module;
#include "profile.h"
#include <cmath>
#include <cstdint>
#include <limits>
#include <mfem.hpp>

module mean_field;
import :operators.gravity_field;
import :solver.fields;
import :operators.kernels.gravity_field;

namespace {
    using namespace mean_field;
    using DomainSchema = utils::domain::CoreEnvelopeVacuumDomainSchema;
    int get_state_width(const mfem::Array<int> &state_offsets) {
        MFEM_VERIFY(state_offsets.Size() >= 2, "The coupled state requires at least one block.");
        MFEM_VERIFY(state_offsets[0] == 0, "The coupled state offsets must begin at zero.");

        for (int i = 0; i < state_offsets.Size() - 1; ++i) {
            MFEM_VERIFY(state_offsets[i + 1] >= state_offsets[i], "The coupled state offsets must be nondecreasing.");
        }

        MFEM_VERIFY(state_offsets.Last() > 0, "The coupled state cannot be empty.");
        return state_offsets.Last();
    }

    int get_gravity_residual_height(const fem::FEM &f) {
        MFEM_VERIFY(
            f.gravityFluxFes != nullptr, "GravityFieldOperator requires the gravity-gradient finite-element "
                                         "space (RT: Raviart-Thomas)."
        );
        MFEM_VERIFY(
            f.gravityPotentialFes != nullptr, "GravityFieldOperator requires the gravity-potential "
                                              "finite-element "
                                              "space (L2: Lebesgue "
                                              "space of square-integrable functions)."
        );
        using DomainSchema = utils::domain::CoreEnvelopeVacuumDomainSchema;
        return field::make_field_dof_map<field::Gravity, DomainSchema>(*f.gravityFluxFes).reduced_size() +
               field::make_field_dof_map<field::Gravity, DomainSchema>(*f.gravityPotentialFes).reduced_size();
    }

    mfem::Array<int> make_gravity_residual_offsets(const fem::FEM &f) {
        mfem::Array<int> offsets(utils::blocks::gravity_field_form::residual_block_count + 1);
        offsets[0]         = 0;
        using DomainSchema = utils::domain::CoreEnvelopeVacuumDomainSchema;
        offsets[1]         = field::make_field_dof_map<field::Gravity, DomainSchema>(*f.gravityFluxFes).reduced_size();
        offsets[2] =
            offsets[1] + field::make_field_dof_map<field::Gravity, DomainSchema>(*f.gravityPotentialFes).reduced_size();
        return offsets;
    }

    template <int index>
    int get_state_block_size(
        const mfem::Array<int> &state_offsets,
        const utils::blocks::value_block<index>
    ) {
        MFEM_VERIFY(index + 1 < state_offsets.Size(), "Value block is not present in the state offsets.");
        return state_offsets[index + 1] - state_offsets[index];
    }

    void validate_state_offsets(
        const fem::FEM &f,
        const mfem::Array<int> &state_offsets
    ) {
        MFEM_VERIFY(f.densityFes != nullptr, "GravityFieldOperator requires the density finite-element space.");
        MFEM_VERIFY(
            f.displacementFes != nullptr, "GravityFieldOperator requires the "
                                          "displacement finite-element space."
        );

        using form                   = utils::blocks::gravity_field_form;

        constexpr auto density_block = utils::blocks::get_value_block<form>(utils::blocks::density_field.mass_term);
        constexpr auto displacement_block =
            utils::blocks::get_value_block<form>(utils::blocks::displacement_field.geometry_term);
        constexpr auto gravity_gradient_block =
            utils::blocks::get_value_block<form>(utils::blocks::gravity_field.gradient_term);
        constexpr auto gravity_potential_block =
            utils::blocks::get_value_block<form>(utils::blocks::gravity_field.poisson_term);

        MFEM_VERIFY(
            state_offsets.Size() == form::value_block_count + 1,
            "The gravity state offsets do not match gravity_field_form."
        );
        using DomainSchema          = utils::domain::CoreEnvelopeVacuumDomainSchema;
        const auto density_map      = field::make_field_dof_map<field::Density, DomainSchema>(*f.densityFes);
        const auto displacement_map = field::make_field_dof_map<field::Displacement, DomainSchema>(*f.displacementFes);
        const auto flux_map         = field::make_field_dof_map<field::Gravity, DomainSchema>(*f.gravityFluxFes);
        const auto potential_map    = field::make_field_dof_map<field::Gravity, DomainSchema>(*f.gravityPotentialFes);

        MFEM_VERIFY(
            get_state_block_size(state_offsets, density_block) == density_map.reduced_size(),
            "The density block does not match the density finite-element space."
        );
        MFEM_VERIFY(
            get_state_block_size(state_offsets, displacement_block) == displacement_map.reduced_size(),
            "The displacement block does not match the displacement "
            "finite-element "
            "space."
        );
        MFEM_VERIFY(
            get_state_block_size(state_offsets, gravity_gradient_block) == flux_map.reduced_size(),
            "The gravity-gradient block does not match the RT finite-element "
            "space."
        );
        MFEM_VERIFY(
            get_state_block_size(state_offsets, gravity_potential_block) == potential_map.reduced_size(),
            "The gravity-potential block does not match the potential "
            "finite-element space."
        );
    }

    void validate_gravity_context(const fem::FEM &f) {
        MFEM_VERIFY(f.quadratureFactory != nullptr, "GravityFieldOperator requires the quadrature-rule factory.");
    }

    [[nodiscard]] std::unique_ptr<mfem::HypreParMatrix> make_gravity_schur_preconditioner(
        const fem::FEM &f,
        const mfem::Vector &mass_diagonal
    ) {
        MFEM_VERIFY(
            mass_diagonal.Size() == f.gravityFluxFes->GetTrueVSize(),
            "The gravity Schur preconditioner requires a full "
            "gravity-gradient mass diagonal."
        );

        mfem::Vector inverse_mass_diagonal(mass_diagonal);

        for (int i = 0; i < inverse_mass_diagonal.Size(); ++i) {
            MFEM_VERIFY(
                std::isfinite(inverse_mass_diagonal(i)) && inverse_mass_diagonal(i) > 0.0,
                "The gravity Schur preconditioner encountered a non-positive "
                "or non-finite mass diagonal."
            );
            inverse_mass_diagonal(i) = 1.0 / inverse_mass_diagonal(i);
        }

        mfem::ParMixedBilinearForm divergence(f.gravityFluxFes.get(), f.gravityPotentialFes.get());
        auto integrator                                   = std::make_unique<mfem::VectorFEDivergenceIntegrator>();

        const mfem::FiniteElement &trial_element          = *f.gravityFluxFes->GetTypicalFE();
        const mfem::FiniteElement &test_element           = *f.gravityPotentialFes->GetTypicalFE();
        const mfem::ElementTransformation &transformation = *f.mesh->GetElementTransformation(0);

        f.quadratureFactory->configure_gravity_divergence(
            *integrator, quadrature::QuadratureRole::preconditioner, trial_element, test_element, transformation,
            utils::DOMAINS::ALL, quadrature::MappingKind::none
        );

        divergence.AddDomainIntegrator(integrator.release());
        divergence.Assemble();
        divergence.Finalize();

        std::unique_ptr<mfem::HypreParMatrix> divergence_matrix(divergence.ParallelAssemble());
        std::unique_ptr<mfem::HypreParMatrix> inverse_mass_divergence_transpose(divergence_matrix->Transpose());
        inverse_mass_divergence_transpose->ScaleRows(inverse_mass_diagonal);

        return std::unique_ptr<mfem::HypreParMatrix>(
            mfem::ParMult(divergence_matrix.get(), inverse_mass_divergence_transpose.get())
        );
    }

    template <int index>
    mfem::Vector make_read_only_value_view(
        const mfem::Vector &vector,
        const mfem::Array<int> &offsets,
        const utils::blocks::value_block<index>
    ) {
        MFEM_VERIFY(index + 1 < offsets.Size(), "Value block is not present in the supplied offset array.");

        const int begin = offsets[index];
        const int size  = offsets[index + 1] - begin;

        MFEM_VERIFY(vector.Size() == offsets.Last(), "Vector size does not match the value-block offsets.");
        return mfem::Vector(const_cast<mfem::real_t *>(vector.GetData()) + begin, size);
    }

    template <int index>
    mfem::Vector make_read_only_residual_view(
        const mfem::Vector &vector,
        const mfem::Array<int> &offsets,
        const utils::blocks::residual_block<index> block
    ) {
        const int block_id = block;
        const int begin    = offsets[block_id];
        const int size     = offsets[block_id + 1] - begin;

        MFEM_VERIFY(vector.Size() == offsets.Last(), "The vector does not match the residual-block layout.");

        mfem::Vector view;
        view.MakeRef(const_cast<mfem::Vector &>(vector), begin, size);
        return view;
    }

    template <int index>
    mfem::Vector make_residual_view(
        mfem::Vector &vector,
        const mfem::Array<int> &offsets,
        const utils::blocks::residual_block<index>
    ) {
        MFEM_VERIFY(index + 1 < offsets.Size(), "Residual block is not present in the supplied offset array.");

        const int begin = offsets[index];
        const int size  = offsets[index + 1] - begin;

        MFEM_VERIFY(vector.Size() == offsets.Last(), "Vector size does not match the residual-block offsets.");
        return mfem::Vector(vector.GetData() + begin, size);
    }
} // namespace

namespace mean_field::operators {
    GravityFieldOperator::GravityFieldOperator(
        fem::FEM &f,
        const mapping::DomainMapper &domain_mapper,
        context::gravity_field::GravityFieldLinearizationContext &linearization_context,
        const mfem::Array<int> &state_offsets,
        GravityFieldJacobianOperator &jacobian
    )
        : Operator(
              get_gravity_residual_height(f),
              get_state_width(state_offsets)
          ),
          m_fem(f),
          m_domain_mapper(domain_mapper),
          m_linearization_context(linearization_context),
          m_state_offsets(state_offsets),
          m_residual_offsets(make_gravity_residual_offsets(f)),
          m_jacobian(jacobian) {
        MFEM_VERIFY(f.mesh != nullptr, "GravityFieldOperator requires a mesh.");
        MFEM_VERIFY(
            f.displacementFes != nullptr, "GravityFieldOperator requires the "
                                          "displacement finite-element space."
        );
        MFEM_VERIFY(
            f.smesh.exterior_coordinate != nullptr, "GravityFieldOperator requires the STROID exterior coordinate."
        );
        MFEM_VERIFY(
            f.smesh.exterior_coordinate->space != nullptr, "GravityFieldOperator requires the exterior-coordinate "
                                                           "finite-element "
                                                           "space."
        );
        MFEM_VERIFY(
            f.smesh.exterior_coordinate->values != nullptr,
            "GravityFieldOperator requires the exterior-coordinate values."
        );
        MFEM_VERIFY(
            domain_mapper.GetDimension() == f.mesh->Dimension(),
            "GravityFieldOperator received a domain mapper with the wrong "
            "dimension."
        );

        validate_state_offsets(f, m_state_offsets);
        validate_gravity_context(f);

        bool has_vacuum_domain = false;

        for (int i = 0; i < f.mesh->attributes.Size(); ++i) {
            if (DomainSchema::template attribute_belongs_to<utils::domain::Vacuum>(f.mesh->attributes[i])) {
                has_vacuum_domain = true;
                break;
            }
        }

        MFEM_VERIFY(has_vacuum_domain, "GravityFieldOperator requires a compactified vacuum domain.");
        MFEM_VERIFY(
            m_residual_offsets.Last() == Height(), "The gravity residual offsets do not match the operator height."
        );
        MFEM_VERIFY(m_state_offsets.Last() == Width(), "The coupled state offsets do not match the operator width.");
    }

    context::gravity_field::GravityFieldPreparationReport GravityFieldOperator::Prepare(
        const mfem::Vector &state,
        const context::gravity_field::GravityFieldRevisions &revisions
    ) {
        using form                   = utils::blocks::gravity_field_form;

        constexpr auto density_block = utils::blocks::get_value_block<form>(utils::blocks::density_field.mass_term);
        constexpr auto displacement_block =
            utils::blocks::get_value_block<form>(utils::blocks::displacement_field.geometry_term);
        constexpr auto gravity_gradient_block =
            utils::blocks::get_value_block<form>(utils::blocks::gravity_field.gradient_term);
        constexpr auto gravity_potential_block =
            utils::blocks::get_value_block<form>(utils::blocks::gravity_field.poisson_term);

        MFEM_VERIFY(
            state.Size() == Width(), "GravityFieldOperator received a "
                                     "preparation state with the wrong size."
        );

        const mfem::Vector density          = make_read_only_value_view(state, m_state_offsets, density_block);
        const mfem::Vector displacement     = make_read_only_value_view(state, m_state_offsets, displacement_block);
        const mfem::Vector gravity_gradient = make_read_only_value_view(state, m_state_offsets, gravity_gradient_block);
        const mfem::Vector gravity_potential =
            make_read_only_value_view(state, m_state_offsets, gravity_potential_block);

        return m_linearization_context.Prepare(
            {.density           = density,
             .displacement      = displacement,
             .gravity_gradient  = gravity_gradient,
             .gravity_potential = gravity_potential},
            revisions
        );
    }

    const mfem::Array<int> &GravityFieldOperator::GetStateOffsets() const noexcept {
        return m_state_offsets;
    }

    const mfem::Array<int> &GravityFieldOperator::GetResidualOffsets() const noexcept {
        return m_residual_offsets;
    }

    void GravityFieldOperator::ApplyGravityUnknowns(
        const mfem::Vector &gravity_gradient,
        const mfem::Vector &gravity_potential,
        const context::gravity_field::GravityFieldGeometryContext &geometry_context,
        mfem::Vector &action
    ) const {
        using form = utils::blocks::gravity_field_form;

        constexpr auto gravity_gradient_residual_block =
            utils::blocks::get_residual_block<form>(utils::blocks::gravity_field.gradient_term);
        constexpr auto gravity_poisson_residual_block =
            utils::blocks::get_residual_block<form>(utils::blocks::gravity_field.poisson_term);

        MFEM_VERIFY(geometry_context.IsPrepared(), "GravityFieldOperator received an unprepared geometry context.");
        MFEM_VERIFY(
            gravity_gradient.Size() == geometry_context.GetMassOperator().GetFluxMap().reduced_size(),
            "GravityFieldOperator received a gravity-gradient vector with the "
            "wrong size."
        );
        MFEM_VERIFY(
            gravity_potential.Size() == geometry_context.GetSourceOperator().GetPotentialMap().reduced_size(),
            "GravityFieldOperator received a gravity-potential vector with the "
            "wrong size."
        );

        action.SetSize(Height());
        action = 0.0;

        mfem::Vector gravity_gradient_action =
            make_residual_view(action, m_residual_offsets, gravity_gradient_residual_block);
        mfem::Vector gravity_poisson_action =
            make_residual_view(action, m_residual_offsets, gravity_poisson_residual_block);
        const field::FieldDofMap &flux_map      = geometry_context.GetMassOperator().GetFluxMap();
        const field::FieldDofMap &potential_map = geometry_context.GetSourceOperator().GetPotentialMap();
        mfem::Vector potential_true(potential_map.full_size());
        mfem::Vector transpose_divergence_action_true(flux_map.full_size());
        mfem::Vector transpose_divergence_action(flux_map.reduced_size());
        mfem::Vector gradient_true(flux_map.full_size());
        mfem::Vector divergence_action_true(potential_map.full_size());

        geometry_context.GetMassOperator().Mult(gravity_gradient, gravity_gradient_action);
        potential_map.scatter(gravity_potential, potential_true);
        geometry_context.GetTransposeDivergenceOperator().Mult(potential_true, transpose_divergence_action_true);
        flux_map.gather(transpose_divergence_action_true, transpose_divergence_action);
        gravity_gradient_action += transpose_divergence_action;
        flux_map.scatter(gravity_gradient, gradient_true);
        geometry_context.GetDivergenceOperator().Mult(gradient_true, divergence_action_true);
        potential_map.gather(divergence_action_true, gravity_poisson_action);
    }

    void GravityFieldOperator::ApplyDensitySource(
        const mfem::Vector &density,
        const context::gravity_field::GravityFieldGeometryContext &geometry_context,
        mfem::Vector &action
    ) const {
        using form = utils::blocks::gravity_field_form;

        constexpr auto gravity_poisson_residual_block =
            utils::blocks::get_residual_block<form>(utils::blocks::gravity_field.poisson_term);

        MFEM_VERIFY(geometry_context.IsPrepared(), "GravityFieldOperator received an unprepared geometry context.");
        MFEM_VERIFY(
            density.Size() == geometry_context.GetSourceOperator().GetDensityMap().reduced_size(),
            "GravityFieldOperator received a density vector with the wrong "
            "size."
        );

        action.SetSize(Height());
        action = 0.0;

        mfem::Vector gravity_poisson_action =
            make_residual_view(action, m_residual_offsets, gravity_poisson_residual_block);
        geometry_context.GetSourceOperator().Mult(density, gravity_poisson_action);
    }

    void GravityFieldOperator::Mult(
        const mfem::Vector &state,
        mfem::Vector &residual
    ) const {
        MEAN_FIELD_PROFILE_SCOPE("GravityFieldOperator::Mult");

        using form                   = utils::blocks::gravity_field_form;

        constexpr auto density_block = utils::blocks::get_value_block<form>(utils::blocks::density_field.mass_term);
        constexpr auto gravity_gradient_block =
            utils::blocks::get_value_block<form>(utils::blocks::gravity_field.gradient_term);
        constexpr auto gravity_potential_block =
            utils::blocks::get_value_block<form>(utils::blocks::gravity_field.poisson_term);

        MFEM_VERIFY(state.Size() == Width(), "GravityFieldOperator received a state with the wrong size.");
        MFEM_VERIFY(
            m_linearization_context.IsPrepared(), "GravityFieldOperator must be prepared before Mult is called."
        );

        const mfem::Vector density          = make_read_only_value_view(state, m_state_offsets, density_block);
        const mfem::Vector gravity_gradient = make_read_only_value_view(state, m_state_offsets, gravity_gradient_block);
        const mfem::Vector gravity_potential =
            make_read_only_value_view(state, m_state_offsets, gravity_potential_block);
        const context::gravity_field::GravityFieldGeometryContext &geometry_context =
            m_linearization_context.GetGeometryContext();

        mfem::Vector source;

        ApplyGravityUnknowns(gravity_gradient, gravity_potential, geometry_context, residual);
        ApplyDensitySource(density, geometry_context, source);

        residual -= source;
    }

    context::gravity_field::GravityFieldLinearizationContext &GravityFieldOperator::GetLinearizationContext() noexcept {
        return m_linearization_context;
    }

    const context::gravity_field::GravityFieldLinearizationContext &
    GravityFieldOperator::GetLinearizationContext() const noexcept {
        return m_linearization_context;
    }

    mfem::Operator &GravityFieldOperator::GetGradient(const mfem::Vector &state) const {
        MFEM_VERIFY(
            state.Size() == Width(), "GravityFieldOperator received a "
                                     "linearization state with the wrong size."
        );
        MFEM_VERIFY(
            m_linearization_context.IsPrepared(), "GravityFieldOperator must be prepared before GetGradient is "
                                                  "called."
        );

        return m_jacobian;
    }
    ReducedGravityFieldOperator::ReducedGravityFieldOperator(
        GravityFieldOperator &gravity_field_operator,
        context::gravity_field::GravityFieldGeometryContext &gravity_field_geometry_context,
        const mfem::Vector &displacement
    )
        : Operator(
              gravity_field_operator.Height(),
              gravity_field_operator.Height()
          ),
          m_gravity_field_operator(gravity_field_operator),
          m_gravity_offsets(gravity_field_operator.GetResidualOffsets()),
          m_gravity_field_geometry_context(gravity_field_geometry_context) {
        using form = utils::blocks::gravity_field_form;

        constexpr auto gravity_gradient_block =
            utils::blocks::get_value_block<form>(utils::blocks::gravity_field.gradient_term);
        constexpr auto gravity_potential_block =
            utils::blocks::get_value_block<form>(utils::blocks::gravity_field.poisson_term);
        constexpr auto gravity_gradient_residual_block =
            utils::blocks::get_residual_block<form>(utils::blocks::gravity_field.gradient_term);
        constexpr auto gravity_poisson_residual_block =
            utils::blocks::get_residual_block<form>(utils::blocks::gravity_field.poisson_term);

        const mfem::Array<int> &state_offsets = m_gravity_field_operator.GetStateOffsets();

        MFEM_VERIFY(
            state_offsets.Size() == form::value_block_count + 1,
            "ReducedGravityFieldOperator received an invalid coupled-state layout."
        );
        MFEM_VERIFY(
            m_gravity_offsets.Size() == form::residual_block_count + 1,
            "ReducedGravityFieldOperator received an invalid gravity-residual "
            "layout."
        );
        MFEM_VERIFY(state_offsets[0] == 0, "The coupled-state offsets must begin at zero.");
        MFEM_VERIFY(m_gravity_offsets[0] == 0, "The reduced gravity offsets must begin at zero.");
        MFEM_VERIFY(
            state_offsets.Last() == m_gravity_field_operator.Width(),
            "The coupled-state offsets do not match the gravity-field operator "
            "width."
        );
        MFEM_VERIFY(
            m_gravity_offsets.Last() == m_gravity_field_operator.Height(),
            "The reduced gravity offsets do not match the gravity-field "
            "operator "
            "height."
        );
        MFEM_VERIFY(Width() == Height(), "ReducedGravityFieldOperator must be square.");

        const int state_gradient_size =
            state_offsets[static_cast<int>(gravity_gradient_block) + 1] - state_offsets[gravity_gradient_block];
        const int state_potential_size =
            state_offsets[static_cast<int>(gravity_potential_block) + 1] - state_offsets[gravity_potential_block];
        const int gravity_gradient_size  = m_gravity_offsets[static_cast<int>(gravity_gradient_residual_block) + 1] -
                                           m_gravity_offsets[gravity_gradient_residual_block];
        const int gravity_potential_size = m_gravity_offsets[static_cast<int>(gravity_poisson_residual_block) + 1] -
                                           m_gravity_offsets[gravity_poisson_residual_block];

        MFEM_VERIFY(
            state_gradient_size == gravity_gradient_size, "The gravity-gradient block does not match the coupled-state "
                                                          "gravity-gradient block."
        );
        MFEM_VERIFY(
            state_potential_size == gravity_potential_size, "The gravity-potential block does not match the Poisson "
                                                            "residual block."
        );

        SetDisplacement(displacement);
    }

    void ReducedGravityFieldOperator::SetDisplacement(const mfem::Vector &displacement) {
        ValidateDisplacement(displacement);

        context::gravity_field::DiscretizationRevision discretization_revision;
        context::gravity_field::DisplacementRevision displacement_revision;

        if (m_gravity_field_geometry_context.IsPrepared()) {
            discretization_revision = m_gravity_field_geometry_context.GetDiscretizationRevision();
            displacement_revision   = m_gravity_field_geometry_context.GetDisplacementRevision();

            MFEM_VERIFY(
                displacement_revision.value < std::numeric_limits<std::uint64_t>::max(),
                "The reduced gravity displacement revision has overflowed."
            );
            ++displacement_revision.value;
        }

        m_gravity_field_geometry_context.Prepare(displacement, discretization_revision, displacement_revision);
        m_displacement = displacement;
    }

    const mfem::Vector &ReducedGravityFieldOperator::GetDisplacement() const {
        return m_displacement;
    }

    void ReducedGravityFieldOperator::BuildRightHandSide(
        const mfem::Vector &density,
        mfem::Vector &right_hand_side
    ) const {
        ValidateDensity(density);

        m_gravity_field_operator.ApplyDensitySource(density, m_gravity_field_geometry_context, right_hand_side);

        MFEM_VERIFY(
            right_hand_side.Size() == Height(), "ReducedGravityFieldOperator produced a right-hand side with the "
                                                "wrong "
                                                "size."
        );
    }

    void ReducedGravityFieldOperator::Mult(
        const mfem::Vector &gravity_state,
        mfem::Vector &action
    ) const {
        MEAN_FIELD_PROFILE_SCOPE("ReducedGravityFieldOperator::Mult");

        using form = utils::blocks::gravity_field_form;

        constexpr auto gravity_gradient_residual_block =
            utils::blocks::get_residual_block<form>(utils::blocks::gravity_field.gradient_term);
        constexpr auto gravity_poisson_residual_block =
            utils::blocks::get_residual_block<form>(utils::blocks::gravity_field.poisson_term);

        ValidateGravityState(gravity_state);

        const mfem::Vector gravity_gradient =
            make_read_only_residual_view(gravity_state, m_gravity_offsets, gravity_gradient_residual_block);
        const mfem::Vector gravity_potential =
            make_read_only_residual_view(gravity_state, m_gravity_offsets, gravity_poisson_residual_block);

        m_gravity_field_operator.ApplyGravityUnknowns(
            gravity_gradient, gravity_potential, m_gravity_field_geometry_context, action
        );

        MFEM_VERIFY(
            action.Size() == Height(), "ReducedGravityFieldOperator produced "
                                       "an action with the wrong size."
        );
    }

    GravityFieldOperator &ReducedGravityFieldOperator::GetGravityFieldOperator() noexcept {
        return m_gravity_field_operator;
    }

    const GravityFieldOperator &ReducedGravityFieldOperator::GetGravityFieldOperator() const noexcept {
        return m_gravity_field_operator;
    }

    context::gravity_field::GravityFieldGeometryContext &ReducedGravityFieldOperator::GetGeometryContext() noexcept {
        return m_gravity_field_geometry_context;
    }

    const context::gravity_field::GravityFieldGeometryContext &
    ReducedGravityFieldOperator::GetGeometryContext() const noexcept {
        return m_gravity_field_geometry_context;
    }

    const mfem::Array<int> &ReducedGravityFieldOperator::GetGravityOffsets() const noexcept {
        return m_gravity_offsets;
    }

    void ReducedGravityFieldOperator::ValidateDisplacement(const mfem::Vector &displacement) const {
        using form = utils::blocks::gravity_field_form;

        constexpr auto displacement_block =
            utils::blocks::get_value_block<form>(utils::blocks::displacement_field.geometry_term);

        const mfem::Array<int> &state_offsets = m_gravity_field_operator.GetStateOffsets();
        const int expected_size =
            state_offsets[static_cast<int>(displacement_block) + 1] - state_offsets[displacement_block];

        MFEM_VERIFY(
            displacement.Size() == expected_size, "ReducedGravityFieldOperator received a displacement with the "
                                                  "wrong "
                                                  "size."
        );

        for (int i = 0; i < displacement.Size(); ++i) {
            MFEM_VERIFY(
                std::isfinite(displacement(i)), "ReducedGravityFieldOperator received a non-finite "
                                                "displacement "
                                                "value."
            );
        }
    }

    void ReducedGravityFieldOperator::ValidateDensity(const mfem::Vector &density) const {
        using form                   = utils::blocks::gravity_field_form;

        constexpr auto density_block = utils::blocks::get_value_block<form>(utils::blocks::density_field.mass_term);

        const mfem::Array<int> &state_offsets = m_gravity_field_operator.GetStateOffsets();
        const int expected_size = state_offsets[static_cast<int>(density_block) + 1] - state_offsets[density_block];

        MFEM_VERIFY(
            density.Size() == expected_size, "ReducedGravityFieldOperator received a density with the wrong "
                                             "size."
        );
    }

    void ReducedGravityFieldOperator::ValidateGravityState(const mfem::Vector &gravity_state) const {
        MFEM_VERIFY(
            gravity_state.Size() == Width(), "ReducedGravityFieldOperator received "
                                             "a gravity state with the wrong size."
        );
    }

    ReducedGravityFieldPreconditioner::ReducedGravityFieldPreconditioner(
        const fem::FEM &f,
        const context::gravity_field::GravityFieldGeometryContext &geometry_context
    )
        : Solver(
              geometry_context.GetMassOperator().GetFluxMap().reduced_size() +
              geometry_context.GetSourceOperator().GetPotentialMap().reduced_size()
          ),
          m_flux_map(geometry_context.GetMassOperator().GetFluxMap()),
          m_potential_map(geometry_context.GetSourceOperator().GetPotentialMap()),
          m_offsets(3) {
        MFEM_VERIFY(geometry_context.IsPrepared(), "The reduced gravity preconditioner requires prepared geometry.");
        MFEM_VERIFY(f.mesh != nullptr, "The reduced gravity preconditioner requires a parallel mesh.");
        MFEM_VERIFY(
            f.gravityFluxFes != nullptr && f.gravityPotentialFes != nullptr,
            "The reduced gravity preconditioner requires both gravity "
            "finite-element spaces."
        );
        MFEM_VERIFY(
            f.quadratureFactory != nullptr, "The reduced gravity preconditioner requires the quadrature-rule "
                                            "factory."
        );

        m_offsets[0] = 0;
        m_offsets[1] = m_flux_map.reduced_size();
        m_offsets[2] = m_offsets[1] + m_potential_map.reduced_size();

        MFEM_VERIFY(m_offsets.Last() == Height(), "The reduced gravity preconditioner has inconsistent offsets.");

        mfem::Vector reduced_mass_diagonal;
        geometry_context.GetMassOperator().AssembleDiagonal(reduced_mass_diagonal);
        m_mass_preconditioner = std::make_unique<mfem::OperatorJacobiSmoother>(reduced_mass_diagonal, m_empty_tdofs);

        mfem::Vector true_mass_diagonal;
        geometry_context.GetMassOperator().AssembleTrueDiagonal(true_mass_diagonal);
        m_schur                    = make_gravity_schur_preconditioner(f, true_mass_diagonal);

        m_potential_preconditioner = std::make_unique<mfem::HypreBoomerAMG>();
        m_potential_preconditioner->SetPrintLevel(0);
        m_potential_preconditioner->SetOperator(*m_schur);
    }

    void ReducedGravityFieldPreconditioner::SetOperator(const mfem::Operator &gravity_operator) {
        MFEM_VERIFY(
            gravity_operator.Width() == Width() && gravity_operator.Height() == Height(),
            "The reduced gravity preconditioner received an operator with "
            "incompatible dimensions."
        );
    }

    void ReducedGravityFieldPreconditioner::Mult(
        const mfem::Vector &right_hand_side,
        mfem::Vector &action
    ) const {
        MFEM_VERIFY(
            right_hand_side.Size() == Width(), "The reduced gravity preconditioner received a right-hand side "
                                               "with the wrong size."
        );

        mfem::Vector gradient_rhs;
        gradient_rhs.MakeRef(const_cast<mfem::Vector &>(right_hand_side), m_offsets[0], m_offsets[1] - m_offsets[0]);
        mfem::Vector potential_rhs;
        potential_rhs.MakeRef(const_cast<mfem::Vector &>(right_hand_side), m_offsets[1], m_offsets[2] - m_offsets[1]);

        action.SetSize(Height());
        mfem::Vector gradient_action;
        gradient_action.MakeRef(action, m_offsets[0], m_offsets[1] - m_offsets[0]);
        mfem::Vector potential_action;
        potential_action.MakeRef(action, m_offsets[1], m_offsets[2] - m_offsets[1]);

        m_mass_preconditioner->Mult(gradient_rhs, gradient_action);

        m_potential_rhs_true.SetSize(m_potential_map.full_size());
        m_potential_action_true.SetSize(m_potential_map.full_size());
        m_potential_map.scatter(potential_rhs, m_potential_rhs_true);
        m_potential_preconditioner->Mult(m_potential_rhs_true, m_potential_action_true);
        m_potential_map.gather(m_potential_action_true, potential_action);
    }

    const mfem::Array<int> &ReducedGravityFieldPreconditioner::GetOffsets() const noexcept {
        return m_offsets;
    }
} // namespace mean_field::operators