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25 // 25 //
26 // class G4HelixMixedStepper 26 // class G4HelixMixedStepper
27 // 27 //
28 // Class description: 28 // Class description:
29 // 29 //
30 // G4HelixMixedStepper split the Method used f 30 // G4HelixMixedStepper split the Method used for Integration in two:
31 // 31 //
32 // If Stepping Angle ( h / R_curve) < pi/3 32 // If Stepping Angle ( h / R_curve) < pi/3
33 // use Stepper for small step(Classical 33 // use Stepper for small step(ClassicalRK4 by default)
34 // Else use HelixExplicitEuler Stepper 34 // Else use HelixExplicitEuler Stepper
35 // 35 //
36 // Created: T.Nikitina, CERN - 18.05.2007, der 36 // Created: T.Nikitina, CERN - 18.05.2007, derived from G4ExactHelicalStepper
37 // ------------------------------------------- 37 // -------------------------------------------------------------------------
38 38
39 #include "G4HelixMixedStepper.hh" 39 #include "G4HelixMixedStepper.hh"
40 #include "G4PhysicalConstants.hh" 40 #include "G4PhysicalConstants.hh"
41 #include "G4ClassicalRK4.hh" 41 #include "G4ClassicalRK4.hh"
42 #include "G4CashKarpRKF45.hh" 42 #include "G4CashKarpRKF45.hh"
43 #include "G4SimpleRunge.hh" 43 #include "G4SimpleRunge.hh"
44 #include "G4HelixImplicitEuler.hh" 44 #include "G4HelixImplicitEuler.hh"
45 #include "G4HelixExplicitEuler.hh" 45 #include "G4HelixExplicitEuler.hh"
46 #include "G4HelixSimpleRunge.hh" 46 #include "G4HelixSimpleRunge.hh"
47 #include "G4ExactHelixStepper.hh" 47 #include "G4ExactHelixStepper.hh"
48 #include "G4ExplicitEuler.hh" 48 #include "G4ExplicitEuler.hh"
49 #include "G4ImplicitEuler.hh" 49 #include "G4ImplicitEuler.hh"
50 #include "G4SimpleHeum.hh" 50 #include "G4SimpleHeum.hh"
51 #include "G4RKG3_Stepper.hh" 51 #include "G4RKG3_Stepper.hh"
52 #include "G4NystromRK4.hh" 52 #include "G4NystromRK4.hh"
53 53
54 // Additional potential steppers 54 // Additional potential steppers
55 #include "G4DormandPrince745.hh" 55 #include "G4DormandPrince745.hh"
56 #include "G4BogackiShampine23.hh" 56 #include "G4BogackiShampine23.hh"
57 #include "G4BogackiShampine45.hh" 57 #include "G4BogackiShampine45.hh"
58 #include "G4TsitourasRK45.hh" 58 #include "G4TsitourasRK45.hh"
59 59
60 #include "G4ThreeVector.hh" 60 #include "G4ThreeVector.hh"
61 #include "G4LineSection.hh" 61 #include "G4LineSection.hh"
62 62
63 // ------------------------------------------- 63 // ---------------------------------------------------------------------------
64 G4HelixMixedStepper:: 64 G4HelixMixedStepper::
65 G4HelixMixedStepper(G4Mag_EqRhs* EqRhs, 65 G4HelixMixedStepper(G4Mag_EqRhs* EqRhs,
66 G4int stepperNumber 66 G4int stepperNumber,
67 G4double angleThreshol 67 G4double angleThreshold)
68 : G4MagHelicalStepper(EqRhs) 68 : G4MagHelicalStepper(EqRhs)
69 { 69 {
70 if( angleThreshold < 0.0 ) 70 if( angleThreshold < 0.0 )
71 { 71 {
72 fAngle_threshold = (1.0/3.0)*pi; 72 fAngle_threshold = (1.0/3.0)*pi;
73 } 73 }
74 else 74 else
75 { 75 {
76 fAngle_threshold = angleThreshold; 76 fAngle_threshold = angleThreshold;
77 } 77 }
78 78
79 if(stepperNumber<0) 79 if(stepperNumber<0)
80 { 80 {
81 // stepperNumber = 4; // Default is RK4 81 // stepperNumber = 4; // Default is RK4 (original)
82 stepperNumber = 745; // Default is Dorm 82 stepperNumber = 745; // Default is DormandPrince745 (ie DoPri5)
83 // stepperNumber = 8; // Default is Cash 83 // stepperNumber = 8; // Default is CashKarp
84 } 84 }
85 85
86 fStepperNumber = stepperNumber; // Store th 86 fStepperNumber = stepperNumber; // Store the choice
87 fRK4Stepper = SetupStepper(EqRhs, fStepper 87 fRK4Stepper = SetupStepper(EqRhs, fStepperNumber);
88 } 88 }
89 89
90 // ------------------------------------------- 90 // ---------------------------------------------------------------------------
91 G4HelixMixedStepper::~G4HelixMixedStepper() 91 G4HelixMixedStepper::~G4HelixMixedStepper()
92 { 92 {
93 delete fRK4Stepper; 93 delete fRK4Stepper;
94 if (fVerbose>0) { PrintCalls(); } 94 if (fVerbose>0) { PrintCalls(); }
95 } 95 }
96 96
97 // ------------------------------------------- 97 // ---------------------------------------------------------------------------
98 void G4HelixMixedStepper::Stepper( const G4do << 98 void G4HelixMixedStepper::Stepper( const G4double yInput[7],
99 const G4do << 99 const G4double dydx[7],
100 G4do 100 G4double Step,
101 G4do << 101 G4double yOut[7],
102 G4do 102 G4double yErr[])
103 { 103 {
104 // Estimation of the Stepping Angle 104 // Estimation of the Stepping Angle
105 // 105 //
106 G4ThreeVector Bfld; 106 G4ThreeVector Bfld;
107 MagFieldEvaluate(yInput, Bfld); 107 MagFieldEvaluate(yInput, Bfld);
108 108
109 G4double Bmag = Bfld.mag(); 109 G4double Bmag = Bfld.mag();
110 const G4double* pIn = yInput+3; 110 const G4double* pIn = yInput+3;
111 G4ThreeVector initVelocity = G4ThreeVector( 111 G4ThreeVector initVelocity = G4ThreeVector( pIn[0], pIn[1], pIn[2] );
112 G4double velocityVal = initVelocity.mag(); 112 G4double velocityVal = initVelocity.mag();
113 113
114 const G4double R_1 = std::abs(GetInverseCurv 114 const G4double R_1 = std::abs(GetInverseCurve(velocityVal,Bmag));
115 // curv = inverse Radius 115 // curv = inverse Radius
116 G4double Ang_curve = R_1 * Step; 116 G4double Ang_curve = R_1 * Step;
117 // SetAngCurve(Ang_curve); 117 // SetAngCurve(Ang_curve);
118 // SetCurve(std::abs(1/R_1)); 118 // SetCurve(std::abs(1/R_1));
119 119
120 if(Ang_curve < fAngle_threshold) 120 if(Ang_curve < fAngle_threshold)
121 { 121 {
122 ++fNumCallsRK4; 122 ++fNumCallsRK4;
123 fRK4Stepper->Stepper(yInput,dydx,Step,yOut 123 fRK4Stepper->Stepper(yInput,dydx,Step,yOut,yErr);
124 } 124 }
125 else 125 else
126 { 126 {
127 constexpr G4int nvar = 6 ; 127 constexpr G4int nvar = 6 ;
128 constexpr G4int nvarMax = 8 ; 128 constexpr G4int nvarMax = 8 ;
129 G4double yTemp[nvarMax], yIn[nvarMax] 129 G4double yTemp[nvarMax], yIn[nvarMax], yTemp2[nvarMax];
130 G4ThreeVector Bfld_midpoint; 130 G4ThreeVector Bfld_midpoint;
131 131
132 SetAngCurve(Ang_curve); 132 SetAngCurve(Ang_curve);
133 SetCurve(std::abs(1.0/R_1)); 133 SetCurve(std::abs(1.0/R_1));
134 ++fNumCallsHelix; 134 ++fNumCallsHelix;
135 135
136 // Saving yInput because yInput and yOut c 136 // Saving yInput because yInput and yOut can be aliases for same array
137 // 137 //
138 for(G4int i=0; i<nvar; ++i) 138 for(G4int i=0; i<nvar; ++i)
139 { 139 {
140 yIn[i]=yInput[i]; 140 yIn[i]=yInput[i];
141 } 141 }
142 142
143 G4double halfS = Step * 0.5; 143 G4double halfS = Step * 0.5;
144 144
145 // 1. Do first half step and full step 145 // 1. Do first half step and full step
146 // 146 //
147 AdvanceHelix(yIn, Bfld, halfS, yTemp, yTem 147 AdvanceHelix(yIn, Bfld, halfS, yTemp, yTemp2); // yTemp2 for s=2*h (halfS)
148 148
149 MagFieldEvaluate(yTemp, Bfld_midpoint) ; 149 MagFieldEvaluate(yTemp, Bfld_midpoint) ;
150 150
151 // 2. Do second half step - with revised f 151 // 2. Do second half step - with revised field
152 // NOTE: Could avoid this call if 'Bfld_m 152 // NOTE: Could avoid this call if 'Bfld_midpoint == Bfld'
153 // or diff 'almost' zero 153 // or diff 'almost' zero
154 // 154 //
155 AdvanceHelix(yTemp, Bfld_midpoint, halfS, 155 AdvanceHelix(yTemp, Bfld_midpoint, halfS, yOut);
156 // Not requesting y at s=2*h (halfS) 156 // Not requesting y at s=2*h (halfS)
157 157
158 // 3. Estimate the integration error 158 // 3. Estimate the integration error
159 // should be (nearly) zero if Bfield= c 159 // should be (nearly) zero if Bfield= constant
160 // 160 //
161 for(G4int i=0; i<nvar; ++i) 161 for(G4int i=0; i<nvar; ++i)
162 { 162 {
163 yErr[i] = yOut[i] - yTemp2[i]; 163 yErr[i] = yOut[i] - yTemp2[i];
164 } 164 }
165 } 165 }
166 } 166 }
167 167
168 // ------------------------------------------- 168 // ---------------------------------------------------------------------------
169 void G4HelixMixedStepper::DumbStepper( const G 169 void G4HelixMixedStepper::DumbStepper( const G4double yIn[],
170 G 170 G4ThreeVector Bfld,
171 G 171 G4double h,
172 G 172 G4double yOut[] )
173 { 173 {
174 AdvanceHelix(yIn, Bfld, h, yOut); 174 AdvanceHelix(yIn, Bfld, h, yOut);
175 } 175 }
176 176
177 // ------------------------------------------- 177 // ---------------------------------------------------------------------------
178 G4double G4HelixMixedStepper::DistChord() cons 178 G4double G4HelixMixedStepper::DistChord() const
179 { 179 {
180 // Implementation : must check whether h/R > 180 // Implementation : must check whether h/R > 2 pi !!
181 // If( h/R < pi) use G4LineSection::DistL 181 // If( h/R < pi) use G4LineSection::DistLine
182 // Else DistChord=R_helix 182 // Else DistChord=R_helix
183 // 183 //
184 G4double distChord; 184 G4double distChord;
185 G4double Ang_curve=GetAngCurve(); 185 G4double Ang_curve=GetAngCurve();
186 186
187 if(Ang_curve<=pi) 187 if(Ang_curve<=pi)
188 { 188 {
189 distChord=GetRadHelix()*(1-std::cos(0.5*An 189 distChord=GetRadHelix()*(1-std::cos(0.5*Ang_curve));
190 } 190 }
191 else 191 else
192 { 192 {
193 if(Ang_curve<twopi) 193 if(Ang_curve<twopi)
194 { 194 {
195 distChord=GetRadHelix()*(1+std::cos(0.5* 195 distChord=GetRadHelix()*(1+std::cos(0.5*(twopi-Ang_curve)));
196 } 196 }
197 else 197 else
198 { 198 {
199 distChord=2.*GetRadHelix(); 199 distChord=2.*GetRadHelix();
200 } 200 }
201 } 201 }
202 202
203 return distChord; 203 return distChord;
204 } 204 }
205 205
206 // ------------------------------------------- 206 // ---------------------------------------------------------------------------
207 void G4HelixMixedStepper::PrintCalls() 207 void G4HelixMixedStepper::PrintCalls()
208 { 208 {
209 G4cout << "In HelixMixedStepper::Number of c 209 G4cout << "In HelixMixedStepper::Number of calls to smallStepStepper = "
210 << fNumCallsRK4 210 << fNumCallsRK4
211 << " and Number of calls to Helix = 211 << " and Number of calls to Helix = " << fNumCallsHelix << G4endl;
212 } 212 }
213 213
214 // ------------------------------------------- 214 // ---------------------------------------------------------------------------
215 G4MagIntegratorStepper* 215 G4MagIntegratorStepper*
216 G4HelixMixedStepper::SetupStepper(G4Mag_EqRhs* 216 G4HelixMixedStepper::SetupStepper(G4Mag_EqRhs* pE, G4int StepperNumber)
217 { 217 {
218 G4MagIntegratorStepper* pStepper; 218 G4MagIntegratorStepper* pStepper;
219 if (fVerbose>0) { G4cout << " G4HelixMixedSt << 219 if (fVerbose>0) G4cout << " G4HelixMixedStepper: ";
220 } <<
221 switch ( StepperNumber ) 220 switch ( StepperNumber )
222 { 221 {
223 // Robust, classic method 222 // Robust, classic method
224 case 4: 223 case 4:
225 pStepper = new G4ClassicalRK4( pE ); 224 pStepper = new G4ClassicalRK4( pE );
226 if (fVerbose>0) { G4cout << "G4Classic << 225 if (fVerbose>0) G4cout << "G4ClassicalRK4";
227 break; 226 break;
228 227
229 // Steppers with embedded estimation of 228 // Steppers with embedded estimation of error
230 case 8: 229 case 8:
231 pStepper = new G4CashKarpRKF45( pE ); 230 pStepper = new G4CashKarpRKF45( pE );
232 if (fVerbose>0) { G4cout << "G4CashKar << 231 if (fVerbose>0) G4cout << "G4CashKarpRKF45";
233 break; 232 break;
234 case 13: 233 case 13:
235 pStepper = new G4NystromRK4( pE ); 234 pStepper = new G4NystromRK4( pE );
236 if (fVerbose>0) { G4cout << "G4Nystrom << 235 if (fVerbose>0) G4cout << "G4NystromRK4";
237 break; 236 break;
238 237
239 // Lowest order RK Stepper - experimenta 238 // Lowest order RK Stepper - experimental
240 case 1: 239 case 1:
241 pStepper = new G4ImplicitEuler( pE ); 240 pStepper = new G4ImplicitEuler( pE );
242 if (fVerbose>0) { G4cout << "G4Implici << 241 if (fVerbose>0) G4cout << "G4ImplicitEuler";
243 break; 242 break;
244 243
245 // Lower order RK Steppers - ok overall, 244 // Lower order RK Steppers - ok overall, good for uneven fields
246 case 2: 245 case 2:
247 pStepper = new G4SimpleRunge( pE ); 246 pStepper = new G4SimpleRunge( pE );
248 if (fVerbose>0) { G4cout << "G4SimpleR << 247 if (fVerbose>0) G4cout << "G4SimpleRunge";
249 break; 248 break;
250 case 3: 249 case 3:
251 pStepper = new G4SimpleHeum( pE ); 250 pStepper = new G4SimpleHeum( pE );
252 if (fVerbose>0) { G4cout << "G4SimpleH << 251 if (fVerbose>0) G4cout << "G4SimpleHeum";
253 break; 252 break;
254 case 23: 253 case 23:
255 pStepper = new G4BogackiShampine23( pE 254 pStepper = new G4BogackiShampine23( pE );
256 if (fVerbose>0) { G4cout << "G4Bogacki << 255 if (fVerbose>0) G4cout << "G4BogackiShampine23";
257 break; 256 break;
258 257
259 // Higher order RK Steppers 258 // Higher order RK Steppers
260 // for smoother fields and high accuracy 259 // for smoother fields and high accuracy requirements
261 case 45: 260 case 45:
262 pStepper = new G4BogackiShampine45( pE 261 pStepper = new G4BogackiShampine45( pE );
263 if (fVerbose>0) { G4cout << "G4Bogacki << 262 if (fVerbose>0) G4cout << "G4BogackiShampine45";
264 break; 263 break;
265 case 145: 264 case 145:
266 pStepper = new G4TsitourasRK45( pE ); 265 pStepper = new G4TsitourasRK45( pE );
267 if (fVerbose>0) { G4cout << "G4Tsitour << 266 if (fVerbose>0) G4cout << "G4TsitourasRK45";
268 break; 267 break;
269 case 745: 268 case 745:
270 pStepper = new G4DormandPrince745( pE 269 pStepper = new G4DormandPrince745( pE );
271 if (fVerbose>0) { G4cout << "G4Dormand << 270 if (fVerbose>0) G4cout << "G4DormandPrince745";
272 break; 271 break;
273 272
274 // Helical Steppers 273 // Helical Steppers
275 case 6: 274 case 6:
276 pStepper = new G4HelixImplicitEuler( p 275 pStepper = new G4HelixImplicitEuler( pE );
277 if (fVerbose>0) { G4cout << "G4HelixIm << 276 if (fVerbose>0) G4cout << "G4HelixImplicitEuler";
278 break; 277 break;
279 case 7: 278 case 7:
280 pStepper = new G4HelixSimpleRunge( pE 279 pStepper = new G4HelixSimpleRunge( pE );
281 if (fVerbose>0) { G4cout << "G4HelixSi << 280 if (fVerbose>0) G4cout << "G4HelixSimpleRunge";
282 break; 281 break;
283 case 5: 282 case 5:
284 pStepper = new G4HelixExplicitEuler( p 283 pStepper = new G4HelixExplicitEuler( pE );
285 if (fVerbose>0) { G4cout << "G4HelixEx << 284 if (fVerbose>0) G4cout << "G4HelixExplicitEuler";
286 break; // Since Helix Explicit is use 285 break; // Since Helix Explicit is used for long steps,
287 // this is useful only to measu 286 // this is useful only to measure overhead.
288 // Exact Helix - likely good only for ca 287 // Exact Helix - likely good only for cases of
289 // i) uniform field (potentia 288 // i) uniform field (potentially over small distances)
290 // ii) segmented uniform field 289 // ii) segmented uniform field (maybe)
291 case 9: 290 case 9:
292 pStepper = new G4ExactHelixStepper( pE 291 pStepper = new G4ExactHelixStepper( pE );
293 if (fVerbose>0) { G4cout << "G4ExactHe << 292 if (fVerbose>0) G4cout << "G4ExactHelixStepper";
294 break; 293 break;
295 case 10: 294 case 10:
296 pStepper = new G4RKG3_Stepper( pE ); 295 pStepper = new G4RKG3_Stepper( pE );
297 if (fVerbose>0) { G4cout << "G4RKG3_St << 296 if (fVerbose>0) G4cout << "G4RKG3_Stepper";
298 break; 297 break;
299 298
300 // Low Order Steppers - not good except 299 // Low Order Steppers - not good except for very weak fields
301 case 11: 300 case 11:
302 pStepper = new G4ExplicitEuler( pE ); 301 pStepper = new G4ExplicitEuler( pE );
303 if (fVerbose>0) { G4cout << "G4Explici << 302 if (fVerbose>0) G4cout << "G4ExplicitEuler";
304 break; 303 break;
305 case 12: 304 case 12:
306 pStepper = new G4ImplicitEuler( pE ); 305 pStepper = new G4ImplicitEuler( pE );
307 if (fVerbose>0) { G4cout << "G4Implici << 306 if (fVerbose>0) G4cout << "G4ImplicitEuler";
308 break; 307 break;
309 308
310 case 0: 309 case 0:
311 case -1: 310 case -1:
312 default: 311 default:
313 pStepper = new G4DormandPrince745( pE 312 pStepper = new G4DormandPrince745( pE ); // Was G4ClassicalRK4( pE );
314 if (fVerbose>0) { G4cout << "G4Dormand << 313 if (fVerbose>0) G4cout << "G4DormandPrince745 (Default)";
315 break; 314 break;
316 } 315 }
317 316
318 if(fVerbose>0) 317 if(fVerbose>0)
319 { 318 {
320 G4cout << " chosen as stepper for small st 319 G4cout << " chosen as stepper for small steps in G4HelixMixedStepper."
321 << G4endl; 320 << G4endl;
322 } 321 }
323 322
324 return pStepper; 323 return pStepper;
325 } 324 }
326 325