| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2022 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are met: |
| // |
| // * Redistributions of source code must retain the above copyright notice, |
| // this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above copyright notice, |
| // this list of conditions and the following disclaimer in the documentation |
| // and/or other materials provided with the distribution. |
| // * Neither the name of Google Inc. nor the names of its contributors may be |
| // used to endorse or promote products derived from this software without |
| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| // POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Author: joydeepb@cs.utexas.edu (Joydeep Biswas) |
| |
| #include <string> |
| |
| #include "ceres/dense_cholesky.h" |
| #include "ceres/internal/config.h" |
| #include "ceres/internal/eigen.h" |
| #include "glog/logging.h" |
| #include "gtest/gtest.h" |
| |
| namespace ceres::internal { |
| |
| #ifndef CERES_NO_CUDA |
| |
| TEST(CUDADenseCholesky, InvalidOptionOnCreate) { |
| LinearSolver::Options options; |
| ContextImpl context; |
| options.context = &context; |
| std::string error; |
| EXPECT_TRUE(context.InitCuda(&error)) << error; |
| auto dense_cuda_solver = CUDADenseCholesky::Create(options); |
| EXPECT_EQ(dense_cuda_solver, nullptr); |
| } |
| |
| // Tests the CUDA Cholesky solver with a simple 4x4 matrix. |
| TEST(CUDADenseCholesky, Cholesky4x4Matrix) { |
| Eigen::Matrix4d A; |
| // clang-format off |
| A << 4, 12, -16, 0, |
| 12, 37, -43, 0, |
| -16, -43, 98, 0, |
| 0, 0, 0, 1; |
| // clang-format on |
| |
| Vector b = Eigen::Vector4d::Ones(); |
| LinearSolver::Options options; |
| ContextImpl context; |
| options.context = &context; |
| std::string error; |
| EXPECT_TRUE(context.InitCuda(&error)) << error; |
| options.dense_linear_algebra_library_type = CUDA; |
| auto dense_cuda_solver = CUDADenseCholesky::Create(options); |
| ASSERT_NE(dense_cuda_solver, nullptr); |
| std::string error_string; |
| ASSERT_EQ(dense_cuda_solver->Factorize(A.cols(), A.data(), &error_string), |
| LinearSolverTerminationType::SUCCESS); |
| Eigen::Vector4d x = Eigen::Vector4d::Zero(); |
| ASSERT_EQ(dense_cuda_solver->Solve(b.data(), x.data(), &error_string), |
| LinearSolverTerminationType::SUCCESS); |
| EXPECT_NEAR(x(0), 113.75 / 3.0, std::numeric_limits<double>::epsilon() * 10); |
| EXPECT_NEAR(x(1), -31.0 / 3.0, std::numeric_limits<double>::epsilon() * 10); |
| EXPECT_NEAR(x(2), 5.0 / 3.0, std::numeric_limits<double>::epsilon() * 10); |
| EXPECT_NEAR(x(3), 1.0000, std::numeric_limits<double>::epsilon() * 10); |
| } |
| |
| TEST(CUDADenseCholesky, SingularMatrix) { |
| Eigen::Matrix3d A; |
| // clang-format off |
| A << 1, 0, 0, |
| 0, 1, 0, |
| 0, 0, 0; |
| // clang-format on |
| |
| LinearSolver::Options options; |
| ContextImpl context; |
| options.context = &context; |
| std::string error; |
| EXPECT_TRUE(context.InitCuda(&error)) << error; |
| options.dense_linear_algebra_library_type = CUDA; |
| auto dense_cuda_solver = CUDADenseCholesky::Create(options); |
| ASSERT_NE(dense_cuda_solver, nullptr); |
| std::string error_string; |
| ASSERT_EQ(dense_cuda_solver->Factorize(A.cols(), A.data(), &error_string), |
| LinearSolverTerminationType::FAILURE); |
| } |
| |
| TEST(CUDADenseCholesky, NegativeMatrix) { |
| Eigen::Matrix3d A; |
| // clang-format off |
| A << 1, 0, 0, |
| 0, 1, 0, |
| 0, 0, -1; |
| // clang-format on |
| |
| LinearSolver::Options options; |
| ContextImpl context; |
| options.context = &context; |
| std::string error; |
| EXPECT_TRUE(context.InitCuda(&error)) << error; |
| options.dense_linear_algebra_library_type = CUDA; |
| auto dense_cuda_solver = CUDADenseCholesky::Create(options); |
| ASSERT_NE(dense_cuda_solver, nullptr); |
| std::string error_string; |
| ASSERT_EQ(dense_cuda_solver->Factorize(A.cols(), A.data(), &error_string), |
| LinearSolverTerminationType::FAILURE); |
| } |
| |
| TEST(CUDADenseCholesky, MustFactorizeBeforeSolve) { |
| const Eigen::Vector3d b = Eigen::Vector3d::Ones(); |
| LinearSolver::Options options; |
| ContextImpl context; |
| options.context = &context; |
| std::string error; |
| EXPECT_TRUE(context.InitCuda(&error)) << error; |
| options.dense_linear_algebra_library_type = CUDA; |
| auto dense_cuda_solver = CUDADenseCholesky::Create(options); |
| ASSERT_NE(dense_cuda_solver, nullptr); |
| std::string error_string; |
| ASSERT_EQ(dense_cuda_solver->Solve(b.data(), nullptr, &error_string), |
| LinearSolverTerminationType::FATAL_ERROR); |
| } |
| |
| TEST(CUDADenseCholesky, Randomized1600x1600Tests) { |
| const int kNumCols = 1600; |
| using LhsType = Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>; |
| using RhsType = Eigen::Matrix<double, Eigen::Dynamic, 1>; |
| using SolutionType = Eigen::Matrix<double, Eigen::Dynamic, 1>; |
| |
| LinearSolver::Options options; |
| ContextImpl context; |
| options.context = &context; |
| std::string error; |
| EXPECT_TRUE(context.InitCuda(&error)) << error; |
| options.dense_linear_algebra_library_type = ceres::CUDA; |
| std::unique_ptr<DenseCholesky> dense_cholesky = |
| CUDADenseCholesky::Create(options); |
| |
| const int kNumTrials = 20; |
| for (int i = 0; i < kNumTrials; ++i) { |
| LhsType lhs = LhsType::Random(kNumCols, kNumCols); |
| lhs = lhs.transpose() * lhs; |
| lhs += 1e-3 * LhsType::Identity(kNumCols, kNumCols); |
| SolutionType x_expected = SolutionType::Random(kNumCols); |
| RhsType rhs = lhs * x_expected; |
| SolutionType x_computed = SolutionType::Zero(kNumCols); |
| // Sanity check the random matrix sizes. |
| EXPECT_EQ(lhs.rows(), kNumCols); |
| EXPECT_EQ(lhs.cols(), kNumCols); |
| EXPECT_EQ(rhs.rows(), kNumCols); |
| EXPECT_EQ(rhs.cols(), 1); |
| EXPECT_EQ(x_expected.rows(), kNumCols); |
| EXPECT_EQ(x_expected.cols(), 1); |
| EXPECT_EQ(x_computed.rows(), kNumCols); |
| EXPECT_EQ(x_computed.cols(), 1); |
| LinearSolver::Summary summary; |
| summary.termination_type = dense_cholesky->FactorAndSolve( |
| kNumCols, lhs.data(), rhs.data(), x_computed.data(), &summary.message); |
| ASSERT_EQ(summary.termination_type, LinearSolverTerminationType::SUCCESS); |
| static const double kEpsilon = std::numeric_limits<double>::epsilon() * 2e5; |
| ASSERT_NEAR( |
| (x_computed - x_expected).norm() / x_expected.norm(), 0.0, kEpsilon); |
| } |
| } |
| |
| TEST(CUDADenseCholeskyMixedPrecision, InvalidOptionsOnCreate) { |
| { |
| // Did not ask for CUDA, and did not ask for mixed precision. |
| LinearSolver::Options options; |
| ContextImpl context; |
| options.context = &context; |
| std::string error; |
| EXPECT_TRUE(context.InitCuda(&error)) << error; |
| auto solver = CUDADenseCholeskyMixedPrecision::Create(options); |
| ASSERT_EQ(solver, nullptr); |
| } |
| { |
| // Asked for CUDA, but did not ask for mixed precision. |
| LinearSolver::Options options; |
| ContextImpl context; |
| options.context = &context; |
| std::string error; |
| EXPECT_TRUE(context.InitCuda(&error)) << error; |
| options.dense_linear_algebra_library_type = ceres::CUDA; |
| auto solver = CUDADenseCholeskyMixedPrecision::Create(options); |
| ASSERT_EQ(solver, nullptr); |
| } |
| } |
| |
| // Tests the CUDA Cholesky solver with a simple 4x4 matrix. |
| TEST(CUDADenseCholeskyMixedPrecision, Cholesky4x4Matrix1Step) { |
| Eigen::Matrix4d A; |
| // clang-format off |
| // A common test Cholesky decomposition test matrix, see : |
| // https://en.wikipedia.org/w/index.php?title=Cholesky_decomposition&oldid=1080607368#Example |
| A << 4, 12, -16, 0, |
| 12, 37, -43, 0, |
| -16, -43, 98, 0, |
| 0, 0, 0, 1; |
| // clang-format on |
| |
| const Eigen::Vector4d b = Eigen::Vector4d::Ones(); |
| LinearSolver::Options options; |
| options.max_num_refinement_iterations = 0; |
| ContextImpl context; |
| options.context = &context; |
| std::string error; |
| EXPECT_TRUE(context.InitCuda(&error)) << error; |
| options.dense_linear_algebra_library_type = CUDA; |
| options.use_mixed_precision_solves = true; |
| auto solver = CUDADenseCholeskyMixedPrecision::Create(options); |
| ASSERT_NE(solver, nullptr); |
| std::string error_string; |
| ASSERT_EQ(solver->Factorize(A.cols(), A.data(), &error_string), |
| LinearSolverTerminationType::SUCCESS); |
| Eigen::Vector4d x = Eigen::Vector4d::Zero(); |
| ASSERT_EQ(solver->Solve(b.data(), x.data(), &error_string), |
| LinearSolverTerminationType::SUCCESS); |
| // A single step of the mixed precision solver will be equivalent to solving |
| // in low precision (FP32). Hence the tolerance is defined w.r.t. FP32 epsilon |
| // instead of FP64 epsilon. |
| static const double kEpsilon = std::numeric_limits<float>::epsilon() * 15.0f; |
| EXPECT_NEAR(x(0), 113.75 / 3.0, kEpsilon); |
| EXPECT_NEAR(x(1), -31.0 / 3.0, kEpsilon); |
| EXPECT_NEAR(x(2), 5.0 / 3.0, kEpsilon); |
| EXPECT_NEAR(x(3), 1.0000, kEpsilon); |
| } |
| |
| // Tests the CUDA Cholesky solver with a simple 4x4 matrix. |
| TEST(CUDADenseCholeskyMixedPrecision, Cholesky4x4Matrix4Steps) { |
| Eigen::Matrix4d A; |
| // clang-format off |
| A << 4, 12, -16, 0, |
| 12, 37, -43, 0, |
| -16, -43, 98, 0, |
| 0, 0, 0, 1; |
| // clang-format on |
| |
| const Eigen::Vector4d b = Eigen::Vector4d::Ones(); |
| LinearSolver::Options options; |
| options.max_num_refinement_iterations = 3; |
| ContextImpl context; |
| options.context = &context; |
| std::string error; |
| EXPECT_TRUE(context.InitCuda(&error)) << error; |
| options.dense_linear_algebra_library_type = CUDA; |
| options.use_mixed_precision_solves = true; |
| auto solver = CUDADenseCholeskyMixedPrecision::Create(options); |
| ASSERT_NE(solver, nullptr); |
| std::string error_string; |
| ASSERT_EQ(solver->Factorize(A.cols(), A.data(), &error_string), |
| LinearSolverTerminationType::SUCCESS); |
| Eigen::Vector4d x = Eigen::Vector4d::Zero(); |
| ASSERT_EQ(solver->Solve(b.data(), x.data(), &error_string), |
| LinearSolverTerminationType::SUCCESS); |
| // The error does not reduce beyond four iterations, and stagnates at this |
| // level of precision. |
| static const double kEpsilon = std::numeric_limits<double>::epsilon() * 3e2; |
| EXPECT_NEAR(x(0), 113.75 / 3.0, kEpsilon); |
| EXPECT_NEAR(x(1), -31.0 / 3.0, kEpsilon); |
| EXPECT_NEAR(x(2), 5.0 / 3.0, kEpsilon); |
| EXPECT_NEAR(x(3), 1.0000, kEpsilon); |
| } |
| |
| TEST(CUDADenseCholeskyMixedPrecision, Randomized1600x1600Tests) { |
| const int kNumCols = 1600; |
| using LhsType = Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>; |
| using RhsType = Eigen::Matrix<double, Eigen::Dynamic, 1>; |
| using SolutionType = Eigen::Matrix<double, Eigen::Dynamic, 1>; |
| |
| LinearSolver::Options options; |
| ContextImpl context; |
| options.context = &context; |
| std::string error; |
| EXPECT_TRUE(context.InitCuda(&error)) << error; |
| options.dense_linear_algebra_library_type = ceres::CUDA; |
| options.use_mixed_precision_solves = true; |
| options.max_num_refinement_iterations = 20; |
| std::unique_ptr<CUDADenseCholeskyMixedPrecision> dense_cholesky = |
| CUDADenseCholeskyMixedPrecision::Create(options); |
| |
| const int kNumTrials = 20; |
| for (int i = 0; i < kNumTrials; ++i) { |
| LhsType lhs = LhsType::Random(kNumCols, kNumCols); |
| lhs = lhs.transpose() * lhs; |
| lhs += 1e-3 * LhsType::Identity(kNumCols, kNumCols); |
| SolutionType x_expected = SolutionType::Random(kNumCols); |
| RhsType rhs = lhs * x_expected; |
| SolutionType x_computed = SolutionType::Zero(kNumCols); |
| // Sanity check the random matrix sizes. |
| EXPECT_EQ(lhs.rows(), kNumCols); |
| EXPECT_EQ(lhs.cols(), kNumCols); |
| EXPECT_EQ(rhs.rows(), kNumCols); |
| EXPECT_EQ(rhs.cols(), 1); |
| EXPECT_EQ(x_expected.rows(), kNumCols); |
| EXPECT_EQ(x_expected.cols(), 1); |
| EXPECT_EQ(x_computed.rows(), kNumCols); |
| EXPECT_EQ(x_computed.cols(), 1); |
| LinearSolver::Summary summary; |
| summary.termination_type = dense_cholesky->FactorAndSolve( |
| kNumCols, lhs.data(), rhs.data(), x_computed.data(), &summary.message); |
| ASSERT_EQ(summary.termination_type, LinearSolverTerminationType::SUCCESS); |
| static const double kEpsilon = std::numeric_limits<double>::epsilon() * 1e6; |
| ASSERT_NEAR( |
| (x_computed - x_expected).norm() / x_expected.norm(), 0.0, kEpsilon); |
| } |
| } |
| |
| #endif // CERES_NO_CUDA |
| |
| } // namespace ceres::internal |