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26 // G4CashKarpRKF45 implementation << 26 //
>> 27 // $Id: G4CashKarpRKF45.cc,v 1.14 2006/06/29 18:23:29 gunter Exp $
>> 28 // GEANT4 tag $Name: geant4-08-02 $
27 // 29 //
28 // The Cash-Karp Runge-Kutta-Fehlberg 4/5 meth 30 // The Cash-Karp Runge-Kutta-Fehlberg 4/5 method is an embedded fourth
29 // order method (giving fifth-order accuracy) 31 // order method (giving fifth-order accuracy) for the solution of an ODE.
30 // Two different fourth order estimates are ca 32 // Two different fourth order estimates are calculated; their difference
31 // gives an error estimate. [ref. Numerical Re 33 // gives an error estimate. [ref. Numerical Recipes in C, 2nd Edition]
32 // It is used to integrate the equations of th 34 // It is used to integrate the equations of the motion of a particle
33 // in a magnetic field. 35 // in a magnetic field.
34 // 36 //
35 // [ref. Numerical Recipes in C, 2nd Edition] << 37 // [ref. Numerical Recipes in C, 2nd Edition]
36 // 38 //
37 // Authors: J.Apostolakis, V.Grichine - 30.01. <<
38 // ------------------------------------------- 39 // -------------------------------------------------------------------
39 40
40 #include "G4CashKarpRKF45.hh" 41 #include "G4CashKarpRKF45.hh"
41 #include "G4LineSection.hh" 42 #include "G4LineSection.hh"
42 43
43 ////////////////////////////////////////////// 44 /////////////////////////////////////////////////////////////////////
44 // 45 //
45 // Constructor 46 // Constructor
46 // << 47
47 G4CashKarpRKF45::G4CashKarpRKF45(G4EquationOfM << 48 G4CashKarpRKF45::G4CashKarpRKF45(G4EquationOfMotion *EqRhs, G4int numberOfVariables, G4bool primary)
48 G4int noInteg << 49 : G4MagIntegratorStepper(EqRhs, numberOfVariables)
49 G4bool primar <<
50 : G4MagIntegratorStepper(EqRhs, noIntegratio <<
51 { 50 {
52 const G4int numberOfVariables = << 51 fNumberOfVariables = numberOfVariables ;
53 std::max( noIntegrationVariables, << 52
54 ( ( (noIntegrationVariables-1)/ << 53 ak2 = new G4double[fNumberOfVariables] ;
55 // For better alignment with cache-line << 54 ak3 = new G4double[fNumberOfVariables] ;
56 << 55 ak4 = new G4double[fNumberOfVariables] ;
57 ak2 = new G4double[numberOfVariables] ; << 56 ak5 = new G4double[fNumberOfVariables] ;
58 ak3 = new G4double[numberOfVariables] ; << 57 ak6 = new G4double[fNumberOfVariables] ;
59 ak4 = new G4double[numberOfVariables] ; << 58 ak7 = 0;
60 ak5 = new G4double[numberOfVariables] ; << 59 yTemp = new G4double[fNumberOfVariables] ;
61 ak6 = new G4double[numberOfVariables] ; << 60 yIn = new G4double[fNumberOfVariables] ;
62 // ak7 = 0; << 61
63 << 62 fLastInitialVector = new G4double[fNumberOfVariables] ;
64 // Must ensure space extra 'state' variables << 63 fLastFinalVector = new G4double[fNumberOfVariables] ;
65 const G4int numStateMax = std::max(GetNumbe << 64 fLastDyDx = new G4double[fNumberOfVariables];
66 const G4int numStateVars = std::max(noIntegr << 65
67 numState << 66 fMidVector = new G4double[fNumberOfVariables];
68 // GetNumbe << 67 fMidError = new G4double[fNumberOfVariables];
69 << 68 fAuxStepper = 0;
70 yTemp = new G4double[numStateVars] ; << 69 if( primary )
71 yIn = new G4double[numStateVars] ; << 70 fAuxStepper = new G4CashKarpRKF45(EqRhs, numberOfVariables, !primary);
72 << 71
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 } 72 }
84 73
85 ////////////////////////////////////////////// 74 /////////////////////////////////////////////////////////////////////
86 // 75 //
87 // Destructor 76 // Destructor
88 // << 77
89 G4CashKarpRKF45::~G4CashKarpRKF45() 78 G4CashKarpRKF45::~G4CashKarpRKF45()
90 { 79 {
91 delete [] ak2; << 80 delete[] ak2;
92 delete [] ak3; << 81 delete[] ak3;
93 delete [] ak4; << 82 delete[] ak4;
94 delete [] ak5; << 83 delete[] ak5;
95 delete [] ak6; << 84 delete[] ak6;
96 // delete [] ak7; << 85 // delete[] ak7;
97 delete [] yTemp; << 86 delete[] yTemp;
98 delete [] yIn; << 87 delete[] yIn;
99 << 88
100 delete [] fLastInitialVector; << 89 delete[] fLastInitialVector;
101 delete [] fLastFinalVector; << 90 delete[] fLastFinalVector;
102 delete [] fLastDyDx; << 91 delete[] fLastDyDx;
103 delete [] fMidVector; << 92 delete[] fMidVector;
104 delete [] fMidError; << 93 delete[] fMidError;
105 94
106 delete fAuxStepper; 95 delete fAuxStepper;
107 } 96 }
108 97
109 ////////////////////////////////////////////// 98 //////////////////////////////////////////////////////////////////////
110 // 99 //
111 // Given values for n = 6 variables yIn[0,..., 100 // Given values for n = 6 variables yIn[0,...,n-1]
112 // known at x, use the fifth-order Cash-Karp 101 // known at x, use the fifth-order Cash-Karp Runge-
113 // Kutta-Fehlberg-4-5 method to advance the so 102 // Kutta-Fehlberg-4-5 method to advance the solution over an interval
114 // Step and return the incremented variables a 103 // Step and return the incremented variables as yOut[0,...,n-1]. Also
115 // return an estimate of the local truncation 104 // return an estimate of the local truncation error yErr[] using the
116 // embedded 4th-order method. The user supplie 105 // embedded 4th-order method. The user supplies routine
117 // RightHandSide(y,dydx), which returns deriva 106 // RightHandSide(y,dydx), which returns derivatives dydx for y .
118 // << 107
119 void 108 void
120 G4CashKarpRKF45::Stepper(const G4double yInput 109 G4CashKarpRKF45::Stepper(const G4double yInput[],
121 const G4double dydx[] 110 const G4double dydx[],
122 G4double Step, 111 G4double Step,
123 G4double yOut[] 112 G4double yOut[],
124 G4double yErr[] 113 G4double yErr[])
125 { 114 {
126 // const G4int nvar = 6 ; 115 // const G4int nvar = 6 ;
127 // const G4double a2 = 0.2 , a3 = 0.3 , a4 = 116 // const G4double a2 = 0.2 , a3 = 0.3 , a4 = 0.6 , a5 = 1.0 , a6 = 0.875;
128 G4int i; << 117 G4int i;
129 118
130 const G4double b21 = 0.2 , << 119 const G4double b21 = 0.2 ,
131 b31 = 3.0/40.0 , b32 = 9.0/4 << 120 b31 = 3.0/40.0 , b32 = 9.0/40.0 ,
132 b41 = 0.3 , b42 = -0.9 , b43 << 121 b41 = 0.3 , b42 = -0.9 , b43 = 1.2 ,
133 122
134 b51 = -11.0/54.0 , b52 = 2.5 << 123 b51 = -11.0/54.0 , b52 = 2.5 , b53 = -70.0/27.0 ,
135 b54 = 35.0/27.0 , << 124 b54 = 35.0/27.0 ,
136 125
137 b61 = 1631.0/55296.0 , b62 = << 126 b61 = 1631.0/55296.0 , b62 = 175.0/512.0 ,
138 b63 = 575.0/13824.0 , b64 = << 127 b63 = 575.0/13824.0 , b64 = 44275.0/110592.0 ,
139 b65 = 253.0/4096.0 , << 128 b65 = 253.0/4096.0 ,
140 129
141 c1 = 37.0/378.0 , c3 = 250.0 << 130 c1 = 37.0/378.0 , c3 = 250.0/621.0 , c4 = 125.0/594.0 ,
142 c6 = 512.0/1771.0 , dc5 = -2 << 131 c6 = 512.0/1771.0 ,
>> 132 dc5 = -277.0/14336.0 ;
143 133
144 const G4double dc1 = c1 - 2825.0/27648.0 , << 134 const G4double dc1 = c1 - 2825.0/27648.0 , dc3 = c3 - 18575.0/48384.0 ,
145 dc4 = c4 - 13525.0/55296.0 , << 135 dc4 = c4 - 13525.0/55296.0 , dc6 = c6 - 0.25 ;
146 136
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]; <<
151 137
152 const G4int numberOfVariables= this->GetNumb << 138 // Saving yInput because yInput and yOut can be aliases for same array
153 // The number of variables to be integrate <<
154 139
155 // Saving yInput because yInput and yOut ca << 140 for(i=0;i<fNumberOfVariables;i++)
>> 141 {
>> 142 yIn[i]=yInput[i];
>> 143 }
>> 144 // RightHandSide(yIn, dydx) ; // 1st Step
156 145
157 for(i=0; i<numberOfVariables; ++i) << 146 for(i=0;i<fNumberOfVariables;i++)
158 { << 147 {
159 yIn[i]=yInput[i]; << 148 yTemp[i] = yIn[i] + b21*Step*dydx[i] ;
160 } << 149 }
161 // RightHandSide(yIn, dydx) ; // << 150 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) ; // <<
168 151
169 for(i=0; i<numberOfVariables; ++i) << 152 for(i=0;i<fNumberOfVariables;i++)
170 { << 153 {
171 yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b3 154 yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b32*ak2[i]) ;
172 } << 155 }
173 RightHandSide(yTemp, ak3) ; // << 156 RightHandSide(yTemp, ak3) ; // 3rd Step
174 157
175 for(i=0; i<numberOfVariables; ++i) << 158 for(i=0;i<fNumberOfVariables;i++)
176 { << 159 {
177 yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b4 160 yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b42*ak2[i] + b43*ak3[i]) ;
178 } << 161 }
179 RightHandSide(yTemp, ak4) ; // << 162 RightHandSide(yTemp, ak4) ; // 4th Step
180 163
181 for(i=0; i<numberOfVariables; ++i) << 164 for(i=0;i<fNumberOfVariables;i++)
182 { << 165 {
183 yTemp[i] = yIn[i] + Step*(b51*dydx[i] << 166 yTemp[i] = yIn[i] + Step*(b51*dydx[i] + b52*ak2[i] + b53*ak3[i] +
184 + b52*ak2[i] + b53*ak3[i << 167 b54*ak4[i]) ;
185 } << 168 }
186 RightHandSide(yTemp, ak5) ; // << 169 RightHandSide(yTemp, ak5) ; // 5th Step
187 << 170
188 for(i=0; i<numberOfVariables; ++i) << 171 for(i=0;i<fNumberOfVariables;i++)
189 { << 172 {
190 yTemp[i] = yIn[i] + Step*(b61*dydx[i] << 173 yTemp[i] = yIn[i] + Step*(b61*dydx[i] + b62*ak2[i] + b63*ak3[i] +
191 + b62*ak2[i] + b63*ak3[i << 174 b64*ak4[i] + b65*ak5[i]) ;
192 } << 175 }
193 RightHandSide(yTemp, ak6) ; // << 176 RightHandSide(yTemp, ak6) ; // 6th Step
194 177
195 for(i=0; i<numberOfVariables; ++i) << 178 for(i=0;i<fNumberOfVariables;i++)
196 { << 179 {
197 // Accumulate increments with proper weigh 180 // Accumulate increments with proper weights
198 // << 181
199 yOut[i] = yIn[i] + Step*(c1*dydx[i] + c3*a 182 yOut[i] = yIn[i] + Step*(c1*dydx[i] + c3*ak3[i] + c4*ak4[i] + c6*ak6[i]) ;
200 183
201 // Estimate error as difference between 4t << 184 // Estimate error as difference between 4th and
202 // << 185 // 5th order methods
203 yErr[i] = Step*(dc1*dydx[i] << 186
204 + dc3*ak3[i] + dc4*ak4[i] + dc5*ak << 187 yErr[i] = Step*(dc1*dydx[i] + dc3*ak3[i] + dc4*ak4[i] +
>> 188 dc5*ak5[i] + dc6*ak6[i]) ;
205 189
206 // Store Input and Final values, for possi 190 // Store Input and Final values, for possible use in calculating chord
207 // <<
208 fLastInitialVector[i] = yIn[i] ; 191 fLastInitialVector[i] = yIn[i] ;
209 fLastFinalVector[i] = yOut[i]; 192 fLastFinalVector[i] = yOut[i];
210 fLastDyDx[i] = dydx[i]; 193 fLastDyDx[i] = dydx[i];
211 } << 194 }
212 // NormaliseTangentVector( yOut ); // Not wa << 195 // NormaliseTangentVector( yOut ); // Not wanted
213 196
214 fLastStepLength = Step; << 197 fLastStepLength =Step;
215 198
216 return; << 199 return ;
217 } 200 }
218 201
219 ////////////////////////////////////////////// 202 ///////////////////////////////////////////////////////////////////////////////
220 // << 203
221 void 204 void
222 G4CashKarpRKF45::StepWithEst( const G4double*, 205 G4CashKarpRKF45::StepWithEst( const G4double*,
223 const G4double*, 206 const G4double*,
224 G4double, 207 G4double,
225 G4double*, 208 G4double*,
226 G4double&, 209 G4double&,
227 G4double&, 210 G4double&,
228 const G4double*, 211 const G4double*,
229 G4double* 212 G4double* )
230 { 213 {
231 G4Exception("G4CashKarpRKF45::StepWithEst()" << 214 G4Exception("G4CashKarpRKF45::StepWithEst()", "ObsoleteMethod",
232 FatalException, "Method no longe 215 FatalException, "Method no longer used.");
233 return ; 216 return ;
234 } 217 }
235 218
236 ////////////////////////////////////////////// 219 /////////////////////////////////////////////////////////////////
237 // << 220
238 G4double G4CashKarpRKF45::DistChord() const 221 G4double G4CashKarpRKF45::DistChord() const
239 { 222 {
240 G4double distLine, distChord; 223 G4double distLine, distChord;
241 G4ThreeVector initialPoint, finalPoint, midP 224 G4ThreeVector initialPoint, finalPoint, midPoint;
242 225
243 // Store last initial and final points << 226 // 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 227 initialPoint = G4ThreeVector( fLastInitialVector[0],
247 fLastInitialVe 228 fLastInitialVector[1], fLastInitialVector[2]);
248 finalPoint = G4ThreeVector( fLastFinalVect 229 finalPoint = G4ThreeVector( fLastFinalVector[0],
249 fLastFinalVect 230 fLastFinalVector[1], fLastFinalVector[2]);
250 231
251 // Do half a step using StepNoErr 232 // Do half a step using StepNoErr
252 // << 233
253 fAuxStepper->Stepper( fLastInitialVector, fL << 234 fAuxStepper->Stepper( fLastInitialVector, fLastDyDx, 0.5 * fLastStepLength,
254 0.5 * fLastStepLength, << 235 fMidVector, fMidError );
255 236
256 midPoint = G4ThreeVector( fMidVector[0], fMi 237 midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2]);
257 238
258 // Use stored values of Initial and Endpoint 239 // Use stored values of Initial and Endpoint + new Midpoint to evaluate
259 // distance of Chord << 240 // distance of Chord
260 // << 241
>> 242
261 if (initialPoint != finalPoint) 243 if (initialPoint != finalPoint)
262 { 244 {
263 distLine = G4LineSection::Distline( midP 245 distLine = G4LineSection::Distline( midPoint, initialPoint, finalPoint );
264 distChord = distLine; 246 distChord = distLine;
265 } 247 }
266 else 248 else
267 { 249 {
268 distChord = (midPoint-initialPoint).mag() 250 distChord = (midPoint-initialPoint).mag();
269 } 251 }
270 return distChord; 252 return distChord;
271 } 253 }
>> 254
>> 255
272 256