refactor: extract math solver boundary

tests/test_math_module_includes.cpp

@@ -0,0 +1,71 @@
+#include "fesa/Math/Math.hpp"
+
+#include <cmath>
+#include <cstdint>
+#include <stdexcept>
+#include <string>
+#include <type_traits>
+#include <vector>
+
+namespace {
+
+void check(bool value, const char* message) {
+  if (!value) {
+    throw std::runtime_error(message);
+  }
+}
+
+void checkNear(fesa::Real actual, fesa::Real expected, fesa::Real tolerance, const char* message) {
+  if (std::fabs(actual - expected) > tolerance) {
+    throw std::runtime_error(message);
+  }
+}
+
+}  // namespace
+
+int main() {
+  static_assert(std::is_same_v<fesa::SparseIndex, std::int64_t>, "SparseIndex must remain int64");
+  static_assert(std::is_same_v<fesa::EquationId, std::int64_t>, "EquationId must remain int64");
+
+  const fesa::Vec3 x{1.0, 0.0, 0.0};
+  const fesa::Vec3 y{0.0, 1.0, 0.0};
+  const auto z = fesa::cross(x, y);
+  checkNear(fesa::dot(x, y), 0.0, 1.0e-12, "Vector dot product changed");
+  checkNear(z.z, 1.0, 1.0e-12, "Vector cross product changed");
+  checkNear(fesa::norm(fesa::Vec3{3.0, 4.0, 0.0}), 5.0, 1.0e-12, "Vector norm changed");
+  check(fesa::normalizedIfValid(fesa::Vec3{0.0, 0.0, 0.0}) == std::nullopt, "Invalid normalization changed");
+
+  fesa::SparsePattern pattern;
+  pattern.equation_count = 3;
+  pattern.entries.push_back({0, 0});
+  pattern.entries.push_back({0, 2});
+  check(pattern.nonzeroCount() == 2, "Sparse nonzero count changed");
+  check(pattern.contains(0, 2), "Sparse pattern lookup changed");
+  check(!pattern.contains(2, 0), "Sparse pattern lookup became nondirectional");
+
+  fesa::DenseMatrix matrix(2, 2);
+  matrix(0, 0) = 2.0;
+  matrix(0, 1) = 1.0;
+  matrix(1, 0) = 1.0;
+  matrix(1, 1) = 3.0;
+  const auto product = matrix.multiply({1.0, 2.0});
+  checkNear(product[0], 4.0, 1.0e-12, "DenseMatrix multiply row 0 changed");
+  checkNear(product[1], 7.0, 1.0e-12, "DenseMatrix multiply row 1 changed");
+
+  const fesa::LinearSolver& solver = fesa::GaussianEliminationSolver{};
+  const auto solved = solver.solve(matrix, {1.0, 2.0});
+  check(solved.ok(), "Gaussian solver unexpectedly failed");
+  checkNear(solved.x[0], 0.2, 1.0e-12, "Gaussian solver x0 changed");
+  checkNear(solved.x[1], 0.6, 1.0e-12, "Gaussian solver x1 changed");
+
+  fesa::DenseMatrix singular(2, 2);
+  singular(0, 0) = 1.0;
+  singular(0, 1) = 2.0;
+  singular(1, 0) = 2.0;
+  singular(1, 1) = 4.0;
+  const auto failed = solver.solve(singular, {1.0, 2.0});
+  check(!failed.ok(), "Singular solve unexpectedly passed");
+  check(fesa::containsDiagnostic(failed.diagnostics, "FESA-SINGULAR-SOLVER"), "Singular diagnostic code changed");
+
+  return 0;
+}