#include <cmath>
#include <print>

#include "serif/eos/evaluation.hpp"
#include "serif/eos/models/polytropic.hpp"
#include "serif/equations/barotropic_density.hpp"
#include "serif/equations/surface_potential.hpp"

/** @brief Evaluate manufactured interior and surface samples and inspect their exact derivatives. */
int main() {
    namespace equations = serif::equations;
    namespace dimensions = serif::dimensions;

    const serif::eos::models::Polytrope eos{1.0, 0.8};
    const double density = 0.5, angular_velocity = 0.3, surface_level = 1.2;
    const dimensions::PressureValue surface_pressure{0.0};
    const equations::BarotropicDensityBalance density_balance{eos, surface_pressure};
    const equations::SurfacePotentialBalance surface;
    using Balance = decltype(density_balance);

    // Density supplies the pressure potential through the EOS; it is not another solved field.
    const auto surface_density = serif::eos::evaluate<dimensions::MassDensity>(eos, surface_pressure);
    const double pressure_potential = serif::eos::evaluate<dimensions::BarotropicPressurePotential>(eos, dimensions::DensityValue{density}).value();
    const double surface_pressure_potential = serif::eos::evaluate<dimensions::BarotropicPressurePotential>(eos, surface_density).value();
    equations::EquationPoint<Balance::Operands> mechanics;
    mechanics.position = {0.3, 0.4, 0.0};
    mechanics.fields.get<Balance::Density>() = density;
    mechanics.fields.get<Balance::AngularVelocity>() = angular_velocity;
    mechanics.fields.get<Balance::SurfaceLevel>() = surface_level;
    mechanics.fields.get<Balance::Potential>() = surface_level - pressure_potential + surface_pressure_potential +
        angular_velocity * angular_velocity * density_balance.rotation().centrifugal_potential(mechanics.position);
    const auto interior_balance = density_balance.evaluate(mechanics);

    equations::EquationPoint<decltype(surface)::Operands> boundary;
    boundary.position = mechanics.position;
    boundary.fields.get<decltype(surface)::Potential>() = surface_level +
        angular_velocity * angular_velocity * surface.rotation().centrifugal_potential(boundary.position);
    boundary.fields.get<decltype(surface)::SurfaceLevel>() = surface_level;
    boundary.fields.get<decltype(surface)::AngularVelocity>() = angular_velocity;
    const auto surface_balance = surface.evaluate(boundary);

    std::println("Density balance residual = {:.3e}; angular-velocity derivative = {}",
        interior_balance.residual, interior_balance.field_derivatives.get<Balance::AngularVelocity>());
    std::println("Surface potential residual = {:.3e}; derivative with respect to surface level = {}",
        surface_balance.residual, surface_balance.field_derivatives.get<decltype(surface)::SurfaceLevel>());
    // complete_sandbox assembles these same physical equations on its finite-element mesh.
    return std::abs(interior_balance.residual) < 1.0e-12 && std::abs(surface_balance.residual) < 1.0e-12 ? 0 : 1;
}