G4RK547FEq1.cc

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// G4RK547FEq1 implementation
//
// The Butcher table of the Higham & Hall 5(4)7 method is:
//
//   0  |
//  2/9 |      2/9
//  1/3 |      1/12      1/4
//  1/2 |      1/8       0          3/8
//  3/5 |      91/500    -27/100    78/125    8/125
//   1  |      -11/20    27/20      12/5      -36/5    5
//   1  |      1/12      0          27/32     -4/3     125/96    5/48
//----------------------------------------------------------------------------
//             1/12      0          27/32     -4/3     125/96    5/48    0
//             2/15      0          27/80     -2/15    25/48     1/24    1/10
//
// Author: Dmitry Sorokin, Google Summer of Code 2017
// Supervision: John Apostolakis, CERN
// --------------------------------------------------------------------
 
#include "G4RK547FEq1.hh"
#include "G4LineSection.hh"
#include "G4FieldUtils.hh"
 
using namespace field_utils;
 
G4RK547FEq1::G4RK547FEq1(G4EquationOfMotion* EqRhs, G4int integrationVariables)
  : G4MagIntegratorStepper(EqRhs, integrationVariables)
{
}
 
void G4RK547FEq1::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 = 2./9.,
                   b31 = 1./12., b32 = 1./4.,
                   b41 = 1./8., b42 = 0., b43 = 3./8.,
                   b51 = 91./500., b52 = -27./100.,
                     b53 = 78./125., b54 = 8./125.,
                   b61 = -11./20., b62 = 27./20., b63 = 12./5.,
                     b64 = -36./5., b65 = 5.,
                   b71 = 1./12.,    b72 = 0., b73 = 27./32.,
                     b74 = -4./3., b75 = 125./96., b76 = 5./48.;
 
    const G4double dc1 = b71 - 2./15.,
                   dc2 = b72 - 0.,
                   dc3 = b73 - 27./80.,
                   dc4 = b74 + 2./15.,
                   dc5 = b75 - 25./48.,
                   dc6 = b76 - 1./24.,
                   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 G4RK547FEq1::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 G4RK547FEq1::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 G4RK547FEq1::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);
}