameters() [2/2]

void TFormula::GetParameters ( Double_t * params ) const

Definition at line 2852 of file TFormula.cxx.

◆ GetParName()

const char * TFormula::GetParName ( Int_t ipar ) const

Return parameter name given by integer.

Definition at line 2831 of file TFormula.cxx.

◆ GetParNumber()

Int_t TFormula::GetParNumber ( const char * name ) const

Return parameter index given a name (return -1 for not existing parameters) non need to print an error.

Definition at line 2793 of file TFormula.cxx.

◆ GetVariable()

Double_t TFormula::GetVariable ( const char * name ) const

Returns variable value.

Definition at line 2658 of file TFormula.cxx.

◆ GetVarName()

TString TFormula::GetVarName ( Int_t ivar ) const

Returns variable name given its position in the array.

Definition at line 2684 of file TFormula.cxx.

◆ GetVarNumber()

Int_t TFormula::GetVarNumber ( const char * name ) const

Returns variable number (positon in array) given its name.

Definition at line 2671 of file TFormula.cxx.

◆ GradientPar() [1/2]

void TFormula::GradientPar	(	const Double_t *	x,
		Double_t *	result
	)

Definition at line 3219 of file TFormula.cxx.

◆ GradientPar() [2/2]

void TFormula::GradientPar	(	const Double_t *	x,
		TFormula::GradientStorage &	result
	)

Compute the gradient employing automatic differentiation.

Parameters

[in]	x	- The given variables, if nullptr the already stored variables are used.
[out]	result	- The result of the computation wrt each direction.

Definition at line 3194 of file TFormula.cxx.

◆ HandleExponentiation()

void TFormula::HandleExponentiation ( TString & formula )

private

Handling exponentiation Can handle multiple carets, eg.

2^3^4 will be treated like 2^(3^4)

Definition at line 1594 of file TFormula.cxx.

◆ HandleFunctionArguments()

void TFormula::HandleFunctionArguments ( TString & formula )

private

Handling user functions (and parametrized functions) to take variables and optionally parameters as arguments.

Definition at line 1310 of file TFormula.cxx.

◆ HandleLinear()

void TFormula::HandleLinear ( TString & formula )

private

Handle linear functions defined with the operator ++.

Definition at line 1688 of file TFormula.cxx.

◆ HandleParametrizedFunctions()

void TFormula::HandleParametrizedFunctions ( TString & formula )

private

Handling parametrized functions Function can be normalized, and have different variable then x.

Variables should be placed in brackets after function name. No brackets are treated like [x]. Normalized function has char 'n' after name, eg. gausn[var](0) will be replaced with [0]*exp(-0.5*((var-[1])/[2])^2)/(sqrt(2*pi)*[2])

Adding function is easy, just follow these rules, and add to TFormula::FillParametrizedFunctions defined further below:

Key for function map is pair of name and dimension of function
value of key is a pair function body and normalized function body
{Vn} is a place where variable appear, n represents n-th variable from variable list. Count starts from 0.
[num] stands for parameter number. If user pass to function argument 5, num will stand for (5 + num) parameter.

Definition at line 1063 of file TFormula.cxx.

◆ HandleParamRanges()

void TFormula::HandleParamRanges ( TString & formula )

private

Handling parameter ranges, in the form of [1..5].

Definition at line 1279 of file TFormula.cxx.

◆ HandlePolN()

void TFormula::HandlePolN ( TString & formula )

private

Handling polN If before 'pol' exist any name, this name will be treated as variable used in polynomial eg.

varpol2(5) will be replaced with: [5] + [6]*var + [7]*var^2 Empty name is treated like variable x.

Definition at line 962 of file TFormula.cxx.

◆ HasGradientGenerationFailed()

bool TFormula::HasGradientGenerationFailed ( ) const

inlineprivate

Definition at line 127 of file TFormula.h.

◆ InitLambdaExpression()

Bool_t TFormula::InitLambdaExpression ( const char * formula )

private

Definition at line 559 of file TFormula.cxx.

◆ InputFormulaIntoCling()

void TFormula::InputFormulaIntoCling ( )

private

Inputs formula, transfered to C++ code into Cling.

Definition at line 836 of file TFormula.cxx.

◆ IsAParameterName()

Bool_t TFormula::IsAParameterName	(	const TString &	formula,
		int	ipos
	)

staticprotected

Definition at line 301 of file TFormula.cxx.

◆ IsBracket()

Bool_t TFormula::IsBracket ( const char c )

staticprotected

Definition at line 242 of file TFormula.cxx.

◆ IsDefaultVariableName()

Bool_t TFormula::IsDefaultVariableName ( const TString & name )

staticprivate

Definition at line 260 of file TFormula.cxx.

◆ IsFunctionNameChar()

Bool_t TFormula::IsFunctionNameChar ( const char c )

staticprotected

Definition at line 254 of file TFormula.cxx.

◆ IsHexadecimal()

Bool_t TFormula::IsHexadecimal	(	const TString &	formula,
		int	ipos
	)

staticprotected

Definition at line 278 of file TFormula.cxx.

◆ IsLinear()

Bool_t TFormula::IsLinear ( ) const

inline

Definition at line 235 of file TFormula.h.

◆ IsOperator()

Bool_t TFormula::IsOperator ( const char c )

staticprotected

Definition at line 234 of file TFormula.cxx.

◆ IsScientificNotation()

Bool_t TFormula::IsScientificNotation	(	const TString &	formula,
		int	ipos
	)

staticprotected

Definition at line 266 of file TFormula.cxx.

◆ IsValid()

Bool_t TFormula::IsValid ( ) const

inline

Definition at line 233 of file TFormula.h.

◆ IsVectorized()

Bool_t TFormula::IsVectorized ( ) const

inline

Definition at line 234 of file TFormula.h.

◆ operator=()

TFormula & TFormula::operator= ( const TFormula & rhs )

= operator.

Definition at line 549 of file TFormula.cxx.

◆ PrepareEvalMethod()

bool TFormula::PrepareEvalMethod ( )

private

Sets TMethodCall to function inside Cling environment.

TFormula uses it to execute function. After call, TFormula should be ready to evaluate formula. Returns false on failure.

Definition at line 820 of file TFormula.cxx.

◆ PrepareFormula()

Bool_t TFormula::PrepareFormula ( TString & formula )

protected

prepare the formula to be executed normally is called with fFormula

Definition at line 1765 of file TFormula.cxx.

◆ PreProcessFormula()

void TFormula::PreProcessFormula ( TString & formula )

protected

Preprocessing of formula Replace all ** by ^, and removes spaces.

Handle also parametrized functions like polN,gaus,expo,landau and exponentiation. Similar functionality should be added here.

Definition at line 1743 of file TFormula.cxx.

◆ Print()

void TFormula::Print ( Option_t * option = "" ) const

virtual

Print the formula and its attributes.

Reimplemented from TNamed.

Definition at line 3565 of file TFormula.cxx.

◆ ProcessFormula()

void TFormula::ProcessFormula ( TString & formula )

protected

Iterates through functors in fFuncs and performs the appropriate action.

If functor has 0 arguments (has only name) can be:

variable
- will be replaced with x[num], where x is an array containing value of this variable under num.
pre-defined formula
- will be replaced with formulas body
constant
- will be replaced with constant value
parameter
- will be replaced with p[num], where p is an array containing value of this parameter under num. If has arguments it can be :
function shortcut, eg. sin
- will be replaced with fullname of function, eg. sin -> TMath::Sin
function from cling environment, eg. TMath::BreitWigner(x,y,z)
- first check if function exists, and has same number of arguments, then accept it and set as found. If all functors after iteration are matched with corresponding action, it inputs C++ code of formula into cling, and sets flag that formula is ready to evaluate.

Definition at line 2049 of file TFormula.cxx.

◆ ReInitializeEvalMethod()

void TFormula::ReInitializeEvalMethod ( )

private

Re-initialize eval method.

This function is called by DoEval and DoEvalVector in case of a previous failure or in case of reading from a file

Definition at line 3427 of file TFormula.cxx.

◆ ReplaceAllNames()

void TFormula::ReplaceAllNames	(	TString &	formula,
		std::map< TString, TString > &	substitutions
	)

private

Definition at line 353 of file TFormula.cxx.

◆ ReplaceParamName()

void TFormula::ReplaceParamName	(	TString &	formula,
		const TString &	oldname,
		const TString &	name
	)

protected

Replace in Formula expression the parameter name.

Definition at line 3042 of file TFormula.cxx.

◆ SetName()

void TFormula::SetName ( const char * name )

virtual

Set the name of the formula.

We need to allow the list of function to properly handle the hashes.

Reimplemented from TNamed.

Definition at line 2612 of file TFormula.cxx.

◆ SetParameter() [1/2]

void TFormula::SetParameter	(	const char *	name,
		Double_t	value
	)

Sets parameter value.

Definition at line 2865 of file TFormula.cxx.

◆ SetParameter() [2/2]

void TFormula::SetParameter	(	Int_t	param,
		Double_t	value
	)

Set a parameter given a parameter index The parameter index is by default the alphabetic order given to the parameters apart if the users has defined explicitly the parameter names.

Definition at line 2973 of file TFormula.cxx.

◆ SetParameters() [1/2]

void TFormula::SetParameters ( const Double_t * params )

Set a vector of parameters value.

Order in the vector is by default the alphabetic order given to the parameters apart if the users has defined explicitly the parameter names

Definition at line 2942 of file TFormula.cxx.

◆ SetParameters() [2/2]

void TFormula::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`
	)

Set a list of parameters.

The order is by default the alphabetic order given to the parameters apart if the users has defined explicitly the parameter names

Definition at line 2952 of file TFormula.cxx.

◆ SetParName()

void TFormula::SetParName	(	Int_t	ipar,
		const char *	name
	)

Definition at line 3012 of file TFormula.cxx.

◆ SetParNames()

void TFormula::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"`
	)

Definition at line 2983 of file TFormula.cxx.

◆ SetPredefinedParamNames()

void TFormula::SetPredefinedParamNames ( )

protected

Set parameter names only in case of pre-defined functions.

Definition at line 2443 of file TFormula.cxx.

◆ SetVariable()

void TFormula::SetVariable	(	const TString &	name,
		Double_t	value
	)

Sets variable value.

Definition at line 2700 of file TFormula.cxx.

◆ SetVariables()

void TFormula::SetVariables	(	const std::pair< TString, Double_t > *	vars,
		const Int_t	size
	)

Sets multiple variables.

First argument is an array of pairs<TString,Double>, where first argument is name of variable, second argument represents value. size - number of variables passed in first argument

Definition at line 2641 of file TFormula.cxx.

◆ SetVectorized()

void TFormula::SetVectorized ( Bool_t vectorized )

Definition at line 3068 of file TFormula.cxx.

Member Data Documentation

◆ fAllParametersSetted

Bool_t TFormula::fAllParametersSetted

private

transient to force re-initialization

Definition at line 94 of file TFormula.h.

◆ fClingInitialized

Bool_t TFormula::fClingInitialized

private

trasient to force initialization

Definition at line 93 of file TFormula.h.

◆ fClingInput

TString TFormula::fClingInput

private

Definition at line 89 of file TFormula.h.

◆ fClingName

TString TFormula::fClingName

private

pointer to a methodcall

Definition at line 98 of file TFormula.h.

◆ fClingParameters

std::vector<Double_t> TFormula::fClingParameters

private

cached variables

Definition at line 91 of file TFormula.h.

◆ fClingVariables

std::vector<Double_t> TFormula::fClingVariables

private

input function passed to Cling

Definition at line 90 of file TFormula.h.

◆ fConsts

std::map<TString,Double_t> TFormula::fConsts

protected

Definition at line 136 of file TFormula.h.

◆ fFormula

TString TFormula::fFormula

protected

Definition at line 138 of file TFormula.h.

◆ fFuncPtr

CallFuncSignature TFormula::fFuncPtr = nullptr

private

input query to clad to generate a gradient

Definition at line 103 of file TFormula.h.

◆ fFuncs

std::list<TFormulaFunction> TFormula::fFuncs

protected

Definition at line 133 of file TFormula.h.

◆ fFunctionsShortcuts

std::map<TString,TString> TFormula::fFunctionsShortcuts

protected

Definition at line 137 of file TFormula.h.

◆ fGradFuncPtr

CallFuncSignature TFormula::fGradFuncPtr = nullptr

private

function pointer, owned by the JIT.

Definition at line 104 of file TFormula.h.

◆ fGradGenerationInput

std::string TFormula::fGradGenerationInput

private

Definition at line 102 of file TFormula.h.

◆ fGradMethod

std::unique_ptr<TMethodCall> TFormula::fGradMethod

private

pointer to methodcall

Definition at line 97 of file TFormula.h.

◆ fIsCladRuntimeIncluded

bool TFormula::fIsCladRuntimeIncluded = false

staticprivate

pointer to the lambda function

Definition at line 106 of file TFormula.h.

◆ fLambdaPtr

void* TFormula::fLambdaPtr = nullptr

private

function pointer, owned by the JIT.

Definition at line 105 of file TFormula.h.

◆ fLazyInitialization

Bool_t TFormula::fLazyInitialization = kFALSE

private

Definition at line 95 of file TFormula.h.

◆ fLinearParts

std::vector<TObject*> TFormula::fLinearParts

protected

Definition at line 142 of file TFormula.h.

◆ fMethod

TMethodCall* TFormula::fMethod

private

transient flag to control lazy initialization (needed for reading from files)

Definition at line 96 of file TFormula.h.

◆ fNdim

Int_t TFormula::fNdim

protected

Definition at line 139 of file TFormula.h.

◆ fNpar

Int_t TFormula::fNpar

protected

Definition at line 140 of file TFormula.h.

◆ fNumber

Int_t TFormula::fNumber

protected

Number of parameter (transient since we save the vector)

Definition at line 141 of file TFormula.h.

◆ fParams

std::map<TString,Int_t,TFormulaParamOrder> TFormula::fParams

protected

list of variable names

Definition at line 135 of file TFormula.h.

◆ fReadyToExecute

Bool_t TFormula::fReadyToExecute

private

Definition at line 92 of file TFormula.h.

◆ fSavedInputFormula

std::string TFormula::fSavedInputFormula

private

unique name passed to Cling to define the function ( double clingName(double*x, double*p) )

Definition at line 99 of file TFormula.h.

◆ fVars

std::map<TString,TFormulaVariable> TFormula::fVars

protected

Definition at line 134 of file TFormula.h.

◆ fVectorized

Bool_t TFormula::fVectorized = false

protected

Definition at line 143 of file TFormula.h.

Libraries for TFormula:

[legend]

Example of valid expressions:

An expanded note on variables and parameters

A note on operators

Public Types

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Private Types

Private Member Functions

Static Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Member Typedef Documentation

◆ CallFuncSignature

◆ GradientStorage

Member Enumeration Documentation

◆ EStatusBits

Constructor & Destructor Documentation

◆ TFormula() [1/4]

◆ ~TFormula()

◆ TFormula() [2/4]

◆ TFormula() [3/4]

◆ TFormula() [4/4]

Member Function Documentation

◆ AddParameter()

◆ AddVariable()

◆ AddVariables()

◆ Clear()

◆ Compile()

◆ Copy()

◆ DoAddParameter()

◆ DoEval()

◆ DoSetParameters()

◆ Eval() [1/4]

◆ Eval() [2/4]

◆ Eval() [3/4]

◆ Eval() [4/4]

◆ EvalPar() [1/2]

◆ EvalPar() [2/2]

◆ ExtractFunctors()

◆ FillDefaults()

◆ FillParametrizedFunctions()

◆ FillVecFunctionsShurtCuts()

◆ GenerateGradientPar()

◆ GetExpFormula()

◆ GetGradientFormula()

◆ GetGradientFuncName()

◆ GetLinearPart()

◆ GetNdim()

◆ GetNpar()

◆ GetNumber()

◆ GetParameter() [1/2]

◆ GetParameter() [2/2]

◆ GetParameters() [1/2]

◆ GetParameters() [2/2]

◆ GetParName()

◆ GetParNumber()

◆ GetVariable()

◆ GetVarName()

◆ GetVarNumber()

◆ GradientPar() [1/2]

◆ GradientPar() [2/2]

◆ HandleExponentiation()

◆ HandleFunctionArguments()

◆ HandleLinear()

◆ HandleParametrizedFunctions()

◆ HandleParamRanges()

◆ HandlePolN()

◆ HasGradientGenerationFailed()

◆ InitLambdaExpression()

◆ InputFormulaIntoCling()

◆ IsAParameterName()

◆ IsBracket()

◆ IsDefaultVariableName()

◆ IsFunctionNameChar()

◆ IsHexadecimal()

◆ IsLinear()

◆ IsOperator()