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26 // G4SimplexDownhill inline methods implementa 26 // G4SimplexDownhill inline methods implementation
27 // 27 //
28 // Author: Tatsumi Koi (SLAC/SCCS), 2007 28 // Author: Tatsumi Koi (SLAC/SCCS), 2007
29 // ------------------------------------------- 29 // --------------------------------------------------------------------------
30 30
31 #include <cfloat> 31 #include <cfloat>
32 #include <iostream> 32 #include <iostream>
33 #include <numeric> 33 #include <numeric>
34 34
35 template <class T> 35 template <class T>
36 void G4SimplexDownhill<T>::init() 36 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 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 template <class T>
62 G4double G4SimplexDownhill<T>::GetMinimum() 62 G4double G4SimplexDownhill<T>::GetMinimum()
63 { 63 {
64 initialize(); 64 initialize();
65 65
66 // First Tryal; 66 // First Tryal;
67 67
68 // G4cout << "Begin First Trials" << G4endl; 68 // G4cout << "Begin First Trials" << G4endl;
69 doDownhill(); 69 doDownhill();
70 // G4cout << "End First Trials" << G4endl; 70 // G4cout << "End First Trials" << G4endl;
71 71
72 auto it_minh = std::min_element(currentHeigh << 72 std::vector<G4double>::const_iterator it_minh =
>> 73 std::min_element(currentHeights.cbegin(), currentHeights.cend());
73 G4int imin = 0; 74 G4int imin = 0;
74 G4int i = 0; 75 G4int i = 0;
75 for(auto it = currentHeights.cbegin(); it != 76 for(auto it = currentHeights.cbegin(); it != currentHeights.cend(); ++it)
76 { 77 {
77 if(it == it_minh) 78 if(it == it_minh)
78 { 79 {
79 imin = i; 80 imin = i;
80 } 81 }
81 ++i; 82 ++i;
82 } 83 }
83 minimumPoint = currentSimplex[imin]; 84 minimumPoint = currentSimplex[imin];
84 85
85 // Second Trial 86 // Second Trial
86 87
87 // std::vector< G4double > minimumPoint = cu 88 // std::vector< G4double > minimumPoint = currentSimplex[ 0 ];
88 initialize(); 89 initialize();
89 90
90 currentSimplex[numberOfVariable] = minimumPo 91 currentSimplex[numberOfVariable] = minimumPoint;
91 92
92 // G4cout << "Begin Second Trials" << G4endl 93 // G4cout << "Begin Second Trials" << G4endl;
93 doDownhill(); 94 doDownhill();
94 // G4cout << "End Second Trials" << G4endl; 95 // G4cout << "End Second Trials" << G4endl;
95 96
96 G4double sum = 97 G4double sum =
97 std::accumulate(currentHeights.begin(), cu 98 std::accumulate(currentHeights.begin(), currentHeights.end(), 0.0);
98 G4double average = sum / (numberOfVariable + 99 G4double average = sum / (numberOfVariable + 1);
99 G4double minimum = average; 100 G4double minimum = average;
100 101
101 minimized = true; 102 minimized = true;
102 103
103 return minimum; 104 return minimum;
104 } 105 }
105 106
106 template <class T> 107 template <class T>
107 void G4SimplexDownhill<T>::initialize() 108 void G4SimplexDownhill<T>::initialize()
108 { 109 {
109 currentSimplex.resize(numberOfVariable + 1); 110 currentSimplex.resize(numberOfVariable + 1);
110 currentHeights.resize(numberOfVariable + 1); 111 currentHeights.resize(numberOfVariable + 1);
111 112
112 for(G4int i = 0; i < numberOfVariable; ++i) 113 for(G4int i = 0; i < numberOfVariable; ++i)
113 { 114 {
114 std::vector<G4double> avec(numberOfVariabl 115 std::vector<G4double> avec(numberOfVariable, 0.0);
115 avec[i] = 1.0; 116 avec[i] = 1.0;
116 currentSimplex[i] = std::move(avec); << 117 currentSimplex[i] = avec;
117 } 118 }
118 119
119 // std::vector< G4double > avec ( numberOfVa 120 // std::vector< G4double > avec ( numberOfVariable , 0.0 );
120 std::vector<G4double> avec(numberOfVariable, 121 std::vector<G4double> avec(numberOfVariable, 1);
121 currentSimplex[numberOfVariable] = std::move << 122 currentSimplex[numberOfVariable] = avec;
122 } 123 }
123 124
124 template <class T> 125 template <class T>
125 void G4SimplexDownhill<T>::calHeights() 126 void G4SimplexDownhill<T>::calHeights()
126 { 127 {
127 for(G4int i = 0; i <= numberOfVariable; ++i) 128 for(G4int i = 0; i <= numberOfVariable; ++i)
128 { 129 {
129 currentHeights[i] = getValue(currentSimple 130 currentHeights[i] = getValue(currentSimplex[i]);
130 } 131 }
131 } 132 }
132 133
133 template <class T> 134 template <class T>
134 std::vector<G4double> G4SimplexDownhill<T>::ca 135 std::vector<G4double> G4SimplexDownhill<T>::calCentroid(G4int ih)
135 { 136 {
136 std::vector<G4double> centroid(numberOfVaria 137 std::vector<G4double> centroid(numberOfVariable, 0.0);
137 138
138 G4int i = 0; 139 G4int i = 0;
139 for(const auto & it : currentSimplex) << 140 for(auto it = currentSimplex.cbegin(); it != currentSimplex.cend(); ++it)
140 { 141 {
141 if(i != ih) 142 if(i != ih)
142 { 143 {
143 for(G4int j = 0; j < numberOfVariable; + 144 for(G4int j = 0; j < numberOfVariable; ++j)
144 { 145 {
145 centroid[j] += it[j] / numberOfVariabl << 146 centroid[j] += (*it)[j] / numberOfVariable;
146 } 147 }
147 } 148 }
148 ++i; 149 ++i;
149 } 150 }
150 151
151 return centroid; 152 return centroid;
152 } 153 }
153 154
154 template <class T> 155 template <class T>
155 std::vector<G4double> G4SimplexDownhill<T>::ge 156 std::vector<G4double> G4SimplexDownhill<T>::getReflectionPoint(
156 std::vector<G4double> p, std::vector<G4doubl 157 std::vector<G4double> p, std::vector<G4double> centroid)
157 { 158 {
158 // G4cout << "Reflection" << G4endl; 159 // G4cout << "Reflection" << G4endl;
159 160
160 std::vector<G4double> reflectionP(numberOfVa 161 std::vector<G4double> reflectionP(numberOfVariable, 0.0);
161 162
162 for(G4int i = 0; i < numberOfVariable; ++i) 163 for(G4int i = 0; i < numberOfVariable; ++i)
163 { 164 {
164 reflectionP[i] = (1 + alpha) * centroid[i] 165 reflectionP[i] = (1 + alpha) * centroid[i] - alpha * p[i];
165 } 166 }
166 167
167 return reflectionP; 168 return reflectionP;
168 } 169 }
169 170
170 template <class T> 171 template <class T>
171 std::vector<G4double> G4SimplexDownhill<T>::ge 172 std::vector<G4double> G4SimplexDownhill<T>::getExpansionPoint(
172 std::vector<G4double> p, std::vector<G4doubl 173 std::vector<G4double> p, std::vector<G4double> centroid)
173 { 174 {
174 // G4cout << "Expantion" << G4endl; 175 // G4cout << "Expantion" << G4endl;
175 176
176 std::vector<G4double> expansionP(numberOfVar 177 std::vector<G4double> expansionP(numberOfVariable, 0.0);
177 178
178 for(G4int i = 0; i < numberOfVariable; ++i) 179 for(G4int i = 0; i < numberOfVariable; ++i)
179 { 180 {
180 expansionP[i] = (1 - gamma) * centroid[i] 181 expansionP[i] = (1 - gamma) * centroid[i] + gamma * p[i];
181 } 182 }
182 183
183 return expansionP; 184 return expansionP;
184 } 185 }
185 186
186 template <class T> 187 template <class T>
187 std::vector<G4double> G4SimplexDownhill<T>::ge 188 std::vector<G4double> G4SimplexDownhill<T>::getContractionPoint(
188 std::vector<G4double> p, std::vector<G4doubl 189 std::vector<G4double> p, std::vector<G4double> centroid)
189 { 190 {
190 std::vector<G4double> contractionP(numberOfV 191 std::vector<G4double> contractionP(numberOfVariable, 0.0);
191 192
192 for(G4int i = 0; i < numberOfVariable; ++i) 193 for(G4int i = 0; i < numberOfVariable; ++i)
193 { 194 {
194 contractionP[i] = (1 - beta) * centroid[i] 195 contractionP[i] = (1 - beta) * centroid[i] + beta * p[i];
195 } 196 }
196 197
197 return contractionP; 198 return contractionP;
198 } 199 }
199 200
200 template <class T> 201 template <class T>
201 G4bool G4SimplexDownhill<T>::isItGoodEnough() 202 G4bool G4SimplexDownhill<T>::isItGoodEnough()
202 { 203 {
>> 204 G4bool result = false;
>> 205
203 G4double sum = 206 G4double sum =
204 std::accumulate(currentHeights.begin(), cu 207 std::accumulate(currentHeights.begin(), currentHeights.end(), 0.0);
205 G4double average = sum / (numberOfVariable + 208 G4double average = sum / (numberOfVariable + 1);
206 209
207 G4double delta = 0.0; 210 G4double delta = 0.0;
208 for(G4int i = 0; i <= numberOfVariable; ++i) 211 for(G4int i = 0; i <= numberOfVariable; ++i)
209 { 212 {
210 delta += std::abs(currentHeights[i] - aver 213 delta += std::abs(currentHeights[i] - average);
211 } 214 }
212 215
213 G4bool result = false; << 216 if(delta / (numberOfVariable + 1) / average < max_ratio)
214 if (average > 0.0) <<
215 { 217 {
216 result = ((delta / (numberOfVariable + 1) << 218 result = true;
217 } 219 }
>> 220
218 return result; 221 return result;
219 } 222 }
220 223
221 template <class T> 224 template <class T>
222 void G4SimplexDownhill<T>::doDownhill() 225 void G4SimplexDownhill<T>::doDownhill()
223 { 226 {
224 G4int nth_trial = 0; 227 G4int nth_trial = 0;
225 228
226 while(nth_trial < maximum_no_trial) 229 while(nth_trial < maximum_no_trial)
227 { 230 {
228 calHeights(); 231 calHeights();
229 232
230 if(isItGoodEnough()) 233 if(isItGoodEnough())
231 { 234 {
232 break; 235 break;
233 } 236 }
234 237
235 auto it_maxh = std::max_element(currentHei << 238 std::vector<G4double>::const_iterator it_maxh =
236 auto it_minh = std::min_element(currentHei << 239 std::max_element(currentHeights.cbegin(), currentHeights.cend());
>> 240 std::vector<G4double>::const_iterator it_minh =
>> 241 std::min_element(currentHeights.cbegin(), currentHeights.cend());
237 242
238 G4double h_H = *it_maxh; 243 G4double h_H = *it_maxh;
239 G4double h_L = *it_minh; 244 G4double h_L = *it_minh;
240 245
241 G4int ih = 0; 246 G4int ih = 0;
242 G4int il = 0; 247 G4int il = 0;
243 G4double h_H2 = 0.0; 248 G4double h_H2 = 0.0;
244 G4int i = 0; 249 G4int i = 0;
245 for(auto it = currentHeights.cbegin(); it 250 for(auto it = currentHeights.cbegin(); it != currentHeights.cend(); ++it)
246 { 251 {
247 if(it == it_maxh) 252 if(it == it_maxh)
248 { 253 {
249 ih = i; 254 ih = i;
250 } 255 }
251 else 256 else
252 { 257 {
253 h_H2 = std::max(h_H2, *it); 258 h_H2 = std::max(h_H2, *it);
254 } 259 }
255 260
256 if(it == it_minh) 261 if(it == it_minh)
257 { 262 {
258 il = i; 263 il = i;
259 } 264 }
260 ++i; 265 ++i;
261 } 266 }
262 267
263 std::vector<G4double> centroidPoint = calC 268 std::vector<G4double> centroidPoint = calCentroid(ih);
264 269
265 // REFLECTION 270 // REFLECTION
266 std::vector<G4double> reflectionPoint = 271 std::vector<G4double> reflectionPoint =
267 getReflectionPoint(currentSimplex[ih], c 272 getReflectionPoint(currentSimplex[ih], centroidPoint);
268 273
269 G4double h = getValue(reflectionPoint); 274 G4double h = getValue(reflectionPoint);
270 275
271 if(h <= h_L) 276 if(h <= h_L)
272 { 277 {
273 // EXPANSION 278 // EXPANSION
274 std::vector<G4double> expansionPoint = 279 std::vector<G4double> expansionPoint =
275 getExpansionPoint(reflectionPoint, std << 280 getExpansionPoint(reflectionPoint, centroidPoint);
276 G4double hh = getValue(expansionPoint); 281 G4double hh = getValue(expansionPoint);
277 282
278 if(hh <= h_L) 283 if(hh <= h_L)
279 { 284 {
280 // Replace 285 // Replace
281 currentSimplex[ih] = std::move(expansi << 286 currentSimplex[ih] = expansionPoint;
282 // G4cout << "A" << G4endl; 287 // G4cout << "A" << G4endl;
283 } 288 }
284 else 289 else
285 { 290 {
286 // Replace 291 // Replace
287 currentSimplex[ih] = std::move(reflect << 292 currentSimplex[ih] = reflectionPoint;
288 // G4cout << "B1" << G4endl; 293 // G4cout << "B1" << G4endl;
289 } 294 }
290 } 295 }
291 else 296 else
292 { 297 {
293 if(h <= h_H2) 298 if(h <= h_H2)
294 { 299 {
295 // Replace 300 // Replace
296 currentSimplex[ih] = std::move(reflect << 301 currentSimplex[ih] = reflectionPoint;
297 // G4cout << "B2" << G4endl; 302 // G4cout << "B2" << G4endl;
298 } 303 }
299 else 304 else
300 { 305 {
301 if(h <= h_H) 306 if(h <= h_H)
302 { 307 {
303 // Replace 308 // Replace
304 currentSimplex[ih] = std::move(refle << 309 currentSimplex[ih] = reflectionPoint;
305 // G4cout << "BC" << G4endl; 310 // G4cout << "BC" << G4endl;
306 } 311 }
307 // CONTRACTION 312 // CONTRACTION
308 std::vector<G4double> contractionPoint 313 std::vector<G4double> contractionPoint =
309 getContractionPoint(currentSimplex[i << 314 getContractionPoint(currentSimplex[ih], centroidPoint);
310 G4double hh = getValue(contractionPoin 315 G4double hh = getValue(contractionPoint);
311 if(hh <= h_H) 316 if(hh <= h_H)
312 { 317 {
313 // Replace 318 // Replace
314 currentSimplex[ih] = std::move(contr << 319 currentSimplex[ih] = contractionPoint;
315 // G4cout << "C" << G4endl; 320 // G4cout << "C" << G4endl;
316 } 321 }
317 else 322 else
318 { 323 {
319 // Replace 324 // Replace
320 for(G4int j = 0; j <= numberOfVariab 325 for(G4int j = 0; j <= numberOfVariable; ++j)
321 { 326 {
322 std::vector<G4double> vec(numberOf 327 std::vector<G4double> vec(numberOfVariable, 0.0);
323 for(G4int k = 0; k < numberOfVaria 328 for(G4int k = 0; k < numberOfVariable; ++k)
324 { 329 {
325 vec[k] = (currentSimplex[j][k] + 330 vec[k] = (currentSimplex[j][k] + currentSimplex[il][k]) / 2.0;
326 } 331 }
327 currentSimplex[j] = std::move(vec) << 332 currentSimplex[j] = vec;
328 } 333 }
329 } 334 }
330 } 335 }
331 } 336 }
332 337
333 ++nth_trial; 338 ++nth_trial;
334 } 339 }
335 } 340 }
336 341
337 template <class T> 342 template <class T>
338 std::vector<G4double> G4SimplexDownhill<T>::Ge 343 std::vector<G4double> G4SimplexDownhill<T>::GetMinimumPoint()
339 { 344 {
340 if(!minimized) << 345 if(minimized != true)
341 { 346 {
342 GetMinimum(); 347 GetMinimum();
343 } 348 }
344 349
345 auto it_minh = std::min_element(currentHeigh << 350 std::vector<G4double>::const_iterator it_minh =
>> 351 std::min_element(currentHeights.cbegin(), currentHeights.cend());
346 352
347 G4int imin = 0; 353 G4int imin = 0;
348 G4int i = 0; 354 G4int i = 0;
349 for(auto it = currentHeights.cbegin(); it != 355 for(auto it = currentHeights.cbegin(); it != currentHeights.cend(); ++it)
350 { 356 {
351 if(it == it_minh) 357 if(it == it_minh)
352 { 358 {
353 imin = i; 359 imin = i;
354 } 360 }
355 ++i; 361 ++i;
356 } 362 }
357 minimumPoint = currentSimplex[imin]; 363 minimumPoint = currentSimplex[imin];
358 364
359 return minimumPoint; 365 return minimumPoint;
360 } 366 }
361 367