ROOT   6.10/09 Reference Guide
TRandom Class Reference

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 (e.g. TRandom1, TRandom2 or TRandom3). Note that this class implements also a very simple generator (linear congruential) with periodicity = 10**9 which is known to have defects (the lower random bits are correlated) and therefore should NOT be used in any statistical study. One should use instead TRandom1, TRandom2 or TRandom3. TRandom3, is based on the "Mersenne Twister generator", and is the recommended one, since it has good random proprieties (period of about 10**6000 ) and it is fast. TRandom1, based on the RANLUX algorithm, has mathematically proven random proprieties and a period of about 10**171. It is however slower than the others. 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 is 10**26.

The following table shows some timings (in nanoseconds/call) for the random numbers obtained using an Intel Pentium 3.0 GHz running Linux and using the gcc 3.2.3 compiler

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

• Exp(tau)
• Integer(imax)
• Gaus(mean,sigma)
• Rndm()
• Uniform(x1)
• Landau(mpv,sigma)
• Poisson(mean)
• Binomial(ntot,prob)

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();

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

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 containes 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
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(). More...

virtual ~TRandom ()
Default destructor. More...

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

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

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

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

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. More...

virtual UInt_t GetSeed () const

virtual UInt_t Integer (UInt_t imax)
Returns a random integer on [ 0, imax-1 ]. More...

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. More...

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

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

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

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

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

virtual Double_t Rndm ()
Machine independent random number generator. More...

virtual Double_t Rndm (Int_t)

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

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

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

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. More...

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

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

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

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 ()

virtual void Clear (Option_t *option="")
Set name and title to empty strings (""). 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 Copy (TObject &named) const
Copy this to obj. More...

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

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

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

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

virtual Bool_t IsSortable () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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...

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...

Bool_t IsOnHeap () const

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...

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...

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

## 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, kBitMask = 0x00ffffff }

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

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

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...

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 ()

#include <TRandom.h>

Inheritance diagram for TRandom:
[legend]

## ◆ TRandom()

 TRandom::TRandom ( UInt_t seed = 65539 )

Default constructor. For seed see SetSeed().

Definition at line 147 of file TRandom.cxx.

## ◆ ~TRandom()

 TRandom::~TRandom ( )
virtual

Default destructor.

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

Definition at line 156 of file TRandom.cxx.

## ◆ 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 172 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 186 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 200 of file TRandom.cxx.

## ◆ Exp()

 Double_t TRandom::Exp ( Double_t tau )
virtual

Returns an exponential deviate.

exp( -t/tau )

Definition at line 212 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.

Implementation taken from UNURAN (c) 2000 W. Hoermann & J. Leydold, Institut f. Statistik, WU Wien

Definition at line 235 of file TRandom.cxx.

## ◆ GetSeed()

 virtual UInt_t TRandom::GetSeed ( ) const
inlinevirtual

Reimplemented in TRandom1, and TRandom3.

Definition at line 40 of file TRandom.h.

## ◆ Integer()

 UInt_t TRandom::Integer ( UInt_t imax )
virtual

Returns a random integer on [ 0, imax-1 ].

Definition at line 320 of file TRandom.cxx.

## ◆ 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 340 of file TRandom.cxx.

## ◆ Poisson()

 Int_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 since is returning 32 bits integer will not work for values larger than 2*10**9. One should then use the Trandom::PoissonD for such large values.

Definition at line 362 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 414 of file TRandom.cxx.

## ◆ Rannor() [1/2]

 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 460 of file TRandom.cxx.

## ◆ Rannor() [2/2]

 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 475 of file TRandom.cxx.

## ◆ ReadRandom()

 void TRandom::ReadRandom ( const char * filename )
virtual

Reads saved random generator status from filename.

Definition at line 490 of file TRandom.cxx.

## ◆ Rndm() [1/2]

 Double_t TRandom::Rndm ( )
virtual

Machine independent random number generator.

Based on the BSD Unix (Rand) Linear congrential 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, TRandomGen< Engine >, TRandom3, and TRandom2.

Definition at line 512 of file TRandom.cxx.

## ◆ Rndm() [2/2]

 virtual Double_t TRandom::Rndm ( Int_t )
inlinevirtual

Definition at line 51 of file TRandom.h.

## ◆ RndmArray() [1/2]

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

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

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

Definition at line 548 of file TRandom.cxx.

## ◆ RndmArray() [2/2]

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

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

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

Definition at line 535 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, TRandomGen< Engine >, TRandom3, and TRandom2.

Definition at line 568 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 588 of file TRandom.cxx.

## ◆ Uniform() [1/2]

 Double_t TRandom::Uniform ( Double_t x1 = 1 )
virtual

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

Definition at line 606 of file TRandom.cxx.

## ◆ Uniform() [2/2]

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

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

Definition at line 615 of file TRandom.cxx.

## ◆ WriteRandom()

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

Writes random generator status to filename.

Definition at line 624 of file TRandom.cxx.

## ◆ fSeed

 UInt_t TRandom::fSeed
protected

Definition at line 30 of file TRandom.h.

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