This is the base class for the ROOT Random number generators.

This class defines the ROOT Random number interface and it should not be instantiated directly but used via its derived classes. The generator provided in TRandom itself is a LCG (Linear Congruential Generator), the BSD rand generator, that it should not be used because its period is only 2**31, i.e. approximately 2 billion events, that can be generated in just few seconds.

To generate random numbers, one should use one of the derived classes, which are:

TRandom3: it is based on the "Mersenne Twister generator", it is fast and a very long period of about \(10^{6000}\). However it fails some of the most stringent tests of the TestU01 suite. In addition this generator provide only numbers with 32 random bits, which might be not sufficient for some application based on double or extended precision. This generator is however used in ROOT used to instantiate the global pointer to the ROOT generator, gRandom.
TRandomRanluxpp : New implementation of the Ranlux generator algorithm based on a fast modular multiplication of 576 bits. This new implementation is built on the idea and the original code of Alexei Sibidanov, described in his paper . It generates random numbers with 52 bit precision (double precision) and it has an higher luxury level than the original Ranlux generator (p = 2048 instead of p=794).
TRandomMixMax: Generator based on the family of the MIXMAX matrix generators (see the MIXMAX HEPFORGE Web page and the documentation of the class ROOT::Math::MixMaxEngine for more information), that are base on the Asanov dynamical C systems. This generator has a state of N=240 64 bit integers, proof random properties, it provides 61 random bits and it has a very large period ( \(10^{4839}\)). Furthermore, it provides the capability to be seeded with the guarantee that, for each given different seed, a different sequence of random numbers will be generated. The only drawback is that the seeding time is time consuming, of the order of 0.1 ms, while the time to generate a number is few ns (more than 10000 faster).
TRandomMixMax17: Another MixMax generator, but with a smaller state, N=17, and this results in a smaller entropy than the generator with N=240. However, it has the same seeding capabilities, with a much faster seeding time (about 200 times less than TRandomMixMax240 and comparable to TRandom3).
TRandomMixMax256 : A variant of the MIXMAX generators, based on a state of N=256, and described in the 2015 paper. This implementation has been modified with respect to the paper, by skipping 2 internal iterations, to provide improved random properties.
TRandomMT64 : Generator based on a the Mersenne-Twister generator with 64 bits, using the implementation provided by the standard library ( std::mt19937_64 )
TRandom1 based on the RANLUX algorithm, has mathematically proven random proprieties and a period of about \(10{171}\). It is however much slower than the others and it has only 24 random bits. It can be constructed with different luxury levels.
TRandomRanlux48 : Generator based on a the RanLux generator with 48 bits and highest luxury level using the implementation provided by the standard library (std::ranlux48). The drawback of this generator is its slow generation time.
TRandom2 is based on the Tausworthe generator of L'Ecuyer, and it has the advantage of being fast and using only 3 words (of 32 bits) for the state. The period however is not impressively long, it is 10**26.

Using the template TRandomGen class (template on the contained Engine type), it is possible to add any generator based on the standard C++ random library (see the C++ random documentation.) or different variants of the MIXMAX generator using the ROOT::Math::MixMaxEngine. Some of the listed generator above (e.g. TRandomMixMax256 or TRandomMT64) are convenient typedef's of generator built using the template TRandomGen class.

Please note also that this class (TRandom) implements also a very simple generator (linear congruential) with period = \(10^9\), known to have defects (the lower random bits are correlated) and it is failing the majority of the random number generator tests. Therefore it should NOT be used in any statistical study.

The following table shows some timings (in nanoseconds/call) for the random numbers obtained using a macbookpro 2.6 GHz Intel Core i7 CPU:

TRandom 3 ns/call (but this is a very BAD Generator, not to be used)
TRandom2 5 ns/call
TRandom3 5 ns/call
TRandomMixMax 6 ns/call
TRandomMixMax17 6 ns/call
TRandomMT64 9 ns/call
TRandomMixMax256 10 ns/call
TRandomRanluxpp 14 ns/call
TRandom1 80 ns/call
TRandomRanlux48 250 ns/call

The following methods are provided to generate random numbers distributed according to some basic distributions:

Random numbers distributed according to 1-d, 2-d or 3-d distributions contained in TF1, TF2 or TF3 objects can also be generated. For example, to get a random number distributed following abs(sin(x)/x)*sqrt(x) you can do :

TF1

*f1 = new TF1("f1","abs(sin(x)/x)*sqrt(x)",0,10); double r = f1->GetRandom();

r

Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t r

Definition TGWin32VirtualXProxy.cxx:168

TF1

1-Dim function class

Definition TF1.h:233

TF1::GetRandom

virtual Double_t GetRandom(TRandom *rng=nullptr, Option_t *opt=nullptr)

Return a random number following this function shape.

Definition TF1.cxx:2192

f1

TF1 * f1

Definition legend1.C:11

or you can use the UNURAN package. You need in this case to initialize UNURAN to the function you would like to generate.

TUnuran u;
 u.Init(TUnuranDistrCont(f1));
 double r = u.Sample();

The techniques of using directly a TF1,2 or 3 function is powerful and can be used to generate numbers in the defined range of the function. Getting a number from a TF1,2,3 function is also quite fast. UNURAN is a powerful and flexible tool which contains various methods for generate random numbers for continuous distributions of one and multi-dimension. It requires some set-up (initialization) phase and can be very fast when the distribution parameters are not changed for every call.

The following table shows some timings (in nanosecond/call) for basic functions, TF1 functions and using UNURAN obtained running the tutorial math/testrandom.C Numbers have been obtained on an Intel Xeon Quad-core Harpertown (E5410) 2.33 GHz running Linux SLC4 64 bit and compiled with gcc 3.4

Distribution            nanoseconds/call
                    TRandom  TRandom1 TRandom2 TRandom3
Rndm..............    5.000  105.000    7.000   10.000
RndmArray.........    4.000  104.000    6.000    9.000
Gaus..............   36.000  180.000   40.000   48.000
Rannor............  118.000  220.000  120.000  124.000
Landau............   22.000  123.000   26.000   31.000
Exponential.......   93.000  198.000   98.000  104.000
Binomial(5,0.5)...   30.000  548.000   46.000   65.000
Binomial(15,0.5)..   75.000 1615.000  125.000  178.000
Poisson(3)........   96.000  494.000  109.000  125.000
Poisson(10).......  138.000 1236.000  165.000  203.000
Poisson(70).......  818.000 1195.000  835.000  844.000
Poisson(100)......  837.000 1218.000  849.000  864.000
GausTF1...........   83.000  180.000   87.000   88.000
LandauTF1.........   80.000  180.000   83.000   86.000
GausUNURAN........   40.000  139.000   41.000   44.000
PoissonUNURAN(10).   85.000  271.000   92.000  102.000
PoissonUNURAN(100)   62.000  256.000   69.000   78.000

Note that the time to generate a number from an arbitrary TF1 function using TF1::GetRandom or using TUnuran is independent of the complexity of the function.

TH1::FillRandom(TH1 *) or TH1::FillRandom(const char *tf1name) can be used to fill an histogram (1-d, 2-d, 3-d from an existing histogram or from an existing function.

Note this interesting feature when working with objects. You can use several TRandom objects, each with their "independent" random sequence. For example, one can imagine

TRandom *eventGenerator = new TRandom();

TRandom *tracking = new TRandom();

eventGenerator can be used to generate the event kinematics. tracking can be used to track the generated particles with random numbers independent from eventGenerator. This very interesting feature gives the possibility to work with simple and very fast random number generators without worrying about random number periodicity as it was the case with Fortran. One can use TRandom::SetSeed to modify the seed of one generator.

A TRandom object may be written to a Root file

as part of another object
or with its own key (example: gRandom->Write("Random") ) ;

Definition at line 27 of file TRandom.h.

Public Member Functions
	TRandom (UInt_t seed=65539)
	Default constructor. For seed see SetSeed().

	~TRandom () override
	Default destructor.

virtual Int_t	Binomial (Int_t ntot, Double_t prob)
	Generates a random integer N according to the binomial law.

virtual Double_t	BreitWigner (Double_t mean=0, Double_t gamma=1)
	Return a number distributed following a BreitWigner function with mean and gamma.

virtual void	Circle (Double_t &x, Double_t &y, Double_t r)
	Generates random vectors, uniformly distributed over a circle of given radius.

virtual Double_t	Exp (Double_t tau)
	Returns an exponential deviate.

virtual Double_t	Gaus (Double_t mean=0, Double_t sigma=1)
	Samples a random number from the standard Normal (Gaussian) Distribution with the given mean and sigma.

virtual UInt_t	GetSeed () const
	Get the random generator seed.

virtual UInt_t	Integer (UInt_t imax)
	Returns a random integer uniformly distributed on the interval [ 0, imax-1 ].

TClass *	IsA () const override

virtual Double_t	Landau (Double_t mean=0, Double_t sigma=1)
	Generate a random number following a Landau distribution with location parameter mu and scale parameter sigma: Landau( (x-mu)/sigma ) Note that mu is not the mpv(most probable value) of the Landa distribution and sigma is not the standard deviation of the distribution which is not defined.

virtual ULong64_t	Poisson (Double_t mean)
	Generates a random integer N according to a Poisson law.

virtual Double_t	PoissonD (Double_t mean)
	Generates a random number according to a Poisson law.

virtual void	Rannor (Double_t &a, Double_t &b)
	Return 2 numbers distributed following a gaussian with mean=0 and sigma=1.

virtual void	Rannor (Float_t &a, Float_t &b)
	Return 2 numbers distributed following a gaussian with mean=0 and sigma=1.

virtual void	ReadRandom (const char *filename)
	Reads saved random generator status from filename.

Double_t	Rndm () override
	Machine independent random number generator.

virtual Double_t	Rndm (Int_t)

virtual void	RndmArray (Int_t n, Double_t *array)
	Return an array of n random numbers uniformly distributed in ]0,1].

virtual void	RndmArray (Int_t n, Float_t *array)
	Return an array of n random numbers uniformly distributed in ]0,1].

virtual void	SetSeed (ULong_t seed=0)
	Set the random generator seed.

virtual void	Sphere (Double_t &x, Double_t &y, Double_t &z, Double_t r)
	Generates random vectors, uniformly distributed over the surface of a sphere of given radius.

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

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

virtual Double_t	Uniform (Double_t x1, Double_t x2)
	Returns a uniform deviate on the interval (x1, x2).

virtual Double_t	Uniform (Double_t x1=1)
	Returns a uniform deviate on the interval (0, x1).

virtual void	WriteRandom (const char *filename) const
	Writes random generator status to filename.

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.

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

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	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 (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)

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.

Public Member Functions inherited from ROOT::Math::TRandomEngine
virtual	~TRandomEngine ()

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 Attributes
UInt_t	fSeed

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

Additional Inherited Members
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 )) }

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

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 ()

#include <TRandom.h>

Inheritance diagram for TRandom:

[legend]

Constructor & Destructor Documentation

◆ TRandom()

TRandom::TRandom ( UInt_t seed = 65539 )

Default constructor. For seed see SetSeed().

Definition at line 187 of file TRandom.cxx.

◆ ~TRandom()

TRandom::~TRandom ( )

override

Default destructor.

Can reset gRandom to 0 if gRandom points to this generator.

Definition at line 196 of file TRandom.cxx.

Member Function Documentation

◆ Binomial()

Int_t TRandom::Binomial	(	Int_t	ntot,
		Double_t	prob
	)

virtual

Generates a random integer N according to the binomial law.

Coded from Los Alamos report LA-5061-MS.

N is binomially distributed between 0 and ntot inclusive with mean prob*ntot and prob is between 0 and 1.

Note: This function should not be used when ntot is large (say >100). The normal approximation is then recommended instead (with mean =*ntot+0.5 and standard deviation sqrt(ntot*prob*(1-prob)).

Definition at line 212 of file TRandom.cxx.

◆ BreitWigner()

Double_t TRandom::BreitWigner	(	Double_t	mean = `0`,
		Double_t	gamma = `1`
	)

virtual

Return a number distributed following a BreitWigner function with mean and gamma.

Definition at line 226 of file TRandom.cxx.

◆ Circle()

void TRandom::Circle	(	Double_t &	x,
		Double_t &	y,
		Double_t	r
	)

virtual

Generates random vectors, uniformly distributed over a circle of given radius.

Input : r = circle radius Output: x,y a random 2-d vector of length r

Definition at line 240 of file TRandom.cxx.

◆ Class()

static TClass * TRandom::Class ( )

static

Returns: TClass describing this class

◆ Class_Name()

static const char * TRandom::Class_Name ( )

static

Returns: Name of this class

◆ Class_Version()

static constexpr Version_t TRandom::Class_Version ( )

inlinestaticconstexpr

Returns: Version of this class

Definition at line 59 of file TRandom.h.

◆ DeclFileName()

static const char * TRandom::DeclFileName ( )

inlinestatic

Returns: Name of the file containing the class declaration

Definition at line 59 of file TRandom.h.

◆ Exp()

Double_t TRandom::Exp ( Double_t tau )

virtual

Returns an exponential deviate.

     exp( -t/tau )

Definition at line 252 of file TRandom.cxx.

◆ Gaus()

Double_t TRandom::Gaus	(	Double_t	mean = `0`,
		Double_t	sigma = `1`
	)

virtual

Samples a random number from the standard Normal (Gaussian) Distribution with the given mean and sigma.

Uses the Acceptance-complement ratio from W. Hoermann and G. Derflinger This is one of the fastest existing method for generating normal random variables. It is a factor 2/3 faster than the polar (Box-Muller) method used in the previous version of TRandom::Gaus. The speed is comparable to the Ziggurat method (from Marsaglia) implemented for example in GSL and available in the MathMore library.

REFERENCE: - W. Hoermann and G. Derflinger (1990): The ACR Method for generating normal random variables, OR Spektrum 12 (1990), 181-185.

Definition at line 275 of file TRandom.cxx.

◆ GetSeed()

UInt_t TRandom::GetSeed ( ) const

virtual

Get the random generator seed.

Warning: Might not be the initial seed!

Note that this function returns the given seed only when using as random generator engine TRandom itself, which is an LCG generator and it has as seed (state) only one 32 bit word. In case of the other generators GetSeed will return one of the state elements and not the given seed. See the documentation of the corresponding generator used (for example TRandom3::GetSeed() when using TRandom3 or gRandom. If one needs to save the generator seed in order to be used later for obtaining reproducible numbers, one should store the full generator, either in a file or in memory in a separate TRandom object. Here is an example on how to store reproducible states:

// set a unique seed
 gRandom->SetSeed(0);
 // save generator state in a different TRandom instance
 TRandom* rngSaved = static_cast<TRandom*>(gRandom->Clone());
 // now both rngSaved and gRandom will produce the same sequence of numbers
 for (int i = 0; i < 10; ++i )
    std::cout << "generated number from gRandom : " << gRandom->Rndm() << "  from saved generator " <<
    rngSaved->Rndm() << std::endl;

Reimplemented in TRandom1, TRandom2, and TRandom3.

Definition at line 651 of file TRandom.cxx.

◆ Integer()

UInt_t TRandom::Integer ( UInt_t imax )

virtual

Returns a random integer uniformly distributed on the interval [ 0, imax-1 ].

Note that the interval contains the values of 0 and imax-1 but not imax.

Definition at line 361 of file TRandom.cxx.

◆ IsA()

TClass * TRandom::IsA ( ) const

inlineoverridevirtual

Returns: TClass describing current object

Reimplemented from TNamed.

Reimplemented in TRandom1, TRandom2, TRandom3, and TRandomGen< Engine >.

Definition at line 59 of file TRandom.h.

◆ Landau()

Double_t TRandom::Landau	(	Double_t	mu = `0`,
		Double_t	sigma = `1`
	)

virtual

Generate a random number following a Landau distribution with location parameter mu and scale parameter sigma: Landau( (x-mu)/sigma ) Note that mu is not the mpv(most probable value) of the Landa distribution and sigma is not the standard deviation of the distribution which is not defined.

For mu =0 and sigma=1, the mpv = -0.22278

The Landau random number generation is implemented using the function landau_quantile(x,sigma), which provides the inverse of the landau cumulative distribution. landau_quantile has been converted from CERNLIB ranlan(G110).

Definition at line 381 of file TRandom.cxx.

◆ Poisson()

ULong64_t TRandom::Poisson ( Double_t mean )

virtual

Generates a random integer N according to a Poisson law.

Prob(N) = exp(-mean)*mean^N/Factorial(N)

Use a different procedure according to the mean value. The algorithm is the same used by CLHEP. For lower value (mean < 25) use the rejection method based on the exponential. For higher values use a rejection method comparing with a Lorentzian distribution, as suggested by several authors. This routine returns now an unsigned 64 bit integer For large values, larger than 1.84e+19, we print an error message advising to use the Trandom::PoissonD for such large values, and return the max value UINT64_MAX

Definition at line 404 of file TRandom.cxx.

◆ PoissonD()

Double_t TRandom::PoissonD ( Double_t mean )

virtual

Generates a random number according to a Poisson law.

Prob(N) = exp(-mean)*mean^N/Factorial(N)

This function is a variant of TRandom::Poisson returning a double instead of an integer.

Definition at line 461 of file TRandom.cxx.

◆ Rannor() [1/2]

void TRandom::Rannor	(	Double_t &	a,
		Double_t &	b
	)

virtual

Return 2 numbers distributed following a gaussian with mean=0 and sigma=1.

Definition at line 522 of file TRandom.cxx.

◆ Rannor() [2/2]

void TRandom::Rannor	(	Float_t &	a,
		Float_t &	b
	)

virtual

Return 2 numbers distributed following a gaussian with mean=0 and sigma=1.

Definition at line 507 of file TRandom.cxx.

◆ ReadRandom()

void TRandom::ReadRandom ( const char * filename )

virtual

Reads saved random generator status from filename.

Definition at line 537 of file TRandom.cxx.

◆ Rndm() [1/2]

Double_t TRandom::Rndm ( )

overridevirtual

Machine independent random number generator.

Based on the BSD Unix (Rand) Linear congruential generator. Produces uniformly-distributed floating points between 0 and 1. Identical sequence on all machines of >= 32 bits. Periodicity = 2**31, generates a number in (0,1). Note that this is a generator which is known to have defects (the lower random bits are correlated) and therefore should NOT be used in any statistical study).

Implements ROOT::Math::TRandomEngine.

Reimplemented in TRandom1, TRandom1, TRandom2, TRandom2, TRandom3, TRandom3, TRandomGen< Engine >, and TRandomGen< Engine >.

Definition at line 559 of file TRandom.cxx.

◆ Rndm() [2/2]

virtual Double_t TRandom::Rndm ( Int_t )

inlinevirtual

Reimplemented in TRandom1, TRandom2, TRandom3, and TRandomGen< Engine >.

Definition at line 51 of file TRandom.h.

◆ RndmArray() [1/2]

void TRandom::RndmArray	(	Int_t	n,
		Double_t *	array
	)

virtual

Return an array of n random numbers uniformly distributed in ]0,1].

Reimplemented in TRandom2, TRandom3, TRandomGen< Engine >, and TRandom1.

Definition at line 582 of file TRandom.cxx.

◆ RndmArray() [2/2]

void TRandom::RndmArray	(	Int_t	n,
		Float_t *	array
	)

virtual

Return an array of n random numbers uniformly distributed in ]0,1].

Reimplemented in TRandom2, TRandom3, TRandomGen< Engine >, and TRandom1.

Definition at line 595 of file TRandom.cxx.

◆ SetSeed()

void TRandom::SetSeed ( ULong_t seed = 0 )

virtual

Set the random generator seed.

Note that default value is zero, which is different than the default value used when constructing the class. If the seed is zero the seed is set to a random value which in case of TRandom depends on the lowest 4 bytes of TUUID The UUID will be identical if SetSeed(0) is called with time smaller than 100 ns Instead if a different generator implementation is used (TRandom1, 2 or 3) the seed is generated using a 128 bit UUID. This results in different seeds and then random sequence for every SetSeed(0) call.

Reimplemented in TRandom1, TRandom2, TRandom3, and TRandomGen< Engine >.

Definition at line 615 of file TRandom.cxx.

◆ Sphere()

void TRandom::Sphere	(	Double_t &	x,
		Double_t &	y,
		Double_t &	z,
		Double_t	r
	)

virtual

Generates random vectors, uniformly distributed over the surface of a sphere of given radius.

Input : r = sphere radius Output: x,y,z a random 3-d vector of length r Method: (based on algorithm suggested by Knuth and attributed to Robert E Knop) which uses less random numbers than the CERNLIB RN23DIM algorithm

Definition at line 664 of file TRandom.cxx.

◆ Streamer()

void TRandom::Streamer ( TBuffer & R__b )

overridevirtual

Stream an object of class TObject.

Reimplemented from TNamed.

Reimplemented in TRandom1, TRandom2, TRandom3, and TRandomGen< Engine >.

◆ StreamerNVirtual()

void TRandom::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )

inline

Definition at line 59 of file TRandom.h.

◆ Uniform() [1/2]

Double_t TRandom::Uniform	(	Double_t	x1,
		Double_t	x2
	)

virtual

Returns a uniform deviate on the interval (x1, x2).

Definition at line 691 of file TRandom.cxx.

◆ Uniform() [2/2]

Double_t TRandom::Uniform ( Double_t x1 = 1 )

virtual

Returns a uniform deviate on the interval (0, x1).

Definition at line 682 of file TRandom.cxx.

◆ WriteRandom()

void TRandom::WriteRandom ( const char * filename ) const

virtual

Writes random generator status to filename.

Definition at line 700 of file TRandom.cxx.

Member Data Documentation

◆ fSeed

UInt_t TRandom::fSeed

protected

Definition at line 30 of file TRandom.h.

Libraries for TRandom:

[legend]

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

math/mathcore/inc/TRandom.h
math/mathcore/src/TRandom.cxx

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ TRandom()

◆ ~TRandom()

Member Function Documentation

◆ Binomial()

◆ BreitWigner()

◆ Circle()

◆ Class()

◆ Class_Name()

◆ Class_Version()

◆ DeclFileName()

◆ Exp()

◆ Gaus()

◆ GetSeed()

◆ Integer()

◆ IsA()

◆ Landau()

◆ Poisson()

◆ PoissonD()

◆ Rannor() [1/2]

◆ Rannor() [2/2]

◆ ReadRandom()

◆ Rndm() [1/2]

◆ Rndm() [2/2]

◆ RndmArray() [1/2]

◆ RndmArray() [2/2]

◆ SetSeed()

◆ Sphere()

◆ Streamer()

◆ StreamerNVirtual()

◆ Uniform() [1/2]

◆ Uniform() [2/2]

◆ WriteRandom()

Member Data Documentation

◆ fSeed