| Geant4 Cross Reference |
1 // -*- C++ -*-
2 //
3 // -----------------------------------------------------------------------
4 // HEP Random
5 // --- RandBinomial ---
6 // class implementation file
7 // -----------------------------------------------------------------------
8
9 // =======================================================================
10 // John Marraffino - Created: 12th May 1998
11 // M Fischler - put and get to/from streams 12/10/04
12 // M Fischler - put/get to/from streams uses pairs of ulongs when
13 // + storing doubles avoid problems with precision
14 // 4/14/05
15 //
16 // =======================================================================
17
18 #include "CLHEP/Random/RandBinomial.h"
19 #include "CLHEP/Random/DoubConv.h"
20 #include "CLHEP/Utility/thread_local.h"
21 #include <algorithm> // for min() and max()
22 #include <cmath> // for exp()
23 #include <iostream>
24 #include <vector>
25
26 namespace CLHEP {
27
28 std::string RandBinomial::name() const {return "RandBinomial";}
29 HepRandomEngine & RandBinomial::engine() {return *localEngine;}
30
31 RandBinomial::~RandBinomial() {
32 }
33
34 double RandBinomial::shoot( HepRandomEngine *anEngine, long n,
35 double p ) {
36 return genBinomial( anEngine, n, p );
37 }
38
39 double RandBinomial::shoot( long n, double p ) {
40 HepRandomEngine *anEngine = HepRandom::getTheEngine();
41 return genBinomial( anEngine, n, p );
42 }
43
44 double RandBinomial::fire( long n, double p ) {
45 return genBinomial( localEngine.get(), n, p );
46 }
47
48 void RandBinomial::shootArray( const int size, double* vect,
49 long n, double p )
50 {
51 for( double* v = vect; v != vect+size; ++v )
52 *v = shoot(n,p);
53 }
54
55 void RandBinomial::shootArray( HepRandomEngine* anEngine,
56 const int size, double* vect,
57 long n, double p )
58 {
59 for( double* v = vect; v != vect+size; ++v )
60 *v = shoot(anEngine,n,p);
61 }
62
63 void RandBinomial::fireArray( const int size, double* vect)
64 {
65 for( double* v = vect; v != vect+size; ++v )
66 *v = fire(defaultN,defaultP);
67 }
68
69 void RandBinomial::fireArray( const int size, double* vect,
70 long n, double p )
71 {
72 for( double* v = vect; v != vect+size; ++v )
73 *v = fire(n,p);
74 }
75
76 /*************************************************************************
77 * *
78 * StirlingCorrection() *
79 * *
80 * Correction term of the Stirling approximation for log(k!) *
81 * (series in 1/k, or table values for small k) *
82 * with long int parameter k *
83 * *
84 *************************************************************************
85 * *
86 * log k! = (k + 1/2)log(k + 1) - (k + 1) + (1/2)log(2Pi) + *
87 * StirlingCorrection(k + 1) *
88 * *
89 * log k! = (k + 1/2)log(k) - k + (1/2)log(2Pi) + *
90 * StirlingCorrection(k) *
91 * *
92 *************************************************************************/
93
94 static double StirlingCorrection(long int k)
95 {
96 #define C1 8.33333333333333333e-02 // +1/12
97 #define C3 -2.77777777777777778e-03 // -1/360
98 #define C5 7.93650793650793651e-04 // +1/1260
99 #define C7 -5.95238095238095238e-04 // -1/1680
100
101 static const double c[31] = { 0.0,
102 8.106146679532726e-02, 4.134069595540929e-02,
103 2.767792568499834e-02, 2.079067210376509e-02,
104 1.664469118982119e-02, 1.387612882307075e-02,
105 1.189670994589177e-02, 1.041126526197209e-02,
106 9.255462182712733e-03, 8.330563433362871e-03,
107 7.573675487951841e-03, 6.942840107209530e-03,
108 6.408994188004207e-03, 5.951370112758848e-03,
109 5.554733551962801e-03, 5.207655919609640e-03,
110 4.901395948434738e-03, 4.629153749334029e-03,
111 4.385560249232324e-03, 4.166319691996922e-03,
112 3.967954218640860e-03, 3.787618068444430e-03,
113 3.622960224683090e-03, 3.472021382978770e-03,
114 3.333155636728090e-03, 3.204970228055040e-03,
115 3.086278682608780e-03, 2.976063983550410e-03,
116 2.873449362352470e-03, 2.777674929752690e-03,
117 };
118 double r, rr;
119
120 if (k > 30L) {
121 r = 1.0 / (double) k; rr = r * r;
122 return(r*(C1 + rr*(C3 + rr*(C5 + rr*C7))));
123 }
124 else return(c[k]);
125 }
126
127 double RandBinomial::genBinomial( HepRandomEngine *anEngine, long n, double p )
128 {
129 /******************************************************************
130 * *
131 * Binomial-Distribution - Acceptance Rejection/Inversion *
132 * *
133 ******************************************************************
134 * *
135 * Acceptance Rejection method combined with Inversion for *
136 * generating Binomial random numbers with parameters *
137 * n (number of trials) and p (probability of success). *
138 * For min(n*p,n*(1-p)) < 10 the Inversion method is applied: *
139 * The random numbers are generated via sequential search, *
140 * starting at the lowest index k=0. The cumulative probabilities *
141 * are avoided by using the technique of chop-down. *
142 * For min(n*p,n*(1-p)) >= 10 Acceptance Rejection is used: *
143 * The algorithm is based on a hat-function which is uniform in *
144 * the centre region and exponential in the tails. *
145 * A triangular immediate acceptance region in the centre speeds *
146 * up the generation of binomial variates. *
147 * If candidate k is near the mode, f(k) is computed recursively *
148 * starting at the mode m. *
149 * The acceptance test by Stirling's formula is modified *
150 * according to W. Hoermann (1992): The generation of binomial *
151 * random variates, to appear in J. Statist. Comput. Simul. *
152 * If p < .5 the algorithm is applied to parameters n, p. *
153 * Otherwise p is replaced by 1-p, and k is replaced by n - k. *
154 * *
155 ******************************************************************
156 * *
157 * FUNCTION: - btpec samples a random number from the binomial *
158 * distribution with parameters n and p and is *
159 * valid for n*min(p,1-p) > 0. *
160 * REFERENCE: - V. Kachitvichyanukul, B.W. Schmeiser (1988): *
161 * Binomial random variate generation, *
162 * Communications of the ACM 31, 216-222. *
163 * SUBPROGRAMS: - StirlingCorrection() *
164 * ... Correction term of the Stirling *
165 * approximation for log(k!) *
166 * (series in 1/k or table values *
167 * for small k) with long int k *
168 * - anEngine ... Pointer to a (0,1)-Uniform *
169 * engine *
170 * *
171 * Implemented by H. Zechner and P. Busswald, September 1992 *
172 ******************************************************************/
173
174 #define C1_3 0.33333333333333333
175 #define C5_8 0.62500000000000000
176 #define C1_6 0.16666666666666667
177 #define DMAX_KM 20L
178
179 static CLHEP_THREAD_LOCAL long int n_last = -1L, n_prev = -1L;
180 static CLHEP_THREAD_LOCAL double par,np,p0,q,p_last = -1.0, p_prev = -1.0;
181 static CLHEP_THREAD_LOCAL long b,m,nm;
182 static CLHEP_THREAD_LOCAL double pq, rc, ss, xm, xl, xr, ll, lr, c,
183 p1, p2, p3, p4, ch;
184
185 long bh,i, K, Km, nK;
186 double f, rm, U, V, X, T, E;
187
188 if (n != n_last || p != p_last) // set-up
189 {
190 n_last = n;
191 p_last = p;
192 par=std::min(p,1.0-p);
193 q=1.0-par;
194 np = n*par;
195
196 // Check for invalid input values
197
198 if( np <= 0.0 ) return (-1.0);
199
200 rm = np + par;
201 m = (long int) rm; // mode, integer
202 if (np<10)
203 {
204 p0=std::exp(n*std::log(q)); // Chop-down
205 bh=(long int)(np+10.0*std::sqrt(np*q));
206 b=std::min(n,bh);
207 }
208 else
209 {
210 rc = (n + 1.0) * (pq = par / q); // recurr. relat.
211 ss = np * q; // variance
212 i = (long int) (2.195*std::sqrt(ss) - 4.6*q); // i = p1 - 0.5
213 xm = m + 0.5;
214 xl = (double) (m - i); // limit left
215 xr = (double) (m + i + 1L); // limit right
216 f = (rm - xl) / (rm - xl*par); ll = f * (1.0 + 0.5*f);
217 f = (xr - rm) / (xr * q); lr = f * (1.0 + 0.5*f);
218 c = 0.134 + 20.5/(15.3 + (double) m); // parallelogram
219 // height
220 p1 = i + 0.5;
221 p2 = p1 * (1.0 + c + c); // probabilities
222 p3 = p2 + c/ll; // of regions 1-4
223 p4 = p3 + c/lr;
224 }
225 }
226 if( np <= 0.0 ) return (-1.0);
227 if (np<10) //Inversion Chop-down
228 {
229 double pk;
230
231 K=0;
232 pk=p0;
233 U=anEngine->flat();
234 while (U>pk)
235 {
236 ++K;
237 if (K>b)
238 {
239 U=anEngine->flat();
240 K=0;
241 pk=p0;
242 }
243 else
244 {
245 U-=pk;
246 pk=(double)(((n-K+1)*par*pk)/(K*q));
247 }
248 }
249 return ((p>0.5) ? (double)(n-K):(double)K);
250 }
251
252 for (;;)
253 {
254 V = anEngine->flat();
255 if ((U = anEngine->flat() * p4) <= p1) // triangular region
256 {
257 K=(long int) (xm - U + p1*V);
258 return ((p>0.5) ? (double)(n-K):(double)K); // immediate accept
259 }
260 if (U <= p2) // parallelogram
261 {
262 X = xl + (U - p1)/c;
263 if ((V = V*c + 1.0 - std::fabs(xm - X)/p1) >= 1.0) continue;
264 K = (long int) X;
265 }
266 else if (U <= p3) // left tail
267 {
268 if ((X = xl + std::log(V)/ll) < 0.0) continue;
269 K = (long int) X;
270 V *= (U - p2) * ll;
271 }
272 else // right tail
273 {
274 if ((K = (long int) (xr - std::log(V)/lr)) > n) continue;
275 V *= (U - p3) * lr;
276 }
277
278 // acceptance test : two cases, depending on |K - m|
279 if ((Km = std::labs(K - m)) <= DMAX_KM || Km + Km + 2L >= ss)
280 {
281
282 // computation of p(K) via recurrence relationship from the mode
283 f = 1.0; // f(m)
284 if (m < K)
285 {
286 for (i = m; i < K; )
287 {
288 if ((f *= (rc / ++i - pq)) < V) break; // multiply f
289 }
290 }
291 else
292 {
293 for (i = K; i < m; )
294 {
295 if ((V *= (rc / ++i - pq)) > f) break; // multiply V
296 }
297 }
298 if (V <= f) break; // acceptance test
299 }
300 else
301 {
302
303 // lower and upper squeeze tests, based on lower bounds for log p(K)
304 V = std::log(V);
305 T = - Km * Km / (ss + ss);
306 E = (Km / ss) * ((Km * (Km * C1_3 + C5_8) + C1_6) / ss + 0.5);
307 if (V <= T - E) break;
308 if (V <= T + E)
309 {
310 if (n != n_prev || par != p_prev)
311 {
312 n_prev = n;
313 p_prev = par;
314
315 nm = n - m + 1L;
316 ch = xm * std::log((m + 1.0)/(pq * nm)) +
317 StirlingCorrection(m + 1L) + StirlingCorrection(nm);
318 }
319 nK = n - K + 1L;
320
321 // computation of log f(K) via Stirling's formula
322 // final acceptance-rejection test
323 if (V <= ch + (n + 1.0)*std::log((double) nm / (double) nK) +
324 (K + 0.5)*std::log(nK * pq / (K + 1.0)) -
325 StirlingCorrection(K + 1L) - StirlingCorrection(nK)) break;
326 }
327 }
328 }
329 return ((p>0.5) ? (double)(n-K):(double)K);
330 }
331
332 std::ostream & RandBinomial::put ( std::ostream & os ) const {
333 long pr=os.precision(20);
334 std::vector<unsigned long> t(2);
335 os << " " << name() << "\n";
336 os << "Uvec" << "\n";
337 t = DoubConv::dto2longs(defaultP);
338 os << defaultN << " " << defaultP << " " << t[0] << " " << t[1] << "\n";
339 os.precision(pr);
340 return os;
341 }
342
343 std::istream & RandBinomial::get ( std::istream & is ) {
344 std::string inName;
345 is >> inName;
346 if (inName != name()) {
347 is.clear(std::ios::badbit | is.rdstate());
348 std::cerr << "Mismatch when expecting to read state of a "
349 << name() << " distribution\n"
350 << "Name found was " << inName
351 << "\nistream is left in the badbit state\n";
352 return is;
353 }
354 if (possibleKeywordInput(is, "Uvec", defaultN)) {
355 std::vector<unsigned long> t(2);
356 is >> defaultN >> defaultP;
357 is >> t[0] >> t[1]; defaultP = DoubConv::longs2double(t);
358 return is;
359 }
360 // is >> defaultN encompassed by possibleKeywordInput
361 is >> defaultP;
362 return is;
363 }
364
365
366 } // namespace CLHEP
367