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24 // ******************************************* 24 // ********************************************************************
25 // 25 //
26 // G4RKG3_Stepper implementation 26 // G4RKG3_Stepper implementation
27 // 27 //
28 // Created: J.Apostolakis, V.Grichine - 30.01. 28 // Created: J.Apostolakis, V.Grichine - 30.01.1997
29 // ------------------------------------------- 29 // -------------------------------------------------------------------
30 30
31 #include "G4RKG3_Stepper.hh" 31 #include "G4RKG3_Stepper.hh"
32 #include "G4LineSection.hh" 32 #include "G4LineSection.hh"
33 #include "G4Mag_EqRhs.hh" 33 #include "G4Mag_EqRhs.hh"
34 34
35 G4RKG3_Stepper::G4RKG3_Stepper(G4Mag_EqRhs* Eq 35 G4RKG3_Stepper::G4RKG3_Stepper(G4Mag_EqRhs* EqRhs)
36 : G4MagIntegratorStepper(EqRhs,6) 36 : G4MagIntegratorStepper(EqRhs,6)
37 { 37 {
38 } 38 }
39 39
40 G4RKG3_Stepper::~G4RKG3_Stepper() = default; << 40 G4RKG3_Stepper::~G4RKG3_Stepper()
>> 41 {
>> 42 }
41 43
42 void G4RKG3_Stepper::Stepper( const G4double y 44 void G4RKG3_Stepper::Stepper( const G4double yInput[], // [8]
43 const G4double d 45 const G4double dydx[], // [6]
44 G4double S 46 G4double Step,
45 G4double y 47 G4double yOut[], // [8]
46 G4double y 48 G4double yErr[] )
47 { 49 {
48 G4double B[3]; 50 G4double B[3];
49 G4int nvar = 6 ; 51 G4int nvar = 6 ;
50 G4double by15 = 1. / 15. ; // was 0.06666 52 G4double by15 = 1. / 15. ; // was 0.066666666 ;
51 53
52 G4double yTemp[8], dydxTemp[6], yIn[8]; 54 G4double yTemp[8], dydxTemp[6], yIn[8];
53 55
54 // Saving yInput because yInput and yOut ca 56 // Saving yInput because yInput and yOut can be aliases for same array
55 // 57 //
56 for(G4int i=0; i<nvar; ++i) 58 for(G4int i=0; i<nvar; ++i)
57 { 59 {
58 yIn[i]=yInput[i]; 60 yIn[i]=yInput[i];
59 } 61 }
60 yIn[6] = yInput[6]; 62 yIn[6] = yInput[6];
61 yIn[7] = yInput[7]; 63 yIn[7] = yInput[7];
62 G4double h = Step * 0.5; 64 G4double h = Step * 0.5;
63 hStep = Step; 65 hStep = Step;
64 // Do two half steps 66 // Do two half steps
65 67
66 StepNoErr(yIn, dydx,h, yTemp,B) ; 68 StepNoErr(yIn, dydx,h, yTemp,B) ;
67 69
68 // Store Bfld for DistChord Calculation 70 // Store Bfld for DistChord Calculation
69 // 71 //
70 for(auto i=0; i<3; ++i) 72 for(auto i=0; i<3; ++i)
71 { 73 {
72 BfldIn[i] = B[i]; 74 BfldIn[i] = B[i];
73 } 75 }
74 // RightHandSide(yTemp,dydxTemp) ; 76 // RightHandSide(yTemp,dydxTemp) ;
75 77
76 GetEquationOfMotion()->EvaluateRhsGivenB(yT 78 GetEquationOfMotion()->EvaluateRhsGivenB(yTemp,B,dydxTemp) ;
77 StepNoErr(yTemp,dydxTemp,h,yOut,B); 79 StepNoErr(yTemp,dydxTemp,h,yOut,B);
78 80
79 // Store midpoint, chord calculation 81 // Store midpoint, chord calculation
80 82
81 fyMidPoint = G4ThreeVector(yTemp[0], yTemp 83 fyMidPoint = G4ThreeVector(yTemp[0], yTemp[1], yTemp[2]);
82 84
83 // Do a full Step 85 // Do a full Step
84 // 86 //
85 h *= 2 ; 87 h *= 2 ;
86 StepNoErr(yIn,dydx,h,yTemp,B); 88 StepNoErr(yIn,dydx,h,yTemp,B);
87 for(G4int i=0; i<nvar; ++i) 89 for(G4int i=0; i<nvar; ++i)
88 { 90 {
89 yErr[i] = yOut[i] - yTemp[i] ; 91 yErr[i] = yOut[i] - yTemp[i] ;
90 yOut[i] += yErr[i]*by15 ; // Pr 92 yOut[i] += yErr[i]*by15 ; // Provides 5th order of accuracy
91 } 93 }
92 94
93 // Store values for DistChord method 95 // Store values for DistChord method
94 // 96 //
95 fyInitial = G4ThreeVector( yIn[0], yIn[1] 97 fyInitial = G4ThreeVector( yIn[0], yIn[1], yIn[2]);
96 fpInitial = G4ThreeVector( yIn[3], yIn[4] 98 fpInitial = G4ThreeVector( yIn[3], yIn[4], yIn[5]);
97 fyFinal = G4ThreeVector( yOut[0], yOut[1 99 fyFinal = G4ThreeVector( yOut[0], yOut[1], yOut[2]);
98 } 100 }
99 101
100 // ------------------------------------------- 102 // ---------------------------------------------------------------------------
101 103
102 // Integrator for RK from G3 with evaluation o 104 // Integrator for RK from G3 with evaluation of error in solution and delta
103 // geometry based on naive similarity with the 105 // geometry based on naive similarity with the case of uniform magnetic field.
104 // B1[3] is input and is the first magnetic f 106 // B1[3] is input and is the first magnetic field values
105 // B2[3] is output and is the final magnetic f 107 // B2[3] is output and is the final magnetic field values.
106 // 108 //
107 void G4RKG3_Stepper::StepWithEst( const G4doub 109 void G4RKG3_Stepper::StepWithEst( const G4double*,
108 const G4doub 110 const G4double*,
109 G4doub 111 G4double,
110 G4doub 112 G4double*,
111 G4doub 113 G4double&,
112 G4doub 114 G4double&,
113 const G4doub 115 const G4double*,
114 G4doub 116 G4double* )
115 117
116 { 118 {
117 G4Exception("G4RKG3_Stepper::StepWithEst()", 119 G4Exception("G4RKG3_Stepper::StepWithEst()", "GeomField0001",
118 FatalException, "Method no longe 120 FatalException, "Method no longer used.");
119 } 121 }
120 122
121 // ------------------------------------------- 123 // -----------------------------------------------------------------
122 124
123 // Integrator RK Stepper from G3 with only two 125 // Integrator RK Stepper from G3 with only two field evaluation per Step.
124 // It is used in propagation initial Step by s 126 // It is used in propagation initial Step by small substeps after solution
125 // error and delta geometry considerations. B[ 127 // error and delta geometry considerations. B[3] is magnetic field which
126 // is passed from substep to substep. 128 // is passed from substep to substep.
127 // 129 //
128 void G4RKG3_Stepper::StepNoErr(const G4double 130 void G4RKG3_Stepper::StepNoErr(const G4double tIn[8],
129 const G4double 131 const G4double dydx[6],
130 G4double 132 G4double Step,
131 G4double 133 G4double tOut[8],
132 G4double 134 G4double B[3] )
133 135
134 { 136 {
135 137
136 // Copy and edit the routine above, to dele 138 // Copy and edit the routine above, to delete alpha2, beta2, ...
137 // 139 //
138 G4double K1[7], K2[7], K3[7], K4[7]; 140 G4double K1[7], K2[7], K3[7], K4[7];
139 G4double tTemp[8]={0.0}, yderiv[6]={0.0}; 141 G4double tTemp[8]={0.0}, yderiv[6]={0.0};
140 142
141 // Need Momentum value to give correct valu 143 // Need Momentum value to give correct values to the coefficients in
142 // equation. Integration on unit velocity, 144 // equation. Integration on unit velocity, but tIn[3,4,5] is momentum
143 145
144 G4double mom, inverse_mom; 146 G4double mom, inverse_mom;
145 const G4double c1=0.5, c2=0.125, c3=1./6.; 147 const G4double c1=0.5, c2=0.125, c3=1./6.;
146 148
147 // Correction for momentum not a velocity 149 // Correction for momentum not a velocity
148 // Need the protection !!! must be not zero 150 // Need the protection !!! must be not zero
149 // 151 //
150 mom = std::sqrt(tIn[3]*tIn[3]+tIn[4]*tIn[4] 152 mom = std::sqrt(tIn[3]*tIn[3]+tIn[4]*tIn[4]+tIn[5]*tIn[5]);
151 inverse_mom = 1./mom; 153 inverse_mom = 1./mom;
152 for(auto i=0; i<3; ++i) 154 for(auto i=0; i<3; ++i)
153 { 155 {
154 K1[i] = Step * dydx[i+3]*inverse_mom; 156 K1[i] = Step * dydx[i+3]*inverse_mom;
155 tTemp[i] = tIn[i] + Step*(c1*tIn[i+3]*in 157 tTemp[i] = tIn[i] + Step*(c1*tIn[i+3]*inverse_mom + c2*K1[i]) ;
156 tTemp[i+3] = tIn[i+3] + c1*K1[i]*mom ; 158 tTemp[i+3] = tIn[i+3] + c1*K1[i]*mom ;
157 } 159 }
158 160
159 GetEquationOfMotion()->EvaluateRhsReturnB(t 161 GetEquationOfMotion()->EvaluateRhsReturnB(tTemp,yderiv,B) ;
160 162
161 for(auto i=0; i<3; ++i) 163 for(auto i=0; i<3; ++i)
162 { 164 {
163 K2[i] = Step * yderiv[i+3]*inverse_mom; 165 K2[i] = Step * yderiv[i+3]*inverse_mom;
164 tTemp[i+3] = tIn[i+3] + c1*K2[i]*mom ; 166 tTemp[i+3] = tIn[i+3] + c1*K2[i]*mom ;
165 } 167 }
166 168
167 // Given B, calculate yderiv ! 169 // Given B, calculate yderiv !
168 // 170 //
169 GetEquationOfMotion()->EvaluateRhsGivenB(tT 171 GetEquationOfMotion()->EvaluateRhsGivenB(tTemp,B,yderiv) ;
170 172
171 for(auto i=0; i<3; ++i) 173 for(auto i=0; i<3; ++i)
172 { 174 {
173 K3[i] = Step * yderiv[i+3]*inverse_mom; 175 K3[i] = Step * yderiv[i+3]*inverse_mom;
174 tTemp[i] = tIn[i] + Step*(tIn[i+3]*inver 176 tTemp[i] = tIn[i] + Step*(tIn[i+3]*inverse_mom + c1*K3[i]) ;
175 tTemp[i+3] = tIn[i+3] + K3[i]*mom ; 177 tTemp[i+3] = tIn[i+3] + K3[i]*mom ;
176 } 178 }
177 179
178 // Calculates y-deriv(atives) & returns B t 180 // Calculates y-deriv(atives) & returns B too!
179 // 181 //
180 GetEquationOfMotion()->EvaluateRhsReturnB(t 182 GetEquationOfMotion()->EvaluateRhsReturnB(tTemp,yderiv,B) ;
181 183
182 for(auto i=0; i<3; ++i) // Output tr 184 for(auto i=0; i<3; ++i) // Output trajectory vector
183 { 185 {
184 K4[i] = Step * yderiv[i+3]*inverse_mom; 186 K4[i] = Step * yderiv[i+3]*inverse_mom;
185 tOut[i] = tIn[i] + Step*(tIn[i+3]*invers 187 tOut[i] = tIn[i] + Step*(tIn[i+3]*inverse_mom+ (K1[i]+K2[i]+K3[i])*c3) ;
186 tOut[i+3] = tIn[i+3] + mom*(K1[i] + 2*K2 188 tOut[i+3] = tIn[i+3] + mom*(K1[i] + 2*K2[i] + 2*K3[i] +K4[i])*c3 ;
187 } 189 }
188 tOut[6] = tIn[6]; 190 tOut[6] = tIn[6];
189 tOut[7] = tIn[7]; 191 tOut[7] = tIn[7];
190 } 192 }
191 193
192 // ------------------------------------------- 194 // ---------------------------------------------------------------------------
193 195
194 G4double G4RKG3_Stepper::DistChord() const 196 G4double G4RKG3_Stepper::DistChord() const
195 { 197 {
196 // Soon: must check whether h/R > 2 pi !! 198 // Soon: must check whether h/R > 2 pi !!
197 // Method below is good only for < 2 pi 199 // Method below is good only for < 2 pi
198 200
199 G4double distChord,distLine; 201 G4double distChord,distLine;
200 202
201 if (fyInitial != fyFinal) 203 if (fyInitial != fyFinal)
202 { 204 {
203 distLine = G4LineSection::Distline(fyMid 205 distLine = G4LineSection::Distline(fyMidPoint,fyInitial,fyFinal);
204 distChord = distLine; 206 distChord = distLine;
205 } 207 }
206 else 208 else
207 { 209 {
208 distChord = (fyMidPoint-fyInitial).mag() 210 distChord = (fyMidPoint-fyInitial).mag();
209 } 211 }
210 212
211 return distChord; 213 return distChord;
212 } 214 }
213 215