| Geant4 Cross Reference |
>> 1 // $Id:$
1 // -*- C++ -*- 2 // -*- C++ -*-
2 // 3 //
3 // ------------------------------------------- 4 // -----------------------------------------------------------------------
4 // HEP Random 5 // HEP Random
5 // --- RandPoissonQ -- 6 // --- RandPoissonQ ---
6 // class implementation f 7 // class implementation file
7 // ------------------------------------------- 8 // -----------------------------------------------------------------------
8 9
9 // =========================================== 10 // =======================================================================
10 // M. Fischler - Implemented new, much fast 11 // M. Fischler - Implemented new, much faster table-driven algorithm
11 // applicable for mu < 100 12 // applicable for mu < 100
12 // - Implemented "quick()" methods, shich 13 // - Implemented "quick()" methods, shich are the same as the
13 // new methods for mu < 100 and are a s 14 // new methods for mu < 100 and are a skew-corrected gaussian
14 // approximation for large mu. 15 // approximation for large mu.
15 // M. Fischler - Removed mean=100 from the 16 // M. Fischler - Removed mean=100 from the table-driven set, since it
16 // uses a value just off the end of the 17 // uses a value just off the end of the table. (April 2004)
17 // M Fischler - put and get to/from stream 18 // M Fischler - put and get to/from streams 12/15/04
18 // M Fischler - Utilize RandGaussQ rather 19 // M Fischler - Utilize RandGaussQ rather than RandGauss, as clearly
19 // intended by the inclusion of RandGau 20 // intended by the inclusion of RandGaussQ.h. Using RandGauss
20 // introduces a subtle trap in that the 21 // introduces a subtle trap in that the state of RandPoissonQ
21 // can never be properly captured witho 22 // can never be properly captured without also saveing the
22 // state of RandGauss! RandGaussQ is, 23 // state of RandGauss! RandGaussQ is, on the other hand,
23 // stateless except for the engine used 24 // stateless except for the engine used.
24 // M Fischler - Modified use of wrong engine << 25 // M Fisculer - Modified use of wrong engine when shoot (anEngine, mean)
25 // is called. This flaw was preventing 26 // is called. This flaw was preventing any hope of proper
26 // saving and restoring in the instance 27 // saving and restoring in the instance cases.
27 // M Fischler - fireArray using defaultMea 28 // M Fischler - fireArray using defaultMean 2/10/05
28 // M Fischler - put/get to/from streams 29 // M Fischler - put/get to/from streams uses pairs of ulongs when
29 // + storing doubles avoid problems with 30 // + storing doubles avoid problems with precision
30 // 4/14/05 31 // 4/14/05
31 // M Fischler - Modified use of shoot (mean) << 32 // M Fisculer - Modified use of shoot (mean) instead of
32 // shoot(getLocalEngine(), mean) when f 33 // shoot(getLocalEngine(), mean) when fire(mean) is called.
33 // This flaw was causing bad "cross-tal 34 // This flaw was causing bad "cross-talk" between modules
34 // in CMS, where one used its own engin 35 // in CMS, where one used its own engine, and the other
35 // used the static generator. 10/18/07 36 // used the static generator. 10/18/07
36 // 37 //
37 // =========================================== 38 // =======================================================================
38 39
39 #include "CLHEP/Random/RandPoissonQ.h" 40 #include "CLHEP/Random/RandPoissonQ.h"
40 #include "CLHEP/Random/RandGaussQ.h" 41 #include "CLHEP/Random/RandGaussQ.h"
41 #include "CLHEP/Random/DoubConv.h" 42 #include "CLHEP/Random/DoubConv.h"
42 #include "CLHEP/Random/Stat.h" 43 #include "CLHEP/Random/Stat.h"
43 #include "CLHEP/Utility/thread_local.h" <<
44 #include <cmath> // for std::pow() 44 #include <cmath> // for std::pow()
45 #include <iostream> <<
46 #include <string> <<
47 #include <vector> <<
48 45
49 namespace CLHEP { 46 namespace CLHEP {
50 47
51 std::string RandPoissonQ::name() const {return 48 std::string RandPoissonQ::name() const {return "RandPoissonQ";}
52 HepRandomEngine & RandPoissonQ::engine() {retu 49 HepRandomEngine & RandPoissonQ::engine() {return RandPoisson::engine();}
53 50
54 // Initialization of static data: Note that t 51 // Initialization of static data: Note that this is all const static data,
55 // so that saveEngineStatus properly saves all 52 // so that saveEngineStatus properly saves all needed information.
56 53
57 // The following MUST MATCH the correspondin 54 // The following MUST MATCH the corresponding values used (in
58 // poissonTables.cc) when poissonTables.cdat 55 // poissonTables.cc) when poissonTables.cdat was created.
59 56
60 const double RandPoissonQ::FIRST_MU = 10;// lo 57 const double RandPoissonQ::FIRST_MU = 10;// lowest mu value in table
61 const double RandPoissonQ::LAST_MU = 95;// hi 58 const double RandPoissonQ::LAST_MU = 95;// highest mu value
62 const double RandPoissonQ::S = 5; // Sp 59 const double RandPoissonQ::S = 5; // Spacing between mu values
63 const int RandPoissonQ::BELOW = 30; // St 60 const int RandPoissonQ::BELOW = 30; // Starting point for N is at mu - BELOW
64 const int RandPoissonQ::ENTRIES = 51; // Nu 61 const int RandPoissonQ::ENTRIES = 51; // Number of entries in each mu row
65 62
66 const double RandPoissonQ::MAXIMUM_POISSON_DEV 63 const double RandPoissonQ::MAXIMUM_POISSON_DEVIATE = 2.0E9;
67 // Careful -- this is NOT the maximum number 64 // Careful -- this is NOT the maximum number that can be held in
68 // a long. It actually should be some large 65 // a long. It actually should be some large number of sigma below
69 // that. 66 // that.
70 67
71 // Here comes the big (9K bytes) table, kept 68 // Here comes the big (9K bytes) table, kept in a file of
72 // ENTRIES * (FIRST_MU - LAST_MU + 1)/S doub 69 // ENTRIES * (FIRST_MU - LAST_MU + 1)/S doubles
73 70
74 static const double poissonTables [ 51 * ( (95 71 static const double poissonTables [ 51 * ( (95-10)/5 + 1 ) ] = {
75 #include "CLHEP/Random/poissonTables.cdat" 72 #include "CLHEP/Random/poissonTables.cdat"
76 }; 73 };
77 74
78 // 75 //
79 // Constructors and destructors: 76 // Constructors and destructors:
80 // 77 //
81 78
82 RandPoissonQ::~RandPoissonQ() { 79 RandPoissonQ::~RandPoissonQ() {
83 } 80 }
84 81
85 void RandPoissonQ::setupForDefaultMu() { 82 void RandPoissonQ::setupForDefaultMu() {
86 83
87 // The following are useful for quick approx 84 // The following are useful for quick approximation, for large mu
88 85
89 double sig2 = defaultMean * (.9998654 - .083 86 double sig2 = defaultMean * (.9998654 - .08346/defaultMean);
90 sigma = std::sqrt(sig2); 87 sigma = std::sqrt(sig2);
91 // sigma for the Guassian which approximates 88 // sigma for the Guassian which approximates the Poisson -- naively
92 // sqrt (defaultMean). 89 // sqrt (defaultMean).
93 // 90 //
94 // The multiplier corrects for fact that dis 91 // The multiplier corrects for fact that discretization of the form
95 // [gaussian+.5] increases the second moment 92 // [gaussian+.5] increases the second moment by a small amount.
96 93
97 double t = 1./(sig2); 94 double t = 1./(sig2);
98 95
99 a2 = t/6 + t*t/324; 96 a2 = t/6 + t*t/324;
100 a1 = std::sqrt (1-2*a2*a2*sig2); 97 a1 = std::sqrt (1-2*a2*a2*sig2);
101 a0 = defaultMean + .5 - sig2 * a2; 98 a0 = defaultMean + .5 - sig2 * a2;
102 99
103 // The formula will be a0 + a1*x + a2*x*x wh 100 // The formula will be a0 + a1*x + a2*x*x where x has 2nd moment of sigma.
104 // The coeffeicients are chosen to match the 101 // The coeffeicients are chosen to match the first THREE moments of the
105 // true Poisson distribution. 102 // true Poisson distribution.
106 // 103 //
107 // Actually, if the correction for discretiz 104 // Actually, if the correction for discretization were not needed, then
108 // a2 could be taken one order higher by add 105 // a2 could be taken one order higher by adding t*t*t/5832. However,
109 // the discretization correction is not perf 106 // the discretization correction is not perfect, leading to inaccuracy
110 // on the order to 1/mu**2, so adding a thir 107 // on the order to 1/mu**2, so adding a third term is overkill.
111 108
112 } // setupForDefaultMu() 109 } // setupForDefaultMu()
113 110
114 111
115 // 112 //
116 // fire, quick, operator(), and shoot methods: 113 // fire, quick, operator(), and shoot methods:
117 // 114 //
118 115
119 long RandPoissonQ::shoot(double xm) { 116 long RandPoissonQ::shoot(double xm) {
120 return shoot(getTheEngine(), xm); 117 return shoot(getTheEngine(), xm);
121 } 118 }
122 119
123 double RandPoissonQ::operator()() { 120 double RandPoissonQ::operator()() {
124 return (double) fire(); 121 return (double) fire();
125 } 122 }
126 123
127 double RandPoissonQ::operator()( double mean ) 124 double RandPoissonQ::operator()( double mean ) {
128 return (double) fire(mean); 125 return (double) fire(mean);
129 } 126 }
130 127
131 long RandPoissonQ::fire(double mean) { 128 long RandPoissonQ::fire(double mean) {
132 return shoot(getLocalEngine(), mean); 129 return shoot(getLocalEngine(), mean);
133 } 130 }
134 131
135 long RandPoissonQ::fire() { 132 long RandPoissonQ::fire() {
136 if ( defaultMean < LAST_MU + S ) { 133 if ( defaultMean < LAST_MU + S ) {
137 return poissonDeviateSmall ( getLocalEngin 134 return poissonDeviateSmall ( getLocalEngine(), defaultMean );
138 } else { 135 } else {
139 return poissonDeviateQuick ( getLocalEngin 136 return poissonDeviateQuick ( getLocalEngine(), a0, a1, a2, sigma );
140 } 137 }
141 } // fire() 138 } // fire()
142 139
143 long RandPoissonQ::shoot(HepRandomEngine* anEn 140 long RandPoissonQ::shoot(HepRandomEngine* anEngine, double mean) {
144 141
145 // The following variables, static to this m 142 // The following variables, static to this method, apply to the
146 // last time a large mean was supplied; they 143 // last time a large mean was supplied; they obviate certain calculations
147 // if consecutive calls use the same mean. 144 // if consecutive calls use the same mean.
148 145
149 static CLHEP_THREAD_LOCAL double lastLargeMe << 146 static double lastLargeMean = -1.; // Mean from previous shoot
150 // requiring poissonDeviateQuick() 147 // requiring poissonDeviateQuick()
151 static CLHEP_THREAD_LOCAL double lastA0; << 148 static double lastA0;
152 static CLHEP_THREAD_LOCAL double lastA1; << 149 static double lastA1;
153 static CLHEP_THREAD_LOCAL double lastA2; << 150 static double lastA2;
154 static CLHEP_THREAD_LOCAL double lastSigma; << 151 static double lastSigma;
155 152
156 if ( mean < LAST_MU + S ) { 153 if ( mean < LAST_MU + S ) {
157 return poissonDeviateSmall ( anEngine, mea 154 return poissonDeviateSmall ( anEngine, mean );
158 } else { 155 } else {
159 if ( mean != lastLargeMean ) { 156 if ( mean != lastLargeMean ) {
160 // Compute the coefficients defining the 157 // Compute the coefficients defining the quadratic transformation from a
161 // Gaussian to a Poisson for this mean. 158 // Gaussian to a Poisson for this mean. Also save these for next time.
162 double sig2 = mean * (.9998654 - .08346/ 159 double sig2 = mean * (.9998654 - .08346/mean);
163 lastSigma = std::sqrt(sig2); 160 lastSigma = std::sqrt(sig2);
164 double t = 1./sig2; 161 double t = 1./sig2;
165 lastA2 = t*(1./6.) + t*t*(1./324.); 162 lastA2 = t*(1./6.) + t*t*(1./324.);
166 lastA1 = std::sqrt (1-2*lastA2*lastA2*si 163 lastA1 = std::sqrt (1-2*lastA2*lastA2*sig2);
167 lastA0 = mean + .5 - sig2 * lastA2; 164 lastA0 = mean + .5 - sig2 * lastA2;
168 } 165 }
169 return poissonDeviateQuick ( anEngine, las 166 return poissonDeviateQuick ( anEngine, lastA0, lastA1, lastA2, lastSigma );
170 } 167 }
171 168
172 } // shoot (anEngine, mean) 169 } // shoot (anEngine, mean)
173 170
174 void RandPoissonQ::shootArray(const int size, 171 void RandPoissonQ::shootArray(const int size, long* vect, double m) {
175 for( long* v = vect; v != vect + size; ++v ) 172 for( long* v = vect; v != vect + size; ++v )
176 *v = shoot(m); 173 *v = shoot(m);
177 // Note: We could test for m > 100, and i 174 // Note: We could test for m > 100, and if it is, precompute a0, a1, a2,
178 // and sigma and call the appropriate for 175 // and sigma and call the appropriate form of poissonDeviateQuick.
179 // But since those are cached anyway, not 176 // But since those are cached anyway, not much time would be saved.
180 } 177 }
181 178
182 void RandPoissonQ::shootArray(HepRandomEngine* <<
183 long* vect, doubl <<
184 for( long* v = vect; v != vect + size; ++v ) <<
185 *v = shoot(anEngine,m1); <<
186 } <<
187 <<
188 void RandPoissonQ::fireArray(const int size, l 179 void RandPoissonQ::fireArray(const int size, long* vect, double m) {
189 for( long* v = vect; v != vect + size; ++v ) 180 for( long* v = vect; v != vect + size; ++v )
190 *v = fire( m ); 181 *v = fire( m );
191 } 182 }
192 183
193 void RandPoissonQ::fireArray(const int size, l 184 void RandPoissonQ::fireArray(const int size, long* vect) {
194 for( long* v = vect; v != vect + size; ++v ) 185 for( long* v = vect; v != vect + size; ++v )
195 *v = fire( defaultMean ); 186 *v = fire( defaultMean );
196 } 187 }
197 188
198 189
199 // Quick Poisson deviate algorithm used by qui 190 // Quick Poisson deviate algorithm used by quick for large mu:
200 191
201 long RandPoissonQ::poissonDeviateQuick ( HepRa 192 long RandPoissonQ::poissonDeviateQuick ( HepRandomEngine *e, double mu ) {
202 193
203 // Compute the coefficients defining the qua 194 // Compute the coefficients defining the quadratic transformation from a
204 // Gaussian to a Poisson: 195 // Gaussian to a Poisson:
205 196
206 double sig2 = mu * (.9998654 - .08346/mu); 197 double sig2 = mu * (.9998654 - .08346/mu);
207 double sig = std::sqrt(sig2); 198 double sig = std::sqrt(sig2);
208 // The multiplier corrects for fact that dis 199 // The multiplier corrects for fact that discretization of the form
209 // [gaussian+.5] increases the second moment 200 // [gaussian+.5] increases the second moment by a small amount.
210 201
211 double t = 1./sig2; 202 double t = 1./sig2;
212 203
213 double sa2 = t*(1./6.) + t*t*(1./324.); 204 double sa2 = t*(1./6.) + t*t*(1./324.);
214 double sa1 = std::sqrt (1-2*sa2*sa2*sig2); 205 double sa1 = std::sqrt (1-2*sa2*sa2*sig2);
215 double sa0 = mu + .5 - sig2 * sa2; 206 double sa0 = mu + .5 - sig2 * sa2;
216 207
217 // The formula will be sa0 + sa1*x + sa2*x*x 208 // The formula will be sa0 + sa1*x + sa2*x*x where x has sigma of sq.
218 // The coeffeicients are chosen to match the 209 // The coeffeicients are chosen to match the first THREE moments of the
219 // true Poisson distribution. 210 // true Poisson distribution.
220 211
221 return poissonDeviateQuick ( e, sa0, sa1, sa 212 return poissonDeviateQuick ( e, sa0, sa1, sa2, sig );
222 } 213 }
223 214
224 215
225 long RandPoissonQ::poissonDeviateQuick ( HepRa 216 long RandPoissonQ::poissonDeviateQuick ( HepRandomEngine *e,
226 double A0, double A1, double A2, double si 217 double A0, double A1, double A2, double sig) {
227 // 218 //
228 // Quick Poisson deviate algorithm used by qui 219 // Quick Poisson deviate algorithm used by quick for large mu:
229 // 220 //
230 // The principle: For very large mu, a poisso 221 // The principle: For very large mu, a poisson distribution can be approximated
231 // by a gaussian: return the integer part of m 222 // by a gaussian: return the integer part of mu + .5 + g where g is a unit
232 // normal. However, this yelds a miserable ap 223 // normal. However, this yelds a miserable approximation at values as
233 // "large" as 100. The primary problem is tha 224 // "large" as 100. The primary problem is that the poisson distribution is
234 // supposed to have a skew of 1/mu**2, and the 225 // supposed to have a skew of 1/mu**2, and the zero skew of the Guassian
235 // leads to errors of order as big as 1/mu**2. 226 // leads to errors of order as big as 1/mu**2.
236 // 227 //
237 // We substitute for the gaussian a quadratic 228 // We substitute for the gaussian a quadratic function of that gaussian random.
238 // The expression looks very nearly like mu + 229 // The expression looks very nearly like mu + .5 - 1/6 + g + g**2/(6*mu).
239 // The small positive quadratic term causes th 230 // The small positive quadratic term causes the resulting variate to have
240 // a positive skew; the -1/6 constant term is 231 // a positive skew; the -1/6 constant term is there to correct for this bias
241 // in the mean. By adjusting these two and th 232 // in the mean. By adjusting these two and the linear term, we can match the
242 // first three moments to high accuracy in 1/m 233 // first three moments to high accuracy in 1/mu.
243 // 234 //
244 // The sigma used is not precisely sqrt(mu) si 235 // The sigma used is not precisely sqrt(mu) since a rounded-off Gaussian
245 // has a second moment which is slightly large 236 // has a second moment which is slightly larger than that of the Gaussian.
246 // To compensate, sig is multiplied by a facto 237 // To compensate, sig is multiplied by a factor which is slightly less than 1.
247 238
248 // double g = RandGauss::shootQuick( e ); 239 // double g = RandGauss::shootQuick( e ); // TEMPORARY MOD:
249 double g = RandGaussQ::shoot( e ); // Unit 240 double g = RandGaussQ::shoot( e ); // Unit normal
250 g *= sig; 241 g *= sig;
251 double p = A2*g*g + A1*g + A0; 242 double p = A2*g*g + A1*g + A0;
252 if ( p < 0 ) return 0; // Shouldn't ever po 243 if ( p < 0 ) return 0; // Shouldn't ever possibly happen since
253 // mean should not be less than 100, b 244 // mean should not be less than 100, but
254 // we check due to paranoia. 245 // we check due to paranoia.
255 if ( p > MAXIMUM_POISSON_DEVIATE ) p = MAXIM 246 if ( p > MAXIMUM_POISSON_DEVIATE ) p = MAXIMUM_POISSON_DEVIATE;
256 247
257 return long(p); 248 return long(p);
258 249
259 } // poissonDeviateQuick () 250 } // poissonDeviateQuick ()
260 251
261 252
262 253
263 long RandPoissonQ::poissonDeviateSmall (HepRan 254 long RandPoissonQ::poissonDeviateSmall (HepRandomEngine * e, double mean) {
264 long N1; 255 long N1;
265 long N2; 256 long N2;
266 // The following are for later use to form a 257 // The following are for later use to form a secondary random s:
267 double rRange; // This will hold the in 258 double rRange; // This will hold the interval between cdf for the
268 // computed N1 and cdf for N1+1. 259 // computed N1 and cdf for N1+1.
269 double rRemainder = 0; // This will hold the 260 double rRemainder = 0; // This will hold the length into that interval.
270 261
271 // Coming in, mean should not be more than L 262 // Coming in, mean should not be more than LAST_MU + S. However, we will
272 // be paranoid and test for this: 263 // be paranoid and test for this:
273 264
274 if ( mean > LAST_MU + S ) { 265 if ( mean > LAST_MU + S ) {
275 return RandPoisson::shoot(e, mean); 266 return RandPoisson::shoot(e, mean);
276 } 267 }
277 268
278 if (mean <= 0) { 269 if (mean <= 0) {
279 return 0; // Perhaps we ought to balk 270 return 0; // Perhaps we ought to balk harder here!
280 } 271 }
281 272
282 // >>> 1 <<< 273 // >>> 1 <<<
283 // Generate the first random, which we alwa 274 // Generate the first random, which we always will need.
284 275
285 double r = e->flat(); 276 double r = e->flat();
286 277
287 // >>> 2 <<< 278 // >>> 2 <<<
288 // For small mean, below the start of the t 279 // For small mean, below the start of the tables,
289 // do the series for cdf directly. 280 // do the series for cdf directly.
290 281
291 // In this case, since we know the series wi 282 // In this case, since we know the series will terminate relatively quickly,
292 // almost alwaye use a precomputed 1/N array 283 // almost alwaye use a precomputed 1/N array without fear of overrunning it.
293 284
294 static const double oneOverN[50] = 285 static const double oneOverN[50] =
295 { 0, 1., 1/2., 1/3., 1/4., 1/5., 286 { 0, 1., 1/2., 1/3., 1/4., 1/5., 1/6., 1/7., 1/8., 1/9.,
296 1/10., 1/11., 1/12., 1/13., 1/14., 1/15., 287 1/10., 1/11., 1/12., 1/13., 1/14., 1/15., 1/16., 1/17., 1/18., 1/19.,
297 1/20., 1/21., 1/22., 1/23., 1/24., 1/25., 288 1/20., 1/21., 1/22., 1/23., 1/24., 1/25., 1/26., 1/27., 1/28., 1/29.,
298 1/30., 1/31., 1/32., 1/33., 1/34., 1/35., 289 1/30., 1/31., 1/32., 1/33., 1/34., 1/35., 1/36., 1/37., 1/38., 1/39.,
299 1/40., 1/41., 1/42., 1/43., 1/44., 1/45., 290 1/40., 1/41., 1/42., 1/43., 1/44., 1/45., 1/46., 1/47., 1/48., 1/49. };
300 291
301 292
302 if ( mean < FIRST_MU ) { 293 if ( mean < FIRST_MU ) {
303 294
304 long N = 0; 295 long N = 0;
305 double term = std::exp(-mean); 296 double term = std::exp(-mean);
306 double cdf = term; 297 double cdf = term;
307 298
308 if ( r < (1 - 1.0E-9) ) { 299 if ( r < (1 - 1.0E-9) ) {
309 // 300 //
310 // **** This is a normal path: **** 301 // **** This is a normal path: ****
311 // 302 //
312 // Except when r is very close to 1, it 303 // Except when r is very close to 1, it is certain that we will exceed r
313 // before the 30-th term in the series, 304 // before the 30-th term in the series, so a simple while loop is OK.
314 const double* oneOverNptr = oneOverN; 305 const double* oneOverNptr = oneOverN;
315 while( cdf <= r ) { 306 while( cdf <= r ) {
316 N++ ; 307 N++ ;
317 oneOverNptr++; 308 oneOverNptr++;
318 term *= ( mean * (*oneOverNptr) ); 309 term *= ( mean * (*oneOverNptr) );
319 cdf += term; 310 cdf += term;
320 } 311 }
321 return N; 312 return N;
322 // 313 //
323 // **** **** 314 // **** ****
324 // 315 //
325 } else { // r is almost 1... 316 } else { // r is almost 1...
326 // For r very near to 1 we would have to 317 // For r very near to 1 we would have to check that we don't fall
327 // off the end of the table of 1/N. Sin 318 // off the end of the table of 1/N. Since this is very rare, we just
328 // ignore the table and do the identical 319 // ignore the table and do the identical while loop, using explicit
329 // division. 320 // division.
330 double cdf0; 321 double cdf0;
331 while ( cdf <= r ) { 322 while ( cdf <= r ) {
332 N++ ; 323 N++ ;
333 term *= ( mean / N ); 324 term *= ( mean / N );
334 cdf0 = cdf; 325 cdf0 = cdf;
335 cdf += term; 326 cdf += term;
336 if (cdf == cdf0) break; // Can't happen, but 327 if (cdf == cdf0) break; // Can't happen, but just in case...
337 } 328 }
338 return N; 329 return N;
339 } // end of if ( r compared to (1 - 1.0E-9 330 } // end of if ( r compared to (1 - 1.0E-9) )
340 331
341 } // End of the code for mean < FIRST_MU 332 } // End of the code for mean < FIRST_MU
342 333
343 // >>> 3 <<< 334 // >>> 3 <<<
344 // Find the row of the tables corresponding 335 // Find the row of the tables corresponding to the highest tabulated mu
345 // which is no greater than our actual mean 336 // which is no greater than our actual mean.
346 337
347 int rowNumber = int((mean - FIRST_MU)/S); 338 int rowNumber = int((mean - FIRST_MU)/S);
348 const double * cdfs = &poissonTables [rowNum 339 const double * cdfs = &poissonTables [rowNumber*ENTRIES];
349 double mu = FIRST_MU + rowNumber*S; 340 double mu = FIRST_MU + rowNumber*S;
350 double deltaMu = mean - mu; 341 double deltaMu = mean - mu;
351 int Nmin = int(mu - BELOW); 342 int Nmin = int(mu - BELOW);
352 if (Nmin < 1) Nmin = 1; 343 if (Nmin < 1) Nmin = 1;
353 int Nmax = Nmin + (ENTRIES - 1); 344 int Nmax = Nmin + (ENTRIES - 1);
354 345
355 346
356 // >>> 4 <<< 347 // >>> 4 <<<
357 // If r is less that the smallest entry in 348 // If r is less that the smallest entry in the row, then
358 // generate the deviate directly from the s 349 // generate the deviate directly from the series.
359 350
360 if ( r < cdfs[0] ) { 351 if ( r < cdfs[0] ) {
361 352
362 // In this case, we are tempted to use the 353 // In this case, we are tempted to use the actual mean, and not
363 // generate a second deviate to account fo 354 // generate a second deviate to account for the leftover part mean - mu.
364 // That would be an error, generating a di 355 // That would be an error, generating a distribution with enough excess
365 // at Nmin + (mean-mu)/2 to be detectable 356 // at Nmin + (mean-mu)/2 to be detectable in 4,000,000 trials.
366 357
367 // Since this case is very rare (never mor 358 // Since this case is very rare (never more than .2% of the r values)
368 // and can happen where N will be large (u 359 // and can happen where N will be large (up to 65 for the mu=95 row)
369 // we use explicit division so as to avoid 360 // we use explicit division so as to avoid having to worry about running
370 // out of oneOverN table. 361 // out of oneOverN table.
371 362
372 long N = 0; 363 long N = 0;
373 double term = std::exp(-mu); 364 double term = std::exp(-mu);
374 double cdf = term; 365 double cdf = term;
375 double cdf0; 366 double cdf0;
376 367
377 while(cdf <= r) { 368 while(cdf <= r) {
378 N++ ; 369 N++ ;
379 term *= ( mu / N ); 370 term *= ( mu / N );
380 cdf0 = cdf; 371 cdf0 = cdf;
381 cdf += term; 372 cdf += term;
382 if (cdf == cdf0) break; // Can't happen, but 373 if (cdf == cdf0) break; // Can't happen, but just in case...
383 } 374 }
384 N1 = N; 375 N1 = N;
385 // std::cout << r << " " << N << " "; 376 // std::cout << r << " " << N << " ";
386 // DBG_small = true; 377 // DBG_small = true;
387 rRange = 0; // In this case there is alw 378 rRange = 0; // In this case there is always a second r needed
388 379
389 } // end of small-r case 380 } // end of small-r case
390 381
391 382
392 // >>> 5 <<< 383 // >>> 5 <<<
393 // Assuming r lies within the scope of the 384 // Assuming r lies within the scope of the row for this mu, find the
394 // largest entry not greater than r. N1 is 385 // largest entry not greater than r. N1 is the N corresponding to the
395 // index a. 386 // index a.
396 387
397 else if ( r < cdfs[ENTRIES-1] ) { // r i 388 else if ( r < cdfs[ENTRIES-1] ) { // r is also >= cdfs[0]
398 389
399 // 390 //
400 // **** This is the normal code path **** 391 // **** This is the normal code path ****
401 // 392 //
402 393
403 int a = 0; // Highest val 394 int a = 0; // Highest value of index such that cdfs[a]
404 // is known NOT to be greater than r. 395 // is known NOT to be greater than r.
405 int b = ENTRIES - 1; // Lowest value of i 396 int b = ENTRIES - 1; // Lowest value of index such that cdfs[b] is
406 // known to exeed r. 397 // known to exeed r.
407 398
408 while (b != (a+1) ) { 399 while (b != (a+1) ) {
409 int c = (a+b+1)>>1; 400 int c = (a+b+1)>>1;
410 if (r > cdfs[c]) { 401 if (r > cdfs[c]) {
411 a = c; 402 a = c;
412 } else { 403 } else {
413 b = c; 404 b = c;
414 } 405 }
415 } 406 }
416 407
417 N1 = Nmin + a; 408 N1 = Nmin + a;
418 rRange = cdfs[a+1] - cdfs[a]; 409 rRange = cdfs[a+1] - cdfs[a];
419 rRemainder = r - cdfs[a]; 410 rRemainder = r - cdfs[a];
420 411
421 // 412 //
422 // **** **** 413 // **** ****
423 // 414 //
424 415
425 } // end of medium-r (normal) case 416 } // end of medium-r (normal) case
426 417
427 418
428 // >>> 6 <<< 419 // >>> 6 <<<
429 // If r exceeds the greatest entry in the t 420 // If r exceeds the greatest entry in the table for this mu, then start
430 // from that cdf, and use the series to com 421 // from that cdf, and use the series to compute from there until r is
431 // exceeded. 422 // exceeded.
432 423
433 else { // if ( r >= cdfs[ENTRIES-1] ) { 424 else { // if ( r >= cdfs[ENTRIES-1] ) {
434 425
435 // Here, division must be done explicitly, 426 // Here, division must be done explicitly, and we must also protect against
436 // roundoff preventing termination. 427 // roundoff preventing termination.
437 428
438 // 429 //
439 //+++ cdfs[ENTRIES-1] is exp(-mu) sum (mu**m 430 //+++ cdfs[ENTRIES-1] is exp(-mu) sum (mu**m/m! , m=0 to Nmax)
440 //+++ (where Nmax = mu - BELOW + ENTRIES - 1 431 //+++ (where Nmax = mu - BELOW + ENTRIES - 1)
441 //+++ cdfs[ENTRIES-1]-cdfs[ENTRIES-2] is exp 432 //+++ cdfs[ENTRIES-1]-cdfs[ENTRIES-2] is exp(-mu) mu**(Nmax)/(Nmax)!
442 //+++ If the sum up to k-1 <= r < sum up to 433 //+++ If the sum up to k-1 <= r < sum up to k, then N = k-1
443 //+++ Consider k = Nmax in the above stateme 434 //+++ Consider k = Nmax in the above statement:
444 //+++ If cdfs[ENTRIES-2] <= r < cdfs[ENTRIES 435 //+++ If cdfs[ENTRIES-2] <= r < cdfs[ENTRIES-1], N would be Nmax-1
445 //+++ But here r >= cdfs[ENTRIES-1] so N >= 436 //+++ But here r >= cdfs[ENTRIES-1] so N >= Nmax
446 // 437 //
447 438
448 // Erroneous: 439 // Erroneous:
449 //+++ cdfs[ENTRIES-1] is exp(-mu) sum (mu**m 440 //+++ cdfs[ENTRIES-1] is exp(-mu) sum (mu**m/m! , m=0 to Nmax-1)
450 //+++ cdfs[ENTRIES-1]-cdfs[ENTRIES-2] is exp 441 //+++ cdfs[ENTRIES-1]-cdfs[ENTRIES-2] is exp(-mu) mu**(Nmax-1)/(Nmax-1)!
451 //+++ If a sum up to k-1 <= r < sum up to k, 442 //+++ If a sum up to k-1 <= r < sum up to k, then N = k-1
452 //+++ So if cdfs[ENTRIES-1] were > r, N woul 443 //+++ So if cdfs[ENTRIES-1] were > r, N would be Nmax-1 (or less)
453 //+++ But here r >= cdfs[ENTRIES-1] so N >= 444 //+++ But here r >= cdfs[ENTRIES-1] so N >= Nmax
454 // 445 //
455 446
456 // std::cout << "r = " << r << " mu = " < 447 // std::cout << "r = " << r << " mu = " << mu << "\n";
457 long N = Nmax -1; 448 long N = Nmax -1;
458 double cdf = cdfs[ENTRIES-1]; 449 double cdf = cdfs[ENTRIES-1];
459 double term = cdf - cdfs[ENTRIES-2]; 450 double term = cdf - cdfs[ENTRIES-2];
460 double cdf0; 451 double cdf0;
461 while(cdf <= r) { 452 while(cdf <= r) {
462 N++ ; 453 N++ ;
463 // std::cout << " N " << N << " term " < 454 // std::cout << " N " << N << " term " <<
464 // term << " cdf " << cdf << "\n"; 455 // term << " cdf " << cdf << "\n";
465 term *= ( mu / N ); 456 term *= ( mu / N );
466 cdf0 = cdf; 457 cdf0 = cdf;
467 cdf += term; 458 cdf += term;
468 if (cdf == cdf0) break; // If term gets so s 459 if (cdf == cdf0) break; // If term gets so small cdf stops increasing,
469 // terminate using that value of N sin 460 // terminate using that value of N since we
470 // would never reach r. 461 // would never reach r.
471 } 462 }
472 N1 = N; 463 N1 = N;
473 rRange = 0; // We can't validly omit the 464 rRange = 0; // We can't validly omit the second true random
474 465
475 // N = Nmax -1; 466 // N = Nmax -1;
476 // cdf = cdfs[ENTRIES-1]; 467 // cdf = cdfs[ENTRIES-1];
477 // term = cdf - cdfs[ENTRIES-2]; 468 // term = cdf - cdfs[ENTRIES-2];
478 // for (int isxz=0; isxz < 100; isxz++) 469 // for (int isxz=0; isxz < 100; isxz++) {
479 // N++ ; 470 // N++ ;
480 // term *= ( mu / N ); 471 // term *= ( mu / N );
481 // cdf0 = cdf; 472 // cdf0 = cdf;
482 // cdf += term; 473 // cdf += term;
483 // } 474 // }
484 // std::cout.precision(20); 475 // std::cout.precision(20);
485 // std::cout << "Final sum is " << cdf 476 // std::cout << "Final sum is " << cdf << "\n";
486 477
487 } // end of large-r case 478 } // end of large-r case
488 479
489 480
490 481
491 // >>> 7 <<< 482 // >>> 7 <<<
492 // Form a second random, s, based on the po 483 // Form a second random, s, based on the position of r within the range
493 // of this table entry to the next entry. 484 // of this table entry to the next entry.
494 485
495 // However, if this range is very small, the 486 // However, if this range is very small, then we lose too many bits of
496 // randomness. In that situation, we genera 487 // randomness. In that situation, we generate a second random for s.
497 488
498 double s; 489 double s;
499 490
500 static const double MINRANGE = .01; // Sac 491 static const double MINRANGE = .01; // Sacrifice up to two digits of
501 // randomness when using r to 492 // randomness when using r to produce
502 // a second random s. Leads to up t 493 // a second random s. Leads to up to
503 // .09 extra randoms each time. 494 // .09 extra randoms each time.
504 495
505 if ( rRange > MINRANGE ) { 496 if ( rRange > MINRANGE ) {
506 // 497 //
507 // **** This path taken 90% of the time ** 498 // **** This path taken 90% of the time ****
508 // 499 //
509 s = rRemainder / rRange; 500 s = rRemainder / rRange;
510 } else { 501 } else {
511 s = e->flat(); // extra true random neede 502 s = e->flat(); // extra true random needed about one time in 10.
512 } 503 }
513 504
514 // >>> 8 <<< 505 // >>> 8 <<<
515 // Use the direct summation method to form 506 // Use the direct summation method to form a second poisson deviate N2
516 // from deltaMu and s. 507 // from deltaMu and s.
517 508
518 N2 = 0; 509 N2 = 0;
519 double term = std::exp(-deltaMu); 510 double term = std::exp(-deltaMu);
520 double cdf = term; 511 double cdf = term;
521 512
522 if ( s < (1 - 1.0E-10) ) { 513 if ( s < (1 - 1.0E-10) ) {
523 // 514 //
524 // This is the normal path: 515 // This is the normal path:
525 // 516 //
526 const double* oneOverNptr = oneOverN; 517 const double* oneOverNptr = oneOverN;
527 while( cdf <= s ) { 518 while( cdf <= s ) {
528 N2++ ; 519 N2++ ;
529 oneOverNptr++; 520 oneOverNptr++;
530 term *= ( deltaMu * (*oneOverNptr) ); 521 term *= ( deltaMu * (*oneOverNptr) );
531 cdf += term; 522 cdf += term;
532 } 523 }
533 } else { // s is almost 1... 524 } else { // s is almost 1...
534 while( cdf <= s ) { 525 while( cdf <= s ) {
535 N2++ ; 526 N2++ ;
536 term *= ( deltaMu / N2 ); 527 term *= ( deltaMu / N2 );
537 cdf += term; 528 cdf += term;
538 } 529 }
539 } // end of if ( s compared to (1 - 1.0E-10) 530 } // end of if ( s compared to (1 - 1.0E-10) )
540 531
541 // >>> 9 <<< 532 // >>> 9 <<<
542 // The result is the sum of those two devia 533 // The result is the sum of those two deviates
543 534
544 // if (DBG_small) { 535 // if (DBG_small) {
545 // std::cout << N2 << " " << N1+N2 << 536 // std::cout << N2 << " " << N1+N2 << "\n";
546 // DBG_small = false; 537 // DBG_small = false;
547 // } 538 // }
548 539
549 return N1 + N2; 540 return N1 + N2;
550 541
551 } // poissonDeviate() 542 } // poissonDeviate()
552 543
553 std::ostream & RandPoissonQ::put ( std::ostrea 544 std::ostream & RandPoissonQ::put ( std::ostream & os ) const {
554 long pr=os.precision(20); << 545 int pr=os.precision(20);
555 std::vector<unsigned long> t(2); 546 std::vector<unsigned long> t(2);
556 os << " " << name() << "\n"; 547 os << " " << name() << "\n";
557 os << "Uvec" << "\n"; 548 os << "Uvec" << "\n";
558 t = DoubConv::dto2longs(a0); 549 t = DoubConv::dto2longs(a0);
559 os << a0 << " " << t[0] << " " << t[1] << "\ 550 os << a0 << " " << t[0] << " " << t[1] << "\n";
560 t = DoubConv::dto2longs(a1); 551 t = DoubConv::dto2longs(a1);
561 os << a1 << " " << t[0] << " " << t[1] << "\ 552 os << a1 << " " << t[0] << " " << t[1] << "\n";
562 t = DoubConv::dto2longs(a2); 553 t = DoubConv::dto2longs(a2);
563 os << a2 << " " << t[0] << " " << t[1] << "\ 554 os << a2 << " " << t[0] << " " << t[1] << "\n";
564 t = DoubConv::dto2longs(sigma); 555 t = DoubConv::dto2longs(sigma);
565 os << sigma << " " << t[0] << " " << t[1] << 556 os << sigma << " " << t[0] << " " << t[1] << "\n";
566 RandPoisson::put(os); 557 RandPoisson::put(os);
567 os.precision(pr); 558 os.precision(pr);
568 return os; 559 return os;
569 #ifdef REMOVED 560 #ifdef REMOVED
570 int pr=os.precision(20); 561 int pr=os.precision(20);
571 os << " " << name() << "\n"; 562 os << " " << name() << "\n";
572 os << a0 << " " << a1 << " " << a2 << "\n"; 563 os << a0 << " " << a1 << " " << a2 << "\n";
573 os << sigma << "\n"; 564 os << sigma << "\n";
574 RandPoisson::put(os); 565 RandPoisson::put(os);
575 os.precision(pr); 566 os.precision(pr);
576 return os; 567 return os;
577 #endif 568 #endif
578 } 569 }
579 570
580 std::istream & RandPoissonQ::get ( std::istrea 571 std::istream & RandPoissonQ::get ( std::istream & is ) {
581 std::string inName; 572 std::string inName;
582 is >> inName; 573 is >> inName;
583 if (inName != name()) { 574 if (inName != name()) {
584 is.clear(std::ios::badbit | is.rdstate()); 575 is.clear(std::ios::badbit | is.rdstate());
585 std::cerr << "Mismatch when expecting to r 576 std::cerr << "Mismatch when expecting to read state of a "
586 << name() << " distribution\n" 577 << name() << " distribution\n"
587 << "Name found was " << inName 578 << "Name found was " << inName
588 << "\nistream is left in the badbit st 579 << "\nistream is left in the badbit state\n";
589 return is; 580 return is;
590 } 581 }
591 if (possibleKeywordInput(is, "Uvec", a0)) { 582 if (possibleKeywordInput(is, "Uvec", a0)) {
592 std::vector<unsigned long> t(2); 583 std::vector<unsigned long> t(2);
593 is >> a0 >> t[0] >> t[1]; a0 = DoubConv::l 584 is >> a0 >> t[0] >> t[1]; a0 = DoubConv::longs2double(t);
594 is >> a1 >> t[0] >> t[1]; a1 = DoubConv::l 585 is >> a1 >> t[0] >> t[1]; a1 = DoubConv::longs2double(t);
595 is >> a2 >> t[0] >> t[1]; a2 = DoubConv::l 586 is >> a2 >> t[0] >> t[1]; a2 = DoubConv::longs2double(t);
596 is >> sigma >> t[0] >> t[1]; sigma = DoubC 587 is >> sigma >> t[0] >> t[1]; sigma = DoubConv::longs2double(t);
597 RandPoisson::get(is); 588 RandPoisson::get(is);
598 return is; 589 return is;
599 } 590 }
600 // is >> a0 encompassed by possibleKeywordIn 591 // is >> a0 encompassed by possibleKeywordInput
601 is >> a1 >> a2 >> sigma; 592 is >> a1 >> a2 >> sigma;
602 RandPoisson::get(is); 593 RandPoisson::get(is);
603 return is; 594 return is;
604 } 595 }
605 596
606 } // namespace CLHEP 597 } // namespace CLHEP
607 598
608 599