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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
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// used to endorse or promote products derived from this software without
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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 "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
class SchurComplementSolverTest : public ::testing::Test {
protected:
void SetUpFromProblemId(int problem_id) {
std::unique_ptr<LinearLeastSquaresProblem> problem(
CreateLinearLeastSquaresProblemFromId(problem_id));
CHECK(problem != nullptr);
A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
b.reset(problem->b.release());
D.reset(problem->D.release());
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,
bool use_postordering) {
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.use_postordering = use_postordering;
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, LINEAR_SOLVER_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, true);
ComputeAndCompareSolutions(2, true, DENSE_SCHUR, EIGEN, SUITE_SPARSE, true);
}
TEST_F(SchurComplementSolverTest, DenseSchurWithEigenLargeProblem) {
ComputeAndCompareSolutions(3, false, DENSE_SCHUR, EIGEN, SUITE_SPARSE, true);
ComputeAndCompareSolutions(3, true, DENSE_SCHUR, EIGEN, SUITE_SPARSE, true);
}
TEST_F(SchurComplementSolverTest, DenseSchurWithEigenVaryingFBlockSize) {
ComputeAndCompareSolutions(4, true, DENSE_SCHUR, EIGEN, SUITE_SPARSE, true);
}
#ifndef CERES_NO_LAPACK
TEST_F(SchurComplementSolverTest, DenseSchurWithLAPACKSmallProblem) {
ComputeAndCompareSolutions(2, false, DENSE_SCHUR, LAPACK, SUITE_SPARSE, true);
ComputeAndCompareSolutions(2, true, DENSE_SCHUR, LAPACK, SUITE_SPARSE, true);
}
TEST_F(SchurComplementSolverTest, DenseSchurWithLAPACKLargeProblem) {
ComputeAndCompareSolutions(3, false, DENSE_SCHUR, LAPACK, SUITE_SPARSE, true);
ComputeAndCompareSolutions(3, true, DENSE_SCHUR, LAPACK, SUITE_SPARSE, true);
}
#endif
#ifndef CERES_NO_SUITESPARSE
TEST_F(SchurComplementSolverTest,
SparseSchurWithSuiteSparseSmallProblemNoPostOrdering) {
ComputeAndCompareSolutions(
2, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, false);
ComputeAndCompareSolutions(2, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, false);
}
TEST_F(SchurComplementSolverTest,
SparseSchurWithSuiteSparseSmallProblemPostOrdering) {
ComputeAndCompareSolutions(2, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, true);
ComputeAndCompareSolutions(2, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, true);
}
TEST_F(SchurComplementSolverTest,
SparseSchurWithSuiteSparseLargeProblemNoPostOrdering) {
ComputeAndCompareSolutions(
3, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, false);
ComputeAndCompareSolutions(3, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, false);
}
TEST_F(SchurComplementSolverTest,
SparseSchurWithSuiteSparseLargeProblemPostOrdering) {
ComputeAndCompareSolutions(3, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, true);
ComputeAndCompareSolutions(3, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, true);
}
#endif // CERES_NO_SUITESPARSE
#ifndef CERES_NO_CXSPARSE
TEST_F(SchurComplementSolverTest,
SparseSchurWithCXSparseSmallProblem) {
ComputeAndCompareSolutions(2, false, SPARSE_SCHUR, EIGEN, CX_SPARSE, true);
ComputeAndCompareSolutions(2, true, SPARSE_SCHUR, EIGEN, CX_SPARSE, true);
}
TEST_F(SchurComplementSolverTest,
SparseSchurWithCXSparseLargeProblem) {
ComputeAndCompareSolutions(3, false, SPARSE_SCHUR, EIGEN, CX_SPARSE, true);
ComputeAndCompareSolutions(3, true, SPARSE_SCHUR, EIGEN, CX_SPARSE, true);
}
#endif // CERES_NO_CXSPARSE
#ifndef CERES_NO_ACCELERATE_SPARSE
TEST_F(SchurComplementSolverTest,
SparseSchurWithAccelerateSparseSmallProblem) {
ComputeAndCompareSolutions(2, false, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, true);
ComputeAndCompareSolutions(2, true, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, true);
}
TEST_F(SchurComplementSolverTest,
SparseSchurWithAccelerateSparseLargeProblem) {
ComputeAndCompareSolutions(3, false, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, true);
ComputeAndCompareSolutions(3, true, SPARSE_SCHUR, EIGEN, ACCELERATE_SPARSE, true);
}
#endif // CERES_NO_ACCELERATE_SPARSE
#ifdef CERES_USE_EIGEN_SPARSE
TEST_F(SchurComplementSolverTest,
SparseSchurWithEigenSparseSmallProblem) {
ComputeAndCompareSolutions(2, false, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, true);
ComputeAndCompareSolutions(2, true, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, true);
}
TEST_F(SchurComplementSolverTest,
SparseSchurWithEigenSparseLargeProblem) {
ComputeAndCompareSolutions(3, false, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, true);
ComputeAndCompareSolutions(3, true, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, true);
}
#endif // CERES_USE_EIGEN_SPARSE
} // namespace internal
} // namespace ceres