This is the base class for the ROOT Random number generators.
This class defines the ROOT Random number interface and it should not be instantiated directly but used via its derived classes. The generator provided in TRandom itself is a LCG (Linear Congruential Generator), the BSD rand
generator, that it should not be used because its period is only 2**31, i.e. approximately 2 billion events, that can be generated in just few seconds.
To generate random numbers, one should use the derived class, which are :
p = 2048
instead of p=794
).Using the template TRandomGen class (template on the contained Engine type), it is possible to add any generator based on the standard C++ random library (see the C++ random documentation.) or different variants of the MIXMAX generator using the ROOT::Math::MixMaxEngine. Some of the listed generator above (e.g. TRandomMixMax256 or TRandomMT64) are convenient typedef's of generator built using the template TRandomGen class.
Please note also that this class (TRandom) implements also a very simple generator (linear congruential) with period = \(10^9\), known to have defects (the lower random bits are correlated) and it is failing the majority of the random number generator tests. Therefore it should NOT be used in any statistical study.
The following table shows some timings (in nanoseconds/call) for the random numbers obtained using a macbookpro 2.6 GHz Intel Core i7 CPU:
The following methods are provided to generate random numbers disctributed according to some basic distributions:
Random numbers distributed according to 1-d, 2-d or 3-d distributions contained in TF1, TF2 or TF3 objects can also be generated. For example, to get a random number distributed following abs(sin(x)/x)*sqrt(x) you can do :
or you can use the UNURAN package. You need in this case to initialize UNURAN to the function you would like to generate.
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 contains 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
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
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
gRandom->Write("Random")
) ; Public Member Functions | |
TRandom (UInt_t seed=65539) | |
Default constructor. For seed see SetSeed(). | |
~TRandom () override | |
Default destructor. | |
virtual Int_t | Binomial (Int_t ntot, Double_t prob) |
Generates a random integer N according to the binomial law. | |
virtual Double_t | BreitWigner (Double_t mean=0, Double_t gamma=1) |
Return a number distributed following a BreitWigner function with mean and gamma. | |
virtual void | Circle (Double_t &x, Double_t &y, Double_t r) |
Generates random vectors, uniformly distributed over a circle of given radius. | |
virtual Double_t | Exp (Double_t tau) |
Returns an exponential deviate. | |
virtual 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. | |
virtual UInt_t | GetSeed () const |
Get the random generator seed. | |
virtual UInt_t | Integer (UInt_t imax) |
Returns a random integer uniformly distributed on the interval [ 0, imax-1 ]. | |
TClass * | IsA () const override |
virtual 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. | |
virtual Int_t | Poisson (Double_t mean) |
Generates a random integer N according to a Poisson law. | |
virtual Double_t | PoissonD (Double_t mean) |
Generates a random number according to a Poisson law. | |
virtual void | Rannor (Double_t &a, Double_t &b) |
Return 2 numbers distributed following a gaussian with mean=0 and sigma=1. | |
virtual void | Rannor (Float_t &a, Float_t &b) |
Return 2 numbers distributed following a gaussian with mean=0 and sigma=1. | |
virtual void | ReadRandom (const char *filename) |
Reads saved random generator status from filename. | |
Double_t | Rndm () override |
Machine independent random number generator. | |
virtual Double_t | Rndm (Int_t) |
virtual void | RndmArray (Int_t n, Double_t *array) |
Return an array of n random numbers uniformly distributed in ]0,1]. | |
virtual void | RndmArray (Int_t n, Float_t *array) |
Return an array of n random numbers uniformly distributed in ]0,1]. | |
virtual void | SetSeed (ULong_t seed=0) |
Set the random generator seed. | |
virtual 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. | |
void | Streamer (TBuffer &) override |
Stream an object of class TObject. | |
void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
virtual Double_t | Uniform (Double_t x1, Double_t x2) |
Returns a uniform deviate on the interval (x1, x2). | |
virtual Double_t | Uniform (Double_t x1=1) |
Returns a uniform deviate on the interval (0, x1). | |
virtual void | WriteRandom (const char *filename) const |
Writes random generator status to filename. | |
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TNamed () | |
TNamed (const char *name, const char *title) | |
TNamed (const TNamed &named) | |
TNamed copy ctor. | |
TNamed (const TString &name, const TString &title) | |
virtual | ~TNamed () |
TNamed destructor. | |
void | Clear (Option_t *option="") override |
Set name and title to empty strings (""). | |
TObject * | Clone (const char *newname="") const override |
Make a clone of an object using the Streamer facility. | |
Int_t | Compare (const TObject *obj) const override |
Compare two TNamed objects. | |
void | Copy (TObject &named) const override |
Copy this to obj. | |
virtual void | FillBuffer (char *&buffer) |
Encode TNamed into output buffer. | |
const char * | GetName () const override |
Returns name of object. | |
const char * | GetTitle () const override |
Returns title of object. | |
ULong_t | Hash () const override |
Return hash value for this object. | |
Bool_t | IsSortable () const override |
void | ls (Option_t *option="") const override |
List TNamed name and title. | |
TNamed & | operator= (const TNamed &rhs) |
TNamed assignment operator. | |
void | Print (Option_t *option="") const override |
Print TNamed name and title. | |
virtual void | SetName (const char *name) |
Set the name of the TNamed. | |
virtual void | SetNameTitle (const char *name, const char *title) |
Set all the TNamed parameters (name and title). | |
virtual void | SetTitle (const char *title="") |
Set the title of the TNamed. | |
virtual Int_t | Sizeof () const |
Return size of the TNamed part of the TObject. | |
void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
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TObject () | |
TObject constructor. | |
TObject (const TObject &object) | |
TObject copy ctor. | |
virtual | ~TObject () |
TObject destructor. | |
void | AbstractMethod (const char *method) const |
Use this method to implement an "abstract" method that you don't want to leave purely abstract. | |
virtual void | AppendPad (Option_t *option="") |
Append graphics object to current pad. | |
virtual void | Browse (TBrowser *b) |
Browse object. May be overridden for another default action. | |
ULong_t | CheckedHash () |
Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object. | |
virtual const char * | ClassName () const |
Returns name of class to which the object belongs. | |
virtual void | Delete (Option_t *option="") |
Delete this object. | |
virtual Int_t | DistancetoPrimitive (Int_t px, Int_t py) |
Computes distance from point (px,py) to the object. | |
virtual void | Draw (Option_t *option="") |
Default Draw method for all objects. | |
virtual void | DrawClass () const |
Draw class inheritance tree of the class to which this object belongs. | |
virtual TObject * | DrawClone (Option_t *option="") const |
Draw a clone of this object in the current selected pad with: gROOT->SetSelectedPad(c1) . | |
virtual void | Dump () const |
Dump contents of object on stdout. | |
virtual void | Error (const char *method, const char *msgfmt,...) const |
Issue error message. | |
virtual void | Execute (const char *method, const char *params, Int_t *error=nullptr) |
Execute method on this object with the given parameter string, e.g. | |
virtual void | Execute (TMethod *method, TObjArray *params, Int_t *error=nullptr) |
Execute method on this object with parameters stored in the TObjArray. | |
virtual void | ExecuteEvent (Int_t event, Int_t px, Int_t py) |
Execute action corresponding to an event at (px,py). | |
virtual void | Fatal (const char *method, const char *msgfmt,...) const |
Issue fatal error message. | |
virtual TObject * | FindObject (const char *name) const |
Must be redefined in derived classes. | |
virtual TObject * | FindObject (const TObject *obj) const |
Must be redefined in derived classes. | |
virtual Option_t * | GetDrawOption () const |
Get option used by the graphics system to draw this object. | |
virtual const char * | GetIconName () const |
Returns mime type name of object. | |
virtual char * | GetObjectInfo (Int_t px, Int_t py) const |
Returns string containing info about the object at position (px,py). | |
virtual Option_t * | GetOption () const |
virtual UInt_t | GetUniqueID () const |
Return the unique object id. | |
virtual Bool_t | HandleTimer (TTimer *timer) |
Execute action in response of a timer timing out. | |
Bool_t | HasInconsistentHash () const |
Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e. | |
virtual void | Info (const char *method, const char *msgfmt,...) const |
Issue info message. | |
virtual Bool_t | InheritsFrom (const char *classname) const |
Returns kTRUE if object inherits from class "classname". | |
virtual Bool_t | InheritsFrom (const TClass *cl) const |
Returns kTRUE if object inherits from TClass cl. | |
virtual void | Inspect () const |
Dump contents of this object in a graphics canvas. | |
void | InvertBit (UInt_t f) |
Bool_t | IsDestructed () const |
IsDestructed. | |
virtual Bool_t | IsEqual (const TObject *obj) const |
Default equal comparison (objects are equal if they have the same address in memory). | |
virtual Bool_t | IsFolder () const |
Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). | |
R__ALWAYS_INLINE Bool_t | IsOnHeap () const |
R__ALWAYS_INLINE Bool_t | IsZombie () const |
void | MayNotUse (const char *method) const |
Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). | |
virtual Bool_t | Notify () |
This method must be overridden to handle object notification (the base implementation is no-op). | |
void | Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const |
Use this method to declare a method obsolete. | |
void | operator delete (void *ptr) |
Operator delete. | |
void | operator delete (void *ptr, void *vp) |
Only called by placement new when throwing an exception. | |
void | operator delete[] (void *ptr) |
Operator delete []. | |
void | operator delete[] (void *ptr, void *vp) |
Only called by placement new[] when throwing an exception. | |
void * | operator new (size_t sz) |
void * | operator new (size_t sz, void *vp) |
void * | operator new[] (size_t sz) |
void * | operator new[] (size_t sz, void *vp) |
TObject & | operator= (const TObject &rhs) |
TObject assignment operator. | |
virtual void | Paint (Option_t *option="") |
This method must be overridden if a class wants to paint itself. | |
virtual void | Pop () |
Pop on object drawn in a pad to the top of the display list. | |
virtual Int_t | Read (const char *name) |
Read contents of object with specified name from the current directory. | |
virtual void | RecursiveRemove (TObject *obj) |
Recursively remove this object from a list. | |
void | ResetBit (UInt_t f) |
virtual void | SaveAs (const char *filename="", Option_t *option="") const |
Save this object in the file specified by filename. | |
virtual void | SavePrimitive (std::ostream &out, Option_t *option="") |
Save a primitive as a C++ statement(s) on output stream "out". | |
void | SetBit (UInt_t f) |
void | SetBit (UInt_t f, Bool_t set) |
Set or unset the user status bits as specified in f. | |
virtual void | SetDrawOption (Option_t *option="") |
Set drawing option for object. | |
virtual void | SetUniqueID (UInt_t uid) |
Set the unique object id. | |
void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
virtual void | SysError (const char *method, const char *msgfmt,...) const |
Issue system error message. | |
R__ALWAYS_INLINE Bool_t | TestBit (UInt_t f) const |
Int_t | TestBits (UInt_t f) const |
virtual void | UseCurrentStyle () |
Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. | |
virtual void | Warning (const char *method, const char *msgfmt,...) const |
Issue warning message. | |
virtual Int_t | Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) |
Write this object to the current directory. | |
virtual Int_t | Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const |
Write this object to the current directory. | |
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virtual | ~TRandomEngine () |
Static Public Member Functions | |
static TClass * | Class () |
static const char * | Class_Name () |
static constexpr Version_t | Class_Version () |
static const char * | DeclFileName () |
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static TClass * | Class () |
static const char * | Class_Name () |
static constexpr Version_t | Class_Version () |
static const char * | DeclFileName () |
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static TClass * | Class () |
static const char * | Class_Name () |
static constexpr Version_t | Class_Version () |
static const char * | DeclFileName () |
static Longptr_t | GetDtorOnly () |
Return destructor only flag. | |
static Bool_t | GetObjectStat () |
Get status of object stat flag. | |
static void | SetDtorOnly (void *obj) |
Set destructor only flag. | |
static void | SetObjectStat (Bool_t stat) |
Turn on/off tracking of objects in the TObjectTable. | |
Protected Attributes | |
UInt_t | fSeed |
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TString | fName |
TString | fTitle |
Additional Inherited Members | |
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enum | { kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff } |
enum | { kSingleKey = (1ULL << ( 0 )) , kOverwrite = (1ULL << ( 1 )) , kWriteDelete = (1ULL << ( 2 )) } |
enum | EDeprecatedStatusBits { kObjInCanvas = (1ULL << ( 3 )) } |
enum | EStatusBits { kCanDelete = (1ULL << ( 0 )) , kMustCleanup = (1ULL << ( 3 )) , kIsReferenced = (1ULL << ( 4 )) , kHasUUID = (1ULL << ( 5 )) , kCannotPick = (1ULL << ( 6 )) , kNoContextMenu = (1ULL << ( 8 )) , kInvalidObject = (1ULL << ( 13 )) } |
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enum | { kOnlyPrepStep = (1ULL << ( 3 )) } |
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virtual void | DoError (int level, const char *location, const char *fmt, va_list va) const |
Interface to ErrorHandler (protected). | |
void | MakeZombie () |
#include <TRandom.h>
TRandom::TRandom | ( | UInt_t | seed = 65539 | ) |
Default constructor. For seed see SetSeed().
Definition at line 186 of file TRandom.cxx.
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override |
Default destructor.
Can reset gRandom to 0 if gRandom points to this generator.
Definition at line 195 of file TRandom.cxx.
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)).
Definition at line 211 of file TRandom.cxx.
Return a number distributed following a BreitWigner function with mean and gamma.
Definition at line 225 of file TRandom.cxx.
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
Definition at line 239 of file TRandom.cxx.
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static |
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inlinestaticconstexpr |
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inlinestatic |
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
Definition at line 274 of file TRandom.cxx.
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virtual |
Get the random generator seed.
Note that this function returns the given seed only when using as random generator engine TRandom itself, which is an LCG generator and it has as seed (state) only one 32 bit word. In case of the other generators GetSeed will return one of the state elements and not the given seed. See the documentation of the corresponding generator used (for example TRandom3::GetSeed() when using TRandom3 or gRandom. If one needs to save the generator seed in order to be used later for obtaining reproducible numbers, one should store the full generator, either in a file or in memory in a separate TRandom object. Here is an example on how to store reproducible states:
Reimplemented in TRandom1, and TRandom3.
Definition at line 641 of file TRandom.cxx.
Returns a random integer uniformly distributed on the interval [ 0, imax-1 ].
Note that the interval contains the values of 0 and imax-1 but not imax.
Definition at line 360 of file TRandom.cxx.
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inlineoverridevirtual |
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).
Definition at line 380 of file TRandom.cxx.
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.
Definition at line 402 of file TRandom.cxx.
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.
Definition at line 454 of file TRandom.cxx.
Return 2 numbers distributed following a gaussian with mean=0 and sigma=1.
Definition at line 515 of file TRandom.cxx.
Return 2 numbers distributed following a gaussian with mean=0 and sigma=1.
Definition at line 500 of file TRandom.cxx.
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virtual |
Reads saved random generator status from filename.
Definition at line 530 of file TRandom.cxx.
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overridevirtual |
Machine independent random number generator.
Based on the BSD Unix (Rand) Linear congruential 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).
Implements ROOT::Math::TRandomEngine.
Reimplemented in TRandom1, TRandom1, TRandom2, TRandom2, TRandom3, TRandom3, TRandomGen< Engine >, and TRandomGen< Engine >.
Definition at line 552 of file TRandom.cxx.
Return an array of n random numbers uniformly distributed in ]0,1].
Reimplemented in TRandom2, TRandom3, TRandomGen< Engine >, and TRandom1.
Definition at line 575 of file TRandom.cxx.
Return an array of n random numbers uniformly distributed in ]0,1].
Reimplemented in TRandom2, TRandom3, TRandomGen< Engine >, and TRandom1.
Definition at line 588 of file TRandom.cxx.
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virtual |
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.
Reimplemented in TRandom1, TRandom2, TRandom3, and TRandomGen< Engine >.
Definition at line 608 of file TRandom.cxx.
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
Definition at line 654 of file TRandom.cxx.
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overridevirtual |
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inline |
Returns a uniform deviate on the interval (x1, x2).
Definition at line 681 of file TRandom.cxx.
Returns a uniform deviate on the interval (0, x1).
Definition at line 672 of file TRandom.cxx.
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virtual |
Writes random generator status to filename.
Definition at line 690 of file TRandom.cxx.