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25 //
26 // G4RK547FEq2 implementation
27 //
28 // The Butcher table of the Higham & Hall 5(4)7 method is:
29 //
30 // 0 |
31 // 2/13 | 2/13
32 // 2/13 | 3/52 9/52
33 // 5/9 | 12955/26244 -15925/8748 12350/6561
34 // 3/4 | -10383/52480 13923/10496 -176553/199424 505197/997120
35 // 1 | 1403/7236 -429/268 733330/309339 -7884/8911 104960/113967
36 // 1 | 181/2700 0 656903/1846800 19683/106400 34112/110565 67/800
37 //----------------------------------------------------------------------------------------------------------------------
38 // 181/2700 0 656903/1846800 19683/106400 34112/110565 67/800 0
39 // 11377/154575 0 35378291/105729300 343359/1522850 535952/1947645 134/17175 1/12
40 //
41 // Author: Dmitry Sorokin, Google Summer of Code 2017
42 // Supervision: John Apostolakis, CERN
43 // --------------------------------------------------------------------
44
45 #include "G4RK547FEq2.hh"
46 #include "G4LineSection.hh"
47 #include "G4FieldUtils.hh"
48
49 using namespace field_utils;
50
51 G4RK547FEq2::G4RK547FEq2(G4EquationOfMotion* EqRhs, G4int integrationVariables)
52 : G4MagIntegratorStepper(EqRhs, integrationVariables)
53 {
54 }
55
56 void G4RK547FEq2::makeStep( const G4double yInput[],
57 const G4double dydx[],
58 const G4double hstep,
59 G4double yOutput[],
60 G4double* dydxOutput,
61 G4double* yError ) const
62 {
63 G4double yTemp[G4FieldTrack::ncompSVEC];
64 for (G4int i=GetNumberOfVariables(); i<GetNumberOfStateVariables(); ++i)
65 {
66 yOutput[i] = yTemp[i] = yInput[i];
67 }
68
69 G4double ak2[G4FieldTrack::ncompSVEC],
70 ak3[G4FieldTrack::ncompSVEC],
71 ak4[G4FieldTrack::ncompSVEC],
72 ak5[G4FieldTrack::ncompSVEC],
73 ak6[G4FieldTrack::ncompSVEC];
74
75 const G4double b21 = 2./13.,
76 b31 = 3./52., b32 = 9./52.,
77 b41 = 12955./26244., b42 = -15925./8748.,
78 b43 = 12350./6561.,
79 b51 = -10383./52480., b52 = 13923./10496.,
80 b53 = -176553./199424., b54 = 505197./997120.,
81 b61 = 1403./7236., b62 = -429./268., b63 = 733330./309339.,
82 b64 = -7884./8911., b65 = 104960./113967.,
83 b71 = 181./2700., b72 = 0., b73 = 656903./1846800.,
84 b74 = 19683./106400., b75 = 34112./110565.,
85 b76 = 67./800.;
86
87 const G4double dc1 = b71 - 11377./154575.,
88 dc2 = b72 - 0.,
89 dc3 = b73 - 35378291./105729300.,
90 dc4 = b74 - 343359./1522850.,
91 dc5 = b75 - 535952./1947645.,
92 dc6 = b76 - 134./17175.,
93 dc7 = 0. - 1./12.;
94
95 // RightHandSide(yInput, dydx);
96 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
97 {
98 yTemp[i] = yInput[i] + hstep * b21 * dydx[i];
99 }
100
101 RightHandSide(yTemp, ak2);
102 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
103 {
104 yTemp[i] = yInput[i] + hstep * (b31 * dydx[i] + b32 * ak2[i]);
105 }
106
107 RightHandSide(yTemp, ak3);
108 for(G4int i = 0;i < GetNumberOfVariables(); ++i)
109 {
110 yTemp[i] = yInput[i] + hstep * (b41 * dydx[i] + b42 * ak2[i] +
111 b43 * ak3[i]);
112 }
113
114 RightHandSide(yTemp, ak4);
115 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
116 {
117 yTemp[i] = yInput[i] + hstep * (b51 * dydx[i] + b52 * ak2[i] +
118 b53 * ak3[i] + b54 * ak4[i]);
119 }
120
121 RightHandSide(yTemp, ak5);
122 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
123 {
124 yTemp[i] = yInput[i] + hstep * (b61 * dydx[i] + b62 * ak2[i] +
125 b63 * ak3[i] + b64 * ak4[i] +
126 b65 * ak5[i]);
127 }
128
129 RightHandSide(yTemp, ak6);
130 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
131 {
132 yOutput[i] = yInput[i] + hstep * (b71 * dydx[i] + b72 * ak2[i] +
133 b73 * ak3[i] + b74 * ak4[i] +
134 b75 * ak5[i] + b76 * ak6[i]);
135 }
136 if ((dydxOutput != nullptr) && (yError != nullptr))
137 {
138 RightHandSide(yOutput, dydxOutput);
139 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
140 {
141 yError[i] = hstep * (dc1 * dydx[i] + dc2 * ak2[i] + dc3 * ak3[i] +
142 dc4 * ak4[i] + dc5 * ak5[i] + dc6 * ak6[i] +
143 dc7 * dydxOutput[i]);
144 }
145 }
146 }
147
148 void G4RK547FEq2::Stepper( const G4double yInput[],
149 const G4double dydx[],
150 G4double hstep,
151 G4double yOutput[],
152 G4double yError[] )
153 {
154 copy(fyIn, yInput);
155 copy(fdydx, dydx);
156 fhstep = hstep;
157
158 makeStep(fyIn, fdydx, fhstep, fyOut, fdydxOut, yError);
159
160 copy(yOutput, fyOut);
161 }
162
163 void G4RK547FEq2::Stepper( const G4double yInput[],
164 const G4double dydx[],
165 G4double hstep,
166 G4double yOutput[],
167 G4double yError[],
168 G4double dydxOutput[] )
169 {
170 copy(fyIn, yInput);
171 copy(fdydx, dydx);
172 fhstep = hstep;
173
174 makeStep(fyIn, fdydx, fhstep, fyOut, fdydxOut, yError);
175
176 copy(yOutput, fyOut);
177 copy(dydxOutput, fdydxOut);
178 }
179
180 G4double G4RK547FEq2::DistChord() const
181 {
182 G4double yMid[G4FieldTrack::ncompSVEC];
183 makeStep(fyIn, fdydx, fhstep / 2., yMid);
184
185 const G4ThreeVector begin = makeVector(fyIn, Value3D::Position);
186 const G4ThreeVector mid = makeVector(yMid, Value3D::Position);
187 const G4ThreeVector end = makeVector(fyOut, Value3D::Position);
188
189 return G4LineSection::Distline(mid, begin, end);
190 }
191