env/ceres-solver/internal/ceres/cuda_dense_qr_test.cc

// Ceres Solver - A fast non-linear least squares minimizer
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// http://ceres-solver.org/
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// Author: joydeepb@cs.utexas.edu (Joydeep Biswas)

#include <string>

#include "ceres/dense_qr.h"
#include "ceres/internal/eigen.h"
#include "glog/logging.h"
#include "gtest/gtest.h"

namespace ceres::internal {

#ifndef CERES_NO_CUDA

TEST(CUDADenseQR, InvalidOptionOnCreate) {
  LinearSolver::Options options;
  ContextImpl context;
  options.context = &context;
  std::string error;
  EXPECT_TRUE(context.InitCuda(&error)) << error;
  auto dense_cuda_solver = CUDADenseQR::Create(options);
  EXPECT_EQ(dense_cuda_solver, nullptr);
}

// Tests the CUDA QR solver with a simple 4x4 matrix.
TEST(CUDADenseQR, QR4x4Matrix) {
  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;
  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 = CUDADenseQR::Create(options);
  ASSERT_NE(dense_cuda_solver, nullptr);
  std::string error_string;
  ASSERT_EQ(
      dense_cuda_solver->Factorize(A.rows(), 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);
  // Empirically observed accuracy of cuSolverDN's QR solver.
  const double kEpsilon = std::numeric_limits<double>::epsilon() * 1500;
  const Eigen::Vector4d x_expected(113.75 / 3.0, -31.0 / 3.0, 5.0 / 3.0, 1.0);
  EXPECT_NEAR((x - x_expected).norm() / x_expected.norm(), 0.0, kEpsilon);
}

// Tests the CUDA QR solver with a simple 4x4 matrix.
TEST(CUDADenseQR, QR4x2Matrix) {
  Eigen::Matrix<double, 4, 2> A;
  // clang-format off
  A <<  4,  12,
       12,  37,
      -16, -43,
        0,   0;
  // clang-format on

  const std::vector<double> b(4, 1.0);
  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 = CUDADenseQR::Create(options);
  ASSERT_NE(dense_cuda_solver, nullptr);
  std::string error_string;
  ASSERT_EQ(
      dense_cuda_solver->Factorize(A.rows(), A.cols(), A.data(), &error_string),
      LinearSolverTerminationType::SUCCESS);
  std::vector<double> x(2, 0);
  ASSERT_EQ(dense_cuda_solver->Solve(b.data(), x.data(), &error_string),
            LinearSolverTerminationType::SUCCESS);
  // Empirically observed accuracy of cuSolverDN's QR solver.
  const double kEpsilon = std::numeric_limits<double>::epsilon() * 10;
  // Solution values computed with Octave.
  const Eigen::Vector2d x_expected(-1.143410852713177, 0.4031007751937981);
  EXPECT_NEAR((x[0] - x_expected[0]) / x_expected[0], 0.0, kEpsilon);
  EXPECT_NEAR((x[1] - x_expected[1]) / x_expected[1], 0.0, kEpsilon);
}

TEST(CUDADenseQR, 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 = CUDADenseQR::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(CUDADenseQR, Randomized1600x100Tests) {
  const int kNumRows = 1600;
  const int kNumCols = 100;
  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<DenseQR> dense_qr = CUDADenseQR::Create(options);

  const int kNumTrials = 20;
  for (int i = 0; i < kNumTrials; ++i) {
    LhsType lhs = LhsType::Random(kNumRows, 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(), kNumRows);
    EXPECT_EQ(lhs.cols(), kNumCols);
    EXPECT_EQ(rhs.rows(), kNumRows);
    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_qr->FactorAndSolve(kNumRows,
                                                        kNumCols,
                                                        lhs.data(),
                                                        rhs.data(),
                                                        x_computed.data(),
                                                        &summary.message);
    ASSERT_EQ(summary.termination_type, LinearSolverTerminationType::SUCCESS);
    ASSERT_NEAR((x_computed - x_expected).norm() / x_expected.norm(),
                0.0,
                std::numeric_limits<double>::epsilon() * 400);
  }
}
#endif  // CERES_NO_CUDA

}  // namespace ceres::internal