KOKO\Mimi
429 lines
18 KiB
C++
429 lines
18 KiB
C++
#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 <cstddef>
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#include <limits>
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#include <stdexcept>
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namespace fesa::dense_blas_internal {
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namespace {
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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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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(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(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(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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const auto zero = ToMklSize(0U);
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ASSERT_TRUE(zero.HasValue());
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EXPECT_EQ(zero.Value(), 0);
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const auto normal = ToMklSize(3U);
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ASSERT_TRUE(normal.HasValue());
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EXPECT_EQ(normal.Value(), 3);
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const std::size_t overflow =
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static_cast<std::size_t>((std::numeric_limits<MKL_INT>::max)()) + 1U;
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const auto rejected = ToMklSize(overflow);
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EXPECT_FALSE(rejected.HasValue());
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EXPECT_FALSE(rejected.GetStatus().IsOk());
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}
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TEST(DenseBlasInternal, CDup003CopiesZeroAndNonzeroContiguousValues) {
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EXPECT_NO_THROW(CopyValues(nullptr, 0U, nullptr));
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const std::array<double, 3U> source{1.25, -2.5, 4.0};
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std::array<double, 3U> destination{};
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CopyValues(source.data(), source.size(), destination.data());
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EXPECT_EQ(destination, source);
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}
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TEST(DenseBlasInternal, TransposeLeftMatchesIndependentRectangularProduct) {
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Matrix left{3U, 2U};
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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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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 Matrix product = MultiplyTransposeLeft(left, right);
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ASSERT_EQ(product.Rows(), 2U);
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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);
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EXPECT_DOUBLE_EQ(product(row, column), expected);
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}
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const auto gram = MultiplyTransposeLeft(left, left);
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EXPECT_DOUBLE_EQ(gram(0U, 0U), 35.0);
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EXPECT_DOUBLE_EQ(gram(0U, 1U), 44.0);
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EXPECT_DOUBLE_EQ(gram(1U, 1U), 56.0);
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}
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TEST(DenseBlasInternal, TransposeLeftRetainsEmptyAndFailureContracts) {
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const auto zeros = MultiplyTransposeLeft(Matrix{0U, 2U}, Matrix{0U, 3U});
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ASSERT_EQ(zeros.Rows(), 2U);
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ASSERT_EQ(zeros.Columns(), 3U);
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EXPECT_DOUBLE_EQ(zeros(1U, 2U), 0.0);
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const auto empty = MultiplyTransposeLeft(
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Matrix{(std::numeric_limits<std::size_t>::max)(), 0U},
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Matrix{(std::numeric_limits<std::size_t>::max)(), 0U});
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EXPECT_EQ(empty.Rows(), 0U);
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EXPECT_EQ(empty.Columns(), 0U);
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EXPECT_THROW(static_cast<void>(MultiplyTransposeLeft(Matrix{1U, 2U},
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Matrix{2U, 1U})),
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std::invalid_argument);
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EXPECT_THROW(static_cast<void>(MultiplyTransposeLeft(
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Matrix{1U, 0U}, Matrix{1U, 1U,
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(std::numeric_limits<double>::quiet_NaN)()})),
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std::invalid_argument);
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}
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TEST(DenseBlasInternal, RawProductsPreserveDestinationOnNonfiniteInput) {
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const double left[]{1.0, 2.0, -3.0, 4.0};
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const double right[]{5.0, -6.0, 7.0, 8.0, -9.0, 10.0};
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std::array<double, 6U> destination{};
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ASSERT_TRUE(MultiplyTransposeRight(left, 2U, right, 3U, 2U,
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destination.data()));
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EXPECT_EQ(destination, (std::array<double, 6U>{-7.0, 23.0, 11.0,
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-39.0, 11.0, 67.0}));
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const double invalid[]{(std::numeric_limits<double>::infinity)(), 1.0};
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destination.fill(42.0);
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EXPECT_FALSE(MultiplyTransposeRight(invalid, 1U, right, 3U, 2U,
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destination.data()));
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EXPECT_FALSE(OuterProduct(left, 2U, invalid, 2U, destination.data()));
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for (const double value : destination) EXPECT_DOUBLE_EQ(value, 42.0);
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ASSERT_TRUE(OuterProduct(left, 2U, right, 3U, destination.data()));
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EXPECT_EQ(destination, (std::array<double, 6U>{5.0, -6.0, 7.0,
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10.0, -12.0, 14.0}));
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}
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TEST(DenseBlasInternal, RawProductZeroDimensionsAndOverflowAreExplicit) {
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EXPECT_TRUE(OuterProduct(nullptr, 0U, nullptr, 3U, nullptr));
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EXPECT_TRUE(MultiplyTransposeRight(nullptr, 2U, nullptr, 0U, 3U, nullptr));
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std::array<double, 6U> zeros{1.0, 2.0, 3.0, 4.0, 5.0, 6.0};
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ASSERT_TRUE(MultiplyTransposeRight(nullptr, 2U, nullptr, 3U, 0U,
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zeros.data()));
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for (const double value : zeros) EXPECT_DOUBLE_EQ(value, 0.0);
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EXPECT_THROW(MultiplyTransposeRight(nullptr, 1U, nullptr, 1U, 1U, nullptr),
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std::invalid_argument);
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const auto overflow =
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static_cast<std::size_t>((std::numeric_limits<MKL_INT>::max)()) + 1U;
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EXPECT_THROW(MultiplyTransposeRight(nullptr, overflow, nullptr, 0U, 0U,
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nullptr), std::length_error);
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double unchanged = 42.0;
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EXPECT_THROW(CopyValues(&unchanged, overflow, &unchanged), std::length_error);
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EXPECT_DOUBLE_EQ(unchanged, 42.0);
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}
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TEST(DenseBlasInternal, ContiguousPrimitivesCheckEmptyAndOverflowBeforeUse) {
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EXPECT_DOUBLE_EQ(DotValues(nullptr, 0U, nullptr), 0.0);
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EXPECT_DOUBLE_EQ(NormValues(nullptr, 0U), 0.0);
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EXPECT_NO_THROW(ScaleValues(2.0, nullptr, 0U));
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EXPECT_NO_THROW(AxpyValues(2.0, nullptr, 0U, nullptr));
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const auto overflow =
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static_cast<std::size_t>((std::numeric_limits<MKL_INT>::max)()) + 1U;
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double unchanged = 42.0;
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EXPECT_THROW(DotValues(nullptr, overflow, nullptr), std::length_error);
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EXPECT_THROW(NormValues(nullptr, overflow), std::length_error);
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EXPECT_THROW(ScaleValues(2.0, &unchanged, overflow), std::length_error);
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EXPECT_THROW(AxpyValues(2.0, nullptr, overflow, &unchanged), std::length_error);
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EXPECT_DOUBLE_EQ(unchanged, 42.0);
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}
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} // namespace
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} // namespace fesa::dense_blas_internal
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namespace fesa::math_internal {
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namespace {
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// Taylor coefficients of t^i s^j through total degree three. This independent
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// polynomial oracle deliberately uses coefficients, not derivative channels.
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struct Polynomial {
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std::array<std::array<double, 4>, 4> c{};
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};
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Polynomial operator-(Polynomial a, const Polynomial& b) {
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for (std::size_t i = 0; i <= 3; ++i)
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for (std::size_t j = 0; i + j <= 3; ++j) a.c[i][j] -= b.c[i][j];
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return a;
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}
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Polynomial operator*(const Polynomial& a, const Polynomial& b) {
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Polynomial result;
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for (std::size_t i = 0; i <= 3; ++i)
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for (std::size_t j = 0; i + j <= 3; ++j)
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for (std::size_t k = 0; k <= i; ++k)
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for (std::size_t l = 0; l <= j; ++l)
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result.c[i][j] += a.c[k][l] * b.c[i-k][j-l];
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return result;
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}
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Polynomial PolynomialConstant(double value) {
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Polynomial p;
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p.c[0][0] = value;
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return p;
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}
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double PolynomialRead(const Polynomial& p, std::size_t degree,
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std::size_t channel) {
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return p.c[channel][degree-channel];
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}
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void PolynomialWrite(Polynomial& p, std::size_t degree, std::size_t channel,
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double value) {
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p.c[channel][degree-channel] = value;
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}
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TEST(JetLinearSolve, RecoversMixedCubicCoefficientsWithOnePrimalFactor) {
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std::array<std::array<Polynomial, 3>, 3> a{};
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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 < 3; ++i)
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for (std::size_t j = 0; j < 3; ++j) {
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a[i][j] = PolynomialConstant(values[3*i+j]);
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for (std::size_t degree = 1; degree <= 3; ++degree)
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for (std::size_t c = 0; c <= degree; ++c)
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a[i][j].c[c][degree-c] = (static_cast<double>(i+2*j+c)-2) / 16;
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}
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std::array<Polynomial, 3> expected{}, rhs{};
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for (std::size_t i = 0; i < 3; ++i)
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for (std::size_t degree = 0; degree <= 3; ++degree)
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for (std::size_t c = 0; c <= degree; ++c)
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expected[i].c[c][degree-c] = (static_cast<double>(i+degree+2*c)-3) / 8;
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// Form the full product independently using exact dyadic long-double sums.
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for (std::size_t row = 0; row < 3; ++row)
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for (std::size_t i = 0; i <= 3; ++i)
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for (std::size_t j = 0; i+j <= 3; ++j) {
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long double sum = 0;
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for (std::size_t column = 0; column < 3; ++column)
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for (std::size_t k = 0; k <= i; ++k)
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for (std::size_t l = 0; l <= j; ++l)
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sum += static_cast<long double>(a[row][column].c[k][l]) *
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expected[column].c[i-k][j-l];
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rhs[row].c[i][j] = static_cast<double>(sum);
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}
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Matrix primal{3, 3};
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for (std::size_t i = 0; i < 3; ++i)
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for (std::size_t j = 0; j < 3; ++j) primal(i,j) = a[i][j].c[0][0];
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const auto factor = dense_blas_internal::DenseFactor::Lu(primal);
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ASSERT_TRUE(factor.HasValue());
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std::array<Polynomial, 3> solved{};
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ASSERT_TRUE(SolveJetAction(a, rhs, factor.Value(), {1,2,3,4},
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PolynomialConstant, PolynomialRead,
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PolynomialWrite, solved));
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for (std::size_t row = 0; row < 3; ++row)
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for (std::size_t i = 0; i <= 3; ++i)
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for (std::size_t j = 0; i+j <= 3; ++j)
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EXPECT_NEAR(solved[row].c[i][j], expected[row].c[i][j], 2e-14);
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}
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TEST(JetLinearSolve, FailedChannelSolvePreservesCandidateAndInputs) {
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std::array<std::array<Polynomial, 3>, 3> a{};
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|
Matrix primal{3, 3};
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for (std::size_t i = 0; i < 3; ++i) {
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primal(i,i) = 1;
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a[i][i] = PolynomialConstant(1);
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|
}
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const auto factor = dense_blas_internal::DenseFactor::Lu(primal);
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ASSERT_TRUE(factor.HasValue());
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|
std::array<Polynomial, 3> rhs{}, solved{};
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rhs[1].c[1][0] = std::numeric_limits<double>::infinity();
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solved[0].c[0][0] = 17;
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EXPECT_FALSE(SolveJetAction(a, rhs, factor.Value(), {1,2,3,4},
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|
PolynomialConstant, PolynomialRead,
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|
PolynomialWrite, solved));
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EXPECT_EQ(solved[0].c[0][0], 17);
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EXPECT_EQ(a[1][1].c[0][0], 1);
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EXPECT_EQ(rhs[1].c[1][0], std::numeric_limits<double>::infinity());
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}
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} // namespace
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} // namespace fesa::math_internal
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