Gabriele Cosmo
325 lines
11 KiB
C++
325 lines
11 KiB
C++
//
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// ********************************************************************
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// * License and Disclaimer *
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// * *
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// * The Geant4 software is copyright of the Copyright Holders of *
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// * the Geant4 Collaboration. It is provided under the terms and *
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// * conditions of the Geant4 Software License, included in the file *
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// * LICENSE and available at http://cern.ch/geant4/license . These *
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// * include a list of copyright holders. *
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// * *
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// * Neither the authors of this software system, nor their employing *
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// * institutes,nor the agencies providing financial support for this *
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// * work make any representation or warranty, express or implied, *
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// * regarding this software system or assume any liability for its *
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// * use. Please see the license in the file LICENSE and URL above *
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// * for the full disclaimer and the limitation of liability. *
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// * *
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// * This code implementation is the result of the scientific and *
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// * technical work of the GEANT4 collaboration. *
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// * By using, copying, modifying or distributing the software (or *
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// * any work based on the software) you agree to acknowledge its *
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// * use in resulting scientific publications, and indicate your *
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// * acceptance of all terms of the Geant4 Software license. *
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// ********************************************************************
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//
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// G4TCashKarpRKF45
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//
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// Class description:
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//
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// Templated version of Cash-Karp 4th/5th order embedded stepper
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//
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// Knowing the type (class) of the equation of motion enables a non-
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// virtual call of its methods.
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// As an embedded 5th order method, it requires fewer field evaluations
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// (1 initial + 5 others per step = 6 per step) than ClassicalRK4 and
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// also non-embedded methods of the same order.
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//
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// Can be used to enable use of non-virtual calls for field, equation,
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// and stepper - potentially with inlined methods.
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//
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// Adapted from G4CashKarpRKF45 class
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// --------------------------------------------------------------------
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// Original description (G4CashKarpRKF45):
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// The Cash-Karp Runge-Kutta-Fehlberg 4/5 method is an embedded fourth
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// order method (giving fifth-order accuracy) for the solution of an ODE.
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// Two different fourth order estimates are calculated; their difference
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// gives an error estimate. [ref. Numerical Recipes in C, 2nd Edition]
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// Used to integrate the equations of motion of a particle in a field.
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// Author: Josh Xie (CERN, Google Summer of Code 2014), June 2014
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// Supervisors: Sandro Wenzel, John Apostolakis (CERN)
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// --------------------------------------------------------------------
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#ifndef G4T_CASH_KARP_RKF45_HH
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#define G4T_CASH_KARP_RKF45_HH
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#include <cassert>
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#include "G4LineSection.hh"
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#include "G4MagIntegratorStepper.hh"
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/**
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* @brief G4TCashKarpRKF45 is a templated version of Cash-Karp
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* 4th/5th order embedded stepper.
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*/
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template <class T_Equation, unsigned int N = 6 >
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class G4TCashKarpRKF45 : public G4MagIntegratorStepper
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{
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public:
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G4TCashKarpRKF45(T_Equation* EqRhs, // G4int noIntegrationVariables = 6,
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G4bool primary = true);
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virtual ~G4TCashKarpRKF45();
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G4TCashKarpRKF45(const G4TCashKarpRKF45&) = delete;
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G4TCashKarpRKF45& operator=(const G4TCashKarpRKF45&) = delete;
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inline void
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StepWithError(const G4double yInput[], // * __restrict__ yInput,
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const G4double dydx[], // * __restrict__ dydx,
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G4double Step,
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G4double yOut[], // * __restrict__ yOut,
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G4double yErr[] ); // * __restrict__ yErr);
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virtual void Stepper(const G4double yInput[],
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const G4double dydx[],
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G4double hstep,
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G4double yOutput[],
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G4double yError[]) override final;
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// __attribute__((always_inline))
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void RightHandSideInl( const G4double y[], // * __restrict__ y,
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G4double dydx[] ) // * __restrict__ dydx )
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{
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fEquation_Rhs->T_Equation::RightHandSide(y, dydx);
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}
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inline G4double DistChord() const override;
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inline G4int IntegratorOrder() const override { return 4; }
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G4StepperType StepperType() const override { return kTCashKarpRKF45; }
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private:
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G4double ak2[N], ak3[N], ak4[N], ak5[N], ak6[N], ak7[N], yTemp[N], yIn[N];
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// scratch space
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G4double fLastStepLength= 0.0;
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G4double* fLastInitialVector;
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G4double* fLastFinalVector;
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G4double* fLastDyDx;
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G4double* fMidVector;
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G4double* fMidError;
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// for DistChord calculations
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G4TCashKarpRKF45* fAuxStepper = nullptr;
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// ... or G4TCashKarpRKF45<T_Equation, N>* fAuxStepper;
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T_Equation* fEquation_Rhs;
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};
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/////////////////////////////////////////////////////////////////////
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//
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// Constructor
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//
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template <class T_Equation, unsigned int N >
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G4TCashKarpRKF45<T_Equation,N>::G4TCashKarpRKF45(T_Equation* EqRhs,
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G4bool primary)
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: G4MagIntegratorStepper(dynamic_cast<G4EquationOfMotion*>(EqRhs), N )
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, fEquation_Rhs(EqRhs)
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{
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if( dynamic_cast<G4EquationOfMotion*>(EqRhs) == nullptr )
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{
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G4Exception("G4TCashKarpRKF45: constructor", "GeomField0001",
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FatalException, "Equation is not an G4EquationOfMotion.");
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}
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fLastInitialVector = new G4double[N];
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fLastFinalVector = new G4double[N];
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fLastDyDx = new G4double[N];
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fMidVector = new G4double[N];
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fMidError = new G4double[N];
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if(primary)
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{
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fAuxStepper = new G4TCashKarpRKF45<T_Equation, N> (EqRhs, !primary);
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}
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}
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template <class T_Equation, unsigned int N >
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G4TCashKarpRKF45<T_Equation,N>::~G4TCashKarpRKF45()
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{
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delete[] fLastInitialVector;
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delete[] fLastFinalVector;
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delete[] fLastDyDx;
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delete[] fMidVector;
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delete[] fMidError;
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delete fAuxStepper;
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}
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//////////////////////////////////////////////////////////////////////
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//
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// Given values for n = 6 variables yIn[0,...,n-1]
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// known at x, use the fifth-order Cash-Karp Runge-
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// Kutta-Fehlberg-4-5 method to advance the solution over an interval
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// Step and return the incremented variables as yOut[0,...,n-1]. Also
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// return an estimate of the local truncation error yErr[] using the
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// embedded 4th-order method. The equation's method is called (inline)
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// via RightHandSideInl(y,dydx), which returns derivatives dydx for y .
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//
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template <class T_Equation, unsigned int N >
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inline void
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G4TCashKarpRKF45<T_Equation,N>::StepWithError(const G4double* yInput,
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const G4double* dydx,
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G4double Step,
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G4double * yOut,
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G4double * yErr)
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{
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// const G4double a2 = 0.2 , a3 = 0.3 , a4 = 0.6 , a5 = 1.0 , a6 = 0.875;
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const G4double b21 = 0.2, b31 = 3.0 / 40.0, b32 = 9.0 / 40.0, b41 = 0.3,
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b42 = -0.9, b43 = 1.2,
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b51 = -11.0 / 54.0, b52 = 2.5, b53 = -70.0 / 27.0,
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b54 = 35.0 / 27.0,
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b61 = 1631.0 / 55296.0, b62 = 175.0 / 512.0,
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b63 = 575.0 / 13824.0, b64 = 44275.0 / 110592.0,
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b65 = 253.0 / 4096.0,
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c1 = 37.0 / 378.0, c3 = 250.0 / 621.0, c4 = 125.0 / 594.0,
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c6 = 512.0 / 1771.0, dc5 = -277.0 / 14336.0;
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const G4double dc1 = c1 - 2825.0 / 27648.0, dc3 = c3 - 18575.0 / 48384.0,
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dc4 = c4 - 13525.0 / 55296.0, dc6 = c6 - 0.25;
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// Initialise time to t0, needed when it is not updated by the integration.
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// [ Note: Only for time dependent fields (usually electric)
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// is it neccessary to integrate the time.]
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// yOut[7] = yTemp[7] = yIn[7];
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// Saving yInput because yInput and yOut can be aliases for same array
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for(unsigned int i = 0; i < N; ++i)
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{
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yIn[i] = yInput[i];
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}
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// RightHandSideInl(yIn, dydx) ; // 1st Step
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for(unsigned int i = 0; i < N; ++i)
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{
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yTemp[i] = yIn[i] + b21 * Step * dydx[i];
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}
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this->RightHandSideInl(yTemp, ak2); // 2nd Step
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for(unsigned int i = 0; i < N; ++i)
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{
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yTemp[i] = yIn[i] + Step * (b31 * dydx[i] + b32 * ak2[i]);
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}
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this->RightHandSideInl(yTemp, ak3); // 3rd Step
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for(unsigned int i = 0; i < N; ++i)
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{
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yTemp[i] = yIn[i] + Step * (b41 * dydx[i] + b42 * ak2[i] + b43 * ak3[i]);
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}
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this->RightHandSideInl(yTemp, ak4); // 4th Step
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for(unsigned int i = 0; i < N; ++i)
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{
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yTemp[i] = yIn[i] + Step * (b51 * dydx[i] + b52 * ak2[i] + b53 * ak3[i] +
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b54 * ak4[i]);
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}
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this->RightHandSideInl(yTemp, ak5); // 5th Step
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for(unsigned int i = 0; i < N; ++i)
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{
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yTemp[i] = yIn[i] + Step * (b61 * dydx[i] + b62 * ak2[i] + b63 * ak3[i] +
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b64 * ak4[i] + b65 * ak5[i]);
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}
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this->RightHandSideInl(yTemp, ak6); // 6th Step
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for(unsigned int i = 0; i < N; ++i)
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{
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// Accumulate increments with proper weights
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yOut[i] = yIn[i] +
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Step * (c1 * dydx[i] + c3 * ak3[i] + c4 * ak4[i] + c6 * ak6[i]);
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}
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for(unsigned int i = 0; i < N; ++i)
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{
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// Estimate error as difference between 4th and
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// 5th order methods
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yErr[i] = Step * (dc1 * dydx[i] + dc3 * ak3[i] + dc4 * ak4[i] +
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dc5 * ak5[i] + dc6 * ak6[i]);
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}
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for(unsigned int i = 0; i < N; ++i)
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{
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// Store Input and Final values, for possible use in calculating chord
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fLastInitialVector[i] = yIn[i];
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fLastFinalVector[i] = yOut[i];
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fLastDyDx[i] = dydx[i];
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}
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// NormaliseTangentVector( yOut ); // Not wanted
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fLastStepLength = Step;
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return;
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}
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template <class T_Equation, unsigned int N >
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inline G4double
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G4TCashKarpRKF45<T_Equation,N>::DistChord() const
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{
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G4double distLine, distChord;
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G4ThreeVector initialPoint, finalPoint, midPoint;
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// Store last initial and final points (they will be overwritten in
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// self-Stepper call!)
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initialPoint = G4ThreeVector(fLastInitialVector[0], fLastInitialVector[1],
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fLastInitialVector[2]);
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finalPoint = G4ThreeVector(fLastFinalVector[0], fLastFinalVector[1],
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fLastFinalVector[2]);
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// Do half a step using StepNoErr
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fAuxStepper->G4TCashKarpRKF45::Stepper(fLastInitialVector, fLastDyDx,
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0.5 * fLastStepLength, fMidVector,
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fMidError);
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midPoint = G4ThreeVector(fMidVector[0], fMidVector[1], fMidVector[2]);
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// Use stored values of Initial and Endpoint + new Midpoint to evaluate
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// distance of Chord
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if(initialPoint != finalPoint)
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{
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distLine = G4LineSection::Distline(midPoint, initialPoint, finalPoint);
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distChord = distLine;
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}
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else
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{
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distChord = (midPoint - initialPoint).mag();
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}
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return distChord;
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}
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template <class T_Equation, unsigned int N >
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inline void
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G4TCashKarpRKF45<T_Equation,N>::Stepper(const G4double yInput[],
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const G4double dydx[],
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G4double Step,
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G4double yOutput[],
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G4double yError[])
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{
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assert( yOutput != yInput );
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assert( yError != yInput );
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StepWithError( yInput, dydx, Step, yOutput, yError);
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}
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#endif
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