internal/ceres/dense_cholesky_test.cc

// Ceres Solver - A fast non-linear least squares minimizer
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include "ceres/dense_cholesky.h"

#include <limits>
#include <memory>
#include <sstream>
#include <string>
#include <utility>

#include "Eigen/Core"
#include "Eigen/Dense"
#include "ceres/context_impl.h"
#include "ceres/internal/config.h"
#include "ceres/internal/eigen.h"
#include "ceres/iterative_refiner.h"
#include "ceres/linear_solver.h"
#include "ceres/types.h"
#include "gmock/gmock.h"
#include "gtest/gtest.h"

namespace ceres::internal {

using Param = ::testing::tuple<DenseLinearAlgebraLibraryType, bool>;
constexpr bool kMixedPrecision = true;
constexpr bool kFullPrecision = false;

namespace {

std::string ParamInfoToString(testing::TestParamInfo<Param> info) {
  Param param = info.param;
  std::stringstream ss;
  ss << DenseLinearAlgebraLibraryTypeToString(::testing::get<0>(param)) << "_"
     << (::testing::get<1>(param) ? "MixedPrecision" : "FullPrecision");
  return ss.str();
}
}  // namespace

class DenseCholeskyTest : public ::testing::TestWithParam<Param> {};

TEST_P(DenseCholeskyTest, FactorAndSolve) {
  // TODO(sameeragarwal): Convert these tests into type parameterized tests so
  // that we can test the single and double precision solvers.

  using Scalar = double;
  using MatrixType = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
  using VectorType = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;

  LinearSolver::Options options;
  ContextImpl context;
#ifndef CERES_NO_CUDA
  options.context = &context;
  std::string error;
  ASSERT_TRUE(context.InitCuda(&error)) << error;
#endif  // CERES_NO_CUDA
  options.dense_linear_algebra_library_type = ::testing::get<0>(GetParam());
  options.use_mixed_precision_solves = ::testing::get<1>(GetParam());
  const int kNumRefinementSteps = 4;
  if (options.use_mixed_precision_solves) {
    options.max_num_refinement_iterations = kNumRefinementSteps;
  }
  auto dense_cholesky = DenseCholesky::Create(options);

  const int kNumTrials = 10;
  const int kMinNumCols = 1;
  const int kMaxNumCols = 10;
  for (int num_cols = kMinNumCols; num_cols < kMaxNumCols; ++num_cols) {
    for (int trial = 0; trial < kNumTrials; ++trial) {
      const MatrixType a = MatrixType::Random(num_cols, num_cols);
      MatrixType lhs = a.transpose() * a;
      lhs += VectorType::Ones(num_cols).asDiagonal();
      Vector x = VectorType::Random(num_cols);
      Vector rhs = lhs * x;
      lhs.triangularView<Eigen::StrictlyUpper>().setZero();
      Vector actual = Vector::Random(num_cols);

      LinearSolver::Summary summary;
      summary.termination_type = dense_cholesky->FactorAndSolve(
          num_cols, lhs.data(), rhs.data(), actual.data(), &summary.message);
      EXPECT_EQ(summary.termination_type, LinearSolverTerminationType::SUCCESS);
      EXPECT_NEAR((x - actual).norm() / x.norm(),
                  0.0,
                  std::numeric_limits<double>::epsilon() * 10)
          << "\nexpected: " << x.transpose()
          << "\nactual  : " << actual.transpose();
    }
  }
}

INSTANTIATE_TEST_SUITE_P(EigenCholesky,
                         DenseCholeskyTest,
                         ::testing::Combine(::testing::Values(EIGEN),
                                            ::testing::Values(kMixedPrecision,
                                                              kFullPrecision)),
                         ParamInfoToString);
#ifndef CERES_NO_LAPACK
INSTANTIATE_TEST_SUITE_P(LapackCholesky,
                         DenseCholeskyTest,
                         ::testing::Combine(::testing::Values(LAPACK),
                                            ::testing::Values(kMixedPrecision,
                                                              kFullPrecision)),
                         ParamInfoToString);
#endif
#ifndef CERES_NO_CUDA
INSTANTIATE_TEST_SUITE_P(CudaCholesky,
                         DenseCholeskyTest,
                         ::testing::Combine(::testing::Values(CUDA),
                                            ::testing::Values(kMixedPrecision,
                                                              kFullPrecision)),
                         ParamInfoToString);
#endif

class MockDenseCholesky : public DenseCholesky {
 public:
  MOCK_METHOD3(Factorize,
               LinearSolverTerminationType(int num_cols,
                                           double* lhs,
                                           std::string* message));
  MOCK_METHOD3(Solve,
               LinearSolverTerminationType(const double* rhs,
                                           double* solution,
                                           std::string* message));
};

class MockDenseIterativeRefiner : public DenseIterativeRefiner {
 public:
  MockDenseIterativeRefiner() : DenseIterativeRefiner(1) {}
  MOCK_METHOD5(Refine,
               void(int num_cols,
                    const double* lhs,
                    const double* rhs,
                    DenseCholesky* dense_cholesky,
                    double* solution));
};

using testing::_;
using testing::Return;

TEST(RefinedDenseCholesky, Factorize) {
  auto dense_cholesky = std::make_unique<MockDenseCholesky>();
  auto iterative_refiner = std::make_unique<MockDenseIterativeRefiner>();
  EXPECT_CALL(*dense_cholesky, Factorize(_, _, _))
      .Times(1)
      .WillRepeatedly(Return(LinearSolverTerminationType::SUCCESS));
  EXPECT_CALL(*iterative_refiner, Refine(_, _, _, _, _)).Times(0);
  RefinedDenseCholesky refined_dense_cholesky(std::move(dense_cholesky),
                                              std::move(iterative_refiner));
  double lhs;
  std::string message;
  EXPECT_EQ(refined_dense_cholesky.Factorize(1, &lhs, &message),
            LinearSolverTerminationType::SUCCESS);
};

TEST(RefinedDenseCholesky, FactorAndSolveWithUnsuccessfulFactorization) {
  auto dense_cholesky = std::make_unique<MockDenseCholesky>();
  auto iterative_refiner = std::make_unique<MockDenseIterativeRefiner>();
  EXPECT_CALL(*dense_cholesky, Factorize(_, _, _))
      .Times(1)
      .WillRepeatedly(Return(LinearSolverTerminationType::FAILURE));
  EXPECT_CALL(*dense_cholesky, Solve(_, _, _)).Times(0);
  EXPECT_CALL(*iterative_refiner, Refine(_, _, _, _, _)).Times(0);
  RefinedDenseCholesky refined_dense_cholesky(std::move(dense_cholesky),
                                              std::move(iterative_refiner));
  double lhs;
  std::string message;
  double rhs;
  double solution;
  EXPECT_EQ(
      refined_dense_cholesky.FactorAndSolve(1, &lhs, &rhs, &solution, &message),
      LinearSolverTerminationType::FAILURE);
};

TEST(RefinedDenseCholesky, FactorAndSolveWithSuccess) {
  auto dense_cholesky = std::make_unique<MockDenseCholesky>();
  auto iterative_refiner = std::make_unique<MockDenseIterativeRefiner>();
  EXPECT_CALL(*dense_cholesky, Factorize(_, _, _))
      .Times(1)
      .WillRepeatedly(Return(LinearSolverTerminationType::SUCCESS));
  EXPECT_CALL(*dense_cholesky, Solve(_, _, _))
      .Times(1)
      .WillRepeatedly(Return(LinearSolverTerminationType::SUCCESS));
  EXPECT_CALL(*iterative_refiner, Refine(_, _, _, _, _)).Times(1);

  RefinedDenseCholesky refined_dense_cholesky(std::move(dense_cholesky),
                                              std::move(iterative_refiner));
  double lhs;
  std::string message;
  double rhs;
  double solution;
  EXPECT_EQ(
      refined_dense_cholesky.FactorAndSolve(1, &lhs, &rhs, &solution, &message),
      LinearSolverTerminationType::SUCCESS);
};

}  // namespace ceres::internal