RungeKuttaFehlbergIvpOdeSolver.cpp

/*

Copyright (C) University of Oxford, 2005-2009

University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.

This file is part of Chaste.

Chaste is free software: you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation, either version 2.1 of the License, or
(at your option) any later version.

Chaste is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details. The offer of Chaste under the terms of the
License is subject to the License being interpreted in accordance with
English Law and subject to any action against the University of Oxford
being under the jurisdiction of the English Courts.

You should have received a copy of the GNU Lesser General Public License
along with Chaste. If not, see <http://www.gnu.org/licenses/>.

*/

#include "RungeKuttaFehlbergIvpOdeSolver.hpp"
#include <cmath>
#include <cfloat>
#include <iostream>

const double smidge = 1e-10;

/*
 * PROTECTED FUNCTIONS =========================================================
 */

void RungeKuttaFehlbergIvpOdeSolver::InternalSolve(OdeSolution& rSolution,
                                                AbstractOdeSystem* pOdeSystem,
                                                std::vector<double>& rYValues,
                                                std::vector<double>& rWorkingMemory,
                                                double startTime,
                                                double endTime,
                                                double maxTimeStep,
                                                double minTimeStep,
                                                double tolerance,
                                                bool outputSolution)
{
    const unsigned number_of_variables = pOdeSystem->GetNumberOfStateVariables();
    mError.reserve(number_of_variables);
    mk1.reserve(number_of_variables);
    mk2.reserve(number_of_variables);
    mk3.reserve(number_of_variables);
    mk4.reserve(number_of_variables);
    mk5.reserve(number_of_variables);
    mk6.reserve(number_of_variables);
    myk2.reserve(number_of_variables);
    myk3.reserve(number_of_variables);
    myk4.reserve(number_of_variables);
    myk5.reserve(number_of_variables);
    myk6.reserve(number_of_variables);

    double current_time = startTime;
    double time_step = maxTimeStep;
    bool got_to_end = false;
    bool accurate_enough = false;
    unsigned number_of_time_steps = 0;

    if (outputSolution)
    {   // Write out ICs
        rSolution.rGetTimes().push_back(current_time);
        rSolution.rGetSolutions().push_back(rYValues);
    }

    // should never get here if this bool has been set to true;
    assert(!mStoppingEventOccurred);
    while (!got_to_end)
    {
        //std::cout << "New timestep\n" << std::flush;
        while (!accurate_enough)
        {
            accurate_enough = true; // assume it is OK until we check and find otherwise

            // Function that calls the appropriate one-step solver
            CalculateNextYValue(pOdeSystem,
                                time_step,
                                current_time,
                                rYValues,
                                rWorkingMemory);

            // Find the maximum error in this vector
            double max_error = -DBL_MAX;
            for (unsigned i=0; i<number_of_variables; i++)
            {
                if (mError[i] > max_error)
                {
                    max_error = mError[i];
                }
            }

            if (max_error > tolerance)
            {// Reject the step-size and do it again.
                accurate_enough = false;
                //std::cout << "Approximation rejected\n" << std::flush;
            }
            else
            {
                // step forward the time since step has now been made
                current_time = current_time + time_step;
                //std::cout << "Approximation accepted with time step = "<< time_step << "\n" << std::flush;
                //std::cout << "max_error = " << max_error << " tolerance = " << tolerance << "\n" << std::flush;
                if (outputSolution)
                {   // Write out ICs
                    //std::cout << "In solver Time = " << current_time << " y = " << rWorkingMemory[0] << "\n" << std::flush;
                    rSolution.rGetTimes().push_back(current_time);
                    rSolution.rGetSolutions().push_back(rWorkingMemory);
                    number_of_time_steps++;
                }
            }

            // Set a new step size based on the accuracy here
            AdjustStepSize(time_step, max_error, tolerance, maxTimeStep, minTimeStep);
        }

        // For the next timestep check the step doesn't go past the end...
        if (current_time + time_step > endTime)
        {   // Allow a smaller timestep for the final step.
            time_step = endTime - current_time;
        }

        if ( pOdeSystem->CalculateStoppingEvent(current_time,
                                                rWorkingMemory) == true )
        {
            mStoppingTime = current_time;
            mStoppingEventOccurred = true;
        }

        if (mStoppingEventOccurred || current_time>=endTime)
        {
            got_to_end = true;
        }

        // Approximation accepted - put it in rYValues
        rYValues.assign(rWorkingMemory.begin(), rWorkingMemory.end());
        accurate_enough = false; // for next loop.
        //std::cout << "Finished Time Step\n" << std::flush;
    }
    rSolution.SetNumberOfTimeSteps(number_of_time_steps);
}

void RungeKuttaFehlbergIvpOdeSolver::CalculateNextYValue(AbstractOdeSystem* pAbstractOdeSystem,
                                                  double timeStep,
                                                  double time,
                                                  std::vector<double>& rCurrentYValues,
                                                  std::vector<double>& rNextYValues)
{
    const unsigned num_equations = pAbstractOdeSystem->GetNumberOfStateVariables();


    std::vector<double>& dy = rNextYValues; // re-use memory (not that it makes much difference here!)

    pAbstractOdeSystem->EvaluateYDerivatives(time, rCurrentYValues, dy);

    for (unsigned i=0; i<num_equations; i++)
    {
        mk1[i] = timeStep*dy[i];
        myk2[i] = rCurrentYValues[i] + 0.25*mk1[i];
    }

    pAbstractOdeSystem->EvaluateYDerivatives(time + 0.25*timeStep, myk2, dy);
    for (unsigned i=0; i<num_equations; i++)
    {
        mk2[i] = timeStep*dy[i];
        myk3[i] = rCurrentYValues[i] + 0.09375*mk1[i] + 0.28125*mk2[i];
    }

    pAbstractOdeSystem->EvaluateYDerivatives(time + 0.375*timeStep, myk3, dy);
    for (unsigned i=0; i<num_equations; i++)
    {
        mk3[i] = timeStep*dy[i];
        myk4[i] = rCurrentYValues[i] + m1932o2197*mk1[i] - m7200o2197*mk2[i]
                    + m7296o2197*mk3[i];
    }

    pAbstractOdeSystem->EvaluateYDerivatives(time+m12o13*timeStep, myk4, dy);
    for (unsigned i=0; i<num_equations; i++)
    {
        mk4[i] = timeStep*dy[i];
        myk5[i] = rCurrentYValues[i] + m439o216*mk1[i] - 8*mk2[i]
                    + m3680o513*mk3[i]- m845o4104*mk4[i];
    }

    pAbstractOdeSystem->EvaluateYDerivatives(time+timeStep, myk5, dy);
    for (unsigned i=0; i<num_equations; i++)
    {
        mk5[i] = timeStep*dy[i];
        myk6[i] = rCurrentYValues[i] - m8o27*mk1[i] + 2*mk2[i] - m3544o2565*mk3[i]
                        + m1859o4104*mk4[i] - 0.275*mk5[i];
    }

    pAbstractOdeSystem->EvaluateYDerivatives(time+0.5*timeStep, myk6, dy);
    for (unsigned i=0; i<num_equations; i++)
    {
        mk6[i] = timeStep*dy[i];
        mError[i] = (1/timeStep)*fabs(m1o360*mk1[i] - m128o4275*mk3[i]
                    - m2197o75240*mk4[i] + 0.02*mk5[i]+ m2o55*mk6[i]);
        rNextYValues[i] = rCurrentYValues[i] + m25o216*mk1[i] + m1408o2565*mk3[i]
                        + m2197o4104*mk4[i] - 0.2*mk5[i];
    }
}

void RungeKuttaFehlbergIvpOdeSolver::AdjustStepSize(double& rCurrentStepSize,
                                const double& rError,
                                const double& rTolerance,
                                const double& rMaxTimeStep,
                                const double& rMinTimeStep)
{
    // Work out scaling factor delta for the step size
    double delta = pow(rTolerance/(2.0*rError), 0.25);

    // Maximum adjustment is *0.1 or *4
    if (delta <= 0.1)
    {
        rCurrentStepSize *= 0.1;
    }
    else if (delta >= 4.0)
    {
        rCurrentStepSize *= 4.0;
    }
    else
    {
        rCurrentStepSize *= delta;
    }

    if (rCurrentStepSize > rMaxTimeStep)
    {
        rCurrentStepSize = rMaxTimeStep;
    }

    if (rCurrentStepSize < rMinTimeStep)
    {
        std::cout << "rCurrentStepSize = " << rCurrentStepSize << "\n" << std::flush;
        std::cout << "rMinTimeStep = " << rMinTimeStep << "\n" << std::flush;

        EXCEPTION("RKF45 Solver: Ode needs a smaller timestep than the set minimum\n");
    }

}


/*
 * PUBLIC FUNCTIONS=============================================================
 */

RungeKuttaFehlbergIvpOdeSolver::RungeKuttaFehlbergIvpOdeSolver()
    : m1932o2197(1932.0/2197.0), // you need the .0 s - caused me no end of trouble.
      m7200o2197(7200.0/2197.0),
      m7296o2197(7296.0/2197.0),
      m12o13(12.0/13.0),
      m439o216(439.0/216.0),
      m3680o513(3680.0/513.0),
      m845o4104(845.0/4104.0),
      m8o27(8.0/27.0),
      m3544o2565(3544.0/2565.0),
      m1859o4104(1859.0/4104.0),
      m1o360(1.0/360.0),
      m128o4275(128.0/4275.0),
      m2197o75240(2197.0/75240.0),
      m2o55(2.0/55.0),
      m25o216(25.0/216.0),
      m1408o2565(1408.0/2565.0),
      m2197o4104(2197.0/4104.0)
{
}

OdeSolution RungeKuttaFehlbergIvpOdeSolver::Solve(AbstractOdeSystem* pOdeSystem,
                                                  std::vector<double>& rYValues,
                                                  double startTime,
                                                  double endTime,
                                                  double timeStep,
                                                  double tolerance)
{
    assert(rYValues.size()==pOdeSystem->GetNumberOfStateVariables());
    assert(endTime > startTime);
    assert(timeStep > 0.0);

    mStoppingEventOccurred = false;
    if ( pOdeSystem->CalculateStoppingEvent(startTime, rYValues) == true )
    {
        EXCEPTION("(Solve with sampling) Stopping event is true for initial condition");
    }
    // Allocate working memory
    std::vector<double> working_memory(rYValues.size());
    // And solve...
    OdeSolution solutions;
    //solutions.SetNumberOfTimeSteps((unsigned)(10.0*(startTime-endTime)/timeStep));
    bool return_solution = true;
    InternalSolve(solutions, pOdeSystem, rYValues, working_memory, startTime, endTime, timeStep, 1e-5, tolerance, return_solution);
    return solutions;
}

void RungeKuttaFehlbergIvpOdeSolver::Solve(AbstractOdeSystem* pOdeSystem,
                                           std::vector<double>& rYValues,
                                           double startTime,
                                           double endTime,
                                           double timeStep)
{
    assert(rYValues.size()==pOdeSystem->GetNumberOfStateVariables());
    assert(endTime > startTime);
    assert(timeStep > 0.0);

    mStoppingEventOccurred = false;
    if ( pOdeSystem->CalculateStoppingEvent(startTime, rYValues) == true )
    {
        EXCEPTION("(Solve without sampling) Stopping event is true for initial condition");
    }
    // Allocate working memory
    std::vector<double> working_memory(rYValues.size());
    // And solve...
    OdeSolution not_required_solution;
    bool return_solution = false;
    InternalSolve(not_required_solution, pOdeSystem, rYValues, working_memory, startTime, endTime, timeStep, 1e-4, 1e-5, return_solution);
}

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