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1 // 1 // 2 // ******************************************* 2 // ******************************************************************** 3 // * License and Disclaimer 3 // * License and Disclaimer * 4 // * 4 // * * 5 // * The Geant4 software is copyright of th 5 // * The Geant4 software is copyright of the Copyright Holders of * 6 // * the Geant4 Collaboration. It is provided 6 // * the Geant4 Collaboration. It is provided under the terms and * 7 // * conditions of the Geant4 Software License 7 // * conditions of the Geant4 Software License, included in the file * 8 // * LICENSE and available at http://cern.ch/ 8 // * LICENSE and available at http://cern.ch/geant4/license . These * 9 // * include a list of copyright holders. 9 // * include a list of copyright holders. * 10 // * 10 // * * 11 // * Neither the authors of this software syst 11 // * Neither the authors of this software system, nor their employing * 12 // * institutes,nor the agencies providing fin 12 // * institutes,nor the agencies providing financial support for this * 13 // * work make any representation or warran 13 // * work make any representation or warranty, express or implied, * 14 // * regarding this software system or assum 14 // * regarding this software system or assume any liability for its * 15 // * use. Please see the license in the file 15 // * use. Please see the license in the file LICENSE and URL above * 16 // * for the full disclaimer and the limitatio 16 // * for the full disclaimer and the limitation of liability. * 17 // * 17 // * * 18 // * This code implementation is the result 18 // * This code implementation is the result of the scientific and * 19 // * technical work of the GEANT4 collaboratio 19 // * technical work of the GEANT4 collaboration. * 20 // * By using, copying, modifying or distri 20 // * By using, copying, modifying or distributing the software (or * 21 // * any work based on the software) you ag 21 // * any work based on the software) you agree to acknowledge its * 22 // * use in resulting scientific publicati 22 // * use in resulting scientific publications, and indicate your * 23 // * acceptance of all terms of the Geant4 Sof 23 // * acceptance of all terms of the Geant4 Software license. * 24 // ******************************************* 24 // ******************************************************************** 25 // 25 // 26 // G4BogackiShampine45 implementation 26 // G4BogackiShampine45 implementation 27 // 27 // 28 // Bogacki-Shampine's RK 5(4) non-FSAL interpo 28 // Bogacki-Shampine's RK 5(4) non-FSAL interpolation method 29 // Definition of the stepper() method that eva 29 // Definition of the stepper() method that evaluates one step in 30 // field propagation. 30 // field propagation. 31 // 31 // 32 // The Butcher table of the Bogacki-Shampine-8 32 // The Butcher table of the Bogacki-Shampine-8-4-5 method is: 33 // 33 // 34 // 0 | 34 // 0 | 35 // 1/6 | 1/6 35 // 1/6 | 1/6 36 // 2/9 | 2/27 4/27 36 // 2/9 | 2/27 4/27 37 // 3/7 | 183/1372 -162/343 1053/1 37 // 3/7 | 183/1372 -162/343 1053/1372 38 // 2/3 | 68/297 -4/11 42/1 38 // 2/3 | 68/297 -4/11 42/143 1960/3861 39 // 3/4 | 597/22528 81/352 63099/5 39 // 3/4 | 597/22528 81/352 63099/585728 58653/366080 4617/20480 40 // 1 | 174197/959244 -30942/79937 8152137/1 40 // 1 | 174197/959244 -30942/79937 8152137/19744439 666106/1039181 -29421/29068 482048/414219 41 // 1 | 587/8064 0 4440339/1 41 // 1 | 587/8064 0 4440339/15491840 24353/124800 387/44800 2152/5985 7267/94080 42 //-------------------------------------------- 42 //------------------------------------------------------------------------------------------------------------------- 43 // 587/8064 0 4440339/1 43 // 587/8064 0 4440339/15491840 24353/124800 387/44800 2152/5985 7267/94080 0 44 // 2479/34992 0 123/4 44 // 2479/34992 0 123/416 612941/3411720 43/1440 2272/6561 79937/1113912 3293/556956 45 // 45 // 46 // Coefficients have been obtained from: 46 // Coefficients have been obtained from: 47 // http://www.netlib.org/ode/rksuite/ 47 // http://www.netlib.org/ode/rksuite/ 48 // 48 // 49 // Note on meaning of label "non-FSAL version" 49 // Note on meaning of label "non-FSAL version": 50 // This method calculates the deriviative dy 50 // This method calculates the deriviative dy/dx at the endpoint of the 51 // integration interval at each step, as par 51 // integration interval at each step, as part of its evaluation of the 52 // endpoint and its error. So this value is 52 // endpoint and its error. So this value is available to be returned, 53 // for re-use in case of a successful step. 53 // for re-use in case of a successful step. 54 // (This is done in a 'later' version using 54 // (This is done in a 'later' version using a refined interface). 55 // 55 // 56 // Created: Somnath Banerjee, Google Summer of 56 // Created: Somnath Banerjee, Google Summer of Code 2015, May-August 2015 57 // Revision: John Apostolakis, CERN, May 2016 57 // Revision: John Apostolakis, CERN, May 2016 58 // ------------------------------------------- 58 // -------------------------------------------------------------------- 59 59 60 #include <cassert> 60 #include <cassert> 61 61 62 #include "G4BogackiShampine45.hh" 62 #include "G4BogackiShampine45.hh" 63 #include "G4LineSection.hh" 63 #include "G4LineSection.hh" 64 64 65 G4bool G4BogackiShampine45::fPreparedConstants 65 G4bool G4BogackiShampine45::fPreparedConstants = false; 66 G4double G4BogackiShampine45::bi[12][7]; 66 G4double G4BogackiShampine45::bi[12][7]; 67 67 68 // Constructor 68 // Constructor 69 // 69 // 70 G4BogackiShampine45::G4BogackiShampine45(G4Equ 70 G4BogackiShampine45::G4BogackiShampine45(G4EquationOfMotion *EqRhs, 71 G4int 71 G4int noIntegrationVariables, 72 G4boo 72 G4bool primary) 73 : G4MagIntegratorStepper(EqRhs, noIntegrati 73 : G4MagIntegratorStepper(EqRhs, noIntegrationVariables) 74 { 74 { 75 const G4int numberOfVariables = noIntegrat 75 const G4int numberOfVariables = noIntegrationVariables; 76 76 77 // New Chunk of memory being created for u 77 // New Chunk of memory being created for use by the stepper 78 78 79 // aki - for storing intermediate RHS 79 // aki - for storing intermediate RHS 80 ak2 = new G4double[numberOfVariables]; 80 ak2 = new G4double[numberOfVariables]; 81 ak3 = new G4double[numberOfVariables]; 81 ak3 = new G4double[numberOfVariables]; 82 ak4 = new G4double[numberOfVariables]; 82 ak4 = new G4double[numberOfVariables]; 83 ak5 = new G4double[numberOfVariables]; 83 ak5 = new G4double[numberOfVariables]; 84 ak6 = new G4double[numberOfVariables]; 84 ak6 = new G4double[numberOfVariables]; 85 ak7 = new G4double[numberOfVariables]; 85 ak7 = new G4double[numberOfVariables]; 86 ak8 = new G4double[numberOfVariables]; 86 ak8 = new G4double[numberOfVariables]; 87 ak9 = new G4double[numberOfVariables]; 87 ak9 = new G4double[numberOfVariables]; 88 ak10 = new G4double[numberOfVariables]; 88 ak10 = new G4double[numberOfVariables]; 89 ak11 = new G4double[numberOfVariables]; 89 ak11 = new G4double[numberOfVariables]; 90 90 91 for (auto & i : p) << 91 for (auto i = 0; i < 6; ++i) 92 { 92 { 93 i= new G4double[numberOfVariables]; << 93 p[i]= new G4double[numberOfVariables]; 94 } 94 } 95 95 96 assert ( GetNumberOfStateVariables() >= 8 96 assert ( GetNumberOfStateVariables() >= 8 ); 97 const G4int numStateVars = std::max(noInte 97 const G4int numStateVars = std::max(noIntegrationVariables, 98 GetNum 98 GetNumberOfStateVariables() ); 99 99 100 // Must ensure space extra 'state' variabl 100 // Must ensure space extra 'state' variables exists - i.e. yIn[7] 101 yTemp = new G4double[numStateVars]; 101 yTemp = new G4double[numStateVars]; 102 yIn = new G4double[numStateVars] ; 102 yIn = new G4double[numStateVars] ; 103 103 104 fLastInitialVector = new G4double[numState 104 fLastInitialVector = new G4double[numStateVars] ; 105 fLastFinalVector = new G4double[numStateVa 105 fLastFinalVector = new G4double[numStateVars] ; 106 fLastDyDx = new G4double[numberOfVariables 106 fLastDyDx = new G4double[numberOfVariables]; // Only derivatives 107 107 108 fMidVector = new G4double[numberOfVariable 108 fMidVector = new G4double[numberOfVariables]; 109 fMidError = new G4double[numberOfVariable 109 fMidError = new G4double[numberOfVariables]; 110 110 111 if( ! fPreparedConstants ) 111 if( ! fPreparedConstants ) 112 { 112 { 113 PrepareConstants(); 113 PrepareConstants(); 114 } 114 } 115 115 116 if( primary ) 116 if( primary ) 117 { 117 { 118 fAuxStepper = new G4BogackiShampine45(E 118 fAuxStepper = new G4BogackiShampine45(EqRhs, numberOfVariables, false); 119 } 119 } 120 } 120 } 121 121 122 // Destructor 122 // Destructor 123 // 123 // 124 G4BogackiShampine45::~G4BogackiShampine45() 124 G4BogackiShampine45::~G4BogackiShampine45() 125 { 125 { 126 // Clear all previously allocated memory f 126 // Clear all previously allocated memory for stepper and DistChord 127 // 127 // 128 delete [] ak2; 128 delete [] ak2; 129 delete [] ak3; 129 delete [] ak3; 130 delete [] ak4; 130 delete [] ak4; 131 delete [] ak5; 131 delete [] ak5; 132 delete [] ak6; 132 delete [] ak6; 133 delete [] ak7; 133 delete [] ak7; 134 delete [] ak8; 134 delete [] ak8; 135 delete [] ak9; 135 delete [] ak9; 136 delete [] ak10; 136 delete [] ak10; 137 delete [] ak11; 137 delete [] ak11; 138 138 139 for (auto & i : p) << 139 for (auto i = 0; i < 6; ++i) 140 { 140 { 141 delete [] i; << 141 delete [] p[i]; 142 } 142 } 143 143 144 delete [] yTemp; 144 delete [] yTemp; 145 delete [] yIn; 145 delete [] yIn; 146 146 147 delete [] fLastInitialVector; 147 delete [] fLastInitialVector; 148 delete [] fLastFinalVector; 148 delete [] fLastFinalVector; 149 delete [] fLastDyDx; 149 delete [] fLastDyDx; 150 delete [] fMidVector; 150 delete [] fMidVector; 151 delete [] fMidError; 151 delete [] fMidError; 152 152 153 delete fAuxStepper; 153 delete fAuxStepper; 154 } 154 } 155 155 156 void G4BogackiShampine45::GetLastDydx( G4doubl 156 void G4BogackiShampine45::GetLastDydx( G4double dyDxLast[] ) 157 { 157 { 158 const G4int numberOfVariables = GetNumberOf 158 const G4int numberOfVariables = GetNumberOfVariables(); 159 159 160 for(G4int i=0; i < numberOfVariables; ++i ) 160 for(G4int i=0; i < numberOfVariables; ++i ) 161 { 161 { 162 dyDxLast[i] = ak9[i]; 162 dyDxLast[i] = ak9[i]; 163 } 163 } 164 } 164 } 165 165 166 // Stepper 166 // Stepper 167 // 167 // 168 // Passing in the value of yInput[],the first 168 // Passing in the value of yInput[],the first time dydx[] and Step length 169 // Giving back yOut and yErr arrays for output 169 // Giving back yOut and yErr arrays for output and error respectively 170 // 170 // 171 void G4BogackiShampine45::Stepper( const G4dou 171 void G4BogackiShampine45::Stepper( const G4double yInput[], 172 const G4dou 172 const G4double DyDx[], 173 G4dou 173 G4double Step, 174 G4dou 174 G4double yOut[], 175 G4dou 175 G4double yErr[] ) 176 { 176 { 177 G4int i; 177 G4int i; 178 178 179 // Constants from the Butcher tableu 179 // Constants from the Butcher tableu 180 // 180 // 181 const G4double 181 const G4double 182 b21 = 1.0/6.0 , 182 b21 = 1.0/6.0 , 183 b31 = 2.0/27.0 , b32 = 4.0/27.0, 183 b31 = 2.0/27.0 , b32 = 4.0/27.0, 184 184 185 b41 = 183.0/1372.0 , b42 = -162.0/343.0 185 b41 = 183.0/1372.0 , b42 = -162.0/343.0, b43 = 1053.0/1372.0, 186 186 187 b51 = 68.0/297.0, b52 = -4.0/11.0, 187 b51 = 68.0/297.0, b52 = -4.0/11.0, 188 b53 = 42.0/143.0, b54 = 1960.0/3861. 188 b53 = 42.0/143.0, b54 = 1960.0/3861.0, 189 189 190 b61 = 597.0/22528.0, b62 = 81.0/352. 190 b61 = 597.0/22528.0, b62 = 81.0/352.0, 191 b63 = 63099.0/585728.0, b64 = 58653.0/3 191 b63 = 63099.0/585728.0, b64 = 58653.0/366080.0, 192 b65 = 4617.0/20480.0, 192 b65 = 4617.0/20480.0, 193 193 194 b71 = 174197.0/959244.0, b72 = -3094 194 b71 = 174197.0/959244.0, b72 = -30942.0/79937.0, 195 b73 = 8152137.0/19744439.0, b74 = 66610 195 b73 = 8152137.0/19744439.0, b74 = 666106.0/1039181.0, 196 b75 = -29421.0/29068.0, b76 = 48204 196 b75 = -29421.0/29068.0, b76 = 482048.0/414219.0, 197 197 198 b81 = 587.0/8064.0, b82 = 0.0, 198 b81 = 587.0/8064.0, b82 = 0.0, 199 b83 = 4440339.0/15491840.0, b84 = 24353 199 b83 = 4440339.0/15491840.0, b84 = 24353.0/124800.0, 200 b85 = 387.0/44800.0, b86 = 2152. 200 b85 = 387.0/44800.0, b86 = 2152.0/5985.0, 201 b87 = 7267.0/94080.0; 201 b87 = 7267.0/94080.0; 202 202 203 // c1 = 2479.0/34992.0, 203 // c1 = 2479.0/34992.0, 204 // c2 = 0.0, 204 // c2 = 0.0, 205 // c3 = 123.0/416.0, 205 // c3 = 123.0/416.0, 206 // c4 = 612941.0/3411720.0, 206 // c4 = 612941.0/3411720.0, 207 // c5 = 43.0/1440.0, 207 // c5 = 43.0/1440.0, 208 // c6 = 2272.0/6561.0, 208 // c6 = 2272.0/6561.0, 209 // c7 = 79937.0/1113912.0, 209 // c7 = 79937.0/1113912.0, 210 // c8 = 3293.0/556956.0, 210 // c8 = 3293.0/556956.0, 211 211 212 // For the embedded higher order method on 212 // For the embedded higher order method only the difference of values 213 // taken and is used directly later (inste 213 // taken and is used directly later (instead of defining the last row 214 // of Butcher table in separate constants 214 // of Butcher table in separate constants and taking the 215 // difference) 215 // difference) 216 // 216 // 217 const G4double 217 const G4double 218 dc1 = b81 - 2479.0 / 34992.0 , 218 dc1 = b81 - 2479.0 / 34992.0 , 219 dc2 = 0.0, 219 dc2 = 0.0, 220 dc3 = b83 - 123.0 / 416.0 , 220 dc3 = b83 - 123.0 / 416.0 , 221 dc4 = b84 - 612941.0 / 3411720.0, 221 dc4 = b84 - 612941.0 / 3411720.0, 222 dc5 = b85 - 43.0 / 1440.0, 222 dc5 = b85 - 43.0 / 1440.0, 223 dc6 = b86 - 2272.0 / 6561.0, 223 dc6 = b86 - 2272.0 / 6561.0, 224 dc7 = b87 - 79937.0 / 1113912.0, 224 dc7 = b87 - 79937.0 / 1113912.0, 225 dc8 = - 3293.0 / 556956.0; 225 dc8 = - 3293.0 / 556956.0; 226 226 227 const G4int numberOfVariables = GetNumberO 227 const G4int numberOfVariables = GetNumberOfVariables(); 228 228 229 // The number of variables to be integrate 229 // The number of variables to be integrated over 230 // 230 // 231 yOut[7] = yTemp[7] = yIn[7] = yInput[7]; 231 yOut[7] = yTemp[7] = yIn[7] = yInput[7]; 232 232 233 // Saving yInput because yInput and yOut c 233 // Saving yInput because yInput and yOut can be aliases for same array 234 // 234 // 235 for(i=0; i<numberOfVariables; ++i) 235 for(i=0; i<numberOfVariables; ++i) 236 { 236 { 237 yIn[i]=yInput[i]; 237 yIn[i]=yInput[i]; 238 } 238 } 239 239 240 // RightHandSide(yIn, dydx) ; 240 // RightHandSide(yIn, dydx) ; 241 // 1st Step - Not doing, getting passed 241 // 1st Step - Not doing, getting passed 242 // 242 // 243 for(i=0; i<numberOfVariables; ++i) 243 for(i=0; i<numberOfVariables; ++i) 244 { 244 { 245 yTemp[i] = yIn[i] + b21*Step*DyDx[i] ; 245 yTemp[i] = yIn[i] + b21*Step*DyDx[i] ; 246 } 246 } 247 RightHandSide(yTemp, ak2) ; / 247 RightHandSide(yTemp, ak2) ; // 2nd Step 248 248 249 for(i=0; i<numberOfVariables; ++i) 249 for(i=0; i<numberOfVariables; ++i) 250 { 250 { 251 yTemp[i] = yIn[i] + Step*(b31*DyDx[i] 251 yTemp[i] = yIn[i] + Step*(b31*DyDx[i] + b32*ak2[i]) ; 252 } 252 } 253 RightHandSide(yTemp, ak3) ; / 253 RightHandSide(yTemp, ak3) ; // 3rd Step 254 254 255 for(i=0; i<numberOfVariables; ++i) 255 for(i=0; i<numberOfVariables; ++i) 256 { 256 { 257 yTemp[i] = yIn[i] + Step*(b41*DyDx[i] 257 yTemp[i] = yIn[i] + Step*(b41*DyDx[i] + b42*ak2[i] + b43*ak3[i]) ; 258 } 258 } 259 RightHandSide(yTemp, ak4) ; / 259 RightHandSide(yTemp, ak4) ; // 4th Step 260 260 261 for(i=0; i<numberOfVariables; ++i) 261 for(i=0; i<numberOfVariables; ++i) 262 { 262 { 263 yTemp[i] = yIn[i] + Step*(b51*DyDx[i] 263 yTemp[i] = yIn[i] + Step*(b51*DyDx[i] + b52*ak2[i] + b53*ak3[i] + 264 b54*ak4[i]) 264 b54*ak4[i]) ; 265 } 265 } 266 RightHandSide(yTemp, ak5) ; / 266 RightHandSide(yTemp, ak5) ; // 5th Step 267 267 268 for(i=0; i<numberOfVariables; ++i) 268 for(i=0; i<numberOfVariables; ++i) 269 { 269 { 270 yTemp[i] = yIn[i] + Step*(b61*DyDx[i] 270 yTemp[i] = yIn[i] + Step*(b61*DyDx[i] + b62*ak2[i] + b63*ak3[i] + 271 b64*ak4[i] + 271 b64*ak4[i] + b65*ak5[i]) ; 272 } 272 } 273 RightHandSide(yTemp, ak6) ; / 273 RightHandSide(yTemp, ak6) ; // 6th Step 274 274 275 for(i=0; i<numberOfVariables; ++i) 275 for(i=0; i<numberOfVariables; ++i) 276 { 276 { 277 yTemp[i] = yIn[i] + Step*(b71*DyDx[i] 277 yTemp[i] = yIn[i] + Step*(b71*DyDx[i] + b72*ak2[i] + b73*ak3[i] + 278 b74*ak4[i] + 278 b74*ak4[i] + b75*ak5[i] + b76*ak6[i]); 279 } 279 } 280 RightHandSide(yTemp, ak7); / 280 RightHandSide(yTemp, ak7); // 7th Step 281 281 282 for(i=0; i<numberOfVariables; ++i) 282 for(i=0; i<numberOfVariables; ++i) 283 { 283 { 284 yOut[i] = yIn[i] + Step*(b81*DyDx[i] + 284 yOut[i] = yIn[i] + Step*(b81*DyDx[i] + b82*ak2[i] + b83*ak3[i] + 285 b84*ak4[i] + 285 b84*ak4[i] + b85*ak5[i] + b86*ak6[i] + 286 b87*ak7[i]); 286 b87*ak7[i]); 287 } 287 } 288 RightHandSide(yOut, ak8); / 288 RightHandSide(yOut, ak8); // 8th Step - Final one Using FSAL 289 289 290 for(i=0; i<numberOfVariables; ++i) 290 for(i=0; i<numberOfVariables; ++i) 291 { 291 { 292 yErr[i] = Step*(dc1*DyDx[i] + dc2*ak2[ 292 yErr[i] = Step*(dc1*DyDx[i] + dc2*ak2[i] + dc3*ak3[i] + dc4*ak4[i] + 293 dc5*ak5[i] + dc6*ak6[i 293 dc5*ak5[i] + dc6*ak6[i] + dc7*ak7[i] + dc8*ak8[i]) ; 294 294 295 // Store Input and Final values, for p 295 // Store Input and Final values, for possible use in calculating chord 296 // 296 // 297 fLastInitialVector[i] = yIn[i] ; 297 fLastInitialVector[i] = yIn[i] ; 298 fLastFinalVector[i] = yOut[i]; 298 fLastFinalVector[i] = yOut[i]; 299 fLastDyDx[i] = DyDx[i]; 299 fLastDyDx[i] = DyDx[i]; 300 } 300 } 301 301 302 fLastStepLength = Step; 302 fLastStepLength = Step; 303 fPreparedInterpolation= false; 303 fPreparedInterpolation= false; 304 304 305 return ; 305 return ; 306 } 306 } 307 307 308 // DistChord 308 // DistChord 309 // 309 // 310 G4double G4BogackiShampine45::DistChord() cons 310 G4double G4BogackiShampine45::DistChord() const 311 { 311 { 312 G4double distLine, distChord; 312 G4double distLine, distChord; 313 G4ThreeVector initialPoint, finalPoint, mi 313 G4ThreeVector initialPoint, finalPoint, midPoint; 314 314 315 // Store last initial and final points 315 // Store last initial and final points 316 // (they will be overwritten in self-Stepp 316 // (they will be overwritten in self-Stepper call!) 317 // 317 // 318 initialPoint = G4ThreeVector(fLastInitialV 318 initialPoint = G4ThreeVector(fLastInitialVector[0], 319 fLastInitialV 319 fLastInitialVector[1], fLastInitialVector[2]); 320 finalPoint = G4ThreeVector(fLastFinalVec 320 finalPoint = G4ThreeVector(fLastFinalVector[0], 321 fLastFinalVec 321 fLastFinalVector[1], fLastFinalVector[2]); 322 322 323 #if 1 323 #if 1 324 // Old method -- Do half a step using Step 324 // Old method -- Do half a step using StepNoErr 325 // 325 // 326 fAuxStepper->Stepper( fLastInitialVector, 326 fAuxStepper->Stepper( fLastInitialVector, fLastDyDx, 0.5*fLastStepLength, 327 fMidVector, fMidErro 327 fMidVector, fMidError); 328 #else 328 #else 329 // New method -- Using interpolation, 329 // New method -- Using interpolation, 330 // requires only 3 extra stages (ie 3 extr 330 // requires only 3 extra stages (ie 3 extra field evaluations ) 331 331 332 // Use Interpolation, instead of auxiliary 332 // Use Interpolation, instead of auxiliary stepper to evaluate midpoint 333 // 333 // 334 if( ! fPreparedInterpolation ) 334 if( ! fPreparedInterpolation ) 335 { 335 { 336 G4BogackiShampine45* cThis = const_cast 336 G4BogackiShampine45* cThis = const_cast<G4BogackiShampine45 *>(this); 337 cThis-> SetupInterpolationHigh(); 337 cThis-> SetupInterpolationHigh(); 338 } 338 } 339 // For calculating the output at the tau f 339 // For calculating the output at the tau fraction of Step 340 // 340 // 341 G4double tau = 0.5; 341 G4double tau = 0.5; 342 InterpolateHigh( tau, fMidVector ); 342 InterpolateHigh( tau, fMidVector ); 343 #endif 343 #endif 344 344 345 midPoint = G4ThreeVector( fMidVector[0], f 345 midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2]); 346 346 347 // Use stored values of Initial and Endpoi 347 // Use stored values of Initial and Endpoint + new Midpoint to evaluate 348 // distance of Chord 348 // distance of Chord 349 349 350 if (initialPoint != finalPoint) 350 if (initialPoint != finalPoint) 351 { 351 { 352 distLine = G4LineSection::Distline( m 352 distLine = G4LineSection::Distline( midPoint,initialPoint,finalPoint ); 353 distChord = distLine; 353 distChord = distLine; 354 } 354 } 355 else 355 else 356 { 356 { 357 distChord = (midPoint-initialPoint).ma 357 distChord = (midPoint-initialPoint).mag(); 358 } 358 } 359 return distChord; 359 return distChord; 360 } 360 } 361 361 362 void G4BogackiShampine45::SetupInterpolationHi 362 void G4BogackiShampine45::SetupInterpolationHigh() 363 { 363 { 364 // Coefficients for the additional stages 364 // Coefficients for the additional stages 365 // 365 // 366 const G4double 366 const G4double 367 a91 = 455.0/6144.0 , 367 a91 = 455.0/6144.0 , 368 a92 = 0.0 , 368 a92 = 0.0 , 369 a93 = 10256301.0/35409920.0 , 369 a93 = 10256301.0/35409920.0 , 370 a94 = 2307361.0/17971200.0 , 370 a94 = 2307361.0/17971200.0 , 371 a95 = -387.0/102400.0 , 371 a95 = -387.0/102400.0 , 372 a96 = 73.0/5130.0 , 372 a96 = 73.0/5130.0 , 373 a97 = -7267.0/215040.0 , 373 a97 = -7267.0/215040.0 , 374 a98 = 1.0/32.0 , 374 a98 = 1.0/32.0 , 375 375 376 a101 = -837888343715.0/13176988637184.0 , 376 a101 = -837888343715.0/13176988637184.0 , 377 a102 = 30409415.0/52955362.0 , 377 a102 = 30409415.0/52955362.0 , 378 a103 = -48321525963.0/759168069632.0 , 378 a103 = -48321525963.0/759168069632.0 , 379 a104 = 8530738453321.0/197654829557760.0 , 379 a104 = 8530738453321.0/197654829557760.0 , 380 a105 = 1361640523001.0/1626788720640.0 , 380 a105 = 1361640523001.0/1626788720640.0 , 381 a106 = -13143060689.0/38604458898.0 , 381 a106 = -13143060689.0/38604458898.0 , 382 a107 = 18700221969.0/379584034816.0 , 382 a107 = 18700221969.0/379584034816.0 , 383 a108 = -5831595.0/847285792.0 , 383 a108 = -5831595.0/847285792.0 , 384 a109 = -5183640.0/26477681.0 , 384 a109 = -5183640.0/26477681.0 , 385 385 386 a111 = 98719073263.0/1551965184000.0 , 386 a111 = 98719073263.0/1551965184000.0 , 387 a112 = 1307.0/123552.0 , 387 a112 = 1307.0/123552.0 , 388 a113 = 4632066559387.0/70181753241600.0 , 388 a113 = 4632066559387.0/70181753241600.0 , 389 a114 = 7828594302389.0/382182512025600.0 , 389 a114 = 7828594302389.0/382182512025600.0 , 390 a115 = 40763687.0/11070259200.0 , 390 a115 = 40763687.0/11070259200.0 , 391 a116 = 34872732407.0/224610586200.0 , 391 a116 = 34872732407.0/224610586200.0 , 392 a117 = -2561897.0/30105600.0 , 392 a117 = -2561897.0/30105600.0 , 393 a118 = 1.0/10.0 , 393 a118 = 1.0/10.0 , 394 a119 = -1.0/10.0 , 394 a119 = -1.0/10.0 , 395 a1110 = -1403317093.0/11371610250.0 ; 395 a1110 = -1403317093.0/11371610250.0 ; 396 396 397 const G4int numberOfVariables= this->GetNu 397 const G4int numberOfVariables= this->GetNumberOfVariables(); 398 const G4double* dydx= fLastDyDx; 398 const G4double* dydx= fLastDyDx; 399 const G4double Step = fLastStepLength; 399 const G4double Step = fLastStepLength; 400 400 401 yTemp[7] = yIn[7]; 401 yTemp[7] = yIn[7]; 402 402 403 // Evaluate the extra stages 403 // Evaluate the extra stages 404 // 404 // 405 for(G4int i=0; i<numberOfVariables; ++i) 405 for(G4int i=0; i<numberOfVariables; ++i) 406 { 406 { 407 yTemp[i] = yIn[i] + Step*(a91*dydx[i] 407 yTemp[i] = yIn[i] + Step*(a91*dydx[i] + a92*ak2[i] + a93*ak3[i] + 408 a94*ak4[i] + 408 a94*ak4[i] + a95*ak5[i] + a96*ak6[i] + 409 a97*ak7[i] + 409 a97*ak7[i] + a98*ak8[i] ); 410 } 410 } 411 411 412 RightHandSide(yTemp, ak9); // 9th stage 412 RightHandSide(yTemp, ak9); // 9th stage 413 413 414 for(G4int i=0; i<numberOfVariables; ++i) 414 for(G4int i=0; i<numberOfVariables; ++i) 415 { 415 { 416 yTemp[i] = yIn[i] + Step*(a101*dydx[i] 416 yTemp[i] = yIn[i] + Step*(a101*dydx[i] + a102*ak2[i] + a103*ak3[i] + 417 a104*ak4[i] 417 a104*ak4[i] + a105*ak5[i] + a106*ak6[i] + 418 a107*ak7[i] 418 a107*ak7[i] + a108*ak8[i] + a109*ak9[i] ); 419 } 419 } 420 420 421 RightHandSide(yTemp, ak10); // 10th stage 421 RightHandSide(yTemp, ak10); // 10th stage 422 422 423 for(G4int i=0; i<numberOfVariables; ++i) 423 for(G4int i=0; i<numberOfVariables; ++i) 424 { 424 { 425 yTemp[i] = yIn[i] + Step*(a111*dydx[i] 425 yTemp[i] = yIn[i] + Step*(a111*dydx[i] + a112*ak2[i] + a113*ak3[i] + 426 a114*ak4[i] 426 a114*ak4[i] + a115*ak5[i] + a116*ak6[i] + 427 a117*ak7[i] 427 a117*ak7[i] + a118*ak8[i] + a119*ak9[i] + 428 a1110*ak10[i 428 a1110*ak10[i] ); 429 } 429 } 430 RightHandSide(yTemp, ak11); // 11th stage 430 RightHandSide(yTemp, ak11); // 11th stage 431 431 432 // In future we can restrict the number o 432 // In future we can restrict the number of variables interpolated 433 // 433 // 434 G4int nwant = numberOfVariables; 434 G4int nwant = numberOfVariables; 435 435 436 // Form the coefficients of the interpola 436 // Form the coefficients of the interpolating polynomial in its shifted 437 // and scaled form. The terms are groupe 437 // and scaled form. The terms are grouped to minimize the errors 438 // of the transformation, to cope with il 438 // of the transformation, to cope with ill-conditioning. ( From RKSUITE ) 439 // 439 // 440 for (G4int l = 0; l < nwant; ++l) 440 for (G4int l = 0; l < nwant; ++l) 441 { 441 { 442 // Coefficient of tau^6 442 // Coefficient of tau^6 443 p[5][l] = bi[5][6]*ak5[l] + 443 p[5][l] = bi[5][6]*ak5[l] + 444 ((bi[10][6]*ak10[l] + bi[8][ 444 ((bi[10][6]*ak10[l] + bi[8][6]*ak8[l]) + 445 (bi[7][6]*ak7[l] + bi[6][6] 445 (bi[7][6]*ak7[l] + bi[6][6]*ak6[l])) + 446 ((bi[4][6]*ak4[l] + bi[9][6] 446 ((bi[4][6]*ak4[l] + bi[9][6]*ak9[l]) + 447 (bi[3][6]*ak3[l] + bi[11][6 447 (bi[3][6]*ak3[l] + bi[11][6]*ak11[l]) + 448 bi[1][6]*dydx[l]); 448 bi[1][6]*dydx[l]); 449 // Coefficient of tau^5 449 // Coefficient of tau^5 450 p[4][l] = (bi[10][5]*ak10[l] + bi[9][5 450 p[4][l] = (bi[10][5]*ak10[l] + bi[9][5]*ak9[l]) + 451 ((bi[7][5]*ak7[l] + bi[6][5]* 451 ((bi[7][5]*ak7[l] + bi[6][5]*ak6[l]) + 452 bi[5][5]*ak5[l]) + ((bi[4 452 bi[5][5]*ak5[l]) + ((bi[4][5]*ak4[l] + 453 bi[8][5]*ak8[l]) + (bi[3][5 453 bi[8][5]*ak8[l]) + (bi[3][5]*ak3[l] + 454 bi[11][5]*ak11[l]) + bi[1][ 454 bi[11][5]*ak11[l]) + bi[1][5]*dydx[l]); 455 // Coefficient of tau^4 455 // Coefficient of tau^4 456 p[3][l] = ((bi[4][4]*ak4[l] + bi[8][4] 456 p[3][l] = ((bi[4][4]*ak4[l] + bi[8][4]*ak8[l]) + 457 (bi[7][4]*ak7[l] + bi[6][4] 457 (bi[7][4]*ak7[l] + bi[6][4]*ak6[l]) + 458 bi[5][4]*ak5[l]) + ((bi[10 458 bi[5][4]*ak5[l]) + ((bi[10][4]*ak10[l] + 459 bi[9][4]*ak9[l]) + (bi[3] 459 bi[9][4]*ak9[l]) + (bi[3][4]*ak3[l] + 460 bi[11][4]*ak11[l]) + bi[1] 460 bi[11][4]*ak11[l]) + bi[1][4]*dydx[l]); 461 // Coefficient of tau^3 461 // Coefficient of tau^3 462 p[2][l] = bi[5][3]*ak5[l] + bi[6][3]* 462 p[2][l] = bi[5][3]*ak5[l] + bi[6][3]*ak6[l] + 463 ((bi[3][3]*ak3[l] + bi[9][3]* 463 ((bi[3][3]*ak3[l] + bi[9][3]*ak9[l]) + 464 (bi[10][3]*ak10[l]+ bi[8][3]* 464 (bi[10][3]*ak10[l]+ bi[8][3]*ak8[l]) + bi[1][3]*dydx[l]) + 465 ((bi[4][3]*ak4[l] + bi[11][3] 465 ((bi[4][3]*ak4[l] + bi[11][3]*ak11[l]) + bi[7][3]*ak7[l]); 466 // Coefficient of tau^2 466 // Coefficient of tau^2 467 p[1][l] = bi[5][2]*ak5[l] + ((bi[6][2 467 p[1][l] = bi[5][2]*ak5[l] + ((bi[6][2]*ak6[l] + 468 bi[8][2]*ak8[l]) + bi[1][2 468 bi[8][2]*ak8[l]) + bi[1][2]*dydx[l]) + 469 ((bi[3][2]*ak3[l] + bi[9][2 469 ((bi[3][2]*ak3[l] + bi[9][2]*ak9[l]) + 470 bi[10][2]*ak10[l])+ ((bi[4][2 470 bi[10][2]*ak10[l])+ ((bi[4][2]*ak4[l] + 471 bi[11][2]*ak2[l]) + bi[7][2 471 bi[11][2]*ak2[l]) + bi[7][2]*ak7[l]); 472 } 472 } 473 473 474 // Scale all the coefficients by the st 474 // Scale all the coefficients by the step size. 475 // 475 // 476 for (auto & i : p) << 476 for (G4int i = 0; i < 6; ++i) 477 { 477 { 478 for (G4int l = 0; l < nwant; ++l) 478 for (G4int l = 0; l < nwant; ++l) 479 { 479 { 480 i[l] *= Step; << 480 p[i][l] *= Step; 481 } 481 } 482 } 482 } 483 483 484 fPreparedInterpolation = true; 484 fPreparedInterpolation = true; 485 } 485 } 486 486 487 void G4BogackiShampine45::PrepareConstants() 487 void G4BogackiShampine45::PrepareConstants() 488 { 488 { 489 for(auto i=1; i<= 11; ++i) 489 for(auto i=1; i<= 11; ++i) 490 { 490 { 491 bi[i][1] = 0.0 ; 491 bi[i][1] = 0.0 ; 492 } 492 } 493 493 494 for(auto i=1; i<=6; ++i) 494 for(auto i=1; i<=6; ++i) 495 { 495 { 496 bi[2][i] = 0.0 ; 496 bi[2][i] = 0.0 ; 497 } 497 } 498 498 499 bi[1][6] = -12134338393.0 / 1050809760.0 , 499 bi[1][6] = -12134338393.0 / 1050809760.0 , 500 bi[1][5] = -1620741229.0 / 50038560.0 , 500 bi[1][5] = -1620741229.0 / 50038560.0 , 501 bi[1][4] = -2048058893.0 / 59875200.0 , 501 bi[1][4] = -2048058893.0 / 59875200.0 , 502 bi[1][3] = -87098480009.0 / 5254048800.0 , 502 bi[1][3] = -87098480009.0 / 5254048800.0 , 503 bi[1][2] = -11513270273.0 / 3502699200.0 , 503 bi[1][2] = -11513270273.0 / 3502699200.0 , 504 // 504 // 505 bi[3][6] = -33197340367.0 / 1218433216.0 505 bi[3][6] = -33197340367.0 / 1218433216.0 , 506 bi[3][5] = -539868024987.0 / 6092166080.0 506 bi[3][5] = -539868024987.0 / 6092166080.0 , 507 bi[3][4] = -39991188681.0 / 374902528.0 , 507 bi[3][4] = -39991188681.0 / 374902528.0 , 508 bi[3][3] = -69509738227.0 / 1218433216.0 508 bi[3][3] = -69509738227.0 / 1218433216.0 , 509 bi[3][2] = -29327744613.0 / 2436866432.0 509 bi[3][2] = -29327744613.0 / 2436866432.0 , 510 // 510 // 511 bi[4][6] = -284800997201.0 / 1990533916 511 bi[4][6] = -284800997201.0 / 19905339168.0 , 512 bi[4][5] = -7896875450471.0 / 16587782640 512 bi[4][5] = -7896875450471.0 / 165877826400.0 , 513 bi[4][4] = -333945812879.0 / 567103680 513 bi[4][4] = -333945812879.0 / 5671036800.0 , 514 bi[4][3] = -16209923456237.0 / 49763347920 514 bi[4][3] = -16209923456237.0 / 497633479200.0 , 515 bi[4][2] = -2382590741699.0 / 33175565280 515 bi[4][2] = -2382590741699.0 / 331755652800.0 , 516 // 516 // 517 bi[5][6] = -540919.0 / 741312.0 , 517 bi[5][6] = -540919.0 / 741312.0 , 518 bi[5][5] = -103626067.0 / 43243200.0 , 518 bi[5][5] = -103626067.0 / 43243200.0 , 519 bi[5][4] = -633779.0 / 211200.0 , 519 bi[5][4] = -633779.0 / 211200.0 , 520 bi[5][3] = -32406787.0 / 18532800.0 , 520 bi[5][3] = -32406787.0 / 18532800.0 , 521 bi[5][2] = -36591193.0 / 86486400.0 , 521 bi[5][2] = -36591193.0 / 86486400.0 , 522 // 522 // 523 bi[6][6] = 7157998304.0 / 374350977.0 , 523 bi[6][6] = 7157998304.0 / 374350977.0 , 524 bi[6][5] = 30405842464.0 / 623918295.0 , 524 bi[6][5] = 30405842464.0 / 623918295.0 , 525 bi[6][4] = 183022264.0 / 5332635.0 , 525 bi[6][4] = 183022264.0 / 5332635.0 , 526 bi[6][3] = -3357024032.0 / 1871754885.0 , 526 bi[6][3] = -3357024032.0 / 1871754885.0 , 527 bi[6][2] = -611586736.0 / 89131185.0 , 527 bi[6][2] = -611586736.0 / 89131185.0 , 528 // 528 // 529 bi[7][6] = -138073.0 / 9408.0 , 529 bi[7][6] = -138073.0 / 9408.0 , 530 bi[7][5] = -719433.0 / 15680.0 , 530 bi[7][5] = -719433.0 / 15680.0 , 531 bi[7][4] = -1620541.0 / 31360.0 , 531 bi[7][4] = -1620541.0 / 31360.0 , 532 bi[7][3] = -385151.0 / 15680.0 , 532 bi[7][3] = -385151.0 / 15680.0 , 533 bi[7][2] = -65403.0 / 15680.0 , 533 bi[7][2] = -65403.0 / 15680.0 , 534 // 534 // 535 bi[8][6] = 1245.0 / 64.0 , 535 bi[8][6] = 1245.0 / 64.0 , 536 bi[8][5] = 3991.0 / 64.0 , 536 bi[8][5] = 3991.0 / 64.0 , 537 bi[8][4] = 4715.0 / 64.0 , 537 bi[8][4] = 4715.0 / 64.0 , 538 bi[8][3] = 2501.0 / 64.0 , 538 bi[8][3] = 2501.0 / 64.0 , 539 bi[8][2] = 149.0 / 16.0 , 539 bi[8][2] = 149.0 / 16.0 , 540 bi[8][1] = 1.0 , 540 bi[8][1] = 1.0 , 541 // 541 // 542 bi[9][6] = 55.0 / 3.0 , 542 bi[9][6] = 55.0 / 3.0 , 543 bi[9][5] = 71.0 , 543 bi[9][5] = 71.0 , 544 bi[9][4] = 103.0 , 544 bi[9][4] = 103.0 , 545 bi[9][3] = 199.0 / 3.0 , 545 bi[9][3] = 199.0 / 3.0 , 546 bi[9][2] = 16.0 , 546 bi[9][2] = 16.0 , 547 // 547 // 548 bi[10][6] = -1774004627.0 / 75810735.0 548 bi[10][6] = -1774004627.0 / 75810735.0 , 549 bi[10][5] = -1774004627.0 / 25270245.0 549 bi[10][5] = -1774004627.0 / 25270245.0 , 550 bi[10][4] = -26477681.0 / 359975.0 550 bi[10][4] = -26477681.0 / 359975.0 , 551 bi[10][3] = -11411880511.0 / 379053675.0 551 bi[10][3] = -11411880511.0 / 379053675.0 , 552 bi[10][2] = -423642896.0 / 126351225.0 552 bi[10][2] = -423642896.0 / 126351225.0 , 553 // 553 // 554 bi[11][6] = 35.0 , 554 bi[11][6] = 35.0 , 555 bi[11][5] = 105.0 , 555 bi[11][5] = 105.0 , 556 bi[11][4] = 117.0 , 556 bi[11][4] = 117.0 , 557 bi[11][3] = 59.0 , 557 bi[11][3] = 59.0 , 558 bi[11][2] = 12.0 ; 558 bi[11][2] = 12.0 ; 559 559 560 fPreparedConstants = true; 560 fPreparedConstants = true; 561 } 561 } 562 562 563 void G4BogackiShampine45::InterpolateHigh(G4do 563 void G4BogackiShampine45::InterpolateHigh(G4double tau, G4double* yOut) const 564 { 564 { 565 G4int numberOfVariables = GetNumberOfVaria 565 G4int numberOfVariables = GetNumberOfVariables(); 566 566 567 G4Exception("G4BogackiShampine45::Interpol 567 G4Exception("G4BogackiShampine45::InterpolateHigh()", "GeomField0001", 568 FatalException, "Method is not 568 FatalException, "Method is not yet validated."); 569 569 570 // const G4double *yIn= fLastInitialVecto 570 // const G4double *yIn= fLastInitialVector; 571 // const G4double *dydx= fLastDyDx; 571 // const G4double *dydx= fLastDyDx; 572 const G4double Step = fLastStepLength; 572 const G4double Step = fLastStepLength; 573 573 574 #if 1 574 #if 1 575 G4int nwant = numberOfVariables; 575 G4int nwant = numberOfVariables; 576 const G4int norder= 6; 576 const G4int norder= 6; 577 G4int l, k; 577 G4int l, k; 578 578 579 for (l = 0; l < nwant; ++l) 579 for (l = 0; l < nwant; ++l) 580 { 580 { 581 yOut[l] = p[norder-1][l] * tau; 581 yOut[l] = p[norder-1][l] * tau; 582 } 582 } 583 for (k = norder - 2; k >= 1; --k) 583 for (k = norder - 2; k >= 1; --k) 584 { 584 { 585 for (l = 0; l < nwant; ++l) 585 for (l = 0; l < nwant; ++l) 586 { 586 { 587 yOut[l] = ( yOut[l] + p[k][l] ) * tau 587 yOut[l] = ( yOut[l] + p[k][l] ) * tau; 588 } 588 } 589 } 589 } 590 for (l = 0; l < nwant; ++l) 590 for (l = 0; l < nwant; ++l) 591 { 591 { 592 yOut[l] = ( yOut[l] + Step * ak8[l] ) * 592 yOut[l] = ( yOut[l] + Step * ak8[l] ) * tau + yIn[l]; 593 } 593 } 594 // The derivative at the end-point is next 594 // The derivative at the end-point is nextDydx[i] = ak8[i]; 595 #else 595 #else 596 // The scheme tries to do the same as the 596 // The scheme tries to do the same as the DormandPrince745 routine, 597 // but fails 597 // but fails 598 598 599 G4double b[12]; 599 G4double b[12]; 600 const G4double* dydx = fLastDyDx; 600 const G4double* dydx = fLastDyDx; 601 601 602 G4double tau0 = tau; 602 G4double tau0 = tau; 603 603 604 for(G4int iStage=1; iStage<=11; ++iStage) 604 for(G4int iStage=1; iStage<=11; ++iStage) // iStage = stage number 605 { 605 { 606 b[iStage] = 0.0; 606 b[iStage] = 0.0; 607 tau = tau0; 607 tau = tau0; 608 for(G4int j=6; j>=1; --j) 608 for(G4int j=6; j>=1; --j) // j reversed 609 { 609 { 610 b[iStage] += bi[iStage][j] * tau; 610 b[iStage] += bi[iStage][j] * tau; 611 tau *= tau0; 611 tau *= tau0; 612 } 612 } 613 } 613 } 614 614 615 for(G4int i=0; i<numberOfVariables; ++i) 615 for(G4int i=0; i<numberOfVariables; ++i) 616 { 616 { 617 yOut[i] = yIn[i] + Step*(b[1]*dydx[i] 617 yOut[i] = yIn[i] + Step*(b[1]*dydx[i] + b[2]*ak2[i] + b[3]*ak3[i] + 618 b[4]*ak4[i] + 618 b[4]*ak4[i] + b[5]*ak5[i] + b[6]*ak6[i] + 619 b[7]*ak7[i] + 619 b[7]*ak7[i] + b[8]*ak8[i] + b[9]*ak9[i] + 620 b[10]*ak10[i] 620 b[10]*ak10[i] + b[11]*ak11[i] ); 621 } 621 } 622 #endif 622 #endif 623 } 623 } 624 624