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25 // 25 //
26 // G4DoLoMcPriRK34 implementation 26 // G4DoLoMcPriRK34 implementation
27 // 27 //
28 // Created: Somnath Banerjee, Google Summer of 28 // Created: Somnath Banerjee, Google Summer of Code 2015, 7 July 2015
29 // Supervision: John Apostolakis, CERN 29 // Supervision: John Apostolakis, CERN
30 // ------------------------------------------- 30 // --------------------------------------------------------------------
31 31
32 #include "G4DoLoMcPriRK34.hh" 32 #include "G4DoLoMcPriRK34.hh"
33 #include "G4LineSection.hh" 33 #include "G4LineSection.hh"
34 34
35 // Constructor 35 // Constructor
36 // 36 //
37 G4DoLoMcPriRK34::G4DoLoMcPriRK34(G4EquationOfM 37 G4DoLoMcPriRK34::G4DoLoMcPriRK34(G4EquationOfMotion* EqRhs,
38 G4int noInte 38 G4int noIntegrationVariables,
39 G4bool prima 39 G4bool primary)
40 : G4MagIntegratorStepper(EqRhs, noIntegrati 40 : G4MagIntegratorStepper(EqRhs, noIntegrationVariables)
41 { 41 {
42 const G4int numberOfVariables = noIntegrati 42 const G4int numberOfVariables = noIntegrationVariables;
43 43
44 // New Chunk of memory being created for us 44 // New Chunk of memory being created for use by the Stepper
45 45
46 // aki - for storing intermediate RHS 46 // aki - for storing intermediate RHS
47 // 47 //
48 ak2 = new G4double[numberOfVariables]; 48 ak2 = new G4double[numberOfVariables];
49 ak3 = new G4double[numberOfVariables]; 49 ak3 = new G4double[numberOfVariables];
50 ak4 = new G4double[numberOfVariables]; 50 ak4 = new G4double[numberOfVariables];
51 ak5 = new G4double[numberOfVariables]; 51 ak5 = new G4double[numberOfVariables];
52 ak6 = new G4double[numberOfVariables]; 52 ak6 = new G4double[numberOfVariables];
53 53
54 yTemp = new G4double[numberOfVariables] ; 54 yTemp = new G4double[numberOfVariables] ;
55 yIn = new G4double[numberOfVariables] ; 55 yIn = new G4double[numberOfVariables] ;
56 56
57 fLastInitialVector = new G4double[numberOfV 57 fLastInitialVector = new G4double[numberOfVariables] ;
58 fLastFinalVector = new G4double[numberOfVar 58 fLastFinalVector = new G4double[numberOfVariables] ;
59 fLastDyDx = new G4double[numberOfVariables] 59 fLastDyDx = new G4double[numberOfVariables];
60 60
61 fMidVector = new G4double[numberOfVariables 61 fMidVector = new G4double[numberOfVariables];
62 fMidError = new G4double[numberOfVariables] 62 fMidError = new G4double[numberOfVariables];
63 if( primary ) 63 if( primary )
64 { 64 {
65 fAuxStepper = new G4DoLoMcPriRK34(EqRhs, 65 fAuxStepper = new G4DoLoMcPriRK34(EqRhs, numberOfVariables, !primary);
66 } 66 }
67 } 67 }
68 68
69 // Destructor 69 // Destructor
70 // 70 //
71 G4DoLoMcPriRK34::~G4DoLoMcPriRK34() 71 G4DoLoMcPriRK34::~G4DoLoMcPriRK34()
72 { 72 {
73 // clear all previously allocated memory fo 73 // clear all previously allocated memory for Stepper and DistChord
74 74
75 delete [] ak2; 75 delete [] ak2;
76 delete [] ak3; 76 delete [] ak3;
77 delete [] ak4; 77 delete [] ak4;
78 delete [] ak5; 78 delete [] ak5;
79 delete [] ak6; 79 delete [] ak6;
80 80
81 delete [] yTemp; 81 delete [] yTemp;
82 delete [] yIn; 82 delete [] yIn;
83 83
84 delete [] fLastInitialVector; 84 delete [] fLastInitialVector;
85 delete [] fLastFinalVector; 85 delete [] fLastFinalVector;
86 delete [] fLastDyDx; 86 delete [] fLastDyDx;
87 delete [] fMidVector; 87 delete [] fMidVector;
88 delete [] fMidError; 88 delete [] fMidError;
89 89
90 delete fAuxStepper; 90 delete fAuxStepper;
91 } 91 }
92 92
93 // Stepper 93 // Stepper
94 // 94 //
95 // Passing in the value of yInput[],the first 95 // Passing in the value of yInput[],the first time dydx[] and Step length
96 // Giving back yOut and yErr arrays for output 96 // Giving back yOut and yErr arrays for output and error respectively
97 // 97 //
98 void G4DoLoMcPriRK34::Stepper(const G4double y 98 void G4DoLoMcPriRK34::Stepper(const G4double yInput[],
99 const G4double D 99 const G4double DyDx[],
100 G4double S 100 G4double Step,
101 G4double y 101 G4double yOut[],
102 G4double y 102 G4double yErr[] )
103 { 103 {
104 G4int i; 104 G4int i;
105 105
106 // The various constants defined on the bas 106 // The various constants defined on the basis of butcher tableu
107 // 107 //
108 const G4double b21 = 7.0/27.0 , 108 const G4double b21 = 7.0/27.0 ,
109 b31 = 7.0/72.0 , 109 b31 = 7.0/72.0 ,
110 b32 = 7.0/24.0 , 110 b32 = 7.0/24.0 ,
111 111
112 b41 = 3043.0/3528.0 , 112 b41 = 3043.0/3528.0 ,
113 b42 = -3757.0/1176.0 , 113 b42 = -3757.0/1176.0 ,
114 b43 = 1445.0/441.0, 114 b43 = 1445.0/441.0,
115 115
116 b51 = 17617.0/11662.0 , 116 b51 = 17617.0/11662.0 ,
117 b52 = -4023.0/686.0 , 117 b52 = -4023.0/686.0 ,
118 b53 = 9372.0/1715.0 , 118 b53 = 9372.0/1715.0 ,
119 b54 = -66.0/595.0 , 119 b54 = -66.0/595.0 ,
120 120
121 b61 = 29.0/238.0 , 121 b61 = 29.0/238.0 ,
122 b62 = 0.0 , 122 b62 = 0.0 ,
123 b63 = 216.0/385.0 , 123 b63 = 216.0/385.0 ,
124 b64 = 54.0/85.0 , 124 b64 = 54.0/85.0 ,
125 b65 = -7.0/22.0 , 125 b65 = -7.0/22.0 ,
126 126
127 dc1 = 363.0/2975.0 - b61 , 127 dc1 = 363.0/2975.0 - b61 ,
128 dc2 = 0.0 - b62 , 128 dc2 = 0.0 - b62 ,
129 dc3 = 981.0/1750.0 - b63, 129 dc3 = 981.0/1750.0 - b63,
130 dc4 = 2709.0/4250.0 - b64 , 130 dc4 = 2709.0/4250.0 - b64 ,
131 dc5 = -3.0/10.0 - b65 , 131 dc5 = -3.0/10.0 - b65 ,
132 dc6 = -1.0/50.0 ; // 132 dc6 = -1.0/50.0 ; // end of declaration
133 133
134 const G4int numberOfVariables = GetNumberOf 134 const G4int numberOfVariables = GetNumberOfVariables();
135 135
136 // The number of variables to be integrated 136 // The number of variables to be integrated over
137 // 137 //
138 yOut[7] = yTemp[7] = yIn[7]; 138 yOut[7] = yTemp[7] = yIn[7];
139 139
140 // Saving yInput because yInput and yOut ca 140 // Saving yInput because yInput and yOut can be aliases for same array
141 // 141 //
142 for(i=0; i<numberOfVariables; ++i) 142 for(i=0; i<numberOfVariables; ++i)
143 { 143 {
144 yIn[i]=yInput[i]; 144 yIn[i]=yInput[i];
145 } 145 }
146 146
147 // RightHandSide(yIn, DyDx) ; // 1st stag 147 // RightHandSide(yIn, DyDx) ; // 1st stage - Not doing, getting passed
148 148
149 for(i=0; i<numberOfVariables; ++i) 149 for(i=0; i<numberOfVariables; ++i)
150 { 150 {
151 yTemp[i] = yIn[i] + b21*Step*DyDx[i] ; 151 yTemp[i] = yIn[i] + b21*Step*DyDx[i] ;
152 } 152 }
153 RightHandSide(yTemp, ak2) ; // 153 RightHandSide(yTemp, ak2) ; // 2nd stage
154 154
155 for(i=0; i<numberOfVariables; ++i) 155 for(i=0; i<numberOfVariables; ++i)
156 { 156 {
157 yTemp[i] = yIn[i] + Step*(b31*DyDx[i] + 157 yTemp[i] = yIn[i] + Step*(b31*DyDx[i] + b32*ak2[i]) ;
158 } 158 }
159 RightHandSide(yTemp, ak3) ; // 159 RightHandSide(yTemp, ak3) ; // 3rd stage
160 160
161 for(i=0; i<numberOfVariables; ++i) 161 for(i=0; i<numberOfVariables; ++i)
162 { 162 {
163 yTemp[i] = yIn[i] + Step*(b41*DyDx[i] + 163 yTemp[i] = yIn[i] + Step*(b41*DyDx[i] + b42*ak2[i] + b43*ak3[i]) ;
164 } 164 }
165 RightHandSide(yTemp, ak4) ; // 165 RightHandSide(yTemp, ak4) ; // 4th stage
166 166
167 for(i=0; i<numberOfVariables; ++i) 167 for(i=0; i<numberOfVariables; ++i)
168 { 168 {
169 yTemp[i] = yIn[i] + Step*(b51*DyDx[i] + 169 yTemp[i] = yIn[i] + Step*(b51*DyDx[i] + b52*ak2[i]
170 + b53*ak3[i] + 170 + b53*ak3[i] + b54*ak4[i]) ;
171 } 171 }
172 RightHandSide(yTemp, ak5) ; // 172 RightHandSide(yTemp, ak5) ; // 5th stage
173 173
174 for(i=0; i<numberOfVariables; ++i) 174 for(i=0; i<numberOfVariables; ++i)
175 { 175 {
176 yOut[i] = yIn[i] + Step*(b61*DyDx[i] + 176 yOut[i] = yIn[i] + Step*(b61*DyDx[i] + b62*ak2[i] + b63*ak3[i]
177 + b64*ak4[i] + b 177 + b64*ak4[i] + b65*ak5[i]) ;
178 } 178 }
179 RightHandSide(yOut, ak6) ; // 179 RightHandSide(yOut, ak6) ; // 6th and Final stage
180 180
181 for(i=0; i<numberOfVariables; ++i) 181 for(i=0; i<numberOfVariables; ++i)
182 { 182 {
183 183
184 yErr[i] = Step*(dc1*DyDx[i] + dc2*ak2[i 184 yErr[i] = Step*(dc1*DyDx[i] + dc2*ak2[i] + dc3*ak3[i] + dc4*ak4[i]
185 + dc5*ak5[i] + dc6*ak6[i] 185 + dc5*ak5[i] + dc6*ak6[i] ) ;
186 186
187 // Store Input and Final values, for po 187 // Store Input and Final values, for possible use in calculating chord
188 // 188 //
189 fLastInitialVector[i] = yIn[i] ; 189 fLastInitialVector[i] = yIn[i] ;
190 fLastFinalVector[i] = yOut[i]; 190 fLastFinalVector[i] = yOut[i];
191 fLastDyDx[i] = DyDx[i]; 191 fLastDyDx[i] = DyDx[i];
192 } 192 }
193 193
194 fLastStepLength = Step; 194 fLastStepLength = Step;
195 195
196 return ; 196 return ;
197 } 197 }
198 198
199 // DistChord 199 // DistChord
200 // 200 //
201 G4double G4DoLoMcPriRK34::DistChord() const 201 G4double G4DoLoMcPriRK34::DistChord() const
202 { 202 {
203 G4double distLine, distChord; 203 G4double distLine, distChord;
204 G4ThreeVector initialPoint, finalPoint, mid 204 G4ThreeVector initialPoint, finalPoint, midPoint;
205 205
206 // Store last initial and final points 206 // Store last initial and final points
207 // (they will be overwritten in self-Steppe 207 // (they will be overwritten in self-Stepper call!)
208 // 208 //
209 initialPoint = G4ThreeVector( fLastInitialV 209 initialPoint = G4ThreeVector( fLastInitialVector[0],
210 fLastInitialV 210 fLastInitialVector[1], fLastInitialVector[2] );
211 finalPoint = G4ThreeVector( fLastFinalVec 211 finalPoint = G4ThreeVector( fLastFinalVector[0],
212 fLastFinalVec 212 fLastFinalVector[1], fLastFinalVector[2] );
213 213
214 // Do half a Step using StepNoErr 214 // Do half a Step using StepNoErr
215 215
216 fAuxStepper->Stepper( fLastInitialVector, f 216 fAuxStepper->Stepper( fLastInitialVector, fLastDyDx, 0.5 * fLastStepLength,
217 fMidVector, fMidError 217 fMidVector, fMidError );
218 218
219 midPoint = G4ThreeVector( fMidVector[0], fM 219 midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2]);
220 220
221 // Use stored values of Initial and Endpoin 221 // Use stored values of Initial and Endpoint + new Midpoint to evaluate
222 // distance of Chord 222 // distance of Chord
223 // 223 //
224 if (initialPoint != finalPoint) 224 if (initialPoint != finalPoint)
225 { 225 {
226 distLine = G4LineSection::Distline( midP 226 distLine = G4LineSection::Distline( midPoint, initialPoint, finalPoint );
227 distChord = distLine; 227 distChord = distLine;
228 } 228 }
229 else 229 else
230 { 230 {
231 distChord = (midPoint-initialPoint).mag() 231 distChord = (midPoint-initialPoint).mag();
232 } 232 }
233 return distChord; 233 return distChord;
234 } 234 }
235 235
236 void G4DoLoMcPriRK34::SetupInterpolation() 236 void G4DoLoMcPriRK34::SetupInterpolation()
237 { 237 {
238 } 238 }
239 239
240 void G4DoLoMcPriRK34::SetupInterpolate( const 240 void G4DoLoMcPriRK34::SetupInterpolate( const G4double /* yInput */ [] ,
241 const 241 const G4double /* dydx */ [] ,
242 const 242 const G4double /* Step */ )
243 { 243 {
244 // Do Nothing 244 // Do Nothing
245 } 245 }
246 246
247 void G4DoLoMcPriRK34::Interpolate( G4double ta 247 void G4DoLoMcPriRK34::Interpolate( G4double tau,
248 G4double yO 248 G4double yOut[] )
249 { 249 {
250 Interpolate( fLastInitialVector, fLastDyDx, 250 Interpolate( fLastInitialVector, fLastDyDx, fLastStepLength, yOut, tau );
251 } 251 }
252 252
253 // Function to evaluate the interpolation at t 253 // Function to evaluate the interpolation at tau fraction of the step
254 // 254 //
255 void G4DoLoMcPriRK34::Interpolate( const G4dou 255 void G4DoLoMcPriRK34::Interpolate( const G4double yInput[],
256 const G4dou 256 const G4double dydx[],
257 const G4dou 257 const G4double Step,
258 G4dou 258 G4double yOut[],
259 G4dou 259 G4double tau )
260 { 260 {
261 G4double bf1, bf2, bf3, bf4, bf5, bf6; 261 G4double bf1, bf2, bf3, bf4, bf5, bf6;
262 262
263 const G4int numberOfVariables = GetNumberOf 263 const G4int numberOfVariables = GetNumberOfVariables();
264 264
265 for(G4int i=0; i<numberOfVariables; ++i) 265 for(G4int i=0; i<numberOfVariables; ++i)
266 { 266 {
267 yIn[i]=yInput[i]; 267 yIn[i]=yInput[i];
268 } 268 }
269 269
270 G4double tau_2 = tau*tau, tau_3 = tau*tau_2 270 G4double tau_2 = tau*tau, tau_3 = tau*tau_2;
271 271
272 // Calculating the polynomials (coefficient 272 // Calculating the polynomials (coefficients for the respective stages)
273 // 273 //
274 bf1 = -(162.0*tau_3 - 504.0*tau_2 + 551.0*t 274 bf1 = -(162.0*tau_3 - 504.0*tau_2 + 551.0*tau - 238.0)/238.0 ,
275 bf2 = 0.0 , 275 bf2 = 0.0 ,
276 bf3 = 27.0*tau*(27.0*tau_2 - 70.0*tau + 51 276 bf3 = 27.0*tau*(27.0*tau_2 - 70.0*tau + 51.0 )/385.0 ,
277 bf4 = -27*tau*(27.0*tau_2 - 50.0*tau + 21.0 277 bf4 = -27*tau*(27.0*tau_2 - 50.0*tau + 21.0)/85.0 ,
278 bf5 = 7.0*tau*(2232.0*tau_2 - 4166.0*tau + 278 bf5 = 7.0*tau*(2232.0*tau_2 - 4166.0*tau + 1785.0 )/3278.0 ,
279 bf6 = tau*(tau - 1.0)*(387.0*tau - 238.0)/1 279 bf6 = tau*(tau - 1.0)*(387.0*tau - 238.0)/149.0 ;
280 280
281 for( G4int i=0; i<numberOfVariables; ++i) 281 for( G4int i=0; i<numberOfVariables; ++i)
282 { 282 {
283 yOut[i] = yIn[i] + Step*tau*(bf1*dydx[i] 283 yOut[i] = yIn[i] + Step*tau*(bf1*dydx[i] + bf2*ak2[i] + bf3*ak3[i]
284 + bf4*ak4[i] + bf5*ak5[i] + bf6*a 284 + bf4*ak4[i] + bf5*ak5[i] + bf6*ak6[i] ) ;
285 } 285 }
286 } 286 }
287 287