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geant4/source/geometry/magneticfield/src/G4FSALBogackiShampine45.cc
T
Gabriele Cosmo 5baee230e9 Import Geant4 10.6.0 source tree
2019-12-06 15:12:28 +01:00

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//
// ********************************************************************
// * License and Disclaimer *
// * *
// * The Geant4 software is copyright of the Copyright Holders of *
// * the Geant4 Collaboration. It is provided under the terms and *
// * conditions of the Geant4 Software License, included in the file *
// * LICENSE and available at http://cern.ch/geant4/license . These *
// * include a list of copyright holders. *
// * *
// * Neither the authors of this software system, nor their employing *
// * institutes,nor the agencies providing financial support for this *
// * work make any representation or warranty, express or implied, *
// * regarding this software system or assume any liability for its *
// * use. Please see the license in the file LICENSE and URL above *
// * for the full disclaimer and the limitation of liability. *
// * *
// * This code implementation is the result of the scientific and *
// * technical work of the GEANT4 collaboration. *
// * By using, copying, modifying or distributing the software (or *
// * any work based on the software) you agree to acknowledge its *
// * use in resulting scientific publications, and indicate your *
// * acceptance of all terms of the Geant4 Software license. *
// ********************************************************************
//
// G4FSALBogackiShampine45 implementation
//
// The Butcher table of the Bogacki-Shampine-8-4-5 method is as follows:
//
// 0 |
// 1/6 | 1/6
// 2/9 | 2/27 4/27
// 3/7 | 183/1372 -162/343 1053/1372
// 2/3 | 68/297 -4/11 42/143 1960/3861
// 3/4 | 597/22528 81/352 63099/585728 58653/366080 4617/20480
// 1 | 174197/959244 -30942/79937 8152137/19744439 666106/1039181 -29421/29068 482048/414219
// 1 | 587/8064 0 4440339/15491840 24353/124800 387/44800 2152/5985 7267/94080
// -------------------------------------------------------------------------------------------------------------------
// 587/8064 0 4440339/15491840 24353/124800 387/44800 2152/5985 7267/94080 0
// 2479/34992 0 123/416 612941/3411720 43/1440 2272/6561 79937/1113912 3293/556956
//
// Created: Somnath Banerjee, Google Summer of Code 2015, 26 May 2015
// Supervision: John Apostolakis, CERN
// --------------------------------------------------------------------
// Plan is that this source file / class will be merged with the updated
// BogackiShampine45 class, which contains improvements (May 2016)
#include <cassert>
#include "G4FSALBogackiShampine45.hh"
#include "G4LineSection.hh"
G4bool G4FSALBogackiShampine45::fPreparedConstants = false;
G4double G4FSALBogackiShampine45::bi[12][7];
// Constructor
//
G4FSALBogackiShampine45::G4FSALBogackiShampine45(G4EquationOfMotion* EqRhs,
G4int noIntegrationVariables,
G4bool primary)
: G4VFSALIntegrationStepper(EqRhs, noIntegrationVariables)
{
const G4int numberOfVariables = noIntegrationVariables;
// New Chunk of memory being created for use by the stepper
// aki - for storing intermediate RHS
//
ak2 = new G4double[numberOfVariables];
ak3 = new G4double[numberOfVariables];
ak4 = new G4double[numberOfVariables];
ak5 = new G4double[numberOfVariables];
ak6 = new G4double[numberOfVariables];
ak7 = new G4double[numberOfVariables];
ak8 = new G4double[numberOfVariables];
ak9 = new G4double[numberOfVariables];
ak10 = new G4double[numberOfVariables];
ak11 = new G4double[numberOfVariables];
DyDx = new G4double[numberOfVariables];
assert ( GetNumberOfStateVariables() >= 8 );
const G4int numStateVars = std::max(noIntegrationVariables,
GetNumberOfStateVariables() );
// Must ensure space extra 'state' variables exists - i.e. yIn[7]
//
yTemp = new G4double[numStateVars];
yIn = new G4double[numStateVars] ;
fLastInitialVector = new G4double[numStateVars] ;
fLastFinalVector = new G4double[numStateVars] ;
fLastDyDx = new G4double[numberOfVariables]; // Only derivatives
fMidVector = new G4double[numStateVars];
fMidError = new G4double[numStateVars];
pseudoDydx_for_DistChord = new G4double[numberOfVariables];
fMidVector = new G4double[numberOfVariables];
fMidError = new G4double[numberOfVariables];
if( primary )
{
fAuxStepper = new G4FSALBogackiShampine45(EqRhs, numberOfVariables,
!primary);
}
if( !fPreparedConstants )
{
PrepareConstants();
}
}
// Destructor
//
G4FSALBogackiShampine45::~G4FSALBogackiShampine45()
{
// Clear all previously allocated memory for stepper and DistChord
delete [] ak2;
delete [] ak3;
delete [] ak4;
delete [] ak5;
delete [] ak6;
delete [] ak7;
delete [] ak8;
delete [] ak9;
delete [] ak10;
delete [] ak11;
delete [] DyDx;
delete [] yTemp;
delete [] yIn;
delete [] fLastInitialVector;
delete [] fLastFinalVector;
delete [] fLastDyDx;
delete [] fMidVector;
delete [] fMidError;
delete fAuxStepper;
delete [] pseudoDydx_for_DistChord;
}
// Stepper
//
// Passing in the value of yInput[],the first time dydx[] and Step length
// Giving back yOut and yErr arrays for output and error respectively
//
void G4FSALBogackiShampine45::Stepper(const G4double yInput[],
const G4double dydx[],
G4double Step,
G4double yOut[],
G4double yErr[],
G4double nextDydx[])
{
G4int i;
// The various constants defined on the basis of butcher tableu
const G4double b21 = 1.0/6.0 ,
b31 = 2.0/27.0 , b32 = 4.0/27.0,
b41 = 183.0/1372.0 , b42 = -162.0/343.0, b43 = 1053.0/1372.0,
b51 = 68.0/297.0, b52 = -4.0/11.0,
b53 = 42.0/143.0, b54 = 1960.0/3861.0,
b61 = 597.0/22528.0, b62 = 81.0/352.0,
b63 = 63099.0/585728.0, b64 = 58653.0/366080.0,
b65 = 4617.0/20480.0,
b71 = 174197.0/959244.0, b72 = -30942.0/79937.0,
b73 = 8152137.0/19744439.0, b74 = 666106.0/1039181.0,
b75 = -29421.0/29068.0, b76 = 482048.0/414219.0,
b81 = 587.0/8064.0, b82 = 0.0,
b83 = 4440339.0/15491840.0, b84 = 24353.0/124800.0,
b85 = 387.0/44800.0, b86 = 2152.0/5985.0,
b87 = 7267.0/94080.0,
// c1 = 2479.0/34992.0,
// c2 = 0.0,
// c3 = 123.0/416.0,
// c4 = 612941.0/3411720.0,
// c5 = 43.0/1440.0,
// c6 = 2272.0/6561.0,
// c7 = 79937.0/1113912.0,
// c8 = 3293.0/556956.0,
// For the embedded higher order method only the difference of values
// taken and is used directly later instead of defining the last row
// of butcher table in a separate set of variables and taking the
// difference there
dc1 = b81 - 2479.0/34992.0 ,
dc2 = 0.0,
dc3 = b83 - 123.0/416.0 ,
dc4 = b84 - 612941.0/3411720.0,
dc5 = b85 - 43.0/1440.0,
dc6 = b86 - 2272.0/6561.0,
dc7 = b87 - 79937.0/1113912.0,
dc8 = -3293.0/556956.0; // end of declaration
const G4int numberOfVariables = GetNumberOfVariables();
// The number of variables to be integrated over
//
yOut[7] = yTemp[7] = yIn[7];
// Saving yInput because yInput and yOut can be aliases for same array
//
for(i=0; i<numberOfVariables; ++i)
{
yIn[i]=yInput[i];
DyDx[i] = dydx[i];
}
// RightHandSide(yIn, dydx) ; // 1st Step - Not doing, getting passed
for(i=0; i<numberOfVariables; ++i)
{
yTemp[i] = yIn[i] + b21*Step*DyDx[i] ;
}
RightHandSide(yTemp, ak2) ; // 2nd Step
for(i=0; i<numberOfVariables; ++i)
{
yTemp[i] = yIn[i] + Step*(b31*DyDx[i] + b32*ak2[i]) ;
}
RightHandSide(yTemp, ak3) ; // 3rd Step
for(i=0; i<numberOfVariables; ++i)
{
yTemp[i] = yIn[i] + Step*(b41*DyDx[i] + b42*ak2[i] + b43*ak3[i]) ;
}
RightHandSide(yTemp, ak4) ; // 4th Step
for(i=0; i<numberOfVariables; ++i)
{
yTemp[i] = yIn[i] + Step*(b51*DyDx[i] + b52*ak2[i] + b53*ak3[i] +
b54*ak4[i]) ;
}
RightHandSide(yTemp, ak5) ; // 5th Step
for(i=0; i<numberOfVariables; ++i)
{
yTemp[i] = yIn[i] + Step*(b61*DyDx[i] + b62*ak2[i] + b63*ak3[i] +
b64*ak4[i] + b65*ak5[i]) ;
}
RightHandSide(yTemp, ak6) ; // 6th Step
for(i=0; i<numberOfVariables; ++i)
{
yTemp[i] = yIn[i] + Step*(b71*DyDx[i] + b72*ak2[i] + b73*ak3[i] +
b74*ak4[i] + b75*ak5[i] + b76*ak6[i]);
}
RightHandSide(yTemp, ak7); // 7th Step
for(i=0; i<numberOfVariables; ++i)
{
yOut[i] = yIn[i] + Step*(b81*DyDx[i] + b82*ak2[i] + b83*ak3[i] +
b84*ak4[i] + b85*ak5[i] + b86*ak6[i] +
b87*ak7[i]);
}
RightHandSide(yOut, ak8); // 8th Step - Final one Using FSAL
for(i=0; i<numberOfVariables; ++i)
{
yErr[i] = Step*(dc1*DyDx[i] + dc2*ak2[i] + dc3*ak3[i] + dc4*ak4[i] +
dc5*ak5[i] + dc6*ak6[i] + dc7*ak7[i] + dc8*ak8[i]) ;
// FSAL stepper : Must pass the last DyDx for the next step, here ak8
//
nextDydx[i] = ak8[i];
// Store Input and Final values, for possible use in calculating chord
//
fLastInitialVector[i] = yIn[i] ;
fLastFinalVector[i] = yOut[i];
fLastDyDx[i] = DyDx[i];
}
fLastStepLength = Step;
return;
}
// DistChord
//
G4double G4FSALBogackiShampine45::DistChord() const
{
G4double distLine, distChord;
G4ThreeVector initialPoint, finalPoint, midPoint;
// Store last initial and final points
// (they will be overwritten in self-Stepper call!)
//
initialPoint = G4ThreeVector( fLastInitialVector[0],
fLastInitialVector[1], fLastInitialVector[2]);
finalPoint = G4ThreeVector( fLastFinalVector[0],
fLastFinalVector[1], fLastFinalVector[2]);
// Do half a step using StepNoErr
fAuxStepper->Stepper( fLastInitialVector, fLastDyDx, 0.5 * fLastStepLength,
fMidVector, fMidError, pseudoDydx_for_DistChord );
midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2] );
// Use stored values of Initial and Endpoint + new Midpoint to evaluate
// distance of Chord
//
if (initialPoint != finalPoint)
{
distLine = G4LineSection::Distline(midPoint, initialPoint, finalPoint);
distChord = distLine;
}
else
{
distChord = (midPoint-initialPoint).mag();
}
return distChord;
}
// PrepareConstants
//
void G4FSALBogackiShampine45::PrepareConstants()
{
// --------------------------------------------------------
// COEFFICIENTS FOR INTERPOLANT bi WITH 11 STAGES
// --------------------------------------------------------
// Initialise all values of G4double bi[12][7]
//
for(auto i=1; i<12; ++i)
{
for(auto j=1; j<7; ++j)
{
bi[i][j] = 0.0 ;
}
}
bi[1][6] = -12134338393.0/1050809760.0 ,
bi[1][5] = -1620741229.0/50038560.0 ,
bi[1][4] = -2048058893.0/59875200.0 ,
bi[1][3] = -87098480009.0/5254048800.0 ,
bi[1][2] = -11513270273.0/3502699200.0 ,
//
bi[3][6] = -33197340367.0/1218433216.0 ,
bi[3][5] = -539868024987.0/6092166080.0 ,
bi[3][4] = -39991188681.0/374902528.0 ,
bi[3][3] = -69509738227.0/1218433216.0 ,
bi[3][2] = -29327744613.0/2436866432.0 ,
//
bi[4][6] = -284800997201.0/19905339168.0 ,
bi[4][5] = -7896875450471.0/165877826400.0 ,
bi[4][4] = -333945812879.0/5671036800.0 ,
bi[4][3] = -16209923456237.0/497633479200.0 ,
bi[4][2] = -2382590741699.0/331755652800.0 ,
//
bi[5][6] = -540919.0/741312.0 ,
bi[5][5] = -103626067.0/43243200.0 ,
bi[5][4] = -633779.0/211200.0 ,
bi[5][3] = -32406787.0/18532800.0 ,
bi[5][2] = -36591193.0/86486400.0 ,
//
bi[6][6] = 7157998304.0/374350977.0 ,
bi[6][5] = 30405842464.0/623918295.0 ,
bi[6][4] = 183022264.0/5332635.0 ,
bi[6][3] = -3357024032.0/1871754885.0 ,
bi[6][2] = -611586736.0/89131185.0 ,
//
bi[7][6] = -138073.0/9408.0 ,
bi[7][5] = -719433.0/15680.0 ,
bi[7][4] = -1620541.0/31360.0 ,
bi[7][3] = -385151.0/15680.0 ,
bi[7][2] = -65403.0/15680.0 ,
//
bi[8][6] = 1245.0/64.0 ,
bi[8][5] = 3991.0/64.0 ,
bi[8][4] = 4715.0/64.0 ,
bi[8][3] = 2501.0/64.0 ,
bi[8][2] = 149.0/16.0 ,
bi[8][1] = 1.0 ,
//
bi[9][6] = 55.0/3.0 ,
bi[9][5] = 71.0 ,
bi[9][4] = 103.0 ,
bi[9][3] = 199.0/3.0 ,
bi[9][2] = 16.0 ,
//
bi[10][6] = -1774004627.0/75810735.0 ,
bi[10][5] = -1774004627.0/25270245.0 ,
bi[10][4] = -26477681.0/359975.0 ,
bi[10][3] = -11411880511.0/379053675.0 ,
bi[10][2] = -423642896.0/126351225.0 ,
//
bi[11][6] = 35.0 ,
bi[11][5] = 105.0 ,
bi[11][4] = 117.0 ,
bi[11][3] = 59.0 ,
bi[11][2] = 12.0 ;
}
// ---------------------------------------------------------------------------------------
void G4FSALBogackiShampine45::interpolate( const G4double yInput[],
const G4double dydx[],
G4double yOut[],
G4double Step,
G4double tau )
{
const G4double a91 = 455.0/6144.0 ,
a92 = 0.0 ,
a93 = 10256301.0/35409920.0 ,
a94 = 2307361.0/17971200.0 ,
a95 = -387.0/102400.0 ,
a96 = 73.0/5130.0 ,
a97 = -7267.0/215040.0 ,
a98 = 1.0/32.0 ,
a101 = -837888343715.0/13176988637184.0 ,
a102 = 30409415.0/52955362.0 ,
a103 = -48321525963.0/759168069632.0 ,
a104 = 8530738453321.0/197654829557760.0 ,
a105 = 1361640523001.0/1626788720640.0 ,
a106 = -13143060689.0/38604458898.0 ,
a107 = 18700221969.0/379584034816.0 ,
a108 = -5831595.0/847285792.0 ,
a109 = -5183640.0/26477681.0 ,
a111 = 98719073263.0/1551965184000.0 ,
a112 = 1307.0/123552.0 ,
a113 = 4632066559387.0/70181753241600.0 ,
a114 = 7828594302389.0/382182512025600.0 ,
a115 = 40763687.0/11070259200.0 ,
a116 = 34872732407.0/224610586200.0 ,
a117 = -2561897.0/30105600.0 ,
a118 = 1.0/10.0 ,
a119 = -1.0/10.0 ,
a1110 = -1403317093.0/11371610250.0 ;
const G4int numberOfVariables = GetNumberOfVariables();
// Saving yInput because yInput and yOut can be aliases for same array
//
for(G4int i=0; i<numberOfVariables; ++i)
{
yIn[i]=yInput[i];
}
// The number of variables to be integrated over
//
yOut[7] = yTemp[7] = yIn[7];
// Calculating extra stages
//
for(G4int i=0; i<numberOfVariables; ++i)
{
yTemp[i] = yIn[i] + Step*(a91*dydx[i] + a92*ak2[i] + a93*ak3[i] +
a94*ak4[i] + a95*ak5[i] + a96*ak6[i] +
a97*ak7[i] + a98*ak8[i] );
}
RightHandSide(yTemp, ak9);
for(G4int i=0; i<numberOfVariables; ++i)
{
yTemp[i] = yIn[i] + Step*(a101*dydx[i] + a102*ak2[i] + a103*ak3[i] +
a104*ak4[i] + a105*ak5[i] + a106*ak6[i] +
a107*ak7[i] + a108*ak8[i] + a109*ak9[i] );
}
RightHandSide(yTemp, ak10);
for(G4int i=0; i<numberOfVariables; ++i)
{
yTemp[i] = yIn[i] + Step*(a111*dydx[i] + a112*ak2[i] + a113*ak3[i] +
a114*ak4[i] + a115*ak5[i] + a116*ak6[i] +
a117*ak7[i] + a118*ak8[i] + a119*ak9[i] +
a1110*ak10[i] );
}
RightHandSide(yTemp, ak11);
G4double tau0 = tau;
// Calculating the polynomials
//
for(auto i=1; i<=11; ++i) // i is NOT the coordinate no., it's stage no.
{
b[i] = 0.0;
tau = tau0;
for(auto j=1; j<=6; ++j)
{
b[i] += bi[i][j]*tau;
tau*=tau0;
}
}
for(G4int i=0; i<numberOfVariables; ++i)
{
yOut[i] = yIn[i] + Step*(b[1]*dydx[i] + b[2]*ak2[i] + b[3]*ak3[i] +
b[4]*ak4[i] + b[5]*ak5[i] + b[6]*ak6[i] +
b[7]*ak7[i] + b[8]*ak8[i] + b[9]*ak9[i] +
b[10]*ak10[i] + b[11]*ak11[i] );
}
}
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