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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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// modification, are permitted provided that the following conditions are met:
//
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// Author: sameeragarwal@google.com (Sameer Agarwal)
//
// TODO(sameeragarwal): Add support for larger, more complicated and
// poorly conditioned problems both for correctness testing as well as
// benchmarking.
#include "ceres/iterative_schur_complement_solver.h"
#include <cstddef>
#include <memory>
#include "Eigen/Dense"
#include "ceres/block_random_access_dense_matrix.h"
#include "ceres/block_sparse_matrix.h"
#include "ceres/casts.h"
#include "ceres/context_impl.h"
#include "ceres/internal/eigen.h"
#include "ceres/linear_least_squares_problems.h"
#include "ceres/linear_solver.h"
#include "ceres/schur_eliminator.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/types.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
using testing::AssertionResult;
const double kEpsilon = 1e-14;
class IterativeSchurComplementSolverTest : public ::testing::Test {
protected:
void SetUpProblem(int problem_id) {
std::unique_ptr<LinearLeastSquaresProblem> problem =
CreateLinearLeastSquaresProblemFromId(problem_id);
CHECK(problem != nullptr);
A_.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
b_ = std::move(problem->b);
D_ = std::move(problem->D);
num_cols_ = A_->num_cols();
num_rows_ = A_->num_rows();
num_eliminate_blocks_ = problem->num_eliminate_blocks;
}
AssertionResult TestSolver(double* D,
PreconditionerType preconditioner_type,
bool use_spse_initialization) {
TripletSparseMatrix triplet_A(
A_->num_rows(), A_->num_cols(), A_->num_nonzeros());
A_->ToTripletSparseMatrix(&triplet_A);
DenseSparseMatrix dense_A(triplet_A);
LinearSolver::Options options;
options.type = DENSE_QR;
ContextImpl context;
options.context = &context;
std::unique_ptr<LinearSolver> qr(LinearSolver::Create(options));
LinearSolver::PerSolveOptions per_solve_options;
per_solve_options.D = D;
Vector reference_solution(num_cols_);
qr->Solve(&dense_A, b_.get(), per_solve_options, reference_solution.data());
options.elimination_groups.push_back(num_eliminate_blocks_);
options.elimination_groups.push_back(0);
options.max_num_iterations = num_cols_;
options.max_num_spse_iterations = 1;
options.use_spse_initialization = use_spse_initialization;
options.preconditioner_type = preconditioner_type;
IterativeSchurComplementSolver isc(options);
Vector isc_sol(num_cols_);
per_solve_options.r_tolerance = 1e-12;
isc.Solve(A_.get(), b_.get(), per_solve_options, isc_sol.data());
double diff = (isc_sol - reference_solution).norm();
if (diff < kEpsilon) {
return testing::AssertionSuccess();
} else {
return testing::AssertionFailure()
<< "The reference solution differs from the ITERATIVE_SCHUR"
<< " solution by " << diff << " which is more than " << kEpsilon;
}
}
int num_rows_;
int num_cols_;
int num_eliminate_blocks_;
std::unique_ptr<BlockSparseMatrix> A_;
std::unique_ptr<double[]> b_;
std::unique_ptr<double[]> D_;
};
TEST_F(IterativeSchurComplementSolverTest, NormalProblemSchurJacobi) {
SetUpProblem(2);
EXPECT_TRUE(TestSolver(nullptr, SCHUR_JACOBI, false));
EXPECT_TRUE(TestSolver(D_.get(), SCHUR_JACOBI, false));
}
TEST_F(IterativeSchurComplementSolverTest,
NormalProblemSchurJacobiWithPowerSeriesExpansionInitialization) {
SetUpProblem(2);
EXPECT_TRUE(TestSolver(nullptr, SCHUR_JACOBI, true));
EXPECT_TRUE(TestSolver(D_.get(), SCHUR_JACOBI, true));
}
TEST_F(IterativeSchurComplementSolverTest,
NormalProblemPowerSeriesExpansionPreconditioner) {
SetUpProblem(5);
EXPECT_TRUE(TestSolver(nullptr, SCHUR_POWER_SERIES_EXPANSION, false));
EXPECT_TRUE(TestSolver(D_.get(), SCHUR_POWER_SERIES_EXPANSION, false));
}
TEST_F(IterativeSchurComplementSolverTest, ProblemWithNoFBlocks) {
SetUpProblem(3);
EXPECT_TRUE(TestSolver(nullptr, SCHUR_JACOBI, false));
EXPECT_TRUE(TestSolver(D_.get(), SCHUR_JACOBI, false));
}
} // namespace internal
} // namespace ceres