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25 // 25 //
26 // G4TMagErrorStepper 26 // G4TMagErrorStepper
27 // 27 //
28 // Class description: 28 // Class description:
29 // 29 //
30 // Templated version of G4MagErrorStepper 30 // Templated version of G4MagErrorStepper
31 // 31 //
32 // 32 //
33 // Created: Josh Xie (supported by Google Sum 33 // Created: Josh Xie (supported by Google Summer of Code 2014 )
34 // Supervisors: Sandro Wenzel, John Apostolak 34 // Supervisors: Sandro Wenzel, John Apostolakis (CERN)
35 // Adapted from G4G4TMagErrorStepper class 35 // Adapted from G4G4TMagErrorStepper class
36 // ------------------------------------------- 36 // --------------------------------------------------------------------
37 #ifndef G4TMAG_ERROR_STEPPER_HH 37 #ifndef G4TMAG_ERROR_STEPPER_HH
38 #define G4TMAG_ERROR_STEPPER_HH 38 #define G4TMAG_ERROR_STEPPER_HH
39 39
40 #include "G4Types.hh" 40 #include "G4Types.hh"
41 #include "G4MagIntegratorStepper.hh" 41 #include "G4MagIntegratorStepper.hh"
42 #include "G4ThreeVector.hh" 42 #include "G4ThreeVector.hh"
43 #include "G4LineSection.hh" 43 #include "G4LineSection.hh"
44 44
45 template <class T_Stepper, class T_Equation, u 45 template <class T_Stepper, class T_Equation, unsigned int N>
46 class G4TMagErrorStepper : public G4MagIntegra 46 class G4TMagErrorStepper : public G4MagIntegratorStepper
47 { 47 {
48 public: // with description 48 public: // with description
49 G4TMagErrorStepper(T_Equation* EqRhs, G4int 49 G4TMagErrorStepper(T_Equation* EqRhs, G4int numberOfVariables,
50 G4int numStateVariables = 50 G4int numStateVariables = 12)
51 : G4MagIntegratorStepper(EqRhs, numberOfVa 51 : G4MagIntegratorStepper(EqRhs, numberOfVariables, numStateVariables)
52 , fEquation_Rhs(EqRhs) 52 , fEquation_Rhs(EqRhs)
53 { 53 {
54 // G4int nvar = std::max(this->GetNumberOf 54 // G4int nvar = std::max(this->GetNumberOfVariables(), 8);
55 } 55 }
56 56
57 virtual ~G4TMagErrorStepper() { ; } 57 virtual ~G4TMagErrorStepper() { ; }
58 58
59 inline void RightHandSide(G4double y[], G4do 59 inline void RightHandSide(G4double y[], G4double dydx[])
60 { 60 {
61 fEquation_Rhs->T_Equation::RightHandSide(y 61 fEquation_Rhs->T_Equation::RightHandSide(y, dydx);
62 } 62 }
63 63
64 inline void Stepper(const G4double yInput[], 64 inline void Stepper(const G4double yInput[], const G4double dydx[],
65 G4double hstep, G4double 65 G4double hstep, G4double yOutput[], G4double yError[]) override final;
66 66
67 inline G4double DistChord() const override f 67 inline G4double DistChord() const override final;
68 68
69 private: 69 private:
70 G4TMagErrorStepper(const G4TMagErrorStepper& 70 G4TMagErrorStepper(const G4TMagErrorStepper&);
71 G4TMagErrorStepper& operator=(const G4TMagEr 71 G4TMagErrorStepper& operator=(const G4TMagErrorStepper&);
72 // Private copy constructor and assignment o 72 // Private copy constructor and assignment operator.
73 73
74 private: 74 private:
75 // STATE 75 // STATE
76 G4ThreeVector fInitialPoint, fMidPoint, fFin 76 G4ThreeVector fInitialPoint, fMidPoint, fFinalPoint;
77 // Data stored in order to find the chord 77 // Data stored in order to find the chord
78 78
79 // Dependent Objects, owned --- part of the 79 // Dependent Objects, owned --- part of the STATE
80 G4double yInitial[N < 8 ? 8 : N]; 80 G4double yInitial[N < 8 ? 8 : N];
81 G4double yMiddle[N < 8 ? 8 : N]; 81 G4double yMiddle[N < 8 ? 8 : N];
82 G4double dydxMid[N < 8 ? 8 : N]; 82 G4double dydxMid[N < 8 ? 8 : N];
83 G4double yOneStep[N < 8 ? 8 : N]; 83 G4double yOneStep[N < 8 ? 8 : N];
84 // The following arrays are used only for te 84 // The following arrays are used only for temporary storage
85 // they are allocated at the class level onl 85 // they are allocated at the class level only for efficiency -
86 // so that calls to new and delete are not m 86 // so that calls to new and delete are not made in Stepper().
87 87
88 T_Equation* fEquation_Rhs; 88 T_Equation* fEquation_Rhs;
89 }; 89 };
90 90
91 // ------------ Implementation ------------- 91 // ------------ Implementation -----------------------
92 92
93 template <class T_Stepper, class T_Equation, u 93 template <class T_Stepper, class T_Equation, unsigned int N >
94 void G4TMagErrorStepper<T_Stepper,T_Equation,N 94 void G4TMagErrorStepper<T_Stepper,T_Equation,N>::
95 Stepper(const G4double yInput[], 95 Stepper(const G4double yInput[],
96 const G4double dydx[], 96 const G4double dydx[],
97 G4double hstep, 97 G4double hstep,
98 G4double yOutput[], 98 G4double yOutput[],
99 G4double yError[]) 99 G4double yError[])
100 // The stepper for the Runge Kutta integration 100 // The stepper for the Runge Kutta integration. The stepsize
101 // is fixed, with the Step size given by hstep 101 // is fixed, with the Step size given by hstep.
102 // Integrates ODE starting values y[0 to N]. 102 // Integrates ODE starting values y[0 to N].
103 // Outputs yout[] and its estimated error yerr 103 // Outputs yout[] and its estimated error yerr[].
104 { 104 {
105 const unsigned int maxvar = GetNumberOfState 105 const unsigned int maxvar = GetNumberOfStateVariables();
106 106
107 // Saving yInput because yInput and yOutput 107 // Saving yInput because yInput and yOutput can be aliases for same array
108 for(unsigned int i = 0; i < N; ++i) 108 for(unsigned int i = 0; i < N; ++i)
109 yInitial[i] = yInput[i]; 109 yInitial[i] = yInput[i];
110 yInitial[7] = 110 yInitial[7] =
111 yInput[7]; // Copy the time in case ... 111 yInput[7]; // Copy the time in case ... even if not really needed
112 yMiddle[7] = yInput[7]; // Copy the time f 112 yMiddle[7] = yInput[7]; // Copy the time from initial value
113 yOneStep[7] = yInput[7]; // As it contribut 113 yOneStep[7] = yInput[7]; // As it contributes to final value of yOutput ?
114 // yOutput[7] = yInput[7]; // -> dumb stepp 114 // yOutput[7] = yInput[7]; // -> dumb stepper does it too for RK4
115 for(unsigned int i = N; i < maxvar; ++i) 115 for(unsigned int i = N; i < maxvar; ++i)
116 yOutput[i] = yInput[i]; 116 yOutput[i] = yInput[i];
117 117
118 G4double halfStep = hstep * 0.5; 118 G4double halfStep = hstep * 0.5;
119 119
120 // Do two half steps 120 // Do two half steps
121 121
122 static_cast<T_Stepper*>(this)->DumbStepper(y 122 static_cast<T_Stepper*>(this)->DumbStepper(yInitial, dydx, halfStep,
123 123 yMiddle);
124 this->RightHandSide(yMiddle, dydxMid); 124 this->RightHandSide(yMiddle, dydxMid);
125 static_cast<T_Stepper*>(this)->DumbStepper(y 125 static_cast<T_Stepper*>(this)->DumbStepper(yMiddle, dydxMid, halfStep,
126 y 126 yOutput);
127 127
128 // Store midpoint, chord calculation 128 // Store midpoint, chord calculation
129 129
130 fMidPoint = G4ThreeVector(yMiddle[0], yMiddl 130 fMidPoint = G4ThreeVector(yMiddle[0], yMiddle[1], yMiddle[2]);
131 131
132 // Do a full Step 132 // Do a full Step
133 static_cast<T_Stepper*>(this)->DumbStepper(y 133 static_cast<T_Stepper*>(this)->DumbStepper(yInitial, dydx, hstep, yOneStep);
134 for(unsigned int i = 0; i < N; ++i) 134 for(unsigned int i = 0; i < N; ++i)
135 { 135 {
136 yError[i] = yOutput[i] - yOneStep[i]; 136 yError[i] = yOutput[i] - yOneStep[i];
137 yOutput[i] += 137 yOutput[i] +=
138 yError[i] * 138 yError[i] *
139 T_Stepper::IntegratorCorrection; // Pr 139 T_Stepper::IntegratorCorrection; // Provides accuracy increased
140 // by 1 order via the 140 // by 1 order via the
141 // Richardson Extrapolation 141 // Richardson Extrapolation
142 } 142 }
143 143
144 fInitialPoint = G4ThreeVector(yInitial[0], y 144 fInitialPoint = G4ThreeVector(yInitial[0], yInitial[1], yInitial[2]);
145 fFinalPoint = G4ThreeVector(yOutput[0], yO 145 fFinalPoint = G4ThreeVector(yOutput[0], yOutput[1], yOutput[2]);
146 146
147 return; 147 return;
148 } 148 }
149 149
150 150
151 template <class T_Stepper, class T_Equation, u 151 template <class T_Stepper, class T_Equation, unsigned int N >
152 inline G4double 152 inline G4double
153 G4TMagErrorStepper<T_Stepper,T_Equation,N>::Di 153 G4TMagErrorStepper<T_Stepper,T_Equation,N>::DistChord() const
154 { 154 {
155 // Estimate the maximum distance from the cu 155 // Estimate the maximum distance from the curve to the chord
156 // 156 //
157 // We estimate this using the distance of t 157 // We estimate this using the distance of the midpoint to
158 // chord (the line between 158 // chord (the line between
159 // 159 //
160 // Method below is good only for angle devi 160 // Method below is good only for angle deviations < 2 pi,
161 // This restriction should not a problem f 161 // This restriction should not a problem for the Runge cutta methods,
162 // which generally cannot integrate accura 162 // which generally cannot integrate accurately for large angle deviations.
163 G4double distLine, distChord; 163 G4double distLine, distChord;
164 164
165 if(fInitialPoint != fFinalPoint) 165 if(fInitialPoint != fFinalPoint)
166 { 166 {
167 distLine = G4LineSection::Distline(fMidPoi 167 distLine = G4LineSection::Distline(fMidPoint, fInitialPoint, fFinalPoint);
168 // This is a class method that gives dista 168 // This is a class method that gives distance of Mid
169 // from the Chord between the Initial and 169 // from the Chord between the Initial and Final points.
170 170
171 distChord = distLine; 171 distChord = distLine;
172 } 172 }
173 else 173 else
174 { 174 {
175 distChord = (fMidPoint - fInitialPoint).m 175 distChord = (fMidPoint - fInitialPoint).mag();
176 } 176 }
177 177
178 return distChord; 178 return distChord;
179 } 179 }
180 180
181 #endif /* G4TMagErrorStepper_HH */ 181 #endif /* G4TMagErrorStepper_HH */
182 182