#include <array>
#include <cmath>
#include <limits>

#include <catch2/catch_test_macros.hpp>
#include <catch2/matchers/catch_matchers_floating_point.hpp>

import mean_field;
import test_helpers;

TEST_CASE("Polytropic EOS Satisfies Its Analytic Identities",
          tags::barotrope_eos_unit) {
  constexpr double polytropic_index = 3.0;
  constexpr double polytropic_constant = 1.5;

  const mean_field::eos::Polytrope barotrope(polytropic_index,
                                             polytropic_constant);

  const std::array<double, 5> densities{1.0e-6, 1.0e-3, 0.1, 0.7, 2.0};

  for (const double density : densities) {
    const double pressure = barotrope.pressure_from_density(density);

    const double enthalpy = barotrope.enthalpy_from_density(density);

    const double reconstructed_density =
        barotrope.density_from_enthalpy(enthalpy);

    const double reconstructed_pressure =
        barotrope.pressure_from_enthalpy(enthalpy);

    const double reconstructed_enthalpy =
        barotrope.enthalpy_from_pressure(pressure);

    CHECK_THAT(reconstructed_density,
               Catch::Matchers::WithinRel(density, 2.0e-14));

    CHECK_THAT(reconstructed_pressure,
               Catch::Matchers::WithinRel(pressure, 2.0e-14));

    CHECK_THAT(reconstructed_enthalpy,
               Catch::Matchers::WithinRel(enthalpy, 2.0e-14));

    CHECK_THAT(pressure,
               Catch::Matchers::WithinRel(
                   density * enthalpy / (polytropic_index + 1.0), 2.0e-14));

    CHECK_THAT(barotrope.pressure_derivative_from_enthalpy(enthalpy),
               Catch::Matchers::WithinRel(density, 2.0e-14));

    CHECK_THAT(
        barotrope.pressure_derivative_from_density(density),
        Catch::Matchers::WithinRel(enthalpy / polytropic_index, 2.0e-14));
  }
}

TEST_CASE("Polytropic EOS Derivatives Match Centered Differences",
          tags::barotrope_eos_jacobian) {
  const mean_field::eos::Polytrope barotrope(3.0, 1.5);

  const std::array<double, 4> enthalpies{0.05, 0.2, 0.7, 1.4};

  for (const double enthalpy : enthalpies) {
    const double step = 1.0e-6 * std::max(1.0, enthalpy);

    const double density_difference =
        (barotrope.density_from_enthalpy(enthalpy + step) -
         barotrope.density_from_enthalpy(enthalpy - step)) /
        (2.0 * step);

    const double pressure_difference =
        (barotrope.pressure_from_enthalpy(enthalpy + step) -
         barotrope.pressure_from_enthalpy(enthalpy - step)) /
        (2.0 * step);

    CHECK_THAT(
        density_difference,
        Catch::Matchers::WithinRel(
            barotrope.density_derivative_from_enthalpy(enthalpy), 5.0e-10));

    CHECK_THAT(
        pressure_difference,
        Catch::Matchers::WithinRel(
            barotrope.pressure_derivative_from_enthalpy(enthalpy), 5.0e-10));
  }
}

TEST_CASE("Polytropic EOS Has An Exact Zero Density Surface",
          tags::barotrope_eos_unit) {
  const mean_field::eos::Polytrope barotrope(3.0, 1.5);

  CHECK(barotrope.density_from_enthalpy(-1.0) == 0.0);
  CHECK(barotrope.density_from_enthalpy(0.0) == 0.0);

  CHECK(barotrope.pressure_from_enthalpy(-1.0) == 0.0);
  CHECK(barotrope.pressure_from_enthalpy(0.0) == 0.0);

  CHECK(barotrope.density_derivative_from_enthalpy(-1.0) == 0.0);

  CHECK(barotrope.density_derivative_from_enthalpy(0.0) == 0.0);

  CHECK(barotrope.pressure_derivative_from_enthalpy(0.0) == 0.0);
}

TEST_CASE("Polytropic EOS Rejects Invalid Material Parameters",
          tags::barotrope_eos_unit) {
  CHECK_THROWS_AS(mean_field::eos::Polytrope(0.5, 1.0), std::invalid_argument);

  CHECK_THROWS_AS(mean_field::eos::Polytrope(3.0, 0.0), std::invalid_argument);

  CHECK_THROWS_AS(
      mean_field::eos::Polytrope(std::numeric_limits<double>::infinity(), 1.0),
      std::invalid_argument);

  const mean_field::eos::Polytrope barotrope(3.0, 1.0);

  CHECK_THROWS_AS(barotrope.pressure_from_density(-1.0), std::domain_error);

  CHECK_THROWS_AS(barotrope.enthalpy_from_density(-1.0), std::domain_error);

  CHECK_THROWS_AS(barotrope.enthalpy_from_pressure(-1.0), std::domain_error);
}