| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2022 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
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| // Author: markshachkov@gmail.com (Mark Shachkov) |
| |
| #include "ceres/power_series_expansion_preconditioner.h" |
| |
| #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; |
| 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_; |
| }; |
| |
| TEST_F(PowerSeriesExpansionPreconditionerTest, |
| InverseValidPreconditionerToleranceReached) { |
| const double spse_tolerance = kEpsilon; |
| const int max_num_iterations = 50; |
| PowerSeriesExpansionPreconditioner preconditioner( |
| isc_.get(), max_num_iterations, spse_tolerance); |
| |
| 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); |
| |
| 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); |
| |
| 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); |
| |
| 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 |