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25 // 25 //
26 // G4SimplexDownhill inline methods implementa << 26 //
>> 27 // $Id: G4SimplexDownhill.icc,v 1.2 2007/05/11 13:05:53 gcosmo Exp $
>> 28 // GEANT4 tag $Name: geant4-09-02 $
27 // 29 //
28 // Author: Tatsumi Koi (SLAC/SCCS), 2007 30 // Author: Tatsumi Koi (SLAC/SCCS), 2007
29 // ------------------------------------------- 31 // --------------------------------------------------------------------------
30 32
31 #include <cfloat> <<
32 #include <iostream> 33 #include <iostream>
33 #include <numeric> 34 #include <numeric>
34 << 35 #include <cfloat>
35 template <class T> << 36
36 void G4SimplexDownhill<T>::init() << 37 template<class T> void G4SimplexDownhill<T>::init()
37 { 38 {
38 alpha = 2.0; // refrection coefficient: 0 << 39 alpha = 2.0; // refrection coefficient: 0 < alpha
39 beta = 0.5; // contraction coefficient: << 40 beta = 0.5; // contraction coefficient: 0 < beta < 1
40 gamma = 2.0; // expantion coefficient: 1 < << 41 gamma = 2.0; // expantion coefficient: 1 < gamma
41 << 42
42 maximum_no_trial = 10000; << 43 maximum_no_trial = 10000;
43 max_se = FLT_MIN; << 44 max_se = FLT_MIN;
44 // max_ratio = FLT_EPSILON/1; << 45 //max_ratio = FLT_EPSILON/1;
45 max_ratio = DBL_EPSILON / 1; << 46 max_ratio = DBL_EPSILON/1;
46 minimized = false; << 47 minimized = false;
47 } 48 }
48 49
>> 50
49 /* 51 /*
50 52
51 void G4SimplexDownhill<class T>:: 53 void G4SimplexDownhill<class T>::
52 SetFunction( G4int n , G4double( *afunc )( std << 54 SetFunction( G4int n , G4double( *afunc )( std::vector < G4double > ) )
53 { 55 {
54 numberOfVariable = n; << 56 numberOfVariable = n;
55 theFunction = afunc; 57 theFunction = afunc;
56 minimized = false; << 58 minimized = false;
57 } 59 }
58 60
59 */ 61 */
60 62
61 template <class T> << 63
>> 64 template<class T>
62 G4double G4SimplexDownhill<T>::GetMinimum() 65 G4double G4SimplexDownhill<T>::GetMinimum()
63 { 66 {
64 initialize(); <<
65 67
66 // First Tryal; << 68 initialize();
67 69
68 // G4cout << "Begin First Trials" << G4endl; << 70 // First Tryal;
69 doDownhill(); << 71
70 // G4cout << "End First Trials" << G4endl; << 72 //G4cout << "Begin First Trials" << G4endl;
71 << 73 doDownhill();
72 auto it_minh = std::min_element(currentHeigh << 74 //G4cout << "End First Trials" << G4endl;
73 G4int imin = 0; << 75
74 G4int i = 0; << 76 std::vector< G4double >::iterator it_minh =
75 for(auto it = currentHeights.cbegin(); it != << 77 std::min_element( currentHeights.begin() , currentHeights.end() );
76 { << 78 G4int imin = -1;
77 if(it == it_minh) << 79 G4int i = 0;
78 { << 80 for ( std::vector< G4double >::iterator it = currentHeights.begin();
79 imin = i; << 81 it != currentHeights.end(); it++ )
80 } << 82 {
81 ++i; << 83 if ( it == it_minh )
82 } << 84 {
83 minimumPoint = currentSimplex[imin]; << 85 imin = i;
>> 86 }
>> 87 i++;
>> 88 }
>> 89 std::vector< G4double > minimumPoint = currentSimplex[ imin ];
84 90
85 // Second Trial << 91 // Second Trial
86 92
87 // std::vector< G4double > minimumPoint = cu << 93 //std::vector< G4double > minimumPoint = currentSimplex[ 0 ];
88 initialize(); << 94 initialize();
89 95
90 currentSimplex[numberOfVariable] = minimumPo << 96 currentSimplex[ numberOfVariable ] = minimumPoint;
91 97
92 // G4cout << "Begin Second Trials" << G4endl << 98 //G4cout << "Begin Second Trials" << G4endl;
93 doDownhill(); << 99 doDownhill();
94 // G4cout << "End Second Trials" << G4endl; << 100 //G4cout << "End Second Trials" << G4endl;
>> 101
>> 102 G4double sum = std::accumulate( currentHeights.begin() ,
>> 103 currentHeights.end() , 0.0 );
>> 104 G4double average = sum/(numberOfVariable+1);
>> 105 G4double minimum = average;
95 106
96 G4double sum = << 107 minimized = true;
97 std::accumulate(currentHeights.begin(), cu <<
98 G4double average = sum / (numberOfVariable + <<
99 G4double minimum = average; <<
100 108
101 minimized = true; << 109 return minimum;
102 110
103 return minimum; <<
104 } 111 }
105 112
106 template <class T> << 113
>> 114
>> 115 template<class T>
107 void G4SimplexDownhill<T>::initialize() 116 void G4SimplexDownhill<T>::initialize()
108 { 117 {
109 currentSimplex.resize(numberOfVariable + 1); <<
110 currentHeights.resize(numberOfVariable + 1); <<
111 118
112 for(G4int i = 0; i < numberOfVariable; ++i) << 119 currentSimplex.resize( numberOfVariable+1 );
113 { << 120 currentHeights.resize( numberOfVariable+1 );
114 std::vector<G4double> avec(numberOfVariabl << 121
115 avec[i] = 1.0; << 122 for ( G4int i = 0 ; i < numberOfVariable ; i++ )
116 currentSimplex[i] = std::move(avec); << 123 {
117 } << 124 std::vector< G4double > avec ( numberOfVariable , 0.0 );
118 << 125 avec[ i ] = 1.0;
119 // std::vector< G4double > avec ( numberOfVa << 126 currentSimplex[ i ] = avec;
120 std::vector<G4double> avec(numberOfVariable, << 127 }
121 currentSimplex[numberOfVariable] = std::move << 128
>> 129 //std::vector< G4double > avec ( numberOfVariable , 0.0 );
>> 130 std::vector< G4double > avec ( numberOfVariable , 1 );
>> 131 currentSimplex[ numberOfVariable ] = avec;
>> 132
122 } 133 }
123 134
124 template <class T> << 135
>> 136
>> 137 template<class T>
125 void G4SimplexDownhill<T>::calHeights() 138 void G4SimplexDownhill<T>::calHeights()
126 { 139 {
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 } <<
150 140
151 return centroid; << 141 for ( G4int i = 0 ; i <= numberOfVariable ; i++ )
>> 142 {
>> 143 currentHeights[i] = getValue ( currentSimplex[i] );
>> 144 }
>> 145
152 } 146 }
153 147
154 template <class T> << 148
155 std::vector<G4double> G4SimplexDownhill<T>::ge << 149
156 std::vector<G4double> p, std::vector<G4doubl << 150 template<class T>
>> 151 std::vector< G4double > G4SimplexDownhill<T>::calCentroid( G4int ih )
157 { 152 {
158 // G4cout << "Reflection" << G4endl; <<
159 153
160 std::vector<G4double> reflectionP(numberOfVa << 154 std::vector< G4double > centroid ( numberOfVariable , 0.0 );
161 155
162 for(G4int i = 0; i < numberOfVariable; ++i) << 156 G4int i = 0;
163 { << 157 for ( std::vector< std::vector< G4double > >::iterator
164 reflectionP[i] = (1 + alpha) * centroid[i] << 158 it = currentSimplex.begin(); it != currentSimplex.end() ; it++ )
165 } << 159 {
>> 160 if ( i != ih )
>> 161 {
>> 162 for ( G4int j = 0 ; j < numberOfVariable ; j++ )
>> 163 {
>> 164 centroid[j] += (*it)[j]/numberOfVariable;
>> 165 }
>> 166 }
>> 167 i++;
>> 168 }
166 169
167 return reflectionP; << 170 return centroid;
168 } 171 }
169 172
170 template <class T> << 173
171 std::vector<G4double> G4SimplexDownhill<T>::ge << 174
172 std::vector<G4double> p, std::vector<G4doubl << 175 template<class T>
>> 176 std::vector< G4double > G4SimplexDownhill<T>::
>> 177 getReflectionPoint( std::vector< G4double > p ,
>> 178 std::vector< G4double > centroid )
173 { 179 {
174 // G4cout << "Expantion" << G4endl; << 180 //G4cout << "Reflection" << G4endl;
>> 181
>> 182 std::vector< G4double > reflectionP ( numberOfVariable , 0.0 );
>> 183
>> 184 for ( G4int i = 0 ; i < numberOfVariable ; i++ )
>> 185 {
>> 186 reflectionP[ i ] = ( 1 + alpha ) * centroid[ i ] - alpha * p[ i ];
>> 187 }
>> 188
>> 189 return reflectionP;
>> 190 }
175 191
176 std::vector<G4double> expansionP(numberOfVar <<
177 192
178 for(G4int i = 0; i < numberOfVariable; ++i) <<
179 { <<
180 expansionP[i] = (1 - gamma) * centroid[i] <<
181 } <<
182 193
183 return expansionP; << 194 template<class T>
>> 195 std::vector< G4double > G4SimplexDownhill<T>::
>> 196 getExpansionPoint( std::vector< G4double > p ,
>> 197 std::vector< G4double > centroid )
>> 198 {
>> 199 //G4cout << "Expantion" << G4endl;
>> 200
>> 201 std::vector< G4double > expansionP ( numberOfVariable , 0.0 );
>> 202
>> 203 for ( G4int i = 0 ; i < numberOfVariable ; i++ )
>> 204 {
>> 205 expansionP[i] = ( 1 - gamma ) * centroid[i] + gamma * p[i];
>> 206 }
>> 207
>> 208 return expansionP;
184 } 209 }
185 210
186 template <class T> << 211 template<class T>
187 std::vector<G4double> G4SimplexDownhill<T>::ge << 212 std::vector< G4double > G4SimplexDownhill<T>::
188 std::vector<G4double> p, std::vector<G4doubl << 213 getContractionPoint( std::vector< G4double > p ,
>> 214 std::vector< G4double > centroid )
189 { 215 {
190 std::vector<G4double> contractionP(numberOfV << 216 //G4cout << "Contraction" << G4endl;
191 217
192 for(G4int i = 0; i < numberOfVariable; ++i) << 218 std::vector< G4double > contractionP ( numberOfVariable , 0.0 );
193 { <<
194 contractionP[i] = (1 - beta) * centroid[i] <<
195 } <<
196 219
197 return contractionP; << 220 for ( G4int i = 0 ; i < numberOfVariable ; i++ )
>> 221 {
>> 222 contractionP[i] = ( 1 - beta ) * centroid[i] + beta * p[i];
>> 223 }
>> 224
>> 225 return contractionP;
198 } 226 }
199 227
200 template <class T> << 228
>> 229
>> 230 template<class T>
201 G4bool G4SimplexDownhill<T>::isItGoodEnough() 231 G4bool G4SimplexDownhill<T>::isItGoodEnough()
202 { 232 {
203 G4double sum = << 233 G4bool result = false;
204 std::accumulate(currentHeights.begin(), cu << 234
205 G4double average = sum / (numberOfVariable + << 235 G4double sum = std::accumulate( currentHeights.begin() ,
206 << 236 currentHeights.end() , 0.0 );
207 G4double delta = 0.0; << 237 G4double average = sum/(numberOfVariable+1);
208 for(G4int i = 0; i <= numberOfVariable; ++i) << 238 //G4cout << "average " << average << G4endl;
209 { << 239
210 delta += std::abs(currentHeights[i] - aver << 240 G4double delta = 0.0;
211 } << 241 for ( G4int i = 0 ; i <= numberOfVariable ; i++ )
212 << 242 {
213 G4bool result = false; << 243 delta += std::abs ( currentHeights[ i ] - average );
214 if (average > 0.0) << 244 }
215 { << 245 //G4cout << "ratio of delta to average is "
216 result = ((delta / (numberOfVariable + 1) << 246 // << delta / (numberOfVariable+1) / average << G4endl;
217 } << 247
218 return result; << 248 if ( delta/(numberOfVariable+1)/average < max_ratio )
>> 249 {
>> 250 result = true;
>> 251 }
>> 252
>> 253 /*
>> 254 G4double sigma = 0.0;
>> 255 G4cout << "average " << average << G4endl;
>> 256 for ( G4int i = 0 ; i <= numberOfVariable ; i++ )
>> 257 {
>> 258 sigma += ( currentHeights[ i ] - average )
>> 259 *( currentHeights[ i ] - average );
>> 260 }
>> 261
>> 262 G4cout << "standard error of hs "
>> 263 << std::sqrt ( sigma ) / (numberOfVariable+1) << G4endl;
>> 264 if ( std::sqrt ( sigma ) / (numberOfVariable+1) < max_se )
>> 265 {
>> 266 result = true;
>> 267 }
>> 268 */
>> 269
>> 270 return result;
219 } 271 }
220 272
221 template <class T> << 273
>> 274
>> 275 template<class T>
222 void G4SimplexDownhill<T>::doDownhill() 276 void G4SimplexDownhill<T>::doDownhill()
223 { 277 {
224 G4int nth_trial = 0; <<
225 278
226 while(nth_trial < maximum_no_trial) << 279 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 <<
237 280
238 G4double h_H = *it_maxh; << 281 while ( nth_trial < maximum_no_trial )
239 G4double h_L = *it_minh; << 282 {
240 283
241 G4int ih = 0; << 284 /*
242 G4int il = 0; << 285 G4cout << "Begining " << nth_trial << "th trial " << G4endl;
243 G4double h_H2 = 0.0; << 286 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 { 287 {
249 ih = i; << 288 G4cout << "SimplexPoint " << j << ": ";
>> 289 for ( G4int i = 0 ; i < numberOfVariable ; i++ )
>> 290 {
>> 291 G4cout << currentSimplex[j][i]
>> 292 << " ";
>> 293 }
>> 294 G4cout << G4endl;
250 } 295 }
251 else << 296 */
252 { << 297
253 h_H2 = std::max(h_H2, *it); << 298 calHeights();
>> 299
>> 300 if ( isItGoodEnough() )
>> 301 {
>> 302 break;
254 } 303 }
255 304
256 if(it == it_minh) << 305 std::vector< G4double >::iterator it_maxh =
>> 306 std::max_element( currentHeights.begin() , currentHeights.end() );
>> 307 std::vector< G4double >::iterator it_minh =
>> 308 std::min_element( currentHeights.begin() , currentHeights.end() );;
>> 309
>> 310 G4double h_H = *it_maxh;
>> 311 G4double h_L = *it_minh;
>> 312
>> 313 G4int ih = 0;;
>> 314 G4int il = 0;
>> 315 G4double h_H2 =0.0;
>> 316 G4int i = 0;
>> 317 for ( std::vector< G4double >::iterator
>> 318 it = currentHeights.begin(); it != currentHeights.end(); it++ )
257 { 319 {
258 il = i; << 320 if ( it == it_maxh )
>> 321 {
>> 322 ih = i;
>> 323 }
>> 324 else
>> 325 {
>> 326 h_H2 = std::max( h_H2 , *it );
>> 327 }
>> 328
>> 329 if ( it == it_minh )
>> 330 {
>> 331 il = i;
>> 332 }
>> 333 i++;
259 } 334 }
260 ++i; <<
261 } <<
262 335
263 std::vector<G4double> centroidPoint = calC << 336 //G4cout << "max " << h_H << " " << ih << G4endl;
>> 337 //G4cout << "max-dash " << h_H2 << G4endl;
>> 338 //G4cout << "min " << h_L << " " << il << G4endl;
264 339
265 // REFLECTION << 340 std::vector< G4double > centroidPoint = calCentroid ( ih );
266 std::vector<G4double> reflectionPoint = <<
267 getReflectionPoint(currentSimplex[ih], c <<
268 341
269 G4double h = getValue(reflectionPoint); << 342 // REFLECTION
>> 343 std::vector< G4double > reflectionPoint =
>> 344 getReflectionPoint( currentSimplex[ ih ] , centroidPoint );
270 345
271 if(h <= h_L) << 346 G4double h = getValue( reflectionPoint );
272 { <<
273 // EXPANSION <<
274 std::vector<G4double> expansionPoint = <<
275 getExpansionPoint(reflectionPoint, std <<
276 G4double hh = getValue(expansionPoint); <<
277 347
278 if(hh <= h_L) << 348 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 { 349 {
295 // Replace << 350 // EXPANSION
296 currentSimplex[ih] = std::move(reflect << 351 std::vector< G4double > expansionPoint =
297 // G4cout << "B2" << G4endl; << 352 getExpansionPoint( reflectionPoint , centroidPoint );
298 } << 353 G4double hh = getValue( expansionPoint );
299 else << 354
>> 355 if ( hh <= h_L )
>> 356 {
>> 357 // Replace
>> 358 currentSimplex[ ih ] = expansionPoint;
>> 359 //G4cout << "A" << G4endl;
>> 360 }
>> 361 else
>> 362 {
>> 363 // Replace
>> 364 currentSimplex[ ih ] = reflectionPoint;
>> 365 //G4cout << "B1" << G4endl;
>> 366 }
>> 367 }
>> 368 else
300 { 369 {
301 if(h <= h_H) << 370 if ( h <= h_H2 )
302 { << 371 {
303 // Replace << 372 // Replace
304 currentSimplex[ih] = std::move(refle << 373 currentSimplex[ ih ] = reflectionPoint;
305 // G4cout << "BC" << G4endl; << 374 //G4cout << "B2" << G4endl;
306 } << 375 }
307 // CONTRACTION << 376 else
308 std::vector<G4double> contractionPoint << 377 {
309 getContractionPoint(currentSimplex[i << 378 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 { 379 {
325 vec[k] = (currentSimplex[j][k] + << 380 // Replace
>> 381 currentSimplex[ ih ] = reflectionPoint;
>> 382 //G4cout << "BC" << G4endl;
326 } 383 }
327 currentSimplex[j] = std::move(vec) << 384 // CONTRACTION
328 } << 385 std::vector< G4double > contractionPoint =
329 } << 386 getContractionPoint( currentSimplex[ ih ] , centroidPoint );
>> 387 G4double hh = getValue( contractionPoint );
>> 388 if ( hh <= h_H )
>> 389 {
>> 390 // Replace
>> 391 currentSimplex[ ih ] = contractionPoint;
>> 392 //G4cout << "C" << G4endl;
>> 393 }
>> 394 else
>> 395 {
>> 396 // Replace
>> 397 for ( G4int j = 0 ; j <= numberOfVariable ; j++ )
>> 398 {
>> 399 std::vector< G4double > vec ( numberOfVariable , 0.0 );
>> 400 for ( G4int k = 0 ; k < numberOfVariable ; k++ )
>> 401 {
>> 402 vec[ k ] = ( currentSimplex[ j ][ k ]
>> 403 + currentSimplex[ il ][ k ] ) / 2.0;
>> 404 }
>> 405 currentSimplex[ j ] = vec;
>> 406 }
>> 407 //G4cout << "D" << G4endl;
>> 408 }
>> 409 }
>> 410
330 } 411 }
331 } <<
332 412
333 ++nth_trial; << 413 nth_trial++;
334 } << 414 }
335 } 415 }
336 416
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]; <<
358 417
359 return minimumPoint; << 418
>> 419 template<class T>
>> 420 std::vector< G4double > G4SimplexDownhill<T>::GetMinimumPoint()
>> 421 {
>> 422 if ( minimized != true )
>> 423 {
>> 424 GetMinimum();
>> 425 }
>> 426
>> 427 std::vector< G4double >::iterator it_minh =
>> 428 std::min_element( currentHeights.begin() , currentHeights.end() );;
>> 429 G4int imin = -1;
>> 430 G4int i = 0;
>> 431 for ( std::vector< G4double >::iterator
>> 432 it = currentHeights.begin(); it != currentHeights.end(); it++ )
>> 433 {
>> 434 if ( it == it_minh )
>> 435 {
>> 436 imin = i;
>> 437 }
>> 438 i++;
>> 439 }
>> 440 std::vector< G4double > minimumPoint = currentSimplex[ imin ];
>> 441
>> 442 return minimumPoint;
360 } 443 }
361 444