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4c039060 | 1 | /************************************************************************** |
2 | * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. * | |
3 | * * | |
4 | * Author: The ALICE Off-line Project. * | |
5 | * Contributors are mentioned in the code where appropriate. * | |
6 | * * | |
7 | * Permission to use, copy, modify and distribute this software and its * | |
8 | * documentation strictly for non-commercial purposes is hereby granted * | |
9 | * without fee, provided that the above copyright notice appears in all * | |
10 | * copies and that both the copyright notice and this permission notice * | |
11 | * appear in the supporting documentation. The authors make no claims * | |
12 | * about the suitability of this software for any purpose. It is * | |
13 | * provided "as is" without express or implied warranty. * | |
14 | **************************************************************************/ | |
15 | ||
f531a546 | 16 | // $Id$ |
4c039060 | 17 | |
959fbac5 | 18 | /////////////////////////////////////////////////////////////////////////// |
19 | // Class AliRandom | |
20 | // Generate universal random numbers on all common machines. | |
21 | // Available distributions : Uniform, Gaussian, Poisson and | |
22 | // User defined function | |
23 | // | |
24 | // Features : | |
25 | // ---------- | |
26 | // 1) Period = 2**144 | |
27 | // 2) Same sequence of 24-bit real numbers on all common machines | |
28 | // | |
29 | // Reference : | |
30 | // ----------- | |
31 | // G.Marsaglia and A.Zaman, FSU-SCRI-87-50, Florida State University, 1987. | |
32 | // | |
33 | // Coding example : | |
34 | // ---------------- | |
35 | // | |
36 | // Float_t rndm; // Variable to hold a single random number | |
37 | // const Int_t n=1000; | |
38 | // Float_t rvec[n]; // Vector to hold n random numbers | |
39 | // | |
40 | // AliRandom r; // Create a Random object with default sequence | |
41 | // | |
42 | // rndm=r.Uniform(); // Provide a uniform random number in <0,1> | |
43 | // Float_t a=3.; | |
44 | // Float_t b=5.; | |
45 | // rndm=r.Uniform(a,b); // Provide a uniform random number in <a,b> | |
46 | // r.Uniform(rvec,n); // Provide n uniform randoms in <0,1> in rvec | |
47 | // r.Uniform(rvec,n,a,b); // Provide n uniform randoms in <a,b> in rvec | |
48 | // | |
49 | // rndm=r.Gauss(); // Provide a Gaussian random number with | |
50 | // // mean=0 and sigma=1 | |
51 | // Float_t mean=25.; | |
52 | // Float_t sigma=5.; | |
53 | // rndm=r.Gauss(mean,sigma); // Provide a Gaussian random number | |
54 | // // with specified mean and sigma | |
55 | // r.Gauss(rvec,n); // n Gaussian randoms mean=0 sigma=1 | |
56 | // r.Gauss(rvec,n,mean,sigma); // n Gaussian randoms with specified | |
57 | // // mean and sigma | |
58 | // | |
59 | // rndm=r.Poisson(mean); // Provide a Poisson random number with | |
60 | // // specified mean | |
61 | // r.Poisson(rvec,nmean); // n Poisson randoms with specified mean | |
62 | // | |
63 | // Int_t seed=1837724 | |
64 | // AliRandom p(seed); // Create a Random object with specified seed. | |
65 | // // The sequence is started from scratch. | |
66 | // Int_t cnt1=25; | |
67 | // Int_t cnt2=8; | |
68 | // AliRandom q(seed,cnt1,cnt2); // Create a Random object with specified seed | |
69 | // // The sequence is started at the location | |
70 | // // denoted by the counters cnt1 and cnt2. | |
71 | // | |
72 | // q.Info(); // Print the current seed, cnt1 and cnt2 values. | |
73 | // q.GetSeed(); // Provide the current seed value. | |
74 | // q.GetCnt1(); // Provide the current cnt1 value. | |
75 | // q.GetCnt2(); // Provide the current cnt2 value. | |
76 | // | |
77 | // Float_t udist(Float_t x) // A user defined distribution | |
78 | // { | |
79 | // return x*x-4.*x; | |
80 | // } | |
81 | // | |
82 | // Int_t nbins=100; | |
83 | // q.SetUser(a,b,nbins,udist); // Initialise generator for udist distribution | |
84 | // q.User(); // Provide a random number according to the udist distribution | |
85 | // q.User(rvec,n); // Provide n randoms according to the udist distribution | |
86 | // | |
87 | // Float_t* x=new Float_t[nbins]; | |
88 | // Float_t* y=new Float_t[nbins]; | |
89 | // | |
90 | // ... code to fill x[] and y[] .. | |
91 | // | |
92 | // AliRandom s; | |
93 | // s.SetUser(x,y,nbins); // Initialise generator for (x[i],y[i]) distribution | |
94 | // s.User(); // Provide a random number according to the user distribution | |
95 | // s.User(rvec,n); // Provide n randoms according to the user distribution | |
96 | // | |
97 | // Notes : | |
98 | // ------- | |
99 | // 1) Allowed seed values : 0 <= seed <= 921350143 | |
100 | // Default seed = 53310452 | |
101 | // 2) To ensure a unique sequence for each run, one can automatically | |
102 | // construct a seed value by e.g. using the date and time. | |
103 | // 3) Using the rvec facility saves a lot of CPU time for large n values. | |
104 | // | |
105 | //--- Author: Nick van Eijndhoven 11-oct-1997 UU-SAP Utrecht | |
f531a546 | 106 | //- Modified: NvE $Date$ UU-SAP Utrecht |
959fbac5 | 107 | /////////////////////////////////////////////////////////////////////////// |
108 | ||
d88f97cc | 109 | #include "AliRandom.h" |
110 | ||
111 | ClassImp(AliRandom) // Class implementation to enable ROOT I/O | |
112 | ||
113 | AliRandom::AliRandom() | |
114 | { | |
959fbac5 | 115 | // Creation of an AliRandom object and default initialisation. |
d88f97cc | 116 | // |
117 | // A seed is used to create the initial u[97] table. | |
118 | // This seed is converted into four startup parameters i j k and l | |
119 | // (see member function "unpack"). | |
120 | // | |
121 | // Suggested test values : i=12 j=34 k=56 l=78 (see article) | |
122 | // which corresponds to : seed = 53310452 | |
123 | ||
124 | Int_t seed=53310452; // Default seed | |
125 | Start(seed,0,0); // Start the sequence for this seed from scratch | |
126 | } | |
127 | /////////////////////////////////////////////////////////////////////////// | |
128 | AliRandom::AliRandom(Int_t seed) | |
129 | { | |
130 | // Creation of an AliRandom object and user defined initialisation | |
131 | ||
132 | Start(seed,0,0); // Start the sequence for this seed from scratch | |
133 | } | |
134 | /////////////////////////////////////////////////////////////////////////// | |
135 | AliRandom::AliRandom(Int_t seed,Int_t cnt1,Int_t cnt2) | |
136 | { | |
137 | // Creation of an AliRandom object and user defined initialisation | |
138 | // | |
139 | // seed is the seed to create the initial u[97] table. | |
140 | // The range of the seed is : 0 <= seed <= 921350143 | |
141 | // | |
142 | // cnt1 and cnt2 are the parameters for the counting system | |
143 | // to enable a start of the sequence at a certain point. | |
144 | // The current values of seed, cnt1 and cnt2 can be obtained | |
145 | // via the member functions "GetSeed", "GetCnt1" and "GetCnt2" resp. | |
146 | // To start from scratch one should select : cnt1=0 and cnt2=0 | |
147 | ||
148 | Start(seed,cnt1,cnt2); // Start the sequence from a user defined point | |
149 | } | |
150 | /////////////////////////////////////////////////////////////////////////// | |
151 | AliRandom::~AliRandom() | |
152 | { | |
153 | // Destructor to delete memory allocated for the area function arrays | |
154 | if (fXa) delete [] fXa; | |
155 | fXa=0; | |
156 | if (fYa) delete [] fYa; | |
157 | fYa=0; | |
158 | if (fIbins) delete [] fIbins; | |
159 | fIbins=0; | |
160 | } | |
161 | /////////////////////////////////////////////////////////////////////////// | |
162 | void AliRandom::Start(Int_t seed,Int_t cnt1,Int_t cnt2) | |
163 | { | |
164 | // Start a certain sequence from scratch or from a user defined point | |
165 | // | |
166 | // The algorithm to start from scratch is based on the routine RSTART | |
167 | // as described in the report by G.Marsaglia and A.Zaman | |
168 | // (FSU-SCRI-87-50 Florida State University 1987). | |
169 | // | |
170 | // seed is the seed to create the initial u[97] table. | |
171 | // This seed is converted into four startup parameters i j k and l | |
172 | // (see the member function "unpack"). | |
173 | // | |
174 | // The range of the seed is : 0 <= seed <= 921350143 | |
175 | // | |
176 | // Suggested test values : i=12 j=34 k=56 l=78 (see article) | |
177 | // which corresponds to : seed = 53310452 | |
178 | // | |
179 | // cnt1 and cnt2 are the parameters for the counting system | |
180 | // to enable a start of the sequence at a certain point. | |
181 | // The current values of seed, cnt1 and cnt2 can be obtained | |
182 | // via the member functions "GetSeed", "GetCnt1" and "GetCnt2" resp. | |
183 | // To start from scratch one should select : cnt1=0 and cnt2=0 | |
184 | ||
185 | // Reset the area function | |
186 | fNa=0; | |
187 | fXa=0; | |
188 | fYa=0; | |
189 | fIbins=0; | |
190 | ||
191 | // Clipping parameter to prevent overflow of the counting system | |
192 | fClip=1000000; | |
193 | ||
194 | // Set the lags for the Fibonacci sequence of the first part | |
195 | // The sequence is set to F(97,33,*) (see article) | |
196 | fI=97; | |
197 | fJ=33; | |
198 | ||
199 | // Unpack the seed value and determine i, j, k and l | |
200 | fSeed=seed; | |
201 | Int_t i,j,k,l; | |
202 | Unpack(seed,i,j,k,l); | |
203 | ||
204 | // Reset counters | |
205 | fCnt1=0; | |
206 | fCnt2=0; | |
207 | ||
208 | // Fill the starting table for the first part of the combination | |
209 | Float_t s,t; | |
210 | Int_t m; | |
211 | for (Int_t ii=0; ii<97; ii++) | |
212 | { | |
213 | s=0.; | |
214 | t=0.5; | |
215 | ||
216 | for (Int_t jj=1; jj<=24; jj++) | |
217 | { | |
218 | m=(((i*j)%179)*k)%179; | |
219 | i=j; | |
220 | j=k; | |
221 | k=m; | |
222 | l=((53*l)+1)%169; | |
223 | if ((l*m)%64 >= 32) s+=t; | |
224 | t=0.5*t; | |
225 | } | |
226 | fU[ii]=s; | |
227 | } | |
228 | ||
229 | // Initialise the second part of the combination | |
230 | fC=362436./16777216.; | |
231 | fCd=7654321./16777216.; | |
232 | fCm=16777213./16777216.; | |
233 | ||
234 | // Generate random numbers upto the user selected starting point | |
235 | // on basis of the counting system | |
236 | if (cnt1 > 0) Uniform(cnt1); | |
237 | if (cnt2 > 0) | |
238 | { | |
239 | for (Int_t n=1; n<=cnt2; n++) | |
240 | { | |
241 | Uniform(fClip); | |
242 | } | |
243 | } | |
244 | } | |
245 | /////////////////////////////////////////////////////////////////////////// | |
246 | void AliRandom::Unpack(Int_t seed,Int_t& i,Int_t& j,Int_t& k,Int_t& l) | |
247 | { | |
248 | // Unpack the seed into the four startup parameters i,j,k and l | |
249 | // | |
250 | // The range of the seed is : 0 <= seed <= 921350143 | |
251 | // | |
252 | // From the article : | |
253 | // The i,j and k values may be chosen in the interval : 1 <= n <= 178 | |
254 | // The l value may be in the interval : 0 <= l <= 168 | |
255 | // | |
256 | // Taking into account the period of the 3-lagged Fibonacci sequence | |
257 | // The following "bad" combinations have to be ruled out : | |
258 | // | |
259 | // i j k l period | |
260 | // 1 1 1 X 1 | |
261 | // 178 1 1 X 4 | |
262 | // 1 178 1 X 2 | |
263 | // 1 1 178 X 4 | |
264 | // 178 178 1 X 4 | |
265 | // 178 1 178 X 2 | |
266 | // 1 178 178 X 4 | |
267 | // 178 178 178 X 1 | |
268 | // | |
269 | // To rule these "bad" combinations out all together, we choose | |
270 | // the following allowed ranges : | |
271 | // The i,j and k values may be chosen in the interval : 2 <= n <= 177 | |
272 | // The l value may be in the interval : 0 <= l <= 168 | |
273 | // | |
274 | // and use the formula : | |
275 | // seed = (i-2)*176*176*169 + (j-2)*176*169 + (k-2)*169 + l | |
276 | ||
277 | if ((seed >= 0) && (seed <= 921350143)) // Check seed value | |
278 | { | |
279 | Int_t idum=seed; | |
280 | Int_t imin2=idum/(176*176*169); | |
281 | idum=idum%(176*176*169); | |
282 | Int_t jmin2=idum/(176*169); | |
283 | idum=idum%(176*169); | |
284 | Int_t kmin2=idum/169; | |
285 | ||
286 | i=imin2+2; | |
287 | j=jmin2+2; | |
288 | k=kmin2+2; | |
289 | l=seed%169; | |
290 | } | |
291 | else | |
292 | { | |
293 | cout << " *AliRandom::unpack()* Unallowed seed value encountered." | |
294 | << " seed = " << seed << endl; | |
295 | cout << " Seed will be set to default value." << endl; | |
296 | ||
297 | seed=53310452; // Default seed | |
298 | Start(seed,0,0); // Start the sequence for this seed from scratch | |
299 | } | |
300 | } | |
301 | /////////////////////////////////////////////////////////////////////////// | |
302 | Int_t AliRandom::GetSeed() | |
303 | { | |
304 | // Provide the current seed value | |
305 | return fSeed; | |
306 | } | |
307 | /////////////////////////////////////////////////////////////////////////// | |
308 | Int_t AliRandom::GetCnt1() | |
309 | { | |
310 | // Provide the current value of the counter cnt1 | |
311 | return fCnt1; | |
312 | } | |
313 | /////////////////////////////////////////////////////////////////////////// | |
314 | Int_t AliRandom::GetCnt2() | |
315 | { | |
316 | // Provide the current value of the counter cnt2 | |
317 | return fCnt2; | |
318 | } | |
319 | /////////////////////////////////////////////////////////////////////////// | |
320 | void AliRandom::Info() | |
321 | { | |
322 | // Print the current seed, cnt1 and cnt2 values | |
323 | cout << " *Random* seed = " << fSeed | |
324 | << " cnt1 = " << fCnt1 << " cnt2 = " << fCnt2 << endl; | |
325 | } | |
326 | /////////////////////////////////////////////////////////////////////////// | |
327 | Float_t AliRandom::Uniform() | |
328 | { | |
329 | // Generate uniform random numbers in the interval <0,1> | |
330 | // | |
331 | // The algorithm is based on lagged Fibonacci sequences (first part) | |
332 | // combined with a congruential method (second part) | |
333 | // as described in the report by G.Marsaglia and A.Zaman | |
334 | // (FSU-SCRI-87-50 Florida State University 1987). | |
335 | // | |
336 | // Features : | |
337 | // 1) Period = 2**144 | |
338 | // 2) Same sequence of 24-bit real numbers on all common machines | |
339 | ||
340 | // First part of the combination : F(97,33,*) (see article for explanation) | |
341 | Float_t unirnu=fU[fI-1]-fU[fJ-1]; | |
342 | if (unirnu < 0) unirnu+=1.; | |
343 | fU[fI-1]=unirnu; | |
344 | fI-=1; | |
345 | if (fI == 0) fI=97; | |
346 | fJ-=1; | |
347 | if (fJ == 0) fJ=97; | |
348 | ||
349 | // Second part of the combination (see article for explanation) | |
350 | fC-=fCd; | |
351 | if (fC < 0.) fC+=fCm; | |
352 | unirnu-=fC; | |
353 | if (unirnu < 0.) unirnu+=1.; | |
354 | ||
355 | // Update the counting system to enable sequence continuation | |
356 | // at an arbitrary starting position. | |
357 | // Two counters have been introduced to avoid overflow | |
358 | // fCnt1 : Counter which goes up to fClip | |
359 | // and is reset when fClip is reached | |
360 | // fCnt2 : Counts the number of times fClip has been reached | |
361 | fCnt1+=1; | |
362 | if (fCnt1 >= fClip) | |
363 | { | |
364 | fCnt1=0; | |
365 | fCnt2+=1; | |
366 | } | |
367 | ||
368 | if (unirnu <= 0.) unirnu=Uniform(); // Exclude 0. from the range | |
369 | ||
370 | return unirnu; | |
371 | } | |
372 | /////////////////////////////////////////////////////////////////////////// | |
373 | Float_t AliRandom::Uniform(Float_t a,Float_t b) | |
374 | { | |
375 | // Generate uniform random numbers in the interval <a,b> | |
376 | Float_t rmin=a; | |
377 | if (a > b) rmin=b; | |
378 | ||
379 | Float_t rndm=Uniform(); | |
380 | rndm=rmin+fabs(rndm*(a-b)); | |
381 | ||
382 | return rndm; | |
383 | } | |
384 | /////////////////////////////////////////////////////////////////////////// | |
385 | void AliRandom::Uniform(Float_t* vec,Int_t n,Float_t a,Float_t b) | |
386 | { | |
387 | // Generate a vector of uniform random numbers in the interval <a,b> | |
388 | // This saves lots of (member)function calls in case many random | |
389 | // numbers are needed at once. | |
390 | // | |
391 | // n = The number of random numbers to be generated | |
392 | // | |
393 | // The algorithm is based on lagged Fibonacci sequences (first part) | |
394 | // combined with a congruential method (second part) | |
395 | // as described in the report by G.Marsaglia and A.Zaman | |
396 | // (FSU-SCRI-87-50 Florida State University 1987). | |
397 | // | |
398 | // Features : | |
399 | // 1) Period = 2**144 | |
400 | // 2) Same sequence of 24-bit real numbers on all common machines | |
401 | ||
402 | // Determine the minimum of a and b | |
403 | Float_t rmin=a; | |
404 | if (a > b) rmin=b; | |
405 | ||
406 | // First generate random numbers within <0,1> | |
407 | if (n > 0) // Check n value | |
408 | { | |
409 | for (Int_t jvec=0; jvec<n; jvec++) | |
410 | { | |
411 | // First part of the combination : F(97,33,*) | |
412 | Float_t unirnu=fU[fI-1]-fU[fJ-1]; | |
413 | if (unirnu < 0) unirnu+=1.; | |
414 | fU[fI-1]=unirnu; | |
415 | fI-=1; | |
416 | if (fI == 0) fI=97; | |
417 | fJ-=1; | |
418 | if (fJ == 0) fJ=97; | |
419 | ||
420 | // Second part of the combination | |
421 | fC-=fCd; | |
422 | if (fC < 0.) fC+=fCm; | |
423 | unirnu-=fC; | |
424 | if (unirnu < 0.) unirnu+=1.; | |
425 | ||
426 | // Update the counting system to enable sequence continuation | |
427 | // at an arbitrary starting position. | |
428 | // Two counters have been introduced to avoid overflow | |
429 | // fCnt1 : Counter which goes up to fClip | |
430 | // and is reset when fClip is reached | |
431 | // fCnt2 : Counts the number of times fClip has been reached | |
432 | fCnt1+=1; | |
433 | if (fCnt1 >= fClip) | |
434 | { | |
435 | fCnt1=0; | |
436 | fCnt2+=1; | |
437 | } | |
438 | ||
439 | if (unirnu <= 0.) unirnu=Uniform(); // Exclude 0. from the range | |
440 | ||
441 | // Fill the vector within the selected range | |
442 | vec[jvec]=rmin+fabs(unirnu*(a-b)); | |
443 | } | |
444 | } | |
445 | else | |
446 | { | |
447 | cout << " *AliRandom::Uniform* Invalid value n = " << n << endl; | |
448 | } | |
449 | } | |
450 | /////////////////////////////////////////////////////////////////////////// | |
451 | void AliRandom::Uniform(Float_t* vec,Int_t n) | |
452 | { | |
453 | // Generate a vector of uniform random numbers in the interval <0,1> | |
454 | // This saves lots of (member)function calls in case many random | |
455 | // numbers are needed at once. | |
456 | // | |
457 | // n = The number of random numbers to be generated | |
458 | ||
459 | Uniform(vec,n,0.,1.); | |
460 | } | |
461 | /////////////////////////////////////////////////////////////////////////// | |
462 | void AliRandom::Uniform(Int_t n) | |
463 | { | |
464 | // Generate n uniform random numbers in in one go. | |
465 | // This saves lots of (member)function calls in case one needs to skip | |
466 | // to a certain point in a sequence. | |
467 | // | |
468 | // n = The number of random numbers to be generated | |
469 | // | |
470 | // Note : No check is made here to exclude 0 from the range. | |
471 | // It's only the number of generated randoms that counts | |
472 | // | |
473 | // The algorithm is based on lagged Fibonacci sequences (first part) | |
474 | // combined with a congruential method (second part) | |
475 | // as described in the report by G.Marsaglia and A.Zaman | |
476 | // (FSU-SCRI-87-50 Florida State University 1987). | |
477 | // | |
478 | // Features : | |
479 | // 1) Period = 2**144 | |
480 | // 2) Same sequence of 24-bit real numbers on all common machines | |
481 | ||
482 | if (n > 0) // Check n value | |
483 | { | |
484 | for (Int_t jvec=0; jvec<n; jvec++) | |
485 | { | |
486 | // First part of the combination : F(97,33,*) | |
487 | Float_t unirnu=fU[fI-1]-fU[fJ-1]; | |
488 | if (unirnu < 0) unirnu+=1.; | |
489 | fU[fI-1]=unirnu; | |
490 | fI-=1; | |
491 | if (fI == 0) fI=97; | |
492 | fJ-=1; | |
493 | if (fJ == 0) fJ=97; | |
494 | ||
495 | // Second part of the combination | |
496 | fC-=fCd; | |
497 | if (fC < 0.) fC+=fCm; | |
498 | unirnu-=fC; | |
499 | if (unirnu < 0.) unirnu+=1.; | |
500 | ||
501 | // Update the counting system to enable sequence continuation | |
502 | // at an arbitrary starting position. | |
503 | // Two counters have been introduced to avoid overflow | |
504 | // fCnt1 : Counter which goes up to fClip | |
505 | // and is reset when fClip is reached | |
506 | // fCnt2 : Counts the number of times fClip has been reached | |
507 | fCnt1+=1; | |
508 | if (fCnt1 >= fClip) | |
509 | { | |
510 | fCnt1=0; | |
511 | fCnt2+=1; | |
512 | } | |
513 | } | |
514 | } | |
515 | else | |
516 | { | |
517 | cout << " *AliRandom::Uniform* Invalid value n = " << n << endl; | |
518 | } | |
519 | } | |
520 | /////////////////////////////////////////////////////////////////////////// | |
521 | Float_t AliRandom::Gauss(Float_t mean,Float_t sigma) | |
522 | { | |
523 | // Generate gaussian distributed random numbers with certain mean and sigma | |
524 | // | |
525 | // Method : | |
526 | // P(x) = The gaussian distribution function | |
527 | // --> ln(P) provides an expression for (x-xmean)**2 from which | |
528 | // the following expression for x can be obtained | |
529 | // | |
530 | // x = xmean +/- sigma * sqrt(-2*ln(q)) | |
531 | // | |
532 | // in which q is an expression in terms of pi, sigma and p and lies within | |
533 | // the interval <0,1>. | |
534 | // | |
535 | // The gaussian distributed x values are obtained as follows : | |
536 | // | |
537 | // 1) Two uniform random numbers q1 and q2 in <0,1> are generated. | |
538 | // 2) q1 is in fact a uniform generated value for P which is substituted | |
539 | // directly in the formula above. | |
540 | // 3) The value of q2 determines whether we use the + or - sign. | |
541 | ||
542 | // Generate the two uniform random numbers q1 and q2 in <0,1> | |
543 | Float_t q1,q2; | |
544 | q1=Uniform(); | |
545 | q2=Uniform(); | |
546 | ||
547 | // Use q1 and q2 to get the gaussian distributed random number | |
548 | Float_t pi=acos(-1.); | |
549 | Float_t unirng=mean+cos(2.*pi*q2)*sigma*sqrt(-2.*log(q1)); | |
550 | ||
551 | return unirng; | |
552 | } | |
553 | /////////////////////////////////////////////////////////////////////////// | |
554 | Float_t AliRandom::Gauss() | |
555 | { | |
556 | // Generate gaussian distributed random numbers with mean=0 and sigma=1 | |
557 | ||
558 | return Gauss(0.,1.); | |
559 | } | |
560 | /////////////////////////////////////////////////////////////////////////// | |
561 | void AliRandom::Gauss(Float_t* vec,Int_t n,Float_t mean,Float_t sigma) | |
562 | { | |
563 | // Generate a vector of gaussian random numbers with certain mean and sigma | |
564 | // This saves lots of (member)function calls in case many random | |
565 | // numbers are needed at once. | |
566 | // | |
567 | // n = The number of random numbers to be generated | |
568 | ||
569 | if (n > 0) // Check n value | |
570 | { | |
571 | // The vector to hold the q1 and q2 values. | |
572 | // Two subsequent q[] values are used for q1 and q2 | |
573 | // in order to obtain identical random numbers in the vector | |
574 | // as when generating n single ones. | |
575 | Int_t m=2*n; | |
576 | Float_t* q=new Float_t[m]; | |
577 | Uniform(q,m); | |
578 | ||
579 | // Fill the vector with gaussian random numbers | |
580 | Float_t pi=acos(-1.); | |
581 | Float_t q1,q2; | |
582 | for (Int_t jvec=0; jvec<n; jvec++) | |
583 | { | |
584 | q1=q[jvec*2]; // use two subsequent q[] values | |
585 | q2=q[(jvec*2)+1]; | |
586 | vec[jvec]=mean+cos(2.*pi*q2)*sigma*sqrt(-2.*log(q1)); | |
587 | } | |
588 | delete [] q; | |
589 | } | |
590 | else | |
591 | { | |
592 | cout << " *AliRandom::Gauss* Invalid value n = " << n << endl; | |
593 | } | |
594 | } | |
595 | /////////////////////////////////////////////////////////////////////////// | |
596 | void AliRandom::Gauss(Float_t* vec,Int_t n) | |
597 | { | |
598 | // Generate a vector of gaussian random numbers with mean=0 and sigma=1 | |
599 | // This saves lots of (member)function calls in case many random | |
600 | // numbers are needed at once. | |
601 | // | |
602 | // n = The number of random numbers to be generated | |
603 | ||
604 | Gauss(vec,n,0.,1.); | |
605 | } | |
606 | /////////////////////////////////////////////////////////////////////////// | |
607 | Float_t AliRandom::Poisson(Float_t mean) | |
608 | { | |
609 | // Generate Poisson distributed random numbers with certain mean | |
610 | // | |
611 | // Method : | |
612 | // | |
613 | // P(n) = exp(-mean)*mean**n/n! is the Poisson distribution function | |
614 | // | |
615 | // with : n = 0,1,2,3,... and mean > 0 | |
616 | // | |
617 | // To generate the distribution, the "sum trick" is used as mentioned | |
618 | // in "Formulae and Methods in Experimental data Evaluation Vol. 1" | |
619 | ||
620 | Float_t unirnp=0.; // Initialise the random number value | |
621 | ||
622 | if (mean <= 0.) // Check the mean value | |
623 | { | |
624 | cout << " *AliRandom::Poisson* Invalid value mean = " << mean | |
625 | << " Should be positive." << endl; | |
626 | } | |
627 | else | |
628 | { | |
629 | if (mean > 80.) // Use gaussian dist. for high mean values to save time | |
630 | { | |
631 | Float_t grndm=Gauss(); | |
632 | Float_t rpois=mean+grndm*sqrt(mean); | |
633 | Int_t npois=int(rpois); | |
634 | if ((rpois-float(npois)) > 0.5) npois++; | |
635 | unirnp=float(npois); | |
636 | } | |
637 | else // Construct a Poisson random number from a uniform one | |
638 | { | |
639 | Int_t npois=-1; | |
640 | Float_t expxm=exp(-mean); | |
641 | Float_t poitst=1.; | |
642 | while (poitst > expxm) | |
643 | { | |
644 | Float_t rndm=Uniform(); | |
645 | npois++; | |
646 | poitst=poitst*rndm; | |
647 | } | |
648 | unirnp=float(npois); | |
649 | } // end of check for using Gauss method | |
650 | } // end of mean validity checkn | |
651 | return unirnp; | |
652 | } | |
653 | /////////////////////////////////////////////////////////////////////////// | |
654 | void AliRandom::Poisson(Float_t* vec,Int_t n,Float_t mean) | |
655 | { | |
656 | // Generate a vector of Poisson dist. random numbers with certain mean | |
657 | // This saves lots of (member)function calls in case many random | |
658 | // numbers are needed at once. | |
659 | // | |
660 | // n = The number of random numbers to be generated | |
661 | // | |
662 | // Method : | |
663 | // | |
664 | // P(n) = exp(-mean)*mean**n/n! is the Poisson distribution function | |
665 | // | |
666 | // with : n = 0,1,2,3,... and mean > 0 | |
667 | // | |
668 | // To generate the distribution, the "sum trick" is used as mentioned | |
669 | // in "Formulae and Methods in Experimental data Evaluation Vol. 1" | |
670 | ||
671 | if (n <= 0) // Check n value | |
672 | { | |
673 | cout << " *AliRandom::Poisson* Invalid value n = " << n << endl; | |
674 | } | |
675 | else | |
676 | { | |
677 | if (mean <= 0.) // Check the mean value | |
678 | { | |
679 | cout << " *AliRandom::Poisson* Invalid value mean = " << mean | |
680 | << " Should be positive." << endl; | |
681 | } | |
682 | else | |
683 | { | |
684 | if (mean > 80.) // Use gaussian dist. for high mean values to save time | |
685 | { | |
686 | Float_t* grndm=new Float_t[n]; | |
687 | Gauss(grndm,n); | |
688 | Int_t npois; | |
689 | Float_t rpois; | |
690 | for (Int_t jvec=0; jvec<n; jvec++) | |
691 | { | |
692 | rpois=mean+grndm[jvec]*sqrt(mean); | |
693 | npois=int(rpois); | |
694 | if ((rpois-float(npois)) > 0.5) npois++; | |
695 | vec[jvec]=float(npois); | |
696 | } | |
697 | delete [] grndm; | |
698 | } | |
699 | else // Construct Poisson random numbers from a uniform ones | |
700 | { | |
701 | Float_t expxm=exp(-mean); | |
702 | Int_t npois; | |
703 | Float_t poitst; | |
704 | for (Int_t jvec=0; jvec<n; jvec++) | |
705 | { | |
706 | npois=-1; | |
707 | poitst=1.; | |
708 | while (poitst > expxm) | |
709 | { | |
710 | Float_t rndm=Uniform(); | |
711 | npois++; | |
712 | poitst=poitst*rndm; | |
713 | } | |
714 | vec[jvec]=float(npois); | |
715 | } | |
716 | } // end of check for using Gauss method | |
717 | } // end of mean validity check | |
718 | } // end of n validity check | |
719 | } | |
720 | /////////////////////////////////////////////////////////////////////////// | |
721 | void AliRandom::SetUser(Float_t a,Float_t b,Int_t n,Float_t (*f)(Float_t)) | |
722 | { | |
723 | // Determine the area under f(x) as a function of x | |
724 | // This is called the "area function" and serves as a basis to | |
725 | // provide random numbers in [a,b] according to the user defined | |
726 | // distribution f(x). | |
727 | // The area function is normalised such that the most extreme | |
728 | // value is 1 or -1. | |
729 | ||
730 | fNa=n+1; // The number of bins for the area function | |
731 | fXa=new Float_t[fNa]; // The binned x values of the area function | |
732 | fYa=new Float_t[fNa]; // The corresponding summed f(x) values | |
733 | fIbins=new Int_t[fNa]; // The bin numbers of the random x candidates | |
734 | ||
735 | Float_t xmin=a; | |
736 | if (a > b) xmin=b; | |
737 | Float_t step=fabs(a-b)/float(n); | |
738 | ||
739 | Float_t x; | |
740 | Float_t extreme=0; | |
741 | for (Int_t i=0; i<fNa; i++) // Fill bins of the area function | |
742 | { | |
743 | x=xmin+float(i)*step; | |
744 | fXa[i]=x; | |
745 | fYa[i]=f(x); | |
746 | if (i > 0) fYa[i]+=fYa[i-1]; | |
747 | if (fabs(fYa[i]) > extreme) extreme=fabs(fYa[i]); | |
748 | } | |
749 | fYamin=fYa[0]/extreme; | |
750 | fYamax=fYa[0]/extreme; | |
751 | for (Int_t j=0; j<fNa; j++) // Normalise the area function | |
752 | { | |
753 | fYa[j]=fYa[j]/extreme; | |
754 | if (fYa[j] < fYamin) fYamin=fYa[j]; | |
755 | if (fYa[j] > fYamax) fYamax=fYa[j]; | |
756 | } | |
757 | } | |
758 | /////////////////////////////////////////////////////////////////////////// | |
759 | void AliRandom::SetUser(Float_t* x,Float_t* y,Int_t n) | |
760 | { | |
761 | // Determine the area under y[i] as a function of x[i] | |
762 | // This is called the "area function" and serves as a basis to | |
763 | // provide random numbers in x according to the user provided | |
764 | // distribution (x[i],y[i]). | |
765 | // The area function is normalised such that the most extreme | |
766 | // value is 1 or -1. | |
767 | ||
768 | fNa=n; // The number of bins for the area function | |
769 | fXa=new Float_t[fNa]; // The binned x values of the area function | |
770 | fYa=new Float_t[fNa]; // The corresponding summed y values | |
771 | fIbins=new Int_t[fNa]; // The bin numbers of the random x candidates | |
772 | ||
773 | // Order input data with increasing x | |
774 | fXa[0]=x[0]; | |
775 | fYa[0]=y[0]; | |
776 | for (Int_t i=1; i<fNa; i++) // Loop over x[] | |
777 | { | |
778 | for (Int_t j=0; j<i; j++) // Loop over xa[] | |
779 | { | |
780 | if (x[i] < fXa[j]) | |
781 | { | |
782 | for (Int_t k=i; k>=j; k--) // Create empty position | |
783 | { | |
784 | fXa[k+1]=fXa[k]; | |
785 | fYa[k+1]=fYa[k]; | |
786 | } | |
787 | fXa[j]=x[i]; // Put x[] value in empty position | |
788 | fYa[j]=y[i]; // Put y[] value in empty position | |
789 | break; // Go for next x[] value | |
790 | } | |
791 | if (j == i-1) // This x[] value is the largest so far | |
792 | { | |
793 | fXa[i]=x[i]; // Put x[] value at the end of x[] | |
794 | fYa[i]=y[i]; // Put y[] value at the end of y[] | |
795 | } | |
796 | } // End loop over fXa[] | |
797 | } // End loop over x[] | |
798 | ||
799 | Float_t extreme=0; | |
800 | for (Int_t l=0; l<fNa; l++) // Fill area function | |
801 | { | |
802 | if (l > 0) fYa[l]+=fYa[l-1]; | |
803 | if (fabs(fYa[l]) > extreme) extreme=fabs(fYa[l]); | |
804 | } | |
805 | fYamin=fYa[0]/extreme; | |
806 | fYamax=fYa[0]/extreme; | |
807 | for (Int_t m=0; m<fNa; m++) // Normalise the area function | |
808 | { | |
809 | fYa[m]=fYa[m]/extreme; | |
810 | if (fYa[m] < fYamin) fYamin=fYa[m]; | |
811 | if (fYa[m] > fYamax) fYamax=fYa[m]; | |
812 | } | |
813 | } | |
814 | /////////////////////////////////////////////////////////////////////////// | |
815 | Float_t AliRandom::User() | |
816 | { | |
817 | // Provide a random number according to the user defined distribution | |
818 | // | |
819 | // Method : | |
820 | // -------- | |
821 | // Select by a uniform random number a certain area fraction (from fYa[]) | |
822 | // of the area function. | |
823 | // The required random number is given by the corresponding x value (fXa[]) | |
824 | // of the area function. | |
825 | // In case of more than one x value candidate, select randomly one of them. | |
826 | ||
827 | Float_t unirnf=0; | |
828 | ||
829 | Float_t ra=Uniform(fYamin,fYamax); // Random value of the area function | |
830 | Float_t dmin=100.*fabs(fYamax-fYamin); // Init. the min. distance encountered | |
831 | Int_t ncand=0; | |
832 | Float_t dist; | |
833 | for (Int_t i=0; i<fNa; i++) // Search for fYa[] value(s) closest to ra | |
834 | { | |
835 | dist=fabs(ra-fYa[i]); | |
836 | if (dist <= dmin) // fYa[i] within smallest distance --> extra candidate | |
837 | { | |
838 | ncand++; | |
839 | if (dist < dmin) ncand=1; // Smallest distance so far --> THE candidate | |
840 | dmin=dist; | |
841 | fIbins[ncand-1]=i+1; | |
842 | } | |
843 | } | |
844 | ||
845 | Int_t jbin=0; // The bin number to hold the required x value | |
846 | if (ncand == 1) jbin=fIbins[0]; | |
847 | ||
848 | if (ncand > 1) // Multiple x value candidates --> pick one randomly | |
849 | { | |
850 | Float_t cand=Uniform(1.,float(ncand)); | |
851 | Int_t jcand=int(cand); | |
852 | if ((cand-float(jcand)) > 0.5) jcand++; | |
853 | jbin=fIbins[jcand-1]; | |
854 | } | |
855 | ||
856 | if (jbin > 0) // Pick randomly a value in this x-bin | |
857 | { | |
858 | Float_t xlow=fXa[jbin-1]; | |
859 | if (jbin > 1) xlow=fXa[jbin-2]; | |
860 | Float_t xup=fXa[jbin-1]; | |
861 | if (jbin < fNa-1) xup=fXa[jbin]; | |
862 | unirnf=Uniform(xlow,xup); | |
863 | } | |
864 | ||
865 | if (ncand == 0) cout << " *AliRandom::User* No candidate found." << endl; | |
866 | ||
867 | return unirnf; | |
868 | } | |
869 | /////////////////////////////////////////////////////////////////////////// | |
870 | void AliRandom::User(Float_t* vec,Int_t n) | |
871 | { | |
872 | // Generate a vector of random numbers according to a user defined dist. | |
873 | // This saves lots of (member)function calls in case many random | |
874 | // numbers are needed at once. | |
875 | // | |
876 | // n = The number of random numbers to be generated | |
877 | // | |
878 | // Method : | |
879 | // -------- | |
880 | // Select by a uniform random number a certain area fraction (from fYa[]) | |
881 | // of the area function. | |
882 | // The required random number is given by the corresponding x value (fXa[]) | |
883 | // of the area function. | |
884 | // In case of more than one x value candidate, select randomly one of them. | |
885 | ||
886 | Float_t unirnf,ra,dmin,dist; | |
887 | Int_t ncand,jbin; | |
888 | for (Int_t jvec=0; jvec<n; jvec++) | |
889 | { | |
890 | unirnf=0; | |
891 | ra=Uniform(fYamin,fYamax); // Random value of the area function | |
892 | dmin=100.*fabs(fYamax-fYamin); // Init. the min. distance encountered | |
893 | ncand=0; | |
894 | for (Int_t i=0; i<fNa; i++) // Search for fYa[] value(s) closest to ra | |
895 | { | |
896 | dist=fabs(ra-fYa[i]); | |
897 | if (dist <= dmin) // fYa[i] within smallest distance --> extra candidate | |
898 | { | |
899 | ncand++; | |
900 | if (dist < dmin) ncand=1; // Smallest distance so far --> THE candidate | |
901 | dmin=dist; | |
902 | fIbins[ncand-1]=i+1; | |
903 | } | |
904 | } | |
905 | ||
906 | jbin=0; // The bin number to hold the required x value | |
907 | if (ncand == 1) jbin=fIbins[0]; | |
908 | ||
909 | if (ncand > 1) // Multiple x value candidates --> pick one randomly | |
910 | { | |
911 | Float_t cand=Uniform(1.,float(ncand)); | |
912 | Int_t jcand=int(cand); | |
913 | if ((cand-float(jcand)) > 0.5) jcand++; | |
914 | jbin=fIbins[jcand-1]; | |
915 | } | |
916 | ||
917 | if (jbin > 0) // Pick randomly a value in this x-bin | |
918 | { | |
919 | Float_t xlow=fXa[jbin-1]; | |
920 | if (jbin > 1) xlow=fXa[jbin-2]; | |
921 | Float_t xup=fXa[jbin-1]; | |
922 | if (jbin < fNa-1) xup=fXa[jbin]; | |
923 | unirnf=Uniform(xlow,xup); | |
924 | } | |
925 | ||
926 | if (ncand == 0) cout << " *AliRandom::User* No candidate found." << endl; | |
927 | ||
928 | vec[jvec]=unirnf; | |
929 | ||
930 | } | |
931 | } | |
932 | /////////////////////////////////////////////////////////////////////////// |