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25 // 25 //
26 // G4ConstRK4 implementation <<
27 // 26 //
28 // Created: J.Apostolakis, T.Nikitina - 18.09. << 27 // $Id: G4ConstRK4.cc 66356 2012-12-18 09:02:32Z gcosmo $
>> 28 //
>> 29 //
>> 30 // - 18.09.2008 - J.Apostolakis, T.Nikitina - Created
29 // ------------------------------------------- 31 // -------------------------------------------------------------------
30 32
31 #include "G4ConstRK4.hh" 33 #include "G4ConstRK4.hh"
32 #include "G4ThreeVector.hh" 34 #include "G4ThreeVector.hh"
33 #include "G4LineSection.hh" 35 #include "G4LineSection.hh"
34 36
35 ////////////////////////////////////////////// 37 //////////////////////////////////////////////////////////////////
36 // 38 //
37 // Constructor sets the number of *State* vari 39 // Constructor sets the number of *State* variables (default = 8)
38 // The number of variables integrated is alw 40 // The number of variables integrated is always 6
39 // << 41
40 G4ConstRK4::G4ConstRK4(G4Mag_EqRhs* EqRhs, G4i 42 G4ConstRK4::G4ConstRK4(G4Mag_EqRhs* EqRhs, G4int numStateVariables)
41 : G4MagErrorStepper(EqRhs, 6, numStateVariab 43 : G4MagErrorStepper(EqRhs, 6, numStateVariables)
42 { 44 {
43 // const G4int numberOfVariables= 6; 45 // const G4int numberOfVariables= 6;
44 if( numStateVariables < 8 ) 46 if( numStateVariables < 8 )
45 { 47 {
46 std::ostringstream message; 48 std::ostringstream message;
47 message << "The number of State variables 49 message << "The number of State variables at least 8 " << G4endl
48 << "Instead it is - numStateVariab 50 << "Instead it is - numStateVariables= " << numStateVariables;
49 G4Exception("G4ConstRK4::G4ConstRK4()", "G 51 G4Exception("G4ConstRK4::G4ConstRK4()", "GeomField0002",
50 FatalException, message, "Use 52 FatalException, message, "Use another Stepper!");
51 } 53 }
52 54
53 fEq = EqRhs; 55 fEq = EqRhs;
54 yMiddle = new G4double[8]; 56 yMiddle = new G4double[8];
55 dydxMid = new G4double[8]; 57 dydxMid = new G4double[8];
56 yInitial = new G4double[8]; 58 yInitial = new G4double[8];
57 yOneStep = new G4double[8]; 59 yOneStep = new G4double[8];
58 60
59 dydxm = new G4double[8]; 61 dydxm = new G4double[8];
60 dydxt = new G4double[8]; 62 dydxt = new G4double[8];
61 yt = new G4double[8]; 63 yt = new G4double[8];
62 Field[0]=0.; Field[1]=0.; Field[2]=0.; 64 Field[0]=0.; Field[1]=0.; Field[2]=0.;
63 } 65 }
64 66
65 ////////////////////////////////////////////// 67 ////////////////////////////////////////////////////////////////
66 // 68 //
67 // Destructor 69 // Destructor
68 70
69 G4ConstRK4::~G4ConstRK4() 71 G4ConstRK4::~G4ConstRK4()
70 { 72 {
71 delete [] yMiddle; 73 delete [] yMiddle;
72 delete [] dydxMid; 74 delete [] dydxMid;
73 delete [] yInitial; 75 delete [] yInitial;
74 delete [] yOneStep; 76 delete [] yOneStep;
75 delete [] dydxm; 77 delete [] dydxm;
76 delete [] dydxt; 78 delete [] dydxt;
77 delete [] yt; 79 delete [] yt;
78 } 80 }
79 81
80 ////////////////////////////////////////////// 82 //////////////////////////////////////////////////////////////////////
81 // 83 //
82 // Given values for the variables y[0,..,n-1] 84 // Given values for the variables y[0,..,n-1] and their derivatives
83 // dydx[0,...,n-1] known at x, use the classic 85 // dydx[0,...,n-1] known at x, use the classical 4th Runge-Kutta
84 // method to advance the solution over an inte 86 // method to advance the solution over an interval h and return the
85 // incremented variables as yout[0,...,n-1], w 87 // incremented variables as yout[0,...,n-1], which is not a distinct
86 // array from y. The user supplies the routine 88 // array from y. The user supplies the routine RightHandSide(x,y,dydx),
87 // which returns derivatives dydx at x. The so 89 // which returns derivatives dydx at x. The source is routine rk4 from
88 // NRC p. 712-713 . 90 // NRC p. 712-713 .
89 // << 91
90 void G4ConstRK4::DumbStepper( const G4double y << 92 void G4ConstRK4::DumbStepper( const G4double yIn[],
91 const G4double d << 93 const G4double dydx[],
92 G4double h << 94 G4double h,
93 G4double y << 95 G4double yOut[])
94 { 96 {
95 G4double hh = h*0.5 , h6 = h/6.0 ; 97 G4double hh = h*0.5 , h6 = h/6.0 ;
96 98
97 // 1st Step K1=h*dydx 99 // 1st Step K1=h*dydx
98 yt[5] = yIn[5] + hh*dydx[5] ; 100 yt[5] = yIn[5] + hh*dydx[5] ;
99 yt[4] = yIn[4] + hh*dydx[4] ; 101 yt[4] = yIn[4] + hh*dydx[4] ;
100 yt[3] = yIn[3] + hh*dydx[3] ; 102 yt[3] = yIn[3] + hh*dydx[3] ;
101 yt[2] = yIn[2] + hh*dydx[2] ; 103 yt[2] = yIn[2] + hh*dydx[2] ;
102 yt[1] = yIn[1] + hh*dydx[1] ; 104 yt[1] = yIn[1] + hh*dydx[1] ;
103 yt[0] = yIn[0] + hh*dydx[0] ; 105 yt[0] = yIn[0] + hh*dydx[0] ;
104 RightHandSideConst(yt,dydxt) ; 106 RightHandSideConst(yt,dydxt) ;
105 107
106 // 2nd Step K2=h*dydxt 108 // 2nd Step K2=h*dydxt
107 yt[5] = yIn[5] + hh*dydxt[5] ; 109 yt[5] = yIn[5] + hh*dydxt[5] ;
108 yt[4] = yIn[4] + hh*dydxt[4] ; 110 yt[4] = yIn[4] + hh*dydxt[4] ;
109 yt[3] = yIn[3] + hh*dydxt[3] ; 111 yt[3] = yIn[3] + hh*dydxt[3] ;
110 yt[2] = yIn[2] + hh*dydxt[2] ; 112 yt[2] = yIn[2] + hh*dydxt[2] ;
111 yt[1] = yIn[1] + hh*dydxt[1] ; 113 yt[1] = yIn[1] + hh*dydxt[1] ;
112 yt[0] = yIn[0] + hh*dydxt[0] ; 114 yt[0] = yIn[0] + hh*dydxt[0] ;
113 RightHandSideConst(yt,dydxm) ; 115 RightHandSideConst(yt,dydxm) ;
114 116
115 // 3rd Step K3=h*dydxm 117 // 3rd Step K3=h*dydxm
116 // now dydxm=(K2+K3)/h 118 // now dydxm=(K2+K3)/h
117 yt[5] = yIn[5] + h*dydxm[5] ; 119 yt[5] = yIn[5] + h*dydxm[5] ;
118 dydxm[5] += dydxt[5] ; 120 dydxm[5] += dydxt[5] ;
119 yt[4] = yIn[4] + h*dydxm[4] ; 121 yt[4] = yIn[4] + h*dydxm[4] ;
120 dydxm[4] += dydxt[4] ; 122 dydxm[4] += dydxt[4] ;
121 yt[3] = yIn[3] + h*dydxm[3] ; 123 yt[3] = yIn[3] + h*dydxm[3] ;
122 dydxm[3] += dydxt[3] ; 124 dydxm[3] += dydxt[3] ;
123 yt[2] = yIn[2] + h*dydxm[2] ; 125 yt[2] = yIn[2] + h*dydxm[2] ;
124 dydxm[2] += dydxt[2] ; 126 dydxm[2] += dydxt[2] ;
125 yt[1] = yIn[1] + h*dydxm[1] ; 127 yt[1] = yIn[1] + h*dydxm[1] ;
126 dydxm[1] += dydxt[1] ; 128 dydxm[1] += dydxt[1] ;
127 yt[0] = yIn[0] + h*dydxm[0] ; 129 yt[0] = yIn[0] + h*dydxm[0] ;
128 dydxm[0] += dydxt[0] ; 130 dydxm[0] += dydxt[0] ;
129 RightHandSideConst(yt,dydxt) ; 131 RightHandSideConst(yt,dydxt) ;
130 132
131 // 4th Step K4=h*dydxt 133 // 4th Step K4=h*dydxt
132 yOut[5] = yIn[5]+h6*(dydx[5]+dydxt[5]+2.0*d 134 yOut[5] = yIn[5]+h6*(dydx[5]+dydxt[5]+2.0*dydxm[5]);
133 yOut[4] = yIn[4]+h6*(dydx[4]+dydxt[4]+2.0*d 135 yOut[4] = yIn[4]+h6*(dydx[4]+dydxt[4]+2.0*dydxm[4]);
134 yOut[3] = yIn[3]+h6*(dydx[3]+dydxt[3]+2.0*d 136 yOut[3] = yIn[3]+h6*(dydx[3]+dydxt[3]+2.0*dydxm[3]);
135 yOut[2] = yIn[2]+h6*(dydx[2]+dydxt[2]+2.0*d 137 yOut[2] = yIn[2]+h6*(dydx[2]+dydxt[2]+2.0*dydxm[2]);
136 yOut[1] = yIn[1]+h6*(dydx[1]+dydxt[1]+2.0*d 138 yOut[1] = yIn[1]+h6*(dydx[1]+dydxt[1]+2.0*dydxm[1]);
137 yOut[0] = yIn[0]+h6*(dydx[0]+dydxt[0]+2.0*d 139 yOut[0] = yIn[0]+h6*(dydx[0]+dydxt[0]+2.0*dydxm[0]);
138 140
139 } // end of DumbStepper ..................... 141 } // end of DumbStepper ....................................................
140 142
141 ////////////////////////////////////////////// 143 ////////////////////////////////////////////////////////////////
142 // 144 //
143 // Stepper 145 // Stepper
144 146
145 void 147 void
146 G4ConstRK4::Stepper( const G4double yInput[], 148 G4ConstRK4::Stepper( const G4double yInput[],
147 const G4double dydx[], 149 const G4double dydx[],
148 G4double hstep, 150 G4double hstep,
149 G4double yOutput[], 151 G4double yOutput[],
150 G4double yError [] 152 G4double yError [] )
151 { 153 {
152 const G4int nvar = 6; // number of variabl 154 const G4int nvar = 6; // number of variables integrated
153 const G4int maxvar = GetNumberOfStateVariab << 155 const G4int maxvar= GetNumberOfStateVariables();
154 156
155 // Correction for Richardson extrapolation 157 // Correction for Richardson extrapolation
156 G4double correction = 1. / ( (1 << Integra 158 G4double correction = 1. / ( (1 << IntegratorOrder()) -1 );
157 159
158 G4int i; 160 G4int i;
159 161
160 // Saving yInput because yInput and yOutput 162 // Saving yInput because yInput and yOutput can be aliases for same array
161 for (i=0; i<maxvar; ++i) { yInitial[i]= << 163 for (i=0; i<maxvar; i++) { yInitial[i]= yInput[i]; }
162 164
163 // Must copy the part of the state *not* in 165 // Must copy the part of the state *not* integrated to the output
164 for (i=nvar; i<maxvar; ++i) { yOutput[i]= << 166 for (i=nvar; i<maxvar; i++) { yOutput[i]= yInput[i]; }
165 167
166 // yInitial[7]= yInput[7]; // The time is 168 // yInitial[7]= yInput[7]; // The time is typically needed
167 yMiddle[7] = yInput[7]; // Copy the time 169 yMiddle[7] = yInput[7]; // Copy the time from initial value
168 yOneStep[7] = yInput[7]; // As it contrib 170 yOneStep[7] = yInput[7]; // As it contributes to final value of yOutput ?
169 // yOutput[7] = yInput[7]; // -> dumb step 171 // yOutput[7] = yInput[7]; // -> dumb stepper does it too for RK4
170 yError[7] = 0.0; 172 yError[7] = 0.0;
171 173
172 G4double halfStep = hstep * 0.5; 174 G4double halfStep = hstep * 0.5;
173 175
174 // Do two half steps 176 // Do two half steps
175 // 177 //
176 GetConstField(yInitial,Field); 178 GetConstField(yInitial,Field);
177 DumbStepper (yInitial, dydx, halfStep, 179 DumbStepper (yInitial, dydx, halfStep, yMiddle);
178 RightHandSideConst(yMiddle, dydxMid); 180 RightHandSideConst(yMiddle, dydxMid);
179 DumbStepper (yMiddle, dydxMid, halfStep, y 181 DumbStepper (yMiddle, dydxMid, halfStep, yOutput);
180 182
181 // Store midpoint, chord calculation 183 // Store midpoint, chord calculation
182 // 184 //
183 fMidPoint = G4ThreeVector( yMiddle[0], yMi 185 fMidPoint = G4ThreeVector( yMiddle[0], yMiddle[1], yMiddle[2]);
184 186
185 // Do a full Step 187 // Do a full Step
186 // 188 //
187 DumbStepper(yInitial, dydx, hstep, yOneStep 189 DumbStepper(yInitial, dydx, hstep, yOneStep);
188 for(i=0; i<nvar; ++i) << 190 for(i=0;i<nvar;i++)
189 { 191 {
190 yError [i] = yOutput[i] - yOneStep[i] ; 192 yError [i] = yOutput[i] - yOneStep[i] ;
191 yOutput[i] += yError[i]*correction ; 193 yOutput[i] += yError[i]*correction ;
192 // Provides accuracy increased by 1 or 194 // Provides accuracy increased by 1 order via the
193 // Richardson extrapolation 195 // Richardson extrapolation
194 } 196 }
195 197
196 fInitialPoint = G4ThreeVector( yInitial[0], 198 fInitialPoint = G4ThreeVector( yInitial[0], yInitial[1], yInitial[2]);
197 fFinalPoint = G4ThreeVector( yOutput[0], 199 fFinalPoint = G4ThreeVector( yOutput[0], yOutput[1], yOutput[2]);
198 200
199 return; 201 return;
200 } 202 }
201 203
202 ////////////////////////////////////////////// 204 ////////////////////////////////////////////////////////////////
203 // 205 //
204 // Estimate the maximum distance from the curv 206 // Estimate the maximum distance from the curve to the chord
205 // 207 //
206 // We estimate this using the distance of the 208 // We estimate this using the distance of the midpoint to chord.
207 // The method below is good only for angle dev 209 // The method below is good only for angle deviations < 2 pi;
208 // this restriction should not be a problem fo 210 // this restriction should not be a problem for the Runge Kutta methods,
209 // which generally cannot integrate accurately 211 // which generally cannot integrate accurately for large angle deviations
210 // << 212
211 G4double G4ConstRK4::DistChord() const 213 G4double G4ConstRK4::DistChord() const
212 { 214 {
213 G4double distLine, distChord; 215 G4double distLine, distChord;
214 216
215 if (fInitialPoint != fFinalPoint) 217 if (fInitialPoint != fFinalPoint)
216 { 218 {
217 distLine= G4LineSection::Distline( fMidPo 219 distLine= G4LineSection::Distline( fMidPoint, fInitialPoint, fFinalPoint );
218 // This is a class method that gives di 220 // This is a class method that gives distance of Mid
219 // from the Chord between the Initial a 221 // from the Chord between the Initial and Final points
220 distChord = distLine; 222 distChord = distLine;
221 } 223 }
222 else 224 else
223 { 225 {
224 distChord = (fMidPoint-fInitialPoint).mag 226 distChord = (fMidPoint-fInitialPoint).mag();
225 } 227 }
226 return distChord; 228 return distChord;
227 } 229 }
228 230