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