Integrate Refactor solver sources and dual MSVC CMake builds
This commit is contained in:
KOKO\Mimi
@@ -1,9 +1,9 @@
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#include "math/dense_blas_internal.h"
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#include "math/jet_linear_solve.h"
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#include <gtest/gtest.h>
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#include <array>
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#include <cmath>
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#include <cstddef>
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#include <limits>
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#include <stdexcept>
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@@ -11,129 +11,197 @@
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namespace fesa::dense_blas_internal {
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namespace {
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TEST(DenseBlasInternal, PolicyQueryPreservesDefaultPositiveAndNestedTls) {
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const int previous = mkl_set_num_threads_local(0);
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struct Restore {
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int previous;
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~Restore() { static_cast<void>(mkl_set_num_threads_local(previous)); }
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} restore{previous};
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const int global = mkl_get_max_threads();
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const int domain = mkl_domain_get_max_threads(MKL_DOMAIN_BLAS);
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const int dynamic = mkl_get_dynamic();
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for (int repeat = 0; repeat < 2; ++repeat) {
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const auto policy = ReadScopedLocalDensePolicy();
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EXPECT_EQ(policy.blas_max_threads, 1);
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EXPECT_EQ(policy.dynamic, dynamic);
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EXPECT_EQ(mkl_set_num_threads_local(0), 0);
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EXPECT_EQ(mkl_get_max_threads(), global);
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EXPECT_EQ(mkl_domain_get_max_threads(MKL_DOMAIN_BLAS), domain);
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EXPECT_EQ(mkl_get_dynamic(), dynamic);
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}
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static_cast<void>(mkl_set_num_threads_local(2));
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EXPECT_EQ(ReadScopedLocalDensePolicy().blas_max_threads, 2);
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EXPECT_EQ(mkl_set_num_threads_local(2), 2);
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static_cast<void>(mkl_set_num_threads_local(0));
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try {
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const ScopedLocalDenseThreads outer{};
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EXPECT_EQ(ReadScopedLocalDensePolicy().blas_max_threads, 1);
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EXPECT_EQ(mkl_set_num_threads_local(1), 1);
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throw std::runtime_error{"policy-query-unwind"};
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} catch (const std::runtime_error&) {
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}
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EXPECT_EQ(mkl_set_num_threads_local(0), 0);
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EXPECT_EQ(mkl_get_dynamic(), dynamic);
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// Forms RHS and residuals independently of the production dense adapter.
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Matrix FactorRhs(const Matrix& a, const Matrix& x, const bool transpose,
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const bool right) {
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Matrix b{x.Rows(), x.Columns()};
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for (std::size_t i = 0; i < b.Rows(); ++i)
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for (std::size_t j = 0; j < b.Columns(); ++j)
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for (std::size_t k = 0; k < a.Rows(); ++k)
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b(i, j) += right ? x(i, k) * (transpose ? a(j, k) : a(k, j))
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: (transpose ? a(k, i) : a(i, k)) * x(k, j);
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return b;
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}
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TEST(DenseBlasInternal,
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OuterProductUsesRectangularStorageAndPreservesRejection) {
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const std::array<double, 2U> left{2.0, -3.0};
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const std::array<double, 3U> right{4.0, -5.0, 0.25};
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std::array<double, 6U> product{};
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ASSERT_TRUE(OuterProduct(left.data(), left.size(), right.data(), right.size(),
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product.data()));
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const std::array<double, 6U> expected{8.0, -10.0, 0.5, -12.0, 15.0, -0.75};
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EXPECT_EQ(product, expected);
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const auto accepted = product;
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const std::array<double, 2U> invalid{
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1.0, std::numeric_limits<double>::quiet_NaN()};
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EXPECT_FALSE(OuterProduct(invalid.data(), invalid.size(), right.data(),
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right.size(), product.data()));
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EXPECT_EQ(product, accepted);
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EXPECT_TRUE(OuterProduct(nullptr, 0U, nullptr, 3U, nullptr));
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EXPECT_TRUE(OuterProduct(nullptr, 2U, nullptr, 0U, nullptr));
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EXPECT_THROW(OuterProduct(nullptr, 2U, right.data(), 3U, product.data()),
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std::invalid_argument);
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const auto too_large =
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static_cast<std::size_t>((std::numeric_limits<MKL_INT>::max)()) + 1U;
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EXPECT_THROW(OuterProduct(nullptr, too_large, nullptr, 1U, nullptr),
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std::length_error);
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const auto too_many_elements =
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std::numeric_limits<std::size_t>::max() / sizeof(double) + 1U;
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EXPECT_THROW(OuterProduct(nullptr, too_many_elements, nullptr, 1U, nullptr),
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std::length_error);
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void ExpectFactorSolution(const Matrix& a, const Matrix& x, const Matrix& b,
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const Matrix& expected, const bool transpose,
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const bool right) {
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ASSERT_EQ(x.Rows(), expected.Rows());
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ASSERT_EQ(x.Columns(), expected.Columns());
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const auto residual = FactorRhs(a, x, transpose, right);
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for (std::size_t i = 0; i < x.Rows(); ++i)
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for (std::size_t j = 0; j < x.Columns(); ++j) {
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EXPECT_DOUBLE_EQ(x(i, j), expected(i, j));
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EXPECT_DOUBLE_EQ(residual(i, j), b(i, j));
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}
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}
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TEST(DenseBlasInternal, LocalDenseScopeRestoresTlsAfterProductsAndUnwind) {
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const int previous = mkl_set_num_threads_local(0);
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struct Restore {
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int previous;
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~Restore() { static_cast<void>(mkl_set_num_threads_local(previous)); }
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} restore{previous};
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const int default_threads = mkl_get_max_threads();
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const std::array<double, 2U> left{0.0, 2.0};
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const std::array<double, 2U> right{3.0, 4.0};
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std::array<double, 4U> product{};
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product.fill(std::numeric_limits<double>::quiet_NaN());
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{
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const ScopedLocalDenseThreads scope{};
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EXPECT_EQ(mkl_get_max_threads(), 1);
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EXPECT_TRUE(
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OuterProduct(left.data(), 2U, right.data(), 2U, product.data()));
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EXPECT_DOUBLE_EQ(product[0U], 0.0);
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EXPECT_DOUBLE_EQ(product[3U], 8.0);
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}
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EXPECT_EQ(mkl_get_max_threads(), default_threads);
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EXPECT_EQ(mkl_set_num_threads_local(0), 0);
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try {
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const ScopedLocalDenseThreads scope{};
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OuterProduct(nullptr, 2U, right.data(), 2U, product.data());
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} catch (const std::invalid_argument&) {
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}
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EXPECT_EQ(mkl_set_num_threads_local(0), 0);
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static_cast<void>(mkl_set_num_threads_local(3));
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{
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const ScopedLocalDenseThreads scope{};
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EXPECT_EQ(mkl_get_max_threads(), 3);
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}
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EXPECT_EQ(mkl_get_max_threads(), 3);
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TEST(DenseFactor, LuSolvesRectangularRhsOnBothSidesAndTransposes) {
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Matrix a{3U, 3U};
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const double values[]{0, 2, 1, 1, 1, 0, 2, 0, 1};
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for (std::size_t i = 0; i < 9U; ++i) a.Data()[i] = values[i];
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auto factor = DenseFactor::Lu(a);
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ASSERT_TRUE(factor.HasValue());
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EXPECT_DOUBLE_EQ(factor.Value().Determinant(), -4.0);
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for (const bool right : {false, true})
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for (const bool transpose : {false, true}) {
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Matrix expected{right ? 2U : 3U, right ? 3U : 2U};
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for (std::size_t i = 0; i < 6U; ++i)
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expected.Data()[i] = static_cast<double>(i) - 2.0;
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const auto b = FactorRhs(a, expected, transpose, right);
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const auto solved = right ? factor.Value().SolveRight(b, transpose)
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: factor.Value().Solve(b, transpose);
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ASSERT_TRUE(solved.HasValue());
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ExpectFactorSolution(a, solved.Value(), b, expected, transpose, right);
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}
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}
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TEST(DenseBlasInternal, OuterProductLeavesFiniteInputOverflowForOwnerGate) {
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const std::array<double, 1U> left{std::numeric_limits<double>::max()};
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const std::array<double, 1U> right{2.0};
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std::array<double, 1U> product{};
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EXPECT_TRUE(OuterProduct(left.data(), 1U, right.data(), 1U, product.data()));
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EXPECT_TRUE(std::isinf(product[0U]));
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TEST(DenseFactor, CholeskySolvesAndWhiteningRetainsScaleAndOrientation) {
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Matrix a{2U, 2U};
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a(0, 0) = 4;
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a(0, 1) = 2;
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a(1, 0) = 2;
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a(1, 1) = 5;
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const auto factor = DenseFactor::Cholesky(a);
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ASSERT_TRUE(factor.HasValue());
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EXPECT_DOUBLE_EQ(factor.Value().Determinant(), 16.0);
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const auto lower = factor.Value().Lower();
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ASSERT_TRUE(lower.HasValue());
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EXPECT_DOUBLE_EQ(lower.Value()(0, 0), 2.0);
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EXPECT_DOUBLE_EQ(lower.Value()(0, 1), 0.0);
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EXPECT_DOUBLE_EQ(lower.Value()(1, 0), 1.0);
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EXPECT_DOUBLE_EQ(lower.Value()(1, 1), 2.0);
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for (const bool right : {false, true})
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for (const bool transpose : {false, true}) {
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Matrix expected{right ? 3U : 2U, right ? 2U : 3U};
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for (std::size_t i = 0; i < 6U; ++i)
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expected.Data()[i] = static_cast<double>(i) - 2.0;
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const auto b = FactorRhs(a, expected, transpose, right);
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const auto solved = right ? factor.Value().SolveRight(b, transpose)
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: factor.Value().Solve(b, transpose);
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ASSERT_TRUE(solved.HasValue());
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ExpectFactorSolution(a, solved.Value(), b, expected, transpose, right);
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const auto triangular_rhs =
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FactorRhs(lower.Value(), expected, transpose, right);
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const auto triangular =
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right ? factor.Value().SolveLowerRight(triangular_rhs, transpose)
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: factor.Value().SolveLower(triangular_rhs, transpose);
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ASSERT_TRUE(triangular.HasValue());
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ExpectFactorSolution(lower.Value(), triangular.Value(), triangular_rhs,
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expected, transpose, right);
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}
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// W = I * L^-T / sqrt(4); verify W^T (4*A) W = I without a procedure.
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Matrix basis{3U, 2U};
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basis(0, 0) = 0.5;
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basis(1, 1) = 0.5;
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const auto w = factor.Value().SolveLowerRight(basis, true);
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ASSERT_TRUE(w.HasValue());
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for (std::size_t i = 0; i < 2U; ++i)
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for (std::size_t j = 0; j < 2U; ++j) {
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double gram = 0;
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for (std::size_t k = 0; k < 2U; ++k)
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for (std::size_t l = 0; l < 2U; ++l)
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gram += w.Value()(k, i) * (4 * a(k, l)) * w.Value()(l, j);
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EXPECT_DOUBLE_EQ(gram, i == j ? 1.0 : 0.0);
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}
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}
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TEST(DenseBlasInternal, TransposeRightProductUsesInnerAndRectangularStrides) {
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const std::array<double, 6U> left{1, 2, 3, 4, 5, 6};
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const std::array<double, 12U> right{7, 8, 9, 10, 11, 12,
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13, 14, 15, 16, 17, 18};
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std::array<double, 8U> product;
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ASSERT_TRUE(MultiplyTransposeRight(left.data(), 2U, right.data(), 4U, 3U,
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product.data()));
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const std::array<double, 8U> expected{50, 68, 86, 104, 122, 167, 212, 257};
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EXPECT_EQ(product, expected);
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EXPECT_TRUE(
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MultiplyTransposeRight(nullptr, 2U, nullptr, 4U, 0U, product.data()));
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for (const auto value : product) EXPECT_DOUBLE_EQ(value, 0.0);
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auto nonfinite = right;
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nonfinite[8U] = std::numeric_limits<double>::infinity();
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product.fill(31.0);
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EXPECT_FALSE(MultiplyTransposeRight(left.data(), 2U, nonfinite.data(), 4U, 3U,
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product.data()));
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for (const auto value : product) EXPECT_DOUBLE_EQ(value, 31.0);
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TEST(DenseFactor, OwnsSnapshotAndFailedCandidatesPreserveReusableFactor) {
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Matrix a{2U, 2U};
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a(0, 0) = 2;
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a(1, 1) = 4;
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auto factor = DenseFactor::Lu(a);
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ASSERT_TRUE(factor.HasValue());
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a(0, 0) = 8;
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const auto changed = DenseFactor::Lu(a);
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ASSERT_TRUE(changed.HasValue());
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Matrix rhs{2U, 1U, 8};
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const auto old_solution = factor.Value().Solve(rhs);
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ASSERT_TRUE(old_solution.HasValue());
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EXPECT_DOUBLE_EQ(old_solution.Value()(0, 0), 4);
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EXPECT_DOUBLE_EQ(changed.Value().Solve(rhs).Value()(0, 0), 1);
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EXPECT_FALSE(DenseFactor::Lu(Matrix{2U, 2U}).HasValue());
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EXPECT_FALSE(DenseFactor::Cholesky(Matrix{2U, 2U}).HasValue());
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a(0, 0) = -1;
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EXPECT_FALSE(DenseFactor::Cholesky(a).HasValue());
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EXPECT_FALSE(DenseFactor::Lu(Matrix{2U, 3U}).HasValue());
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a(0, 0) = (std::numeric_limits<double>::quiet_NaN)();
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EXPECT_FALSE(DenseFactor::Lu(a).HasValue());
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EXPECT_FALSE(DenseFactor::Cholesky(a).HasValue());
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EXPECT_FALSE(factor.Value().Solve(Matrix{3U, 1U}).HasValue());
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EXPECT_FALSE(factor.Value().SolveRight(Matrix{1U, 3U}).HasValue());
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EXPECT_FALSE(factor.Value().SolveLower(rhs).HasValue());
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rhs(0, 0) = (std::numeric_limits<double>::infinity)();
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EXPECT_FALSE(factor.Value().Solve(rhs).HasValue());
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EXPECT_DOUBLE_EQ(old_solution.Value()(0, 0), 4);
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rhs(0, 0) = 8;
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EXPECT_DOUBLE_EQ(factor.Value().Solve(rhs).Value()(0, 0), 4);
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Matrix tiny{1U, 1U, (std::numeric_limits<double>::min)()};
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const auto tiny_factor = DenseFactor::Lu(tiny);
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ASSERT_TRUE(tiny_factor.HasValue());
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EXPECT_FALSE(tiny_factor.Value()
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.Solve(Matrix{1U, 1U, (std::numeric_limits<double>::max)()})
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.HasValue());
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EXPECT_DOUBLE_EQ(tiny_factor.Value().Solve(tiny).Value()(0, 0), 1);
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}
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TEST(DenseFactor, EmptyAndInfinityConditionBoundaryAreExplicit) {
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for (const bool positive : {false, true}) {
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const auto empty = positive ? DenseFactor::Cholesky(Matrix{0U, 0U})
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: DenseFactor::Lu(Matrix{0U, 0U});
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ASSERT_TRUE(empty.HasValue());
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const auto left = empty.Value().Solve(Matrix{0U, 3U});
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ASSERT_TRUE(left.HasValue());
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EXPECT_EQ(left.Value().Columns(), 3U);
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const auto right = empty.Value().SolveRight(Matrix{4U, 0U});
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ASSERT_TRUE(right.HasValue());
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EXPECT_EQ(right.Value().Rows(), 4U);
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EXPECT_FALSE(empty.Value().ReciprocalConditionInfinity().HasValue());
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for (const double diagonal : {0x1p-31, 0x1p-32, 0x1p-33}) {
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Matrix a{2U, 2U};
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a(0, 0) = 1;
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a(1, 1) = diagonal;
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const auto factor =
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positive ? DenseFactor::Cholesky(a) : DenseFactor::Lu(a);
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ASSERT_TRUE(factor.HasValue());
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const auto rcond = factor.Value().ReciprocalConditionInfinity();
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ASSERT_TRUE(rcond.HasValue());
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EXPECT_DOUBLE_EQ(rcond.Value(), diagonal);
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EXPECT_EQ(rcond.Value() >= 0x1p-32, diagonal >= 0x1p-32);
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EXPECT_EQ(factor.Value().Solve(Matrix{2U, 0U}).Value().Columns(), 0U);
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EXPECT_EQ(factor.Value().SolveRight(Matrix{0U, 2U}).Value().Rows(), 0U);
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}
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}
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}
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TEST(DenseFactor, GeneralDimensionAndNonDiagonalConditionUseFullCoefficient) {
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Matrix a{8U, 8U};
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a(0, 0) = 4;
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for (std::size_t i = 1; i < 8U; ++i) {
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a(i, i) = 5;
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a(i, i - 1U) = 2;
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a(i - 1U, i) = 2;
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}
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const auto factor = DenseFactor::Cholesky(a);
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ASSERT_TRUE(factor.HasValue());
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Matrix expected{8U, 3U};
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for (std::size_t i = 0; i < 24U; ++i)
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expected.Data()[i] = static_cast<double>(i) - 8;
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const auto rhs = FactorRhs(a, expected, false, false);
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const auto solved = factor.Value().Solve(rhs);
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ASSERT_TRUE(solved.HasValue());
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ExpectFactorSolution(a, solved.Value(), rhs, expected, false, false);
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Matrix general{2U, 2U};
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general(0, 0) = 2;
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general(0, 1) = 1;
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general(1, 1) = 1;
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const auto lu = DenseFactor::Lu(general);
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ASSERT_TRUE(lu.HasValue());
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EXPECT_DOUBLE_EQ(lu.Value().ReciprocalConditionInfinity().Value(), 1.0 / 3.0);
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EXPECT_FALSE(lu.Value().Lower().HasValue());
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Matrix overflow{2U, 2U, (std::numeric_limits<double>::max)()};
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overflow(1, 0) = -overflow(1, 0);
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EXPECT_FALSE(DenseFactor::Lu(overflow).HasValue());
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}
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TEST(DenseBlasInternal, CDup003ConvertsZeroNormalAndOverflowLengths) {
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@@ -162,138 +230,199 @@ TEST(DenseBlasInternal, CDup003CopiesZeroAndNonzeroContiguousValues) {
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EXPECT_EQ(destination, source);
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}
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TEST(DenseBlasInternal, TransposeProductChecksShapeAndKnownRectangularAction) {
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TEST(DenseBlasInternal, TransposeLeftMatchesIndependentRectangularProduct) {
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Matrix left{3U, 2U};
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Matrix right{3U, 1U};
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Matrix right{3U, 4U};
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for (std::size_t row = 0; row < 3U; ++row) {
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left(row, 0U) = static_cast<double>(row + 1U);
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left(row, 1U) = 2.0;
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right(row, 0U) = static_cast<double>(row);
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for (std::size_t column = 0; column < 2U; ++column)
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left(row, column) = static_cast<double>(1U + row * 2U + column);
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for (std::size_t column = 0; column < 4U; ++column)
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right(row, column) = static_cast<double>(row + column) - 2.0;
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}
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const auto product = MultiplyTransposeLeft(left, right);
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const Matrix product = MultiplyTransposeLeft(left, right);
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ASSERT_EQ(product.Rows(), 2U);
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ASSERT_EQ(product.Columns(), 1U);
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EXPECT_DOUBLE_EQ(product(0U, 0U), 8.0);
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EXPECT_DOUBLE_EQ(product(1U, 0U), 6.0);
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EXPECT_THROW(static_cast<void>(MultiplyTransposeLeft(left, Matrix{2U, 1U})),
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ASSERT_EQ(product.Columns(), 4U);
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for (std::size_t row = 0; row < 2U; ++row)
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for (std::size_t column = 0; column < 4U; ++column) {
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double expected = 0.0;
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for (std::size_t inner = 0; inner < 3U; ++inner)
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expected += left(inner, row) * right(inner, column);
|
||||
EXPECT_DOUBLE_EQ(product(row, column), expected);
|
||||
}
|
||||
const auto gram = MultiplyTransposeLeft(left, left);
|
||||
EXPECT_DOUBLE_EQ(gram(0U, 0U), 35.0);
|
||||
EXPECT_DOUBLE_EQ(gram(0U, 1U), 44.0);
|
||||
EXPECT_DOUBLE_EQ(gram(1U, 1U), 56.0);
|
||||
}
|
||||
|
||||
TEST(DenseBlasInternal, TransposeLeftRetainsEmptyAndFailureContracts) {
|
||||
const auto zeros = MultiplyTransposeLeft(Matrix{0U, 2U}, Matrix{0U, 3U});
|
||||
ASSERT_EQ(zeros.Rows(), 2U);
|
||||
ASSERT_EQ(zeros.Columns(), 3U);
|
||||
EXPECT_DOUBLE_EQ(zeros(1U, 2U), 0.0);
|
||||
const auto empty = MultiplyTransposeLeft(
|
||||
Matrix{(std::numeric_limits<std::size_t>::max)(), 0U},
|
||||
Matrix{(std::numeric_limits<std::size_t>::max)(), 0U});
|
||||
EXPECT_EQ(empty.Rows(), 0U);
|
||||
EXPECT_EQ(empty.Columns(), 0U);
|
||||
EXPECT_THROW(static_cast<void>(MultiplyTransposeLeft(Matrix{1U, 2U},
|
||||
Matrix{2U, 1U})),
|
||||
std::invalid_argument);
|
||||
const auto empty = MultiplyTransposeLeft(Matrix{0U, 2U}, Matrix{0U, 3U});
|
||||
EXPECT_EQ(empty.Rows(), 2U);
|
||||
EXPECT_EQ(empty.Columns(), 3U);
|
||||
EXPECT_DOUBLE_EQ(empty(1U, 2U), 0.0);
|
||||
left(0U, 0U) = std::numeric_limits<double>::quiet_NaN();
|
||||
EXPECT_THROW(static_cast<void>(MultiplyTransposeLeft(left, right)),
|
||||
std::invalid_argument);
|
||||
left(0U, 0U) = 1.0;
|
||||
right(0U, 0U) = std::numeric_limits<double>::infinity();
|
||||
EXPECT_THROW(static_cast<void>(MultiplyTransposeLeft(left, right)),
|
||||
EXPECT_THROW(static_cast<void>(MultiplyTransposeLeft(
|
||||
Matrix{1U, 0U}, Matrix{1U, 1U,
|
||||
(std::numeric_limits<double>::quiet_NaN)()})),
|
||||
std::invalid_argument);
|
||||
}
|
||||
|
||||
TEST(DenseBlasInternal, DiagonalProductKeepsEntrywiseCancellationAndChecks) {
|
||||
Vector diagonal{3U};
|
||||
diagonal[0U] = 4;
|
||||
diagonal[1U] = 2;
|
||||
diagonal[2U] = -1;
|
||||
Vector input{3U};
|
||||
const double large = std::ldexp(1.0, 56);
|
||||
input[0U] = 1;
|
||||
input[1U] = -large;
|
||||
input[2U] = 2 * large;
|
||||
const auto product = MultiplyDiagonal(diagonal, input);
|
||||
EXPECT_DOUBLE_EQ(product[0U] + (product[1U] - product[2U]), 4);
|
||||
EXPECT_EQ(MultiplyDiagonal(Vector{0U}, Vector{0U}).Size(), 0U);
|
||||
EXPECT_THROW(static_cast<void>(MultiplyDiagonal(diagonal, Vector{2U})),
|
||||
std::invalid_argument);
|
||||
input[0U] = std::numeric_limits<double>::infinity();
|
||||
EXPECT_THROW(static_cast<void>(MultiplyDiagonal(diagonal, input)),
|
||||
std::invalid_argument);
|
||||
input[0U] = 1;
|
||||
diagonal[0U] = std::numeric_limits<double>::quiet_NaN();
|
||||
EXPECT_THROW(static_cast<void>(MultiplyDiagonal(diagonal, input)),
|
||||
std::invalid_argument);
|
||||
TEST(DenseBlasInternal, RawProductsPreserveDestinationOnNonfiniteInput) {
|
||||
const double left[]{1.0, 2.0, -3.0, 4.0};
|
||||
const double right[]{5.0, -6.0, 7.0, 8.0, -9.0, 10.0};
|
||||
std::array<double, 6U> destination{};
|
||||
ASSERT_TRUE(MultiplyTransposeRight(left, 2U, right, 3U, 2U,
|
||||
destination.data()));
|
||||
EXPECT_EQ(destination, (std::array<double, 6U>{-7.0, 23.0, 11.0,
|
||||
-39.0, 11.0, 67.0}));
|
||||
const double invalid[]{(std::numeric_limits<double>::infinity)(), 1.0};
|
||||
destination.fill(42.0);
|
||||
EXPECT_FALSE(MultiplyTransposeRight(invalid, 1U, right, 3U, 2U,
|
||||
destination.data()));
|
||||
EXPECT_FALSE(OuterProduct(left, 2U, invalid, 2U, destination.data()));
|
||||
for (const double value : destination) EXPECT_DOUBLE_EQ(value, 42.0);
|
||||
ASSERT_TRUE(OuterProduct(left, 2U, right, 3U, destination.data()));
|
||||
EXPECT_EQ(destination, (std::array<double, 6U>{5.0, -6.0, 7.0,
|
||||
10.0, -12.0, 14.0}));
|
||||
}
|
||||
|
||||
TEST(DenseBlasInternal, CholeskyAndInverseMatchKnownFactorsAndKeepFailedOutput) {
|
||||
Matrix matrix{2U, 2U};
|
||||
matrix(0U, 0U) = 4;
|
||||
matrix(0U, 1U) = 2;
|
||||
matrix(1U, 0U) = 2;
|
||||
matrix(1U, 1U) = 5;
|
||||
Matrix lower{0U, 0U}, inverse{0U, 0U};
|
||||
ASSERT_TRUE(CholeskyLowerAndInverse(matrix, lower, inverse));
|
||||
EXPECT_DOUBLE_EQ(lower(0U, 0U), 2);
|
||||
EXPECT_DOUBLE_EQ(lower(1U, 0U), 1);
|
||||
EXPECT_DOUBLE_EQ(lower(1U, 1U), 2);
|
||||
EXPECT_DOUBLE_EQ(lower(0U, 1U), 0);
|
||||
EXPECT_DOUBLE_EQ(inverse(0U, 0U), .5);
|
||||
EXPECT_DOUBLE_EQ(inverse(1U, 0U), -.25);
|
||||
EXPECT_DOUBLE_EQ(inverse(1U, 1U), .5);
|
||||
matrix(1U, 1U) = 0;
|
||||
EXPECT_FALSE(CholeskyLowerAndInverse(matrix, lower, inverse));
|
||||
EXPECT_DOUBLE_EQ(lower(1U, 1U), 2);
|
||||
EXPECT_DOUBLE_EQ(inverse(1U, 1U), .5);
|
||||
EXPECT_THROW(static_cast<void>(CholeskyLowerAndInverse(
|
||||
Matrix{2U, 1U}, lower, inverse)), std::invalid_argument);
|
||||
matrix(0U, 0U) = std::numeric_limits<double>::quiet_NaN();
|
||||
EXPECT_THROW(static_cast<void>(CholeskyLowerAndInverse(matrix, lower, inverse)),
|
||||
TEST(DenseBlasInternal, RawProductZeroDimensionsAndOverflowAreExplicit) {
|
||||
EXPECT_TRUE(OuterProduct(nullptr, 0U, nullptr, 3U, nullptr));
|
||||
EXPECT_TRUE(MultiplyTransposeRight(nullptr, 2U, nullptr, 0U, 3U, nullptr));
|
||||
std::array<double, 6U> zeros{1.0, 2.0, 3.0, 4.0, 5.0, 6.0};
|
||||
ASSERT_TRUE(MultiplyTransposeRight(nullptr, 2U, nullptr, 3U, 0U,
|
||||
zeros.data()));
|
||||
for (const double value : zeros) EXPECT_DOUBLE_EQ(value, 0.0);
|
||||
EXPECT_THROW(MultiplyTransposeRight(nullptr, 1U, nullptr, 1U, 1U, nullptr),
|
||||
std::invalid_argument);
|
||||
const auto overflow =
|
||||
static_cast<std::size_t>((std::numeric_limits<MKL_INT>::max)()) + 1U;
|
||||
EXPECT_THROW(MultiplyTransposeRight(nullptr, overflow, nullptr, 0U, 0U,
|
||||
nullptr), std::length_error);
|
||||
double unchanged = 42.0;
|
||||
EXPECT_THROW(CopyValues(&unchanged, overflow, &unchanged), std::length_error);
|
||||
EXPECT_DOUBLE_EQ(unchanged, 42.0);
|
||||
}
|
||||
|
||||
TEST(DenseBlasInternal,
|
||||
CholeskyFailureReasonPreservesCandidatesAndResetsOnReuse) {
|
||||
Matrix matrix{2U, 2U};
|
||||
matrix(0U, 0U) = 4.0;
|
||||
matrix(1U, 1U) = 9.0;
|
||||
Matrix lower{0U, 0U};
|
||||
Matrix inverse{0U, 0U};
|
||||
auto reason = CholeskyFailure::kInverse;
|
||||
ASSERT_TRUE(CholeskyLowerAndInverse(matrix, lower, inverse, &reason));
|
||||
EXPECT_EQ(reason, CholeskyFailure::kNone);
|
||||
matrix(1U, 1U) = -1.0;
|
||||
EXPECT_FALSE(CholeskyLowerAndInverse(matrix, lower, inverse, &reason));
|
||||
EXPECT_EQ(reason, CholeskyFailure::kPivot);
|
||||
EXPECT_DOUBLE_EQ(lower(1U, 1U), 3.0);
|
||||
EXPECT_DOUBLE_EQ(inverse(1U, 1U), 1.0 / 3.0);
|
||||
matrix(1U, 1U) = 9.0;
|
||||
EXPECT_TRUE(CholeskyLowerAndInverse(matrix, lower, inverse, &reason));
|
||||
EXPECT_EQ(reason, CholeskyFailure::kNone);
|
||||
reason = CholeskyFailure::kInverse;
|
||||
EXPECT_THROW(CholeskyLowerAndInverse(Matrix{2U, 1U}, lower, inverse, &reason),
|
||||
std::invalid_argument);
|
||||
EXPECT_EQ(reason, CholeskyFailure::kNone);
|
||||
}
|
||||
|
||||
TEST(DenseBlasInternal, SingleEquationScopeRestoresTlsAndRespectsOverrides) {
|
||||
const int previous = mkl_set_num_threads_local(0);
|
||||
struct Restore {
|
||||
int previous;
|
||||
~Restore() { static_cast<void>(mkl_set_num_threads_local(previous)); }
|
||||
} restore{previous};
|
||||
const int default_threads = mkl_get_max_threads();
|
||||
{
|
||||
const ScopedSingleEquationThreads scope{1U};
|
||||
EXPECT_EQ(mkl_get_max_threads(), 1);
|
||||
}
|
||||
EXPECT_EQ(mkl_get_max_threads(), default_threads);
|
||||
EXPECT_EQ(mkl_set_num_threads_local(0), 0);
|
||||
{
|
||||
const ScopedSingleEquationThreads scope{2U};
|
||||
EXPECT_EQ(mkl_get_max_threads(), default_threads);
|
||||
}
|
||||
try {
|
||||
const ScopedSingleEquationThreads scope{1U};
|
||||
throw std::runtime_error{"scope failure"};
|
||||
} catch (const std::runtime_error&) {
|
||||
}
|
||||
EXPECT_EQ(mkl_set_num_threads_local(0), 0);
|
||||
static_cast<void>(mkl_set_num_threads_local(3));
|
||||
{
|
||||
const ScopedSingleEquationThreads scope{1U};
|
||||
EXPECT_EQ(mkl_get_max_threads(), 3);
|
||||
}
|
||||
EXPECT_EQ(mkl_get_max_threads(), 3);
|
||||
TEST(DenseBlasInternal, ContiguousPrimitivesCheckEmptyAndOverflowBeforeUse) {
|
||||
EXPECT_DOUBLE_EQ(DotValues(nullptr, 0U, nullptr), 0.0);
|
||||
EXPECT_DOUBLE_EQ(NormValues(nullptr, 0U), 0.0);
|
||||
EXPECT_NO_THROW(ScaleValues(2.0, nullptr, 0U));
|
||||
EXPECT_NO_THROW(AxpyValues(2.0, nullptr, 0U, nullptr));
|
||||
const auto overflow =
|
||||
static_cast<std::size_t>((std::numeric_limits<MKL_INT>::max)()) + 1U;
|
||||
double unchanged = 42.0;
|
||||
EXPECT_THROW(DotValues(nullptr, overflow, nullptr), std::length_error);
|
||||
EXPECT_THROW(NormValues(nullptr, overflow), std::length_error);
|
||||
EXPECT_THROW(ScaleValues(2.0, &unchanged, overflow), std::length_error);
|
||||
EXPECT_THROW(AxpyValues(2.0, nullptr, overflow, &unchanged), std::length_error);
|
||||
EXPECT_DOUBLE_EQ(unchanged, 42.0);
|
||||
}
|
||||
|
||||
} // namespace
|
||||
} // namespace fesa::dense_blas_internal
|
||||
|
||||
namespace fesa::math_internal {
|
||||
namespace {
|
||||
// Taylor coefficients of t^i s^j through total degree three. This independent
|
||||
// polynomial oracle deliberately uses coefficients, not derivative channels.
|
||||
struct Polynomial {
|
||||
std::array<std::array<double, 4>, 4> c{};
|
||||
};
|
||||
Polynomial operator-(Polynomial a, const Polynomial& b) {
|
||||
for (std::size_t i = 0; i <= 3; ++i)
|
||||
for (std::size_t j = 0; i + j <= 3; ++j) a.c[i][j] -= b.c[i][j];
|
||||
return a;
|
||||
}
|
||||
Polynomial operator*(const Polynomial& a, const Polynomial& b) {
|
||||
Polynomial result;
|
||||
for (std::size_t i = 0; i <= 3; ++i)
|
||||
for (std::size_t j = 0; i + j <= 3; ++j)
|
||||
for (std::size_t k = 0; k <= i; ++k)
|
||||
for (std::size_t l = 0; l <= j; ++l)
|
||||
result.c[i][j] += a.c[k][l] * b.c[i-k][j-l];
|
||||
return result;
|
||||
}
|
||||
Polynomial PolynomialConstant(double value) {
|
||||
Polynomial p;
|
||||
p.c[0][0] = value;
|
||||
return p;
|
||||
}
|
||||
double PolynomialRead(const Polynomial& p, std::size_t degree,
|
||||
std::size_t channel) {
|
||||
return p.c[channel][degree-channel];
|
||||
}
|
||||
void PolynomialWrite(Polynomial& p, std::size_t degree, std::size_t channel,
|
||||
double value) {
|
||||
p.c[channel][degree-channel] = value;
|
||||
}
|
||||
TEST(JetLinearSolve, RecoversMixedCubicCoefficientsWithOnePrimalFactor) {
|
||||
std::array<std::array<Polynomial, 3>, 3> a{};
|
||||
const double values[]{0, 2, 1, 1, 1, 0, 2, 0, 1};
|
||||
for (std::size_t i = 0; i < 3; ++i)
|
||||
for (std::size_t j = 0; j < 3; ++j) {
|
||||
a[i][j] = PolynomialConstant(values[3*i+j]);
|
||||
for (std::size_t degree = 1; degree <= 3; ++degree)
|
||||
for (std::size_t c = 0; c <= degree; ++c)
|
||||
a[i][j].c[c][degree-c] = (static_cast<double>(i+2*j+c)-2) / 16;
|
||||
}
|
||||
std::array<Polynomial, 3> expected{}, rhs{};
|
||||
for (std::size_t i = 0; i < 3; ++i)
|
||||
for (std::size_t degree = 0; degree <= 3; ++degree)
|
||||
for (std::size_t c = 0; c <= degree; ++c)
|
||||
expected[i].c[c][degree-c] = (static_cast<double>(i+degree+2*c)-3) / 8;
|
||||
// Form the full product independently using exact dyadic long-double sums.
|
||||
for (std::size_t row = 0; row < 3; ++row)
|
||||
for (std::size_t i = 0; i <= 3; ++i)
|
||||
for (std::size_t j = 0; i+j <= 3; ++j) {
|
||||
long double sum = 0;
|
||||
for (std::size_t column = 0; column < 3; ++column)
|
||||
for (std::size_t k = 0; k <= i; ++k)
|
||||
for (std::size_t l = 0; l <= j; ++l)
|
||||
sum += static_cast<long double>(a[row][column].c[k][l]) *
|
||||
expected[column].c[i-k][j-l];
|
||||
rhs[row].c[i][j] = static_cast<double>(sum);
|
||||
}
|
||||
Matrix primal{3, 3};
|
||||
for (std::size_t i = 0; i < 3; ++i)
|
||||
for (std::size_t j = 0; j < 3; ++j) primal(i,j) = a[i][j].c[0][0];
|
||||
const auto factor = dense_blas_internal::DenseFactor::Lu(primal);
|
||||
ASSERT_TRUE(factor.HasValue());
|
||||
std::array<Polynomial, 3> solved{};
|
||||
ASSERT_TRUE(SolveJetAction(a, rhs, factor.Value(), {1,2,3,4},
|
||||
PolynomialConstant, PolynomialRead,
|
||||
PolynomialWrite, solved));
|
||||
for (std::size_t row = 0; row < 3; ++row)
|
||||
for (std::size_t i = 0; i <= 3; ++i)
|
||||
for (std::size_t j = 0; i+j <= 3; ++j)
|
||||
EXPECT_NEAR(solved[row].c[i][j], expected[row].c[i][j], 2e-14);
|
||||
}
|
||||
TEST(JetLinearSolve, FailedChannelSolvePreservesCandidateAndInputs) {
|
||||
std::array<std::array<Polynomial, 3>, 3> a{};
|
||||
Matrix primal{3, 3};
|
||||
for (std::size_t i = 0; i < 3; ++i) {
|
||||
primal(i,i) = 1;
|
||||
a[i][i] = PolynomialConstant(1);
|
||||
}
|
||||
const auto factor = dense_blas_internal::DenseFactor::Lu(primal);
|
||||
ASSERT_TRUE(factor.HasValue());
|
||||
std::array<Polynomial, 3> rhs{}, solved{};
|
||||
rhs[1].c[1][0] = std::numeric_limits<double>::infinity();
|
||||
solved[0].c[0][0] = 17;
|
||||
EXPECT_FALSE(SolveJetAction(a, rhs, factor.Value(), {1,2,3,4},
|
||||
PolynomialConstant, PolynomialRead,
|
||||
PolynomialWrite, solved));
|
||||
EXPECT_EQ(solved[0].c[0][0], 17);
|
||||
EXPECT_EQ(a[1][1].c[0][0], 1);
|
||||
EXPECT_EQ(rhs[1].c[1][0], std::numeric_limits<double>::infinity());
|
||||
}
|
||||
} // namespace
|
||||
} // namespace fesa::math_internal
|
||||
|
||||
Reference in New Issue
Block a user