BackwardEulerIvpOdeSolver.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 "BackwardEulerIvpOdeSolver.hpp"
#include <cmath>

void BackwardEulerIvpOdeSolver::ComputeResidual(AbstractOdeSystem* pAbstractOdeSystem,
                                                double timeStep,
                                                double time,
                                                std::vector<double>& rCurrentYValues,
                                                std::vector<double>& rCurrentGuess)
{
    std::vector<double> dy(mSizeOfOdeSystem); //For JC to optimize
    pAbstractOdeSystem->EvaluateYDerivatives(time, rCurrentGuess, dy);
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        mResidual[i] = rCurrentGuess[i] - timeStep * dy[i] - rCurrentYValues[i];
    }
}

void BackwardEulerIvpOdeSolver::ComputeJacobian(AbstractOdeSystem* pAbstractOdeSystem,
                                                double timeStep,
                                                double time,
                                                std::vector<double>& rCurrentYValues,
                                                std::vector<double>& rCurrentGuess)
{
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        for (unsigned j=0; j<mSizeOfOdeSystem; j++)
        {
            mJacobian[i][j] = 0.0;
        }
    }

    if (pAbstractOdeSystem->GetUseAnalyticJacobian() && !mForceUseOfNumericalJacobian)
    {
        // The ODE system has an analytic jacobian, so use that
        AbstractOdeSystemWithAnalyticJacobian *p_ode_system
            = static_cast<AbstractOdeSystemWithAnalyticJacobian*>(pAbstractOdeSystem);
        p_ode_system->AnalyticJacobian(rCurrentGuess, mJacobian, time, timeStep);
    }
    else
    {
        ComputeNumericalJacobian(pAbstractOdeSystem,
                                 timeStep,
                                 time,
                                 rCurrentYValues,
                                 rCurrentGuess);
    }
}

void BackwardEulerIvpOdeSolver::SolveLinearSystem()
{
    double fact;
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        for (unsigned ii=i+1; ii<mSizeOfOdeSystem; ii++)
        {
            fact = mJacobian[ii][i]/mJacobian[i][i];
            for (unsigned j=i; j<mSizeOfOdeSystem; j++)
            {
                mJacobian[ii][j] -= fact*mJacobian[i][j];
            }
            mResidual[ii] -= fact*mResidual[i];
        }
    }
    // This needs to int, since a downloop in unsigned won't terminate properly
    for (int i=mSizeOfOdeSystem-1; i>=0; i--)
    {
        mUpdate[i] = mResidual[i];
        for (unsigned j=i+1; j<mSizeOfOdeSystem; j++)
        {
            mUpdate[i] -= mJacobian[i][j]*mUpdate[j];
        }
        mUpdate[i] /= mJacobian[i][i];
    }
}

double BackwardEulerIvpOdeSolver::ComputeNorm(double* pVector)
{
    double norm = 0.0;
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        if (fabs(pVector[i]) > norm)
        {
            norm = fabs(pVector[i]);
        }
    }
    return norm;
}

void BackwardEulerIvpOdeSolver::ComputeNumericalJacobian(AbstractOdeSystem* pAbstractOdeSystem,
                                                         double timeStep,
                                                         double time,
                                                         std::vector<double>& rCurrentYValues,
                                                         std::vector<double>& rCurrentGuess)
{
    std::vector<double> residual(mSizeOfOdeSystem);
    std::vector<double> residual_perturbed(mSizeOfOdeSystem);
    std::vector<double> guess_perturbed(mSizeOfOdeSystem);

    double epsilon = mNumericalJacobianEpsilon;

    ComputeResidual(pAbstractOdeSystem, timeStep, time, rCurrentYValues, rCurrentGuess);
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        residual[i] = mResidual[i];
    }

    for (unsigned global_column=0; global_column<mSizeOfOdeSystem; global_column++)
    {
        for (unsigned i=0; i<mSizeOfOdeSystem; i++)
        {
            guess_perturbed[i] = rCurrentGuess[i];
        }

        guess_perturbed[global_column] += epsilon;

        ComputeResidual(pAbstractOdeSystem, timeStep, time, rCurrentYValues, guess_perturbed);
        for (unsigned i=0; i<mSizeOfOdeSystem; i++)
        {
            residual_perturbed[i] = mResidual[i];
        }

        // Compute residual_perturbed - residual
        double one_over_eps = 1.0/epsilon;
        for (unsigned i=0; i<mSizeOfOdeSystem; i++)
        {
            mJacobian[i][global_column] = one_over_eps*(residual_perturbed[i] - residual[i]);
        }
    }
}

void BackwardEulerIvpOdeSolver::CalculateNextYValue(AbstractOdeSystem* pAbstractOdeSystem,
                                                    double timeStep,
                                                    double time,
                                                    std::vector<double>& rCurrentYValues,
                                                    std::vector<double>& rNextYValues)
{
    // check the size of the ode system matches the solvers expected
    assert(mSizeOfOdeSystem == pAbstractOdeSystem->GetNumberOfStateVariables());

    unsigned counter = 0;
//        const double eps = 1e-6 * rCurrentGuess[0]; // Our tolerance (should use min(guess) perhaps?)
    const double eps = 1e-6; // JonW tolerance
    double norm = 2*eps;

    std::vector<double> current_guess(mSizeOfOdeSystem);
    current_guess.assign(rCurrentYValues.begin(), rCurrentYValues.end());

    while (norm > eps)
    {
        // Calculate Jacobian and mResidual for current guess
        ComputeResidual(pAbstractOdeSystem, timeStep, time, rCurrentYValues, current_guess);
        ComputeJacobian(pAbstractOdeSystem, timeStep, time, rCurrentYValues, current_guess);
//            // Update norm (our style)
//            norm = ComputeNorm(mResidual);

        // Solve Newton linear system
        SolveLinearSystem();

        // Update norm (JonW style)
        norm = ComputeNorm(mUpdate);

        // Update current guess
        for (unsigned i=0; i<mSizeOfOdeSystem; i++)
        {
            current_guess[i] -= mUpdate[i];
        }

        counter++;
        assert(counter < 20); // avoid infinite loops
    }
    rNextYValues.assign(current_guess.begin(), current_guess.end());
}

BackwardEulerIvpOdeSolver::BackwardEulerIvpOdeSolver(unsigned sizeOfOdeSystem)
{
    mSizeOfOdeSystem = sizeOfOdeSystem;

    // default epsilon
    mNumericalJacobianEpsilon = 1e-6;
    mForceUseOfNumericalJacobian = false;

    // allocate memory
    mResidual = new double[mSizeOfOdeSystem];
    mUpdate = new double[mSizeOfOdeSystem];

    mJacobian = new double*[mSizeOfOdeSystem];
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        mJacobian[i] = new double[mSizeOfOdeSystem];
    }
}

BackwardEulerIvpOdeSolver::~BackwardEulerIvpOdeSolver()
{
    // Delete pointers
    delete[] mResidual;
    delete[] mUpdate;

    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        delete[] mJacobian[i];
    }
    delete[] mJacobian;
}

void BackwardEulerIvpOdeSolver::SetEpsilonForNumericalJacobian(double epsilon)
{
    assert(epsilon > 0);
    mNumericalJacobianEpsilon = epsilon;
}

void BackwardEulerIvpOdeSolver::ForceUseOfNumericalJacobian()
{
    mForceUseOfNumericalJacobian = true;
}

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