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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 // History:
>> 37 // Derived from ExactHelicalStepper 18/05/07
>> 38 //
37 // ------------------------------------------- 39 // -------------------------------------------------------------------------
38 40
39 #include "G4HelixMixedStepper.hh" 41 #include "G4HelixMixedStepper.hh"
40 #include "G4PhysicalConstants.hh" 42 #include "G4PhysicalConstants.hh"
41 #include "G4ClassicalRK4.hh" 43 #include "G4ClassicalRK4.hh"
42 #include "G4CashKarpRKF45.hh" 44 #include "G4CashKarpRKF45.hh"
43 #include "G4SimpleRunge.hh" 45 #include "G4SimpleRunge.hh"
44 #include "G4HelixImplicitEuler.hh" 46 #include "G4HelixImplicitEuler.hh"
45 #include "G4HelixExplicitEuler.hh" 47 #include "G4HelixExplicitEuler.hh"
46 #include "G4HelixSimpleRunge.hh" 48 #include "G4HelixSimpleRunge.hh"
47 #include "G4ExactHelixStepper.hh" 49 #include "G4ExactHelixStepper.hh"
48 #include "G4ExplicitEuler.hh" 50 #include "G4ExplicitEuler.hh"
49 #include "G4ImplicitEuler.hh" 51 #include "G4ImplicitEuler.hh"
50 #include "G4SimpleHeum.hh" 52 #include "G4SimpleHeum.hh"
51 #include "G4RKG3_Stepper.hh" 53 #include "G4RKG3_Stepper.hh"
52 #include "G4NystromRK4.hh" 54 #include "G4NystromRK4.hh"
53 << 55 // Additional potential stepper
54 // Additional potential steppers <<
55 #include "G4DormandPrince745.hh" 56 #include "G4DormandPrince745.hh"
56 #include "G4BogackiShampine23.hh" 57 #include "G4BogackiShampine23.hh"
57 #include "G4BogackiShampine45.hh" 58 #include "G4BogackiShampine45.hh"
58 #include "G4TsitourasRK45.hh" 59 #include "G4TsitourasRK45.hh"
59 60
60 #include "G4ThreeVector.hh" 61 #include "G4ThreeVector.hh"
61 #include "G4LineSection.hh" 62 #include "G4LineSection.hh"
62 63
63 // ------------------------------------------- <<
64 G4HelixMixedStepper:: 64 G4HelixMixedStepper::
65 G4HelixMixedStepper(G4Mag_EqRhs* EqRhs, << 65 G4HelixMixedStepper(G4Mag_EqRhs *EqRhs, G4int stepperNumber,
66 G4int stepperNumber << 66 G4double angleThreshold)
67 G4double angleThreshol << 67 : G4MagHelicalStepper(EqRhs), fNumCallsRK4(0), fNumCallsHelix(0)
68 : G4MagHelicalStepper(EqRhs) <<
69 { 68 {
70 if( angleThreshold < 0.0 ) << 69 SetVerbose(1);
71 { << 70 if( angleThreshold < 0.0 ){
72 fAngle_threshold = (1.0/3.0)*pi; << 71 fAngle_threshold= 0.33*pi;
73 } << 72 }else{
74 else << 73 fAngle_threshold= angleThreshold;
75 { <<
76 fAngle_threshold = angleThreshold; <<
77 } 74 }
78 75
79 if(stepperNumber<0) 76 if(stepperNumber<0)
80 { << 77 stepperNumber=4; // Default is RK4 (original)
81 // stepperNumber = 4; // Default is RK4 << 78 // stepperNumber=745; // Default is DormandPrince745 (ie DoPri5)
82 stepperNumber = 745; // Default is Dorm << 79 // stepperNumber=8; // Default is CashKarp
83 // stepperNumber = 8; // Default is Cash <<
84 } <<
85 80
86 fStepperNumber = stepperNumber; // Store th 81 fStepperNumber = stepperNumber; // Store the choice
87 fRK4Stepper = SetupStepper(EqRhs, fStepper 82 fRK4Stepper = SetupStepper(EqRhs, fStepperNumber);
88 } 83 }
89 84
90 // ------------------------------------------- <<
91 G4HelixMixedStepper::~G4HelixMixedStepper() 85 G4HelixMixedStepper::~G4HelixMixedStepper()
92 { 86 {
93 delete fRK4Stepper; << 87 delete(fRK4Stepper);
94 if (fVerbose>0) { PrintCalls(); } << 88 if (fVerbose>0){ PrintCalls();};
95 } 89 }
96 90
97 // ------------------------------------------- << 91 void G4HelixMixedStepper::Stepper( const G4double yInput[7],
98 void G4HelixMixedStepper::Stepper( const G4do << 92 const G4double dydx[7],
99 const G4do << 93 G4double Step,
100 G4do << 94 G4double yOut[7],
101 G4do << 95 G4double yErr[])
102 G4do <<
103 { 96 {
104 // Estimation of the Stepping Angle << 97 //Estimation of the Stepping Angle
105 // <<
106 G4ThreeVector Bfld; 98 G4ThreeVector Bfld;
107 MagFieldEvaluate(yInput, Bfld); 99 MagFieldEvaluate(yInput, Bfld);
108 100
109 G4double Bmag = Bfld.mag(); 101 G4double Bmag = Bfld.mag();
110 const G4double* pIn = yInput+3; << 102 const G4double *pIn = yInput+3;
111 G4ThreeVector initVelocity = G4ThreeVector( << 103 G4ThreeVector initVelocity= G4ThreeVector( pIn[0], pIn[1], pIn[2]);
112 G4double velocityVal = initVelocity.mag(); << 104 G4double velocityVal = initVelocity.mag();
113 << 105 G4double R_1;
114 const G4double R_1 = std::abs(GetInverseCurv << 106 G4double Ang_curve;
115 // curv = inverse Radius << 107
116 G4double Ang_curve = R_1 * Step; << 108 R_1=std::abs(GetInverseCurve(velocityVal,Bmag));
117 // SetAngCurve(Ang_curve); << 109 Ang_curve=R_1*Step;
118 // SetCurve(std::abs(1/R_1)); << 110 SetAngCurve(Ang_curve);
119 << 111 SetCurve(std::abs(1/R_1));
120 if(Ang_curve < fAngle_threshold) << 112
121 { << 113 if(Ang_curve< fAngle_threshold){
122 ++fNumCallsRK4; << 114 fNumCallsRK4++;
123 fRK4Stepper->Stepper(yInput,dydx,Step,yOut 115 fRK4Stepper->Stepper(yInput,dydx,Step,yOut,yErr);
124 } 116 }
125 else 117 else
126 { 118 {
127 constexpr G4int nvar = 6 ; << 119 fNumCallsHelix++;
128 constexpr G4int nvarMax = 8 ; << 120 const G4int nvar = 6 ;
129 G4double yTemp[nvarMax], yIn[nvarMax] << 121 const G4int nvarMax = 8 ;
130 G4ThreeVector Bfld_midpoint; << 122 G4int i;
131 << 123 G4double yTemp[nvarMax], yIn[nvarMax], yTemp2[nvarMax];
132 SetAngCurve(Ang_curve); << 124 G4ThreeVector Bfld_midpoint;
133 SetCurve(std::abs(1.0/R_1)); << 125
134 ++fNumCallsHelix; << 126 // Saving yInput because yInput and yOut can be aliases for same array
135 << 127 for(i=0;i<nvar;i++) yIn[i]=yInput[i];
136 // Saving yInput because yInput and yOut c <<
137 // <<
138 for(G4int i=0; i<nvar; ++i) <<
139 { <<
140 yIn[i]=yInput[i]; <<
141 } <<
142 128
143 G4double halfS = Step * 0.5; 129 G4double halfS = Step * 0.5;
144 <<
145 // 1. Do first half step and full step 130 // 1. Do first half step and full step
146 // <<
147 AdvanceHelix(yIn, Bfld, halfS, yTemp, yTem 131 AdvanceHelix(yIn, Bfld, halfS, yTemp, yTemp2); // yTemp2 for s=2*h (halfS)
>> 132 //**********
148 133
149 MagFieldEvaluate(yTemp, Bfld_midpoint) ; 134 MagFieldEvaluate(yTemp, Bfld_midpoint) ;
150 135
151 // 2. Do second half step - with revised f 136 // 2. Do second half step - with revised field
152 // NOTE: Could avoid this call if 'Bfld_m 137 // NOTE: Could avoid this call if 'Bfld_midpoint == Bfld'
153 // or diff 'almost' zero 138 // or diff 'almost' zero
154 // <<
155 AdvanceHelix(yTemp, Bfld_midpoint, halfS, 139 AdvanceHelix(yTemp, Bfld_midpoint, halfS, yOut);
156 // Not requesting y at s=2*h (halfS) << 140 // Not requesting y at s=2*h (halfS)
>> 141 //**********
157 142
158 // 3. Estimate the integration error 143 // 3. Estimate the integration error
159 // should be (nearly) zero if Bfield= c 144 // should be (nearly) zero if Bfield= constant
160 // << 145 for(i=0;i<nvar;i++) {
161 for(G4int i=0; i<nvar; ++i) << 146 yErr[i] = yOut[i] - yTemp2[i] ;
162 { <<
163 yErr[i] = yOut[i] - yTemp2[i]; <<
164 } 147 }
165 } 148 }
166 } 149 }
167 150
168 // ------------------------------------------- << 151 void
169 void G4HelixMixedStepper::DumbStepper( const G << 152 G4HelixMixedStepper::DumbStepper( const G4double yIn[],
170 G << 153 G4ThreeVector Bfld,
171 G << 154 G4double h,
172 G << 155 G4double yOut[])
173 { 156 {
174 AdvanceHelix(yIn, Bfld, h, yOut); 157 AdvanceHelix(yIn, Bfld, h, yOut);
175 } 158 }
176 159
177 // ------------------------------------------- << 160 G4double G4HelixMixedStepper::DistChord() const
178 G4double G4HelixMixedStepper::DistChord() cons <<
179 { 161 {
180 // Implementation : must check whether h/R > 162 // Implementation : must check whether h/R > 2 pi !!
181 // If( h/R < pi) use G4LineSection::DistL 163 // If( h/R < pi) use G4LineSection::DistLine
182 // Else DistChord=R_helix 164 // Else DistChord=R_helix
183 // 165 //
184 G4double distChord; 166 G4double distChord;
185 G4double Ang_curve=GetAngCurve(); 167 G4double Ang_curve=GetAngCurve();
186 168
187 if(Ang_curve<=pi) << 169 if(Ang_curve<=pi){
188 { <<
189 distChord=GetRadHelix()*(1-std::cos(0.5*An 170 distChord=GetRadHelix()*(1-std::cos(0.5*Ang_curve));
190 } 171 }
191 else 172 else
192 { 173 {
193 if(Ang_curve<twopi) << 174 if(Ang_curve<twopi){
194 { <<
195 distChord=GetRadHelix()*(1+std::cos(0.5* 175 distChord=GetRadHelix()*(1+std::cos(0.5*(twopi-Ang_curve)));
196 } 176 }
197 else << 177 else{
198 { <<
199 distChord=2.*GetRadHelix(); 178 distChord=2.*GetRadHelix();
200 } 179 }
201 } 180 }
202 181
203 return distChord; 182 return distChord;
204 } 183 }
205 184
206 // ------------------------------------------- 185 // ---------------------------------------------------------------------------
207 void G4HelixMixedStepper::PrintCalls() 186 void G4HelixMixedStepper::PrintCalls()
208 { 187 {
209 G4cout << "In HelixMixedStepper::Number of c 188 G4cout << "In HelixMixedStepper::Number of calls to smallStepStepper = "
210 << fNumCallsRK4 189 << fNumCallsRK4
211 << " and Number of calls to Helix = 190 << " and Number of calls to Helix = " << fNumCallsHelix << G4endl;
212 } 191 }
213 192
214 // ------------------------------------------- <<
215 G4MagIntegratorStepper* 193 G4MagIntegratorStepper*
216 G4HelixMixedStepper::SetupStepper(G4Mag_EqRhs* 194 G4HelixMixedStepper::SetupStepper(G4Mag_EqRhs* pE, G4int StepperNumber)
217 { 195 {
218 G4MagIntegratorStepper* pStepper; 196 G4MagIntegratorStepper* pStepper;
219 if (fVerbose>0) { G4cout << " G4HelixMixedSt << 197 if (fVerbose>0) G4cout << " G4HelixMixedStepper: ";
220 } <<
221 switch ( StepperNumber ) 198 switch ( StepperNumber )
222 { << 199 {
223 // Robust, classic method 200 // Robust, classic method
224 case 4: 201 case 4:
225 pStepper = new G4ClassicalRK4( pE ); 202 pStepper = new G4ClassicalRK4( pE );
226 if (fVerbose>0) { G4cout << "G4Classic << 203 if (fVerbose>0) G4cout << "G4ClassicalRK4";
227 break; 204 break;
228 205
229 // Steppers with embedded estimation of 206 // Steppers with embedded estimation of error
230 case 8: 207 case 8:
231 pStepper = new G4CashKarpRKF45( pE ); 208 pStepper = new G4CashKarpRKF45( pE );
232 if (fVerbose>0) { G4cout << "G4CashKar << 209 if (fVerbose>0) G4cout << "G4CashKarpRKF45";
233 break; 210 break;
234 case 13: 211 case 13:
235 pStepper = new G4NystromRK4( pE ); 212 pStepper = new G4NystromRK4( pE );
236 if (fVerbose>0) { G4cout << "G4Nystrom << 213 if (fVerbose>0) G4cout << "G4NystromRK4";
237 break; 214 break;
238 215
239 // Lowest order RK Stepper - experimenta 216 // Lowest order RK Stepper - experimental
240 case 1: 217 case 1:
241 pStepper = new G4ImplicitEuler( pE ); 218 pStepper = new G4ImplicitEuler( pE );
242 if (fVerbose>0) { G4cout << "G4Implici << 219 if (fVerbose>0) G4cout << "G4ImplicitEuler";
243 break; 220 break;
244 221
245 // Lower order RK Steppers - ok overall, 222 // Lower order RK Steppers - ok overall, good for uneven fields
246 case 2: 223 case 2:
247 pStepper = new G4SimpleRunge( pE ); 224 pStepper = new G4SimpleRunge( pE );
248 if (fVerbose>0) { G4cout << "G4SimpleR << 225 if (fVerbose>0) G4cout << "G4SimpleRunge";
249 break; 226 break;
250 case 3: 227 case 3:
251 pStepper = new G4SimpleHeum( pE ); 228 pStepper = new G4SimpleHeum( pE );
252 if (fVerbose>0) { G4cout << "G4SimpleH << 229 if (fVerbose>0) G4cout << "G4SimpleHeum";
253 break; 230 break;
254 case 23: 231 case 23:
255 pStepper = new G4BogackiShampine23( pE 232 pStepper = new G4BogackiShampine23( pE );
256 if (fVerbose>0) { G4cout << "G4Bogacki << 233 if (fVerbose>0) G4cout << "G4BogackiShampine23";
257 break; 234 break;
258 235
259 // Higher order RK Steppers 236 // Higher order RK Steppers
260 // for smoother fields and high accuracy 237 // for smoother fields and high accuracy requirements
261 case 45: 238 case 45:
262 pStepper = new G4BogackiShampine45( pE 239 pStepper = new G4BogackiShampine45( pE );
263 if (fVerbose>0) { G4cout << "G4Bogacki << 240 if (fVerbose>0) G4cout << "G4BogackiShampine45";
264 break; 241 break;
265 case 145: 242 case 145:
266 pStepper = new G4TsitourasRK45( pE ); 243 pStepper = new G4TsitourasRK45( pE );
267 if (fVerbose>0) { G4cout << "G4Tsitour << 244 if (fVerbose>0) G4cout << "G4TsitourasRK45";
268 break; 245 break;
269 case 745: 246 case 745:
270 pStepper = new G4DormandPrince745( pE 247 pStepper = new G4DormandPrince745( pE );
271 if (fVerbose>0) { G4cout << "G4Dormand << 248 if (fVerbose>0) G4cout << "G4DormandPrince745";
272 break; 249 break;
273 250
274 // Helical Steppers 251 // Helical Steppers
275 case 6: 252 case 6:
276 pStepper = new G4HelixImplicitEuler( p 253 pStepper = new G4HelixImplicitEuler( pE );
277 if (fVerbose>0) { G4cout << "G4HelixIm << 254 if (fVerbose>0) G4cout << "G4HelixImplicitEuler";
278 break; 255 break;
279 case 7: 256 case 7:
280 pStepper = new G4HelixSimpleRunge( pE 257 pStepper = new G4HelixSimpleRunge( pE );
281 if (fVerbose>0) { G4cout << "G4HelixSi << 258 if (fVerbose>0) G4cout << "G4HelixSimpleRunge";
282 break; 259 break;
283 case 5: 260 case 5:
284 pStepper = new G4HelixExplicitEuler( p 261 pStepper = new G4HelixExplicitEuler( pE );
285 if (fVerbose>0) { G4cout << "G4HelixEx << 262 if (fVerbose>0) G4cout << "G4HelixExplicitEuler";
286 break; // Since Helix Explicit is use 263 break; // Since Helix Explicit is used for long steps,
287 // this is useful only to measu 264 // this is useful only to measure overhead.
288 // Exact Helix - likely good only for ca 265 // Exact Helix - likely good only for cases of
289 // i) uniform field (potentia 266 // i) uniform field (potentially over small distances)
290 // ii) segmented uniform field 267 // ii) segmented uniform field (maybe)
291 case 9: 268 case 9:
292 pStepper = new G4ExactHelixStepper( pE 269 pStepper = new G4ExactHelixStepper( pE );
293 if (fVerbose>0) { G4cout << "G4ExactHe << 270 if (fVerbose>0) G4cout << "G4ExactHelixStepper";
294 break; 271 break;
295 case 10: 272 case 10:
296 pStepper = new G4RKG3_Stepper( pE ); 273 pStepper = new G4RKG3_Stepper( pE );
297 if (fVerbose>0) { G4cout << "G4RKG3_St << 274 if (fVerbose>0) G4cout << "G4RKG3_Stepper";
298 break; 275 break;
299 276
300 // Low Order Steppers - not good except 277 // Low Order Steppers - not good except for very weak fields
301 case 11: 278 case 11:
302 pStepper = new G4ExplicitEuler( pE ); 279 pStepper = new G4ExplicitEuler( pE );
303 if (fVerbose>0) { G4cout << "G4Explici << 280 if (fVerbose>0) G4cout << "G4ExplicitEuler";
304 break; 281 break;
305 case 12: 282 case 12:
306 pStepper = new G4ImplicitEuler( pE ); 283 pStepper = new G4ImplicitEuler( pE );
307 if (fVerbose>0) { G4cout << "G4Implici << 284 if (fVerbose>0) G4cout << "G4ImplicitEuler";
308 break; 285 break;
309 286
310 case 0: 287 case 0:
311 case -1: 288 case -1:
312 default: 289 default:
313 pStepper = new G4DormandPrince745( pE << 290 pStepper = new G4ClassicalRK4( pE );
314 if (fVerbose>0) { G4cout << "G4Dormand << 291 if (fVerbose>0) G4cout << "G4ClassicalRK4 (Default)";
315 break; 292 break;
316 } << 293 }
317 <<
318 if(fVerbose>0) 294 if(fVerbose>0)
319 { <<
320 G4cout << " chosen as stepper for small st 295 G4cout << " chosen as stepper for small steps in G4HelixMixedStepper."
321 << G4endl; 296 << G4endl;
322 } <<
323 297
324 return pStepper; 298 return pStepper;
325 } 299 }
326 300