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25 // 25 //
26 // G4CashKarpRKF45 implementation << 26 //
>> 27 // $Id: G4CashKarpRKF45.cc 97598 2016-06-06 07:19:46Z 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 =
53 std::max( noIntegrationVariables, 54 std::max( noIntegrationVariables,
54 ( ( (noIntegrationVariables-1)/ 55 ( ( (noIntegrationVariables-1)/4 + 1 ) * 4 ) );
55 // For better alignment with cache-line 56 // For better alignment with cache-line
56 57
57 ak2 = new G4double[numberOfVariables] ; 58 ak2 = new G4double[numberOfVariables] ;
58 ak3 = new G4double[numberOfVariables] ; 59 ak3 = new G4double[numberOfVariables] ;
59 ak4 = new G4double[numberOfVariables] ; 60 ak4 = new G4double[numberOfVariables] ;
60 ak5 = new G4double[numberOfVariables] ; 61 ak5 = new G4double[numberOfVariables] ;
61 ak6 = new G4double[numberOfVariables] ; 62 ak6 = new G4double[numberOfVariables] ;
62 // ak7 = 0; 63 // ak7 = 0;
63 64
64 // Must ensure space extra 'state' variables 65 // Must ensure space extra 'state' variables exists - i.e. yIn[7]
65 const G4int numStateMax = std::max(GetNumbe 66 const G4int numStateMax = std::max(GetNumberOfStateVariables(), 8);
66 const G4int numStateVars = std::max(noIntegr 67 const G4int numStateVars = std::max(noIntegrationVariables,
67 numState 68 numStateMax );
68 // GetNumbe 69 // GetNumberOfStateVariables() );
69 70
70 yTemp = new G4double[numStateVars] ; 71 yTemp = new G4double[numStateVars] ;
71 yIn = new G4double[numStateVars] ; 72 yIn = new G4double[numStateVars] ;
72 73
73 fLastInitialVector = new G4double[numStateVa 74 fLastInitialVector = new G4double[numStateVars] ;
74 fLastFinalVector = new G4double[numStateVars 75 fLastFinalVector = new G4double[numStateVars] ;
75 fLastDyDx = new G4double[numberOfVariables]; 76 fLastDyDx = new G4double[numberOfVariables];
76 77
77 fMidVector = new G4double[numStateVars]; 78 fMidVector = new G4double[numStateVars];
78 fMidError = new G4double[numStateVars]; 79 fMidError = new G4double[numStateVars];
79 if( primary ) 80 if( primary )
80 { 81 {
81 fAuxStepper = new G4CashKarpRKF45(EqRhs, n 82 fAuxStepper = new G4CashKarpRKF45(EqRhs, numberOfVariables, !primary);
82 } 83 }
83 } 84 }
84 85
85 ////////////////////////////////////////////// 86 /////////////////////////////////////////////////////////////////////
86 // 87 //
87 // Destructor 88 // Destructor
88 // << 89
89 G4CashKarpRKF45::~G4CashKarpRKF45() 90 G4CashKarpRKF45::~G4CashKarpRKF45()
90 { 91 {
91 delete [] ak2; << 92 delete[] ak2;
92 delete [] ak3; << 93 delete[] ak3;
93 delete [] ak4; << 94 delete[] ak4;
94 delete [] ak5; << 95 delete[] ak5;
95 delete [] ak6; << 96 delete[] ak6;
96 // delete [] ak7; << 97 // delete[] ak7;
97 delete [] yTemp; << 98 delete[] yTemp;
98 delete [] yIn; << 99 delete[] yIn;
99 << 100
100 delete [] fLastInitialVector; << 101 delete[] fLastInitialVector;
101 delete [] fLastFinalVector; << 102 delete[] fLastFinalVector;
102 delete [] fLastDyDx; << 103 delete[] fLastDyDx;
103 delete [] fMidVector; << 104 delete[] fMidVector;
104 delete [] fMidError; << 105 delete[] fMidError;
105 106
106 delete fAuxStepper; 107 delete fAuxStepper;
107 } 108 }
108 109
109 ////////////////////////////////////////////// 110 //////////////////////////////////////////////////////////////////////
110 // 111 //
111 // Given values for n = 6 variables yIn[0,..., 112 // Given values for n = 6 variables yIn[0,...,n-1]
112 // known at x, use the fifth-order Cash-Karp 113 // known at x, use the fifth-order Cash-Karp Runge-
113 // Kutta-Fehlberg-4-5 method to advance the so 114 // Kutta-Fehlberg-4-5 method to advance the solution over an interval
114 // Step and return the incremented variables a 115 // Step and return the incremented variables as yOut[0,...,n-1]. Also
115 // return an estimate of the local truncation 116 // return an estimate of the local truncation error yErr[] using the
116 // embedded 4th-order method. The user supplie 117 // embedded 4th-order method. The user supplies routine
117 // RightHandSide(y,dydx), which returns deriva 118 // RightHandSide(y,dydx), which returns derivatives dydx for y .
118 // << 119
119 void 120 void
120 G4CashKarpRKF45::Stepper(const G4double yInput 121 G4CashKarpRKF45::Stepper(const G4double yInput[],
121 const G4double dydx[] 122 const G4double dydx[],
122 G4double Step, 123 G4double Step,
123 G4double yOut[] 124 G4double yOut[],
124 G4double yErr[] 125 G4double yErr[])
125 { 126 {
126 // const G4int nvar = 6 ; 127 // const G4int nvar = 6 ;
127 // const G4double a2 = 0.2 , a3 = 0.3 , a4 = 128 // const G4double a2 = 0.2 , a3 = 0.3 , a4 = 0.6 , a5 = 1.0 , a6 = 0.875;
128 G4int i; << 129 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 <<
141 c1 = 37.0/378.0 , c3 = 250.0 <<
142 c6 = 512.0/1771.0 , dc5 = -2 <<
143 130
144 const G4double dc1 = c1 - 2825.0/27648.0 , << 131 const G4double b21 = 0.2 ,
145 dc4 = c4 - 13525.0/55296.0 , << 132 b31 = 3.0/40.0 , b32 = 9.0/40.0 ,
>> 133 b41 = 0.3 , b42 = -0.9 , b43 = 1.2 ,
>> 134
>> 135 b51 = -11.0/54.0 , b52 = 2.5 , b53 = -70.0/27.0 ,
>> 136 b54 = 35.0/27.0 ,
>> 137
>> 138 b61 = 1631.0/55296.0 , b62 = 175.0/512.0 ,
>> 139 b63 = 575.0/13824.0 , b64 = 44275.0/110592.0 ,
>> 140 b65 = 253.0/4096.0 ,
>> 141
>> 142 c1 = 37.0/378.0 , c3 = 250.0/621.0 , c4 = 125.0/594.0 ,
>> 143 c6 = 512.0/1771.0 ,
>> 144 dc5 = -277.0/14336.0 ;
>> 145
>> 146 const G4double dc1 = c1 - 2825.0/27648.0 , dc3 = c3 - 18575.0/48384.0 ,
>> 147 dc4 = c4 - 13525.0/55296.0 , dc6 = c6 - 0.25 ;
>> 148
>> 149 // Initialise time to t0, needed when it is not updated by the integration.
>> 150 // [ Note: Only for time dependent fields (usually electric)
>> 151 // is it neccessary to integrate the time.]
>> 152 yOut[7] = yTemp[7] = yIn[7];
>> 153
>> 154 const G4int numberOfVariables= this->GetNumberOfVariables();
>> 155 // The number of variables to be integrated over
>> 156
>> 157 // Saving yInput because yInput and yOut can be aliases for same array
>> 158
>> 159 for(i=0;i<numberOfVariables;i++)
>> 160 {
>> 161 yIn[i]=yInput[i];
>> 162 }
>> 163 // RightHandSide(yIn, dydx) ; // 1st Step
>> 164
>> 165 for(i=0;i<numberOfVariables;i++)
>> 166 {
>> 167 yTemp[i] = yIn[i] + b21*Step*dydx[i] ;
>> 168 }
>> 169 RightHandSide(yTemp, ak2) ; // 2nd Step
146 170
147 // Initialise time to t0, needed when it is << 171 for(i=0;i<numberOfVariables;i++)
148 // [ Note: Only for time dependent fi << 172 {
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 173 yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b32*ak2[i]) ;
172 } << 174 }
173 RightHandSide(yTemp, ak3) ; // << 175 RightHandSide(yTemp, ak3) ; // 3rd Step
174 176
175 for(i=0; i<numberOfVariables; ++i) << 177 for(i=0;i<numberOfVariables;i++)
176 { << 178 {
177 yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b4 179 yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b42*ak2[i] + b43*ak3[i]) ;
178 } << 180 }
179 RightHandSide(yTemp, ak4) ; // << 181 RightHandSide(yTemp, ak4) ; // 4th Step
180 182
181 for(i=0; i<numberOfVariables; ++i) << 183 for(i=0;i<numberOfVariables;i++)
182 { << 184 {
183 yTemp[i] = yIn[i] + Step*(b51*dydx[i] << 185 yTemp[i] = yIn[i] + Step*(b51*dydx[i] + b52*ak2[i] + b53*ak3[i] +
184 + b52*ak2[i] + b53*ak3[i << 186 b54*ak4[i]) ;
185 } << 187 }
186 RightHandSide(yTemp, ak5) ; // << 188 RightHandSide(yTemp, ak5) ; // 5th Step
>> 189
>> 190 for(i=0;i<numberOfVariables;i++)
>> 191 {
>> 192 yTemp[i] = yIn[i] + Step*(b61*dydx[i] + b62*ak2[i] + b63*ak3[i] +
>> 193 b64*ak4[i] + b65*ak5[i]) ;
>> 194 }
>> 195 RightHandSide(yTemp, ak6) ; // 6th Step
187 196
188 for(i=0; i<numberOfVariables; ++i) << 197 for(i=0;i<numberOfVariables;i++)
189 { << 198 {
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 199 // Accumulate increments with proper weights
198 // << 200
199 yOut[i] = yIn[i] + Step*(c1*dydx[i] + c3*a 201 yOut[i] = yIn[i] + Step*(c1*dydx[i] + c3*ak3[i] + c4*ak4[i] + c6*ak6[i]) ;
200 202
201 // Estimate error as difference between 4t << 203 // Estimate error as difference between 4th and
202 // << 204 // 5th order methods
203 yErr[i] = Step*(dc1*dydx[i] << 205
204 + dc3*ak3[i] + dc4*ak4[i] + dc5*ak << 206 yErr[i] = Step*(dc1*dydx[i] + dc3*ak3[i] + dc4*ak4[i] +
>> 207 dc5*ak5[i] + dc6*ak6[i]) ;
205 208
206 // Store Input and Final values, for possi 209 // Store Input and Final values, for possible use in calculating chord
207 // <<
208 fLastInitialVector[i] = yIn[i] ; 210 fLastInitialVector[i] = yIn[i] ;
209 fLastFinalVector[i] = yOut[i]; 211 fLastFinalVector[i] = yOut[i];
210 fLastDyDx[i] = dydx[i]; 212 fLastDyDx[i] = dydx[i];
211 } << 213 }
212 // NormaliseTangentVector( yOut ); // Not wa << 214 // NormaliseTangentVector( yOut ); // Not wanted
213 215
214 fLastStepLength = Step; << 216 fLastStepLength =Step;
215 217
216 return; << 218 return ;
217 } 219 }
218 220
219 ////////////////////////////////////////////// 221 ///////////////////////////////////////////////////////////////////////////////
220 // << 222
221 void 223 void
222 G4CashKarpRKF45::StepWithEst( const G4double*, 224 G4CashKarpRKF45::StepWithEst( const G4double*,
223 const G4double*, 225 const G4double*,
224 G4double, 226 G4double,
225 G4double*, 227 G4double*,
226 G4double&, 228 G4double&,
227 G4double&, 229 G4double&,
228 const G4double*, 230 const G4double*,
229 G4double* 231 G4double* )
230 { 232 {
231 G4Exception("G4CashKarpRKF45::StepWithEst()" 233 G4Exception("G4CashKarpRKF45::StepWithEst()", "GeomField0001",
232 FatalException, "Method no longe 234 FatalException, "Method no longer used.");
233 return ; 235 return ;
234 } 236 }
235 237
236 ////////////////////////////////////////////// 238 /////////////////////////////////////////////////////////////////
237 // << 239
238 G4double G4CashKarpRKF45::DistChord() const 240 G4double G4CashKarpRKF45::DistChord() const
239 { 241 {
240 G4double distLine, distChord; 242 G4double distLine, distChord;
241 G4ThreeVector initialPoint, finalPoint, midP 243 G4ThreeVector initialPoint, finalPoint, midPoint;
242 244
243 // Store last initial and final points << 245 // 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 246 initialPoint = G4ThreeVector( fLastInitialVector[0],
247 fLastInitialVe 247 fLastInitialVector[1], fLastInitialVector[2]);
248 finalPoint = G4ThreeVector( fLastFinalVect 248 finalPoint = G4ThreeVector( fLastFinalVector[0],
249 fLastFinalVect 249 fLastFinalVector[1], fLastFinalVector[2]);
250 250
251 // Do half a step using StepNoErr 251 // Do half a step using StepNoErr
252 // << 252
253 fAuxStepper->Stepper( fLastInitialVector, fL << 253 fAuxStepper->Stepper( fLastInitialVector, fLastDyDx, 0.5 * fLastStepLength,
254 0.5 * fLastStepLength, << 254 fMidVector, fMidError );
255 255
256 midPoint = G4ThreeVector( fMidVector[0], fMi 256 midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2]);
257 257
258 // Use stored values of Initial and Endpoint 258 // Use stored values of Initial and Endpoint + new Midpoint to evaluate
259 // distance of Chord << 259 // distance of Chord
260 // << 260
>> 261
261 if (initialPoint != finalPoint) 262 if (initialPoint != finalPoint)
262 { 263 {
263 distLine = G4LineSection::Distline( midP 264 distLine = G4LineSection::Distline( midPoint, initialPoint, finalPoint );
264 distChord = distLine; 265 distChord = distLine;
265 } 266 }
266 else 267 else
267 { 268 {
268 distChord = (midPoint-initialPoint).mag() 269 distChord = (midPoint-initialPoint).mag();
269 } 270 }
270 return distChord; 271 return distChord;
271 } 272 }
>> 273
>> 274
272 275