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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:

• 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 (&amp;&amp;, ||, ==, &lt;=, &gt;=, !)

Examples:

sin(x*(x&lt;0.5 || x&gt;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&lt;0.5 || x&gt;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&lt;0.5 || x&gt;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);
#define f(i)
Definition RSha256.hxx:104
double Double_t
Definition RtypesCore.h:59
winID h TVirtualViewer3D TVirtualGLPainter p
The Formula class.
Definition TFormula.h:89
Definition TFormula.h:184
Double_t x[n]
Definition legend1.C:17

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:

f.HessianPar(x, hess);

### List of predefined functions

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

1. 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.
2. 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.
3. 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")

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
const Int_t n
Definition legend1.C:16

where n is the first previously unused parameter number.

Definition at line 88 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 ,
}

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)

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.

template<typename... Args>
Double_t Eval (Args... args) const
Set first 1, 2, 3 or 4 variables (e.g.

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

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

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 GetHessianFormula () const

const TObjectGetLinearPart (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_tGetParameters () 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.

TString GetUniqueFuncName () const

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.

Compute the gradient employing automatic differentiation.

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.

TClassIsA () const override

Bool_t IsLinear () const

Bool_t IsValid () const

Bool_t IsVectorized () const

TFormulaoperator= (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.

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

template<typename... Args>
void SetParameters (Double_t arg1, Args &&... args)
Set a list of parameters.

void SetParName (Int_t ipar, const char *name)

template<typename... Args>
void SetParNames (Args &&... args)
Set parameter names.

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 ("").

TObjectClone (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.

TClassIsA () const override

Bool_t IsSortable () const override

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

TNamedoperator= (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.

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 TObjectDrawClone (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 TObjectFindObject (const char *name) const
Must be redefined in derived classes.

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

virtual Option_tGetDrawOption () 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_tGetOption () 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 (the base implementation is no-op).

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, void *vp)
Only called by placement new when throwing an exception.

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

void operator delete[] (void *ptr, void *vp)
Only called by placement new[] when throwing an exception.

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)

TObjectoperator= (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 TClassClass ()

static const char * Class_Name ()

static constexpr Version_t Class_Version ()

static const char * DeclFileName ()

Static Public Member Functions inherited from TNamed
static TClassClass ()

static const char * Class_Name ()

static constexpr Version_t Class_Version ()

static const char * DeclFileName ()

Static Public Member Functions inherited from TObject
static TClassClass ()

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)

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_tfConsts
!

TString fFormula
String representing the formula expression.

std::list< TFormulaFunctionfFuncs
!

std::map< TString, TStringfFunctionsShortcuts
!

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, TFormulaParamOrderfParams
|| List of parameter names

std::map< TString, TFormulaVariablefVars
! 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 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 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

Flag to control if all parameters are setted.

std::atomic< Bool_tfClingInitialized
! 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(double*x, double*p) )

std::vector< Double_tfClingParameters
Parameter values.

std::vector< Double_tfClingVariables
! Cached variables

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

! Function pointer, owned by the JIT.

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< TMethodCallfMethod
! Pointer to methodcall

! 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

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

#include "inc/TFormula.h"

Inheritance diagram for TFormula:
[legend]

## ◆ CallFuncSignature

 private

Definition at line 104 of file TFormula.h.

Definition at line 184 of file TFormula.h.

## ◆ 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.

## ◆ TFormula() [1/4]

 TFormula::TFormula ( )

Definition at line 438 of file TFormula.cxx.

## ◆ ~TFormula()

 TFormula::~TFormula ( )
override

Definition at line 465 of file TFormula.cxx.

## ◆ TFormula() [2/4]

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

Definition at line 482 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 528 of file TFormula.cxx.

## ◆ TFormula() [4/4]

 TFormula::TFormula ( const TFormula & formula )

Definition at line 575 of file TFormula.cxx.

## Member Function Documentation

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

Definition at line 194 of file TFormula.h.

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

Adds variable to known variables, and reprocess formula.

Definition at line 2569 of file TFormula.cxx.

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

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 2602 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 767 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 650 of file TFormula.cxx.

## ◆ Copy()

 void TFormula::Copy ( TObject & object ) const
overridevirtual

Copy this to obj.

Reimplemented from TObject.

Definition at line 684 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.

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

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

Definition at line 2743 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 3370 of file TFormula.cxx.

## ◆ DoSetParameters()

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

Definition at line 2949 of file TFormula.cxx.

## ◆ Eval()

template<typename... Args>
 Double_t TFormula::Eval ( Args... args ) const

Set first 1, 2, 3 or 4 variables (e.g.

x, y, z and t) and evaluate formula.

Definition at line 324 of file TFormula.h.

## ◆ EvalPar() [1/2]

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

Definition at line 3078 of file TFormula.cxx.

## ◆ EvalPar() [2/2]

template<class T >
 T TFormula::EvalPar ( const T * x, const Double_t * params = nullptr ) const
inline

Definition at line 244 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 1832 of file TFormula.cxx.

## ◆ FillDefaults()

 void TFormula::FillDefaults ( )
private

Fill structures with default variables, constants and function shortcuts.

Definition at line 902 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 2417 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 970 of file TFormula.cxx.

Generate gradient computation routine with respect to the parameters.

returns true on success.

Returns

Definition at line 3203 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 3267 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 3535 of file TFormula.cxx.

Definition at line 3605 of file TFormula.cxx.

inlineprivate

Definition at line 128 of file TFormula.h.

## ◆ GetHessianFormula()

 TString TFormula::GetHessianFormula ( ) const

Definition at line 3613 of file TFormula.cxx.

## ◆ GetHessianFuncName()

 std::string TFormula::GetHessianFuncName ( ) const
inlineprivate

Definition at line 131 of file TFormula.h.

## ◆ GetLinearPart()

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

Return linear part.

Definition at line 2553 of file TFormula.cxx.

## ◆ GetNdim()

 Int_t TFormula::GetNdim ( ) const
inline

Definition at line 259 of file TFormula.h.

## ◆ GetNpar()

 Int_t TFormula::GetNpar ( ) const
inline

Definition at line 260 of file TFormula.h.

## ◆ GetNumber()

 Int_t TFormula::GetNumber ( ) const
inline

Definition at line 261 of file TFormula.h.

## ◆ GetParameter() [1/2]

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

Returns parameter value given by string.

Definition at line 2833 of file TFormula.cxx.

## ◆ GetParameter() [2/2]

 Double_t TFormula::GetParameter ( Int_t param ) const

Return parameter value given by integer.

Definition at line 2847 of file TFormula.cxx.

## ◆ GetParameters() [1/2]

 Double_t * TFormula::GetParameters ( ) const

Definition at line 2873 of file TFormula.cxx.

## ◆ GetParameters() [2/2]

 void TFormula::GetParameters ( Double_t * params ) const

Definition at line 2880 of file TFormula.cxx.

## ◆ GetParName()

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

Return parameter name given by integer.

Definition at line 2859 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 2821 of file TFormula.cxx.

## ◆ GetUniqueFuncName()

 TString TFormula::GetUniqueFuncName ( ) const
inline

Definition at line 253 of file TFormula.h.

## ◆ GetVariable()

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

Returns variable value.

Definition at line 2686 of file TFormula.cxx.

## ◆ GetVarName()

 TString TFormula::GetVarName ( Int_t ivar ) const

Returns variable name given its position in the array.

Definition at line 2712 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 2699 of file TFormula.cxx.

 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 3260 of file TFormula.cxx.

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.

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 3233 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 1635 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 1351 of file TFormula.cxx.

## ◆ HandleLinear()

 void TFormula::HandleLinear ( TString & formula )
private

Handle linear functions defined with the operator ++.

Definition at line 1735 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 1103 of file TFormula.cxx.

## ◆ HandleParamRanges()

 void TFormula::HandleParamRanges ( TString & formula )
private

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

Definition at line 1320 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 1002 of file TFormula.cxx.

inline

Definition at line 232 of file TFormula.h.

## ◆ HasGeneratedHessian()

 bool TFormula::HasGeneratedHessian ( ) const
inline

Definition at line 237 of file TFormula.h.

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 3322 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 3297 of file TFormula.cxx.

## ◆ InitLambdaExpression()

 Bool_t TFormula::InitLambdaExpression ( const char * formula )
private

Definition at line 605 of file TFormula.cxx.

## ◆ InputFormulaIntoCling()

 void TFormula::InputFormulaIntoCling ( )
private

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

Definition at line 876 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 )
staticprotected

Definition at line 353 of file TFormula.cxx.

## ◆ IsBracket()

 Bool_t TFormula::IsBracket ( const char c )
staticprotected

Definition at line 294 of file TFormula.cxx.

## ◆ IsDefaultVariableName()

 Bool_t TFormula::IsDefaultVariableName ( const TString & name )
staticprivate

Definition at line 312 of file TFormula.cxx.

## ◆ IsFunctionNameChar()

 Bool_t TFormula::IsFunctionNameChar ( const char c )
staticprotected

Definition at line 306 of file TFormula.cxx.

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

Definition at line 330 of file TFormula.cxx.

## ◆ IsLinear()

 Bool_t TFormula::IsLinear ( ) const
inline

Definition at line 273 of file TFormula.h.

## ◆ IsOperator()

 Bool_t TFormula::IsOperator ( const char c )
staticprotected

Definition at line 286 of file TFormula.cxx.

## ◆ IsScientificNotation()

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

Definition at line 318 of file TFormula.cxx.

## ◆ IsValid()

 Bool_t TFormula::IsValid ( ) const
inline

Definition at line 271 of file TFormula.h.

## ◆ IsVectorized()

 Bool_t TFormula::IsVectorized ( ) const
inline

Definition at line 272 of file TFormula.h.

## ◆ operator=()

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

= operator.

Definition at line 597 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 861 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 1793 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 1771 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 3622 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 2077 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 3478 of file TFormula.cxx.

## ◆ ReplaceAllNames()

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

Definition at line 405 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 3020 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 2640 of file TFormula.cxx.

## ◆ SetParameter() [1/2]

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

Sets parameter value.

Definition at line 2893 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 2980 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 2970 of file TFormula.cxx.

## ◆ SetParameters() [2/2]

template<typename... Args>
 void TFormula::SetParameters ( Double_t arg1, Args &&... args )

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. NaN values will be skipped, meaning that the corresponding parameters will not be changed.

Definition at line 299 of file TFormula.h.

## ◆ SetParName()

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

Definition at line 2990 of file TFormula.cxx.

## ◆ SetParNames()

template<typename... Args>
 void TFormula::SetParNames ( Args &&... args )

Set parameter names.

Empty strings will be skipped, meaning that the corresponding name will not be changed.

Definition at line 311 of file TFormula.h.

## ◆ SetPredefinedParamNames()

 void TFormula::SetPredefinedParamNames ( )
protected

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

Definition at line 2471 of file TFormula.cxx.

## ◆ SetVariable()

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

Sets variable value.

Definition at line 2728 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 2669 of file TFormula.cxx.

## ◆ SetVectorized()

 void TFormula::SetVectorized ( Bool_t vectorized )

Definition at line 3046 of file TFormula.cxx.

## ◆ Streamer()

 void TFormula::Streamer ( TBuffer & b )
overridevirtual

Stream a class object.

Reimplemented from TObject.

Definition at line 3690 of file TFormula.cxx.

## ◆ StreamerNVirtual()

 void TFormula::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )
inline

Definition at line 289 of file TFormula.h.

## Member Data Documentation

private

Flag to control if all parameters are setted.

Definition at line 98 of file TFormula.h.

## ◆ fClingInitialized

 std::atomic TFormula::fClingInitialized
private

! Transient to force re-initialization

Definition at line 97 of file TFormula.h.

## ◆ fClingInput

 TString TFormula::fClingInput
private

! Input function passed to Cling

Definition at line 93 of file TFormula.h.

## ◆ fClingName

 TString TFormula::fClingName
private

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

Definition at line 101 of file TFormula.h.

## ◆ fClingParameters

 std::vector TFormula::fClingParameters
private

Parameter values.

Definition at line 95 of file TFormula.h.

## ◆ fClingVariables

 std::vector TFormula::fClingVariables
private

! Cached variables

Definition at line 94 of file TFormula.h.

## ◆ fConsts

 std::map TFormula::fConsts
protected

!

Definition at line 146 of file TFormula.h.

## ◆ fFormula

 TString TFormula::fFormula
protected

String representing the formula expression.

Definition at line 148 of file TFormula.h.

## ◆ fFuncPtr

 CallFuncSignature TFormula::fFuncPtr = nullptr
private

! Function pointer, owned by the JIT.

Definition at line 107 of file TFormula.h.

## ◆ fFuncs

 std::list TFormula::fFuncs
protected

!

Definition at line 143 of file TFormula.h.

## ◆ fFunctionsShortcuts

 std::map TFormula::fFunctionsShortcuts
protected

!

Definition at line 147 of file TFormula.h.

private

! Function pointer, owned by the JIT.

Definition at line 108 of file TFormula.h.

private

Definition at line 105 of file TFormula.h.

## ◆ fHessFuncPtr

 CallFuncSignature TFormula::fHessFuncPtr = nullptr
private

! Function pointer, owned by the JIT.

Definition at line 109 of file TFormula.h.

## ◆ fHessGenerationInput

 std::string TFormula::fHessGenerationInput
private

! Input query to clad to generate a hessian

Definition at line 106 of file TFormula.h.

staticprivate

Definition at line 111 of file TFormula.h.

## ◆ fLambdaPtr

 void* TFormula::fLambdaPtr = nullptr
private

! Pointer to the lambda function

Definition at line 110 of file TFormula.h.

## ◆ fLazyInitialization

 Bool_t TFormula::fLazyInitialization = kFALSE
private

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

Definition at line 99 of file TFormula.h.

## ◆ fLinearParts

 std::vector TFormula::fLinearParts
protected

Vector of linear functions.

Definition at line 152 of file TFormula.h.

## ◆ fMethod

 std::unique_ptr TFormula::fMethod
private

! Pointer to methodcall

Definition at line 100 of file TFormula.h.

## ◆ fNdim

 Int_t TFormula::fNdim
protected

Dimension - needed for lambda expressions.

Definition at line 149 of file TFormula.h.

## ◆ fNpar

 Int_t TFormula::fNpar
protected

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

Definition at line 150 of file TFormula.h.

## ◆ fNumber

 Int_t TFormula::fNumber
protected

!

Definition at line 151 of file TFormula.h.

## ◆ fParams

 std::map TFormula::fParams
protected

|| List of parameter names

Definition at line 145 of file TFormula.h.

private

! Transient to force initialization

Definition at line 96 of file TFormula.h.

## ◆ fSavedInputFormula

 std::string TFormula::fSavedInputFormula
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 102 of file TFormula.h.

## ◆ fVars

 std::map TFormula::fVars
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:

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