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128 lines
4.6 KiB
C++
128 lines
4.6 KiB
C++
/*=========================================================================
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Program: Visualization Toolkit
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Module: vtkRungeKutta45.h
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Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
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All rights reserved.
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See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
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This software is distributed WITHOUT ANY WARRANTY; without even
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the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
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PURPOSE. See the above copyright notice for more information.
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=========================================================================*/
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/**
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* @class vtkRungeKutta45
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* @brief Integrate an initial value problem using 5th
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* order Runge-Kutta method with adaptive stepsize control.
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*
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*
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* This is a concrete sub-class of vtkInitialValueProblemSolver.
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* It uses a 5th order Runge-Kutta method with stepsize control to obtain
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* the values of a set of functions at the next time step. The stepsize
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* is adjusted by calculating an estimated error using an embedded 4th
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* order Runge-Kutta formula:
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* Press, W. H. et al., 1992, Numerical Recipes in Fortran, Second
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* Edition, Cambridge University Press
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* Cash, J.R. and Karp, A.H. 1990, ACM Transactions on Mathematical
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* Software, vol 16, pp 201-222
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*
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* @sa
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* vtkInitialValueProblemSolver vtkRungeKutta4 vtkRungeKutta2 vtkFunctionSet
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*/
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#ifndef vtkRungeKutta45_h
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#define vtkRungeKutta45_h
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#include "vtkCommonMathModule.h" // For export macro
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#include "vtkInitialValueProblemSolver.h"
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class VTKCOMMONMATH_EXPORT vtkRungeKutta45 : public vtkInitialValueProblemSolver
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{
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public:
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vtkTypeMacro(vtkRungeKutta45, vtkInitialValueProblemSolver);
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void PrintSelf(ostream& os, vtkIndent indent) override;
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/**
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* Construct a vtkRungeKutta45 with no initial FunctionSet.
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*/
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static vtkRungeKutta45* New();
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using Superclass::ComputeNextStep;
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//@{
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/**
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* Given initial values, xprev , initial time, t and a requested time
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* interval, delT calculate values of x at t+delTActual (xnext).
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* Possibly delTActual != delT. This may occur
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* because this solver supports adaptive stepsize control. It tries
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* to change to stepsize such that
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* the (estimated) error of the integration is less than maxError.
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* The solver will not set the stepsize smaller than minStep or
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* larger than maxStep (note that maxStep and minStep should both
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* be positive, whereas delT can be negative).
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* Also note that delT is an in/out argument. vtkRungeKutta45
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* will modify delT to reflect the best (estimated) size for the next
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* integration step.
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* An estimated value for the error is returned (by reference) in error.
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* This is the norm of the error vector if there are more than
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* one function to be integrated.
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* This method returns an error code representing the nature of
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* the failure:
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* OutOfDomain = 1,
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* NotInitialized = 2,
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* UnexpectedValue = 3
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*/
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int ComputeNextStep(double* xprev, double* xnext, double t, double& delT, double maxError,
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double& error, void* userData) override
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{
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double minStep = delT;
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double maxStep = delT;
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double delTActual;
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return this->ComputeNextStep(
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xprev, nullptr, xnext, t, delT, delTActual, minStep, maxStep, maxError, error, userData);
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}
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int ComputeNextStep(double* xprev, double* dxprev, double* xnext, double t, double& delT,
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double maxError, double& error, void* userData) override
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{
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double minStep = delT;
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double maxStep = delT;
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double delTActual;
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return this->ComputeNextStep(
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xprev, dxprev, xnext, t, delT, delTActual, minStep, maxStep, maxError, error, userData);
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}
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int ComputeNextStep(double* xprev, double* xnext, double t, double& delT, double& delTActual,
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double minStep, double maxStep, double maxError, double& error, void* userData) override
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{
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return this->ComputeNextStep(
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xprev, nullptr, xnext, t, delT, delTActual, minStep, maxStep, maxError, error, userData);
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}
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int ComputeNextStep(double* xprev, double* dxprev, double* xnext, double t, double& delT,
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double& delTActual, double minStep, double maxStep, double maxError, double& error,
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void* userData) override;
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//@}
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protected:
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vtkRungeKutta45();
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~vtkRungeKutta45() override;
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void Initialize() override;
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// Cash-Karp parameters
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static double A[5];
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static double B[5][5];
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static double C[6];
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static double DC[6];
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double* NextDerivs[6];
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int ComputeAStep(double* xprev, double* dxprev, double* xnext, double t, double& delT,
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double& delTActual, double& error, void* userData);
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private:
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vtkRungeKutta45(const vtkRungeKutta45&) = delete;
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void operator=(const vtkRungeKutta45&) = delete;
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};
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#endif
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