RungeKuttaFehlbergIvpOdeSolver.cpp

/*

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

/*
 * 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.resize(number_of_variables);
    mk1.resize(number_of_variables);
    mk2.resize(number_of_variables);
    mk3.resize(number_of_variables);
    mk4.resize(number_of_variables);
    mk5.resize(number_of_variables);
    mk6.resize(number_of_variables);
    myk2.resize(number_of_variables);
    myk3.resize(number_of_variables);
    myk4.resize(number_of_variables);
    myk5.resize(number_of_variables);
    myk6.resize(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);
}


// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
CHASTE_CLASS_EXPORT(RungeKuttaFehlbergIvpOdeSolver)