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G4NystromRK4.cc
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27 // $Id: G4NystromRK4.cc 106565 2017-10-13 09:20:14Z gcosmo $
28 //
29 // History:
30 // - Created: I.Gavrilenko 15.05.2009 (as G4AtlasRK4)
31 // - Adaptations: J. Apostolakis May-Nov 2009
32 // -------------------------------------------------------------------
33 
34 #include <iostream>
35 #include "G4NystromRK4.hh"
36 
38 // Constructor - with optional distance ( has default value)
40 
41 G4NystromRK4::G4NystromRK4(G4Mag_EqRhs* magEqRhs, G4double distanceConstField)
42  : G4MagIntegratorStepper(magEqRhs, 6), // number of variables
43  m_fEq( magEqRhs ),
44  m_magdistance( distanceConstField ),
45  m_cof( 0.0 ),
46  m_mom( 0.0 ),
47  m_imom( 0.0 ),
48  m_cachedMom( false )
49 {
50  m_fldPosition[0] = m_iPoint[0] = m_fPoint[0] = m_mPoint[0] = 9.9999999e+99 ;
51  m_fldPosition[1] = m_iPoint[1] = m_fPoint[1] = m_mPoint[1] = 9.9999999e+99 ;
52  m_fldPosition[2] = m_iPoint[2] = m_fPoint[2] = m_mPoint[2] = 9.9999999e+99 ;
53  m_fldPosition[3] = -9.9999999e+99;
54  m_lastField[0] = m_lastField[1] = m_lastField[2] = 0.0;
55 
56  m_magdistance2 = distanceConstField*distanceConstField;
57 }
58 
60 // Destructor
62 
64 {
65 }
66 
68 // Integration in one step
70 
71 void
73 (const G4double P[],const G4double dPdS[],G4double Step,G4double Po[],G4double Err[])
74 {
75  const G4double perMillion = 1.0e-6;
76  G4double R[4] = { P[0], P[1] , P[2], P[7] }; // x, y, z, t
77  G4double A[3] = {dPdS[0], dPdS[1], dPdS[2]};
78 
79  m_iPoint[0]=R[0]; m_iPoint[1]=R[1]; m_iPoint[2]=R[2];
80 
81  constexpr G4double one_sixth= 1./6.;
82  const G4double S = Step ;
83  const G4double S5 = .5*Step ;
84  const G4double S4 = .25*Step ;
85  const G4double S6 = Step * one_sixth; // Step / 6.;
86 
87  // Ensure that the location and cached field value are correct
88  getField( R );
89 
90  // Ensure that the momentum is set correctly.
91 
92  // - Quick check momentum magnitude (squared) against previous value
93  G4double newmom2 = (P[3]*P[3]+P[4]*P[4]+P[5]*P[5]);
94  G4double oldmom2 = m_mom * m_mom;
95  if( std::fabs(newmom2 - oldmom2) > perMillion * oldmom2 ) {
96  m_mom = sqrt(newmom2) ;
97  m_imom = 1./m_mom;
98  m_cof = m_fEq->FCof()*m_imom;
99  }
100 
101 #ifdef G4DEBUG_FIELD
102  CheckCachedMomemtum( P, m_mom );
103  CheckFieldPosition( P, m_fldPosition );
104 #endif
105 
106  // Point 1
107  //
108  G4double K1[3] = { m_imom*dPdS[3], m_imom*dPdS[4], m_imom*dPdS[5] };
109 
110  // Point2
111  //
112  G4double p[4] = {R[0]+S5*(A[0]+S4*K1[0]),
113  R[1]+S5*(A[1]+S4*K1[1]),
114  R[2]+S5*(A[2]+S4*K1[2]),
115  P[7] };
116  getField(p);
117 
118  G4double A2[3] = {A[0]+S5*K1[0],A[1]+S5*K1[1],A[2]+S5*K1[2]};
119  G4double K2[3] = {(A2[1]*m_lastField[2]-A2[2]*m_lastField[1])*m_cof,
120  (A2[2]*m_lastField[0]-A2[0]*m_lastField[2])*m_cof,
121  (A2[0]*m_lastField[1]-A2[1]*m_lastField[0])*m_cof};
122 
123  m_mPoint[0]=p[0]; m_mPoint[1]=p[1]; m_mPoint[2]=p[2];
124 
125  // Point 3 with the same magnetic field
126  //
127  G4double A3[3] = {A[0]+S5*K2[0],A[1]+S5*K2[1],A[2]+S5*K2[2]};
128  G4double K3[3] = {(A3[1]*m_lastField[2]-A3[2]*m_lastField[1])*m_cof,
129  (A3[2]*m_lastField[0]-A3[0]*m_lastField[2])*m_cof,
130  (A3[0]*m_lastField[1]-A3[1]*m_lastField[0])*m_cof};
131 
132  // Point 4
133  //
134  p[0] = R[0]+S*(A[0]+S5*K3[0]);
135  p[1] = R[1]+S*(A[1]+S5*K3[1]);
136  p[2] = R[2]+S*(A[2]+S5*K3[2]);
137 
138  getField(p);
139 
140  G4double A4[3] = {A[0]+S*K3[0],A[1]+S*K3[1],A[2]+S*K3[2]};
141  G4double K4[3] = {(A4[1]*m_lastField[2]-A4[2]*m_lastField[1])*m_cof,
142  (A4[2]*m_lastField[0]-A4[0]*m_lastField[2])*m_cof,
143  (A4[0]*m_lastField[1]-A4[1]*m_lastField[0])*m_cof};
144 
145  // New position
146  //
147  Po[0] = P[0]+S*(A[0]+S6*(K1[0]+K2[0]+K3[0]));
148  Po[1] = P[1]+S*(A[1]+S6*(K1[1]+K2[1]+K3[1]));
149  Po[2] = P[2]+S*(A[2]+S6*(K1[2]+K2[2]+K3[2]));
150 
151  m_fPoint[0]=Po[0]; m_fPoint[1]=Po[1]; m_fPoint[2]=Po[2];
152 
153  // New direction
154  //
155  Po[3] = A[0]+S6*(K1[0]+K4[0]+2.*(K2[0]+K3[0]));
156  Po[4] = A[1]+S6*(K1[1]+K4[1]+2.*(K2[1]+K3[1]));
157  Po[5] = A[2]+S6*(K1[2]+K4[2]+2.*(K2[2]+K3[2]));
158 
159  // Errors
160  //
161  Err[3] = S*std::fabs(K1[0]-K2[0]-K3[0]+K4[0]);
162  Err[4] = S*std::fabs(K1[1]-K2[1]-K3[1]+K4[1]);
163  Err[5] = S*std::fabs(K1[2]-K2[2]-K3[2]+K4[2]);
164  Err[0] = S*Err[3] ;
165  Err[1] = S*Err[4] ;
166  Err[2] = S*Err[5] ;
167  Err[3]*= m_mom ;
168  Err[4]*= m_mom ;
169  Err[5]*= m_mom ;
170 
171  // Normalize momentum
172  //
173  G4double normF = m_mom/std::sqrt(Po[3]*Po[3]+Po[4]*Po[4]+Po[5]*Po[5]);
174  Po [3]*=normF; Po[4]*=normF; Po[5]*=normF;
175 
176  // Pass Energy, time unchanged -- time is not integrated !!
177  Po[6]=P[6]; Po[7]=P[7];
178 }
179 
180 
182 // Estimate the maximum distance from the curve to the chord
184 
185 G4double
187 {
188  G4double ax = m_fPoint[0]-m_iPoint[0];
189  G4double ay = m_fPoint[1]-m_iPoint[1];
190  G4double az = m_fPoint[2]-m_iPoint[2];
191  G4double dx = m_mPoint[0]-m_iPoint[0];
192  G4double dy = m_mPoint[1]-m_iPoint[1];
193  G4double dz = m_mPoint[2]-m_iPoint[2];
194  G4double d2 = (ax*ax+ay*ay+az*az) ;
195 
196  if(d2!=0.) {
197  G4double ds = (ax*dx+ay*dy+az*dz)/d2;
198  dx -= (ds*ax) ;
199  dy -= (ds*ay) ;
200  dz -= (ds*az) ;
201  }
202  return std::sqrt(dx*dx+dy*dy+dz*dz);
203 }
204 
206 // Derivatives calculation - caching the momentum value
208 
209 void
211 {
212  G4double P4vec[4]= { P[0], P[1], P[2], P[7] }; // Time is P[7]
213  getField(P4vec);
214  m_mom = std::sqrt(P[3]*P[3]+P[4]*P[4]+P[5]*P[5]) ;
215  m_imom = 1./m_mom ;
216  m_cof = m_fEq->FCof()*m_imom ;
217  m_cachedMom = true ; // Caching the value
218  dPdS[0] = P[3]*m_imom ; // dx /ds
219  dPdS[1] = P[4]*m_imom ; // dy /ds
220  dPdS[2] = P[5]*m_imom ; // dz /ds
221  dPdS[3] = m_cof*(P[4]*m_lastField[2]-P[5]*m_lastField[1]) ; // dPx/ds
222  dPdS[4] = m_cof*(P[5]*m_lastField[0]-P[3]*m_lastField[2]) ; // dPy/ds
223  dPdS[5] = m_cof*(P[3]*m_lastField[1]-P[4]*m_lastField[0]) ; // dPz/ds
224 }
225 
227 // Check that the location is (almost) unmoved from 'last' field evaluation
229 
230 G4bool
231 G4NystromRK4::CheckFieldPosition( const G4double Position[3],
232  const G4double lastPosition[3] )
233 {
234  G4bool ok= true;
235  G4double dx = Position[0] - lastPosition[0];
236  G4double dy = Position[1] - lastPosition[1];
237  G4double dz = Position[2] - lastPosition[2];
238  G4double distMag2 = dx*dx+dy*dy+dz*dz;
239  if( distMag2 > m_magdistance2) {
240  const G4double allowedDist = std::sqrt( m_magdistance2 );
241  G4double dist= std::sqrt( distMag2 );
242  G4cerr << " NystromRK4::Stepper> ERROR> Moved from correct field position by "
243  << dist << "( larger than allowed = " << allowedDist << " ) "
244  << G4endl;
245  ok= false;
246  }
247  return ok;
248 }
249 
251 // Check magnitude of momentum against saved value
253 
254 G4bool G4NystromRK4::CheckCachedMomemtum( const G4double PosMom[6],
255  G4double savedMom )
256 {
257  constexpr G4double perThousand = 1.0e-3;
258  G4bool ok= true;
259  G4double new_mom2= (PosMom[3]*PosMom[3]+PosMom[4]*PosMom[4]+PosMom[5]*PosMom[5]);
260  G4double new_mom= std::sqrt(new_mom2);
261  if( std::fabs(new_mom - savedMom ) > perThousand * savedMom ) {
262  G4cerr << " Nystrom::Stepper WARNING: momentum magnitude is invalid / has changed "
263  << G4endl
264  << " new value (p-mag) = " << new_mom << G4endl
265  << " cached value (p-mag) = " << savedMom << G4endl;
266  if( savedMom > 0.0 ) {
267  G4cerr << " ratio (new/old) = " << new_mom / savedMom << G4endl;
268  }
269  ok= false;
270  }
271  return ok;
272 }
static constexpr double perMillion
Definition: G4SIunits.hh:334
double S(double temp)
const char * p
Definition: xmltok.h:285
static const G4double d2
virtual void ComputeRightHandSide(const G4double P[], G4double dPdS[])
static double P[]
G4NystromRK4(G4Mag_EqRhs *EquationMotion, G4double distanceConstField=0.0)
Definition: G4NystromRK4.cc:41
double A(double temperature)
G4double FCof() const
Definition: G4Mag_EqRhs.hh:84
bool G4bool
Definition: G4Types.hh:79
Definition: Step.hh:41
#define G4endl
Definition: G4ios.hh:61
G4double DistChord() const
static constexpr double perThousand
Definition: G4SIunits.hh:333
double G4double
Definition: G4Types.hh:76
void Stepper(const G4double P[], const G4double dPdS[], G4double step, G4double Po[], G4double Err[])
Definition: G4NystromRK4.cc:73
G4GLOB_DLL std::ostream G4cerr