void checkFluidSystem()
{
    std::cout << "Testing fluid system '" << Dune::className<FluidSystem>() << "'\n";

    // make sure the fluid system provides the number of phases and
    // the number of components
    enum { numPhases = FluidSystem::numPhases };
    enum { numComponents = FluidSystem::numComponents };

    typedef HairSplittingFluidState<RhsEval, FluidSystem> FluidState;
    FluidState fs;
    fs.allowTemperature(true);
    fs.allowPressure(true);
    fs.allowComposition(true);
    fs.restrictToPhase(-1);

    // initialize memory the fluid state
    fs.base().setTemperature(273.15 + 20.0);
    for (int phaseIdx = 0; phaseIdx < numPhases; ++ phaseIdx) {
        fs.base().setPressure(phaseIdx, 1e5);
        fs.base().setSaturation(phaseIdx, 1.0/numPhases);
        for (int compIdx = 0; compIdx < numComponents; ++ compIdx) {
            fs.base().setMoleFraction(phaseIdx, compIdx, 1.0/numComponents);
        }
    }

    static_assert(std::is_same<typename FluidSystem::Scalar, Scalar>::value,
                  "The type used for floating point used by the fluid system must be the same"
                  " as the one passed to the checkFluidSystem() function");

    // check whether the parameter cache adheres to the API
    typedef typename FluidSystem::template ParameterCache<LhsEval> ParameterCache;

    ParameterCache paramCache;
    try { paramCache.updateAll(fs); } catch (...) {};
    try { paramCache.updateAll(fs, /*except=*/ParameterCache::None); } catch (...) {};
    try { paramCache.updateAll(fs, /*except=*/ParameterCache::Temperature | ParameterCache::Pressure | ParameterCache::Composition); } catch (...) {};
    try { paramCache.updateAllPressures(fs); } catch (...) {};

    for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx) {
        fs.restrictToPhase(static_cast<int>(phaseIdx));
        try { paramCache.updatePhase(fs, phaseIdx); } catch (...) {};
        try { paramCache.updatePhase(fs, phaseIdx, /*except=*/ParameterCache::None); } catch (...) {};
        try { paramCache.updatePhase(fs, phaseIdx, /*except=*/ParameterCache::Temperature | ParameterCache::Pressure | ParameterCache::Composition); } catch (...) {};
        try { paramCache.updateTemperature(fs, phaseIdx); } catch (...) {};
        try { paramCache.updatePressure(fs, phaseIdx); } catch (...) {};
        try { paramCache.updateComposition(fs, phaseIdx); } catch (...) {};
        try { paramCache.updateSingleMoleFraction(fs, phaseIdx, /*compIdx=*/0); } catch (...) {};
    }

    // some value to make sure the return values of the fluid system
    // are convertible to scalars
    LhsEval val = 0.0;
    Scalar scalarVal = 0.0;

    scalarVal = 2*scalarVal; // get rid of GCC warning (only occurs with paranoid warning flags)
    val = 2*val; // get rid of GCC warning (only occurs with paranoid warning flags)

    // actually check the fluid system API
    try { FluidSystem::init(); } catch (...) {};
    for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++ phaseIdx) {
        fs.restrictToPhase(static_cast<int>(phaseIdx));
        fs.allowPressure(FluidSystem::isCompressible(phaseIdx));
        fs.allowComposition(true);
        fs.allowDensity(false);
        try { auto tmpVal OPM_UNUSED = FluidSystem::density(fs, paramCache, phaseIdx); static_assert(std::is_same<decltype(tmpVal), RhsEval>::value, "The default return value must be the scalar used by the fluid state!"); } catch (...) {};
        try { val = FluidSystem::template density<FluidState, LhsEval>(fs, paramCache, phaseIdx); } catch (...) {};
        try { scalarVal = FluidSystem::template density<FluidState, Scalar>(fs, paramCache, phaseIdx); } catch (...) {};

        fs.allowPressure(true);
        fs.allowDensity(true);
        try { auto tmpVal OPM_UNUSED = FluidSystem::viscosity(fs, paramCache, phaseIdx); static_assert(std::is_same<decltype(tmpVal), RhsEval>::value, "The default return value must be the scalar used by the fluid state!"); } catch (...) {};
        try { auto tmpVal OPM_UNUSED = FluidSystem::enthalpy(fs, paramCache, phaseIdx); static_assert(std::is_same<decltype(tmpVal), RhsEval>::value, "The default return value must be the scalar used by the fluid state!"); } catch (...) {};
        try { auto tmpVal OPM_UNUSED = FluidSystem::heatCapacity(fs, paramCache, phaseIdx); static_assert(std::is_same<decltype(tmpVal), RhsEval>::value, "The default return value must be the scalar used by the fluid state!"); } catch (...) {};
        try { auto tmpVal OPM_UNUSED= FluidSystem::thermalConductivity(fs, paramCache, phaseIdx); static_assert(std::is_same<decltype(tmpVal), RhsEval>::value, "The default return value must be the scalar used by the fluid state!"); } catch (...) {};
        try { val = FluidSystem::template viscosity<FluidState, LhsEval>(fs, paramCache, phaseIdx); } catch (...) {};
        try { val = FluidSystem::template enthalpy<FluidState, LhsEval>(fs, paramCache, phaseIdx); } catch (...) {};
        try { val = FluidSystem::template heatCapacity<FluidState, LhsEval>(fs, paramCache, phaseIdx); } catch (...) {};
        try { val = FluidSystem::template thermalConductivity<FluidState, LhsEval>(fs, paramCache, phaseIdx); } catch (...) {};
        try { scalarVal = FluidSystem::template viscosity<FluidState, Scalar>(fs, paramCache, phaseIdx); } catch (...) {};
        try { scalarVal = FluidSystem::template enthalpy<FluidState, Scalar>(fs, paramCache, phaseIdx); } catch (...) {};
        try { scalarVal = FluidSystem::template heatCapacity<FluidState, Scalar>(fs, paramCache, phaseIdx); } catch (...) {};
        try { scalarVal = FluidSystem::template thermalConductivity<FluidState, Scalar>(fs, paramCache, phaseIdx); } catch (...) {};

        for (unsigned compIdx = 0; compIdx < numComponents; ++ compIdx) {
            fs.allowComposition(!FluidSystem::isIdealMixture(phaseIdx));
            try { auto tmpVal OPM_UNUSED = FluidSystem::fugacityCoefficient(fs, paramCache, phaseIdx, compIdx); static_assert(std::is_same<decltype(tmpVal), RhsEval>::value, "The default return value must be the scalar used by the fluid state!"); } catch (...) {};
            try { val = FluidSystem::template fugacityCoefficient<FluidState, LhsEval>(fs, paramCache, phaseIdx, compIdx); } catch (...) {};
            try { scalarVal = FluidSystem::template fugacityCoefficient<FluidState, Scalar>(fs, paramCache, phaseIdx, compIdx); } catch (...) {};
            fs.allowComposition(true);
            try { auto tmpVal OPM_UNUSED = FluidSystem::diffusionCoefficient(fs, paramCache, phaseIdx, compIdx); static_assert(std::is_same<decltype(tmpVal), RhsEval>::value, "The default return value must be the scalar used by the fluid state!"); } catch (...) {};
            try { val = FluidSystem::template diffusionCoefficient<FluidState, LhsEval>(fs, paramCache, phaseIdx, compIdx); } catch (...) {};
            try { scalarVal = FluidSystem::template fugacityCoefficient<FluidState, Scalar>(fs, paramCache, phaseIdx, compIdx); } catch (...) {};
        }
    }

    // test for phaseName(), isLiquid() and isIdealGas()
    for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++ phaseIdx) {
        std::string name OPM_UNUSED = FluidSystem::phaseName(phaseIdx);
        bool bVal = FluidSystem::isLiquid(phaseIdx);
        bVal = FluidSystem::isIdealGas(phaseIdx);
        bVal = !bVal; // get rid of GCC warning (only occurs with paranoid warning flags)
    }

    // test for molarMass() and componentName()
    for (unsigned compIdx = 0; compIdx < numComponents; ++ compIdx) {
        val = FluidSystem::molarMass(compIdx);
        std::string name = FluidSystem::componentName(compIdx);
    }

    std::cout << "----------------------------------\n";
}
    static Scalar linearize_(Dune::FieldMatrix<Evaluation, numComponents, numComponents> &J,
                             Dune::FieldVector<Evaluation, numComponents> &defect,
                             FluidState &fluidState,
                             ParameterCache &paramCache,
                             int phaseIdx,
                             const ComponentVector &targetFug)
    {
        typedef MathToolbox<Evaluation> Toolbox;

        // reset jacobian
        J = 0;

        Scalar absError = 0;
        // calculate the defect (deviation of the current fugacities
        // from the target fugacities)
        for (int i = 0; i < numComponents; ++ i) {
            const Evaluation& phi = FluidSystem::fugacityCoefficient(fluidState,
                                                          paramCache,
                                                          phaseIdx,
                                                          i);
            const Evaluation& f = phi*fluidState.pressure(phaseIdx)*fluidState.moleFraction(phaseIdx, i);
            fluidState.setFugacityCoefficient(phaseIdx, i, phi);

            defect[i] = targetFug[i] - f;
            absError = std::max(absError, std::abs(Toolbox::value(defect[i])));
        }

        // assemble jacobian matrix of the constraints for the composition
        static const Scalar eps = std::numeric_limits<Scalar>::epsilon()*1e6;
        for (int i = 0; i < numComponents; ++ i) {
            ////////
            // approximately calculate partial derivatives of the
            // fugacity defect of all components in regard to the mole
            // fraction of the i-th component. This is done via
            // forward differences

            // deviate the mole fraction of the i-th component
            Evaluation xI = fluidState.moleFraction(phaseIdx, i);
            fluidState.setMoleFraction(phaseIdx, i, xI + eps);
            paramCache.updateSingleMoleFraction(fluidState, phaseIdx, i);

            // compute new defect and derivative for all component
            // fugacities
            for (int j = 0; j < numComponents; ++j) {
                // compute the j-th component's fugacity coefficient ...
                const Evaluation& phi = FluidSystem::fugacityCoefficient(fluidState,
                                                                         paramCache,
                                                                         phaseIdx,
                                                                         j);
                // ... and its fugacity ...
                const Evaluation& f =
                    phi *
                    fluidState.pressure(phaseIdx) *
                    fluidState.moleFraction(phaseIdx, j);
                // as well as the defect for this fugacity
                const Evaluation& defJPlusEps = targetFug[j] - f;

                // use forward differences to calculate the defect's
                // derivative
                J[j][i] = (defJPlusEps - defect[j])/eps;
            }

            // reset composition to original value
            fluidState.setMoleFraction(phaseIdx, i, xI);
            paramCache.updateSingleMoleFraction(fluidState, phaseIdx, i);

            // end forward differences
            ////////
        }

        return absError;
    }