1 // Ceres Solver - A fast non-linear least squares minimizer
2 // Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
3 // http://code.google.com/p/ceres-solver/
4 //
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6 // modification, are permitted provided that the following conditions are met:
7 //
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16 //
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28 //
29 // Author: sameeragarwal@google.com (Sameer Agarwal)
30
31 #include "ceres/schur_eliminator.h"
32
33 #include "Eigen/Dense"
34 #include "ceres/block_random_access_dense_matrix.h"
35 #include "ceres/block_sparse_matrix.h"
36 #include "ceres/casts.h"
37 #include "ceres/detect_structure.h"
38 #include "ceres/internal/eigen.h"
39 #include "ceres/internal/scoped_ptr.h"
40 #include "ceres/linear_least_squares_problems.h"
41 #include "ceres/test_util.h"
42 #include "ceres/triplet_sparse_matrix.h"
43 #include "ceres/types.h"
44 #include "glog/logging.h"
45 #include "gtest/gtest.h"
46
47 // TODO(sameeragarwal): Reduce the size of these tests and redo the
48 // parameterization to be more efficient.
49
50 namespace ceres {
51 namespace internal {
52
53 class SchurEliminatorTest : public ::testing::Test {
54 protected:
SetUpFromId(int id)55 void SetUpFromId(int id) {
56 scoped_ptr<LinearLeastSquaresProblem>
57 problem(CreateLinearLeastSquaresProblemFromId(id));
58 CHECK_NOTNULL(problem.get());
59 SetupHelper(problem.get());
60 }
61
SetupHelper(LinearLeastSquaresProblem * problem)62 void SetupHelper(LinearLeastSquaresProblem* problem) {
63 A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
64 b.reset(problem->b.release());
65 D.reset(problem->D.release());
66
67 num_eliminate_blocks = problem->num_eliminate_blocks;
68 num_eliminate_cols = 0;
69 const CompressedRowBlockStructure* bs = A->block_structure();
70
71 for (int i = 0; i < num_eliminate_blocks; ++i) {
72 num_eliminate_cols += bs->cols[i].size;
73 }
74 }
75
76 // Compute the golden values for the reduced linear system and the
77 // solution to the linear least squares problem using dense linear
78 // algebra.
ComputeReferenceSolution(const Vector & D)79 void ComputeReferenceSolution(const Vector& D) {
80 Matrix J;
81 A->ToDenseMatrix(&J);
82 VectorRef f(b.get(), J.rows());
83
84 Matrix H = (D.cwiseProduct(D)).asDiagonal();
85 H.noalias() += J.transpose() * J;
86
87 const Vector g = J.transpose() * f;
88 const int schur_size = J.cols() - num_eliminate_cols;
89
90 lhs_expected.resize(schur_size, schur_size);
91 lhs_expected.setZero();
92
93 rhs_expected.resize(schur_size);
94 rhs_expected.setZero();
95
96 sol_expected.resize(J.cols());
97 sol_expected.setZero();
98
99 Matrix P = H.block(0, 0, num_eliminate_cols, num_eliminate_cols);
100 Matrix Q = H.block(0,
101 num_eliminate_cols,
102 num_eliminate_cols,
103 schur_size);
104 Matrix R = H.block(num_eliminate_cols,
105 num_eliminate_cols,
106 schur_size,
107 schur_size);
108 int row = 0;
109 const CompressedRowBlockStructure* bs = A->block_structure();
110 for (int i = 0; i < num_eliminate_blocks; ++i) {
111 const int block_size = bs->cols[i].size;
112 P.block(row, row, block_size, block_size) =
113 P
114 .block(row, row, block_size, block_size)
115 .llt()
116 .solve(Matrix::Identity(block_size, block_size));
117 row += block_size;
118 }
119
120 lhs_expected
121 .triangularView<Eigen::Upper>() = R - Q.transpose() * P * Q;
122 rhs_expected =
123 g.tail(schur_size) - Q.transpose() * P * g.head(num_eliminate_cols);
124 sol_expected = H.llt().solve(g);
125 }
126
EliminateSolveAndCompare(const VectorRef & diagonal,bool use_static_structure,const double relative_tolerance)127 void EliminateSolveAndCompare(const VectorRef& diagonal,
128 bool use_static_structure,
129 const double relative_tolerance) {
130 const CompressedRowBlockStructure* bs = A->block_structure();
131 const int num_col_blocks = bs->cols.size();
132 vector<int> blocks(num_col_blocks - num_eliminate_blocks, 0);
133 for (int i = num_eliminate_blocks; i < num_col_blocks; ++i) {
134 blocks[i - num_eliminate_blocks] = bs->cols[i].size;
135 }
136
137 BlockRandomAccessDenseMatrix lhs(blocks);
138
139 const int num_cols = A->num_cols();
140 const int schur_size = lhs.num_rows();
141
142 Vector rhs(schur_size);
143
144 LinearSolver::Options options;
145 options.elimination_groups.push_back(num_eliminate_blocks);
146 if (use_static_structure) {
147 DetectStructure(*bs,
148 num_eliminate_blocks,
149 &options.row_block_size,
150 &options.e_block_size,
151 &options.f_block_size);
152 }
153
154 scoped_ptr<SchurEliminatorBase> eliminator;
155 eliminator.reset(SchurEliminatorBase::Create(options));
156 eliminator->Init(num_eliminate_blocks, A->block_structure());
157 eliminator->Eliminate(A.get(), b.get(), diagonal.data(), &lhs, rhs.data());
158
159 MatrixRef lhs_ref(lhs.mutable_values(), lhs.num_rows(), lhs.num_cols());
160 Vector reduced_sol =
161 lhs_ref
162 .selfadjointView<Eigen::Upper>()
163 .llt()
164 .solve(rhs);
165
166 // Solution to the linear least squares problem.
167 Vector sol(num_cols);
168 sol.setZero();
169 sol.tail(schur_size) = reduced_sol;
170 eliminator->BackSubstitute(A.get(),
171 b.get(),
172 diagonal.data(),
173 reduced_sol.data(),
174 sol.data());
175
176 Matrix delta = (lhs_ref - lhs_expected).selfadjointView<Eigen::Upper>();
177 double diff = delta.norm();
178 EXPECT_NEAR(diff / lhs_expected.norm(), 0.0, relative_tolerance);
179 EXPECT_NEAR((rhs - rhs_expected).norm() / rhs_expected.norm(), 0.0,
180 relative_tolerance);
181 EXPECT_NEAR((sol - sol_expected).norm() / sol_expected.norm(), 0.0,
182 relative_tolerance);
183 }
184
185 scoped_ptr<BlockSparseMatrix> A;
186 scoped_array<double> b;
187 scoped_array<double> D;
188 int num_eliminate_blocks;
189 int num_eliminate_cols;
190
191 Matrix lhs_expected;
192 Vector rhs_expected;
193 Vector sol_expected;
194 };
195
TEST_F(SchurEliminatorTest,ScalarProblem)196 TEST_F(SchurEliminatorTest, ScalarProblem) {
197 SetUpFromId(2);
198 Vector zero(A->num_cols());
199 zero.setZero();
200
201 ComputeReferenceSolution(VectorRef(zero.data(), A->num_cols()));
202 EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), true, 1e-14);
203 EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), false, 1e-14);
204
205 ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
206 EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
207 EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
208 }
209
210 } // namespace internal
211 } // namespace ceres
212