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25 //
26 // G4RK547FEq1 implementation
27 //
28 // The Butcher table of the Higham & Hall 5(4)7 method is:
29 //
30 // 0 |
31 // 2/9 | 2/9
32 // 1/3 | 1/12 1/4
33 // 1/2 | 1/8 0 3/8
34 // 3/5 | 91/500 -27/100 78/125 8/125
35 // 1 | -11/20 27/20 12/5 -36/5 5
36 // 1 | 1/12 0 27/32 -4/3 125/96 5/48
37 //----------------------------------------------------------------------------
38 // 1/12 0 27/32 -4/3 125/96 5/48 0
39 // 2/15 0 27/80 -2/15 25/48 1/24 1/10
40 //
41 // Author: Dmitry Sorokin, Google Summer of Code 2017
42 // Supervision: John Apostolakis, CERN
43 // --------------------------------------------------------------------
44
45 #include "G4RK547FEq1.hh"
46 #include "G4LineSection.hh"
47 #include "G4FieldUtils.hh"
48
49 using namespace field_utils;
50
51 G4RK547FEq1::G4RK547FEq1(G4EquationOfMotion* EqRhs, G4int integrationVariables)
52 : G4MagIntegratorStepper(EqRhs, integrationVariables)
53 {
54 }
55
56 void G4RK547FEq1::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./9.,
76 b31 = 1./12., b32 = 1./4.,
77 b41 = 1./8., b42 = 0., b43 = 3./8.,
78 b51 = 91./500., b52 = -27./100.,
79 b53 = 78./125., b54 = 8./125.,
80 b61 = -11./20., b62 = 27./20., b63 = 12./5.,
81 b64 = -36./5., b65 = 5.,
82 b71 = 1./12., b72 = 0., b73 = 27./32.,
83 b74 = -4./3., b75 = 125./96., b76 = 5./48.;
84
85 const G4double dc1 = b71 - 2./15.,
86 dc2 = b72 - 0.,
87 dc3 = b73 - 27./80.,
88 dc4 = b74 + 2./15.,
89 dc5 = b75 - 25./48.,
90 dc6 = b76 - 1./24.,
91 dc7 = 0. - 1./10.;
92
93 // RightHandSide(yInput, dydx);
94 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
95 {
96 yTemp[i] = yInput[i] + hstep * b21 * dydx[i];
97 }
98
99 RightHandSide(yTemp, ak2);
100 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
101 {
102 yTemp[i] = yInput[i] + hstep * (b31 * dydx[i] + b32 * ak2[i]);
103 }
104
105 RightHandSide(yTemp, ak3);
106 for(G4int i = 0;i < GetNumberOfVariables(); ++i)
107 {
108 yTemp[i] = yInput[i] + hstep * (b41 * dydx[i] + b42 * ak2[i] +
109 b43 * ak3[i]);
110 }
111
112 RightHandSide(yTemp, ak4);
113 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
114 {
115 yTemp[i] = yInput[i] + hstep * (b51 * dydx[i] + b52 * ak2[i] +
116 b53 * ak3[i] + b54 * ak4[i]);
117 }
118
119 RightHandSide(yTemp, ak5);
120 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
121 {
122 yTemp[i] = yInput[i] + hstep * (b61 * dydx[i] + b62 * ak2[i] +
123 b63 * ak3[i] + b64 * ak4[i] +
124 b65 * ak5[i]);
125 }
126
127 RightHandSide(yTemp, ak6);
128 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
129 {
130 yOutput[i] = yInput[i] + hstep * (b71 * dydx[i] + b72 * ak2[i] +
131 b73 * ak3[i] + b74 * ak4[i] +
132 b75 * ak5[i] + b76 * ak6[i]);
133 }
134 if ((dydxOutput != nullptr) && (yError != nullptr))
135 {
136 RightHandSide(yOutput, dydxOutput);
137 for(G4int i = 0; i < GetNumberOfVariables(); ++i)
138 {
139 yError[i] = hstep * (dc1 * dydx[i] + dc2 * ak2[i] + dc3 * ak3[i] +
140 dc4 * ak4[i] + dc5 * ak5[i] + dc6 * ak6[i] +
141 dc7 * dydxOutput[i]);
142 }
143 }
144 }
145
146 void G4RK547FEq1::Stepper( const G4double yInput[],
147 const G4double dydx[],
148 G4double hstep,
149 G4double yOutput[],
150 G4double yError[] )
151 {
152 copy(fyIn, yInput);
153 copy(fdydx, dydx);
154 fhstep = hstep;
155
156 makeStep(fyIn, fdydx, fhstep, fyOut, fdydxOut, yError);
157
158 copy(yOutput, fyOut);
159 }
160
161 void G4RK547FEq1::Stepper( const G4double yInput[],
162 const G4double dydx[],
163 G4double hstep,
164 G4double yOutput[],
165 G4double yError[],
166 G4double dydxOutput[] )
167 {
168 copy(fyIn, yInput);
169 copy(fdydx, dydx);
170 fhstep = hstep;
171
172 makeStep(fyIn,fdydx, fhstep, fyOut, fdydxOut, yError);
173
174 copy(yOutput, fyOut);
175 copy(dydxOutput, fdydxOut);
176 }
177
178 G4double G4RK547FEq1::DistChord() const
179 {
180 G4double yMid[G4FieldTrack::ncompSVEC];
181 makeStep(fyIn, fdydx, fhstep / 2., yMid);
182
183 const G4ThreeVector begin = makeVector(fyIn, Value3D::Position);
184 const G4ThreeVector mid = makeVector(yMid, Value3D::Position);
185 const G4ThreeVector end = makeVector(fyOut, Value3D::Position);
186
187 return G4LineSection::Distline(mid, begin, end);
188 }
189