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25 // 25 //
26 // G4FSALBogackiShampine45 implementation << 26 // Bogacki-Shampine - 8 - 5(4) FSAL implementation by Somnath Banerjee
>> 27 // Supervision / code review: John Apostolakis
27 // 28 //
28 // The Butcher table of the Bogacki-Shampine-8 << 29 // Sponsored by Google in Google Summer of Code 2015.
>> 30 //
>> 31 // First version: 26 May 2015
29 // 32 //
30 // 0 | << 33 // History
31 // 1/6 | 1/6 << 34 // -----------------------------
32 // 2/9 | 2/27 4/27 << 35 // Created by Somnath on 26 May 2015
33 // 3/7 | 183/1372 -162/343 1053/1372 << 36 //
34 // 2/3 | 68/297 -4/11 42/143 196 << 37 ///////////////////////////////////////////////////////////////////////////////
35 // 3/4 | 597/22528 81/352 63099/5857 << 38 // Renamed to G4 standard naming
36 // 1 | 174197/959244 -30942/79937 8152137/19 << 39 // Plan is that this source file / class will be merged with the updated
37 // 1 | 587/8064 0 4440339/15 << 40 // BogackiShampine45 class, which contains improvements (May 2016)
38 // ------------------------------------------- << 41 // J. Apostolakis, 31 May 2016
39 // 587/8064 0 4440339/15 << 42 ///////////////////////////////////////////////////////////////////////////////
40 // 2479/34992 0 123/416 <<
41 // 43 //
42 // Created: Somnath Banerjee, Google Summer of << 44 //
43 // Supervision: John Apostolakis, CERN << 45 //This is the source file of BogackiShampine45 class containing the
44 // ------------------------------------------- << 46 //definition of the stepper() method that evaluates one step in
45 << 47 //field propagation.
46 // Plan is that this source file / class will << 48 //The Butcher table of the Bogacki-Shampine-8-4-5 method is as follows :
47 // BogackiShampine45 class, which contains imp << 49 //
>> 50 //0 |
>> 51 //1/6 | 1/6
>> 52 //2/9 | 2/27 4/27
>> 53 //3/7 | 183/1372 -162/343 1053/1372
>> 54 //2/3 | 68/297 -4/11 42/143 1960/3861
>> 55 //3/4 | 597/22528 81/352 63099/585728 58653/366080 4617/20480
>> 56 //1 | 174197/959244 -30942/79937 8152137/19744439 666106/1039181 -29421/29068 482048/414219
>> 57 //1 | 587/8064 0 4440339/15491840 24353/124800 387/44800 2152/5985 7267/94080
>> 58 //-------------------------------------------------------------------------------------------------------------------
>> 59 // 587/8064 0 4440339/15491840 24353/124800 387/44800 2152/5985 7267/94080 0
>> 60 // 2479/34992 0 123/416 612941/3411720 43/1440 2272/6561 79937/1113912 3293/556956
48 61
49 #include <cassert> 62 #include <cassert>
50 63
51 #include "G4FSALBogackiShampine45.hh" 64 #include "G4FSALBogackiShampine45.hh"
52 #include "G4LineSection.hh" 65 #include "G4LineSection.hh"
53 66
54 G4bool G4FSALBogackiShampine45::fPreparedCon << 67 G4bool G4FSALBogackiShampine45::fPreparedConstants= false;
55 G4double G4FSALBogackiShampine45::bi[12][7]; 68 G4double G4FSALBogackiShampine45::bi[12][7];
56 69
57 // Constructor << 70 //Constructor
58 // << 71 G4FSALBogackiShampine45::G4FSALBogackiShampine45(G4EquationOfMotion *EqRhs,
59 G4FSALBogackiShampine45::G4FSALBogackiShampine << 72 G4int noIntegrationVariables,
60 << 73 G4bool primary)
61 << 74 : G4VFSALIntegrationStepper(EqRhs, noIntegrationVariables),
62 : G4VFSALIntegrationStepper(EqRhs, noIntegr << 75 fLastStepLength( -1.0 ), fAuxStepper( nullptr )
63 { 76 {
64 const G4int numberOfVariables = noIntegrat 77 const G4int numberOfVariables = noIntegrationVariables;
65 78
66 // New Chunk of memory being created for u << 79 //New Chunk of memory being created for use by the stepper
67 80
68 // aki - for storing intermediate RHS << 81 //aki - for storing intermediate RHS
69 // <<
70 ak2 = new G4double[numberOfVariables]; 82 ak2 = new G4double[numberOfVariables];
71 ak3 = new G4double[numberOfVariables]; 83 ak3 = new G4double[numberOfVariables];
72 ak4 = new G4double[numberOfVariables]; 84 ak4 = new G4double[numberOfVariables];
73 ak5 = new G4double[numberOfVariables]; 85 ak5 = new G4double[numberOfVariables];
74 ak6 = new G4double[numberOfVariables]; 86 ak6 = new G4double[numberOfVariables];
75 ak7 = new G4double[numberOfVariables]; 87 ak7 = new G4double[numberOfVariables];
76 ak8 = new G4double[numberOfVariables]; 88 ak8 = new G4double[numberOfVariables];
77 89
78 ak9 = new G4double[numberOfVariables]; 90 ak9 = new G4double[numberOfVariables];
79 ak10 = new G4double[numberOfVariables]; 91 ak10 = new G4double[numberOfVariables];
80 ak11 = new G4double[numberOfVariables]; 92 ak11 = new G4double[numberOfVariables];
81 DyDx = new G4double[numberOfVariables]; 93 DyDx = new G4double[numberOfVariables];
82 94
83 assert ( GetNumberOfStateVariables() >= 8 95 assert ( GetNumberOfStateVariables() >= 8 );
84 const G4int numStateVars = std::max(noInte 96 const G4int numStateVars = std::max(noIntegrationVariables,
85 GetNum 97 GetNumberOfStateVariables() );
86 98
87 // Must ensure space extra 'state' variabl 99 // Must ensure space extra 'state' variables exists - i.e. yIn[7]
88 // <<
89 yTemp = new G4double[numStateVars]; 100 yTemp = new G4double[numStateVars];
90 yIn = new G4double[numStateVars] ; 101 yIn = new G4double[numStateVars] ;
91 102
92 fLastInitialVector = new G4double[numState 103 fLastInitialVector = new G4double[numStateVars] ;
93 fLastFinalVector = new G4double[numStateVa 104 fLastFinalVector = new G4double[numStateVars] ;
94 fLastDyDx = new G4double[numberOfVariables 105 fLastDyDx = new G4double[numberOfVariables]; // Only derivatives
95 106
96 fMidVector = new G4double[numStateVars]; 107 fMidVector = new G4double[numStateVars];
97 fMidError = new G4double[numStateVars]; 108 fMidError = new G4double[numStateVars];
98 109
99 pseudoDydx_for_DistChord = new G4double[nu 110 pseudoDydx_for_DistChord = new G4double[numberOfVariables];
100 111
101 fMidVector = new G4double[numberOfVariable 112 fMidVector = new G4double[numberOfVariables];
102 fMidError = new G4double[numberOfVariable 113 fMidError = new G4double[numberOfVariables];
103 if( primary ) 114 if( primary )
104 { 115 {
105 fAuxStepper = new G4FSALBogackiShampine4 << 116 fAuxStepper = new G4FSALBogackiShampine45(EqRhs, numberOfVariables,
106 << 117 !primary);
107 } 118 }
108 if( !fPreparedConstants ) << 119 if( ! fPreparedConstants )
109 { <<
110 PrepareConstants(); 120 PrepareConstants();
111 } <<
112 } 121 }
113 122
114 // Destructor <<
115 // <<
116 G4FSALBogackiShampine45::~G4FSALBogackiShampin <<
117 { <<
118 // Clear all previously allocated memory f <<
119 123
120 delete [] ak2; << 124 //Destructor
121 delete [] ak3; << 125 G4FSALBogackiShampine45::~G4FSALBogackiShampine45(){
122 delete [] ak4; << 126 //clear all previously allocated memory for stepper and DistChord
123 delete [] ak5; << 127 delete[] ak2;
124 delete [] ak6; << 128 delete[] ak3;
125 delete [] ak7; << 129 delete[] ak4;
126 delete [] ak8; << 130 delete[] ak5;
127 delete [] ak9; << 131 delete[] ak6;
128 delete [] ak10; << 132 delete[] ak7;
129 delete [] ak11; << 133 delete[] ak8;
130 delete [] DyDx; << 134 delete[] ak9;
131 delete [] yTemp; << 135 delete[] ak10;
132 delete [] yIn; << 136 delete[] ak11;
133 << 137 delete[] DyDx;
134 delete [] fLastInitialVector; << 138 delete[] yTemp;
135 delete [] fLastFinalVector; << 139 delete[] yIn;
136 delete [] fLastDyDx; << 140
137 delete [] fMidVector; << 141 delete[] fLastInitialVector;
138 delete [] fMidError; << 142 delete[] fLastFinalVector;
>> 143 delete[] fLastDyDx;
>> 144 delete[] fMidVector;
>> 145 delete[] fMidError;
139 146
140 delete fAuxStepper; 147 delete fAuxStepper;
141 148
142 delete [] pseudoDydx_for_DistChord; << 149 delete[] pseudoDydx_for_DistChord;
143 } 150 }
144 151
145 // Stepper << 152
146 // << 153 //Stepper :
>> 154
147 // Passing in the value of yInput[],the first 155 // Passing in the value of yInput[],the first time dydx[] and Step length
148 // Giving back yOut and yErr arrays for output 156 // Giving back yOut and yErr arrays for output and error respectively
149 // << 157
150 void G4FSALBogackiShampine45::Stepper(const G4 158 void G4FSALBogackiShampine45::Stepper(const G4double yInput[],
151 const G4 << 159 const G4double dydx[],
152 G4 << 160 G4double Step,
153 G4 << 161 G4double yOut[],
154 G4 << 162 G4double yErr[],
155 G4 << 163 G4double nextDydx[])
156 { 164 {
157 G4int i; 165 G4int i;
158 166
159 // The various constants defined on the ba << 167 //The various constants defined on the basis of butcher tableu
160 << 168 const G4double //G4double - only once
161 const G4double b21 = 1.0/6.0 , << 169
162 b31 = 2.0/27.0 , b32 = 4.0/ << 170 b21 = 1.0/6.0 ,
>> 171 b31 = 2.0/27.0 , b32 = 4.0/27.0,
163 172
164 b41 = 183.0/1372.0 , b42 = << 173 b41 = 183.0/1372.0 , b42 = -162.0/343.0, b43 = 1053.0/1372.0,
165 174
166 b51 = 68.0/297.0, b52 = -4. << 175 b51 = 68.0/297.0, b52 = -4.0/11.0,
167 b53 = 42.0/143.0, b54 = 196 << 176 b53 = 42.0/143.0, b54 = 1960.0/3861.0,
168 177
169 b61 = 597.0/22528.0, b62 = << 178 b61 = 597.0/22528.0, b62 = 81.0/352.0,
170 b63 = 63099.0/585728.0, b64 << 179 b63 = 63099.0/585728.0, b64 = 58653.0/366080.0,
171 b65 = 4617.0/20480.0, << 180 b65 = 4617.0/20480.0,
172 181
173 b71 = 174197.0/959244.0, b7 << 182 b71 = 174197.0/959244.0, b72 = -30942.0/79937.0,
174 b73 = 8152137.0/19744439.0, << 183 b73 = 8152137.0/19744439.0, b74 = 666106.0/1039181.0,
175 b75 = -29421.0/29068.0, b7 << 184 b75 = -29421.0/29068.0, b76 = 482048.0/414219.0,
176 185
177 b81 = 587.0/8064.0, b82 = << 186 b81 = 587.0/8064.0, b82 = 0.0,
178 b83 = 4440339.0/15491840.0, << 187 b83 = 4440339.0/15491840.0, b84 = 24353.0/124800.0,
179 b85 = 387.0/44800.0, b86 = << 188 b85 = 387.0/44800.0, b86 = 2152.0/5985.0,
180 b87 = 7267.0/94080.0, << 189 b87 = 7267.0/94080.0,
181 190
182 191
183 // c1 = 2479.0/34992.0, << 192 // c1 = 2479.0/34992.0,
184 // c2 = 0.0, << 193 // c2 = 0.0,
185 // c3 = 123.0/416.0, << 194 // c3 = 123.0/416.0,
186 // c4 = 612941.0/3411720.0, << 195 // c4 = 612941.0/3411720.0,
187 // c5 = 43.0/1440.0, << 196 // c5 = 43.0/1440.0,
188 // c6 = 2272.0/6561.0, << 197 // c6 = 2272.0/6561.0,
189 // c7 = 79937.0/1113912.0, << 198 // c7 = 79937.0/1113912.0,
190 // c8 = 3293.0/556956.0, << 199 // c8 = 3293.0/556956.0,
191 200
192 // For the embedded higher order method on << 201 //For the embedded higher order method only the difference of values
193 // taken and is used directly later instea 202 // taken and is used directly later instead of defining the last row
194 // of butcher table in a separate set of v 203 // of butcher table in a separate set of variables and taking the
195 // difference there 204 // difference there
196 <<
197 dc1 = b81 - 2479.0/34992.0 <<
198 dc2 = 0.0, <<
199 dc3 = b83 - 123.0/416.0 , <<
200 dc4 = b84 - 612941.0/341172 <<
201 dc5 = b85 - 43.0/1440.0, <<
202 dc6 = b86 - 2272.0/6561.0, <<
203 dc7 = b87 - 79937.0/1113912 <<
204 dc8 = -3293.0/556956.0; / <<
205 205
206 const G4int numberOfVariables = GetNumberO << 206
>> 207 dc1 = b81 - 2479.0/34992.0 ,
>> 208 dc2 = 0.0,
>> 209 dc3 = b83 - 123.0/416.0 ,
>> 210 dc4 = b84 - 612941.0/3411720.0,
>> 211 dc5 = b85 - 43.0/1440.0,
>> 212 dc6 = b86 - 2272.0/6561.0,
>> 213 dc7 = b87 - 79937.0/1113912.0,
>> 214 dc8 = -3293.0/556956.0; //end of declaration
>> 215
>> 216
>> 217 const G4int numberOfVariables= this->GetNumberOfVariables();
207 218
208 // The number of variables to be integrate 219 // The number of variables to be integrated over
209 // <<
210 yOut[7] = yTemp[7] = yIn[7]; 220 yOut[7] = yTemp[7] = yIn[7];
211 <<
212 // Saving yInput because yInput and yOut 221 // Saving yInput because yInput and yOut can be aliases for same array
213 // << 222
214 for(i=0; i<numberOfVariables; ++i) << 223 for(i=0;i<numberOfVariables;i++)
215 { 224 {
216 yIn[i]=yInput[i]; 225 yIn[i]=yInput[i];
217 DyDx[i] = dydx[i]; 226 DyDx[i] = dydx[i];
218 } 227 }
219 // RightHandSide(yIn, dydx) ; // 1st Ste <<
220 228
221 for(i=0; i<numberOfVariables; ++i) << 229
>> 230 // RightHandSide(yIn, dydx) ;
>> 231 // 1st Step - Not doing, getting passed
>> 232
>> 233 for(i=0;i<numberOfVariables;i++)
222 { 234 {
223 yTemp[i] = yIn[i] + b21*Step*DyDx[i] ; 235 yTemp[i] = yIn[i] + b21*Step*DyDx[i] ;
224 } 236 }
225 RightHandSide(yTemp, ak2) ; / 237 RightHandSide(yTemp, ak2) ; // 2nd Step
226 238
227 for(i=0; i<numberOfVariables; ++i) << 239 for(i=0;i<numberOfVariables;i++)
228 { 240 {
229 yTemp[i] = yIn[i] + Step*(b31*DyDx[i] 241 yTemp[i] = yIn[i] + Step*(b31*DyDx[i] + b32*ak2[i]) ;
230 } 242 }
231 RightHandSide(yTemp, ak3) ; / 243 RightHandSide(yTemp, ak3) ; // 3rd Step
232 244
233 for(i=0; i<numberOfVariables; ++i) << 245 for(i=0;i<numberOfVariables;i++)
234 { 246 {
235 yTemp[i] = yIn[i] + Step*(b41*DyDx[i] 247 yTemp[i] = yIn[i] + Step*(b41*DyDx[i] + b42*ak2[i] + b43*ak3[i]) ;
236 } 248 }
237 RightHandSide(yTemp, ak4) ; / 249 RightHandSide(yTemp, ak4) ; // 4th Step
238 250
239 for(i=0; i<numberOfVariables; ++i) << 251 for(i=0;i<numberOfVariables;i++)
240 { 252 {
241 yTemp[i] = yIn[i] + Step*(b51*DyDx[i] 253 yTemp[i] = yIn[i] + Step*(b51*DyDx[i] + b52*ak2[i] + b53*ak3[i] +
242 b54*ak4[i]) 254 b54*ak4[i]) ;
243 } 255 }
244 RightHandSide(yTemp, ak5) ; / 256 RightHandSide(yTemp, ak5) ; // 5th Step
245 257
246 for(i=0; i<numberOfVariables; ++i) << 258 for(i=0;i<numberOfVariables;i++)
247 { 259 {
248 yTemp[i] = yIn[i] + Step*(b61*DyDx[i] 260 yTemp[i] = yIn[i] + Step*(b61*DyDx[i] + b62*ak2[i] + b63*ak3[i] +
249 b64*ak4[i] + 261 b64*ak4[i] + b65*ak5[i]) ;
250 } 262 }
251 RightHandSide(yTemp, ak6) ; / 263 RightHandSide(yTemp, ak6) ; // 6th Step
252 264
253 for(i=0; i<numberOfVariables; ++i) << 265 for(i=0;i<numberOfVariables;i++)
254 { 266 {
255 yTemp[i] = yIn[i] + Step*(b71*DyDx[i] 267 yTemp[i] = yIn[i] + Step*(b71*DyDx[i] + b72*ak2[i] + b73*ak3[i] +
256 b74*ak4[i] + 268 b74*ak4[i] + b75*ak5[i] + b76*ak6[i]);
257 } 269 }
258 RightHandSide(yTemp, ak7); / << 270 RightHandSide(yTemp, ak7); //7th Step
259 271
260 for(i=0; i<numberOfVariables; ++i) << 272 for(i=0;i<numberOfVariables;i++)
261 { 273 {
262 yOut[i] = yIn[i] + Step*(b81*DyDx[i] + 274 yOut[i] = yIn[i] + Step*(b81*DyDx[i] + b82*ak2[i] + b83*ak3[i] +
263 b84*ak4[i] + 275 b84*ak4[i] + b85*ak5[i] + b86*ak6[i] +
264 b87*ak7[i]); 276 b87*ak7[i]);
265 } 277 }
266 RightHandSide(yOut, ak8); / << 278 RightHandSide(yOut, ak8); //8th Step - Final one Using FSAL
267 279
268 280
269 for(i=0; i<numberOfVariables; ++i) << 281 for(i=0;i<numberOfVariables;i++)
270 { 282 {
271 283
272 yErr[i] = Step*(dc1*DyDx[i] + dc2*ak2[ 284 yErr[i] = Step*(dc1*DyDx[i] + dc2*ak2[i] + dc3*ak3[i] + dc4*ak4[i] +
273 dc5*ak5[i] + dc6*ak6[i 285 dc5*ak5[i] + dc6*ak6[i] + dc7*ak7[i] + dc8*ak8[i]) ;
274 286
275 287
276 // FSAL stepper : Must pass the last D << 288 //FSAL stepper : Must pass the last DyDx for the next step, here ak8
277 // <<
278 nextDydx[i] = ak8[i]; 289 nextDydx[i] = ak8[i];
279 290
280 // Store Input and Final values, for p 291 // Store Input and Final values, for possible use in calculating chord
281 // <<
282 fLastInitialVector[i] = yIn[i] ; 292 fLastInitialVector[i] = yIn[i] ;
283 fLastFinalVector[i] = yOut[i]; 293 fLastFinalVector[i] = yOut[i];
284 fLastDyDx[i] = DyDx[i]; 294 fLastDyDx[i] = DyDx[i];
>> 295
285 } 296 }
>> 297
286 fLastStepLength = Step; 298 fLastStepLength = Step;
287 299
288 return; << 300 return ;
289 } 301 }
290 <<
291 // DistChord <<
292 // 302 //
293 G4double G4FSALBogackiShampine45::DistChord() << 303 //G4double* G4FSALBogackiShampine45::getLastDydx(){
>> 304 // return ak8;
>> 305 //}
>> 306
>> 307 //The following has not been tested
>> 308
>> 309 //The DistChord() function fot the class - must define it here.
>> 310 G4double G4FSALBogackiShampine45::DistChord() const
294 { 311 {
295 G4double distLine, distChord; 312 G4double distLine, distChord;
296 G4ThreeVector initialPoint, finalPoint, mi 313 G4ThreeVector initialPoint, finalPoint, midPoint;
297 << 314
298 // Store last initial and final points << 315
299 // (they will be overwritten in self-Stepp << 316 // Store last initial and final points (they will be overwritten in self-Stepper call!)
300 // <<
301 initialPoint = G4ThreeVector( fLastInitial 317 initialPoint = G4ThreeVector( fLastInitialVector[0],
302 fLastInitialV 318 fLastInitialVector[1], fLastInitialVector[2]);
303 finalPoint = G4ThreeVector( fLastFinalVe 319 finalPoint = G4ThreeVector( fLastFinalVector[0],
304 fLastFinalVec 320 fLastFinalVector[1], fLastFinalVector[2]);
305 321
306 // Do half a step using StepNoErr 322 // Do half a step using StepNoErr
307 323
308 fAuxStepper->Stepper( fLastInitialVector, 324 fAuxStepper->Stepper( fLastInitialVector, fLastDyDx, 0.5 * fLastStepLength,
309 fMidVector, fMidErro << 325 fMidVector, fMidError, pseudoDydx_for_DistChord );
310 326
311 midPoint = G4ThreeVector( fMidVector[0], f << 327 midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2]);
312 328
313 // Use stored values of Initial and Endpoi 329 // Use stored values of Initial and Endpoint + new Midpoint to evaluate
314 // distance of Chord << 330 // distance of Chord
315 // << 331
>> 332
316 if (initialPoint != finalPoint) 333 if (initialPoint != finalPoint)
317 { 334 {
318 distLine = G4LineSection::Distline(mid << 335 distLine = G4LineSection::Distline( midPoint, initialPoint, finalPoint );
319 distChord = distLine; 336 distChord = distLine;
320 } 337 }
321 else 338 else
322 { 339 {
323 distChord = (midPoint-initialPoint).ma 340 distChord = (midPoint-initialPoint).mag();
324 } 341 }
325 return distChord; 342 return distChord;
326 } 343 }
327 344
328 // PrepareConstants << 345 // ---------------------------------------------------------------------------------------
329 // << 346
330 void G4FSALBogackiShampine45::PrepareConstants 347 void G4FSALBogackiShampine45::PrepareConstants()
331 { 348 {
332 // -------------------------------------- 349 // --------------------------------------------------------
333 // COEFFICIENTS FOR INTERPOLANT bi WITH 350 // COEFFICIENTS FOR INTERPOLANT bi WITH 11 STAGES
334 // -------------------------------------- 351 // --------------------------------------------------------
335 352
336 // Initialise all values of G4double bi[12 << 353 // Initialise all values of G4double bi[12][7]
337 // << 354 for(int i=1; i<12; i++){
338 for(auto i=1; i<12; ++i) << 355 for(int j=1; j<7; j++){
339 { <<
340 for(auto j=1; j<7; ++j) <<
341 { <<
342 bi[i][j] = 0.0 ; 356 bi[i][j] = 0.0 ;
343 } 357 }
344 } 358 }
345 359
346 bi[1][6] = -12134338393.0/1050809760.0 , 360 bi[1][6] = -12134338393.0/1050809760.0 ,
347 bi[1][5] = -1620741229.0/50038560.0 , 361 bi[1][5] = -1620741229.0/50038560.0 ,
348 bi[1][4] = -2048058893.0/59875200.0 , 362 bi[1][4] = -2048058893.0/59875200.0 ,
349 bi[1][3] = -87098480009.0/5254048800.0 , 363 bi[1][3] = -87098480009.0/5254048800.0 ,
350 bi[1][2] = -11513270273.0/3502699200.0 , 364 bi[1][2] = -11513270273.0/3502699200.0 ,
351 // 365 //
352 bi[3][6] = -33197340367.0/1218433216.0 , 366 bi[3][6] = -33197340367.0/1218433216.0 ,
353 bi[3][5] = -539868024987.0/6092166080.0 , 367 bi[3][5] = -539868024987.0/6092166080.0 ,
354 bi[3][4] = -39991188681.0/374902528.0 , 368 bi[3][4] = -39991188681.0/374902528.0 ,
355 bi[3][3] = -69509738227.0/1218433216.0 , 369 bi[3][3] = -69509738227.0/1218433216.0 ,
356 bi[3][2] = -29327744613.0/2436866432.0 , 370 bi[3][2] = -29327744613.0/2436866432.0 ,
357 // 371 //
358 bi[4][6] = -284800997201.0/19905339168.0 , 372 bi[4][6] = -284800997201.0/19905339168.0 ,
359 bi[4][5] = -7896875450471.0/165877826400.0 373 bi[4][5] = -7896875450471.0/165877826400.0 ,
360 bi[4][4] = -333945812879.0/5671036800.0 , 374 bi[4][4] = -333945812879.0/5671036800.0 ,
361 bi[4][3] = -16209923456237.0/497633479200. 375 bi[4][3] = -16209923456237.0/497633479200.0 ,
362 bi[4][2] = -2382590741699.0/331755652800.0 376 bi[4][2] = -2382590741699.0/331755652800.0 ,
363 // 377 //
364 bi[5][6] = -540919.0/741312.0 , 378 bi[5][6] = -540919.0/741312.0 ,
365 bi[5][5] = -103626067.0/43243200.0 , 379 bi[5][5] = -103626067.0/43243200.0 ,
366 bi[5][4] = -633779.0/211200.0 , 380 bi[5][4] = -633779.0/211200.0 ,
367 bi[5][3] = -32406787.0/18532800.0 , 381 bi[5][3] = -32406787.0/18532800.0 ,
368 bi[5][2] = -36591193.0/86486400.0 , 382 bi[5][2] = -36591193.0/86486400.0 ,
369 // 383 //
370 bi[6][6] = 7157998304.0/374350977.0 , 384 bi[6][6] = 7157998304.0/374350977.0 ,
371 bi[6][5] = 30405842464.0/623918295.0 , 385 bi[6][5] = 30405842464.0/623918295.0 ,
372 bi[6][4] = 183022264.0/5332635.0 , 386 bi[6][4] = 183022264.0/5332635.0 ,
373 bi[6][3] = -3357024032.0/1871754885.0 , 387 bi[6][3] = -3357024032.0/1871754885.0 ,
374 bi[6][2] = -611586736.0/89131185.0 , 388 bi[6][2] = -611586736.0/89131185.0 ,
375 // 389 //
376 bi[7][6] = -138073.0/9408.0 , 390 bi[7][6] = -138073.0/9408.0 ,
377 bi[7][5] = -719433.0/15680.0 , 391 bi[7][5] = -719433.0/15680.0 ,
378 bi[7][4] = -1620541.0/31360.0 , 392 bi[7][4] = -1620541.0/31360.0 ,
379 bi[7][3] = -385151.0/15680.0 , 393 bi[7][3] = -385151.0/15680.0 ,
380 bi[7][2] = -65403.0/15680.0 , 394 bi[7][2] = -65403.0/15680.0 ,
381 // 395 //
382 bi[8][6] = 1245.0/64.0 , 396 bi[8][6] = 1245.0/64.0 ,
383 bi[8][5] = 3991.0/64.0 , 397 bi[8][5] = 3991.0/64.0 ,
384 bi[8][4] = 4715.0/64.0 , 398 bi[8][4] = 4715.0/64.0 ,
385 bi[8][3] = 2501.0/64.0 , 399 bi[8][3] = 2501.0/64.0 ,
386 bi[8][2] = 149.0/16.0 , 400 bi[8][2] = 149.0/16.0 ,
387 bi[8][1] = 1.0 , 401 bi[8][1] = 1.0 ,
388 // 402 //
389 bi[9][6] = 55.0/3.0 , 403 bi[9][6] = 55.0/3.0 ,
390 bi[9][5] = 71.0 , 404 bi[9][5] = 71.0 ,
391 bi[9][4] = 103.0 , 405 bi[9][4] = 103.0 ,
392 bi[9][3] = 199.0/3.0 , 406 bi[9][3] = 199.0/3.0 ,
393 bi[9][2] = 16.0 , 407 bi[9][2] = 16.0 ,
394 // 408 //
395 bi[10][6] = -1774004627.0/75810735.0 , 409 bi[10][6] = -1774004627.0/75810735.0 ,
396 bi[10][5] = -1774004627.0/25270245.0 , 410 bi[10][5] = -1774004627.0/25270245.0 ,
397 bi[10][4] = -26477681.0/359975.0 , 411 bi[10][4] = -26477681.0/359975.0 ,
398 bi[10][3] = -11411880511.0/379053675.0 , 412 bi[10][3] = -11411880511.0/379053675.0 ,
399 bi[10][2] = -423642896.0/126351225.0 , 413 bi[10][2] = -423642896.0/126351225.0 ,
400 // 414 //
401 bi[11][6] = 35.0 , 415 bi[11][6] = 35.0 ,
402 bi[11][5] = 105.0 , 416 bi[11][5] = 105.0 ,
403 bi[11][4] = 117.0 , 417 bi[11][4] = 117.0 ,
404 bi[11][3] = 59.0 , 418 bi[11][3] = 59.0 ,
405 bi[11][2] = 12.0 ; 419 bi[11][2] = 12.0 ;
406 } 420 }
407 421
408 // ------------------------------------------- 422 // ---------------------------------------------------------------------------------------
409 423
410 void G4FSALBogackiShampine45::interpolate( con 424 void G4FSALBogackiShampine45::interpolate( const G4double yInput[],
411 con << 425 const G4double dydx[],
412 << 426 G4double yOut[],
413 << 427 G4double Step,
414 << 428 G4double tau
>> 429 )
415 { 430 {
416 const G4double a91 = 455.0/6144.0 , << 431 const G4double
417 a92 = 0.0 , << 432 a91 = 455.0/6144.0 ,
418 a93 = 10256301.0/35409920.0 << 433 a92 = 0.0 ,
419 a94 = 2307361.0/17971200.0 << 434 a93 = 10256301.0/35409920.0 ,
420 a95 = -387.0/102400.0 , << 435 a94 = 2307361.0/17971200.0 ,
421 a96 = 73.0/5130.0 , << 436 a95 = -387.0/102400.0 ,
422 a97 = -7267.0/215040.0 , << 437 a96 = 73.0/5130.0 ,
423 a98 = 1.0/32.0 , << 438 a97 = -7267.0/215040.0 ,
424 << 439 a98 = 1.0/32.0 ,
425 a101 = -837888343715.0/1317 << 440
426 a102 = 30409415.0/52955362. << 441 a101 = -837888343715.0/13176988637184.0 ,
427 a103 = -48321525963.0/75916 << 442 a102 = 30409415.0/52955362.0 ,
428 a104 = 8530738453321.0/1976 << 443 a103 = -48321525963.0/759168069632.0 ,
429 a105 = 1361640523001.0/1626 << 444 a104 = 8530738453321.0/197654829557760.0 ,
430 a106 = -13143060689.0/38604 << 445 a105 = 1361640523001.0/1626788720640.0 ,
431 a107 = 18700221969.0/379584 << 446 a106 = -13143060689.0/38604458898.0 ,
432 a108 = -5831595.0/847285792 << 447 a107 = 18700221969.0/379584034816.0 ,
433 a109 = -5183640.0/26477681. << 448 a108 = -5831595.0/847285792.0 ,
434 << 449 a109 = -5183640.0/26477681.0 ,
435 a111 = 98719073263.0/155196 << 450
436 a112 = 1307.0/123552.0 , << 451 a111 = 98719073263.0/1551965184000.0 ,
437 a113 = 4632066559387.0/7018 << 452 a112 = 1307.0/123552.0 ,
438 a114 = 7828594302389.0/3821 << 453 a113 = 4632066559387.0/70181753241600.0 ,
439 a115 = 40763687.0/110702592 << 454 a114 = 7828594302389.0/382182512025600.0 ,
440 a116 = 34872732407.0/224610 << 455 a115 = 40763687.0/11070259200.0 ,
441 a117 = -2561897.0/30105600. << 456 a116 = 34872732407.0/224610586200.0 ,
442 a118 = 1.0/10.0 , << 457 a117 = -2561897.0/30105600.0 ,
443 a119 = -1.0/10.0 , << 458 a118 = 1.0/10.0 ,
444 a1110 = -1403317093.0/11371 << 459 a119 = -1.0/10.0 ,
>> 460 a1110 = -1403317093.0/11371610250.0 ;
445 461
446 const G4int numberOfVariables = GetNumberO << 462 const G4int numberOfVariables= this->GetNumberOfVariables();
447 463
448 // Saving yInput because yInput and yOut c << 464 // Saving yInput because yInput and yOut can be aliases for same array
449 // << 465 for(int i=0;i<numberOfVariables;i++)
450 for(G4int i=0; i<numberOfVariables; ++i) <<
451 { 466 {
452 yIn[i]=yInput[i]; 467 yIn[i]=yInput[i];
453 } 468 }
454 469
455 // The number of variables to be integrate 470 // The number of variables to be integrated over
456 // <<
457 yOut[7] = yTemp[7] = yIn[7]; 471 yOut[7] = yTemp[7] = yIn[7];
458 472
459 // Calculating extra stages << 473 // calculating extra stages
460 // << 474 for(int i=0; i<numberOfVariables; i++){
461 for(G4int i=0; i<numberOfVariables; ++i) <<
462 { <<
463 yTemp[i] = yIn[i] + Step*(a91*dydx[i] 475 yTemp[i] = yIn[i] + Step*(a91*dydx[i] + a92*ak2[i] + a93*ak3[i] +
464 a94*ak4[i] + 476 a94*ak4[i] + a95*ak5[i] + a96*ak6[i] +
465 a97*ak7[i] + 477 a97*ak7[i] + a98*ak8[i] );
466 } 478 }
467 479
468 RightHandSide(yTemp, ak9); 480 RightHandSide(yTemp, ak9);
469 481
470 for(G4int i=0; i<numberOfVariables; ++i) << 482 for(int i=0; i<numberOfVariables; i++){
471 { <<
472 yTemp[i] = yIn[i] + Step*(a101*dydx[i] 483 yTemp[i] = yIn[i] + Step*(a101*dydx[i] + a102*ak2[i] + a103*ak3[i] +
473 a104*ak4[i] 484 a104*ak4[i] + a105*ak5[i] + a106*ak6[i] +
474 a107*ak7[i] 485 a107*ak7[i] + a108*ak8[i] + a109*ak9[i] );
475 } 486 }
476 487
477 RightHandSide(yTemp, ak10); 488 RightHandSide(yTemp, ak10);
478 489
479 for(G4int i=0; i<numberOfVariables; ++i) << 490 for(int i=0; i<numberOfVariables; i++){
480 { <<
481 yTemp[i] = yIn[i] + Step*(a111*dydx[i] 491 yTemp[i] = yIn[i] + Step*(a111*dydx[i] + a112*ak2[i] + a113*ak3[i] +
482 a114*ak4[i] 492 a114*ak4[i] + a115*ak5[i] + a116*ak6[i] +
483 a117*ak7[i] 493 a117*ak7[i] + a118*ak8[i] + a119*ak9[i] +
484 a1110*ak10[i 494 a1110*ak10[i] );
485 } 495 }
486 496
487 RightHandSide(yTemp, ak11); 497 RightHandSide(yTemp, ak11);
488 498
489 G4double tau0 = tau; 499 G4double tau0 = tau;
490 << 500 // Calculating the polynomials :
491 // Calculating the polynomials << 501 for(int i=1; i<=11; i++){ //Here i is NOT the coordinate no. , it's stage no.
492 // <<
493 for(auto i=1; i<=11; ++i) // i is NOT the <<
494 { <<
495 b[i] = 0.0; 502 b[i] = 0.0;
496 tau = tau0; 503 tau = tau0;
497 for(auto j=1; j<=6; ++j) << 504 for(int j=1; j<=6; j++){
498 { <<
499 b[i] += bi[i][j]*tau; 505 b[i] += bi[i][j]*tau;
500 tau*=tau0; 506 tau*=tau0;
501 } 507 }
502 } 508 }
503 509
504 for(G4int i=0; i<numberOfVariables; ++i) << 510 for(int i=0; i<numberOfVariables; i++){
505 { <<
506 yOut[i] = yIn[i] + Step*(b[1]*dydx[i] 511 yOut[i] = yIn[i] + Step*(b[1]*dydx[i] + b[2]*ak2[i] + b[3]*ak3[i] +
507 b[4]*ak4[i] + 512 b[4]*ak4[i] + b[5]*ak5[i] + b[6]*ak6[i] +
508 b[7]*ak7[i] + 513 b[7]*ak7[i] + b[8]*ak8[i] + b[9]*ak9[i] +
509 b[10]*ak10[i] 514 b[10]*ak10[i] + b[11]*ak11[i] );
510 } 515 }
511 } 516 }
>> 517
>> 518
>> 519
>> 520
512 521