internal/ceres/cuda_dense_cholesky_test.cc

// Ceres Solver - A fast non-linear least squares minimizer
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// 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 {
namespace internal {

#ifndef CERES_NO_CUDA

TEST(CUDADenseCholesky, InvalidOptionOnCreate) {
  LinearSolver::Options options;
  ContextImpl context;
  options.context = &context;
  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;
  A <<  4,  12, -16, 0,
       12,  37, -43, 0,
      -16, -43,  98, 0,
        0,   0,   0, 1;
  const Eigen::Vector4d b = Eigen::Vector4d::Ones();
  LinearSolver::Options options;
  ContextImpl context;
  options.context = &context;
  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::LINEAR_SOLVER_SUCCESS);
  Eigen::Vector4d x = Eigen::Vector4d::Zero();
  ASSERT_EQ(dense_cuda_solver->Solve(b.data(), x.data(), &error_string),
            LinearSolverTerminationType::LINEAR_SOLVER_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;
  A <<  1, 0, 0,
        0, 1, 0,
        0, 0, 0;
  const Eigen::Vector3d b = Eigen::Vector3d::Ones();
  LinearSolver::Options options;
  ContextImpl context;
  options.context = &context;
  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::LINEAR_SOLVER_FAILURE);
}

TEST(CUDADenseCholesky, NegativeMatrix) {
  Eigen::Matrix3d A;
  A <<  1, 0, 0,
        0, 1, 0,
        0, 0, -1;
  const Eigen::Vector3d b = Eigen::Vector3d::Ones();
  LinearSolver::Options options;
  ContextImpl context;
  options.context = &context;
  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::LINEAR_SOLVER_FAILURE);
}

TEST(CUDADenseCholesky, MustFactorizeBeforeSolve) {
  const Eigen::Vector3d b = Eigen::Vector3d::Ones();
  LinearSolver::Options options;
  ContextImpl context;
  options.context = &context;
  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::LINEAR_SOLVER_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;
  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, LINEAR_SOLVER_SUCCESS);
    ASSERT_NEAR((x_computed - x_expected).norm() / x_expected.norm(),
                0.0,
                1e-10);
  }
}

#endif  // CERES_NO_CUDA

}  // namespace internal
}  // namespace ceres