feat(linear-static-3d-euler-beam): step 20 - mkl-pardiso-solver
This commit is contained in:
KOKO\Mimi
@@ -22,6 +22,8 @@ add_executable(
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unit/model/domain_test.cpp
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unit/model/model_types_test.cpp
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unit/results/result_records_test.cpp
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unit/solvers/linear/linear_solver_test.cpp
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unit/solvers/linear/mkl_pardiso_solver_test.cpp
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)
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target_link_libraries(
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@@ -0,0 +1,113 @@
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#include "fesa/solvers/linear/linear_solver.hpp"
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#include "fesa/solvers/linear/mkl_pardiso_solver.hpp"
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#include "fesa/fem/dof_manager.hpp"
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#include "fesa/math/sparse_matrix.hpp"
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#include <gtest/gtest.h>
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#include <type_traits>
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#include <utility>
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#include <vector>
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namespace {
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fesa::SparseMatrix makeDenseCsr(
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const std::size_t rows,
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const std::size_t columns,
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const std::vector<double>& values) {
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EXPECT_EQ(values.size(), rows * columns);
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fesa::SparsePattern pattern;
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std::vector<fesa::CooContribution> contributions;
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pattern.rowOffsets.reserve(rows + 1U);
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pattern.rowOffsets.push_back(0U);
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for (std::size_t row = 0U; row < rows; ++row) {
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for (std::size_t column = 0U; column < columns; ++column) {
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pattern.columnIndices.push_back(column);
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contributions.push_back({
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row,
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column,
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values[row * columns + column],
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row,
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column});
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}
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pattern.rowOffsets.push_back(pattern.columnIndices.size());
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}
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auto matrix = fesa::SparseMatrix::fromCoo(
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rows, columns, std::move(contributions), pattern);
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EXPECT_TRUE(matrix.hasValue());
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return std::move(matrix.value());
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}
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void expectSolverFailure(const fesa::Status& status) {
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EXPECT_FALSE(status.isOk());
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EXPECT_EQ(status.failureCategory(), fesa::FailureCategory::solver);
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ASSERT_FALSE(status.diagnostics().empty());
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EXPECT_EQ(status.diagnostics().front().severity, fesa::Severity::error);
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}
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} // namespace
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TEST(MklPardisoSolver, RejectsInvalidCsrStateAndDimensions) {
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static_assert(std::is_base_of_v<fesa::LinearSolver, fesa::MklPardisoSolver>);
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static_assert(std::has_virtual_destructor_v<fesa::LinearSolver>);
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fesa::MklPardisoSolver solver;
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fesa::Vector solution{2U};
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expectSolverFailure(solver.solve(fesa::Vector{2U, 1.0}, solution));
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EXPECT_EQ(
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solver.solve(fesa::Vector{2U, 1.0}, solution)
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.diagnostics()
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.front()
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.code,
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"solver-not-factorized");
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const auto rectangular = makeDenseCsr(
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2U, 3U, {2.0, 0.0, 0.0, 0.0, 3.0, 0.0});
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const auto rectangularStatus = solver.factorize(rectangular);
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expectSolverFailure(rectangularStatus);
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EXPECT_EQ(
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rectangularStatus.diagnostics().front().code,
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"solver-matrix-not-square");
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const auto empty = makeDenseCsr(0U, 0U, {});
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const auto emptyStatus = solver.factorize(empty);
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expectSolverFailure(emptyStatus);
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EXPECT_EQ(emptyStatus.diagnostics().front().code, "solver-empty-matrix");
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fesa::SparsePattern invalidPattern{{0U, 2U}, {0U}};
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auto invalidCsr = fesa::SparseMatrix::fromCoo(
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1U,
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1U,
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{{0U, 0U, 1.0, 0U, 0U}},
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invalidPattern);
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EXPECT_FALSE(invalidCsr.hasValue());
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const auto nonsymmetric = makeDenseCsr(2U, 2U, {2.0, 1.0, 0.0, 3.0});
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const auto nonsymmetricStatus = solver.factorize(nonsymmetric);
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expectSolverFailure(nonsymmetricStatus);
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EXPECT_EQ(
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nonsymmetricStatus.diagnostics().front().code,
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"solver-matrix-not-symmetric");
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fesa::SparsePattern noDiagonalPattern{{0U, 1U, 2U}, {1U, 0U}};
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auto noDiagonal = fesa::SparseMatrix::fromCoo(
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2U,
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2U,
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{{0U, 1U, 1.0, 0U, 0U}, {1U, 0U, 1.0, 1U, 0U}},
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noDiagonalPattern);
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ASSERT_TRUE(noDiagonal.hasValue());
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const auto noDiagonalStatus = solver.factorize(noDiagonal.value());
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expectSolverFailure(noDiagonalStatus);
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EXPECT_EQ(
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noDiagonalStatus.diagnostics().front().code,
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"solver-missing-diagonal");
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const auto spd = makeDenseCsr(2U, 2U, {4.0, 1.0, 1.0, 3.0});
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ASSERT_TRUE(solver.factorize(spd).isOk());
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expectSolverFailure(solver.solve(fesa::Vector{1U, 1.0}, solution));
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fesa::Vector wrongSolution{1U};
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expectSolverFailure(solver.solve(fesa::Vector{2U, 1.0}, wrongSolution));
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}
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@@ -0,0 +1,251 @@
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#include "fesa/solvers/linear/mkl_pardiso_solver.hpp"
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#include "fesa/fem/dof_manager.hpp"
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#include "fesa/math/sparse_matrix.hpp"
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#include <gtest/gtest.h>
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#include <algorithm>
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#include <cmath>
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#include <initializer_list>
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#include <limits>
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#include <string>
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#include <utility>
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#include <vector>
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namespace {
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fesa::SparseMatrix makeDenseCsr(
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const std::size_t size,
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const std::vector<double>& values) {
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EXPECT_EQ(values.size(), size * size);
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fesa::SparsePattern pattern;
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std::vector<fesa::CooContribution> contributions;
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pattern.rowOffsets.reserve(size + 1U);
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pattern.rowOffsets.push_back(0U);
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for (std::size_t row = 0U; row < size; ++row) {
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for (std::size_t column = 0U; column < size; ++column) {
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pattern.columnIndices.push_back(column);
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contributions.push_back({
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row,
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column,
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values[row * size + column],
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row,
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column});
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}
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pattern.rowOffsets.push_back(pattern.columnIndices.size());
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}
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auto matrix = fesa::SparseMatrix::fromCoo(
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size, size, std::move(contributions), pattern);
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EXPECT_TRUE(matrix.hasValue());
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return std::move(matrix.value());
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}
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fesa::Vector makeVector(const std::initializer_list<double> values) {
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fesa::Vector result{values.size()};
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std::size_t index = 0U;
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for (const double value : values) {
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result[index++] = value;
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}
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return result;
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}
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double normalizedResidual(
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const fesa::SparseMatrix& matrix,
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const fesa::Vector& solution,
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const fesa::Vector& rhs) {
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auto residual = matrix.multiply(solution);
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residual.axpy(-1.0, rhs);
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return residual.norm() / (std::max)(1.0, rhs.norm());
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}
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double relativeError(
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const fesa::Vector& actual,
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const fesa::Vector& expected) {
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auto difference = actual;
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difference.axpy(-1.0, expected);
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return difference.norm() / (std::max)(1.0, expected.norm());
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}
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void expectStructuredSolverFailure(const fesa::Status& status) {
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EXPECT_FALSE(status.isOk());
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EXPECT_EQ(status.failureCategory(), fesa::FailureCategory::solver);
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ASSERT_EQ(status.diagnostics().size(), 1U);
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EXPECT_EQ(status.diagnostics()[0U].severity, fesa::Severity::error);
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EXPECT_FALSE(status.diagnostics()[0U].code.empty());
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EXPECT_FALSE(status.diagnostics()[0U].message.empty());
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}
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} // namespace
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TEST(MklPardisoSolver, SolvesKnownSpdWithNormalizedResidual) {
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const auto matrix = makeDenseCsr(3U, {
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6.0, 2.0, 1.0,
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2.0, 5.0, 2.0,
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1.0, 2.0, 4.0});
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const auto expected = makeVector({1.0, -2.0, 3.0});
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const auto rhs = matrix.multiply(expected);
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fesa::MklPardisoSolver concreteSolver;
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fesa::LinearSolver& solver = concreteSolver;
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ASSERT_TRUE(solver.factorize(matrix).isOk());
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fesa::Vector solution{3U};
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ASSERT_TRUE(solver.solve(rhs, solution).isOk());
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EXPECT_LE(normalizedResidual(matrix, solution, rhs), 1.0e-10);
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EXPECT_LE(relativeError(solution, expected), 1.0e-9);
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}
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TEST(MklPardisoSolver, ReusesOneFactorizationForRepeatedRhs) {
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const auto matrix = makeDenseCsr(2U, {4.0, 1.0, 1.0, 3.0});
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const auto expectedFirst = makeVector({1.0, 2.0});
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const auto expectedSecond = makeVector({-2.0, 0.5});
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const auto rhsFirst = matrix.multiply(expectedFirst);
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const auto rhsSecond = matrix.multiply(expectedSecond);
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fesa::MklPardisoSolver solver;
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ASSERT_TRUE(solver.factorize(matrix).isOk());
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fesa::Vector first{2U};
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fesa::Vector second{2U};
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ASSERT_TRUE(solver.solve(rhsFirst, first).isOk());
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ASSERT_TRUE(solver.solve(rhsSecond, second).isOk());
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EXPECT_LE(relativeError(first, expectedFirst), 1.0e-9);
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EXPECT_LE(relativeError(second, expectedSecond), 1.0e-9);
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EXPECT_LE(normalizedResidual(matrix, first, rhsFirst), 1.0e-10);
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EXPECT_LE(normalizedResidual(matrix, second, rhsSecond), 1.0e-10);
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}
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TEST(MklPardisoSolver, RefactorizesWithoutLeakingState) {
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const auto firstMatrix = makeDenseCsr(2U, {4.0, 1.0, 1.0, 3.0});
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const auto secondMatrix = makeDenseCsr(2U, {2.0, 0.0, 0.0, 5.0});
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const auto firstExpected = makeVector({1.0, 2.0});
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const auto secondExpected = makeVector({-3.0, 4.0});
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fesa::MklPardisoSolver solver;
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ASSERT_TRUE(solver.factorize(firstMatrix).isOk());
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fesa::Vector firstSolution{2U};
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ASSERT_TRUE(
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solver.solve(firstMatrix.multiply(firstExpected), firstSolution).isOk());
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EXPECT_LE(relativeError(firstSolution, firstExpected), 1.0e-9);
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ASSERT_TRUE(solver.factorize(secondMatrix).isOk());
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fesa::Vector secondSolution{2U};
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const auto secondRhs = secondMatrix.multiply(secondExpected);
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ASSERT_TRUE(solver.solve(secondRhs, secondSolution).isOk());
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EXPECT_LE(relativeError(secondSolution, secondExpected), 1.0e-9);
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EXPECT_LE(
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normalizedResidual(secondMatrix, secondSolution, secondRhs), 1.0e-10);
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}
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TEST(MklPardisoSolver, ClassifiesSingularIndefiniteAndNonfiniteFailures) {
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fesa::MklPardisoSolver solver;
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const auto singular = makeDenseCsr(2U, {1.0, 1.0, 1.0, 1.0});
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const auto singularStatus = solver.factorize(singular);
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expectStructuredSolverFailure(singularStatus);
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EXPECT_TRUE(
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singularStatus.diagnostics()[0U].code ==
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"pardiso-zero-or-negative-pivot" ||
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singularStatus.diagnostics()[0U].code ==
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"pardiso-singular-diagonal");
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EXPECT_NE(
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singularStatus.diagnostics()[0U].entityIdentity.find(
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"phase=22,error="),
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std::string::npos);
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const auto indefinite = makeDenseCsr(2U, {1.0, 2.0, 2.0, 1.0});
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const auto indefiniteStatus = solver.factorize(indefinite);
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expectStructuredSolverFailure(indefiniteStatus);
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EXPECT_TRUE(
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indefiniteStatus.diagnostics()[0U].code ==
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"pardiso-zero-or-negative-pivot" ||
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indefiniteStatus.diagnostics()[0U].code ==
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"pardiso-singular-diagonal");
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EXPECT_NE(
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indefiniteStatus.diagnostics()[0U].entityIdentity.find(
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"phase=22,error="),
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std::string::npos);
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const auto spd = makeDenseCsr(2U, {3.0, 1.0, 1.0, 2.0});
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ASSERT_TRUE(solver.factorize(spd).isOk());
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auto rhs = makeVector({1.0, 2.0});
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rhs[1U] = (std::numeric_limits<double>::infinity)();
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fesa::Vector solution{2U};
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const auto rhsStatus = solver.solve(rhs, solution);
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expectStructuredSolverFailure(rhsStatus);
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EXPECT_EQ(rhsStatus.diagnostics()[0U].code, "nonfinite-solver-rhs");
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fesa::SparsePattern pattern{{0U, 1U}, {0U}};
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auto nonfiniteMatrix = fesa::SparseMatrix::fromCoo(
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1U,
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1U,
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{{0U,
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0U,
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(std::numeric_limits<double>::quiet_NaN)(),
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0U,
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0U}},
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pattern);
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EXPECT_FALSE(nonfiniteMatrix.hasValue());
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EXPECT_EQ(
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nonfiniteMatrix.status().diagnostics()[0U].code,
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"nonfinite-sparse-value");
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}
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TEST(MklPardisoSolver, ConditioningSweepPassesResolvedCasesAndFailsUnresolvedCasesExplicitly) {
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const std::vector<double> commonScales{1.0e-12, 1.0, 1.0e12};
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for (const double scale : commonScales) {
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const auto matrix = makeDenseCsr(2U, {
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4.0 * scale, 1.0 * scale,
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1.0 * scale, 3.0 * scale});
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const auto expected = makeVector({1.25, -0.75});
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const auto rhs = matrix.multiply(expected);
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fesa::MklPardisoSolver solver;
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ASSERT_TRUE(solver.factorize(matrix).isOk()) << "scale=" << scale;
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fesa::Vector solution{2U};
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ASSERT_TRUE(solver.solve(rhs, solution).isOk()) << "scale=" << scale;
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EXPECT_LE(normalizedResidual(matrix, solution, rhs), 1.0e-10);
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EXPECT_LE(relativeError(solution, expected), 1.0e-9);
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}
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const double resolvedRatio = 1.0e-8;
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const auto resolvedMatrix = makeDenseCsr(
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2U, {1.0, 0.0, 0.0, resolvedRatio});
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const auto resolvedExpected = makeVector({0.5, -2.0});
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const auto resolvedRhs = resolvedMatrix.multiply(resolvedExpected);
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fesa::MklPardisoSolver resolvedSolver;
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ASSERT_TRUE(resolvedSolver.factorize(resolvedMatrix).isOk());
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fesa::Vector resolvedSolution{2U};
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ASSERT_TRUE(resolvedSolver.solve(resolvedRhs, resolvedSolution).isOk());
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EXPECT_LE(
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normalizedResidual(resolvedMatrix, resolvedSolution, resolvedRhs),
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1.0e-10);
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EXPECT_LE(relativeError(resolvedSolution, resolvedExpected), 1.0e-9);
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const std::vector<double> unresolvedCandidates{1.0e-16, 1.0e-300};
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for (const double ratio : unresolvedCandidates) {
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const auto matrix = makeDenseCsr(2U, {1.0, 0.0, 0.0, ratio});
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const auto expected = makeVector({0.5, -2.0});
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const auto rhs = matrix.multiply(expected);
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fesa::MklPardisoSolver solver;
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const auto factorStatus = solver.factorize(matrix);
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if (!factorStatus.isOk()) {
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expectStructuredSolverFailure(factorStatus);
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continue;
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}
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fesa::Vector solution{2U};
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const auto solveStatus = solver.solve(rhs, solution);
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if (!solveStatus.isOk()) {
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expectStructuredSolverFailure(solveStatus);
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continue;
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}
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EXPECT_LE(normalizedResidual(matrix, solution, rhs), 1.0e-10);
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EXPECT_LE(relativeError(solution, expected), 1.0e-9);
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}
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}
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