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25 // 25 //
26 // G4SimplexDownhill inline methods implementa << 26 //
>> 27 // $Id$
27 // 28 //
28 // Author: Tatsumi Koi (SLAC/SCCS), 2007 29 // Author: Tatsumi Koi (SLAC/SCCS), 2007
29 // ------------------------------------------- 30 // --------------------------------------------------------------------------
30 31
31 #include <cfloat> <<
32 #include <iostream> 32 #include <iostream>
33 #include <numeric> 33 #include <numeric>
34 << 34 #include <cfloat>
35 template <class T> << 35
36 void G4SimplexDownhill<T>::init() << 36 template<class T> void G4SimplexDownhill<T>::init()
37 { 37 {
38 alpha = 2.0; // refrection coefficient: 0 << 38 alpha = 2.0; // refrection coefficient: 0 < alpha
39 beta = 0.5; // contraction coefficient: << 39 beta = 0.5; // contraction coefficient: 0 < beta < 1
40 gamma = 2.0; // expantion coefficient: 1 < << 40 gamma = 2.0; // expantion coefficient: 1 < gamma
41 << 41
42 maximum_no_trial = 10000; << 42 maximum_no_trial = 10000;
43 max_se = FLT_MIN; << 43 max_se = FLT_MIN;
44 // max_ratio = FLT_EPSILON/1; << 44 //max_ratio = FLT_EPSILON/1;
45 max_ratio = DBL_EPSILON / 1; << 45 max_ratio = DBL_EPSILON/1;
46 minimized = false; << 46 minimized = false;
47 } 47 }
48 48
>> 49
49 /* 50 /*
50 51
51 void G4SimplexDownhill<class T>:: 52 void G4SimplexDownhill<class T>::
52 SetFunction( G4int n , G4double( *afunc )( std << 53 SetFunction( G4int n , G4double( *afunc )( std::vector < G4double > ) )
53 { 54 {
54 numberOfVariable = n; << 55 numberOfVariable = n;
55 theFunction = afunc; 56 theFunction = afunc;
56 minimized = false; << 57 minimized = false;
57 } 58 }
58 59
59 */ 60 */
60 61
61 template <class T> << 62
>> 63 template<class T>
62 G4double G4SimplexDownhill<T>::GetMinimum() 64 G4double G4SimplexDownhill<T>::GetMinimum()
63 { 65 {
64 initialize(); <<
65 66
66 // First Tryal; << 67 initialize();
67 68
68 // G4cout << "Begin First Trials" << G4endl; << 69 // First Tryal;
69 doDownhill(); << 70
70 // G4cout << "End First Trials" << G4endl; << 71 //G4cout << "Begin First Trials" << G4endl;
71 << 72 doDownhill();
72 auto it_minh = std::min_element(currentHeigh << 73 //G4cout << "End First Trials" << G4endl;
73 G4int imin = 0; << 74
74 G4int i = 0; << 75 std::vector< G4double >::iterator it_minh =
75 for(auto it = currentHeights.cbegin(); it != << 76 std::min_element( currentHeights.begin() , currentHeights.end() );
76 { << 77 G4int imin = -1;
77 if(it == it_minh) << 78 G4int i = 0;
78 { << 79 for ( std::vector< G4double >::iterator it = currentHeights.begin();
79 imin = i; << 80 it != currentHeights.end(); it++ )
80 } << 81 {
81 ++i; << 82 if ( it == it_minh )
82 } << 83 {
83 minimumPoint = currentSimplex[imin]; << 84 imin = i;
>> 85 }
>> 86 i++;
>> 87 }
>> 88 minimumPoint = currentSimplex[ imin ];
84 89
85 // Second Trial << 90 // Second Trial
86 91
87 // std::vector< G4double > minimumPoint = cu << 92 //std::vector< G4double > minimumPoint = currentSimplex[ 0 ];
88 initialize(); << 93 initialize();
89 94
90 currentSimplex[numberOfVariable] = minimumPo << 95 currentSimplex[ numberOfVariable ] = minimumPoint;
91 96
92 // G4cout << "Begin Second Trials" << G4endl << 97 //G4cout << "Begin Second Trials" << G4endl;
93 doDownhill(); << 98 doDownhill();
94 // G4cout << "End Second Trials" << G4endl; << 99 //G4cout << "End Second Trials" << G4endl;
>> 100
>> 101 G4double sum = std::accumulate( currentHeights.begin() ,
>> 102 currentHeights.end() , 0.0 );
>> 103 G4double average = sum/(numberOfVariable+1);
>> 104 G4double minimum = average;
95 105
96 G4double sum = << 106 minimized = true;
97 std::accumulate(currentHeights.begin(), cu <<
98 G4double average = sum / (numberOfVariable + <<
99 G4double minimum = average; <<
100 107
101 minimized = true; << 108 return minimum;
102 109
103 return minimum; <<
104 } 110 }
105 111
106 template <class T> << 112
>> 113
>> 114 template<class T>
107 void G4SimplexDownhill<T>::initialize() 115 void G4SimplexDownhill<T>::initialize()
108 { 116 {
109 currentSimplex.resize(numberOfVariable + 1); <<
110 currentHeights.resize(numberOfVariable + 1); <<
111 117
112 for(G4int i = 0; i < numberOfVariable; ++i) << 118 currentSimplex.resize( numberOfVariable+1 );
113 { << 119 currentHeights.resize( numberOfVariable+1 );
114 std::vector<G4double> avec(numberOfVariabl << 120
115 avec[i] = 1.0; << 121 for ( G4int i = 0 ; i < numberOfVariable ; i++ )
116 currentSimplex[i] = std::move(avec); << 122 {
117 } << 123 std::vector< G4double > avec ( numberOfVariable , 0.0 );
118 << 124 avec[ i ] = 1.0;
119 // std::vector< G4double > avec ( numberOfVa << 125 currentSimplex[ i ] = avec;
120 std::vector<G4double> avec(numberOfVariable, << 126 }
121 currentSimplex[numberOfVariable] = std::move << 127
>> 128 //std::vector< G4double > avec ( numberOfVariable , 0.0 );
>> 129 std::vector< G4double > avec ( numberOfVariable , 1 );
>> 130 currentSimplex[ numberOfVariable ] = avec;
>> 131
122 } 132 }
123 133
124 template <class T> << 134
>> 135
>> 136 template<class T>
125 void G4SimplexDownhill<T>::calHeights() 137 void G4SimplexDownhill<T>::calHeights()
126 { 138 {
127 for(G4int i = 0; i <= numberOfVariable; ++i) <<
128 { <<
129 currentHeights[i] = getValue(currentSimple <<
130 } <<
131 } <<
132 <<
133 template <class T> <<
134 std::vector<G4double> G4SimplexDownhill<T>::ca <<
135 { <<
136 std::vector<G4double> centroid(numberOfVaria <<
137 <<
138 G4int i = 0; <<
139 for(const auto & it : currentSimplex) <<
140 { <<
141 if(i != ih) <<
142 { <<
143 for(G4int j = 0; j < numberOfVariable; + <<
144 { <<
145 centroid[j] += it[j] / numberOfVariabl <<
146 } <<
147 } <<
148 ++i; <<
149 } <<
150 139
151 return centroid; << 140 for ( G4int i = 0 ; i <= numberOfVariable ; i++ )
>> 141 {
>> 142 currentHeights[i] = getValue ( currentSimplex[i] );
>> 143 }
>> 144
152 } 145 }
153 146
154 template <class T> << 147
155 std::vector<G4double> G4SimplexDownhill<T>::ge << 148
156 std::vector<G4double> p, std::vector<G4doubl << 149 template<class T>
>> 150 std::vector< G4double > G4SimplexDownhill<T>::calCentroid( G4int ih )
157 { 151 {
158 // G4cout << "Reflection" << G4endl; <<
159 152
160 std::vector<G4double> reflectionP(numberOfVa << 153 std::vector< G4double > centroid ( numberOfVariable , 0.0 );
161 154
162 for(G4int i = 0; i < numberOfVariable; ++i) << 155 G4int i = 0;
163 { << 156 for ( std::vector< std::vector< G4double > >::iterator
164 reflectionP[i] = (1 + alpha) * centroid[i] << 157 it = currentSimplex.begin(); it != currentSimplex.end() ; it++ )
165 } << 158 {
>> 159 if ( i != ih )
>> 160 {
>> 161 for ( G4int j = 0 ; j < numberOfVariable ; j++ )
>> 162 {
>> 163 centroid[j] += (*it)[j]/numberOfVariable;
>> 164 }
>> 165 }
>> 166 i++;
>> 167 }
166 168
167 return reflectionP; << 169 return centroid;
168 } 170 }
169 171
170 template <class T> << 172
171 std::vector<G4double> G4SimplexDownhill<T>::ge << 173
172 std::vector<G4double> p, std::vector<G4doubl << 174 template<class T>
>> 175 std::vector< G4double > G4SimplexDownhill<T>::
>> 176 getReflectionPoint( std::vector< G4double > p ,
>> 177 std::vector< G4double > centroid )
173 { 178 {
174 // G4cout << "Expantion" << G4endl; << 179 //G4cout << "Reflection" << G4endl;
>> 180
>> 181 std::vector< G4double > reflectionP ( numberOfVariable , 0.0 );
>> 182
>> 183 for ( G4int i = 0 ; i < numberOfVariable ; i++ )
>> 184 {
>> 185 reflectionP[ i ] = ( 1 + alpha ) * centroid[ i ] - alpha * p[ i ];
>> 186 }
>> 187
>> 188 return reflectionP;
>> 189 }
175 190
176 std::vector<G4double> expansionP(numberOfVar <<
177 191
178 for(G4int i = 0; i < numberOfVariable; ++i) <<
179 { <<
180 expansionP[i] = (1 - gamma) * centroid[i] <<
181 } <<
182 192
183 return expansionP; << 193 template<class T>
>> 194 std::vector< G4double > G4SimplexDownhill<T>::
>> 195 getExpansionPoint( std::vector< G4double > p ,
>> 196 std::vector< G4double > centroid )
>> 197 {
>> 198 //G4cout << "Expantion" << G4endl;
>> 199
>> 200 std::vector< G4double > expansionP ( numberOfVariable , 0.0 );
>> 201
>> 202 for ( G4int i = 0 ; i < numberOfVariable ; i++ )
>> 203 {
>> 204 expansionP[i] = ( 1 - gamma ) * centroid[i] + gamma * p[i];
>> 205 }
>> 206
>> 207 return expansionP;
184 } 208 }
185 209
186 template <class T> << 210 template<class T>
187 std::vector<G4double> G4SimplexDownhill<T>::ge << 211 std::vector< G4double > G4SimplexDownhill<T>::
188 std::vector<G4double> p, std::vector<G4doubl << 212 getContractionPoint( std::vector< G4double > p ,
>> 213 std::vector< G4double > centroid )
189 { 214 {
190 std::vector<G4double> contractionP(numberOfV << 215 //G4cout << "Contraction" << G4endl;
191 216
192 for(G4int i = 0; i < numberOfVariable; ++i) << 217 std::vector< G4double > contractionP ( numberOfVariable , 0.0 );
193 { <<
194 contractionP[i] = (1 - beta) * centroid[i] <<
195 } <<
196 218
197 return contractionP; << 219 for ( G4int i = 0 ; i < numberOfVariable ; i++ )
>> 220 {
>> 221 contractionP[i] = ( 1 - beta ) * centroid[i] + beta * p[i];
>> 222 }
>> 223
>> 224 return contractionP;
198 } 225 }
199 226
200 template <class T> << 227
>> 228
>> 229 template<class T>
201 G4bool G4SimplexDownhill<T>::isItGoodEnough() 230 G4bool G4SimplexDownhill<T>::isItGoodEnough()
202 { 231 {
203 G4double sum = << 232 G4bool result = false;
204 std::accumulate(currentHeights.begin(), cu << 233
205 G4double average = sum / (numberOfVariable + << 234 G4double sum = std::accumulate( currentHeights.begin() ,
206 << 235 currentHeights.end() , 0.0 );
207 G4double delta = 0.0; << 236 G4double average = sum/(numberOfVariable+1);
208 for(G4int i = 0; i <= numberOfVariable; ++i) << 237 //G4cout << "average " << average << G4endl;
209 { << 238
210 delta += std::abs(currentHeights[i] - aver << 239 G4double delta = 0.0;
211 } << 240 for ( G4int i = 0 ; i <= numberOfVariable ; i++ )
212 << 241 {
213 G4bool result = false; << 242 delta += std::abs ( currentHeights[ i ] - average );
214 if (average > 0.0) << 243 }
215 { << 244 //G4cout << "ratio of delta to average is "
216 result = ((delta / (numberOfVariable + 1) << 245 // << delta / (numberOfVariable+1) / average << G4endl;
217 } << 246
218 return result; << 247 if ( delta/(numberOfVariable+1)/average < max_ratio )
>> 248 {
>> 249 result = true;
>> 250 }
>> 251
>> 252 /*
>> 253 G4double sigma = 0.0;
>> 254 G4cout << "average " << average << G4endl;
>> 255 for ( G4int i = 0 ; i <= numberOfVariable ; i++ )
>> 256 {
>> 257 sigma += ( currentHeights[ i ] - average )
>> 258 *( currentHeights[ i ] - average );
>> 259 }
>> 260
>> 261 G4cout << "standard error of hs "
>> 262 << std::sqrt ( sigma ) / (numberOfVariable+1) << G4endl;
>> 263 if ( std::sqrt ( sigma ) / (numberOfVariable+1) < max_se )
>> 264 {
>> 265 result = true;
>> 266 }
>> 267 */
>> 268
>> 269 return result;
219 } 270 }
220 271
221 template <class T> << 272
>> 273
>> 274 template<class T>
222 void G4SimplexDownhill<T>::doDownhill() 275 void G4SimplexDownhill<T>::doDownhill()
223 { 276 {
224 G4int nth_trial = 0; <<
225 277
226 while(nth_trial < maximum_no_trial) << 278 G4int nth_trial = 0;
227 { <<
228 calHeights(); <<
229 <<
230 if(isItGoodEnough()) <<
231 { <<
232 break; <<
233 } <<
234 <<
235 auto it_maxh = std::max_element(currentHei <<
236 auto it_minh = std::min_element(currentHei <<
237 279
238 G4double h_H = *it_maxh; << 280 while ( nth_trial < maximum_no_trial )
239 G4double h_L = *it_minh; << 281 {
240 282
241 G4int ih = 0; << 283 /*
242 G4int il = 0; << 284 G4cout << "Begining " << nth_trial << "th trial " << G4endl;
243 G4double h_H2 = 0.0; << 285 for ( G4int j = 0 ; j <= numberOfVariable ; j++ )
244 G4int i = 0; <<
245 for(auto it = currentHeights.cbegin(); it <<
246 { <<
247 if(it == it_maxh) <<
248 { 286 {
249 ih = i; << 287 G4cout << "SimplexPoint " << j << ": ";
>> 288 for ( G4int i = 0 ; i < numberOfVariable ; i++ )
>> 289 {
>> 290 G4cout << currentSimplex[j][i]
>> 291 << " ";
>> 292 }
>> 293 G4cout << G4endl;
250 } 294 }
251 else << 295 */
252 { << 296
253 h_H2 = std::max(h_H2, *it); << 297 calHeights();
>> 298
>> 299 if ( isItGoodEnough() )
>> 300 {
>> 301 break;
254 } 302 }
255 303
256 if(it == it_minh) << 304 std::vector< G4double >::iterator it_maxh =
>> 305 std::max_element( currentHeights.begin() , currentHeights.end() );
>> 306 std::vector< G4double >::iterator it_minh =
>> 307 std::min_element( currentHeights.begin() , currentHeights.end() );;
>> 308
>> 309 G4double h_H = *it_maxh;
>> 310 G4double h_L = *it_minh;
>> 311
>> 312 G4int ih = 0;;
>> 313 G4int il = 0;
>> 314 G4double h_H2 =0.0;
>> 315 G4int i = 0;
>> 316 for ( std::vector< G4double >::iterator
>> 317 it = currentHeights.begin(); it != currentHeights.end(); it++ )
257 { 318 {
258 il = i; << 319 if ( it == it_maxh )
>> 320 {
>> 321 ih = i;
>> 322 }
>> 323 else
>> 324 {
>> 325 h_H2 = std::max( h_H2 , *it );
>> 326 }
>> 327
>> 328 if ( it == it_minh )
>> 329 {
>> 330 il = i;
>> 331 }
>> 332 i++;
259 } 333 }
260 ++i; <<
261 } <<
262 334
263 std::vector<G4double> centroidPoint = calC << 335 //G4cout << "max " << h_H << " " << ih << G4endl;
>> 336 //G4cout << "max-dash " << h_H2 << G4endl;
>> 337 //G4cout << "min " << h_L << " " << il << G4endl;
264 338
265 // REFLECTION << 339 std::vector< G4double > centroidPoint = calCentroid ( ih );
266 std::vector<G4double> reflectionPoint = <<
267 getReflectionPoint(currentSimplex[ih], c <<
268 340
269 G4double h = getValue(reflectionPoint); << 341 // REFLECTION
>> 342 std::vector< G4double > reflectionPoint =
>> 343 getReflectionPoint( currentSimplex[ ih ] , centroidPoint );
270 344
271 if(h <= h_L) << 345 G4double h = getValue( reflectionPoint );
272 { <<
273 // EXPANSION <<
274 std::vector<G4double> expansionPoint = <<
275 getExpansionPoint(reflectionPoint, std <<
276 G4double hh = getValue(expansionPoint); <<
277 346
278 if(hh <= h_L) << 347 if ( h <= h_L )
279 { <<
280 // Replace <<
281 currentSimplex[ih] = std::move(expansi <<
282 // G4cout << "A" << G4endl; <<
283 } <<
284 else <<
285 { <<
286 // Replace <<
287 currentSimplex[ih] = std::move(reflect <<
288 // G4cout << "B1" << G4endl; <<
289 } <<
290 } <<
291 else <<
292 { <<
293 if(h <= h_H2) <<
294 { 348 {
295 // Replace << 349 // EXPANSION
296 currentSimplex[ih] = std::move(reflect << 350 std::vector< G4double > expansionPoint =
297 // G4cout << "B2" << G4endl; << 351 getExpansionPoint( reflectionPoint , centroidPoint );
298 } << 352 G4double hh = getValue( expansionPoint );
299 else << 353
>> 354 if ( hh <= h_L )
>> 355 {
>> 356 // Replace
>> 357 currentSimplex[ ih ] = expansionPoint;
>> 358 //G4cout << "A" << G4endl;
>> 359 }
>> 360 else
>> 361 {
>> 362 // Replace
>> 363 currentSimplex[ ih ] = reflectionPoint;
>> 364 //G4cout << "B1" << G4endl;
>> 365 }
>> 366 }
>> 367 else
300 { 368 {
301 if(h <= h_H) << 369 if ( h <= h_H2 )
302 { << 370 {
303 // Replace << 371 // Replace
304 currentSimplex[ih] = std::move(refle << 372 currentSimplex[ ih ] = reflectionPoint;
305 // G4cout << "BC" << G4endl; << 373 //G4cout << "B2" << G4endl;
306 } << 374 }
307 // CONTRACTION << 375 else
308 std::vector<G4double> contractionPoint << 376 {
309 getContractionPoint(currentSimplex[i << 377 if ( h <= h_H )
310 G4double hh = getValue(contractionPoin <<
311 if(hh <= h_H) <<
312 { <<
313 // Replace <<
314 currentSimplex[ih] = std::move(contr <<
315 // G4cout << "C" << G4endl; <<
316 } <<
317 else <<
318 { <<
319 // Replace <<
320 for(G4int j = 0; j <= numberOfVariab <<
321 { <<
322 std::vector<G4double> vec(numberOf <<
323 for(G4int k = 0; k < numberOfVaria <<
324 { 378 {
325 vec[k] = (currentSimplex[j][k] + << 379 // Replace
>> 380 currentSimplex[ ih ] = reflectionPoint;
>> 381 //G4cout << "BC" << G4endl;
326 } 382 }
327 currentSimplex[j] = std::move(vec) << 383 // CONTRACTION
328 } << 384 std::vector< G4double > contractionPoint =
329 } << 385 getContractionPoint( currentSimplex[ ih ] , centroidPoint );
>> 386 G4double hh = getValue( contractionPoint );
>> 387 if ( hh <= h_H )
>> 388 {
>> 389 // Replace
>> 390 currentSimplex[ ih ] = contractionPoint;
>> 391 //G4cout << "C" << G4endl;
>> 392 }
>> 393 else
>> 394 {
>> 395 // Replace
>> 396 for ( G4int j = 0 ; j <= numberOfVariable ; j++ )
>> 397 {
>> 398 std::vector< G4double > vec ( numberOfVariable , 0.0 );
>> 399 for ( G4int k = 0 ; k < numberOfVariable ; k++ )
>> 400 {
>> 401 vec[ k ] = ( currentSimplex[ j ][ k ]
>> 402 + currentSimplex[ il ][ k ] ) / 2.0;
>> 403 }
>> 404 currentSimplex[ j ] = vec;
>> 405 }
>> 406 //G4cout << "D" << G4endl;
>> 407 }
>> 408 }
>> 409
330 } 410 }
331 } <<
332 411
333 ++nth_trial; << 412 nth_trial++;
334 } << 413 }
335 } 414 }
336 415
337 template <class T> <<
338 std::vector<G4double> G4SimplexDownhill<T>::Ge <<
339 { <<
340 if(!minimized) <<
341 { <<
342 GetMinimum(); <<
343 } <<
344 <<
345 auto it_minh = std::min_element(currentHeigh <<
346 <<
347 G4int imin = 0; <<
348 G4int i = 0; <<
349 for(auto it = currentHeights.cbegin(); it != <<
350 { <<
351 if(it == it_minh) <<
352 { <<
353 imin = i; <<
354 } <<
355 ++i; <<
356 } <<
357 minimumPoint = currentSimplex[imin]; <<
358 416
359 return minimumPoint; << 417
>> 418 template<class T>
>> 419 std::vector< G4double > G4SimplexDownhill<T>::GetMinimumPoint()
>> 420 {
>> 421 if ( minimized != true )
>> 422 {
>> 423 GetMinimum();
>> 424 }
>> 425
>> 426 std::vector< G4double >::iterator it_minh =
>> 427 std::min_element( currentHeights.begin() , currentHeights.end() );;
>> 428 G4int imin = -1;
>> 429 G4int i = 0;
>> 430 for ( std::vector< G4double >::iterator
>> 431 it = currentHeights.begin(); it != currentHeights.end(); it++ )
>> 432 {
>> 433 if ( it == it_minh )
>> 434 {
>> 435 imin = i;
>> 436 }
>> 437 i++;
>> 438 }
>> 439 minimumPoint = currentSimplex[ imin ];
>> 440
>> 441 return minimumPoint;
360 } 442 }
361 443