 # 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

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 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)

public:
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

## Class Charts ## Function documentation

TRandom(UInt_t seed = 65539)
``` Default constructor. For seed see SetSeed().
```
~TRandom()
``` Default destructor. Can reset gRandom to 0 if gRandom points to this
generator.
```
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
```
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.
```
``` 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).
```

``` 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;}`