AbstractCvodeSystem.cpp

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*/
 
#ifdef CHASTE_CVODE
 
#include <cassert>
#include <sstream>
 
#include "AbstractCvodeSystem.hpp"
#include "CvodeAdaptor.hpp" // For CvodeErrorHandler
#include "Exception.hpp"
#include "MathsCustomFunctions.hpp" // For tolerance comparison
#include "TimeStepper.hpp"
#include "VectorHelperFunctions.hpp"
 
// CVODE headers
#include <cvode/cvode.h>
#include <sundials/sundials_nvector.h>
 
#if CHASTE_SUNDIALS_VERSION >= 30000
#if CHASTE_SUNDIALS_VERSION < 70000
#include <cvode/cvode_direct.h> /* access to CVDls interface            */
#endif
#include <sundials/sundials_types.h> /* defs. of realtype, sunindextype      */
#include <sunlinsol/sunlinsol_dense.h> /* access to dense SUNLinearSolver      */
#include <sunmatrix/sunmatrix_dense.h> /* access to dense SUNMatrix            */
#else
#include <cvode/cvode_dense.h>
#endif
 
#if CHASTE_SUNDIALS_VERSION >= 60000
#include "CvodeContextManager.hpp"  // access to shared SUNContext object required by Sundials 6.0+
#endif
 
//#include "Debug.hpp"
//void DebugSteps(void* pCvodeMem, AbstractCvodeSystem* pSys)
//{
//    long int num_jac_evals, nniters, num_steps;
//    CVDenseGetNumJacEvals(pCvodeMem, &num_jac_evals);
//    CVodeGetNumNonlinSolvIters(pCvodeMem, &nniters);
//    CVodeGetNumSteps(pCvodeMem, &num_steps);
//    double num_newton_iters = nniters;
//    PRINT_3_VARIABLES(pSys->GetSystemName(), num_newton_iters/num_steps, num_jac_evals/num_newton_iters);
//}
int AbstractCvodeSystemRhsAdaptor(realtype t, N_Vector y, N_Vector ydot, void* pData)
{
    assert(pData != nullptr);
    AbstractCvodeSystem* p_ode_system = (AbstractCvodeSystem*)pData;
    try
    {
        p_ode_system->EvaluateYDerivatives(t, y, ydot);
    }
    catch (const Exception& e)
    {
#if CHASTE_SUNDIALS_VERSION <= 20300
        // Really old CVODE used to solve past the requested time points and could trigger this exception unnecessarily...
        if (e.CheckShortMessageContains("is outside the times stored in the data clamp") == "")
        {
            return 1; // This may be a recoverable error!
        }
#endif
 
        std::cerr << "CVODE RHS Exception: " << e.GetMessage()
                  << std::endl
                  << std::flush;
        return -1;
    }
 
    //    Something like this might help CVODE when things are a bit unstable...
    //    We tried this again in Jan 2023 but now with VerifyStateVariables() returning a recoverable error when values look off. However this didn't improve the situation.
    //    See: https://github.com/Chaste/Chaste/issues/46
    //    try
    //    {
    //        p_ode_system->VerifyStateVariables();
    //    }
    //    catch (const Exception &e)
    //    {
    //        std::cout << "t = " << t << ":\t" <<  e.GetMessage() << std::endl << std::flush;
    //        return 1; // A positive return flag to CVODE tells it there's been an error but it might be recoverable.
    //    }
 
    return 0;
}
 
/*
 * Absolute chaos here with four different possible interfaces to the jacobian.
 */
#if CHASTE_SUNDIALS_VERSION >= 30000
// Sundials 3.0 - has taken away the argument N at the top...
int AbstractCvodeSystemJacAdaptor(realtype t, N_Vector y, N_Vector ydot, CHASTE_CVODE_DENSE_MATRIX jacobian,
#elif CHASTE_SUNDIALS_VERSION >= 20500
// Sundials 2.5
int AbstractCvodeSystemJacAdaptor(long int N, realtype t, N_Vector y, N_Vector ydot, CHASTE_CVODE_DENSE_MATRIX jacobian,
#elif CHASTE_SUNDIALS_VERSION >= 20400
// Sundials 2.4
int AbstractCvodeSystemJacAdaptor(int N, realtype t, N_Vector y, N_Vector ydot, DlsMat jacobian,
#else
// Sundials 2.3 and below (not sure how far below, but this is 2006 so old enough).
int AbstractCvodeSystemJacAdaptor(long int N, DenseMat jacobian, realtype t, N_Vector y, N_Vector ydot,
#endif
                                  void* pData, N_Vector tmp1, N_Vector tmp2, N_Vector tmp3)
{
    assert(pData != nullptr);
    AbstractCvodeSystem* p_ode_system = (AbstractCvodeSystem*)pData;
    try
    {
        p_ode_system->EvaluateAnalyticJacobian(t, y, ydot, jacobian, tmp1, tmp2, tmp3);
    }
    catch (const Exception& e)
    {
        std::cerr << "CVODE Jacobian Exception: " << e.GetMessage() << std::endl
                  << std::flush;
        return -1;
    }
    return 0;
}
 
AbstractCvodeSystem::AbstractCvodeSystem(unsigned numberOfStateVariables)
        : AbstractParameterisedSystem<N_Vector>(numberOfStateVariables),
          mLastSolutionState(nullptr),
          mLastSolutionTime(0.0),
#if CHASTE_SUNDIALS_VERSION >= 20400
          mForceReset(false),
#else
          // Old Sundials don't seem to 'go back' when something has changed
          // properly, and give more inaccurate answers.
          mForceReset(true),
#endif
          mForceMinimalReset(false),
#if CHASTE_SUNDIALS_VERSION >= 30000
          mpSundialsDenseMatrix(nullptr),
          mpSundialsLinearSolver(nullptr),
#endif
          mHasAnalyticJacobian(false),
          mUseAnalyticJacobian(false),
          mpCvodeMem(nullptr),
          mMaxSteps(0),
          mLastInternalStepSize(0)
{
    SetTolerances(); // Set the tolerances to the defaults.
}
 
void AbstractCvodeSystem::Init()
{
    DeleteVector(mStateVariables);
    mStateVariables = GetInitialConditions();
    DeleteVector(mParameters);
#if CHASTE_SUNDIALS_VERSION >= 60000
    mParameters = N_VNew_Serial(rGetParameterNames().size(), CvodeContextManager::Instance()->GetSundialsContext());
#else
    mParameters = N_VNew_Serial(rGetParameterNames().size());
#endif
    for (int i = 0; i < NV_LENGTH_S(mParameters); i++)
    {
        NV_Ith_S(mParameters, i) = 0.0;
    }
}
 
AbstractCvodeSystem::~AbstractCvodeSystem()
{
    FreeCvodeMemory();
    DeleteVector(mStateVariables);
    DeleteVector(mParameters);
    DeleteVector(mLastSolutionState);
}
 
//
//double AbstractCvodeSystem::CalculateRootFunction(double time, const std::vector<double>& rY)
//{
//    bool stop = CalculateStoppingEvent(time, rY);
//    return stop ? 0.0 : 1.0;
//}
 
OdeSolution AbstractCvodeSystem::Solve(realtype tStart,
                                       realtype tEnd,
                                       realtype maxDt,
                                       realtype tSamp)
{
    assert(tEnd >= tStart);
    assert(tSamp > 0.0);
 
    SetupCvode(mStateVariables, tStart, maxDt);
 
    TimeStepper stepper(tStart, tEnd, tSamp);
 
    // Set up ODE solution
    OdeSolution solutions;
    solutions.SetNumberOfTimeSteps(stepper.EstimateTimeSteps());
    solutions.rGetSolutions().push_back(MakeStdVec(mStateVariables));
    solutions.rGetTimes().push_back(tStart);
    solutions.SetOdeSystemInformation(mpSystemInfo);
 
    // Main time sampling loop
    while (!stepper.IsTimeAtEnd())
    {
        // This should stop CVODE going past the end of where we wanted and interpolating back.
        int ierr = CVodeSetStopTime(mpCvodeMem, stepper.GetNextTime());
        assert(ierr == CV_SUCCESS);
        UNUSED_OPT(ierr); // avoid unused var warning
 
        //        // This parameter governs how many times we allow a recoverable right hand side failure
        //        int ierr = CVodeSetMaxConvFails(mpCvodeMem, 1000);
        //        assert(ierr == CV_SUCCESS); UNUSED_OPT(ierr); // avoid unused var warning
 
        double cvode_stopped_at = stepper.GetTime();
        ierr = CVode(mpCvodeMem, stepper.GetNextTime(), mStateVariables,
                     &cvode_stopped_at, CV_NORMAL);
        if (ierr < 0)
        {
            //            DebugSteps(mpCvodeMem, this);
            CvodeError(ierr, "CVODE failed to solve system", cvode_stopped_at, stepper.GetTime(), stepper.GetNextTime());
        }
        // Not root finding, so should have reached requested time
        assert(fabs(cvode_stopped_at - stepper.GetNextTime()) < DBL_EPSILON);
#ifndef NDEBUG
        VerifyStateVariables();
#endif
        // Store solution
        solutions.rGetSolutions().push_back(MakeStdVec(mStateVariables));
        solutions.rGetTimes().push_back(cvode_stopped_at);
        stepper.AdvanceOneTimeStep();
    }
 
    // stepper.EstimateTimeSteps may have been an overestimate...
    solutions.SetNumberOfTimeSteps(stepper.GetTotalTimeStepsTaken());
 
    int ierr = CVodeGetLastStep(mpCvodeMem, &mLastInternalStepSize);
    assert(ierr == CV_SUCCESS);
    UNUSED_OPT(ierr); // avoid unused var warning
 
    RecordStoppingPoint(tEnd);
 
    return solutions;
}
 
void AbstractCvodeSystem::Solve(realtype tStart,
                                realtype tEnd,
                                realtype maxDt)
{
    assert(tEnd >= tStart);
 
    SetupCvode(mStateVariables, tStart, maxDt);
 
    // This should stop CVODE going past the end of where we wanted and interpolating back.
    int ierr = CVodeSetStopTime(mpCvodeMem, tEnd);
    assert(ierr == CV_SUCCESS);
    UNUSED_OPT(ierr); // avoid unused var warning
 
    double cvode_stopped_at = tStart;
    ierr = CVode(mpCvodeMem, tEnd, mStateVariables, &cvode_stopped_at, CV_NORMAL);
    if (ierr < 0)
    {
        //        DebugSteps(mpCvodeMem, this);
        CvodeError(ierr, "CVODE failed to solve system", cvode_stopped_at, tStart, tEnd);
    }
    // Not root finding, so should have reached requested time
    assert(fabs(cvode_stopped_at - tEnd) < DBL_EPSILON);
 
    ierr = CVodeGetLastStep(mpCvodeMem, &mLastInternalStepSize);
    assert(ierr == CV_SUCCESS);
    UNUSED_OPT(ierr); // avoid unused var warning
 
    RecordStoppingPoint(cvode_stopped_at);
 
//
//    long int nst, nfe, nsetups, nje, nfeLS, nni, ncfn, netf, nge;
//
//
//    CVodeGetNumSteps(mpCvodeMem, &nst);
//    CVodeGetNumRhsEvals(mpCvodeMem, &nfe);
//    CVodeGetNumLinSolvSetups(mpCvodeMem, &nsetups);
//    CVodeGetNumErrTestFails(mpCvodeMem, &netf);
//    CVodeGetNumNonlinSolvIters(mpCvodeMem, &nni);
//    CVodeGetNumNonlinSolvConvFails(mpCvodeMem, &ncfn);
//    CVDlsGetNumJacEvals(mpCvodeMem, &nje);
//    CVDlsGetNumRhsEvals(mpCvodeMem, &nfeLS);
//    CVodeGetNumGEvals(mpCvodeMem, &nge);
//
//    printf("\nFinal Statistics:\n");
//    printf("nst = %-6ld nfe  = %-6ld nsetups = %-6ld nfeLS = %-6ld nje = %ld\n",
//       nst, nfe, nsetups, nfeLS, nje);
//    printf("nni = %-6ld ncfn = %-6ld netf = %-6ld nge = %ld\n \n",
//       nni, ncfn, netf, nge);
//    std::cout << std::flush;
#ifndef NDEBUG
    VerifyStateVariables();
#endif
}
 
void AbstractCvodeSystem::SetMaxSteps(long int numSteps)
{
    mMaxSteps = numSteps;
}
 
long int AbstractCvodeSystem::GetMaxSteps()
{
    return mMaxSteps;
}
 
void AbstractCvodeSystem::SetTolerances(double relTol, double absTol)
{
    mRelTol = relTol;
    mAbsTol = absTol;
    ResetSolver();
}
 
double AbstractCvodeSystem::GetRelativeTolerance()
{
    return mRelTol;
}
 
double AbstractCvodeSystem::GetAbsoluteTolerance()
{
    return mAbsTol;
}
 
double AbstractCvodeSystem::GetLastStepSize()
{
    return mLastInternalStepSize;
}
 
void AbstractCvodeSystem::SetForceReset(bool autoReset)
{
    mForceReset = autoReset;
    if (mForceReset)
    {
        ResetSolver();
    }
}
 
bool AbstractCvodeSystem::GetMinimalReset()
{
    return mForceMinimalReset;
}
 
bool AbstractCvodeSystem::GetForceReset()
{
    return mForceReset;
}
 
void AbstractCvodeSystem::SetMinimalReset(bool minimalReset)
{
    mForceMinimalReset = minimalReset;
    if (mForceMinimalReset)
    {
        SetForceReset(false);
    }
}
 
void AbstractCvodeSystem::ResetSolver()
{
    DeleteVector(mLastSolutionState);
}
 
void AbstractCvodeSystem::SetupCvode(N_Vector initialConditions,
                                     realtype tStart,
                                     realtype maxDt)
{
    assert((unsigned)NV_LENGTH_S(initialConditions) == GetNumberOfStateVariables());
    assert(maxDt >= 0.0);
 
    // Find out if we need to (re-)initialise
    //std::cout << "!mpCvodeMem = " << !mpCvodeMem << ", mForceReset = " << mForceReset << ", !mLastSolutionState = " << !mLastSolutionState << ", comp doubles = " << !CompareDoubles::WithinAnyTolerance(tStart, mLastSolutionTime) << "\n";
    bool reinit = !mpCvodeMem || mForceReset || !mLastSolutionState || !CompareDoubles::WithinAnyTolerance(tStart, mLastSolutionTime);
    if (!reinit && !mForceMinimalReset)
    {
        const unsigned size = GetNumberOfStateVariables();
        for (unsigned i = 0; i < size; i++)
        {
            if (!CompareDoubles::WithinAnyTolerance(GetVectorComponent(mLastSolutionState, i), GetVectorComponent(mStateVariables, i)))
            {
                reinit = true;
                break;
            }
        }
    }
 
    if (!mpCvodeMem)
    {
        //std::cout << "New CVODE solver\n";
#if CHASTE_SUNDIALS_VERSION >= 60000
        mpCvodeMem = CVodeCreate(CV_BDF, CvodeContextManager::Instance()->GetSundialsContext());
#elif CHASTE_SUNDIALS_VERSION >= 40000
        //  v4.0.0 release notes: instead of specifying the nonlinear iteration type when creating the CVODE(S) memory structure,
        //  CVODE(S) uses the SUNNONLINSOL_NEWTON module implementation of a Newton iteration by default.
        mpCvodeMem = CVodeCreate(CV_BDF);
#else
        mpCvodeMem = CVodeCreate(CV_BDF, CV_NEWTON);
#endif
        if (mpCvodeMem == nullptr)
            EXCEPTION("Failed to SetupCvode CVODE"); // LCOV_EXCL_LINE
 
        // Set error handler
#if CHASTE_SUNDIALS_VERSION >= 70000
    SUNContext_PushErrHandler(CvodeContextManager::Instance()->GetSundialsContext(),  CvodeErrorHandler, nullptr);
#else
        CVodeSetErrHandlerFn(mpCvodeMem, CvodeErrorHandler, nullptr);
#endif
// Set the user data
#if CHASTE_SUNDIALS_VERSION >= 20400
        CVodeSetUserData(mpCvodeMem, (void*)(this));
#else
        CVodeSetFdata(mpCvodeMem, (void*)(this));
#endif
// Setup CVODE
#if CHASTE_SUNDIALS_VERSION >= 20400
        CVodeInit(mpCvodeMem, AbstractCvodeSystemRhsAdaptor, tStart, initialConditions);
        CVodeSStolerances(mpCvodeMem, mRelTol, mAbsTol);
#else
        CVodeMalloc(mpCvodeMem, AbstractCvodeSystemRhsAdaptor, tStart, initialConditions,
                    CV_SS, mRelTol, &mAbsTol);
#endif
 
#if CHASTE_SUNDIALS_VERSION >= 60000
        /* Create dense matrix SUNDenseMatrix for use in linear solves */
        mpSundialsDenseMatrix = SUNDenseMatrix(NV_LENGTH_S(initialConditions), NV_LENGTH_S(initialConditions), CvodeContextManager::Instance()->GetSundialsContext());
#elif CHASTE_SUNDIALS_VERSION >= 30000
        /* Create dense matrix SUNDenseMatrix for use in linear solves */
        mpSundialsDenseMatrix = SUNDenseMatrix(NV_LENGTH_S(initialConditions), NV_LENGTH_S(initialConditions));
#endif
 
#if CHASTE_SUNDIALS_VERSION >= 60000
        /* Create dense SUNLinSol_Dense object for use by CVode */
        mpSundialsLinearSolver = SUNLinSol_Dense(initialConditions, mpSundialsDenseMatrix, CvodeContextManager::Instance()->GetSundialsContext());
 
        /* Call CVodeSetLinearSolver to attach the matrix and linear solver to CVode */
        CVodeSetLinearSolver(mpCvodeMem, mpSundialsLinearSolver, mpSundialsDenseMatrix);
#elif CHASTE_SUNDIALS_VERSION >= 40000
        /* Create dense SUNLinSol_Dense object for use by CVode */
        mpSundialsLinearSolver = SUNLinSol_Dense(initialConditions, mpSundialsDenseMatrix);
 
        /* Call CVodeSetLinearSolver to attach the matrix and linear solver to CVode */
        CVodeSetLinearSolver(mpCvodeMem, mpSundialsLinearSolver, mpSundialsDenseMatrix);
#elif CHASTE_SUNDIALS_VERSION >= 30000
        /* Create dense SUNDenseLinearSolver object for use by CVode */
        mpSundialsLinearSolver = SUNDenseLinearSolver(initialConditions, mpSundialsDenseMatrix);
 
        /* Call CVDlsSetLinearSolver to attach the matrix and linear solver to CVode */
        CVDlsSetLinearSolver(mpCvodeMem, mpSundialsLinearSolver, mpSundialsDenseMatrix);
#else
        // CVODE < v3.0.0
        // Attach a linear solver for Newton iteration
        CVDense(mpCvodeMem, NV_LENGTH_S(initialConditions));
#endif
 
        if (mUseAnalyticJacobian)
        {
#if CHASTE_SUNDIALS_VERSION >= 40000
            CVodeSetJacFn(mpCvodeMem, AbstractCvodeSystemJacAdaptor);
#elif CHASTE_SUNDIALS_VERSION >= 30000
            CVDlsSetJacFn(mpCvodeMem, AbstractCvodeSystemJacAdaptor);
#elif CHASTE_SUNDIALS_VERSION >= 20400
            CVDlsSetDenseJacFn(mpCvodeMem, AbstractCvodeSystemJacAdaptor);
#else
            CVDenseSetJacFn(mpCvodeMem, AbstractCvodeSystemJacAdaptor, (void*)(this));
#endif
        }
    }
    else if (reinit)
    {
//std::cout << "Resetting CVODE solver\n";
#if CHASTE_SUNDIALS_VERSION >= 20400
        CVodeReInit(mpCvodeMem, tStart, initialConditions);
        //CVodeSStolerances(mpCvodeMem, mRelTol, mAbsTol); - "all solver inputs remain in effect" so we don't need this.
#else
        CVodeReInit(mpCvodeMem, AbstractCvodeSystemRhsAdaptor, tStart, initialConditions,
                    CV_SS, mRelTol, &mAbsTol);
#endif
    }
 
    // Set max dt and change max steps if wanted
    if (maxDt > 0)
    {
        CVodeSetMaxStep(mpCvodeMem, maxDt);
    }
 
    if (mMaxSteps > 0)
    {
        CVodeSetMaxNumSteps(mpCvodeMem, mMaxSteps);
        CVodeSetMaxErrTestFails(mpCvodeMem, 15);
    }
}
 
void AbstractCvodeSystem::RecordStoppingPoint(double stopTime)
{
    //    DebugSteps(mpCvodeMem, this);
 
    // If we're forcing a reset then we don't record the stopping time
    // as a result it won't match and we will force a reset in SetupCvode() on
    // the next solve call.
    if (mForceReset)
        return;
 
    // Otherwise we will store the state variables and time for comparison on the
    // next solve call, to work out whether we need to reset.
    const unsigned size = GetNumberOfStateVariables();
    CreateVectorIfEmpty(mLastSolutionState, size);
    for (unsigned i = 0; i < size; i++)
    {
        SetVectorComponent(mLastSolutionState, i, GetVectorComponent(mStateVariables, i));
    }
    mLastSolutionTime = stopTime;
}
 
void AbstractCvodeSystem::FreeCvodeMemory()
{
    if (mpCvodeMem)
    {
        CVodeFree(&mpCvodeMem);
    }
    mpCvodeMem = nullptr;
 
#if CHASTE_SUNDIALS_VERSION >= 30000
    if (mpSundialsLinearSolver)
    {
        /* Free the linear solver memory */
        SUNLinSolFree(mpSundialsLinearSolver);
    }
    mpSundialsLinearSolver = nullptr;
 
    if (mpSundialsDenseMatrix)
    {
        /* Free the matrix memory */
        SUNMatDestroy(mpSundialsDenseMatrix);
    }
    mpSundialsDenseMatrix = nullptr;
#endif
}
 
void AbstractCvodeSystem::CvodeError(int flag, const char* msg,
                                     const double& rTime, const double& rStartTime, const double& rEndTime)
{
    std::stringstream err;
    char* p_flag_name = CVodeGetReturnFlagName(flag);
    err << msg << ": " << p_flag_name;
    free(p_flag_name);
    if (flag == CV_LSETUP_FAIL)
    {
#if CHASTE_SUNDIALS_VERSION >= 20500
        long int ls_flag;
#else
        int ls_flag;
#endif
        char* p_ls_flag_name;
 
#if CHASTE_SUNDIALS_VERSION >= 40000
        CVodeGetLastLinFlag(mpCvodeMem, &ls_flag);
        p_ls_flag_name = CVodeGetLinReturnFlagName(ls_flag);
#elif CHASTE_SUNDIALS_VERSION >= 20400
        CVDlsGetLastFlag(mpCvodeMem, &ls_flag);
        p_ls_flag_name = CVDlsGetReturnFlagName(ls_flag);
#else
        CVDenseGetLastFlag(mpCvodeMem, &ls_flag);
        p_ls_flag_name = CVDenseGetReturnFlagName(ls_flag);
#endif
        err << " (LS flag=" << ls_flag << ":" << p_ls_flag_name << ")";
        free(p_ls_flag_name);
    }
 
    err << "\nGot from time " << rStartTime << " to time " << rTime << ", was supposed to finish at time " << rEndTime << "\n";
    err << "\nState variables are now:\n";
    std::vector<double> state_vars = MakeStdVec(mStateVariables);
    std::vector<std::string> state_var_names = rGetStateVariableNames();
    for (unsigned i = 0; i < state_vars.size(); i++)
    {
        err << "\t" << state_var_names[i] << "\t:\t" << state_vars[i] << std::endl;
    }
 
    FreeCvodeMemory();
    std::cerr << err.str() << std::endl
              << std::flush;
    EXCEPTION(err.str());
}
 
bool AbstractCvodeSystem::HasAnalyticJacobian() const
{
    return mHasAnalyticJacobian;
}
 
bool AbstractCvodeSystem::GetUseAnalyticJacobian() const
{
    return mUseAnalyticJacobian;
}
 
void AbstractCvodeSystem::ForceUseOfNumericalJacobian(bool useNumericalJacobian)
{
    if (!useNumericalJacobian && !mHasAnalyticJacobian)
    {
        EXCEPTION("Analytic Jacobian requested, but this ODE system doesn't have one. You can check this with HasAnalyticJacobian().");
    }
 
    if (mUseAnalyticJacobian == useNumericalJacobian)
    {
        mUseAnalyticJacobian = !useNumericalJacobian;
        // We need to re-initialise the solver completely to change this.
        this->FreeCvodeMemory();
    }
}
 
//#include "MathsCustomFunctions.hpp"
//#include <algorithm>
//void AbstractCvodeSystem::CheckAnalyticJacobian(realtype time, N_Vector y, N_Vector ydot,
//                                                CHASTE_CVODE_DENSE_MATRIX jacobian,
//                                                N_Vector tmp1, N_Vector tmp2, N_Vector tmp3)
//{
//    N_Vector nudge_ydot = tmp1;
//    N_Vector numeric_jth_col = tmp2;
//    N_Vector ewt = tmp3;
//    const unsigned size = GetNumberOfStateVariables();
//    const double rel_tol = 1e-1;
//    const double abs_tol = 1e-6;
//    realtype* p_y = N_VGetArrayPointer(y);
//    realtype* p_numeric_jth_col = N_VGetArrayPointer(numeric_jth_col);
//
//    // CVODE internal data for computing the numeric J
//    realtype h;
//    CVodeGetLastStep(mpCvodeMem, &h);
//    CVodeGetErrWeights(mpCvodeMem, ewt);
//    realtype* p_ewt = N_VGetArrayPointer(ewt);
//    // Compute minimum nudge
//    realtype srur = sqrt(DBL_EPSILON);
//    realtype fnorm = N_VWrmsNorm(ydot, ewt);
//    realtype min_nudge = (fnorm != 0.0) ?
//            (1000.0 * fabs(h) * DBL_EPSILON * size * fnorm) : 1.0;
//
//    for (unsigned j=0; j<size; j++)
//    {
//        // Check the j'th column of the Jacobian
//        realtype yjsaved = p_y[j];
//        realtype nudge = std::max(srur*fabs(yjsaved), min_nudge/p_ewt[j]);
//        p_y[j] += nudge;
//        EvaluateYDerivatives(time, y, nudge_ydot);
//        p_y[j] = yjsaved;
//        realtype nudge_inv = 1.0 / nudge;
//        N_VLinearSum(nudge_inv, nudge_ydot, -nudge_inv, ydot, numeric_jth_col);
//        realtype* p_analytic_jth_col = DENSE_COL(jacobian, j);
//
//        for (unsigned i=0; i<size; i++)
//        {
//            if (!CompareDoubles::WithinAnyTolerance(p_numeric_jth_col[i], p_analytic_jth_col[i], rel_tol, abs_tol))
//            {
//                EXCEPTION("Analytic Jacobian appears dodgy at time " << time << " entry (" << i << "," << j << ").\n"
//                          << "Analytic=" << p_analytic_jth_col[i] << "; numeric=" << p_numeric_jth_col[i] << "."
//                          << DumpState("", y, time));
//            }
//        }
//    }
//}
 
#endif // CHASTE_CVODE