Logo ROOT   6.19/01
Reference Guide
TFormula Class Reference

The Formula class.

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

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

Example of valid expressions:

  • sin(x)/x
  • [0]*sin(x) + [1]*exp(-[2]*x)
  • x + y**2
  • x^2 + y^2
  • [0]*pow([1],4)
  • 2*pi*sqrt(x/y)
  • gaus(0)*expo(3) + ypol3(5)*x
  • gausn(0)*expo(3) + ypol3(5)*x
  • gaus(x, [0..2]) + expo(y, [3..4])

In the last examples above:

  • gaus(0) is a substitute for [0]*exp(-0.5*((x-[1])/[2])**2) and (0) means start numbering parameters at 0
  • gausn(0) is a substitute for [0]*exp(-0.5*((x-[1])/[2])**2)/(sqrt(2*pi)*[2])) and (0) means start numbering parameters at 0
  • expo(3) is a substitute for exp([3]+[4]*x)
  • pol3(5) is a substitute for par[5]+par[6]*x+par[7]*x**2+par[8]*x**3 (PolN stands for Polynomial of degree N)
  • gaus(x, [0..2]) is a more explicit way of writing gaus(0)
  • expo(y, [3..4]) is a substitute for exp([3]+[4]*y)

TMath functions can be part of the expression, eg:

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

Formula may contain constants, eg:

  • sqrt2
  • e
  • pi
  • ln10
  • infinity

and more.

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

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

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

Comparisons operators are also supported (&&, ||, ==, <=, >=, !)

Examples:

sin(x*(x<0.5 || x>1))

If the result of a comparison is TRUE, the result is 1, otherwise 0.

Already predefined names can be given. For example, if the formula

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

one can assign a name to the formula. By default the name of the object = title = formula itself.

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

is equivalent to:

TFormula new("new","x*sin(x*(x&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.

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 root -l -q -e TFormula("", "x+(10%3)").Eval(0) but not root -l -q -e TFormula("", "x%10").Eval(0).

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

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

Definition at line 83 of file TFormula.h.

Public Types

enum  EStatusBits { kNotGlobal = BIT(10), kNormalized = BIT(14), kLinear = BIT(16), kLambda = BIT(17) }
 
using GradientStorage = std::vector< Double_t >
 
- Public Types inherited from TObject
enum  {
  kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kInconsistent = 0x08000000,
  kBitMask = 0x00ffffff
}
 
enum  { kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) }
 
enum  EDeprecatedStatusBits { kObjInCanvas = BIT(3) }
 
enum  EStatusBits {
  kCanDelete = BIT(0), kMustCleanup = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5),
  kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13)
}
 

Public Member Functions

 TFormula ()
 
 TFormula (const char *name, const char *formula="", bool addToGlobList=true, bool vectorize=false)
 
 TFormula (const char *name, const char *formula, int ndim, int npar, bool addToGlobList=true)
 Constructor from a full compile-able C++ expression. More...
 
 TFormula (const TFormula &formula)
 
virtual ~TFormula ()
 
void AddParameter (const TString &name, Double_t value=0)
 
void AddVariable (const TString &name, Double_t value=0)
 
void AddVariables (const TString *vars, const Int_t size)
 
virtual void Clear (Option_t *option="")
 Clear the formula setting expression to empty and reset the variables and parameters containers. More...
 
Int_t Compile (const char *expression="")
 Compile the given expression with Cling backward compatibility method to be used in combination with the empty constructor if no expression is given , the current stored formula (retrieved with GetExpFormula()) or the title is used. More...
 
virtual void Copy (TObject &f1) const
 Copy this to obj. More...
 
Double_t Eval (Double_t x) const
 
Double_t Eval (Double_t x, Double_t y) const
 
Double_t Eval (Double_t x, Double_t y, Double_t z) const
 
Double_t Eval (Double_t x, Double_t y, Double_t z, Double_t t) const
 
Double_t EvalPar (const Double_t *x, const Double_t *params=0) const
 
template<class T >
EvalPar (const T *x, const Double_t *params=0) const
 
bool GenerateGradientPar ()
 Generate gradient computation routine with respect to the parameters. More...
 
TString GetExpFormula (Option_t *option="") const
 
TString GetGradientFormula () const
 
const TObjectGetLinearPart (Int_t i) const
 
Int_t GetNdim () const
 
Int_t GetNpar () const
 
Int_t GetNumber () const
 
Double_t GetParameter (const char *name) const
 
Double_t GetParameter (Int_t param) const
 
Double_tGetParameters () const
 
void GetParameters (Double_t *params) const
 
const char * GetParName (Int_t ipar) const
 
Int_t GetParNumber (const char *name) const
 
Double_t GetVariable (const char *name) const
 
TString GetVarName (Int_t ivar) const
 
Int_t GetVarNumber (const char *name) const
 
void GradientPar (const Double_t *x, TFormula::GradientStorage &result)
 Compute the gradient employing automatic differentiation. More...
 
void GradientPar (const Double_t *x, Double_t *result)
 
Bool_t IsLinear () const
 
Bool_t IsValid () const
 
Bool_t IsVectorized () const
 
TFormulaoperator= (const TFormula &rhs)
 = operator. More...
 
void Print (Option_t *option="") const
 Print TNamed name and title. More...
 
void SetName (const char *name)
 Set the name of the TNamed. More...
 
void SetParameter (const char *name, Double_t value)
 
void SetParameter (Int_t param, Double_t value)
 
void SetParameters (const Double_t *params)
 
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)
 
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)
 
void SetVariables (const std::pair< TString, Double_t > *vars, const Int_t size)
 
void SetVectorized (Bool_t vectorized)
 
- Public Member Functions inherited from TNamed
 TNamed ()
 
 TNamed (const char *name, const char *title)
 
 TNamed (const TString &name, const TString &title)
 
 TNamed (const TNamed &named)
 TNamed copy ctor. More...
 
virtual ~TNamed ()
 TNamed destructor. More...
 
virtual TObjectClone (const char *newname="") const
 Make a clone of an object using the Streamer facility. More...
 
virtual Int_t Compare (const TObject *obj) const
 Compare two TNamed objects. More...
 
virtual void FillBuffer (char *&buffer)
 Encode TNamed into output buffer. More...
 
virtual const char * GetName () const
 Returns name of object. More...
 
virtual const char * GetTitle () const
 Returns title of object. More...
 
virtual ULong_t Hash () const
 Return hash value for this object. More...
 
virtual Bool_t IsSortable () const
 
virtual void ls (Option_t *option="") const
 List TNamed name and title. More...
 
TNamedoperator= (const TNamed &rhs)
 TNamed assignment operator. More...
 
virtual void SetNameTitle (const char *name, const char *title)
 Set all the TNamed parameters (name and title). More...
 
virtual void SetTitle (const char *title="")
 Set the title of the TNamed. More...
 
virtual Int_t Sizeof () const
 Return size of the TNamed part of the TObject. More...
 
- Public Member Functions inherited from TObject
 TObject ()
 TObject constructor. More...
 
 TObject (const TObject &object)
 TObject copy ctor. More...
 
virtual ~TObject ()
 TObject destructor. More...
 
void AbstractMethod (const char *method) const
 Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...
 
virtual void AppendPad (Option_t *option="")
 Append graphics object to current pad. More...
 
virtual void Browse (TBrowser *b)
 Browse object. May be overridden for another default action. More...
 
ULong_t CheckedHash ()
 Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object. More...
 
virtual const char * ClassName () const
 Returns name of class to which the object belongs. More...
 
virtual void Delete (Option_t *option="")
 Delete this object. More...
 
virtual Int_t DistancetoPrimitive (Int_t px, Int_t py)
 Computes distance from point (px,py) to the object. More...
 
virtual void Draw (Option_t *option="")
 Default Draw method for all objects. More...
 
virtual void DrawClass () const
 Draw class inheritance tree of the class to which this object belongs. More...
 
virtual TObjectDrawClone (Option_t *option="") const
 Draw a clone of this object in the current selected pad for instance with: gROOT->SetSelectedPad(gPad). More...
 
virtual void Dump () const
 Dump contents of object on stdout. More...
 
virtual void Error (const char *method, const char *msgfmt,...) const
 Issue error message. More...
 
virtual void Execute (const char *method, const char *params, Int_t *error=0)
 Execute method on this object with the given parameter string, e.g. More...
 
virtual void Execute (TMethod *method, TObjArray *params, Int_t *error=0)
 Execute method on this object with parameters stored in the TObjArray. More...
 
virtual void ExecuteEvent (Int_t event, Int_t px, Int_t py)
 Execute action corresponding to an event at (px,py). More...
 
virtual void Fatal (const char *method, const char *msgfmt,...) const
 Issue fatal error message. More...
 
virtual TObjectFindObject (const char *name) const
 Must be redefined in derived classes. More...
 
virtual TObjectFindObject (const TObject *obj) const
 Must be redefined in derived classes. More...
 
virtual Option_tGetDrawOption () const
 Get option used by the graphics system to draw this object. More...
 
virtual const char * GetIconName () const
 Returns mime type name of object. More...
 
virtual char * GetObjectInfo (Int_t px, Int_t py) const
 Returns string containing info about the object at position (px,py). More...
 
virtual Option_tGetOption () const
 
virtual UInt_t GetUniqueID () const
 Return the unique object id. More...
 
virtual Bool_t HandleTimer (TTimer *timer)
 Execute action in response of a timer timing out. More...
 
Bool_t HasInconsistentHash () const
 Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e. More...
 
virtual void Info (const char *method, const char *msgfmt,...) const
 Issue info message. More...
 
virtual Bool_t InheritsFrom (const char *classname) const
 Returns kTRUE if object inherits from class "classname". More...
 
virtual Bool_t InheritsFrom (const TClass *cl) const
 Returns kTRUE if object inherits from TClass cl. More...
 
virtual void Inspect () const
 Dump contents of this object in a graphics canvas. More...
 
void InvertBit (UInt_t f)
 
virtual Bool_t IsEqual (const TObject *obj) const
 Default equal comparison (objects are equal if they have the same address in memory). More...
 
virtual Bool_t IsFolder () const
 Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...
 
R__ALWAYS_INLINE Bool_t IsOnHeap () const
 
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). More...
 
virtual Bool_t Notify ()
 This method must be overridden to handle object notification. More...
 
void Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const
 Use this method to declare a method obsolete. More...
 
void operator delete (void *ptr)
 Operator delete. More...
 
void operator delete[] (void *ptr)
 Operator delete []. More...
 
voidoperator new (size_t sz)
 
voidoperator new (size_t sz, void *vp)
 
voidoperator new[] (size_t sz)
 
voidoperator new[] (size_t sz, void *vp)
 
TObjectoperator= (const TObject &rhs)
 TObject assignment operator. More...
 
virtual void Paint (Option_t *option="")
 This method must be overridden if a class wants to paint itself. More...
 
virtual void Pop ()
 Pop on object drawn in a pad to the top of the display list. More...
 
virtual Int_t Read (const char *name)
 Read contents of object with specified name from the current directory. More...
 
virtual void RecursiveRemove (TObject *obj)
 Recursively remove this object from a list. More...
 
void ResetBit (UInt_t f)
 
virtual void SaveAs (const char *filename="", Option_t *option="") const
 Save this object in the file specified by filename. More...
 
virtual void SavePrimitive (std::ostream &out, Option_t *option="")
 Save a primitive as a C++ statement(s) on output stream "out". More...
 
void SetBit (UInt_t f, Bool_t set)
 Set or unset the user status bits as specified in f. More...
 
void SetBit (UInt_t f)
 
virtual void SetDrawOption (Option_t *option="")
 Set drawing option for object. More...
 
virtual void SetUniqueID (UInt_t uid)
 Set the unique object id. More...
 
virtual void SysError (const char *method, const char *msgfmt,...) const
 Issue system error message. More...
 
R__ALWAYS_INLINE Bool_t TestBit (UInt_t f) const
 
Int_t TestBits (UInt_t f) const
 
virtual void UseCurrentStyle ()
 Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More...
 
virtual void Warning (const char *method, const char *msgfmt,...) const
 Issue warning message. More...
 
virtual Int_t Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
 Write this object to the current directory. More...
 
virtual Int_t Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
 Write this object to the current directory. More...
 

Protected Member Functions

void DoAddParameter (const TString &name, Double_t value, bool processFormula)
 
Double_t DoEval (const Double_t *x, const Double_t *p=nullptr) const
 
void DoSetParameters (const Double_t *p, Int_t size)
 
void ExtractFunctors (TString &formula)
 
Bool_t PrepareFormula (TString &formula)
 
void PreProcessFormula (TString &formula)
 
void ProcessFormula (TString &formula)
 
void ReplaceParamName (TString &formula, const TString &oldname, const TString &name)
 
void SetPredefinedParamNames ()
 
- Protected Member Functions inherited from TObject
virtual void DoError (int level, const char *location, const char *fmt, va_list va) const
 Interface to ErrorHandler (protected). More...
 
void MakeZombie ()
 

Static Protected Member Functions

static Bool_t IsAParameterName (const TString &formula, int ipos)
 
static Bool_t IsBracket (const char c)
 
static Bool_t IsFunctionNameChar (const char c)
 
static Bool_t IsHexadecimal (const TString &formula, int ipos)
 
static Bool_t IsOperator (const char c)
 
static Bool_t IsScientificNotation (const TString &formula, int ipos)
 

Protected Attributes

std::map< TString, Double_tfConsts
 
TString fFormula
 
std::list< TFormulaFunctionfFuncs
 
std::map< TString, TStringfFunctionsShortcuts
 
std::vector< TObject * > fLinearParts
 
Int_t fNdim
 
Int_t fNpar
 
Int_t fNumber
 Number of parameter (transient since we save the vector) More...
 
std::map< TString, Int_t, TFormulaParamOrderfParams
 list of variable names More...
 
std::map< TString, TFormulaVariablefVars
 
Bool_t fVectorized = false
 
- Protected Attributes inherited from TNamed
TString fName
 
TString fTitle
 

Private Types

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

Private Member Functions

void FillDefaults ()
 Fill structures with default variables, constants and function shortcuts. More...
 
void FillParametrizedFunctions (std::map< std::pair< TString, Int_t >, std::pair< TString, TString >> &functions)
 
void FillVecFunctionsShurtCuts ()
 Fill the shortcuts for vectorized functions We will replace for example sin with vecCore::Mat::Sin. More...
 
std::string GetGradientFuncName () const
 
void HandleExponentiation (TString &formula)
 
void HandleFunctionArguments (TString &formula)
 
void HandleLinear (TString &formula)
 
void HandleParametrizedFunctions (TString &formula)
 Handling parametrized functions Function can be normalized, and have different variable then x. More...
 
void HandleParamRanges (TString &formula)
 Handling parameter ranges, in the form of [1..5]. More...
 
void HandlePolN (TString &formula)
 Handling polN If before 'pol' exist any name, this name will be treated as variable used in polynomial eg. More...
 
bool HasGradientGenerationFailed () const
 
Bool_t InitLambdaExpression (const char *formula)
 
void InputFormulaIntoCling ()
 Inputs formula, transfered to C++ code into Cling. More...
 
Bool_t PrepareEvalMethod ()
 Sets TMethodCall to function inside Cling environment. More...
 
void ReInitializeEvalMethod ()
 
void ReplaceAllNames (TString &formula, std::map< TString, TString > &substitutions)
 

Static Private Member Functions

static Bool_t IsDefaultVariableName (const TString &name)
 

Private Attributes

Bool_t fAllParametersSetted
 transient to force re-initialization More...
 
Bool_t fClingInitialized
 trasient to force initialization More...
 
TString fClingInput
 
TString fClingName
 pointer to a methodcall More...
 
std::vector< Double_tfClingParameters
 cached variables More...
 
std::vector< Double_tfClingVariables
 input function passed to Cling More...
 
CallFuncSignature fFuncPtr = nullptr
 input query to clad to generate a gradient More...
 
CallFuncSignature fGradFuncPtr = nullptr
 function pointer, owned by the JIT. More...
 
std::string fGradGenerationInput
 
std::unique_ptr< TMethodCallfGradMethod
 pointer to methodcall More...
 
voidfLambdaPtr = nullptr
 function pointer, owned by the JIT. More...
 
Bool_t fLazyInitialization = kFALSE
 
TMethodCallfMethod
 transient flag to control lazy initialization (needed for reading from files) More...
 
Bool_t fReadyToExecute
 
std::string fSavedInputFormula
 unique name passed to Cling to define the function ( double clingName(double*x, double*p) ) More...
 

Static Private Attributes

static bool fIsCladRuntimeIncluded
 pointer to the lambda function More...
 

Additional Inherited Members

- Static Public Member Functions inherited from TObject
static Long_t GetDtorOnly ()
 Return destructor only flag. More...
 
static Bool_t GetObjectStat ()
 Get status of object stat flag. More...
 
static void SetDtorOnly (void *obj)
 Set destructor only flag. More...
 
static void SetObjectStat (Bool_t stat)
 Turn on/off tracking of objects in the TObjectTable. More...
 

#include "inc/TFormula.h"

Inheritance diagram for TFormula:
[legend]

Member Typedef Documentation

◆ CallFuncSignature

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

Definition at line 101 of file TFormula.h.

◆ GradientStorage

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

Definition at line 174 of file TFormula.h.

Member Enumeration Documentation

◆ EStatusBits

Enumerator
kNotGlobal 
kNormalized 
kLinear 
kLambda 

Definition at line 168 of file TFormula.h.

Constructor & Destructor Documentation

◆ TFormula() [1/4]

TFormula::TFormula ( )

Definition at line 386 of file TFormula.cxx.

◆ ~TFormula()

TFormula::~TFormula ( )
virtual

Definition at line 413 of file TFormula.cxx.

◆ TFormula() [2/4]

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

Definition at line 433 of file TFormula.cxx.

◆ TFormula() [3/4]

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

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

Definition at line 480 of file TFormula.cxx.

◆ TFormula() [4/4]

TFormula::TFormula ( const TFormula formula)

Definition at line 527 of file TFormula.cxx.

Member Function Documentation

◆ AddParameter()

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

Definition at line 184 of file TFormula.h.

◆ AddVariable()

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

◆ AddVariables()

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

◆ Clear()

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

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

Reimplemented from TNamed.

Definition at line 726 of file TFormula.cxx.

◆ Compile()

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

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

return 0 if the formula compilation is successful

Definition at line 604 of file TFormula.cxx.

◆ Copy()

void TFormula::Copy ( TObject named) const
virtual

Copy this to obj.

Reimplemented from TNamed.

Definition at line 638 of file TFormula.cxx.

◆ DoAddParameter()

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

◆ DoEval()

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

◆ DoSetParameters()

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

◆ Eval() [1/4]

Double_t TFormula::Eval ( Double_t  x) const

◆ Eval() [2/4]

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

◆ Eval() [3/4]

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

◆ Eval() [4/4]

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

◆ EvalPar() [1/2]

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

◆ EvalPar() [2/2]

template<class T >
T TFormula::EvalPar ( const T *  x,
const Double_t params = 0 
) const
inline

Definition at line 212 of file TFormula.h.

◆ ExtractFunctors()

void TFormula::ExtractFunctors ( TString formula)
protected

◆ FillDefaults()

void TFormula::FillDefaults ( )
private

Fill structures with default variables, constants and function shortcuts.

Definition at line 862 of file TFormula.cxx.

◆ FillParametrizedFunctions()

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

◆ FillVecFunctionsShurtCuts()

void TFormula::FillVecFunctionsShurtCuts ( )
private

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

Definition at line 930 of file TFormula.cxx.

◆ GenerateGradientPar()

bool TFormula::GenerateGradientPar ( )

Generate gradient computation routine with respect to the parameters.

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

◆ GetExpFormula()

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

◆ GetGradientFormula()

TString TFormula::GetGradientFormula ( ) const

◆ GetGradientFuncName()

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

Definition at line 123 of file TFormula.h.

◆ GetLinearPart()

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

◆ GetNdim()

Int_t TFormula::GetNdim ( ) const
inline

Definition at line 221 of file TFormula.h.

◆ GetNpar()

Int_t TFormula::GetNpar ( ) const
inline

Definition at line 222 of file TFormula.h.

◆ GetNumber()

Int_t TFormula::GetNumber ( ) const
inline

Definition at line 223 of file TFormula.h.

◆ GetParameter() [1/2]

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

◆ GetParameter() [2/2]

Double_t TFormula::GetParameter ( Int_t  param) const

◆ GetParameters() [1/2]

Double_t* TFormula::GetParameters ( ) const

◆ GetParameters() [2/2]

void TFormula::GetParameters ( Double_t params) const

◆ GetParName()

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

◆ GetParNumber()

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

◆ GetVariable()

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

◆ GetVarName()

TString TFormula::GetVarName ( Int_t  ivar) const

◆ GetVarNumber()

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

◆ GradientPar() [1/2]

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

Compute the gradient employing automatic differentiation.

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

◆ GradientPar() [2/2]

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

◆ HandleExponentiation()

void TFormula::HandleExponentiation ( TString formula)
private

◆ HandleFunctionArguments()

void TFormula::HandleFunctionArguments ( TString formula)
private

◆ HandleLinear()

void TFormula::HandleLinear ( TString formula)
private

◆ HandleParametrizedFunctions()

void TFormula::HandleParametrizedFunctions ( TString formula)
private

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

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

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

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

Definition at line 1063 of file TFormula.cxx.

◆ HandleParamRanges()

void TFormula::HandleParamRanges ( TString formula)
private

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

Definition at line 1279 of file TFormula.cxx.

◆ HandlePolN()

void TFormula::HandlePolN ( TString formula)
private

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

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

Definition at line 962 of file TFormula.cxx.

◆ HasGradientGenerationFailed()

bool TFormula::HasGradientGenerationFailed ( ) const
inlineprivate

Definition at line 127 of file TFormula.h.

◆ InitLambdaExpression()

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

Definition at line 559 of file TFormula.cxx.

◆ InputFormulaIntoCling()

void TFormula::InputFormulaIntoCling ( )
private

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

Definition at line 836 of file TFormula.cxx.

◆ IsAParameterName()

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

Definition at line 301 of file TFormula.cxx.

◆ IsBracket()

Bool_t TFormula::IsBracket ( const char  c)
staticprotected

Definition at line 242 of file TFormula.cxx.

◆ IsDefaultVariableName()

Bool_t TFormula::IsDefaultVariableName ( const TString name)
staticprivate

Definition at line 260 of file TFormula.cxx.

◆ IsFunctionNameChar()

Bool_t TFormula::IsFunctionNameChar ( const char  c)
staticprotected

Definition at line 254 of file TFormula.cxx.

◆ IsHexadecimal()

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

Definition at line 278 of file TFormula.cxx.

◆ IsLinear()

Bool_t TFormula::IsLinear ( ) const
inline

Definition at line 235 of file TFormula.h.

◆ IsOperator()

Bool_t TFormula::IsOperator ( const char  c)
staticprotected

Definition at line 234 of file TFormula.cxx.

◆ IsScientificNotation()

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

Definition at line 266 of file TFormula.cxx.

◆ IsValid()

Bool_t TFormula::IsValid ( ) const
inline

Definition at line 233 of file TFormula.h.

◆ IsVectorized()

Bool_t TFormula::IsVectorized ( ) const
inline

Definition at line 234 of file TFormula.h.

◆ operator=()

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

= operator.

Definition at line 549 of file TFormula.cxx.

◆ PrepareEvalMethod()

bool TFormula::PrepareEvalMethod ( )
private

Sets TMethodCall to function inside Cling environment.

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

Definition at line 820 of file TFormula.cxx.

◆ PrepareFormula()

Bool_t TFormula::PrepareFormula ( TString formula)
protected

◆ PreProcessFormula()

void TFormula::PreProcessFormula ( TString formula)
protected

◆ Print()

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

Print TNamed name and title.

Reimplemented from TNamed.

◆ ProcessFormula()

void TFormula::ProcessFormula ( TString formula)
protected

◆ ReInitializeEvalMethod()

void TFormula::ReInitializeEvalMethod ( )
private

◆ ReplaceAllNames()

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

Definition at line 353 of file TFormula.cxx.

◆ ReplaceParamName()

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

◆ SetName()

void TFormula::SetName ( const char *  name)
virtual

Set the name of the TNamed.

WARNING: if the object is a member of a THashTable or THashList container the container must be Rehash()'ed after SetName(). For example the list of objects in the current directory is a THashList.

Reimplemented from TNamed.

◆ SetParameter() [1/2]

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

◆ SetParameter() [2/2]

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

◆ SetParameters() [1/2]

void TFormula::SetParameters ( const Double_t params)

◆ 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 
)

◆ SetParName()

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

◆ 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" 
)

◆ SetPredefinedParamNames()

void TFormula::SetPredefinedParamNames ( )
protected

◆ SetVariable()

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

◆ SetVariables()

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

◆ SetVectorized()

void TFormula::SetVectorized ( Bool_t  vectorized)

Member Data Documentation

◆ fAllParametersSetted

Bool_t TFormula::fAllParametersSetted
private

transient to force re-initialization

Definition at line 94 of file TFormula.h.

◆ fClingInitialized

Bool_t TFormula::fClingInitialized
private

trasient to force initialization

Definition at line 93 of file TFormula.h.

◆ fClingInput

TString TFormula::fClingInput
private

Definition at line 89 of file TFormula.h.

◆ fClingName

TString TFormula::fClingName
private

pointer to a methodcall

Definition at line 98 of file TFormula.h.

◆ fClingParameters

std::vector<Double_t> TFormula::fClingParameters
private

cached variables

Definition at line 91 of file TFormula.h.

◆ fClingVariables

std::vector<Double_t> TFormula::fClingVariables
private

input function passed to Cling

Definition at line 90 of file TFormula.h.

◆ fConsts

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

Definition at line 136 of file TFormula.h.

◆ fFormula

TString TFormula::fFormula
protected

Definition at line 138 of file TFormula.h.

◆ fFuncPtr

CallFuncSignature TFormula::fFuncPtr = nullptr
private

input query to clad to generate a gradient

Definition at line 103 of file TFormula.h.

◆ fFuncs

std::list<TFormulaFunction> TFormula::fFuncs
protected

Definition at line 133 of file TFormula.h.

◆ fFunctionsShortcuts

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

Definition at line 137 of file TFormula.h.

◆ fGradFuncPtr

CallFuncSignature TFormula::fGradFuncPtr = nullptr
private

function pointer, owned by the JIT.

Definition at line 104 of file TFormula.h.

◆ fGradGenerationInput

std::string TFormula::fGradGenerationInput
private

Definition at line 102 of file TFormula.h.

◆ fGradMethod

std::unique_ptr<TMethodCall> TFormula::fGradMethod
private

pointer to methodcall

Definition at line 97 of file TFormula.h.

◆ fIsCladRuntimeIncluded

bool TFormula::fIsCladRuntimeIncluded
staticprivate

pointer to the lambda function

Definition at line 106 of file TFormula.h.

◆ fLambdaPtr

void* TFormula::fLambdaPtr = nullptr
private

function pointer, owned by the JIT.

Definition at line 105 of file TFormula.h.

◆ fLazyInitialization

Bool_t TFormula::fLazyInitialization = kFALSE
private

Definition at line 95 of file TFormula.h.

◆ fLinearParts

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

Definition at line 142 of file TFormula.h.

◆ fMethod

TMethodCall* TFormula::fMethod
private

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

Definition at line 96 of file TFormula.h.

◆ fNdim

Int_t TFormula::fNdim
protected

Definition at line 139 of file TFormula.h.

◆ fNpar

Int_t TFormula::fNpar
protected

Definition at line 140 of file TFormula.h.

◆ fNumber

Int_t TFormula::fNumber
protected

Number of parameter (transient since we save the vector)

Definition at line 141 of file TFormula.h.

◆ fParams

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

list of variable names

Definition at line 135 of file TFormula.h.

◆ fReadyToExecute

Bool_t TFormula::fReadyToExecute
private

Definition at line 92 of file TFormula.h.

◆ fSavedInputFormula

std::string TFormula::fSavedInputFormula
private

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

Definition at line 99 of file TFormula.h.

◆ fVars

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

Definition at line 134 of file TFormula.h.

◆ fVectorized

Bool_t TFormula::fVectorized = false
protected

Definition at line 143 of file TFormula.h.

Libraries for TFormula:
[legend]

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