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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 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");

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 = "")MENU
virtual Int_tTObject::DistancetoPrimitive(Int_t px, Int_t py)
virtual voidTObject::Draw(Option_t* option = "")
virtual voidTObject::DrawClass() constMENU
virtual TObject*TObject::DrawClone(Option_t* option = "") constMENU
virtual voidTObject::Dump() constMENU
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() const
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() constMENU
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()
voidTObject::Obsolete(const char* method, const char* asOfVers, const char* removedFromVers) const
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 = "") constMENU
virtual voidTObject::SavePrimitive(ostream& out, Option_t* option = "")
voidTObject::SetBit(UInt_t f)
voidTObject::SetBit(UInt_t f, Bool_t set)
virtual voidTObject::SetDrawOption(Option_t* option = "")MENU
static voidTObject::SetDtorOnly(void* obj)
virtual voidTNamed::SetName(const char* name)MENU
virtual voidTNamed::SetNameTitle(const char* name, const char* title)
static voidTObject::SetObjectStat(Bool_t stat)
virtual voidSetSeed(UInt_t seed = 0)
virtual voidTNamed::SetTitle(const char* title = "")MENU
virtual voidTObject::SetUniqueID(UInt_t uid)
virtual voidShowMembers(TMemberInspector&)
virtual Int_tTNamed::Sizeof() const
virtual voidSphere(Double_t& x, Double_t& y, Double_t& z, Double_t r)
virtual voidStreamer(TBuffer&)
voidStreamerNVirtual(TBuffer& ClassDef_StreamerNVirtual_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

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 = 65539)
 Default constructor. For seed see SetSeed().
 Default destructor. Can reset gRandom to 0 if gRandom points to this
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 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)).
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 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).
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 = 0)
 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.
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() const
{return fSeed;}