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