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)

See below the full list of predefined functions which can be used as shortcuts in TFormula.

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:

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.

TFormula supports gradient and hessian calculations through clad. To calculate the gradient one needs to first declare a CladStorage of the same size as the number of parameters and then pass the variables and the created CladStorage:

TFormula f("f", "x*[0] - y*[1]");
Double_t p[] = {40, 30};
Double_t x[] = {1, 2};
f.SetParameters(p);
TFormula::CladStorage grad(2);
f.GradientPar(x, grad);

The process is similar for hessians, except that the size of the created CladStorage should be the square of the number of parameters because HessianPar returns a flattened matrix:

TFormula::CladStorage hess(4);

f.HessianPar(x, hess);

List of predefined functions

The list of available predefined functions which can be used as shortcuts is the following:

One Dimensional functions:
- gaus is a substitute for [Constant]*exp(-0.5*((x-[Mean])/[Sigma])*((x-[Mean])/[Sigma]))
- landau is a substitute for [Constant]*TMath::Landau (x,[MPV],[Sigma],false)
- expo is a substitute for exp([Constant]+[Slope]*x)
- crystalball is substitute for [Constant]*ROOT::Math::crystalball_function (x,[Alpha],[N],[Sigma],[Mean])
- breitwigner is a substitute for [p0]*ROOT::Math::breitwigner_pdf (x,[p2],[p1])
- pol0,1,2,...N is a substitute for a polynomial of degree N : ([p0]+[p1]*x+[p2]*pow(x,2)+....[pN]*pow(x,N)
- cheb0,1,2,...N is a substitute for a Chebyshev polynomial of degree N: ROOT::Math::Chebyshev10(x,[p0],[p1],[p2],...[pN]). Note the maximum N allowed here is 10.
Two Dimensional functions:
- xygaus is a substitute for [Constant]*exp(-0.5*pow(((x-[MeanX])/[SigmaX]),2 )- 0.5*pow(((y-[MeanY])/[SigmaY]),2)), a 2d Gaussian without correlation.
- bigaus is a substitute for [Constant]*ROOT::Math::bigaussian_pdf (x,y,[SigmaX],[SigmaY],[Rho],[MeanX],[MeanY]), a 2d gaussian including a correlation parameter.
Three Dimensional functions:
- xyzgaus is for a 3d Gaussians without correlations: [Constant]*exp(-0.5*pow(((x-[MeanX])/[SigmaX]),2 )- 0.5*pow(((y-[MeanY])/[SigmaY]),2 )- 0.5*pow(((z-[MeanZ])/[SigmaZ]),2))

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:439

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

-l -q -e TFormula("", "x+(10%3)").Eval(0)

but not

-l -q -e TFormula("", "x%10").Eval(0)

.

The operator ^ is defined to mean exponentiation instead of the C/C++ interpretation 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

n

const Int_t n

Definition legend1.C:16

where n is the first previously unused parameter number.

Definition at line 86 of file TFormula.h.

Public Types
using	CladStorage = std::vector< Double_t >

enum	EStatusBits { kNotGlobal = (1ULL << ( 10 )) , kNormalized = (1ULL << ( 14 )) , kLinear = (1ULL << ( 16 )) , kLambda = (1ULL << ( 17 )) }

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

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

enum	EDeprecatedStatusBits { kObjInCanvas = (1ULL << ( 3 )) }

enum	EStatusBits { kCanDelete = (1ULL << ( 0 )) , kMustCleanup = (1ULL << ( 3 )) , kIsReferenced = (1ULL << ( 4 )) , kHasUUID = (1ULL << ( 5 )) , kCannotPick = (1ULL << ( 6 )) , kNoContextMenu = (1ULL << ( 8 )) , kInvalidObject = (1ULL << ( 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.

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

	TFormula (const TFormula &formula)

	~TFormula () override

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.

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

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

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.

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

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

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

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.

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.

Double_t	EvalPar (const Double_t x, const Double_t params=nullptr) 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.

bool	GenerateHessianPar ()
	Generate hessian computation routine with respect to the parameters.

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

TString	GetGradientFormula () const

TString	GetHessianFormula () const

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

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.

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

Double_t *	GetParameters () const

void	GetParameters (Double_t *params) const

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

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.

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

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

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

void	GradientPar (const Double_t x, Double_t result)
	Compute the gradient with respect to the parameter passing a buffer with a size at least equal to the number of parameters.

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

bool	HasGeneratedGradient () const

bool	HasGeneratedHessian () const

void	HessianPar (const Double_t x, Double_t result)

void	HessianPar (const Double_t *x, TFormula::CladStorage &result)
	Compute the gradient employing automatic differentiation.

TClass *	IsA () const override

Bool_t	IsLinear () const

Bool_t	IsValid () const

Bool_t	IsVectorized () const

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

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

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

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

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.

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

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.

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.

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

void	SetVectorized (Bool_t vectorized)

void	Streamer (TBuffer &) override
	Stream a class object.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TNamed
	TNamed ()

	TNamed (const char name, const char title)

	TNamed (const TNamed &named)
	TNamed copy ctor.

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

virtual	~TNamed ()
	TNamed destructor.

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

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

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

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

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

const char *	GetName () const override
	Returns name of object.

const char *	GetTitle () const override
	Returns title of object.

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

TClass *	IsA () const override

Bool_t	IsSortable () const override

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

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

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

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

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

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

void	Streamer (TBuffer &) override
	Stream an object of class TObject.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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

	TObject (const TObject &object)
	TObject copy ctor.

virtual	~TObject ()
	TObject destructor.

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

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

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

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.

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

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

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

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

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

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad with: `gROOT->SetSelectedPad(c1)`.

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

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

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

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

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

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

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

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

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

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

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

virtual Option_t *	GetOption () const

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

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

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.

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

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

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

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

void	InvertBit (UInt_t f)

Bool_t	IsDestructed () const
	IsDestructed.

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

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

R__ALWAYS_INLINE Bool_t	IsOnHeap () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

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).

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

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

void	operator delete (void *ptr)
	Operator delete.

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

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.

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

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

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

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

void	ResetBit (UInt_t f)

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

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

void	SetBit (UInt_t f)

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

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

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

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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

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.

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

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

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

Static Public Member Functions
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TNamed
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TObject
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

static Longptr_t	GetDtorOnly ()
	Return destructor only flag.

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

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

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

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

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

void	DoSetParameters (const Double_t *p, Int_t size)

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

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

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

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

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

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

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).

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
	String representing the formula expression.

std::list< TFormulaFunction >	fFuncs
	!

std::map< TString, TString >	fFunctionsShortcuts
	!

std::vector< TObject * >	fLinearParts
	Vector of linear functions.

Int_t	fNdim
	Dimension - needed for lambda expressions.

Int_t	fNpar
	! Number of parameter (transient since we save the vector)

Int_t	fNumber
	!

std::map< TString, Int_t, TFormulaParamOrder >	fParams
	\|\| List of parameter names

std::map< TString, TFormulaVariable >	fVars
	! List of variable names

Bool_t	fVectorized = false
	Whether we should use vectorized or regular variables.

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

Private Types
using	CallFuncSignature = TInterpreter::CallFuncIFacePtr_t::Generic_t

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

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

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

std::string	GetGradientFuncName () const

std::string	GetHessianFuncName () const

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

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

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

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

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

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

bool	HasGradientGenerationFailed () const

bool	HasHessianGenerationFailed () const

Bool_t	InitLambdaExpression (const char *formula)

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

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

void	ReInitializeEvalMethod ()
	Re-initialize eval method.

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
	Flag to control if all parameters are setted.

std::atomic< Bool_t >	fClingInitialized
	! Transient to force re-initialization

TString	fClingInput
	! Input function passed to Cling

TString	fClingName
	! Unique name passed to Cling to define the function ( double clingName(doublex, doublep) )

std::vector< Double_t >	fClingParameters
	Parameter values.

std::vector< Double_t >	fClingVariables
	! Cached variables

CallFuncSignature	fFuncPtr = nullptr
	! Function pointer, owned by the JIT.

CallFuncSignature	fGradFuncPtr = nullptr
	! Function pointer, owned by the JIT.

std::string	fGradGenerationInput
	! Input query to clad to generate a gradient

CallFuncSignature	fHessFuncPtr = nullptr
	! Function pointer, owned by the JIT.

std::string	fHessGenerationInput
	! Input query to clad to generate a hessian

void *	fLambdaPtr = nullptr
	! Pointer to the lambda function

Bool_t	fLazyInitialization = kFALSE
	! Transient flag to control lazy initialization (needed for reading from files)

std::unique_ptr< TMethodCall >	fMethod
	! Pointer to methodcall

Bool_t	fReadyToExecute
	! Transient to force initialization

std::string	fSavedInputFormula
	! Unique name used to defined the function and used in the global map (need to be saved in case of lazy initialization)

Static Private Attributes
static bool	fIsCladRuntimeIncluded = false

Additional Inherited Members
Protected Types inherited from TObject
enum	{ kOnlyPrepStep = (1ULL << ( 3 )) }

#include "inc/TFormula.h"

Inheritance diagram for TFormula:

[legend]

Member Typedef Documentation

◆ CallFuncSignature

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

private

Definition at line 102 of file TFormula.h.

◆ CladStorage

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

Definition at line 184 of file TFormula.h.

Member Enumeration Documentation

◆ EStatusBits

enum TFormula::EStatusBits

Enumerator
kNotGlobal	Don't store in gROOT->GetListOfFunction (it should be protected)
kNormalized	Set to true if the TFormula (ex gausn) is normalized.
kLinear	Set to true if the TFormula is for linear fitting.
kLambda	Set to true if TFormula has been build with a lambda.

Definition at line 178 of file TFormula.h.

Constructor & Destructor Documentation

◆ TFormula() [1/4]

TFormula::TFormula ( )

Definition at line 439 of file TFormula.cxx.

◆ ~TFormula()

TFormula::~TFormula ( )

override

Definition at line 466 of file TFormula.cxx.

◆ TFormula() [2/4]

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

Definition at line 483 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 529 of file TFormula.cxx.

◆ TFormula() [4/4]

TFormula::TFormula ( const TFormula & formula )

Definition at line 576 of file TFormula.cxx.

Member Function Documentation

◆ AddParameter()

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

inline

Definition at line 194 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 2570 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 2603 of file TFormula.cxx.

◆ Class()

static TClass * TFormula::Class ( )

static

Returns: TClass describing this class

◆ Class_Name()

static const char * TFormula::Class_Name ( )

static

Returns: Name of this class

◆ Class_Version()

static constexpr Version_t TFormula::Class_Version ( )

inlinestaticconstexpr

Returns: Version of this class

Definition at line 289 of file TFormula.h.

◆ Clear()

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

overridevirtual

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

Reimplemented from TObject.

Definition at line 768 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 651 of file TFormula.cxx.

◆ Copy()

void TFormula::Copy ( TObject & object ) const

overridevirtual

Copy this to obj.

Reimplemented from TObject.

Definition at line 685 of file TFormula.cxx.

◆ DeclFileName()

static const char * TFormula::DeclFileName ( )

inlinestatic

Returns: Name of the file containing the class declaration

Definition at line 289 of file TFormula.h.

◆ 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 2744 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 3457 of file TFormula.cxx.

◆ DoSetParameters()

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

protected

Definition at line 2950 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 3445 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 3436 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 3427 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 3418 of file TFormula.cxx.

◆ EvalPar() [1/2]

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

Definition at line 3129 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 246 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 1833 of file TFormula.cxx.

◆ FillDefaults()

void TFormula::FillDefaults ( )

private

Fill structures with default variables, constants and function shortcuts.

Definition at line 903 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 2418 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 971 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 3254 of file TFormula.cxx.

◆ GenerateHessianPar()

bool TFormula::GenerateHessianPar ( )

Generate hessian computation routine with respect to the parameters.

returns true on success.

Returns: true if a hessian was generated and HessianPar can be called.

Definition at line 3318 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 3622 of file TFormula.cxx.

◆ GetGradientFormula()

TString TFormula::GetGradientFormula ( ) const

Definition at line 3692 of file TFormula.cxx.

◆ GetGradientFuncName()

std::string TFormula::GetGradientFuncName ( ) const

inlineprivate

Definition at line 126 of file TFormula.h.

◆ GetHessianFormula()

TString TFormula::GetHessianFormula ( ) const

Definition at line 3700 of file TFormula.cxx.

◆ GetHessianFuncName()

std::string TFormula::GetHessianFuncName ( ) const

inlineprivate

Definition at line 130 of file TFormula.h.

◆ GetLinearPart()

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

Return linear part.

Definition at line 2554 of file TFormula.cxx.

◆ GetNdim()

Int_t TFormula::GetNdim ( ) const

inline

Definition at line 256 of file TFormula.h.

◆ GetNpar()

Int_t TFormula::GetNpar ( ) const

inline

Definition at line 257 of file TFormula.h.

◆ GetNumber()

Int_t TFormula::GetNumber ( ) const

inline

Definition at line 258 of file TFormula.h.

◆ GetParameter() [1/2]

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

Returns parameter value given by string.

Definition at line 2834 of file TFormula.cxx.

◆ GetParameter() [2/2]

Double_t TFormula::GetParameter ( Int_t param ) const

Return parameter value given by integer.

Definition at line 2848 of file TFormula.cxx.

◆ GetParameters() [1/2]

Double_t * TFormula::GetParameters ( ) const

Definition at line 2874 of file TFormula.cxx.

◆ GetParameters() [2/2]

void TFormula::GetParameters ( Double_t * params ) const

Definition at line 2881 of file TFormula.cxx.

◆ GetParName()

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

Return parameter name given by integer.

Definition at line 2860 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 2822 of file TFormula.cxx.

◆ GetVariable()

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

Returns variable value.

Definition at line 2687 of file TFormula.cxx.

◆ GetVarName()

TString TFormula::GetVarName ( Int_t ivar ) const

Returns variable name given its position in the array.

Definition at line 2713 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 2700 of file TFormula.cxx.

◆ GradientPar() [1/2]

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

Compute the gradient with respect to the parameter passing a buffer with a size at least equal to the number of parameters.

Note that the result buffer needs to be initialized to zero before passed to this function.

Definition at line 3311 of file TFormula.cxx.

◆ GradientPar() [2/2]

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

Compute the gradient employing automatic differentiation.

a CladStorageObject, i.e.

Parameters

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

a std::vector, which has the size as the nnumber of parameters. Note that the result buffer needs to be initialized to zero before passing it to this function.

Definition at line 3284 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 1636 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 1352 of file TFormula.cxx.

◆ HandleLinear()

void TFormula::HandleLinear ( TString & formula )

private

Handle linear functions defined with the operator ++.

Definition at line 1736 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 1104 of file TFormula.cxx.

◆ HandleParamRanges()

void TFormula::HandleParamRanges ( TString & formula )

private

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

Definition at line 1321 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 1003 of file TFormula.cxx.

◆ HasGeneratedGradient()

bool TFormula::HasGeneratedGradient ( ) const

inline

Definition at line 234 of file TFormula.h.

◆ HasGeneratedHessian()

bool TFormula::HasGeneratedHessian ( ) const

inline

Definition at line 239 of file TFormula.h.

◆ HasGradientGenerationFailed()

bool TFormula::HasGradientGenerationFailed ( ) const

inlineprivate

Definition at line 134 of file TFormula.h.

◆ HasHessianGenerationFailed()

bool TFormula::HasHessianGenerationFailed ( ) const

inlineprivate

Definition at line 137 of file TFormula.h.

◆ HessianPar() [1/2]

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

Definition at line 3373 of file TFormula.cxx.

◆ HessianPar() [2/2]

void TFormula::HessianPar	(	const Double_t *	x,
		TFormula::CladStorage &	result
	)

Compute the gradient employing automatic differentiation.

Parameters

[in]	x	- The given variables, if nullptr the already stored variables are used.
[out]	result	- The 2D hessian matrix flattened to form a vector in row-major order.

Definition at line 3348 of file TFormula.cxx.

◆ InitLambdaExpression()

Bool_t TFormula::InitLambdaExpression ( const char * formula )

private

Definition at line 606 of file TFormula.cxx.

◆ InputFormulaIntoCling()

void TFormula::InputFormulaIntoCling ( )

private

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

Definition at line 877 of file TFormula.cxx.

◆ IsA()

TClass * TFormula::IsA ( ) const

inlineoverridevirtual

Returns: TClass describing current object

Reimplemented from TObject.

Definition at line 289 of file TFormula.h.

◆ IsAParameterName()

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

◆ PrepareFormula()

Bool_t TFormula::PrepareFormula ( TString & formula )

protected

prepare the formula to be executed normally is called with fFormula

Definition at line 1794 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 1772 of file TFormula.cxx.

◆ Print()

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

overridevirtual

Print the formula and its attributes.

Reimplemented from TObject.

Definition at line 3709 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 2078 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 3565 of file TFormula.cxx.

◆ ReplaceAllNames()

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

private

Definition at line 406 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 3071 of file TFormula.cxx.

◆ SetName()

void TFormula::SetName ( const char * name )

overridevirtual

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 2641 of file TFormula.cxx.

◆ SetParameter() [1/2]

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

Sets parameter value.

Definition at line 2894 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 3002 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 2971 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 2981 of file TFormula.cxx.

◆ SetParName()

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

Definition at line 3041 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 3012 of file TFormula.cxx.

◆ SetPredefinedParamNames()

void TFormula::SetPredefinedParamNames ( )

protected

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

Definition at line 2472 of file TFormula.cxx.

◆ SetVariable()

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

Sets variable value.

Definition at line 2729 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 2670 of file TFormula.cxx.

◆ SetVectorized()

void TFormula::SetVectorized ( Bool_t vectorized )

Definition at line 3097 of file TFormula.cxx.

◆ Streamer()

void TFormula::Streamer ( TBuffer & b )

protected

! List of variable names

Definition at line 144 of file TFormula.h.

◆ fVectorized

Bool_t TFormula::fVectorized = false

protected

Whether we should use vectorized or regular variables.

Definition at line 153 of file TFormula.h.

Libraries for TFormula:

[legend]

The documentation for this class was generated from the following files:

hist/hist/inc/v5/TFormula.h
hist/hist/src/TFormula.cxx

Example of valid expressions:

List of predefined functions

An expanded note on variables and parameters

A note on operators

Public Types

Public Member Functions

Static 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

◆ CladStorage

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()

◆ Class()

◆ Class_Name()

◆ Class_Version()

◆ Clear()

◆ Compile()

◆ Copy()

◆ DeclFileName()

◆ 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()

◆ GenerateHessianPar()

◆ GetExpFormula()

◆ GetGradientFormula()

◆ GetGradientFuncName()

◆ GetHessianFormula()

◆ GetHessianFuncName()

◆ 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()

◆ HasGeneratedGradient()