#include "fesa/elements/thermal_shell.h"

#include <gtest/gtest.h>

#include <algorithm>
#include <array>
#include <cmath>
#include <limits>
#include <numeric>

namespace {
using fesa::Matrix;
using fesa::Vector3;
using Patch = std::array<Vector3, 4>;
const Patch kSquare{{{0, 0, 0}, {1, 0, 0}, {1, 1, 0}, {0, 1, 0}}};

double Gamma(int operations) {
  const double product = operations * std::ldexp(1., -53);
  return product / (1 - product);
}
double Norm(const Matrix& matrix) {
  double norm = 0;
  for (std::size_t i = 0; i < matrix.Rows(); ++i)
    for (std::size_t j = 0; j < matrix.Columns(); ++j)
      norm = std::hypot(norm, matrix(i, j));
  return norm;
}
double Difference(const Matrix& a, const Matrix& b) {
  double norm = 0;
  for (std::size_t i = 0; i < a.Rows(); ++i)
    for (std::size_t j = 0; j < a.Columns(); ++j)
      norm = std::hypot(norm, a(i, j) - b(i, j));
  return norm;
}
fesa::Result<fesa::ThermalShell> Kernel(const Patch& patch = kSquare,
                                        double h = 2, double k = 1) {
  return fesa::ThermalShell::Create({"patch", 19, "0019"}, {{7, 2, 9, 4}},
                                    patch, k, 1, 1, h, {"kernel.inp", 42});
}
struct Oracle {
  Matrix c{20, 20};
  Matrix k{20, 20};
  Matrix pc{20, 20};
  Matrix pk{20, 20};
};

// Independently integrated exact rational unit-square matrices, h variable.
// The signed products are kept separate from their absolute contribution sums.
Oracle Rational(double h) {
  constexpr int mass[4][4] = {
      {4, 2, 1, 2}, {2, 4, 2, 1}, {1, 2, 4, 2}, {2, 1, 2, 4}};
  constexpr int stiffness[4][4] = {
      {4, -1, -2, -1}, {-1, 4, -1, -2}, {-2, -1, 4, -1}, {-1, -2, -1, 4}};
  constexpr int z0[5][5] = {{4, 2, -1, 0, 0},
                            {2, 16, 2, 0, 0},
                            {-1, 2, 8, 2, -1},
                            {0, 0, 2, 16, 2},
                            {0, 0, -1, 2, 4}};
  constexpr int z1[5][5] = {{7, -8, 1, 0, 0},
                            {-8, 16, -8, 0, 0},
                            {1, -8, 14, -8, 1},
                            {0, 0, -8, 16, -8},
                            {0, 0, 1, -8, 7}};
  Oracle result;
  for (std::size_t p = 0; p < 20; ++p)
    for (std::size_t q = 0; q < 20; ++q) {
      const auto i = p / 5, j = q / 5, a = p % 5, b = q % 5;
      result.c(p, q) = h * mass[i][j] * z0[a][b] / 2160.;
      const double tangential = h * stiffness[i][j] * z0[a][b] / 360.;
      const double normal = mass[i][j] * z1[a][b] / (54. * h);
      result.k(p, q) = tangential + normal;
      result.pc(p, q) = std::abs(result.c(p, q));
      const double sx[4] = {-1, 1, 1, -1}, sy[4] = {-1, -1, 1, 1};
      const double ps = (sx[i] == sx[j] ? 1. / 3 : 1. / 6) +
                        (sy[i] == sy[j] ? 1. / 3 : 1. / 6);
      result.pk(p, q) = h * ps * std::abs(z0[a][b]) / 60 + std::abs(normal);
    }
  return result;
}

// Independent 54-point B^T B/H^T H oracle: no exact-Z or production helper.
Oracle Direct54(const Patch& coordinates, double h) {
  Oracle result;
  const double g = std::sqrt(.6);
  const std::array<double, 3> gauss{{-g, 0, g}},
      weight{{5. / 9, 8. / 9, 5. / 9}};
  constexpr double sx[4] = {-1, 1, 1, -1}, sy[4] = {-1, -1, 1, 1};
  for (std::size_t ix = 0; ix < 3; ++ix)
    for (std::size_t iy = 0; iy < 3; ++iy) {
      std::array<double, 4> n{}, dx{}, dy{};
      Vector3 a1, a2;
      for (std::size_t i = 0; i < 4; ++i) {
        n[i] = (1 + sx[i] * gauss[ix]) * (1 + sy[i] * gauss[iy]) / 4;
        dx[i] = sx[i] * (1 + sy[i] * gauss[iy]) / 4;
        dy[i] = sy[i] * (1 + sx[i] * gauss[ix]) / 4;
        a1 = a1 + dx[i] * coordinates[i];
        a2 = a2 + dy[i] * coordinates[i];
      }
      const double aa = a1.Dot(a1), bb = a2.Dot(a2), ab = a1.Dot(a2);
      const double det = aa * bb - ab * ab;
      const Vector3 normal = a1.Cross(a2) / std::sqrt(det);
      const Vector3 reciprocal1 = (bb * a1 - ab * a2) / det;
      const Vector3 reciprocal2 = (aa * a2 - ab * a1) / det;
      for (std::size_t segment = 0; segment < 2; ++segment)
        for (std::size_t iz = 0; iz < 3; ++iz) {
          const double s = gauss[iz];
          const std::array<double, 3> l{
              {s * (s - 1) / 2, 1 - s * s, s * (s + 1) / 2}};
          const std::array<double, 3> dl{{2 * s - 1, -4 * s, 2 * s + 1}};
          std::array<double, 20> shape{};
          std::array<Vector3, 20> gradient{};
          const double w =
              weight[ix] * weight[iy] * weight[iz] * std::sqrt(det) * h / 4;
          for (std::size_t i = 0; i < 4; ++i)
            for (std::size_t a = 0; a < 3; ++a) {
              const auto p = 5 * i + 2 * segment + a;
              shape[p] = n[i] * l[a];
              gradient[p] = l[a] * (dx[i] * reciprocal1 + dy[i] * reciprocal2) +
                            (2 * n[i] * dl[a] / h) * normal;
            }
          for (std::size_t p = 0; p < 20; ++p)
            for (std::size_t q = 0; q < 20; ++q) {
              const double c = shape[p] * shape[q] * w;
              const double k = gradient[p].Dot(gradient[q]) * w;
              result.c(p, q) += c;
              result.k(p, q) += k;
              result.pc(p, q) += std::abs(c);
              // Component products, not absolute signed dot products.
              for (std::size_t axis = 0; axis < 3; ++axis)
                result.pk(p, q) +=
                    std::abs(gradient[p][axis] * gradient[q][axis] * w);
            }
        }
    }
  return result;
}

// Direct recovery operator and absolute propagation scale, independent of the
// production cache. Rows preserve the two one-sided center derivatives.
struct FluxOracle {
  std::array<Vector3, 24> value{};
  std::array<double, 24> scale{};
};
FluxOracle Flux(const Patch& patch, double h, const std::array<double, 20>& t) {
  FluxOracle result;
  const double g = 1 / std::sqrt(3.);
  const double sx[4] = {-1, 1, 1, -1}, sy[4] = {-1, -1, 1, 1};
  for (std::size_t ip = 0; ip < 4; ++ip) {
    std::array<double, 4> n{}, dx{}, dy{};
    Vector3 a1, a2;
    for (std::size_t i = 0; i < 4; ++i) {
      n[i] = (1 + sx[i] * sx[ip] * g) * (1 + sy[i] * sy[ip] * g) / 4;
      dx[i] = sx[i] * (1 + sy[i] * sy[ip] * g) / 4;
      dy[i] = sy[i] * (1 + sx[i] * sx[ip] * g) / 4;
      a1 = a1 + dx[i] * patch[i];
      a2 = a2 + dy[i] * patch[i];
    }
    const double aa = a1.Dot(a1), bb = a2.Dot(a2), ab = a1.Dot(a2),
                 det = aa * bb - ab * ab;
    const Vector3 normal = a1.Cross(a2) / std::sqrt(det);
    const Vector3 r1 = (bb * a1 - ab * a2) / det,
                  r2 = (aa * a2 - ab * a1) / det;
    for (std::size_t trace = 0; trace < 6; ++trace) {
      const double x = static_cast<double>(trace % 3) - 1;
      const double l[3] = {x * (x - 1) / 2, 1 - x * x, x * (x + 1) / 2};
      const double dl[3] = {2 * x - 1, -4 * x, 2 * x + 1};
      const auto row = 6 * ip + trace;
      for (std::size_t i = 0; i < 4; ++i)
        for (std::size_t a = 0; a < 3; ++a) {
          const auto p = 5 * i + (trace < 3 ? 0 : 2) + a;
          const Vector3 first = (l[a] * dx[i]) * r1;
          const Vector3 second = (l[a] * dy[i]) * r2;
          const Vector3 third = (2 * n[i] * dl[a] / h) * normal;
          result.value[row] =
              result.value[row] - t[p] * (first + second + third);
          result.scale[row] +=
              std::abs(t[p]) * (first.Norm() + second.Norm() + third.Norm());
        }
    }
  }
  return result;
}

// Jacobi orthogonal diagonalization plus a posteriori residual and
// orthogonality budget. No guessed eigenvalue epsilon is used for the rank
// decision.
std::pair<double, double> EigenExtrema(const Matrix& original,
                                       double& backward) {
  Matrix a = original;
  const auto n = a.Rows();
  Matrix v{n, n};
  for (std::size_t i = 0; i < n; ++i) v(i, i) = 1;
  for (int sweep = 0; sweep < 100; ++sweep) {
    for (std::size_t p = 0; p < n; ++p)
      for (std::size_t q = p + 1; q < n; ++q) {
        if (a(p, q) == 0) continue;
        const double tau = (a(q, q) - a(p, p)) / (2 * a(p, q));
        const double t =
            std::copysign(1., tau) / (std::abs(tau) + std::hypot(1., tau));
        const double c = 1 / std::hypot(1., t), s = t * c;
        const double off = a(p, q);
        a(p, p) -= t * off;
        a(q, q) += t * off;
        a(p, q) = a(q, p) = 0;
        for (std::size_t j = 0; j < n; ++j) {
          if (j != p && j != q) {
            const double x = a(j, p), y = a(j, q);
            a(j, p) = a(p, j) = c * x - s * y;
            a(j, q) = a(q, j) = s * x + c * y;
          }
          const double x = v(j, p), y = v(j, q);
          v(j, p) = c * x - s * y;
          v(j, q) = s * x + c * y;
        }
      }
  }
  double residual = 0, orthogonality = 0;
  for (std::size_t i = 0; i < n; ++i)
    for (std::size_t j = 0; j < n; ++j) {
      double av = 0, vv = 0, absolute = 0;
      for (std::size_t k = 0; k < n; ++k) {
        av += original(i, k) * v(k, j);
        absolute += std::abs(original(i, k) * v(k, j));
        vv += v(k, i) * v(k, j);
      }
      residual = std::hypot(residual,
                            std::abs(av - v(i, j) * a(j, j)) +
                                Gamma(2 * static_cast<int>(n) + 2) *
                                    (absolute + std::abs(v(i, j) * a(j, j))));
      orthogonality =
          std::hypot(orthogonality, std::abs(vv - (i == j ? 1. : 0.)) +
                                        Gamma(2 * static_cast<int>(n) + 2));
    }
  EXPECT_LT(orthogonality, 1.);
  backward =
      (residual + 2 * Norm(original) * orthogonality) / (1 - orthogonality);
  double low = a(0, 0), high = a(0, 0);
  for (std::size_t i = 1; i < n; ++i) {
    low = std::min(low, a(i, i));
    high = std::max(high, a(i, i));
  }
  return {low, high};
}
}  // namespace

TEST(ThermalShell, RationalMatricesSymmetryAndConstantModeUseFixedBudgets) {
  const auto created = Kernel();
  ASSERT_TRUE(created.HasValue());
  const auto& kernel = created.Value();
  const auto exact = Rational(2);
  const double ec = Gamma(4096) * Norm(exact.pc),
               ek = Gamma(4096) * Norm(exact.pk);
  EXPECT_LE(Difference(kernel.Capacity(), exact.c), ec);
  EXPECT_LE(Difference(kernel.Conductivity(), exact.k), ek);
  double cs = 0, ks = 0, null = 0, total = 0;
  for (std::size_t i = 0; i < 20; ++i) {
    double row = 0;
    for (std::size_t j = 0; j < 20; ++j) {
      cs = std::hypot(cs, kernel.Capacity()(i, j) - kernel.Capacity()(j, i));
      ks = std::hypot(
          ks, kernel.Conductivity()(i, j) - kernel.Conductivity()(j, i));
      row += kernel.Conductivity()(i, j);
      total += kernel.Capacity()(i, j);
    }
    null = std::hypot(null, row);
  }
  EXPECT_LE(cs, 2 * ec);
  EXPECT_LE(ks, 2 * ek);
  EXPECT_LE(null, std::sqrt(20.) * ek);
  EXPECT_LE(std::abs(total - 2), 20 * ec);
  EXPECT_EQ(kernel.SourceId().source_label_text, "0019");
  EXPECT_EQ(kernel.NodeIndices(),
            (std::array<fesa::EntityIndex, 4>{{7, 2, 9, 4}}));
}

TEST(ThermalShell, CapacityIsPositiveAndConductionHasExactlyOneNullMode) {
  const auto created = Kernel();
  ASSERT_TRUE(created.HasValue());
  const auto exact = Rational(2);
  double backward = 0;
  const auto capacity = EigenExtrema(created.Value().Capacity(), backward);
  EXPECT_GT(capacity.first, Gamma(4096) * Norm(exact.pc) + backward);
  const auto conduction =
      EigenExtrema(created.Value().Conductivity(), backward);
  EXPECT_LE(std::abs(conduction.first),
            Gamma(4096) * Norm(exact.pk) + backward);
  // Helmert columns form an independent orthonormal basis of 1-perp.
  Matrix basis{20, 19};
  for (std::size_t j = 0; j < 19; ++j) {
    const double norm = std::sqrt(static_cast<double>((j + 1) * (j + 2)));
    for (std::size_t i = 0; i <= j; ++i) basis(i, j) = 1 / norm;
    basis(j + 1, j) = -static_cast<double>(j + 1) / norm;
  }
  Matrix restricted{19, 19};
  for (std::size_t i = 0; i < 19; ++i)
    for (std::size_t j = 0; j < 19; ++j)
      for (std::size_t p = 0; p < 20; ++p)
        for (std::size_t q = 0; q < 20; ++q)
          restricted(i, j) +=
              basis(p, i) * created.Value().Conductivity()(p, q) * basis(q, j);
  const auto positive = EigenExtrema(restricted, backward);
  const double projection_budget = Gamma(8192) * Norm(exact.pk) * 20;
  EXPECT_GT(positive.first,
            Gamma(4096) * Norm(exact.pk) + backward + projection_budget);
}

TEST(ThermalShell,
     Direct54MatchesSeparatedOperatorsOnActualThreeDimensionalPatches) {
  const std::array<Patch, 5> patches{
      {kSquare,
       {{{0, 0, 0}, {2, 0, 0}, {1.5, 1, 0}, {0, 1, 0}}},
       {{{-1, -1, .1}, {1, -1, -.1}, {1, 1, .1}, {-1, 1, -.1}}},
       {{{-1, -1, .5}, {1, -1, -.5}, {1, 1, .5}, {-1, 1, -.5}}},
       {{{-1, -1, 2}, {1, -1, -2}, {1, 1, 2}, {-1, 1, -2}}}}};
  for (const auto& patch : patches) {
    const auto created = Kernel(patch);
    ASSERT_TRUE(created.HasValue());
    const auto direct = Direct54(patch, 2);
    const auto& kernel = created.Value();
    // General-geometry separation error is the propagated interval enclosure;
    // direct 54's independent arithmetic has the prescribed gamma8192 budget.
    EXPECT_LE(Difference(kernel.Capacity(), direct.c),
              Norm(kernel.CapacityError()) + Gamma(8192) * Norm(direct.pc));
    EXPECT_LE(Difference(kernel.Conductivity(), direct.k),
              Norm(kernel.ConductivityError()) + Gamma(8192) * Norm(direct.pk));
  }
}

TEST(ThermalShell, ThicknessScalingPreservesBothConductionTermsAndCapacity) {
  for (double h : {.5, 1., 2.}) {
    const auto created = Kernel(kSquare, h);
    ASSERT_TRUE(created.HasValue());
    const auto exact = Rational(h);
    EXPECT_LE(Difference(created.Value().Capacity(), exact.c),
              Gamma(4096) * Norm(exact.pc));
    EXPECT_LE(Difference(created.Value().Conductivity(), exact.k),
              Gamma(4096) * Norm(exact.pk));
  }
}

TEST(ThermalShell, AffineLinearFluxFramesAndSeparateMidsurfaceTraces) {
  const auto created = Kernel();
  ASSERT_TRUE(created.HasValue());
  std::array<double, 20> temperature{};
  for (std::size_t i = 0; i < 4; ++i)
    for (std::size_t a = 0; a < 5; ++a)
      temperature[5 * i + a] =
          2 + 3 * kSquare[i].X() - 2 * kSquare[i].Y() + 4 * (-1 + .5 * a);
  const auto recovery = created.Value().Recover(temperature);
  ASSERT_TRUE(recovery.HasValue());
  const auto linear_scale = Flux(kSquare, 2, temperature);
  for (std::size_t row = 0; row < 24; ++row)
    EXPECT_LE(
        (recovery.Value().global_flux[row] - Vector3{-3, 2, -4}).Norm(),
        Gamma(2048) * (linear_scale.scale[row] + Vector3{3, -2, 4}.Norm()));
  for (const auto& frame : recovery.Value().frames) {
    for (std::size_t i = 0; i < 3; ++i)
      for (std::size_t j = 0; j < 3; ++j)
        EXPECT_NEAR(frame[i].Dot(frame[j]), i == j ? 1. : 0., Gamma(2048));
    EXPECT_NEAR(frame[0].Cross(frame[1]).Dot(frame[2]), 1., Gamma(2048));
  }
  for (std::size_t i = 0; i < 4; ++i)
    for (std::size_t a = 0; a < 5; ++a)
      temperature[5 * i + a] = a < 3 ? 0. : static_cast<double>(a - 2);
  const auto traces = created.Value().Recover(temperature);
  ASSERT_TRUE(traces.HasValue());
  for (std::size_t ip = 0; ip < 4; ++ip) {
    EXPECT_EQ(traces.Value().global_flux[6 * ip + 2].Z(), 0.);
    EXPECT_NEAR(traces.Value().global_flux[6 * ip + 3].Z(), -2.,
                Gamma(2048) * 2);
  }
  temperature.fill(2);
  const auto constant = created.Value().Recover(temperature);
  ASSERT_TRUE(constant.HasValue());
  const auto constant_scale = Flux(kSquare, 2, temperature);
  for (std::size_t row = 0; row < 24; ++row)
    EXPECT_LE(constant.Value().global_flux[row].Norm(),
              Gamma(2048) * constant_scale.scale[row]);
}

TEST(ThermalShell, TranslationRotationAndReversedNormalPreservePhysicalFlux) {
  const auto base = Kernel();
  ASSERT_TRUE(base.HasValue());
  Patch translated = kSquare, rotated = kSquare, reversed{};
  const auto rotate = [](Vector3 p) { return Vector3{p.Z(), p.X(), p.Y()}; };
  for (std::size_t i = 0; i < 4; ++i) {
    translated[i] = kSquare[i] + Vector3{1048576, -1048576, 1048576};
    rotated[i] = rotate(kSquare[i]);
    reversed[i] = kSquare[(4 - i) % 4];
  }
  const auto moved = Kernel(translated), turned = Kernel(rotated),
             flipped = Kernel(reversed);
  ASSERT_TRUE(moved.HasValue());
  ASSERT_TRUE(turned.HasValue());
  ASSERT_TRUE(flipped.HasValue());
  EXPECT_LE(
      Difference(base.Value().Capacity(), moved.Value().Capacity()),
      Norm(base.Value().CapacityError()) + Norm(moved.Value().CapacityError()));
  EXPECT_LE(
      Difference(base.Value().Conductivity(), turned.Value().Conductivity()),
      Norm(base.Value().ConductivityError()) +
          Norm(turned.Value().ConductivityError()));
  std::array<double, 20> temperature{}, reverse_temperature{};
  for (std::size_t i = 0; i < 4; ++i)
    for (std::size_t a = 0; a < 5; ++a) {
      temperature[5 * i + a] =
          2 + 3 * kSquare[i].X() - 2 * kSquare[i].Y() + 4 * (-1 + .5 * a);
      reverse_temperature[5 * i + a] =
          2 + 3 * reversed[i].X() - 2 * reversed[i].Y() - 4 * (-1 + .5 * a);
    }
  const auto flux = turned.Value().Recover(temperature),
             reverse = flipped.Value().Recover(reverse_temperature);
  ASSERT_TRUE(flux.HasValue());
  ASSERT_TRUE(reverse.HasValue());
  const auto turn_scale = Flux(rotated, 2, temperature);
  const auto reverse_scale = Flux(reversed, 2, reverse_temperature);
  for (std::size_t row = 0; row < 24; ++row) {
    EXPECT_LE((flux.Value().global_flux[row] - rotate({-3, 2, -4})).Norm(),
              Gamma(2048) * (turn_scale.scale[row] + Vector3{3, -2, 4}.Norm()));
    EXPECT_LE(
        (reverse.Value().global_flux[row] - Vector3{-3, 2, -4}).Norm(),
        Gamma(2048) * (reverse_scale.scale[row] + Vector3{3, -2, 4}.Norm()));
  }
}

TEST(ThermalShell, CheckedCreationAndRecoveryRetainSourceAndRejectNonfinite) {
  for (double bad : {0., -1., std::numeric_limits<double>::infinity(),
                     std::numeric_limits<double>::quiet_NaN()}) {
    EXPECT_FALSE(Kernel(kSquare, bad).HasValue());
    EXPECT_FALSE(Kernel(kSquare, 2, bad).HasValue());
  }
  const auto created = Kernel();
  ASSERT_TRUE(created.HasValue());
  std::array<double, 20> temperature{};
  temperature[3] = std::numeric_limits<double>::quiet_NaN();
  const auto bad = created.Value().Recover(temperature);
  ASSERT_FALSE(bad.HasValue());
  EXPECT_EQ(bad.GetStatus().Diagnostics()[0].entity_identity, "patch:0019");
  EXPECT_EQ(bad.GetStatus().Diagnostics()[0].location.line, 42U);
  temperature.fill(std::numeric_limits<double>::max());
  temperature[0] = -temperature[0];
  EXPECT_FALSE(created.Value().Recover(temperature).HasValue());
}

TEST(ThermalShell, GeneralWarpedFluxUsesActualReciprocalTangentsAndTraceOrder) {
  const Patch saddle{{{-1, -1, 2}, {1, -1, -2}, {1, 1, 2}, {-1, 1, -2}}};
  const auto created = Kernel(saddle, 1);
  ASSERT_TRUE(created.HasValue());
  std::array<double, 20> temperature{};
  for (std::size_t p = 0; p < 20; ++p)
    temperature[p] = static_cast<double>((p * 7) % 11) - 4;
  const auto actual = created.Value().Recover(temperature);
  ASSERT_TRUE(actual.HasValue());
  const auto expected = Flux(saddle, 1, temperature);
  for (std::size_t row = 0; row < 24; ++row)
    EXPECT_LE((actual.Value().global_flux[row] - expected.value[row]).Norm(),
              2 * Gamma(2048) * expected.scale[row]);
  // Local normals vary around this saddle; recovery must retain those frames.
  EXPECT_GT((actual.Value().frames[0][2] - actual.Value().frames[1][2]).Norm(),
            1.);
}

TEST(ThermalShell, PowerOfTwoCoordinateScalingPreservesDimensionedOperators) {
  for (int exponent : {-200, 200}) {
    Patch patch = kSquare;
    const double scale = std::ldexp(1., exponent);
    for (auto& point : patch) point = scale * point;
    const auto created = Kernel(patch, 2);
    ASSERT_TRUE(created.HasValue());
    const auto unit = Rational(2);
    const auto very_thick = Rational(2 / scale);
    // Area multiplies C by s^2; surface conduction is invariant, while the
    // normal term multiplies by s^2. Equivalent expression uses h/s and k*s.
    Matrix c{20, 20}, k{20, 20};
    for (std::size_t p = 0; p < 20; ++p)
      for (std::size_t q = 0; q < 20; ++q) {
        c(p, q) = std::ldexp(unit.c(p, q), 2 * exponent);
        k(p, q) = scale * very_thick.k(p, q);
      }
    EXPECT_LE(Difference(created.Value().Capacity(), c),
              Norm(created.Value().CapacityError()) + Gamma(4096) * Norm(c));
    EXPECT_LE(
        Difference(created.Value().Conductivity(), k),
        Norm(created.Value().ConductivityError()) + Gamma(4096) * Norm(k));
  }
}

TEST(ThermalShell, RejectsUnrepresentablePositivePropertiesWithoutClamping) {
  const auto underflow =
      fesa::ThermalShell::Create({"patch", 19, "0019"}, {{0, 1, 2, 3}}, kSquare,
                                 1, std::numeric_limits<double>::denorm_min(),
                                 std::numeric_limits<double>::denorm_min(), 1);
  EXPECT_FALSE(underflow.HasValue());
  const auto overflow =
      fesa::ThermalShell::Create({"patch", 19, "0019"}, {{0, 1, 2, 3}}, kSquare,
                                 1, std::numeric_limits<double>::max(), 2, 1);
  EXPECT_FALSE(overflow.HasValue());
}