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