library: libCore #include "TRandom.h"

# TRandom

class description - source file - inheritance tree (.pdf)

## class TRandom : public TNamed

| Inheritance Chart:
`TObject`
| <- | `TNamed`
| <- | `TRandom` |
<- |
`TRandom2` |
`TRandom3` |

        public:

                           TRandom(UInt_t seed = 65539)
                           TRandom(const TRandom&)
                   virtual ~TRandom()
             virtual Int_t Binomial(Int_t ntot, Double_t prob)
          virtual Double_t BreitWigner(Double_t mean = 0, Double_t gamma = 1)
            static TClass* Class()
          virtual Double_t Exp(Double_t tau)
          virtual Double_t Gaus(Double_t mean = 0, Double_t sigma = 1)
            virtual UInt_t GetSeed()
            virtual UInt_t Integer(UInt_t imax)
           virtual TClass* IsA() const
          virtual Double_t Landau(Double_t mean = 0, Double_t sigma = 1)
                  TRandom& operator=(const TRandom&)
             virtual Int_t Poisson(Double_t mean)
          virtual Double_t PoissonD(Double_t mean)
              virtual void Rannor(Float_t& a, Float_t& b)
              virtual void Rannor(Double_t& a, Double_t& b)
              virtual void ReadRandom(const char* filename)
          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 SetSeed(UInt_t seed = 65539)
              virtual void ShowMembers(TMemberInspector& insp, char* parent)
              virtual void Sphere(Double_t& x, Double_t& y, Double_t& z, Double_t xlong)
              virtual void Streamer(TBuffer& b)
                      void StreamerNVirtual(TBuffer& b)
          virtual Double_t Uniform(Double_t x1 = 1)
          virtual Double_t Uniform(Double_t x1, Double_t x2)
              virtual void WriteRandom(const char* filename)

### Data Members

        protected:

          UInt_t fSeed  Random number generator seed

## Class Description

     TRandom

     basic Random number generator class (periodicity = 10**8).

     The following basic Random generators 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();
     The technique of using a TF1,2 or 3 function is very powerful.
     It is also more precise than using the basic functions (except Rndm).
     With a TF1 function, for example, the real integral of the function
     is correctly calculated in the specified range of the function.
     Getting a number from a TF1 function is also very fast.
     The following table shows some timings (in microsecons/call)
     for basic functions and TF1 functions.
     The left column is with the compiler, the right column with CINT.
     Numbers have been obtained on a Pentium 233Mhz running Linux.

                              g++        CINT
       Rndm..............    0.330       4.15
       Gaus..............    2.220       6.77
       Landau............   21.590      46.82
       Binomial(5,0.5)...    0.890       5.34
       Binomial(15,0.5)..    0.920       5.36
       Poisson(3)........    2.170       5.93
       Poisson(10).......    4.160       7.95
       Poisson(70).......   21.510      25.27
       Poisson(100)......    2.910       6.72
       GausTF1...........    2.070       4.73
       LandauTF1.........    2.100       4.73

      Note that the time to generate a number from an arbitrary TF1 function
      is independent of the complexity of the function.
      For Landau distribution, it is recommended to use the TF1 technique.

      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");

      The small program below has been used to get the values in the table above.
       #ifndef __CINT__
          #include "TROOT.h"
       #include "TF1.h"
       #include "TRandom.h"
       #include "TStopwatch.h"
       void rand();

       //______________________________________________________________________________
       int main()
       {
         TROOT simple("simple","Test of random numbers");

         rand();
       }
       #endif
       void rand() {
         int i, N = 1000000;
         double cpn = 1000000./N;
         double x;
         TStopwatch sw;
         sw.Start();
         for (i=0;i<N;i++) {
            x = gRandom->Rndm(i);
         }
         printf("Rndm.............. %8.3f microseconds/call\n",sw.CpuTime()*cpn);
         sw.Start();
         for (i=0;i<N;i++) {
            x = gRandom->Gaus(0,1);
         }
         printf("Gaus.............. %8.3f\n",sw.CpuTime()*cpn);
         sw.Start();
         for (i=0;i<N;i++) {
            x = gRandom->Landau(0,1);
         }
         printf("Landau............ %8.3f\n",sw.CpuTime()*cpn);
         sw.Start();
         for (i=0;i<N;i++) {
            x = gRandom->Binomial(5,0.5);
         }
         printf("Binomial(5,0.5)... %8.3f\n",sw.CpuTime()*cpn);
         sw.Start();
         for (i=0;i<N;i++) {
            x = gRandom->Binomial(15,0.5);
         }
         printf("Binomial(15,0.5).. %8.3f\n",sw.CpuTime()*cpn);
         sw.Start();
         for (i=0;i<N;i++) {
            x = gRandom->Poisson(3);
         }
         printf("Poisson(3)........ %8.3f\n",sw.CpuTime()*cpn);
         sw.Start();
         for (i=0;i<N;i++) {
            x = gRandom->Poisson(10);
         }
         printf("Poisson(10)....... %8.3f\n",sw.CpuTime()*cpn);
         sw.Start();
         for (i=0;i<N;i++) {
            x = gRandom->Poisson(70);
         }
         printf("Poisson(70)....... %8.3f\n",sw.CpuTime()*cpn);
         sw.Start();
         for (i=0;i<N;i++) {
            x = gRandom->Poisson(100);
         }
         printf("Poisson(100)...... %8.3f\n",sw.CpuTime()*cpn);

         TF1 *f1 = new TF1("f1","gaus",-4,4);
         f1->SetParameters(1,0,1);
         sw.Start();
         for (i=0;i<N;i++) {
            x = f1->GetRandom();
         }
         printf("GausTF1........... %8.3f\n",sw.CpuTime()*cpn);

         TF1 *f2 = new TF1("f2","landau",-5,15);
         f2->SetParameters(1,0,1);
         sw.Start();
         for (i=0;i<N;i++) {
            x = f2->GetRandom();
         }
         printf("LandauTF1......... %8.3f\n",sw.CpuTime()*cpn);

       }

TRandom(UInt_t seed): TNamed("Random","Default Random number generator")

    *-*-*-*-*-*-*-*-*-*-*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, Double_t gamma)

      Return a number distributed following a BreitWigner function with mean and gamma

Double_t Exp(Double_t tau)

     returns an exponential deviate.

              exp( -t/tau )

Double_t Gaus(Double_t mean, Double_t sigma)

          Return a number distributed following a gaussian with mean and sigma

UInt_t Integer(UInt_t imax)

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

Double_t Landau(Double_t mpv, Double_t sigma)

      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.
     Coded from Los Alamos report LA-5061-MS
     Prob(N) = exp(-mean)*mean^N/Factorial(N)

Double_t PoissonD(Double_t mean)

     Generates a random number according to a Poisson law.
     Coded from Los Alamos report LA-5061-MS
     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)

      Machine independent random number generator.
      Produces uniformly-distributed floating points between 0 and 1.
      Identical sequence on all machines of >= 32 bits.
      Periodicity = 10**8
      Universal version (Fred James 1985).
      generates a number in ]0,1]

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)

      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 xlong)

     generates random vectors, uniformly distributed over the surface
     of a sphere of given radius.
       Input : xlong = sphere radius
       Output: x,y,z a random 3-d vector of length xlong
     Method:  (based on CERNLIB RN3DIM)
     A random vector in the unit cube is generated  and is rejected if it lies outside the unit sphere.
     This rejection technique uses on average about 6 random numbers per vector, where only two are
     needed in principle. However, it is faster than the classical two-number technique which requires
     a square root, a sine, and a cosine.

Double_t Uniform(Double_t x1)

     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

### Inline Functions

                 UInt_t GetSeed()
                TClass* Class()
                TClass* IsA() const
                   void ShowMembers(TMemberInspector& insp, char* parent)
                   void Streamer(TBuffer& b)
                   void StreamerNVirtual(TBuffer& b)
                TRandom TRandom(const TRandom&)
               TRandom& operator=(const TRandom&)

Author: Rene Brun 15/12/95
Last update: root/base:$Name: $:$Id: TRandom.cxx,v 1.20 2005/01/27 20:14:09 brun Exp $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *