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Please see the license in the file LICENSE and URL above * 16 // * for the full disclaimer and the limitation of liability. * 17 // * * 18 // * This code implementation is the result of the scientific and * 19 // * technical work of the GEANT4 collaboration. * 20 // * By using, copying, modifying or distributing the software (or * 21 // * any work based on the software) you agree to acknowledge its * 22 // * use in resulting scientific publications, and indicate your * 23 // * acceptance of all terms of the Geant4 Software license. * 24 // ******************************************************************** 25 // 26 // G4TsitourasRK45 implementation 27 // 28 // Author: Somnath Banerjee, Google Summer of Code 2015, 11.06.2015 29 // Supervision: John Apostolakis, CERN 30 // ------------------------------------------------------------------- 31 32 #include "G4TsitourasRK45.hh" 33 #include "G4LineSection.hh" 34 35 ///////////////////////////////////////////////////////////////////// 36 // 37 // Constructor 38 // 39 G4TsitourasRK45::G4TsitourasRK45(G4EquationOfMotion *EqRhs, 40 G4int noIntegrationVariables, 41 G4bool primary) 42 : G4MagIntegratorStepper(EqRhs, noIntegrationVariables) 43 { 44 const G4int numberOfVariables = noIntegrationVariables; 45 46 ak2 = new G4double[numberOfVariables] ; 47 ak3 = new G4double[numberOfVariables] ; 48 ak4 = new G4double[numberOfVariables] ; 49 ak5 = new G4double[numberOfVariables] ; 50 ak6 = new G4double[numberOfVariables] ; 51 ak7 = new G4double[numberOfVariables] ; 52 ak8 = new G4double[numberOfVariables] ; 53 54 // Must ensure space extra 'state' variables exists - i.e. yIn[7] 55 // 56 const G4int numStateMax = std::max(GetNumberOfStateVariables(), 8); 57 const G4int numStateVars = std::max(noIntegrationVariables, 58 numStateMax ); 59 60 yTemp = new G4double[numStateVars] ; 61 yIn = new G4double[numStateVars] ; 62 63 fLastInitialVector = new G4double[numberOfVariables] ; 64 fLastFinalVector = new G4double[numberOfVariables] ; 65 66 fLastDyDx = new G4double[numberOfVariables]; 67 68 fMidVector = new G4double[numberOfVariables]; 69 fMidError = new G4double[numberOfVariables]; 70 71 if( primary ) 72 { 73 fAuxStepper = new G4TsitourasRK45(EqRhs, numberOfVariables, !primary); 74 } 75 } 76 77 ///////////////////////////////////////////////////////////////////// 78 // 79 // Destructor 80 // 81 G4TsitourasRK45::~G4TsitourasRK45() 82 { 83 delete [] ak2; 84 delete [] ak3; 85 delete [] ak4; 86 delete [] ak5; 87 delete [] ak6; 88 delete [] ak7; 89 delete [] ak8; 90 91 delete [] yTemp; 92 delete [] yIn; 93 94 delete [] fLastInitialVector; 95 delete [] fLastFinalVector; 96 delete [] fLastDyDx; 97 delete [] fMidVector; 98 delete [] fMidError; 99 100 delete fAuxStepper; 101 } 102 103 // The following coefficients have been obtained from 104 // Table 1: The Coefficients of the new pair 105 // 106 // C. Tsitouras, "Runge–Kutta pairs of order 5(4) satisfying only 107 // the first column simplifying assumption" 108 // Computers & Mathematics with Applications, vol.62, no.2, pp.770-775, 2011. 109 // 110 // A corresponding matlab code was also found at: 111 // http://users.ntua.gr/tsitoura/new54.m 112 // 113 // Doing a step 114 // 115 void 116 G4TsitourasRK45::Stepper( const G4double yInput[], 117 const G4double dydx[], 118 G4double Step, 119 G4double yOut[], 120 G4double yErr[] ) 121 { 122 const G4double b21 = 0.161 , 123 b31 = -0.00848065549235698854 , 124 b32 = 0.335480655492356989 , 125 126 b41 = 2.89715305710549343 , 127 b42 = -6.35944848997507484 , 128 b43 = 4.36229543286958141 , 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 = -0.0282690503940683829, 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 - b71 , // - 0.001780011052226, 157 dc2 = 0.00865288314156636761 - b72, // - 0.000816434459657, 158 dc3 = 0.492893099131431868 - b73 , // + 0.007880878010262, 159 dc4 = 1.14023541226785810 - b74 , // 0.144711007173263, 160 dc5 = - 2.3291801924393646 - b75, // + 0.582357165452555, 161 dc6 = 1.56887504931661552 - b76 , // - 0.458082105929187, 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 ; 171 172 const G4int numberOfVariables = GetNumberOfVariables(); 173 174 // The number of variables to be integrated over 175 // 176 yOut[7] = yTemp[7] = yIn[7] = yInput[7]; 177 178 // Saving yInput because yInput and yOut can be aliases for same array 179 // 180 for(G4int i=0; i<numberOfVariables; ++i) 181 { 182 yIn[i]=yInput[i]; 183 } 184 // RightHandSide(yIn, dydx) ; // 1st Step - Not doing, getting passed 185 186 for(G4int i=0; i<numberOfVariables; ++i) 187 { 188 yTemp[i] = yIn[i] + b21*Step*dydx[i] ; 189 } 190 RightHandSide(yTemp, ak2) ; // 2nd Stage 191 192 for(G4int i=0; i<numberOfVariables; ++i) 193 { 194 yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b32*ak2[i]) ; 195 } 196 RightHandSide(yTemp, ak3) ; // 3rd Stage 197 198 for(G4int i=0; i<numberOfVariables; ++i) 199 { 200 yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b42*ak2[i] + b43*ak3[i]) ; 201 } 202 RightHandSide(yTemp, ak4) ; // 4th Stage 203 204 for(G4int i=0; i<numberOfVariables; ++i) 205 { 206 yTemp[i] = yIn[i] + Step*(b51*dydx[i] + b52*ak2[i] + b53*ak3[i] + 207 b54*ak4[i]) ; 208 } 209 RightHandSide(yTemp, ak5) ; // 5th Stage 210 211 for(G4int i=0; i<numberOfVariables; ++i) 212 { 213 yTemp[i] = yIn[i] + Step*(b61*dydx[i] + b62*ak2[i] + b63*ak3[i] + 214 b64*ak4[i] + b65*ak5[i]) ; 215 } 216 RightHandSide(yTemp, ak6) ; // 6th Stage 217 218 for(G4int i=0; i<numberOfVariables; ++i) 219 { 220 yOut[i] = yIn[i] + Step*(b71*dydx[i] + b72*ak2[i] + b73*ak3[i] + 221 b74*ak4[i] + b75*ak5[i] + b76*ak6[i]); 222 } 223 RightHandSide(yOut, ak7); // 7th Stage 224 225 //Calculate the error in the step: 226 for(G4int i=0; i<numberOfVariables; ++i) 227 { 228 yErr[i] = Step*(dc1*dydx[i] + dc2*ak2[i] + dc3*ak3[i] + dc4*ak4[i] + 229 dc5*ak5[i] + dc6*ak6[i] + dc7*ak7[i] ) ; 230 231 // Store Input and Final values, for possible use in calculating chord 232 // 233 fLastInitialVector[i] = yIn[i] ; 234 fLastFinalVector[i] = yOut[i]; 235 fLastDyDx[i] = dydx[i]; 236 } 237 238 fLastStepLength = Step; 239 240 return ; 241 } 242 243 void G4TsitourasRK45::SetupInterpolation() 244 // (const G4double *yInput, const G4double *dydx, const G4double Step) 245 { 246 // Nothing to be done 247 } 248 249 void G4TsitourasRK45::Interpolate(const G4double* yInput, 250 const G4double* dydx, 251 const G4double Step, 252 G4double* yOut, 253 G4double tau) 254 { 255 G4double bf1, bf2, bf3, bf4, bf5, bf6, bf7; 256 // Coefficients for all the seven stages. 257 258 const G4int numberOfVariables = GetNumberOfVariables(); 259 260 G4double tau0 = tau; 261 262 for(G4int i=0; i<numberOfVariables; ++i) 263 { 264 yIn[i] = yInput[i]; 265 } 266 267 G4double tau_2 = tau0*tau0 ; 268 // tau_3 = tau0*tau_2, 269 // tau_4 = tau_2*tau_2; 270 271 bf1 = -1.0530884977290216*tau*(tau - 1.3299890189751412)*(tau_2 - 272 1.4364028541716351*tau + 0.7139816917074209); 273 bf2 = 0.1017*tau_2*(tau_2 - 2.1966568338249754*tau + 274 1.2949852507374631); 275 bf3 = 2.490627285651252793*tau_2*(tau_2 - 2.38535645472061657*tau 276 + 1.57803468208092486); 277 bf4 = -16.54810288924490272*(tau - 1.21712927295533244)* 278 (tau - 0.61620406037800089)*tau_2; 279 bf5 = 47.37952196281928122*(tau - 1.203071208372362603)* 280 (tau - 0.658047292653547382)*tau_2; 281 bf6 = -34.87065786149660974*(tau - 1.2)*(tau - 282 0.666666666666666667)*tau_2; 283 bf7 = 2.5*(tau - 1.0)*(tau - 0.6)*tau_2; 284 285 // Putting together the coefficients calculated as the respective 286 // stage coefficients 287 // 288 for(G4int i=0; i<numberOfVariables; ++i) 289 { 290 yOut[i] = yIn[i] + Step*( bf1*dydx[i] + bf2*ak2[i] + bf3*ak3[i] 291 + bf4*ak4[i] + bf5*ak5[i] + bf6*ak6[i] 292 + bf7*ak7[i] ) ; 293 } 294 } 295 296 G4double G4TsitourasRK45::DistChord() const 297 { 298 G4double distLine, distChord; 299 G4ThreeVector initialPoint, finalPoint, midPoint; 300 301 // Store last initial and final points (they will be 302 // overwritten in self-Stepper call!) 303 // 304 initialPoint = G4ThreeVector( fLastInitialVector[0], 305 fLastInitialVector[1], fLastInitialVector[2]); 306 finalPoint = G4ThreeVector( fLastFinalVector[0], 307 fLastFinalVector[1], fLastFinalVector[2]); 308 309 // Do half a step using StepNoErr 310 // 311 fAuxStepper->Stepper( fLastInitialVector, fLastDyDx, 0.5 * fLastStepLength, 312 fMidVector, fMidError ); 313 314 midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2]); 315 316 // Use stored values of Initial and Endpoint + new Midpoint to evaluate 317 // distance of Chord 318 // 319 if (initialPoint != finalPoint) 320 { 321 distLine = G4LineSection::Distline( midPoint, initialPoint, finalPoint ); 322 distChord = distLine; 323 } 324 else 325 { 326 distChord = (midPoint-initialPoint).mag(); 327 } 328 return distChord; 329 } 330