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