1// Ceres Solver - A fast non-linear least squares minimizer
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3// http://code.google.com/p/ceres-solver/
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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
50namespace ceres {
51namespace internal {
52
53class SchurEliminatorTest : public ::testing::Test {
54 protected:
55  void SetUpFromId(int id) {
56    scoped_ptr<LinearLeastSquaresProblem>
57        problem(CreateLinearLeastSquaresProblemFromId(id));
58    CHECK_NOTNULL(problem.get());
59    SetupHelper(problem.get());
60  }
61
62  void SetUpFromFilename(const string& filename) {
63    scoped_ptr<LinearLeastSquaresProblem>
64        problem(CreateLinearLeastSquaresProblemFromFile(filename));
65    CHECK_NOTNULL(problem.get());
66    SetupHelper(problem.get());
67  }
68
69  void SetupHelper(LinearLeastSquaresProblem* problem) {
70    A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
71    b.reset(problem->b.release());
72    D.reset(problem->D.release());
73
74    num_eliminate_blocks = problem->num_eliminate_blocks;
75    num_eliminate_cols = 0;
76    const CompressedRowBlockStructure* bs = A->block_structure();
77
78    for (int i = 0; i < num_eliminate_blocks; ++i) {
79      num_eliminate_cols += bs->cols[i].size;
80    }
81  }
82
83  // Compute the golden values for the reduced linear system and the
84  // solution to the linear least squares problem using dense linear
85  // algebra.
86  void ComputeReferenceSolution(const Vector& D) {
87    Matrix J;
88    A->ToDenseMatrix(&J);
89    VectorRef f(b.get(), J.rows());
90
91    Matrix H  =  (D.cwiseProduct(D)).asDiagonal();
92    H.noalias() += J.transpose() * J;
93
94    const Vector g = J.transpose() * f;
95    const int schur_size = J.cols() - num_eliminate_cols;
96
97    lhs_expected.resize(schur_size, schur_size);
98    lhs_expected.setZero();
99
100    rhs_expected.resize(schur_size);
101    rhs_expected.setZero();
102
103    sol_expected.resize(J.cols());
104    sol_expected.setZero();
105
106    Matrix P = H.block(0, 0, num_eliminate_cols, num_eliminate_cols);
107    Matrix Q = H.block(0,
108                       num_eliminate_cols,
109                       num_eliminate_cols,
110                       schur_size);
111    Matrix R = H.block(num_eliminate_cols,
112                       num_eliminate_cols,
113                       schur_size,
114                       schur_size);
115    int row = 0;
116    const CompressedRowBlockStructure* bs = A->block_structure();
117    for (int i = 0; i < num_eliminate_blocks; ++i) {
118      const int block_size =  bs->cols[i].size;
119      P.block(row, row,  block_size, block_size) =
120          P
121          .block(row, row,  block_size, block_size)
122          .ldlt()
123          .solve(Matrix::Identity(block_size, block_size));
124      row += block_size;
125    }
126
127    lhs_expected
128        .triangularView<Eigen::Upper>() = R - Q.transpose() * P * Q;
129    rhs_expected =
130        g.tail(schur_size) - Q.transpose() * P * g.head(num_eliminate_cols);
131    sol_expected = H.ldlt().solve(g);
132  }
133
134  void EliminateSolveAndCompare(const VectorRef& diagonal,
135                                bool use_static_structure,
136                                const double relative_tolerance) {
137    const CompressedRowBlockStructure* bs = A->block_structure();
138    const int num_col_blocks = bs->cols.size();
139    vector<int> blocks(num_col_blocks - num_eliminate_blocks, 0);
140    for (int i = num_eliminate_blocks; i < num_col_blocks; ++i) {
141      blocks[i - num_eliminate_blocks] = bs->cols[i].size;
142    }
143
144    BlockRandomAccessDenseMatrix lhs(blocks);
145
146    const int num_cols = A->num_cols();
147    const int schur_size = lhs.num_rows();
148
149    Vector rhs(schur_size);
150
151    LinearSolver::Options options;
152    options.elimination_groups.push_back(num_eliminate_blocks);
153    if (use_static_structure) {
154      DetectStructure(*bs,
155                      num_eliminate_blocks,
156                      &options.row_block_size,
157                      &options.e_block_size,
158                      &options.f_block_size);
159    }
160
161    scoped_ptr<SchurEliminatorBase> eliminator;
162    eliminator.reset(SchurEliminatorBase::Create(options));
163    eliminator->Init(num_eliminate_blocks, A->block_structure());
164    eliminator->Eliminate(A.get(), b.get(), diagonal.data(), &lhs, rhs.data());
165
166    MatrixRef lhs_ref(lhs.mutable_values(), lhs.num_rows(), lhs.num_cols());
167    Vector reduced_sol  =
168        lhs_ref
169        .selfadjointView<Eigen::Upper>()
170        .ldlt()
171        .solve(rhs);
172
173    // Solution to the linear least squares problem.
174    Vector sol(num_cols);
175    sol.setZero();
176    sol.tail(schur_size) = reduced_sol;
177    eliminator->BackSubstitute(A.get(),
178                               b.get(),
179                               diagonal.data(),
180                               reduced_sol.data(),
181                               sol.data());
182
183    Matrix delta = (lhs_ref - lhs_expected).selfadjointView<Eigen::Upper>();
184    double diff = delta.norm();
185    EXPECT_NEAR(diff / lhs_expected.norm(), 0.0, relative_tolerance);
186    EXPECT_NEAR((rhs - rhs_expected).norm() / rhs_expected.norm(), 0.0,
187                relative_tolerance);
188    EXPECT_NEAR((sol - sol_expected).norm() / sol_expected.norm(), 0.0,
189                relative_tolerance);
190  }
191
192  scoped_ptr<BlockSparseMatrix> A;
193  scoped_array<double> b;
194  scoped_array<double> D;
195  int num_eliminate_blocks;
196  int num_eliminate_cols;
197
198  Matrix lhs_expected;
199  Vector rhs_expected;
200  Vector sol_expected;
201};
202
203TEST_F(SchurEliminatorTest, ScalarProblem) {
204  SetUpFromId(2);
205  Vector zero(A->num_cols());
206  zero.setZero();
207
208  ComputeReferenceSolution(VectorRef(zero.data(), A->num_cols()));
209  EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), true, 1e-14);
210  EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), false, 1e-14);
211
212  ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
213  EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
214  EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
215}
216
217#ifndef CERES_NO_PROTOCOL_BUFFERS
218TEST_F(SchurEliminatorTest, BlockProblem) {
219  const string input_file = TestFileAbsolutePath("problem-6-1384-000.lsqp");
220
221  SetUpFromFilename(input_file);
222  ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
223  EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-10);
224  EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-10);
225}
226#endif  // CERES_NO_PROTOCOL_BUFFERS
227
228}  // namespace internal
229}  // namespace ceres
230