G4RK547FEq3.cc

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//
// G4RK547FEq3 implementation
//
// The Butcher table of the Higham & Hall 5(4)7 method is:
//
//   0    |
//  11/45 |    11/45
//  11/30 |    11/120          11/40
//  55/56 |    106865/87808    -408375/87808    193875/43904
//  9/10  |    79503/121000    -1053/440        147753/56870       27048/710875
//   1    |    89303/78045     -2025/473        994650/244541      -2547216/28122215     475/2967
//   1    |    1247/10890      0                57375/108053       -1229312/1962015      125/207     43/114
//---------------------------------------------------------------------------------------------------------------------
//             1247/10890      0                57375/108053       -1229312/1962015      125/207     43/114       0
//             21487/185130    0                963225/1836901     -39864832/33354255    2575/3519   4472/4845    -1/10
//
// Author: Dmitry Sorokin, Google Summer of Code 2017
// Supervision: John Apostolakis, CERN
// --------------------------------------------------------------------
 
#include "G4RK547FEq3.hh"
#include "G4LineSection.hh"
#include "G4FieldUtils.hh"
 
using namespace field_utils;
 
G4RK547FEq3::G4RK547FEq3(G4EquationOfMotion* EqRhs, G4int integrationVariables)
  : G4MagIntegratorStepper(EqRhs, integrationVariables)
{
}
 
void G4RK547FEq3::makeStep( const G4double yInput[],
                            const G4double dydx[],
                            const G4double hstep,
                                  G4double yOutput[],
                                  G4double* dydxOutput,
                                  G4double* yError ) const
{
    G4double yTemp[G4FieldTrack::ncompSVEC];
    for (G4int i=GetNumberOfVariables(); i<GetNumberOfStateVariables(); ++i)
    {
        yOutput[i] = yTemp[i] = yInput[i];
    }
 
    G4double ak2[G4FieldTrack::ncompSVEC],
             ak3[G4FieldTrack::ncompSVEC],
             ak4[G4FieldTrack::ncompSVEC],
             ak5[G4FieldTrack::ncompSVEC],
             ak6[G4FieldTrack::ncompSVEC];
 
    const G4double b21 = 11./45.,
                   b31 = 11./120., b32 = 11./40.,
                   b41 = 106865./87808., b42 = -408375./87808.,
                       b43 = 193875./43904.,
                   b51 = 79503./121000., b52 = -1053./440.,
                       b53 = 147753./56870., b54 =  27048./710875.,
                   b61 = 89303./78045., b62 = -2025./473.,
                       b63 = 994650./244541., b64 = -2547216./28122215.,
                       b65 = 475./2967.,
                   b71 = 1247./10890., b72 = 0., b73 = 57375./108053.,
                       b74 = -1229312./1962015., b75 = 125./207.,
                       b76 = 43./114.;
 
    const G4double dc1 = b71 - 21487./185130.,
                   dc2 = b72 - 0.,
                   dc3 = b73 - 963225./1836901.,
                   dc4 = b74 + 39864832./33354255.,
                   dc5 = b75 - 2575./3519.,
                   dc6 = b76 - 4472./4845.,
                   dc7 = 0. + 1./10.;
 
    // RightHandSide(yInput, dydx);
    for(G4int i = 0; i < GetNumberOfVariables(); ++i)
    {
      yTemp[i] = yInput[i] + hstep * b21 * dydx[i];
    }
 
    RightHandSide(yTemp, ak2);
    for(G4int i = 0; i < GetNumberOfVariables(); ++i)
    {
      yTemp[i] = yInput[i] + hstep * (b31 * dydx[i] + b32 * ak2[i]);
    }
 
    RightHandSide(yTemp, ak3);
    for(G4int i = 0;i < GetNumberOfVariables(); ++i)
    {
      yTemp[i] = yInput[i] + hstep * (b41 * dydx[i] + b42 * ak2[i] +
                                      b43 * ak3[i]);
    }
 
    RightHandSide(yTemp, ak4);
    for(G4int i = 0; i < GetNumberOfVariables(); ++i)
    {
      yTemp[i] = yInput[i] + hstep * (b51 * dydx[i] + b52 * ak2[i] +
                                      b53 * ak3[i] + b54 * ak4[i]);
    }
 
    RightHandSide(yTemp, ak5);
    for(G4int i = 0; i < GetNumberOfVariables(); ++i)
    {
      yTemp[i] = yInput[i] + hstep * (b61 * dydx[i] + b62 * ak2[i] +
                                      b63 * ak3[i] + b64 * ak4[i] +
                                      b65 * ak5[i]);
    }
 
    RightHandSide(yTemp, ak6);
    for(G4int i = 0; i < GetNumberOfVariables(); ++i)
    {
      yOutput[i] = yInput[i] + hstep * (b71 * dydx[i] + b72 * ak2[i] +
                                        b73 * ak3[i] + b74 * ak4[i] +
                                        b75 * ak5[i] + b76 * ak6[i]);
    }
    if ((dydxOutput != nullptr) && (yError != nullptr))
    {
        RightHandSide(yOutput, dydxOutput);
        for(G4int i = 0; i < GetNumberOfVariables(); ++i)
        {
          yError[i] = hstep * (dc1 * dydx[i] + dc2 * ak2[i] + dc3 * ak3[i] +
                               dc4 * ak4[i] + dc5 * ak5[i] + dc6 * ak6[i] +
                               dc7 * dydxOutput[i]);
        }
    }
}
 
void G4RK547FEq3::Stepper( const G4double yInput[],
                           const G4double dydx[],
                                 G4double hstep,
                                 G4double yOutput[],
                                 G4double yError[] )
{
    copy(fyIn, yInput);
    copy(fdydx, dydx);
    fhstep = hstep;
 
    makeStep(fyIn, fdydx, fhstep, fyOut, fdydxOut, yError);
 
    copy(yOutput, fyOut);
}
 
void G4RK547FEq3::Stepper( const G4double yInput[],
                           const G4double dydx[],
                                 G4double hstep,
                                 G4double yOutput[],
                                 G4double yError[],
                                 G4double dydxOutput[] )
{
    copy(fyIn, yInput);
    copy(fdydx, dydx);
    fhstep = hstep;
 
    makeStep(fyIn, fdydx, fhstep, fyOut, fdydxOut, yError);
 
    copy(yOutput, fyOut);
    copy(dydxOutput, fdydxOut);
}
 
G4double G4RK547FEq3::DistChord() const
{
    G4double yMid[G4FieldTrack::ncompSVEC];
    makeStep(fyIn, fdydx, fhstep / 2., yMid);
 
    const G4ThreeVector begin = makeVector(fyIn, Value3D::Position);
    const G4ThreeVector mid = makeVector(yMid, Value3D::Position);
    const G4ThreeVector end = makeVector(fyOut, Value3D::Position);
 
    return G4LineSection::Distline(mid, begin, end);
}