class TRandom: public TNamed


 basic Random number generator class (periodicity = 10**9).
 Note that this is a very simple generator (linear congruential)
 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

    TRandom           34   ns/call     (BAD Generator)
    TRandom1          242  ns/call
    TRandom2          37   ns/call
    TRandom3          45   ns/call

 The following basic Random distributions are provided:


 Random numbers distributed according to 1-d, 2-d or 3-d distributions

 contained in TF1, TF2 or TF3 objects.
 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.
   TUnuran u;
   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 a Intel 2GHz Dual Core running MacOSX and compiled with gcc 4.0.1

  Distribution            nanoseconds/call

                      TRandom  TRandom1 TRandom2 TRandom3

  Rndm..............   24.000  137.000   29.000   30.000
  RndmArray.........   17.000  128.000   22.000   22.000
  Gaus..............   86.000  242.000   92.000   96.000
  Rannor............  141.000  258.000  148.000  147.000
  Landau............   68.000  173.000   73.000   74.000
  Binomial(5,0.5)...  152.000  695.000  171.000  179.000
  Binomial(15,0.5)..  414.000 2060.000  480.000  497.000
  Poisson(3)........  212.000  653.000  231.000  234.000
  Poisson(10).......  402.000 1618.000  456.000  460.000
  Poisson(70)....... 1225.000 1651.000 1253.000 1250.000
  Poisson(100)...... 1233.000 1664.000 1260.000 1262.000
  GausTF1...........  210.000  326.000  218.000  216.000
  LandauTF1.........  209.000  325.000  217.000  213.000
  GausUNURAN........   90.000  202.000   97.000   96.000
  PoissonUNURAN(10).  160.000  361.000  170.000  170.000
  PoissonUNURAN(100)  139.000  347.000  148.000  149.000

  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");

Function Members (Methods)

TRandom(UInt_t seed = 65539)
TRandom(const TRandom&)
voidTObject::AbstractMethod(const char* method) const
virtual voidTObject::AppendPad(Option_t* option = "")
virtual Int_tBinomial(Int_t ntot, Double_t prob)
virtual Double_tBreitWigner(Double_t mean = 0, Double_t gamma = 1)
virtual voidTObject::Browse(TBrowser* b)
virtual voidCircle(Double_t& x, Double_t& y, Double_t r)
static TClass*Class()
virtual const char*TObject::ClassName() const
virtual voidTNamed::Clear(Option_t* option = "")
virtual TObject*TNamed::Clone(const char* newname = "") const
virtual Int_tTNamed::Compare(const TObject* obj) const
virtual voidTNamed::Copy(TObject& named) const
virtual voidTObject::Delete(Option_t* option = "")
virtual Int_tTObject::DistancetoPrimitive(Int_t px, Int_t py)
virtual voidTObject::Draw(Option_t* option = "")
virtual voidTObject::DrawClass() const
virtual TObject*TObject::DrawClone(Option_t* option = "") const
virtual voidTObject::Dump() const
virtual voidTObject::Error(const char* method, const char* msgfmt) const
virtual voidTObject::Execute(const char* method, const char* params, Int_t* error = 0)
virtual voidTObject::Execute(TMethod* method, TObjArray* params, Int_t* error = 0)
virtual voidTObject::ExecuteEvent(Int_t event, Int_t px, Int_t py)
virtual Double_tExp(Double_t tau)
virtual voidTObject::Fatal(const char* method, const char* msgfmt) const
virtual voidTNamed::FillBuffer(char*& buffer)
virtual TObject*TObject::FindObject(const char* name) const
virtual TObject*TObject::FindObject(const TObject* obj) const
virtual Double_tGaus(Double_t mean = 0, Double_t sigma = 1)
virtual Option_t*TObject::GetDrawOption() const
static Long_tTObject::GetDtorOnly()
virtual const char*TObject::GetIconName() const
virtual const char*TNamed::GetName() const
virtual char*TObject::GetObjectInfo(Int_t px, Int_t py) const
static Bool_tTObject::GetObjectStat()
virtual Option_t*TObject::GetOption() const
virtual UInt_tGetSeed()
virtual const char*TNamed::GetTitle() const
virtual UInt_tTObject::GetUniqueID() const
virtual Bool_tTObject::HandleTimer(TTimer* timer)
virtual ULong_tTNamed::Hash() const
virtual voidTObject::Info(const char* method, const char* msgfmt) const
virtual Bool_tTObject::InheritsFrom(const char* classname) const
virtual Bool_tTObject::InheritsFrom(const TClass* cl) const
virtual voidTObject::Inspect() const
virtual UInt_tInteger(UInt_t imax)
voidTObject::InvertBit(UInt_t f)
virtual TClass*IsA() const
virtual Bool_tTObject::IsEqual(const TObject* obj) const
virtual Bool_tTObject::IsFolder() const
Bool_tTObject::IsOnHeap() const
virtual Bool_tTNamed::IsSortable() const
Bool_tTObject::IsZombie() const
virtual Double_tLandau(Double_t mean = 0, Double_t sigma = 1)
virtual voidTNamed::ls(Option_t* option = "") const
voidTObject::MayNotUse(const char* method) const
virtual Bool_tTObject::Notify()
static voidTObject::operator delete(void* ptr)
static voidTObject::operator delete(void* ptr, void* vp)
static voidTObject::operator delete[](void* ptr)
static voidTObject::operator delete[](void* ptr, void* vp)
void*TObject::operator new(size_t sz)
void*TObject::operator new(size_t sz, void* vp)
void*TObject::operator new[](size_t sz)
void*TObject::operator new[](size_t sz, void* vp)
TRandom&operator=(const TRandom&)
virtual voidTObject::Paint(Option_t* option = "")
virtual Int_tPoisson(Double_t mean)
virtual Double_tPoissonD(Double_t mean)
virtual voidTObject::Pop()
virtual voidTNamed::Print(Option_t* option = "") const
virtual voidRannor(Float_t& a, Float_t& b)
virtual voidRannor(Double_t& a, Double_t& b)
virtual Int_tTObject::Read(const char* name)
virtual voidReadRandom(const char* filename)
virtual voidTObject::RecursiveRemove(TObject* obj)
voidTObject::ResetBit(UInt_t f)
virtual Double_tRndm(Int_t i = 0)
virtual voidRndmArray(Int_t n, Float_t* array)
virtual voidRndmArray(Int_t n, Double_t* array)
virtual voidTObject::SaveAs(const char* filename = "", Option_t* option = "") const
virtual voidTObject::SavePrimitive(basic_ostream<char,char_traits<char> >& out, Option_t* option = "")
voidTObject::SetBit(UInt_t f)
voidTObject::SetBit(UInt_t f, Bool_t set)
virtual voidTObject::SetDrawOption(Option_t* option = "")
static voidTObject::SetDtorOnly(void* obj)
virtual voidTNamed::SetName(const char* name)
virtual voidTNamed::SetNameTitle(const char* name, const char* title)
static voidTObject::SetObjectStat(Bool_t stat)
virtual voidSetSeed(UInt_t seed = 65539)
virtual voidTNamed::SetTitle(const char* title = "")
virtual voidTObject::SetUniqueID(UInt_t uid)
virtual voidShowMembers(TMemberInspector& insp, char* parent)
virtual Int_tTNamed::Sizeof() const
virtual voidSphere(Double_t& x, Double_t& y, Double_t& z, Double_t r)
virtual voidStreamer(TBuffer& b)
voidStreamerNVirtual(TBuffer& b)
virtual voidTObject::SysError(const char* method, const char* msgfmt) const
Bool_tTObject::TestBit(UInt_t f) const
Int_tTObject::TestBits(UInt_t f) const
virtual Double_tUniform(Double_t x1 = 1)
virtual Double_tUniform(Double_t x1, Double_t x2)
virtual voidTObject::UseCurrentStyle()
virtual voidTObject::Warning(const char* method, const char* msgfmt) const
virtual Int_tTObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0)
virtual Int_tTObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) const
virtual voidWriteRandom(const char* filename)
virtual voidTObject::DoError(int level, const char* location, const char* fmt, va_list va) const

Data Members

enum TObject::EStatusBits { kCanDelete
enum TObject::[unnamed] { kIsOnHeap
TStringTNamed::fNameobject identifier
UInt_tfSeedRandom number generator seed
TStringTNamed::fTitleobject title

Class Charts

Inheritance Inherited Members Includes Libraries
Class Charts

Function documentation

TRandom(UInt_t seed)
default constructor*-*-*-*-
*-*                  ===================
default destructor*-*-*-*-
*-*                  ==================
Int_t Binomial(Int_t ntot, Double_t prob)
 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.
 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)).
Double_t BreitWigner(Double_t mean = 0, Double_t gamma = 1)
  Return a number distributed following a BreitWigner function with mean and gamma
void Circle(Double_t& x, Double_t& y, Double_t r)
 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
Double_t Exp(Double_t tau)
 returns an exponential deviate.

          exp( -t/tau )
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.
  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

UInt_t Integer(UInt_t imax)
  returns a random integer on [ 0, imax-1 ].
Double_t Landau(Double_t mean = 0, Double_t sigma = 1)
  Generate a random number following a Landau distribution
  with mpv(most probable value) and sigma
  Converted by Rene Brun from CERNLIB routine ranlan(G110)
Int_t Poisson(Double_t mean)
 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

Double_t PoissonD(Double_t mean)
 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.

void Rannor(Float_t &a, Float_t &b)
      Return 2 numbers distributed following a gaussian with mean=0 and sigma=1
void Rannor(Double_t &a, Double_t &b)
      Return 2 numbers distributed following a gaussian with mean=0 and sigma=1
void ReadRandom(const char* filename)
 Reads saved random generator status from filename

Double_t Rndm(Int_t i = 0)
  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.
void RndmArray(Int_t n, Double_t *array)
 Return an array of n random numbers uniformly distributed in ]0,1]
void RndmArray(Int_t n, Float_t *array)
 Return an array of n random numbers uniformly distributed in ]0,1]
void SetSeed(UInt_t seed = 65539)
  Set the random generator seed
  if seed is zero, the seed is set to the current  machine clock
  Note that the machine clock is returned with a precision of 1 second.
  If one calls SetSeed(0) within a loop and the loop time is less than 1s,
  all generated numbers will be identical!
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.
   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
Double_t Uniform(Double_t x1 = 1)
 returns a uniform deviate on the interval  ]0, x1].
Double_t Uniform(Double_t x1, Double_t x2)
 returns a uniform deviate on the interval ]x1, x2].
void WriteRandom(const char* filename)
 Writes random generator status to filename

TRandom(UInt_t seed=65539)
UInt_t GetSeed()
{return fSeed;}

Author: Rene Brun 15/12/95
Last update: root/math:$Id: TRandom.h 20882 2007-11-19 11:31:26Z rdm $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *

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