internal/ceres/power_series_expansion_preconditioner_test.cc

// Ceres Solver - A fast non-linear least squares minimizer
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// Author: markshachkov@gmail.com (Mark Shachkov)

#include "ceres/power_series_expansion_preconditioner.h"

#include <memory>

#include "Eigen/Dense"
#include "ceres/linear_least_squares_problems.h"
#include "gtest/gtest.h"

namespace ceres::internal {

const double kEpsilon = 1e-14;

class PowerSeriesExpansionPreconditionerTest : public ::testing::Test {
 protected:
  void SetUp() final {
    problem_ = CreateLinearLeastSquaresProblemFromId(5);
    const auto A = down_cast<BlockSparseMatrix*>(problem_->A.get());
    const auto D = problem_->D.get();

    options_.elimination_groups.push_back(problem_->num_eliminate_blocks);
    options_.preconditioner_type = SCHUR_POWER_SERIES_EXPANSION;
    preconditioner_options_ = Preconditioner::Options(options_);
    isc_ = std::make_unique<ImplicitSchurComplement>(options_);
    isc_->Init(*A, D, problem_->b.get());
    num_f_cols_ = isc_->rhs().rows();
    const int num_rows = A->num_rows(), num_cols = A->num_cols(),
              num_e_cols = num_cols - num_f_cols_;

    // Using predefined linear operator with schur structure and block-diagonal
    // F'F to explicitly construct schur complement and to calculate its inverse
    // to be used as a reference.
    Matrix A_dense, E, F, DE, DF;
    problem_->A->ToDenseMatrix(&A_dense);
    E = A_dense.leftCols(num_e_cols);
    F = A_dense.rightCols(num_f_cols_);
    DE = VectorRef(D, num_e_cols).asDiagonal();
    DF = VectorRef(D + num_e_cols, num_f_cols_).asDiagonal();

    sc_inverse_expected_ =
        (F.transpose() *
             (Matrix::Identity(num_rows, num_rows) -
              E * (E.transpose() * E + DE).inverse() * E.transpose()) *
             F +
         DF)
            .inverse();
  }
  std::unique_ptr<LinearLeastSquaresProblem> problem_;
  std::unique_ptr<ImplicitSchurComplement> isc_;
  int num_f_cols_;
  Matrix sc_inverse_expected_;
  LinearSolver::Options options_;
  Preconditioner::Options preconditioner_options_;
};

TEST_F(PowerSeriesExpansionPreconditionerTest,
       InverseValidPreconditionerToleranceReached) {
  const double spse_tolerance = kEpsilon;
  const int max_num_iterations = 50;
  PowerSeriesExpansionPreconditioner preconditioner(
      isc_.get(), max_num_iterations, spse_tolerance, preconditioner_options_);

  Vector x(num_f_cols_), y(num_f_cols_);
  for (int i = 0; i < num_f_cols_; i++) {
    x.setZero();
    x(i) = 1.0;

    y.setZero();
    preconditioner.RightMultiplyAndAccumulate(x.data(), y.data());
    EXPECT_LT((y - sc_inverse_expected_.col(i)).norm(), kEpsilon)
        << "Reference Schur complement inverse and its estimate via "
           "PowerSeriesExpansionPreconditioner differs in "
        << i
        << " column.\nreference : " << sc_inverse_expected_.col(i).transpose()
        << "\nestimated: " << y.transpose();
  }
}

TEST_F(PowerSeriesExpansionPreconditionerTest,
       InverseValidPreconditionerMaxIterations) {
  const double spse_tolerance = 0;
  const int max_num_iterations = 50;
  PowerSeriesExpansionPreconditioner preconditioner_fixed_n_iterations(
      isc_.get(), max_num_iterations, spse_tolerance, preconditioner_options_);

  Vector x(num_f_cols_), y(num_f_cols_);
  for (int i = 0; i < num_f_cols_; i++) {
    x.setZero();
    x(i) = 1.0;

    y.setZero();
    preconditioner_fixed_n_iterations.RightMultiplyAndAccumulate(x.data(),
                                                                 y.data());
    EXPECT_LT((y - sc_inverse_expected_.col(i)).norm(), kEpsilon)
        << "Reference Schur complement inverse and its estimate via "
           "PowerSeriesExpansionPreconditioner differs in "
        << i
        << " column.\nreference : " << sc_inverse_expected_.col(i).transpose()
        << "\nestimated: " << y.transpose();
  }
}

TEST_F(PowerSeriesExpansionPreconditionerTest,
       InverseInvalidBadPreconditionerTolerance) {
  const double spse_tolerance = 1 / kEpsilon;
  const int max_num_iterations = 50;
  PowerSeriesExpansionPreconditioner preconditioner_bad_tolerance(
      isc_.get(), max_num_iterations, spse_tolerance, preconditioner_options_);

  Vector x(num_f_cols_), y(num_f_cols_);
  for (int i = 0; i < num_f_cols_; i++) {
    x.setZero();
    x(i) = 1.0;

    y.setZero();
    preconditioner_bad_tolerance.RightMultiplyAndAccumulate(x.data(), y.data());
    EXPECT_GT((y - sc_inverse_expected_.col(i)).norm(), kEpsilon)
        << "Reference Schur complement inverse and its estimate via "
           "PowerSeriesExpansionPreconditioner are too similar, tolerance "
           "stopping criteria failed.";
  }
}

TEST_F(PowerSeriesExpansionPreconditionerTest,
       InverseInvalidBadPreconditionerMaxIterations) {
  const double spse_tolerance = kEpsilon;
  const int max_num_iterations = 1;
  PowerSeriesExpansionPreconditioner preconditioner_bad_iterations_limit(
      isc_.get(), max_num_iterations, spse_tolerance, preconditioner_options_);

  Vector x(num_f_cols_), y(num_f_cols_);
  for (int i = 0; i < num_f_cols_; i++) {
    x.setZero();
    x(i) = 1.0;

    y.setZero();
    preconditioner_bad_iterations_limit.RightMultiplyAndAccumulate(x.data(),
                                                                   y.data());
    EXPECT_GT((y - sc_inverse_expected_.col(i)).norm(), kEpsilon)
        << "Reference Schur complement inverse and its estimate via "
           "PowerSeriesExpansionPreconditioner are too similar, maximum "
           "iterations stopping criteria failed.";
  }
}

}  // namespace ceres::internal