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Reference Guide
TRandom.cxx
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1// @(#)root/mathcore:$Id$
2// Author: Rene Brun, Lorenzo Moneta 15/12/95
3
4/*************************************************************************
5 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *
6 * All rights reserved. *
7 * *
8 * For the licensing terms see $ROOTSYS/LICENSE. *
9 * For the list of contributors see $ROOTSYS/README/CREDITS. *
10 *************************************************************************/
11
12/**
13
14\class TRandom
15
16@ingroup Random
17
18This is the base class for the ROOT Random number generators.
19This class defines the ROOT Random number interface and it should not be instantiated directly but used via its derived classes.
20The generator provided in TRandom itself is a LCG (Linear Congruential Generator), the <a href="https://www.gnu.org/software/gsl/manual/html_node/Unix-random-number-generators.html">BSD `rand`
21generator</a>, that it should not be used because its period is only 2**31, i.e. approximatly 2 billion events, that can be generated in just few seconds.
22
23To generate random numbers, one should use the derived class, which are :
24- TRandom3: it is based on the "Mersenne Twister generator",
25it is fast and a very long period of about \f$10^{6000}\f$. However it fails some of the most stringent tests of the
26<a href="http://simul.iro.umontreal.ca/testu01/tu01.html">TestU01 suite</a>.
27In addition this generator provide only numbers with 32 random bits, which might be not sufficient for some application based on double or extended precision.
28This generator is however used in ROOT used to instantiate the global pointer to the ROOT generator, *gRandom*.
29- ::TRandomMixMax: Generator based on the family of the MIXMAX matrix generators (see the <a href="https://mixmax.hepforge.org">MIXMAX HEPFORGE Web page</a> and the
30 the documentation of the class ROOT::Math::MixMaxEngine for more information), that are base on the Asanov dynamical C systems.
31This generator has a state of N=240 64 bit integers, proof random properties, it provides 61 random bits and it has a very large period (\f$10^{4839}\f$).
32Furthermore, it provides the capability to be seeded with the guarantee that, for each given different seed, a different sequence of random numbers will be generated.
33The only drawback is that the seeding time is time consuming, of the order of 0.1 ms, while the time to generate a number is few ns (more than 10000 faster).
34- ::TRandomMixMax17: Another MixMax generator, but with a smaller state, N=17, and this results in a smaller entropy than the generator with N=240. However, it has the same seeding capabilities, with a much faster seeding time (about 200 times less than TRandomMixMax240 and comparable to TRandom3).
35- ::TRandomMixMax256 : A variant of the MIXMAX generators, based on a state of N=256, and described in the
36 <a href="http://arxiv.org/abs/1403.5355">2015 paper</a>. This implementation has been modified with respect to the paper, by skipping 2 internal interations,
37 to provide improved random properties.
38- TRandomMT64 : Generator based on a the Mersenne-Twister generator with 64 bits,
39 using the implementation provided by the standard library ( <a href="http://www.cplusplus.com/reference/random/mt19937_64/">std::mt19937_64</a> )
40- TRandom1 based on the RANLUX algorithm, has mathematically proven random proprieties
41 and a period of about \f$10{171}\f$. It is however much slower than the others and it has only 24 random bits. It can be constructed with different luxury levels.
42- TRandomRanlux48 : Generator based on a the RanLux generator with 48 bits and highest luxury level
43 using the implementation provided by the standard library (<a href="http://www.cplusplus.com/reference/random/ranlux48/">std::ranlux48</a>). The drawback of this generator is its slow generation
44 time.
45- TRandom2 is based on the Tausworthe generator of L'Ecuyer, and it has the advantage
46of being fast and using only 3 words (of 32 bits) for the state. The period however is not impressively long, it is 10**26.
47
48Using the template TRandomGen class (template on the contained Engine type), it is possible to add any generator based on the standard C++ random library
49(see the C++ <a href="http://www.cplusplus.com/reference/random/">random</a> documentation.) or different variants of the MIXMAX generator using the
50ROOT::Math::MixMaxEngine. Some of the listed generator above (e.g. TRandomMixMax256 or TRandomMT64) are convenient typedef's of generator built using the
51template TRandomGen class.
52
53Please note also that this class (TRandom) implements also a very simple generator (linear congruential) with period = \f$10^9\f$, known to have defects (the lower random bits are correlated) and it
54is failing the majority of the random number generator tests. Therefore it should NOT be used in any statistical study.
55
56The following table shows some timings (in nanoseconds/call)
57for the random numbers obtained using a macbookpro 2.6 GHz Intel Core i7 CPU:
58
59
60- TRandom 3 ns/call (but this is a very BAD Generator, not to be used)
61- TRandom2 5 ns/call
62- TRandom3 5 ns/call
63- ::TRandomMixMax 6 ns/call
64- ::TRandomMixMax17 6 ns/call
65- ::TRandomMT64 9 ns/call
66- ::TRandomMixMax256 10 ns/call
67- ::TRandom1 80 ns/call
68- ::TRandomRanlux48 250 ns/call
69
70The following methods are provided to generate random numbers disctributed according to some basic distributions:
71
72- `::Exp(tau)`
73- `::Integer(imax)`
74- `::Gaus(mean,sigma)`
75- `::Rndm()`
76- `::Uniform(x1)`
77- `::Landau(mpv,sigma)`
78- `::Poisson(mean)`
79- `::Binomial(ntot,prob)`
80
81Random numbers distributed according to 1-d, 2-d or 3-d distributions contained in TF1, TF2 or TF3 objects can also be generated.
82For example, to get a random number distributed following abs(sin(x)/x)*sqrt(x)
83you can do :
84\code{.cpp}
85 TF1 *f1 = new TF1("f1","abs(sin(x)/x)*sqrt(x)",0,10);
86 double r = f1->GetRandom();
87\endcode
88or you can use the UNURAN package. You need in this case to initialize UNURAN
89to the function you would like to generate.
90\code{.cpp}
91 TUnuran u;
92 u.Init(TUnuranDistrCont(f1));
93 double r = u.Sample();
94\endcode
95
96The techniques of using directly a TF1,2 or 3 function is powerful and
97can be used to generate numbers in the defined range of the function.
98Getting a number from a TF1,2,3 function is also quite fast.
99UNURAN is a powerful and flexible tool which containes various methods for
100generate random numbers for continuous distributions of one and multi-dimension.
101It requires some set-up (initialization) phase and can be very fast when the distribution
102parameters are not changed for every call.
103
104The following table shows some timings (in nanosecond/call)
105for basic functions, TF1 functions and using UNURAN obtained running
106the tutorial math/testrandom.C
107Numbers have been obtained on an Intel Xeon Quad-core Harpertown (E5410) 2.33 GHz running
108Linux SLC4 64 bit and compiled with gcc 3.4
109
110~~~~
111Distribution nanoseconds/call
112 TRandom TRandom1 TRandom2 TRandom3
113Rndm.............. 5.000 105.000 7.000 10.000
114RndmArray......... 4.000 104.000 6.000 9.000
115Gaus.............. 36.000 180.000 40.000 48.000
116Rannor............ 118.000 220.000 120.000 124.000
117Landau............ 22.000 123.000 26.000 31.000
118Exponential....... 93.000 198.000 98.000 104.000
119Binomial(5,0.5)... 30.000 548.000 46.000 65.000
120Binomial(15,0.5).. 75.000 1615.000 125.000 178.000
121Poisson(3)........ 96.000 494.000 109.000 125.000
122Poisson(10)....... 138.000 1236.000 165.000 203.000
123Poisson(70)....... 818.000 1195.000 835.000 844.000
124Poisson(100)...... 837.000 1218.000 849.000 864.000
125GausTF1........... 83.000 180.000 87.000 88.000
126LandauTF1......... 80.000 180.000 83.000 86.000
127GausUNURAN........ 40.000 139.000 41.000 44.000
128PoissonUNURAN(10). 85.000 271.000 92.000 102.000
129PoissonUNURAN(100) 62.000 256.000 69.000 78.000
130~~~~
131
132Note that the time to generate a number from an arbitrary TF1 function
133using TF1::GetRandom or using TUnuran is independent of the complexity of the function.
134
135TH1::FillRandom(TH1 *) or TH1::FillRandom(const char *tf1name)
136can be used to fill an histogram (1-d, 2-d, 3-d from an existing histogram
137or from an existing function.
138
139Note this interesting feature when working with objects.
140 You can use several TRandom objects, each with their "independent"
141 random sequence. For example, one can imagine
142~~~~
143 TRandom *eventGenerator = new TRandom();
144 TRandom *tracking = new TRandom();
145~~~~
146 `eventGenerator` can be used to generate the event kinematics.
147 tracking can be used to track the generated particles with random numbers
148 independent from eventGenerator.
149 This very interesting feature gives the possibility to work with simple
150 and very fast random number generators without worrying about
151 random number periodicity as it was the case with Fortran.
152 One can use TRandom::SetSeed to modify the seed of one generator.
153
154A TRandom object may be written to a Root file
155
156- as part of another object
157- or with its own key (example: `gRandom->Write("Random")` ) ;
158
159*/
160
161#include "TROOT.h"
162#include "TMath.h"
163#include "TRandom.h"
164#include "TRandom3.h"
165#include "TSystem.h"
166#include "TDirectory.h"
168#include "TUUID.h"
169
171
172////////////////////////////////////////////////////////////////////////////////
173/// Default constructor. For seed see SetSeed().
174
175TRandom::TRandom(UInt_t seed): TNamed("Random","Default Random number generator")
176{
177 SetSeed(seed);
178}
179
180////////////////////////////////////////////////////////////////////////////////
181/// Default destructor. Can reset gRandom to 0 if gRandom points to this
182/// generator.
183
185{
186 if (gRandom == this) gRandom = 0;
187}
188
189////////////////////////////////////////////////////////////////////////////////
190/// Generates a random integer N according to the binomial law.
191/// Coded from Los Alamos report LA-5061-MS.
192///
193/// N is binomially distributed between 0 and ntot inclusive
194/// with mean prob*ntot and prob is between 0 and 1.
195///
196/// Note: This function should not be used when ntot is large (say >100).
197/// The normal approximation is then recommended instead
198/// (with mean =*ntot+0.5 and standard deviation sqrt(ntot*prob*(1-prob)).
199
201{
202 if (prob < 0 || prob > 1) return 0;
203 Int_t n = 0;
204 for (Int_t i=0;i<ntot;i++) {
205 if (Rndm() > prob) continue;
206 n++;
207 }
208 return n;
209}
210
211////////////////////////////////////////////////////////////////////////////////
212/// Return a number distributed following a BreitWigner function with mean and gamma.
213
215{
216 Double_t rval, displ;
217 rval = 2*Rndm() - 1;
218 displ = 0.5*gamma*TMath::Tan(rval*TMath::PiOver2());
219
220 return (mean+displ);
221}
222
223////////////////////////////////////////////////////////////////////////////////
224/// Generates random vectors, uniformly distributed over a circle of given radius.
225/// Input : r = circle radius
226/// Output: x,y a random 2-d vector of length r
227
229{
230 Double_t phi = Uniform(0,TMath::TwoPi());
231 x = r*TMath::Cos(phi);
232 y = r*TMath::Sin(phi);
233}
234
235////////////////////////////////////////////////////////////////////////////////
236/// Returns an exponential deviate.
237///
238/// exp( -t/tau )
239
241{
242 Double_t x = Rndm(); // uniform on ] 0, 1 ]
243 Double_t t = -tau * TMath::Log( x ); // convert to exponential distribution
244 return t;
245}
246
247////////////////////////////////////////////////////////////////////////////////
248/// Samples a random number from the standard Normal (Gaussian) Distribution
249/// with the given mean and sigma.
250/// Uses the Acceptance-complement ratio from W. Hoermann and G. Derflinger
251/// This is one of the fastest existing method for generating normal random variables.
252/// It is a factor 2/3 faster than the polar (Box-Muller) method used in the previous
253/// version of TRandom::Gaus. The speed is comparable to the Ziggurat method (from Marsaglia)
254/// implemented for example in GSL and available in the MathMore library.
255///
256/// REFERENCE: - W. Hoermann and G. Derflinger (1990):
257/// The ACR Method for generating normal random variables,
258/// OR Spektrum 12 (1990), 181-185.
259///
260/// Implementation taken from
261/// UNURAN (c) 2000 W. Hoermann & J. Leydold, Institut f. Statistik, WU Wien
262
264{
265 const Double_t kC1 = 1.448242853;
266 const Double_t kC2 = 3.307147487;
267 const Double_t kC3 = 1.46754004;
268 const Double_t kD1 = 1.036467755;
269 const Double_t kD2 = 5.295844968;
270 const Double_t kD3 = 3.631288474;
271 const Double_t kHm = 0.483941449;
272 const Double_t kZm = 0.107981933;
273 const Double_t kHp = 4.132731354;
274 const Double_t kZp = 18.52161694;
275 const Double_t kPhln = 0.4515827053;
276 const Double_t kHm1 = 0.516058551;
277 const Double_t kHp1 = 3.132731354;
278 const Double_t kHzm = 0.375959516;
279 const Double_t kHzmp = 0.591923442;
280 /*zhm 0.967882898*/
281
282 const Double_t kAs = 0.8853395638;
283 const Double_t kBs = 0.2452635696;
284 const Double_t kCs = 0.2770276848;
285 const Double_t kB = 0.5029324303;
286 const Double_t kX0 = 0.4571828819;
287 const Double_t kYm = 0.187308492 ;
288 const Double_t kS = 0.7270572718 ;
289 const Double_t kT = 0.03895759111;
290
291 Double_t result;
292 Double_t rn,x,y,z;
293
294 do {
295 y = Rndm();
296
297 if (y>kHm1) {
298 result = kHp*y-kHp1; break; }
299
300 else if (y<kZm) {
301 rn = kZp*y-1;
302 result = (rn>0) ? (1+rn) : (-1+rn);
303 break;
304 }
305
306 else if (y<kHm) {
307 rn = Rndm();
308 rn = rn-1+rn;
309 z = (rn>0) ? 2-rn : -2-rn;
310 if ((kC1-y)*(kC3+TMath::Abs(z))<kC2) {
311 result = z; break; }
312 else {
313 x = rn*rn;
314 if ((y+kD1)*(kD3+x)<kD2) {
315 result = rn; break; }
316 else if (kHzmp-y<exp(-(z*z+kPhln)/2)) {
317 result = z; break; }
318 else if (y+kHzm<exp(-(x+kPhln)/2)) {
319 result = rn; break; }
320 }
321 }
322
323 while (1) {
324 x = Rndm();
325 y = kYm * Rndm();
326 z = kX0 - kS*x - y;
327 if (z>0)
328 rn = 2+y/x;
329 else {
330 x = 1-x;
331 y = kYm-y;
332 rn = -(2+y/x);
333 }
334 if ((y-kAs+x)*(kCs+x)+kBs<0) {
335 result = rn; break; }
336 else if (y<x+kT)
337 if (rn*rn<4*(kB-log(x))) {
338 result = rn; break; }
339 }
340 } while(0);
341
342 return mean + sigma * result;
343}
344
345////////////////////////////////////////////////////////////////////////////////
346/// Returns a random integer uniformly distributed on the interval [ 0, imax-1 ].
347/// Note that the interfal contains the values of 0 and imax-1 but not imax.
348
350{
351 UInt_t ui;
352 ui = (UInt_t)(imax*Rndm());
353 return ui;
354}
355
356////////////////////////////////////////////////////////////////////////////////
357/// Generate a random number following a Landau distribution
358/// with location parameter mu and scale parameter sigma:
359/// Landau( (x-mu)/sigma )
360/// Note that mu is not the mpv(most probable value) of the Landa distribution
361/// and sigma is not the standard deviation of the distribution which is not defined.
362/// For mu =0 and sigma=1, the mpv = -0.22278
363///
364/// The Landau random number generation is implemented using the
365/// function landau_quantile(x,sigma), which provides
366/// the inverse of the landau cumulative distribution.
367/// landau_quantile has been converted from CERNLIB ranlan(G110).
368
370{
371 if (sigma <= 0) return 0;
372 Double_t x = Rndm();
374 return res;
375}
376
377////////////////////////////////////////////////////////////////////////////////
378/// Generates a random integer N according to a Poisson law.
379/// Prob(N) = exp(-mean)*mean^N/Factorial(N)
380///
381/// Use a different procedure according to the mean value.
382/// The algorithm is the same used by CLHEP.
383/// For lower value (mean < 25) use the rejection method based on
384/// the exponential.
385/// For higher values use a rejection method comparing with a Lorentzian
386/// distribution, as suggested by several authors.
387/// This routine since is returning 32 bits integer will not work for values
388/// larger than 2*10**9.
389/// One should then use the Trandom::PoissonD for such large values.
390
392{
393 Int_t n;
394 if (mean <= 0) return 0;
395 if (mean < 25) {
396 Double_t expmean = TMath::Exp(-mean);
397 Double_t pir = 1;
398 n = -1;
399 while(1) {
400 n++;
401 pir *= Rndm();
402 if (pir <= expmean) break;
403 }
404 return n;
405 }
406 // for large value we use inversion method
407 else if (mean < 1E9) {
408 Double_t em, t, y;
409 Double_t sq, alxm, g;
411
412 sq = TMath::Sqrt(2.0*mean);
413 alxm = TMath::Log(mean);
414 g = mean*alxm - TMath::LnGamma(mean + 1.0);
415
416 do {
417 do {
418 y = TMath::Tan(pi*Rndm());
419 em = sq*y + mean;
420 } while( em < 0.0 );
421
422 em = TMath::Floor(em);
423 t = 0.9*(1.0 + y*y)* TMath::Exp(em*alxm - TMath::LnGamma(em + 1.0) - g);
424 } while( Rndm() > t );
425
426 return static_cast<Int_t> (em);
427
428 }
429 else {
430 // use Gaussian approximation vor very large values
431 n = Int_t(Gaus(0,1)*TMath::Sqrt(mean) + mean +0.5);
432 return n;
433 }
434}
435
436////////////////////////////////////////////////////////////////////////////////
437/// Generates a random number according to a Poisson law.
438/// Prob(N) = exp(-mean)*mean^N/Factorial(N)
439///
440/// This function is a variant of TRandom::Poisson returning a double
441/// instead of an integer.
442
444{
445 Int_t n;
446 if (mean <= 0) return 0;
447 if (mean < 25) {
448 Double_t expmean = TMath::Exp(-mean);
449 Double_t pir = 1;
450 n = -1;
451 while(1) {
452 n++;
453 pir *= Rndm();
454 if (pir <= expmean) break;
455 }
456 return static_cast<Double_t>(n);
457 }
458 // for large value we use inversion method
459 else if (mean < 1E9) {
460 Double_t em, t, y;
461 Double_t sq, alxm, g;
463
464 sq = TMath::Sqrt(2.0*mean);
465 alxm = TMath::Log(mean);
466 g = mean*alxm - TMath::LnGamma(mean + 1.0);
467
468 do {
469 do {
470 y = TMath::Tan(pi*Rndm());
471 em = sq*y + mean;
472 } while( em < 0.0 );
473
474 em = TMath::Floor(em);
475 t = 0.9*(1.0 + y*y)* TMath::Exp(em*alxm - TMath::LnGamma(em + 1.0) - g);
476 } while( Rndm() > t );
477
478 return em;
479
480 } else {
481 // use Gaussian approximation vor very large values
482 return Gaus(0,1)*TMath::Sqrt(mean) + mean +0.5;
483 }
484}
485
486////////////////////////////////////////////////////////////////////////////////
487/// Return 2 numbers distributed following a gaussian with mean=0 and sigma=1.
488
490{
491 Double_t r, x, y, z;
492
493 y = Rndm();
494 z = Rndm();
495 x = z * 6.28318530717958623;
496 r = TMath::Sqrt(-2*TMath::Log(y));
497 a = (Float_t)(r * TMath::Sin(x));
498 b = (Float_t)(r * TMath::Cos(x));
499}
500
501////////////////////////////////////////////////////////////////////////////////
502/// Return 2 numbers distributed following a gaussian with mean=0 and sigma=1.
503
505{
506 Double_t r, x, y, z;
507
508 y = Rndm();
509 z = Rndm();
510 x = z * 6.28318530717958623;
511 r = TMath::Sqrt(-2*TMath::Log(y));
512 a = r * TMath::Sin(x);
513 b = r * TMath::Cos(x);
514}
515
516////////////////////////////////////////////////////////////////////////////////
517/// Reads saved random generator status from filename.
518
519void TRandom::ReadRandom(const char *filename)
520{
521 if (!gDirectory) return;
522 char *fntmp = gSystem->ExpandPathName(filename);
523 TDirectory *file = (TDirectory*)gROOT->ProcessLine(Form("TFile::Open(\"%s\");",fntmp));
524 delete [] fntmp;
525 if(file && file->GetFile()) {
526 gDirectory->ReadTObject(this,GetName());
527 delete file;
528 }
529}
530
531////////////////////////////////////////////////////////////////////////////////
532/// Machine independent random number generator.
533/// Based on the BSD Unix (Rand) Linear congrential generator.
534/// Produces uniformly-distributed floating points between 0 and 1.
535/// Identical sequence on all machines of >= 32 bits.
536/// Periodicity = 2**31, generates a number in (0,1).
537/// Note that this is a generator which is known to have defects
538/// (the lower random bits are correlated) and therefore should NOT be
539/// used in any statistical study).
540
542{
543#ifdef OLD_TRANDOM_IMPL
544 const Double_t kCONS = 4.6566128730774E-10;
545 const Int_t kMASK24 = 2147483392;
546
547 fSeed *= 69069;
548 UInt_t jy = (fSeed&kMASK24); // Set lower 8 bits to zero to assure exact float
549 if (jy) return kCONS*jy;
550 return Rndm();
551#endif
552
553 // kCONS = 1./2147483648 = 1./(RAND_MAX+1) and RAND_MAX= 0x7fffffffUL
554 const Double_t kCONS = 4.6566128730774E-10; // (1/pow(2,31)
555 fSeed = (1103515245 * fSeed + 12345) & 0x7fffffffUL;
556
557 if (fSeed) return kCONS*fSeed;
558 return Rndm();
559}
560
561////////////////////////////////////////////////////////////////////////////////
562/// Return an array of n random numbers uniformly distributed in ]0,1].
563
565{
566 const Double_t kCONS = 4.6566128730774E-10; // (1/pow(2,31))
567 Int_t i=0;
568 while (i<n) {
569 fSeed = (1103515245 * fSeed + 12345) & 0x7fffffffUL;
570 if (fSeed) {array[i] = kCONS*fSeed; i++;}
571 }
572}
573
574////////////////////////////////////////////////////////////////////////////////
575/// Return an array of n random numbers uniformly distributed in ]0,1].
576
578{
579 const Double_t kCONS = 4.6566128730774E-10; // (1/pow(2,31))
580 Int_t i=0;
581 while (i<n) {
582 fSeed = (1103515245 * fSeed + 12345) & 0x7fffffffUL;
583 if (fSeed) {array[i] = Float_t(kCONS*fSeed); i++;}
584 }
585}
586
587////////////////////////////////////////////////////////////////////////////////
588/// Set the random generator seed. Note that default value is zero, which is
589/// different than the default value used when constructing the class.
590/// If the seed is zero the seed is set to a random value
591/// which in case of TRandom depends on the lowest 4 bytes of TUUID
592/// The UUID will be identical if SetSeed(0) is called with time smaller than 100 ns
593/// Instead if a different generator implementation is used (TRandom1, 2 or 3)
594/// the seed is generated using a 128 bit UUID. This results in different seeds
595/// and then random sequence for every SetSeed(0) call.
596
598{
599 if( seed==0 ) {
600 TUUID u;
601 UChar_t uuid[16];
602 u.GetUUID(uuid);
603 fSeed = UInt_t(uuid[3])*16777216 + UInt_t(uuid[2])*65536 + UInt_t(uuid[1])*256 + UInt_t(uuid[0]);
604 } else {
605 fSeed = seed;
606 }
607}
608
609////////////////////////////////////////////////////////////////////////////////
610/// Generates random vectors, uniformly distributed over the surface
611/// of a sphere of given radius.
612/// Input : r = sphere radius
613/// Output: x,y,z a random 3-d vector of length r
614/// Method: (based on algorithm suggested by Knuth and attributed to Robert E Knop)
615/// which uses less random numbers than the CERNLIB RN23DIM algorithm
616
618{
619 Double_t a=0,b=0,r2=1;
620 while (r2 > 0.25) {
621 a = Rndm() - 0.5;
622 b = Rndm() - 0.5;
623 r2 = a*a + b*b;
624 }
625 z = r* ( -1. + 8.0 * r2 );
626
627 Double_t scale = 8.0 * r * TMath::Sqrt(0.25 - r2);
628 x = a*scale;
629 y = b*scale;
630}
631
632////////////////////////////////////////////////////////////////////////////////
633/// Returns a uniform deviate on the interval (0, x1).
634
636{
637 Double_t ans = Rndm();
638 return x1*ans;
639}
640
641////////////////////////////////////////////////////////////////////////////////
642/// Returns a uniform deviate on the interval (x1, x2).
643
645{
646 Double_t ans= Rndm();
647 return x1 + (x2-x1)*ans;
648}
649
650////////////////////////////////////////////////////////////////////////////////
651/// Writes random generator status to filename.
652
653void TRandom::WriteRandom(const char *filename) const
654{
655 if (!gDirectory) return;
656 char *fntmp = gSystem->ExpandPathName(filename);
657 TDirectory *file = (TDirectory*)gROOT->ProcessLine(Form("TFile::Open(\"%s\",\"recreate\");",fntmp));
658 delete [] fntmp;
659 if(file && file->GetFile()) {
660 gDirectory->WriteTObject(this,GetName());
661 delete file;
662 }
663}
ROOT::R::TRInterface & r
Definition: Object.C:4
#define b(i)
Definition: RSha256.hxx:100
#define g(i)
Definition: RSha256.hxx:105
static const double x2[5]
static const double x1[5]
int Int_t
Definition: RtypesCore.h:41
unsigned char UChar_t
Definition: RtypesCore.h:34
unsigned int UInt_t
Definition: RtypesCore.h:42
unsigned long ULong_t
Definition: RtypesCore.h:51
double Double_t
Definition: RtypesCore.h:55
float Float_t
Definition: RtypesCore.h:53
#define ClassImp(name)
Definition: Rtypes.h:365
#define gDirectory
Definition: TDirectory.h:218
double exp(double)
double log(double)
#define gROOT
Definition: TROOT.h:414
R__EXTERN TRandom * gRandom
Definition: TRandom.h:62
char * Form(const char *fmt,...)
R__EXTERN TSystem * gSystem
Definition: TSystem.h:560
Describe directory structure in memory.
Definition: TDirectory.h:34
The TNamed class is the base class for all named ROOT classes.
Definition: TNamed.h:29
virtual const char * GetName() const
Returns name of object.
Definition: TNamed.h:47
This is the base class for the ROOT Random number generators.
Definition: TRandom.h:27
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 sigm...
Definition: TRandom.cxx:263
virtual void RndmArray(Int_t n, Float_t *array)
Return an array of n random numbers uniformly distributed in ]0,1].
Definition: TRandom.cxx:577
virtual Int_t Poisson(Double_t mean)
Generates a random integer N according to a Poisson law.
Definition: TRandom.cxx:391
virtual void SetSeed(ULong_t seed=0)
Set the random generator seed.
Definition: TRandom.cxx:597
virtual void WriteRandom(const char *filename) const
Writes random generator status to filename.
Definition: TRandom.cxx:653
UInt_t fSeed
Definition: TRandom.h:30
virtual void Rannor(Float_t &a, Float_t &b)
Return 2 numbers distributed following a gaussian with mean=0 and sigma=1.
Definition: TRandom.cxx:489
virtual Double_t PoissonD(Double_t mean)
Generates a random number according to a Poisson law.
Definition: TRandom.cxx:443
virtual void ReadRandom(const char *filename)
Reads saved random generator status from filename.
Definition: TRandom.cxx:519
virtual Double_t Exp(Double_t tau)
Returns an exponential deviate.
Definition: TRandom.cxx:240
virtual void Circle(Double_t &x, Double_t &y, Double_t r)
Generates random vectors, uniformly distributed over a circle of given radius.
Definition: TRandom.cxx:228
virtual Double_t Uniform(Double_t x1=1)
Returns a uniform deviate on the interval (0, x1).
Definition: TRandom.cxx:635
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.
Definition: TRandom.cxx:617
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 paramet...
Definition: TRandom.cxx:369
virtual ~TRandom()
Default destructor.
Definition: TRandom.cxx:184
TRandom(UInt_t seed=65539)
Default constructor. For seed see SetSeed().
Definition: TRandom.cxx:175
virtual Int_t Binomial(Int_t ntot, Double_t prob)
Generates a random integer N according to the binomial law.
Definition: TRandom.cxx:200
virtual Double_t BreitWigner(Double_t mean=0, Double_t gamma=1)
Return a number distributed following a BreitWigner function with mean and gamma.
Definition: TRandom.cxx:214
virtual Double_t Rndm()
Machine independent random number generator.
Definition: TRandom.cxx:541
virtual UInt_t Integer(UInt_t imax)
Returns a random integer uniformly distributed on the interval [ 0, imax-1 ].
Definition: TRandom.cxx:349
virtual Bool_t ExpandPathName(TString &path)
Expand a pathname getting rid of special shell characters like ~.
Definition: TSystem.cxx:1264
This class defines a UUID (Universally Unique IDentifier), also known as GUIDs (Globally Unique IDent...
Definition: TUUID.h:42
void GetUUID(UChar_t uuid[16]) const
Return uuid in specified buffer (16 byte = 128 bits).
Definition: TUUID.cxx:684
double landau_quantile(double z, double xi=1)
Inverse ( ) of the cumulative distribution function of the lower tail of the Landau distribution (lan...
const Double_t sigma
Double_t y[n]
Definition: legend1.C:17
Double_t x[n]
Definition: legend1.C:17
const Int_t n
Definition: legend1.C:16
double gamma(double x)
static constexpr double pi
Double_t Exp(Double_t x)
Definition: TMath.h:715
Double_t Floor(Double_t x)
Definition: TMath.h:691
constexpr Double_t PiOver2()
Definition: TMath.h:52
Double_t Log(Double_t x)
Definition: TMath.h:748
Double_t Sqrt(Double_t x)
Definition: TMath.h:679
Double_t Cos(Double_t)
Definition: TMath.h:629
constexpr Double_t Pi()
Definition: TMath.h:38
Double_t LnGamma(Double_t z)
Computation of ln[gamma(z)] for all z.
Definition: TMath.cxx:486
Double_t Sin(Double_t)
Definition: TMath.h:625
Double_t Tan(Double_t)
Definition: TMath.h:633
Short_t Abs(Short_t d)
Definition: TMathBase.h:120
constexpr Double_t TwoPi()
Definition: TMath.h:45
Definition: file.py:1
auto * a
Definition: textangle.C:12