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25 // 25 //
26 // G4TsitourasRK45 implementation <<
27 // 26 //
28 // Author: Somnath Banerjee, Google Summer of << 27 // Tsitouras - 5(4) RK steppers ( non-FSAL version )
29 // Supervision: John Apostolakis, CERN << 28 //
>> 29 // Implements RK tableau from 'Table 1' of
>> 30 // C. Tsitouras, “Runge–Kutta pairs of order 5(4) satisfying only
>> 31 // the first column simplifying assumption,”
>> 32 // Computers & Mathematics with Applications,
>> 33 // vol. 62, no. 2, pp. 770–775, 2011.
>> 34 //
>> 35 // Adaptation / Geant4 implementation by Somnath Banerjee
>> 36 // Supervision / code review: John Apostolakis
>> 37 //
>> 38 // Sponsored by Google in Google Summer of Code 2015.
>> 39 //
>> 40 // First version: 12 June 2015
>> 41 //
30 // ------------------------------------------- 42 // -------------------------------------------------------------------
31 43
32 #include "G4TsitourasRK45.hh" 44 #include "G4TsitourasRK45.hh"
33 #include "G4LineSection.hh" 45 #include "G4LineSection.hh"
34 46
35 ////////////////////////////////////////////// 47 /////////////////////////////////////////////////////////////////////
36 // 48 //
37 // Constructor 49 // Constructor
38 // << 50
39 G4TsitourasRK45::G4TsitourasRK45(G4EquationOfM 51 G4TsitourasRK45::G4TsitourasRK45(G4EquationOfMotion *EqRhs,
40 G4int noInteg << 52 G4int noIntegrationVariables,
41 G4bool primar << 53 G4bool primary)
42 : G4MagIntegratorStepper(EqRhs, noIntegratio << 54 : G4MagIntegratorStepper(EqRhs, noIntegrationVariables),
>> 55 fLastStepLength(0.), fAuxStepper(0)
43 { 56 {
44 const G4int numberOfVariables = noIntegratio 57 const G4int numberOfVariables = noIntegrationVariables;
>> 58 // G4cout << "G4TsitourasRK45 constructor called." << G4endl;
45 59
46 ak2 = new G4double[numberOfVariables] ; 60 ak2 = new G4double[numberOfVariables] ;
47 ak3 = new G4double[numberOfVariables] ; 61 ak3 = new G4double[numberOfVariables] ;
48 ak4 = new G4double[numberOfVariables] ; 62 ak4 = new G4double[numberOfVariables] ;
49 ak5 = new G4double[numberOfVariables] ; 63 ak5 = new G4double[numberOfVariables] ;
50 ak6 = new G4double[numberOfVariables] ; 64 ak6 = new G4double[numberOfVariables] ;
51 ak7 = new G4double[numberOfVariables] ; 65 ak7 = new G4double[numberOfVariables] ;
52 ak8 = new G4double[numberOfVariables] ; 66 ak8 = new G4double[numberOfVariables] ;
53 67
>> 68
54 // Must ensure space extra 'state' variables 69 // Must ensure space extra 'state' variables exists - i.e. yIn[7]
55 // <<
56 const G4int numStateMax = std::max(GetNumbe 70 const G4int numStateMax = std::max(GetNumberOfStateVariables(), 8);
57 const G4int numStateVars = std::max(noIntegr 71 const G4int numStateVars = std::max(noIntegrationVariables,
58 numState 72 numStateMax );
>> 73 // GetNumberOfStateVariables() );
59 74
60 yTemp = new G4double[numStateVars] ; 75 yTemp = new G4double[numStateVars] ;
61 yIn = new G4double[numStateVars] ; 76 yIn = new G4double[numStateVars] ;
62 77
63 fLastInitialVector = new G4double[numberOfVa 78 fLastInitialVector = new G4double[numberOfVariables] ;
64 fLastFinalVector = new G4double[numberOfVari 79 fLastFinalVector = new G4double[numberOfVariables] ;
65 80
66 fLastDyDx = new G4double[numberOfVariables]; 81 fLastDyDx = new G4double[numberOfVariables];
67 82
68 fMidVector = new G4double[numberOfVariables] 83 fMidVector = new G4double[numberOfVariables];
69 fMidError = new G4double[numberOfVariables] 84 fMidError = new G4double[numberOfVariables];
70 <<
71 if( primary ) 85 if( primary )
72 { 86 {
73 fAuxStepper = new G4TsitourasRK45(EqRhs, n 87 fAuxStepper = new G4TsitourasRK45(EqRhs, numberOfVariables, !primary);
74 } 88 }
75 } 89 }
76 90
77 ////////////////////////////////////////////// 91 /////////////////////////////////////////////////////////////////////
78 // 92 //
79 // Destructor 93 // Destructor
80 // << 94
81 G4TsitourasRK45::~G4TsitourasRK45() 95 G4TsitourasRK45::~G4TsitourasRK45()
82 { 96 {
83 delete [] ak2; << 97 delete[] ak2;
84 delete [] ak3; << 98 delete[] ak3;
85 delete [] ak4; << 99 delete[] ak4;
86 delete [] ak5; << 100 delete[] ak5;
87 delete [] ak6; << 101 delete[] ak6;
88 delete [] ak7; << 102 delete[] ak7;
89 delete [] ak8; << 103 delete[] ak8;
90 << 104
91 delete [] yTemp; << 105 delete[] yTemp;
92 delete [] yIn; << 106 delete[] yIn;
93 << 107
94 delete [] fLastInitialVector; << 108 delete[] fLastInitialVector;
95 delete [] fLastFinalVector; << 109 delete[] fLastFinalVector;
96 delete [] fLastDyDx; << 110 delete[] fLastDyDx;
97 delete [] fMidVector; << 111 delete[] fMidVector;
98 delete [] fMidError; << 112 delete[] fMidError;
99 113
100 delete fAuxStepper; 114 delete fAuxStepper;
101 } 115 }
102 116
103 // The following coefficients have been obtain << 117 //The following coefficients have been obtained from
104 // Table 1: The Coefficients of the new pair 118 // Table 1: The Coefficients of the new pair
105 // << 119 //---Ref---
106 // C. Tsitouras, "Runge–Kutta pairs of order << 120 // C. Tsitouras, “Runge–Kutta pairs of order 5(4) satisfying only
107 // the first column simplifying << 121 // the first column simplifying assumption,”
108 // Computers & Mathematics with Applications, << 122 // Computers & Mathematics with Applications,
109 // << 123 // vol. 62, no. 2, pp. 770–775, 2011.
110 // A corresponding matlab code was also found << 124 //-----------------------------------
111 // http://users.ntua.gr/tsitoura/new54.m << 125 // A corresponding matlab code was also found @ http://users.ntua.gr/tsitoura/new54.m
112 // << 126
113 // Doing a step 127 // Doing a step
114 // <<
115 void 128 void
116 G4TsitourasRK45::Stepper( const G4double yInpu << 129 G4TsitourasRK45::Stepper( const G4double yInput[],
117 const G4double dydx[ << 130 const G4double dydx[],
118 G4double Step, << 131 G4double Step,
119 G4double yOut[ << 132 G4double yOut[],
120 G4double yErr[ << 133 G4double yErr[])
121 { 134 {
122 const G4double b21 = 0.161 , << 135 G4int i;
123 b31 = -0.008480655492356988 << 136
124 b32 = 0.335480655492356989 << 137 const G4double
125 << 138 b21 = 0.161 ,
126 b41 = 2.89715305710549343 << 139
127 b42 = -6.35944848997507484 << 140 b31 = -0.00848065549235698854 ,
128 b43 = 4.36229543286958141 , << 141 b32 = 0.335480655492356989 ,
129 <<
130 b51 = 5.325864828439257, <<
131 b52 = -11.748883564062828, <<
132 b53 = 7.49553934288983621 , <<
133 b54 = -0.09249506636175525, <<
134 <<
135 b61 = 5.8614554429464200, <<
136 b62 = -12.9209693178471093 <<
137 b63 = 8.1593678985761586 , <<
138 b64 = -0.071584973281400997 <<
139 b65 = -0.028269050394068382 <<
140 <<
141 b71 = 0.0964607668180652295 <<
142 b72 = 0.01, <<
143 b73 = 0.479889650414499575, <<
144 b74 = 1.37900857410374189, <<
145 b75 = -3.2900695154360807, <<
146 b76 = 2.32471052409977398, <<
147 <<
148 // c1 = 0.001780011052226 , <<
149 // c2 = 0.000816434459657 , <<
150 // c3 = -0.007880878010262 , <<
151 // c4 = 0.144711007173263 , <<
152 // c5 = -0.582357165452555 , <<
153 // c6 = 0.458082105929187 , <<
154 // c7 = 1.0/66.0 ; <<
155 <<
156 dc1 = 0.0935237485818927066 <<
157 dc2 = 0.0086528831415663676 <<
158 dc3 = 0.492893099131431868 <<
159 dc4 = 1.14023541226785810 - <<
160 dc5 = - 2.3291801924393646 <<
161 dc6 = 1.56887504931661552 - <<
162 dc7 = 0.025; //- 1.0/66.0 ; <<
163 <<
164 // dc1 = -3.0/1280.0, <<
165 // dc2 = 0.0, <<
166 // dc3 = 6561.0/632320.0, <<
167 // dc4 = -343.0/20800.0, <<
168 // dc5 = 243.0/12800.0, <<
169 // dc6 = -1.0/95.0, <<
170 // dc7 = 0.0 ; <<
171 142
172 const G4int numberOfVariables = GetNumberO << 143 b41 = 2.89715305710549343 ,
>> 144 b42 = -6.35944848997507484 ,
>> 145 b43 = 4.36229543286958141 ,
>> 146
>> 147 b51 = 5.325864828439257,
>> 148 b52 = -11.748883564062828,
>> 149 b53 = 7.49553934288983621 ,
>> 150 b54 = -0.09249506636175525,
>> 151
>> 152 b61 = 5.8614554429464200,
>> 153 b62 = -12.9209693178471093 ,
>> 154 b63 = 8.1593678985761586 ,
>> 155 b64 = -0.071584973281400997,
>> 156 b65 = -0.0282690503940683829,
>> 157
>> 158
>> 159 b71 = 0.0964607668180652295 ,
>> 160 b72 = 0.01,
>> 161 b73 = 0.479889650414499575,
>> 162 b74 = 1.37900857410374189,
>> 163 b75 = -3.2900695154360807,
>> 164 b76 = 2.32471052409977398,
>> 165
>> 166 // c1 = 0.001780011052226 ,
>> 167 // c2 = 0.000816434459657 ,
>> 168 // c3 = -0.007880878010262 ,
>> 169 // c4 = 0.144711007173263 ,
>> 170 // c5 = -0.582357165452555 ,
>> 171 // c6 = 0.458082105929187 ,
>> 172 // c7 = 1.0/66.0 ;
>> 173
>> 174 dc1 = 0.0935237485818927066 - b71 , // - 0.001780011052226,
>> 175 dc2 = 0.00865288314156636761 - b72, // - 0.000816434459657,
>> 176 dc3 = 0.492893099131431868 - b73 , // + 0.007880878010262,
>> 177 dc4 = 1.14023541226785810 - b74 , // 0.144711007173263,
>> 178 dc5 = - 2.3291801924393646 - b75, // + 0.582357165452555,
>> 179 dc6 = 1.56887504931661552 - b76 , // - 0.458082105929187,
>> 180 dc7 = 0.025; //- 1.0/66.0 ;
>> 181
>> 182 // dc1 = -3.0/1280.0,
>> 183 // dc2 = 0.0,
>> 184 // dc3 = 6561.0/632320.0,
>> 185 // dc4 = -343.0/20800.0,
>> 186 // dc5 = 243.0/12800.0,
>> 187 // dc6 = -1.0/95.0,
>> 188 // dc7 = 0.0 ;
>> 189
>> 190 const G4int numberOfVariables= this->GetNumberOfVariables();
173 191
174 // The number of variables to be integrate 192 // The number of variables to be integrated over
175 // <<
176 yOut[7] = yTemp[7] = yIn[7] = yInput[7]; 193 yOut[7] = yTemp[7] = yIn[7] = yInput[7];
177 <<
178 // Saving yInput because yInput and yOut 194 // Saving yInput because yInput and yOut can be aliases for same array
179 // << 195
180 for(G4int i=0; i<numberOfVariables; ++i) << 196 for(i=0;i<numberOfVariables;i++)
181 { 197 {
182 yIn[i]=yInput[i]; 198 yIn[i]=yInput[i];
183 } 199 }
184 // RightHandSide(yIn, dydx) ; // 1st Ste << 200
>> 201 // RightHandSide(yIn, dydx) ;
>> 202 // 1st Step - Not doing, getting passed
185 203
186 for(G4int i=0; i<numberOfVariables; ++i) << 204 for(i=0;i<numberOfVariables;i++)
187 { 205 {
188 yTemp[i] = yIn[i] + b21*Step*dydx[i] ; 206 yTemp[i] = yIn[i] + b21*Step*dydx[i] ;
189 } 207 }
190 RightHandSide(yTemp, ak2) ; / 208 RightHandSide(yTemp, ak2) ; // 2nd Stage
191 209
192 for(G4int i=0; i<numberOfVariables; ++i) << 210 for(i=0;i<numberOfVariables;i++)
193 { 211 {
194 yTemp[i] = yIn[i] + Step*(b31*dydx[i] 212 yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b32*ak2[i]) ;
195 } 213 }
196 RightHandSide(yTemp, ak3) ; / 214 RightHandSide(yTemp, ak3) ; // 3rd Stage
197 215
198 for(G4int i=0; i<numberOfVariables; ++i) << 216 for(i=0;i<numberOfVariables;i++)
199 { 217 {
200 yTemp[i] = yIn[i] + Step*(b41*dydx[i] 218 yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b42*ak2[i] + b43*ak3[i]) ;
201 } 219 }
202 RightHandSide(yTemp, ak4) ; / 220 RightHandSide(yTemp, ak4) ; // 4th Stage
203 221
204 for(G4int i=0; i<numberOfVariables; ++i) << 222 for(i=0;i<numberOfVariables;i++)
205 { 223 {
206 yTemp[i] = yIn[i] + Step*(b51*dydx[i] 224 yTemp[i] = yIn[i] + Step*(b51*dydx[i] + b52*ak2[i] + b53*ak3[i] +
207 b54*ak4[i]) 225 b54*ak4[i]) ;
208 } 226 }
209 RightHandSide(yTemp, ak5) ; / 227 RightHandSide(yTemp, ak5) ; // 5th Stage
210 228
211 for(G4int i=0; i<numberOfVariables; ++i) << 229 for(i=0;i<numberOfVariables;i++)
212 { 230 {
213 yTemp[i] = yIn[i] + Step*(b61*dydx[i] 231 yTemp[i] = yIn[i] + Step*(b61*dydx[i] + b62*ak2[i] + b63*ak3[i] +
214 b64*ak4[i] + 232 b64*ak4[i] + b65*ak5[i]) ;
215 } 233 }
216 RightHandSide(yTemp, ak6) ; / 234 RightHandSide(yTemp, ak6) ; // 6th Stage
217 235
218 for(G4int i=0; i<numberOfVariables; ++i) << 236 for(i=0;i<numberOfVariables;i++)
219 { 237 {
220 yOut[i] = yIn[i] + Step*(b71*dydx[i] + 238 yOut[i] = yIn[i] + Step*(b71*dydx[i] + b72*ak2[i] + b73*ak3[i] +
221 b74*ak4[i] + 239 b74*ak4[i] + b75*ak5[i] + b76*ak6[i]);
222 } 240 }
223 RightHandSide(yOut, ak7); / << 241 RightHandSide(yOut, ak7); //7th Stage
224 242
225 //Calculate the error in the step: 243 //Calculate the error in the step:
226 for(G4int i=0; i<numberOfVariables; ++i) << 244 for(i=0;i<numberOfVariables;i++)
227 { 245 {
228 yErr[i] = Step*(dc1*dydx[i] + dc2*ak2[ 246 yErr[i] = Step*(dc1*dydx[i] + dc2*ak2[i] + dc3*ak3[i] + dc4*ak4[i] +
229 dc5*ak5[i] + dc6*ak6[ 247 dc5*ak5[i] + dc6*ak6[i] + dc7*ak7[i] ) ;
230 248
231 // Store Input and Final values, for p 249 // Store Input and Final values, for possible use in calculating chord
232 // <<
233 fLastInitialVector[i] = yIn[i] ; 250 fLastInitialVector[i] = yIn[i] ;
234 fLastFinalVector[i] = yOut[i]; 251 fLastFinalVector[i] = yOut[i];
235 fLastDyDx[i] = dydx[i]; 252 fLastDyDx[i] = dydx[i];
236 } 253 }
237 254
238 fLastStepLength = Step; 255 fLastStepLength = Step;
239 256
240 return ; 257 return ;
241 } 258 }
242 259
243 void G4TsitourasRK45::SetupInterpolation() << 260 void G4TsitourasRK45::SetupInterpolation() // (const G4double *yInput, const G4double *dydx, const G4double Step)
244 // (const G4double *yInput, const G4double * <<
245 { 261 {
246 // Nothing to be done << 262 //Nothing to be done
247 } 263 }
248 264
249 void G4TsitourasRK45::Interpolate(const G4doub << 265
250 const G4doub << 266 void G4TsitourasRK45::Interpolate(const G4double *yInput, const G4double *dydx, const G4double Step, G4double *yOut, G4double tau){
251 const G4doub << 267
252 G4doub << 268
253 G4doub <<
254 { <<
255 G4double bf1, bf2, bf3, bf4, bf5, bf6, bf7 269 G4double bf1, bf2, bf3, bf4, bf5, bf6, bf7;
256 // Coefficients for all the seven stages << 270 // Coefficients for all the seven stages.
257 271
258 const G4int numberOfVariables = GetNumberO << 272 const G4int numberOfVariables= this->GetNumberOfVariables();
259 273
260 G4double tau0 = tau; 274 G4double tau0 = tau;
261 275
262 for(G4int i=0; i<numberOfVariables; ++i) << 276 for(int i=0;i<numberOfVariables;i++)
263 { 277 {
264 yIn[i] = yInput[i]; << 278 yIn[i]=yInput[i];
265 } 279 }
266 280
267 G4double tau_2 = tau0*tau0 ; << 281 G4double
268 // tau_3 = tau0*tau_2, << 282 tau_2 = tau0*tau0 ;
269 // tau_4 = tau_2*tau_2; << 283 // tau_3 = tau0*tau_2,
>> 284 // tau_4 = tau_2*tau_2;
270 285
271 bf1 = -1.0530884977290216*tau*(tau - 1.329 286 bf1 = -1.0530884977290216*tau*(tau - 1.3299890189751412)*(tau_2 -
272 1.4364028541716351*tau + 0.713 << 287 1.4364028541716351*tau + 0.7139816917074209),
273 bf2 = 0.1017*tau_2*(tau_2 - 2.196656833824 288 bf2 = 0.1017*tau_2*(tau_2 - 2.1966568338249754*tau +
274 1.2949852507374631); << 289 1.2949852507374631),
275 bf3 = 2.490627285651252793*tau_2*(tau_2 - 290 bf3 = 2.490627285651252793*tau_2*(tau_2 - 2.38535645472061657*tau
276 + 1.5780 << 291 + 1.57803468208092486) ,
277 bf4 = -16.54810288924490272*(tau - 1.21712 292 bf4 = -16.54810288924490272*(tau - 1.21712927295533244)*
278 (tau - 0.6 << 293 (tau - 0.61620406037800089)*tau_2,
279 bf5 = 47.37952196281928122*(tau - 1.203071 294 bf5 = 47.37952196281928122*(tau - 1.203071208372362603)*
280 (tau - 0.6 << 295 (tau - 0.658047292653547382)*tau_2,
281 bf6 = -34.87065786149660974*(tau - 1.2)*(t 296 bf6 = -34.87065786149660974*(tau - 1.2)*(tau -
282 0.666666666666 << 297 0.666666666666666667)*tau_2,
283 bf7 = 2.5*(tau - 1.0)*(tau - 0.6)*tau_2; 298 bf7 = 2.5*(tau - 1.0)*(tau - 0.6)*tau_2;
284 299
285 // Putting together the coefficients calcu << 300 //Putting together the coefficients calculated as the respective stage coefficients
286 // stage coefficients << 301 for( int i=0; i<numberOfVariables; i++){
287 // << 302 yOut[i] = yIn[i] + Step*( bf1*dydx[i] + bf2*ak2[i] + bf3*ak3[i] + bf4*ak4[i]
288 for(G4int i=0; i<numberOfVariables; ++i) << 303 + bf5*ak5[i] + bf6*ak6[i] + bf7*ak7[i] ) ;
289 { <<
290 yOut[i] = yIn[i] + Step*( bf1*dydx[i] <<
291 + bf4*ak4[i] <<
292 + bf7*ak7[i] <<
293 } 304 }
294 } 305 }
295 306
>> 307 ///////////////////////////////////////////////////////////////////////////////
>> 308
296 G4double G4TsitourasRK45::DistChord() const 309 G4double G4TsitourasRK45::DistChord() const
297 { 310 {
298 G4double distLine, distChord; 311 G4double distLine, distChord;
299 G4ThreeVector initialPoint, finalPoint, midP 312 G4ThreeVector initialPoint, finalPoint, midPoint;
300 313
301 // Store last initial and final points (they << 314 // Store last initial and final points (they will be overwritten in self-Stepper call!)
302 // overwritten in self-Stepper call!) <<
303 // <<
304 initialPoint = G4ThreeVector( fLastInitialVe 315 initialPoint = G4ThreeVector( fLastInitialVector[0],
305 fLastInitialVe 316 fLastInitialVector[1], fLastInitialVector[2]);
306 finalPoint = G4ThreeVector( fLastFinalVect 317 finalPoint = G4ThreeVector( fLastFinalVector[0],
307 fLastFinalVect 318 fLastFinalVector[1], fLastFinalVector[2]);
308 319
309 // Do half a step using StepNoErr 320 // Do half a step using StepNoErr
310 // << 321
311 fAuxStepper->Stepper( fLastInitialVector, fL 322 fAuxStepper->Stepper( fLastInitialVector, fLastDyDx, 0.5 * fLastStepLength,
312 fMidVector, fMidError ); 323 fMidVector, fMidError );
313 324
314 midPoint = G4ThreeVector( fMidVector[0], fMi 325 midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2]);
315 326
316 // Use stored values of Initial and Endpoint 327 // Use stored values of Initial and Endpoint + new Midpoint to evaluate
317 // distance of Chord 328 // distance of Chord
318 // << 329
>> 330
319 if (initialPoint != finalPoint) 331 if (initialPoint != finalPoint)
320 { 332 {
321 distLine = G4LineSection::Distline( midP 333 distLine = G4LineSection::Distline( midPoint, initialPoint, finalPoint );
322 distChord = distLine; 334 distChord = distLine;
323 } 335 }
324 else 336 else
325 { 337 {
326 distChord = (midPoint-initialPoint).mag() 338 distChord = (midPoint-initialPoint).mag();
327 } 339 }
328 return distChord; 340 return distChord;
329 } 341 }
330 342