feat(equation-and-linear-solve): step 2 — pardiso-linear-solver

tests/unit/solvers/linear/pardiso_linear_solver_test.cpp

@@ -0,0 +1,148 @@
+#include <fesa/solvers/linear/pardiso_linear_solver.hpp>
+
+#include <algorithm>
+#include <cmath>
+#include <cstddef>
+#include <cstdint>
+#include <span>
+#include <string_view>
+#include <vector>
+
+#include <gtest/gtest.h>
+
+namespace {
+
+fesa::SymmetricCsr spd_matrix() {
+    return {
+        3,
+        {0, 2, 4, 5},
+        {0, 1, 1, 2, 2},
+        {4.0, 1.0, 3.0, 1.0, 2.0},
+    };
+}
+
+double independent_relative_residual(
+    const fesa::SymmetricCsr& matrix,
+    const std::span<const double> rhs,
+    const std::span<const double> solution) {
+    std::vector<double> residual(rhs.begin(), rhs.end());
+    for (double& value : residual) {
+        value = -value;
+    }
+
+    for (std::size_t row = 0; row < matrix.order; ++row) {
+        const std::size_t begin =
+            static_cast<std::size_t>(matrix.row_offsets[row]);
+        const std::size_t end =
+            static_cast<std::size_t>(matrix.row_offsets[row + 1]);
+        for (std::size_t entry = begin; entry < end; ++entry) {
+            const std::size_t column =
+                static_cast<std::size_t>(matrix.column_indices[entry]);
+            const double value = matrix.values[entry];
+            residual[row] += value * solution[column];
+            if (column != row) {
+                residual[column] += value * solution[row];
+            }
+        }
+    }
+
+    double residual_squared = 0.0;
+    double rhs_squared = 0.0;
+    for (std::size_t index = 0; index < rhs.size(); ++index) {
+        residual_squared += residual[index] * residual[index];
+        rhs_squared += rhs[index] * rhs[index];
+    }
+    const double residual_norm = std::sqrt(residual_squared);
+    const double rhs_norm = std::sqrt(rhs_squared);
+    return rhs_norm == 0.0 ? residual_norm : residual_norm / rhs_norm;
+}
+
+bool has_diagnostic(
+    const fesa::LinearSolveResult& result,
+    const std::string_view code) {
+    return std::ranges::find(
+               result.diagnostics, code, &fesa::Diagnostic::code) !=
+           result.diagnostics.end();
+}
+
+TEST(PardisoLinearSolver, SolvesThreeByThreeSpdSystem) {
+    fesa::PardisoLinearSolver pardiso;
+    fesa::LinearSolver& solver = pardiso;
+    const fesa::SymmetricCsr matrix = spd_matrix();
+    const std::vector<double> rhs{6.0, 10.0, 8.0};
+
+    const fesa::LinearSolveResult result = solver.solve(matrix, rhs);
+
+    ASSERT_TRUE(result.diagnostics.empty());
+    ASSERT_EQ(result.solution.size(), 3);
+    EXPECT_NEAR(result.solution[0], 1.0, 1.0e-12);
+    EXPECT_NEAR(result.solution[1], 2.0, 1.0e-12);
+    EXPECT_NEAR(result.solution[2], 3.0, 1.0e-12);
+    const double independent =
+        independent_relative_residual(matrix, rhs, result.solution);
+    EXPECT_NEAR(result.relative_residual, independent, 1.0e-15);
+    EXPECT_LT(result.relative_residual, 1.0e-12);
+}
+
+TEST(PardisoLinearSolver, SupportsRepeatedSolve) {
+    fesa::PardisoLinearSolver solver;
+    const fesa::SymmetricCsr matrix = spd_matrix();
+
+    const fesa::LinearSolveResult first =
+        solver.solve(matrix, std::vector<double>{6.0, 10.0, 8.0});
+    const fesa::LinearSolveResult second =
+        solver.solve(matrix, std::vector<double>{-3.5, 2.5, 4.5});
+
+    ASSERT_TRUE(first.diagnostics.empty());
+    ASSERT_TRUE(second.diagnostics.empty());
+    ASSERT_EQ(second.solution.size(), 3);
+    EXPECT_NEAR(second.solution[0], -1.0, 1.0e-12);
+    EXPECT_NEAR(second.solution[1], 0.5, 1.0e-12);
+    EXPECT_NEAR(second.solution[2], 2.0, 1.0e-12);
+}
+
+TEST(LinearSolver, RejectsInvalidUpperTriangleCsr) {
+    fesa::PardisoLinearSolver solver;
+    fesa::SymmetricCsr invalid = spd_matrix();
+    invalid.column_indices[2] = 0;
+
+    const fesa::LinearSolveResult result =
+        solver.solve(invalid, std::vector<double>{6.0, 10.0, 8.0});
+
+    EXPECT_TRUE(result.solution.empty());
+    EXPECT_TRUE(has_diagnostic(result, "solver.invalid_csr"));
+}
+
+TEST(LinearSolver, RejectsRhsDimensionMismatch) {
+    fesa::PardisoLinearSolver solver;
+
+    const fesa::LinearSolveResult result =
+        solver.solve(spd_matrix(), std::vector<double>{1.0, 2.0});
+
+    EXPECT_TRUE(result.solution.empty());
+    EXPECT_TRUE(has_diagnostic(result, "solver.dimension_mismatch"));
+}
+
+TEST(PardisoLinearSolver, ReportsSingularMatrix) {
+    fesa::PardisoLinearSolver solver;
+    const fesa::SymmetricCsr singular{
+        2,
+        {0, 2, 3},
+        {0, 1, 1},
+        {1.0, 1.0, 1.0},
+    };
+
+    const fesa::LinearSolveResult result =
+        solver.solve(singular, std::vector<double>{2.0, 2.0});
+
+    EXPECT_TRUE(result.solution.empty());
+    EXPECT_FALSE(result.diagnostics.empty());
+    EXPECT_TRUE(std::ranges::all_of(
+        result.diagnostics,
+        [](const fesa::Diagnostic& diagnostic) {
+            return diagnostic.stage == fesa::DiagnosticStage::solver &&
+                   diagnostic.severity == fesa::Severity::error;
+        }));
+}
+
+}  // namespace