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25 // 25 //
26 // G4CashKarpRKF45 implementation << 26 //
>> 27 // $Id: G4CashKarpRKF45.cc 66356 2012-12-18 09:02:32Z gcosmo $
27 // 28 //
28 // The Cash-Karp Runge-Kutta-Fehlberg 4/5 meth 29 // The Cash-Karp Runge-Kutta-Fehlberg 4/5 method is an embedded fourth
29 // order method (giving fifth-order accuracy) 30 // order method (giving fifth-order accuracy) for the solution of an ODE.
30 // Two different fourth order estimates are ca 31 // Two different fourth order estimates are calculated; their difference
31 // gives an error estimate. [ref. Numerical Re 32 // gives an error estimate. [ref. Numerical Recipes in C, 2nd Edition]
32 // It is used to integrate the equations of th 33 // It is used to integrate the equations of the motion of a particle
33 // in a magnetic field. 34 // in a magnetic field.
34 // 35 //
35 // [ref. Numerical Recipes in C, 2nd Edition] << 36 // [ref. Numerical Recipes in C, 2nd Edition]
36 // 37 //
37 // Authors: J.Apostolakis, V.Grichine - 30.01. <<
38 // ------------------------------------------- 38 // -------------------------------------------------------------------
39 39
40 #include "G4CashKarpRKF45.hh" 40 #include "G4CashKarpRKF45.hh"
41 #include "G4LineSection.hh" 41 #include "G4LineSection.hh"
42 42
43 ////////////////////////////////////////////// 43 /////////////////////////////////////////////////////////////////////
44 // 44 //
45 // Constructor 45 // Constructor
46 // << 46
47 G4CashKarpRKF45::G4CashKarpRKF45(G4EquationOfM 47 G4CashKarpRKF45::G4CashKarpRKF45(G4EquationOfMotion *EqRhs,
48 G4int noInteg << 48 G4int noIntegrationVariables,
49 G4bool primar << 49 G4bool primary)
50 : G4MagIntegratorStepper(EqRhs, noIntegratio << 50 : G4MagIntegratorStepper(EqRhs, noIntegrationVariables),
>> 51 fLastStepLength(0.), fAuxStepper(0)
51 { 52 {
52 const G4int numberOfVariables = << 53 const G4int numberOfVariables = noIntegrationVariables;
53 std::max( noIntegrationVariables, <<
54 ( ( (noIntegrationVariables-1)/ <<
55 // For better alignment with cache-line <<
56 <<
57 ak2 = new G4double[numberOfVariables] ; <<
58 ak3 = new G4double[numberOfVariables] ; <<
59 ak4 = new G4double[numberOfVariables] ; <<
60 ak5 = new G4double[numberOfVariables] ; <<
61 ak6 = new G4double[numberOfVariables] ; <<
62 // ak7 = 0; <<
63 <<
64 // Must ensure space extra 'state' variables <<
65 const G4int numStateMax = std::max(GetNumbe <<
66 const G4int numStateVars = std::max(noIntegr <<
67 numState <<
68 // GetNumbe <<
69 <<
70 yTemp = new G4double[numStateVars] ; <<
71 yIn = new G4double[numStateVars] ; <<
72 54
73 fLastInitialVector = new G4double[numStateVa << 55 ak2 = new G4double[numberOfVariables] ;
74 fLastFinalVector = new G4double[numStateVars << 56 ak3 = new G4double[numberOfVariables] ;
>> 57 ak4 = new G4double[numberOfVariables] ;
>> 58 ak5 = new G4double[numberOfVariables] ;
>> 59 ak6 = new G4double[numberOfVariables] ;
>> 60 ak7 = 0;
>> 61 yTemp = new G4double[numberOfVariables] ;
>> 62 yIn = new G4double[numberOfVariables] ;
>> 63
>> 64 fLastInitialVector = new G4double[numberOfVariables] ;
>> 65 fLastFinalVector = new G4double[numberOfVariables] ;
75 fLastDyDx = new G4double[numberOfVariables]; 66 fLastDyDx = new G4double[numberOfVariables];
76 67
77 fMidVector = new G4double[numStateVars]; << 68 fMidVector = new G4double[numberOfVariables];
78 fMidError = new G4double[numStateVars]; << 69 fMidError = new G4double[numberOfVariables];
79 if( primary ) 70 if( primary )
80 { 71 {
81 fAuxStepper = new G4CashKarpRKF45(EqRhs, n 72 fAuxStepper = new G4CashKarpRKF45(EqRhs, numberOfVariables, !primary);
82 } 73 }
83 } 74 }
84 75
85 ////////////////////////////////////////////// 76 /////////////////////////////////////////////////////////////////////
86 // 77 //
87 // Destructor 78 // Destructor
88 // << 79
89 G4CashKarpRKF45::~G4CashKarpRKF45() 80 G4CashKarpRKF45::~G4CashKarpRKF45()
90 { 81 {
91 delete [] ak2; << 82 delete[] ak2;
92 delete [] ak3; << 83 delete[] ak3;
93 delete [] ak4; << 84 delete[] ak4;
94 delete [] ak5; << 85 delete[] ak5;
95 delete [] ak6; << 86 delete[] ak6;
96 // delete [] ak7; << 87 // delete[] ak7;
97 delete [] yTemp; << 88 delete[] yTemp;
98 delete [] yIn; << 89 delete[] yIn;
99 << 90
100 delete [] fLastInitialVector; << 91 delete[] fLastInitialVector;
101 delete [] fLastFinalVector; << 92 delete[] fLastFinalVector;
102 delete [] fLastDyDx; << 93 delete[] fLastDyDx;
103 delete [] fMidVector; << 94 delete[] fMidVector;
104 delete [] fMidError; << 95 delete[] fMidError;
105 96
106 delete fAuxStepper; 97 delete fAuxStepper;
107 } 98 }
108 99
109 ////////////////////////////////////////////// 100 //////////////////////////////////////////////////////////////////////
110 // 101 //
111 // Given values for n = 6 variables yIn[0,..., 102 // Given values for n = 6 variables yIn[0,...,n-1]
112 // known at x, use the fifth-order Cash-Karp 103 // known at x, use the fifth-order Cash-Karp Runge-
113 // Kutta-Fehlberg-4-5 method to advance the so 104 // Kutta-Fehlberg-4-5 method to advance the solution over an interval
114 // Step and return the incremented variables a 105 // Step and return the incremented variables as yOut[0,...,n-1]. Also
115 // return an estimate of the local truncation 106 // return an estimate of the local truncation error yErr[] using the
116 // embedded 4th-order method. The user supplie 107 // embedded 4th-order method. The user supplies routine
117 // RightHandSide(y,dydx), which returns deriva 108 // RightHandSide(y,dydx), which returns derivatives dydx for y .
118 // << 109
119 void 110 void
120 G4CashKarpRKF45::Stepper(const G4double yInput 111 G4CashKarpRKF45::Stepper(const G4double yInput[],
121 const G4double dydx[] 112 const G4double dydx[],
122 G4double Step, 113 G4double Step,
123 G4double yOut[] 114 G4double yOut[],
124 G4double yErr[] 115 G4double yErr[])
125 { 116 {
126 // const G4int nvar = 6 ; 117 // const G4int nvar = 6 ;
127 // const G4double a2 = 0.2 , a3 = 0.3 , a4 = 118 // const G4double a2 = 0.2 , a3 = 0.3 , a4 = 0.6 , a5 = 1.0 , a6 = 0.875;
128 G4int i; << 119 G4int i;
129 <<
130 const G4double b21 = 0.2 , <<
131 b31 = 3.0/40.0 , b32 = 9.0/4 <<
132 b41 = 0.3 , b42 = -0.9 , b43 <<
133 <<
134 b51 = -11.0/54.0 , b52 = 2.5 <<
135 b54 = 35.0/27.0 , <<
136 <<
137 b61 = 1631.0/55296.0 , b62 = <<
138 b63 = 575.0/13824.0 , b64 = <<
139 b65 = 253.0/4096.0 , <<
140 120
141 c1 = 37.0/378.0 , c3 = 250.0 << 121 const G4double b21 = 0.2 ,
142 c6 = 512.0/1771.0 , dc5 = -2 << 122 b31 = 3.0/40.0 , b32 = 9.0/40.0 ,
>> 123 b41 = 0.3 , b42 = -0.9 , b43 = 1.2 ,
>> 124
>> 125 b51 = -11.0/54.0 , b52 = 2.5 , b53 = -70.0/27.0 ,
>> 126 b54 = 35.0/27.0 ,
>> 127
>> 128 b61 = 1631.0/55296.0 , b62 = 175.0/512.0 ,
>> 129 b63 = 575.0/13824.0 , b64 = 44275.0/110592.0 ,
>> 130 b65 = 253.0/4096.0 ,
>> 131
>> 132 c1 = 37.0/378.0 , c3 = 250.0/621.0 , c4 = 125.0/594.0 ,
>> 133 c6 = 512.0/1771.0 ,
>> 134 dc5 = -277.0/14336.0 ;
>> 135
>> 136 const G4double dc1 = c1 - 2825.0/27648.0 , dc3 = c3 - 18575.0/48384.0 ,
>> 137 dc4 = c4 - 13525.0/55296.0 , dc6 = c6 - 0.25 ;
>> 138
>> 139 // Initialise time to t0, needed when it is not updated by the integration.
>> 140 // [ Note: Only for time dependent fields (usually electric)
>> 141 // is it neccessary to integrate the time.]
>> 142 yOut[7] = yTemp[7] = yIn[7];
>> 143
>> 144 const G4int numberOfVariables= this->GetNumberOfVariables();
>> 145 // The number of variables to be integrated over
>> 146
>> 147 // Saving yInput because yInput and yOut can be aliases for same array
>> 148
>> 149 for(i=0;i<numberOfVariables;i++)
>> 150 {
>> 151 yIn[i]=yInput[i];
>> 152 }
>> 153 // RightHandSide(yIn, dydx) ; // 1st Step
>> 154
>> 155 for(i=0;i<numberOfVariables;i++)
>> 156 {
>> 157 yTemp[i] = yIn[i] + b21*Step*dydx[i] ;
>> 158 }
>> 159 RightHandSide(yTemp, ak2) ; // 2nd Step
143 160
144 const G4double dc1 = c1 - 2825.0/27648.0 , << 161 for(i=0;i<numberOfVariables;i++)
145 dc4 = c4 - 13525.0/55296.0 , << 162 {
146 <<
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 <<
152 const G4int numberOfVariables= this->GetNumb <<
153 // The number of variables to be integrate <<
154 <<
155 // Saving yInput because yInput and yOut ca <<
156 <<
157 for(i=0; i<numberOfVariables; ++i) <<
158 { <<
159 yIn[i]=yInput[i]; <<
160 } <<
161 // RightHandSide(yIn, dydx) ; // <<
162 <<
163 for(i=0; i<numberOfVariables; ++i) <<
164 { <<
165 yTemp[i] = yIn[i] + b21*Step*dydx[i] ; <<
166 } <<
167 RightHandSide(yTemp, ak2) ; // <<
168 <<
169 for(i=0; i<numberOfVariables; ++i) <<
170 { <<
171 yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b3 163 yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b32*ak2[i]) ;
172 } << 164 }
173 RightHandSide(yTemp, ak3) ; // << 165 RightHandSide(yTemp, ak3) ; // 3rd Step
174 166
175 for(i=0; i<numberOfVariables; ++i) << 167 for(i=0;i<numberOfVariables;i++)
176 { << 168 {
177 yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b4 169 yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b42*ak2[i] + b43*ak3[i]) ;
178 } << 170 }
179 RightHandSide(yTemp, ak4) ; // << 171 RightHandSide(yTemp, ak4) ; // 4th Step
180 172
181 for(i=0; i<numberOfVariables; ++i) << 173 for(i=0;i<numberOfVariables;i++)
182 { << 174 {
183 yTemp[i] = yIn[i] + Step*(b51*dydx[i] << 175 yTemp[i] = yIn[i] + Step*(b51*dydx[i] + b52*ak2[i] + b53*ak3[i] +
184 + b52*ak2[i] + b53*ak3[i << 176 b54*ak4[i]) ;
185 } << 177 }
186 RightHandSide(yTemp, ak5) ; // << 178 RightHandSide(yTemp, ak5) ; // 5th Step
>> 179
>> 180 for(i=0;i<numberOfVariables;i++)
>> 181 {
>> 182 yTemp[i] = yIn[i] + Step*(b61*dydx[i] + b62*ak2[i] + b63*ak3[i] +
>> 183 b64*ak4[i] + b65*ak5[i]) ;
>> 184 }
>> 185 RightHandSide(yTemp, ak6) ; // 6th Step
187 186
188 for(i=0; i<numberOfVariables; ++i) << 187 for(i=0;i<numberOfVariables;i++)
189 { << 188 {
190 yTemp[i] = yIn[i] + Step*(b61*dydx[i] <<
191 + b62*ak2[i] + b63*ak3[i <<
192 } <<
193 RightHandSide(yTemp, ak6) ; // <<
194 <<
195 for(i=0; i<numberOfVariables; ++i) <<
196 { <<
197 // Accumulate increments with proper weigh 189 // Accumulate increments with proper weights
198 // << 190
199 yOut[i] = yIn[i] + Step*(c1*dydx[i] + c3*a 191 yOut[i] = yIn[i] + Step*(c1*dydx[i] + c3*ak3[i] + c4*ak4[i] + c6*ak6[i]) ;
200 192
201 // Estimate error as difference between 4t << 193 // Estimate error as difference between 4th and
202 // << 194 // 5th order methods
203 yErr[i] = Step*(dc1*dydx[i] << 195
204 + dc3*ak3[i] + dc4*ak4[i] + dc5*ak << 196 yErr[i] = Step*(dc1*dydx[i] + dc3*ak3[i] + dc4*ak4[i] +
>> 197 dc5*ak5[i] + dc6*ak6[i]) ;
205 198
206 // Store Input and Final values, for possi 199 // Store Input and Final values, for possible use in calculating chord
207 // <<
208 fLastInitialVector[i] = yIn[i] ; 200 fLastInitialVector[i] = yIn[i] ;
209 fLastFinalVector[i] = yOut[i]; 201 fLastFinalVector[i] = yOut[i];
210 fLastDyDx[i] = dydx[i]; 202 fLastDyDx[i] = dydx[i];
211 } << 203 }
212 // NormaliseTangentVector( yOut ); // Not wa << 204 // NormaliseTangentVector( yOut ); // Not wanted
213 205
214 fLastStepLength = Step; << 206 fLastStepLength =Step;
215 207
216 return; << 208 return ;
217 } 209 }
218 210
219 ////////////////////////////////////////////// 211 ///////////////////////////////////////////////////////////////////////////////
220 // << 212
221 void 213 void
222 G4CashKarpRKF45::StepWithEst( const G4double*, 214 G4CashKarpRKF45::StepWithEst( const G4double*,
223 const G4double*, 215 const G4double*,
224 G4double, 216 G4double,
225 G4double*, 217 G4double*,
226 G4double&, 218 G4double&,
227 G4double&, 219 G4double&,
228 const G4double*, 220 const G4double*,
229 G4double* 221 G4double* )
230 { 222 {
231 G4Exception("G4CashKarpRKF45::StepWithEst()" 223 G4Exception("G4CashKarpRKF45::StepWithEst()", "GeomField0001",
232 FatalException, "Method no longe 224 FatalException, "Method no longer used.");
233 return ; 225 return ;
234 } 226 }
235 227
236 ////////////////////////////////////////////// 228 /////////////////////////////////////////////////////////////////
237 // << 229
238 G4double G4CashKarpRKF45::DistChord() const 230 G4double G4CashKarpRKF45::DistChord() const
239 { 231 {
240 G4double distLine, distChord; 232 G4double distLine, distChord;
241 G4ThreeVector initialPoint, finalPoint, midP 233 G4ThreeVector initialPoint, finalPoint, midPoint;
242 234
243 // Store last initial and final points << 235 // 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 236 initialPoint = G4ThreeVector( fLastInitialVector[0],
247 fLastInitialVe 237 fLastInitialVector[1], fLastInitialVector[2]);
248 finalPoint = G4ThreeVector( fLastFinalVect 238 finalPoint = G4ThreeVector( fLastFinalVector[0],
249 fLastFinalVect 239 fLastFinalVector[1], fLastFinalVector[2]);
250 240
251 // Do half a step using StepNoErr 241 // Do half a step using StepNoErr
252 // << 242
253 fAuxStepper->Stepper( fLastInitialVector, fL << 243 fAuxStepper->Stepper( fLastInitialVector, fLastDyDx, 0.5 * fLastStepLength,
254 0.5 * fLastStepLength, << 244 fMidVector, fMidError );
255 245
256 midPoint = G4ThreeVector( fMidVector[0], fMi 246 midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2]);
257 247
258 // Use stored values of Initial and Endpoint 248 // Use stored values of Initial and Endpoint + new Midpoint to evaluate
259 // distance of Chord << 249 // distance of Chord
260 // << 250
>> 251
261 if (initialPoint != finalPoint) 252 if (initialPoint != finalPoint)
262 { 253 {
263 distLine = G4LineSection::Distline( midP 254 distLine = G4LineSection::Distline( midPoint, initialPoint, finalPoint );
264 distChord = distLine; 255 distChord = distLine;
265 } 256 }
266 else 257 else
267 { 258 {
268 distChord = (midPoint-initialPoint).mag() 259 distChord = (midPoint-initialPoint).mag();
269 } 260 }
270 return distChord; 261 return distChord;
271 } 262 }
>> 263
>> 264
272 265