1 // Ceres Solver - A fast non-linear least squares minimizer
2 // Copyright 2015 Google Inc. All rights reserved.
3 // http://ceres-solver.org/
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29 // Author: sameeragarwal@google.com (Sameer Agarwal)
30 //
31 // TODO(sameeragarwal): Add support for larger, more complicated and
32 // poorly conditioned problems both for correctness testing as well as
33 // benchmarking.
34 
35 #include "ceres/iterative_schur_complement_solver.h"
36 
37 #include <cstddef>
38 #include "Eigen/Dense"
39 #include "ceres/block_random_access_dense_matrix.h"
40 #include "ceres/block_sparse_matrix.h"
41 #include "ceres/casts.h"
42 #include "ceres/internal/eigen.h"
43 #include "ceres/internal/scoped_ptr.h"
44 #include "ceres/linear_least_squares_problems.h"
45 #include "ceres/linear_solver.h"
46 #include "ceres/schur_eliminator.h"
47 #include "ceres/triplet_sparse_matrix.h"
48 #include "ceres/types.h"
49 #include "glog/logging.h"
50 #include "gtest/gtest.h"
51 
52 namespace ceres {
53 namespace internal {
54 
55 using testing::AssertionResult;
56 
57 const double kEpsilon = 1e-14;
58 
59 class IterativeSchurComplementSolverTest : public ::testing::Test {
60  protected :
SetUpProblem(int problem_id)61   void SetUpProblem(int problem_id) {
62     scoped_ptr<LinearLeastSquaresProblem> problem(
63         CreateLinearLeastSquaresProblemFromId(problem_id));
64 
65     CHECK_NOTNULL(problem.get());
66     A_.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
67     b_.reset(problem->b.release());
68     D_.reset(problem->D.release());
69 
70     num_cols_ = A_->num_cols();
71     num_rows_ = A_->num_rows();
72     num_eliminate_blocks_ = problem->num_eliminate_blocks;
73   }
74 
TestSolver(double * D)75   AssertionResult TestSolver(double* D) {
76     TripletSparseMatrix triplet_A(A_->num_rows(),
77                                   A_->num_cols(),
78                                   A_->num_nonzeros());
79     A_->ToTripletSparseMatrix(&triplet_A);
80 
81     DenseSparseMatrix dense_A(triplet_A);
82 
83     LinearSolver::Options options;
84     options.type = DENSE_QR;
85     scoped_ptr<LinearSolver> qr(LinearSolver::Create(options));
86 
87     LinearSolver::PerSolveOptions per_solve_options;
88     per_solve_options.D = D;
89     Vector reference_solution(num_cols_);
90     qr->Solve(&dense_A, b_.get(), per_solve_options, reference_solution.data());
91 
92     options.elimination_groups.push_back(num_eliminate_blocks_);
93     options.elimination_groups.push_back(0);
94     options.max_num_iterations = num_cols_;
95     options.preconditioner_type = SCHUR_JACOBI;
96     IterativeSchurComplementSolver isc(options);
97 
98     Vector isc_sol(num_cols_);
99     per_solve_options.r_tolerance  = 1e-12;
100     isc.Solve(A_.get(), b_.get(), per_solve_options, isc_sol.data());
101     double diff = (isc_sol - reference_solution).norm();
102     if (diff < kEpsilon) {
103       return testing::AssertionSuccess();
104     } else {
105       return testing::AssertionFailure()
106           << "The reference solution differs from the ITERATIVE_SCHUR"
107           << " solution by " << diff << " which is more than " << kEpsilon;
108     }
109   }
110 
111   int num_rows_;
112   int num_cols_;
113   int num_eliminate_blocks_;
114   scoped_ptr<BlockSparseMatrix> A_;
115   scoped_array<double> b_;
116   scoped_array<double> D_;
117 };
118 
TEST_F(IterativeSchurComplementSolverTest,NormalProblem)119 TEST_F(IterativeSchurComplementSolverTest, NormalProblem) {
120   SetUpProblem(2);
121   EXPECT_TRUE(TestSolver(NULL));
122   EXPECT_TRUE(TestSolver(D_.get()));
123 }
124 
TEST_F(IterativeSchurComplementSolverTest,ProblemWithNoFBlocks)125 TEST_F(IterativeSchurComplementSolverTest, ProblemWithNoFBlocks) {
126   SetUpProblem(3);
127   EXPECT_TRUE(TestSolver(NULL));
128   EXPECT_TRUE(TestSolver(D_.get()));
129 }
130 
131 }  // namespace internal
132 }  // namespace ceres
133