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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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// Author: sameeragarwal@google.com (Sameer Agarwal)
#include "ceres/schur_complement_solver.h"
#include <cstddef>
#include <memory>
#include "ceres/block_sparse_matrix.h"
#include "ceres/block_structure.h"
#include "ceres/casts.h"
#include "ceres/context_impl.h"
#include "ceres/detect_structure.h"
#include "ceres/linear_least_squares_problems.h"
#include "ceres/linear_solver.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/types.h"
#include "gtest/gtest.h"
namespace ceres::internal {
class SchurComplementSolverTest : public ::testing::Test {
protected:
void SetUpFromProblemId(int problem_id) {
std::unique_ptr<LinearLeastSquaresProblem> problem =
CreateLinearLeastSquaresProblemFromId(problem_id);
ASSERT_TRUE(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;
x.resize(num_cols);
sol.resize(num_cols);
sol_d.resize(num_cols);
LinearSolver::Options options;
options.type = DENSE_QR;
ContextImpl context;
options.context = &context;
std::unique_ptr<LinearSolver> qr(LinearSolver::Create(options));
TripletSparseMatrix triplet_A(
A->num_rows(), A->num_cols(), A->num_nonzeros());
A->ToTripletSparseMatrix(&triplet_A);
// Gold standard solutions using dense QR factorization.
DenseSparseMatrix dense_A(triplet_A);
qr->Solve(&dense_A, b.get(), LinearSolver::PerSolveOptions(), sol.data());
// Gold standard solution with appended diagonal.
LinearSolver::PerSolveOptions per_solve_options;
per_solve_options.D = D.get();
qr->Solve(&dense_A, b.get(), per_solve_options, sol_d.data());
}
void ComputeAndCompareSolutions(
int problem_id,
bool regularization,
ceres::LinearSolverType linear_solver_type,
ceres::DenseLinearAlgebraLibraryType dense_linear_algebra_library_type,
ceres::SparseLinearAlgebraLibraryType sparse_linear_algebra_library_type,
ceres::internal::OrderingType ordering_type) {
SetUpFromProblemId(problem_id);
LinearSolver::Options options;
options.elimination_groups.push_back(num_eliminate_blocks);
options.elimination_groups.push_back(A->block_structure()->cols.size() -
num_eliminate_blocks);
options.type = linear_solver_type;
options.dense_linear_algebra_library_type =
dense_linear_algebra_library_type;
options.sparse_linear_algebra_library_type =
sparse_linear_algebra_library_type;
options.ordering_type = ordering_type;
ContextImpl context;
options.context = &context;
DetectStructure(*A->block_structure(),
num_eliminate_blocks,
&options.row_block_size,
&options.e_block_size,
&options.f_block_size);
std::unique_ptr<LinearSolver> solver(LinearSolver::Create(options));
LinearSolver::PerSolveOptions per_solve_options;
LinearSolver::Summary summary;
if (regularization) {
per_solve_options.D = D.get();
}
summary = solver->Solve(A.get(), b.get(), per_solve_options, x.data());
EXPECT_EQ(summary.termination_type, LinearSolverTerminationType::SUCCESS);
if (regularization) {
ASSERT_NEAR((sol_d - x).norm() / num_cols, 0, 1e-10)
<< "Regularized Expected solution: " << sol_d.transpose()
<< " Actual solution: " << x.transpose();
} else {
ASSERT_NEAR((sol - x).norm() / num_cols, 0, 1e-10)
<< "Unregularized Expected solution: " << sol.transpose()
<< " Actual solution: " << x.transpose();
}
}
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;
Vector x;
Vector sol;
Vector sol_d;
};
// TODO(sameeragarwal): Refactor these using value parameterized tests.
// TODO(sameeragarwal): More extensive tests using random matrices.
TEST_F(SchurComplementSolverTest, DenseSchurWithEigenSmallProblem) {
ComputeAndCompareSolutions(
2, false, DENSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NATURAL);
ComputeAndCompareSolutions(
2, true, DENSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NATURAL);
}
TEST_F(SchurComplementSolverTest, DenseSchurWithEigenLargeProblem) {
ComputeAndCompareSolutions(
3, false, DENSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NATURAL);
ComputeAndCompareSolutions(
3, true, DENSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NATURAL);
}
TEST_F(SchurComplementSolverTest, DenseSchurWithEigenVaryingFBlockSize) {
ComputeAndCompareSolutions(
4, true, DENSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NATURAL);
}
#ifndef CERES_NO_LAPACK
TEST_F(SchurComplementSolverTest, DenseSchurWithLAPACKSmallProblem) {
ComputeAndCompareSolutions(
2, false, DENSE_SCHUR, LAPACK, SUITE_SPARSE, OrderingType::NATURAL);
ComputeAndCompareSolutions(
2, true, DENSE_SCHUR, LAPACK, SUITE_SPARSE, OrderingType::NATURAL);
}
TEST_F(SchurComplementSolverTest, DenseSchurWithLAPACKLargeProblem) {
ComputeAndCompareSolutions(
3, false, DENSE_SCHUR, LAPACK, SUITE_SPARSE, OrderingType::NATURAL);
ComputeAndCompareSolutions(
3, true, DENSE_SCHUR, LAPACK, SUITE_SPARSE, OrderingType::NATURAL);
}
#endif
#ifndef CERES_NO_SUITESPARSE
TEST_F(SchurComplementSolverTest,
SparseSchurWithSuiteSparseSmallProblemNATURAL) {
ComputeAndCompareSolutions(
2, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NATURAL);
ComputeAndCompareSolutions(
2, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NATURAL);
}
TEST_F(SchurComplementSolverTest,
SparseSchurWithSuiteSparseLargeProblemNATURAL) {
ComputeAndCompareSolutions(
3, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NATURAL);
ComputeAndCompareSolutions(
3, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NATURAL);
}
TEST_F(SchurComplementSolverTest, SparseSchurWithSuiteSparseSmallProblemAMD) {
ComputeAndCompareSolutions(
2, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::AMD);
ComputeAndCompareSolutions(
2, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::AMD);
}
TEST_F(SchurComplementSolverTest, SparseSchurWithSuiteSparseLargeProblemAMD) {
ComputeAndCompareSolutions(
3, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::AMD);
ComputeAndCompareSolutions(
3, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::AMD);
}
#ifndef CERES_NO_EIGEN_METIS
TEST_F(SchurComplementSolverTest,
SparseSchurWithSuiteSparseSmallProblemNESDIS) {
ComputeAndCompareSolutions(
2, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NESDIS);
ComputeAndCompareSolutions(
2, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NESDIS);
}
TEST_F(SchurComplementSolverTest,
SparseSchurWithSuiteSparseLargeProblemNESDIS) {
ComputeAndCompareSolutions(
3, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NESDIS);
ComputeAndCompareSolutions(
3, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, OrderingType::NESDIS);
}
#endif // CERES_NO_EIGEN_METIS
#endif // CERES_NO_SUITESPARSE
#ifndef CERES_NO_ACCELERATE_SPARSE
TEST_F(SchurComplementSolverTest,
SparseSchurWithAccelerateSparseSmallProblemAMD) {
ComputeAndCompareSolutions(
2, false, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, OrderingType::AMD);
ComputeAndCompareSolutions(
2, true, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, OrderingType::AMD);
}
TEST_F(SchurComplementSolverTest,
SparseSchurWithAccelerateSparseSmallProblemNESDIS) {
ComputeAndCompareSolutions(
2, false, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, OrderingType::NESDIS);
ComputeAndCompareSolutions(
2, true, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, OrderingType::NESDIS);
}
TEST_F(SchurComplementSolverTest,
SparseSchurWithAccelerateSparseLargeProblemAMD) {
ComputeAndCompareSolutions(
3, false, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, OrderingType::AMD);
ComputeAndCompareSolutions(
3, true, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, OrderingType::AMD);
}
TEST_F(SchurComplementSolverTest,
SparseSchurWithAccelerateSparseLargeProblemNESDIS) {
ComputeAndCompareSolutions(
3, false, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, OrderingType::NESDIS);
ComputeAndCompareSolutions(
3, true, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, OrderingType::NESDIS);
}
#endif // CERES_NO_ACCELERATE_SPARSE
#ifdef CERES_USE_EIGEN_SPARSE
TEST_F(SchurComplementSolverTest, SparseSchurWithEigenSparseSmallProblemAMD) {
ComputeAndCompareSolutions(
2, false, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::AMD);
ComputeAndCompareSolutions(
2, true, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::AMD);
}
#ifndef CERES_NO_EIGEN_METIS
TEST_F(SchurComplementSolverTest,
SparseSchurWithEigenSparseSmallProblemNESDIS) {
ComputeAndCompareSolutions(
2, false, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::NESDIS);
ComputeAndCompareSolutions(
2, true, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::NESDIS);
}
#endif
TEST_F(SchurComplementSolverTest,
SparseSchurWithEigenSparseSmallProblemNATURAL) {
ComputeAndCompareSolutions(
2, false, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::NATURAL);
ComputeAndCompareSolutions(
2, true, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::NATURAL);
}
TEST_F(SchurComplementSolverTest, SparseSchurWithEigenSparseLargeProblemAMD) {
ComputeAndCompareSolutions(
3, false, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::AMD);
ComputeAndCompareSolutions(
3, true, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::AMD);
}
#ifndef CERES_NO_EIGEN_METIS
TEST_F(SchurComplementSolverTest,
SparseSchurWithEigenSparseLargeProblemNESDIS) {
ComputeAndCompareSolutions(
3, false, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::NESDIS);
ComputeAndCompareSolutions(
3, true, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::NESDIS);
}
#endif
TEST_F(SchurComplementSolverTest,
SparseSchurWithEigenSparseLargeProblemNATURAL) {
ComputeAndCompareSolutions(
3, false, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::NATURAL);
ComputeAndCompareSolutions(
3, true, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, OrderingType::NATURAL);
}
#endif // CERES_USE_EIGEN_SPARSE
} // namespace ceres::internal