# class TRandom: public TNamed

TRandom

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:

-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.
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;
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 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)

public:
 TRandom(UInt_t seed = 65539) TRandom(const TRandom&) virtual ~TRandom() void TObject::AbstractMethod(const char* method) const virtual void TObject::AppendPad(Option_t* option = "") virtual Int_t Binomial(Int_t ntot, Double_t prob) virtual Double_t BreitWigner(Double_t mean = 0, Double_t gamma = 1) virtual void TObject::Browse(TBrowser* b) virtual void Circle(Double_t& x, Double_t& y, Double_t r) static TClass* Class() virtual const char* TObject::ClassName() const virtual void TNamed::Clear(Option_t* option = "") virtual TObject* TNamed::Clone(const char* newname = "") const virtual Int_t TNamed::Compare(const TObject* obj) const virtual void TNamed::Copy(TObject& named) const virtual void TObject::Delete(Option_t* option = "") virtual Int_t TObject::DistancetoPrimitive(Int_t px, Int_t py) virtual void TObject::Draw(Option_t* option = "") virtual void TObject::DrawClass() const virtual TObject* TObject::DrawClone(Option_t* option = "") const virtual void TObject::Dump() const virtual void TObject::Error(const char* method, const char* msgfmt) const virtual void TObject::Execute(const char* method, const char* params, Int_t* error = 0) virtual void TObject::Execute(TMethod* method, TObjArray* params, Int_t* error = 0) virtual void TObject::ExecuteEvent(Int_t event, Int_t px, Int_t py) virtual Double_t Exp(Double_t tau) virtual void TObject::Fatal(const char* method, const char* msgfmt) const virtual void TNamed::FillBuffer(char*& buffer) virtual TObject* TObject::FindObject(const char* name) const virtual TObject* TObject::FindObject(const TObject* obj) const virtual Double_t Gaus(Double_t mean = 0, Double_t sigma = 1) virtual Option_t* TObject::GetDrawOption() const static Long_t TObject::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_t TObject::GetObjectStat() virtual Option_t* TObject::GetOption() const virtual UInt_t GetSeed() virtual const char* TNamed::GetTitle() const virtual UInt_t TObject::GetUniqueID() const virtual Bool_t TObject::HandleTimer(TTimer* timer) virtual ULong_t TNamed::Hash() const virtual void TObject::Info(const char* method, const char* msgfmt) const virtual Bool_t TObject::InheritsFrom(const char* classname) const virtual Bool_t TObject::InheritsFrom(const TClass* cl) const virtual void TObject::Inspect() const virtual UInt_t Integer(UInt_t imax) void TObject::InvertBit(UInt_t f) virtual TClass* IsA() const virtual Bool_t TObject::IsEqual(const TObject* obj) const virtual Bool_t TObject::IsFolder() const Bool_t TObject::IsOnHeap() const virtual Bool_t TNamed::IsSortable() const Bool_t TObject::IsZombie() const virtual Double_t Landau(Double_t mean = 0, Double_t sigma = 1) virtual void TNamed::ls(Option_t* option = "") const void TObject::MayNotUse(const char* method) const virtual Bool_t TObject::Notify() static void TObject::operator delete(void* ptr) static void TObject::operator delete(void* ptr, void* vp) static void TObject::operator delete[](void* ptr) static void TObject::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 void TObject::Paint(Option_t* option = "") virtual Int_t Poisson(Double_t mean) virtual Double_t PoissonD(Double_t mean) virtual void TObject::Pop() virtual void TNamed::Print(Option_t* option = "") const virtual void Rannor(Float_t& a, Float_t& b) virtual void Rannor(Double_t& a, Double_t& b) virtual Int_t TObject::Read(const char* name) virtual void ReadRandom(const char* filename) virtual void TObject::RecursiveRemove(TObject* obj) void TObject::ResetBit(UInt_t f) virtual Double_t Rndm(Int_t i = 0) virtual void RndmArray(Int_t n, Float_t* array) virtual void RndmArray(Int_t n, Double_t* array) virtual void TObject::SaveAs(const char* filename = "", Option_t* option = "") const virtual void TObject::SavePrimitive(basic_ostream >& out, Option_t* option = "") void TObject::SetBit(UInt_t f) void TObject::SetBit(UInt_t f, Bool_t set) virtual void TObject::SetDrawOption(Option_t* option = "") static void TObject::SetDtorOnly(void* obj) virtual void TNamed::SetName(const char* name) virtual void TNamed::SetNameTitle(const char* name, const char* title) static void TObject::SetObjectStat(Bool_t stat) virtual void SetSeed(UInt_t seed = 65539) virtual void TNamed::SetTitle(const char* title = "") virtual void TObject::SetUniqueID(UInt_t uid) virtual void ShowMembers(TMemberInspector& insp, char* parent) virtual Int_t TNamed::Sizeof() const virtual void Sphere(Double_t& x, Double_t& y, Double_t& z, Double_t r) virtual void Streamer(TBuffer& b) void StreamerNVirtual(TBuffer& b) virtual void TObject::SysError(const char* method, const char* msgfmt) const Bool_t TObject::TestBit(UInt_t f) const Int_t TObject::TestBits(UInt_t f) const virtual Double_t Uniform(Double_t x1 = 1) virtual Double_t Uniform(Double_t x1, Double_t x2) virtual void TObject::UseCurrentStyle() virtual void TObject::Warning(const char* method, const char* msgfmt) const virtual Int_t TObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) virtual Int_t TObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) const virtual void WriteRandom(const char* filename)
protected:
 virtual void TObject::DoError(int level, const char* location, const char* fmt, va_list va) const void TObject::MakeZombie()

## Data Members

public:
 enum TObject::EStatusBits { kCanDelete kMustCleanup kObjInCanvas kIsReferenced kHasUUID kCannotPick kNoContextMenu kInvalidObject }; enum TObject::[unnamed] { kIsOnHeap kNotDeleted kZombie kBitMask kSingleKey kOverwrite kWriteDelete };
protected:
 TString TNamed::fName object identifier UInt_t fSeed Random number generator seed TString TNamed::fTitle object title

## Function documentation

TRandom(UInt_t seed)
default constructor*-*-*-*-
*-*                  ===================
~TRandom()
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].

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)

{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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