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Geant4/geometry/magneticfield/src/G4CashKarpRKF45.cc

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Differences between /geometry/magneticfield/src/G4CashKarpRKF45.cc (Version 11.3.0) and /geometry/magneticfield/src/G4CashKarpRKF45.cc (Version 6.2.p2)


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 24 // *******************************************     21 // ********************************************************************
 25 //                                                 22 //
 26 // G4CashKarpRKF45 implementation              <<  23 //
                                                   >>  24 // $Id: G4CashKarpRKF45.cc,v 1.13 2003/10/31 14:35:53 gcosmo Exp $
                                                   >>  25 // GEANT4 tag $Name: geant4-06-00-patch-01 $
 27 //                                                 26 //
 28 // The Cash-Karp Runge-Kutta-Fehlberg 4/5 meth     27 // The Cash-Karp Runge-Kutta-Fehlberg 4/5 method is an embedded fourth
 29 // order method (giving fifth-order accuracy)      28 // order method (giving fifth-order accuracy) for the solution of an ODE.
 30 // Two different fourth order estimates are ca     29 // Two different fourth order estimates are calculated; their difference
 31 // gives an error estimate. [ref. Numerical Re     30 // gives an error estimate. [ref. Numerical Recipes in C, 2nd Edition]
 32 // It is used to integrate the equations of th     31 // It is used to integrate the equations of the motion of a particle 
 33 // in a magnetic field.                            32 // in a magnetic field.
 34 //                                                 33 //
 35 // [ref. Numerical Recipes in C, 2nd Edition]  <<  34 //  [ref. Numerical Recipes in C, 2nd Edition]
 36 //                                                 35 //
 37 // Authors: J.Apostolakis, V.Grichine - 30.01. << 
 38 // -------------------------------------------     36 // -------------------------------------------------------------------
 39                                                    37 
 40 #include "G4CashKarpRKF45.hh"                      38 #include "G4CashKarpRKF45.hh"
 41 #include "G4LineSection.hh"                        39 #include "G4LineSection.hh"
 42                                                    40 
 43 //////////////////////////////////////////////     41 /////////////////////////////////////////////////////////////////////
 44 //                                                 42 //
 45 // Constructor                                     43 // Constructor
 46 //                                             <<  44 
 47 G4CashKarpRKF45::G4CashKarpRKF45(G4EquationOfM <<  45 G4CashKarpRKF45::G4CashKarpRKF45(G4EquationOfMotion *EqRhs, G4int numberOfVariables, G4bool primary)
 48                                  G4int noInteg <<  46   : G4MagIntegratorStepper(EqRhs, numberOfVariables)
 49                                  G4bool primar << 
 50   : G4MagIntegratorStepper(EqRhs, noIntegratio << 
 51 {                                                  47 {
 52   const G4int numberOfVariables =              <<  48   fNumberOfVariables = numberOfVariables ;
 53       std::max( noIntegrationVariables,        <<  49 
 54                ( ( (noIntegrationVariables-1)/ <<  50   ak2 = new G4double[fNumberOfVariables] ;  
 55   // For better alignment with cache-line      <<  51   ak3 = new G4double[fNumberOfVariables] ; 
 56                                                <<  52   ak4 = new G4double[fNumberOfVariables] ; 
 57   ak2 = new G4double[numberOfVariables] ;      <<  53   ak5 = new G4double[fNumberOfVariables] ; 
 58   ak3 = new G4double[numberOfVariables] ;      <<  54   ak6 = new G4double[fNumberOfVariables] ; 
 59   ak4 = new G4double[numberOfVariables] ;      <<  55   ak7 = 0;
 60   ak5 = new G4double[numberOfVariables] ;      <<  56   yTemp = new G4double[fNumberOfVariables] ; 
 61   ak6 = new G4double[numberOfVariables] ;      <<  57   yIn = new G4double[fNumberOfVariables] ;
 62   // ak7 = 0;                                  <<  58 
 63                                                <<  59   fLastInitialVector = new G4double[fNumberOfVariables] ;
 64   // Must ensure space extra 'state' variables <<  60   fLastFinalVector = new G4double[fNumberOfVariables] ;
 65   const G4int numStateMax  = std::max(GetNumbe <<  61   fLastDyDx = new G4double[fNumberOfVariables];
 66   const G4int numStateVars = std::max(noIntegr <<  62 
 67                                       numState <<  63   fMidVector = new G4double[fNumberOfVariables];
 68                                    // GetNumbe <<  64   fMidError =  new G4double[fNumberOfVariables];
 69                                                <<  65   fAuxStepper = 0;   
 70   yTemp = new G4double[numStateVars] ;         <<  66   if( primary ) 
 71   yIn = new G4double[numStateVars] ;           <<  67       fAuxStepper = new G4CashKarpRKF45(EqRhs, numberOfVariables, !primary);
 72                                                <<  68 
 73   fLastInitialVector = new G4double[numStateVa << 
 74   fLastFinalVector = new G4double[numStateVars << 
 75   fLastDyDx = new G4double[numberOfVariables]; << 
 76                                                << 
 77   fMidVector = new G4double[numStateVars];     << 
 78   fMidError =  new G4double[numStateVars];     << 
 79   if( primary )                                << 
 80   {                                            << 
 81     fAuxStepper = new G4CashKarpRKF45(EqRhs, n << 
 82   }                                            << 
 83 }                                                  69 }
 84                                                    70 
 85 //////////////////////////////////////////////     71 /////////////////////////////////////////////////////////////////////
 86 //                                                 72 //
 87 // Destructor                                      73 // Destructor
 88 //                                             <<  74 
 89 G4CashKarpRKF45::~G4CashKarpRKF45()                75 G4CashKarpRKF45::~G4CashKarpRKF45()
 90 {                                                  76 {
 91   delete [] ak2;                               <<  77   delete[] ak2;
 92   delete [] ak3;                               <<  78   delete[] ak3;
 93   delete [] ak4;                               <<  79   delete[] ak4;
 94   delete [] ak5;                               <<  80   delete[] ak5;
 95   delete [] ak6;                               <<  81   delete[] ak6;
 96   // delete [] ak7;                            <<  82   // delete[] ak7;
 97   delete [] yTemp;                             <<  83   delete[] yTemp;
 98   delete [] yIn;                               <<  84   delete[] yIn;
 99                                                <<  85 
100   delete [] fLastInitialVector;                <<  86   delete[] fLastInitialVector;
101   delete [] fLastFinalVector;                  <<  87   delete[] fLastFinalVector;
102   delete [] fLastDyDx;                         <<  88   delete[] fLastDyDx;
103   delete [] fMidVector;                        <<  89   delete[] fMidVector;
104   delete [] fMidError;                         <<  90   delete[] fMidError; 
105                                                    91 
106   delete fAuxStepper;                              92   delete fAuxStepper;
107 }                                                  93 }
108                                                    94 
109 //////////////////////////////////////////////     95 //////////////////////////////////////////////////////////////////////
110 //                                                 96 //
111 // Given values for n = 6 variables yIn[0,...,     97 // Given values for n = 6 variables yIn[0,...,n-1] 
112 // known  at x, use the fifth-order Cash-Karp      98 // known  at x, use the fifth-order Cash-Karp Runge-
113 // Kutta-Fehlberg-4-5 method to advance the so     99 // Kutta-Fehlberg-4-5 method to advance the solution over an interval
114 // Step and return the incremented variables a    100 // Step and return the incremented variables as yOut[0,...,n-1]. Also
115 // return an estimate of the local truncation     101 // return an estimate of the local truncation error yErr[] using the
116 // embedded 4th-order method. The user supplie    102 // embedded 4th-order method. The user supplies routine
117 // RightHandSide(y,dydx), which returns deriva    103 // RightHandSide(y,dydx), which returns derivatives dydx for y .
118 //                                             << 104 
119 void                                              105 void
120 G4CashKarpRKF45::Stepper(const G4double yInput    106 G4CashKarpRKF45::Stepper(const G4double yInput[],
121                          const G4double dydx[]    107                          const G4double dydx[],
122                                G4double Step,     108                                G4double Step,
123                                G4double yOut[]    109                                G4double yOut[],
124                                G4double yErr[]    110                                G4double yErr[])
125 {                                                 111 {
126   // const G4int nvar = 6 ;                       112   // const G4int nvar = 6 ;
127   // const G4double a2 = 0.2 , a3 = 0.3 , a4 =    113   // const G4double a2 = 0.2 , a3 = 0.3 , a4 = 0.6 , a5 = 1.0 , a6 = 0.875;
128   G4int i;                                     << 114  G4int i;
129                                                   115 
130   const G4double  b21 = 0.2 ,                  << 116  const G4double  b21 = 0.2 ,
131                   b31 = 3.0/40.0 , b32 = 9.0/4 << 117                  b31 = 3.0/40.0 , b32 = 9.0/40.0 ,
132                   b41 = 0.3 , b42 = -0.9 , b43 << 118                  b41 = 0.3 , b42 = -0.9 , b43 = 1.2 ,
133                                                   119 
134                   b51 = -11.0/54.0 , b52 = 2.5 << 120                  b51 = -11.0/54.0 , b52 = 2.5 , b53 = -70.0/27.0 ,
135                   b54 = 35.0/27.0 ,            << 121                  b54 = 35.0/27.0 ,
136                                                   122 
137                   b61 = 1631.0/55296.0 , b62 = << 123                  b61 = 1631.0/55296.0 , b62 =   175.0/512.0 ,
138                   b63 =  575.0/13824.0 , b64 = << 124                  b63 =  575.0/13824.0 , b64 = 44275.0/110592.0 ,
139                   b65 =  253.0/4096.0 ,        << 125                  b65 =  253.0/4096.0 ,
140                                                   126 
141                   c1 = 37.0/378.0 , c3 = 250.0 << 127                  c1 = 37.0/378.0 , c3 = 250.0/621.0 , c4 = 125.0/594.0 ,
142                   c6 = 512.0/1771.0 , dc5 = -2 << 128                  c6 = 512.0/1771.0 ,
                                                   >> 129                                           dc5 = -277.0/14336.0 ;
143                                                   130 
144   const G4double dc1 = c1 - 2825.0/27648.0 ,   << 131  const G4double dc1 = c1 - 2825.0/27648.0 ,  dc3 = c3 - 18575.0/48384.0 ,
145                  dc4 = c4 - 13525.0/55296.0 ,  << 132     dc4 = c4 - 13525.0/55296.0 , dc6 = c6 - 0.25 ;
146                                                   133 
147   // Initialise time to t0, needed when it is  << 
148   //        [ Note: Only for time dependent fi << 
149   //                  is it neccessary to inte << 
150   yOut[7] = yTemp[7] = yIn[7] = yInput[7];     << 
151                                                   134 
152   const G4int numberOfVariables= this->GetNumb << 135    //  Saving yInput because yInput and yOut can be aliases for same array
153     // The number of variables to be integrate << 
154                                                   136 
155   //  Saving yInput because yInput and yOut ca << 137    for(i=0;i<fNumberOfVariables;i++) 
                                                   >> 138    {
                                                   >> 139      yIn[i]=yInput[i];
                                                   >> 140    }
                                                   >> 141  // RightHandSide(yIn, dydx) ;              // 1st Step
156                                                   142 
157   for(i=0; i<numberOfVariables; ++i)           << 143  for(i=0;i<fNumberOfVariables;i++) 
158   {                                            << 144  {
159     yIn[i]=yInput[i];                          << 145    yTemp[i] = yIn[i] + b21*Step*dydx[i] ;
160   }                                            << 146  }
161   // RightHandSide(yIn, dydx) ;            //  << 147  RightHandSide(yTemp, ak2) ;              // 2nd Step
162                                                << 
163   for(i=0; i<numberOfVariables; ++i)           << 
164   {                                            << 
165     yTemp[i] = yIn[i] + b21*Step*dydx[i] ;     << 
166   }                                            << 
167   RightHandSide(yTemp, ak2) ;              //  << 
168                                                   148 
169   for(i=0; i<numberOfVariables; ++i)           << 149  for(i=0;i<fNumberOfVariables;i++)
170   {                                            << 150  {
171     yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b3    151     yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b32*ak2[i]) ;
172   }                                            << 152  }
173   RightHandSide(yTemp, ak3) ;              //  << 153  RightHandSide(yTemp, ak3) ;              // 3rd Step
174                                                   154 
175   for(i=0; i<numberOfVariables; ++i)           << 155  for(i=0;i<fNumberOfVariables;i++)
176   {                                            << 156  {
177     yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b4    157     yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b42*ak2[i] + b43*ak3[i]) ;
178   }                                            << 158  }
179   RightHandSide(yTemp, ak4) ;              //  << 159  RightHandSide(yTemp, ak4) ;              // 4th Step
180                                                   160 
181   for(i=0; i<numberOfVariables; ++i)           << 161  for(i=0;i<fNumberOfVariables;i++)
182   {                                            << 162  {
183     yTemp[i] = yIn[i] + Step*(b51*dydx[i]      << 163     yTemp[i] = yIn[i] + Step*(b51*dydx[i] + b52*ak2[i] + b53*ak3[i] +
184                       + b52*ak2[i] + b53*ak3[i << 164                       b54*ak4[i]) ;
185   }                                            << 165  }
186   RightHandSide(yTemp, ak5) ;              //  << 166  RightHandSide(yTemp, ak5) ;              // 5th Step
187                                                << 167 
188   for(i=0; i<numberOfVariables; ++i)           << 168  for(i=0;i<fNumberOfVariables;i++)
189   {                                            << 169  {
190     yTemp[i] = yIn[i] + Step*(b61*dydx[i]      << 170     yTemp[i] = yIn[i] + Step*(b61*dydx[i] + b62*ak2[i] + b63*ak3[i] +
191                       + b62*ak2[i] + b63*ak3[i << 171                       b64*ak4[i] + b65*ak5[i]) ;
192   }                                            << 172  }
193   RightHandSide(yTemp, ak6) ;              //  << 173  RightHandSide(yTemp, ak6) ;              // 6th Step
194                                                   174 
195   for(i=0; i<numberOfVariables; ++i)           << 175  for(i=0;i<fNumberOfVariables;i++)
196   {                                            << 176  {
197     // Accumulate increments with proper weigh    177     // Accumulate increments with proper weights
198     //                                         << 178 
199     yOut[i] = yIn[i] + Step*(c1*dydx[i] + c3*a    179     yOut[i] = yIn[i] + Step*(c1*dydx[i] + c3*ak3[i] + c4*ak4[i] + c6*ak6[i]) ;
200                                                   180 
201     // Estimate error as difference between 4t << 181     // Estimate error as difference between 4th and
202     //                                         << 182     // 5th order methods
203     yErr[i] = Step*(dc1*dydx[i]                << 183 
204             + dc3*ak3[i] + dc4*ak4[i] + dc5*ak << 184     yErr[i] = Step*(dc1*dydx[i] + dc3*ak3[i] + dc4*ak4[i] +
                                                   >> 185               dc5*ak5[i] + dc6*ak6[i]) ;
205                                                   186 
206     // Store Input and Final values, for possi    187     // Store Input and Final values, for possible use in calculating chord
207     //                                         << 
208     fLastInitialVector[i] = yIn[i] ;              188     fLastInitialVector[i] = yIn[i] ;
209     fLastFinalVector[i]   = yOut[i];              189     fLastFinalVector[i]   = yOut[i];
210     fLastDyDx[i]          = dydx[i];              190     fLastDyDx[i]          = dydx[i];
211   }                                            << 191  }
212   // NormaliseTangentVector( yOut ); // Not wa << 192  // NormaliseTangentVector( yOut ); // Not wanted
213                                                   193 
214   fLastStepLength = Step;                      << 194  fLastStepLength =Step;
215                                                   195 
216   return;                                      << 196  return ;
217 }                                                 197 } 
218                                                   198 
219 //////////////////////////////////////////////    199 ///////////////////////////////////////////////////////////////////////////////
220 //                                             << 200 
221 void                                              201 void
222 G4CashKarpRKF45::StepWithEst( const G4double*,    202 G4CashKarpRKF45::StepWithEst( const G4double*,
223                               const G4double*,    203                               const G4double*,
224                                     G4double,     204                                     G4double,
225                                     G4double*,    205                                     G4double*,
226                                     G4double&,    206                                     G4double&,
227                                     G4double&,    207                                     G4double&,
228                               const G4double*,    208                               const G4double*,
229                                     G4double*     209                                     G4double*  )    
230 {                                                 210 {
231   G4Exception("G4CashKarpRKF45::StepWithEst()" << 211   G4Exception("G4CashKarpRKF45::StepWithEst()", "ObsoleteMethod",
232               FatalException, "Method no longe    212               FatalException, "Method no longer used.");
233   return ;                                        213   return ;
234 }                                                 214 }
235                                                   215 
236 //////////////////////////////////////////////    216 /////////////////////////////////////////////////////////////////
237 //                                             << 217 
238 G4double  G4CashKarpRKF45::DistChord() const      218 G4double  G4CashKarpRKF45::DistChord() const
239 {                                                 219 {
240   G4double distLine, distChord;                   220   G4double distLine, distChord; 
241   G4ThreeVector initialPoint, finalPoint, midP    221   G4ThreeVector initialPoint, finalPoint, midPoint;
242                                                   222 
243   // Store last initial and final points       << 223   // Store last initial and final points (they will be overwritten in self-Stepper call!)
244   // (they will be overwritten in self-Stepper << 
245   //                                           << 
246   initialPoint = G4ThreeVector( fLastInitialVe    224   initialPoint = G4ThreeVector( fLastInitialVector[0], 
247                                 fLastInitialVe    225                                 fLastInitialVector[1], fLastInitialVector[2]); 
248   finalPoint   = G4ThreeVector( fLastFinalVect    226   finalPoint   = G4ThreeVector( fLastFinalVector[0],  
249                                 fLastFinalVect    227                                 fLastFinalVector[1],  fLastFinalVector[2]); 
250                                                   228 
251   // Do half a step using StepNoErr               229   // Do half a step using StepNoErr
252   //                                           << 230 
253   fAuxStepper->Stepper( fLastInitialVector, fL << 231   fAuxStepper->Stepper( fLastInitialVector, fLastDyDx, 0.5 * fLastStepLength, 
254                         0.5 * fLastStepLength, << 232            fMidVector,   fMidError );
255                                                   233 
256   midPoint = G4ThreeVector( fMidVector[0], fMi    234   midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2]);       
257                                                   235 
258   // Use stored values of Initial and Endpoint    236   // Use stored values of Initial and Endpoint + new Midpoint to evaluate
259   // distance of Chord                         << 237   //  distance of Chord
260   //                                           << 238 
                                                   >> 239 
261   if (initialPoint != finalPoint)                 240   if (initialPoint != finalPoint) 
262   {                                               241   {
263      distLine  = G4LineSection::Distline( midP    242      distLine  = G4LineSection::Distline( midPoint, initialPoint, finalPoint );
264      distChord = distLine;                        243      distChord = distLine;
265   }                                               244   }
266   else                                            245   else
267   {                                               246   {
268      distChord = (midPoint-initialPoint).mag()    247      distChord = (midPoint-initialPoint).mag();
269   }                                               248   }
270   return distChord;                               249   return distChord;
271 }                                                 250 }
                                                   >> 251 
                                                   >> 252 
272                                                   253