internal/ceres/schur_eliminator_test.cc

   1 // Ceres Solver - A fast non-linear least squares minimizer
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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
  50 namespace ceres {
  51 namespace internal {
  52
  53 class 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 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.
  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
 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     std::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     const bool kFullRankETE = true;
 157     eliminator->Init(num_eliminate_blocks, kFullRankETE, A->block_structure());
 158     eliminator->Eliminate(A.get(), b.get(), diagonal.data(), &lhs, rhs.data());
 159
 160     MatrixRef lhs_ref(lhs.mutable_values(), lhs.num_rows(), lhs.num_cols());
 161     Vector reduced_sol  =
 162         lhs_ref
 163         .selfadjointView<Eigen::Upper>()
 164         .llt()
 165         .solve(rhs);
 166
 167     // Solution to the linear least squares problem.
 168     Vector sol(num_cols);
 169     sol.setZero();
 170     sol.tail(schur_size) = reduced_sol;
 171     eliminator->BackSubstitute(A.get(),
 172                                b.get(),
 173                                diagonal.data(),
 174                                reduced_sol.data(),
 175                                sol.data());
 176
 177     Matrix delta = (lhs_ref - lhs_expected).selfadjointView<Eigen::Upper>();
 178     double diff = delta.norm();
 179     EXPECT_NEAR(diff / lhs_expected.norm(), 0.0, relative_tolerance);
 180     EXPECT_NEAR((rhs - rhs_expected).norm() / rhs_expected.norm(), 0.0,
 181                 relative_tolerance);
 182     EXPECT_NEAR((sol - sol_expected).norm() / sol_expected.norm(), 0.0,
 183                 relative_tolerance);
 184   }
 185
 186   scoped_ptr<BlockSparseMatrix> A;
 187   scoped_array<double> b;
 188   scoped_array<double> D;
 189   int num_eliminate_blocks;
 190   int num_eliminate_cols;
 191
 192   Matrix lhs_expected;
 193   Vector rhs_expected;
 194   Vector sol_expected;
 195 };
 196
 197 TEST_F(SchurEliminatorTest, ScalarProblemNoRegularization) {
 198   SetUpFromId(2);
 199   Vector zero(A->num_cols());
 200   zero.setZero();
 201
 202   ComputeReferenceSolution(VectorRef(zero.data(), A->num_cols()));
 203   EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), true, 1e-14);
 204   EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), false, 1e-14);
 205 }
 206
 207 TEST_F(SchurEliminatorTest, ScalarProblemWithRegularization) {
 208   SetUpFromId(2);
 209   ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
 210   EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
 211   EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
 212 }
 213
 214 TEST_F(SchurEliminatorTest, VaryingFBlockSizeWithStaticStructure) {
 215   SetUpFromId(4);
 216   ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
 217   EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
 218 }
 219
 220 TEST_F(SchurEliminatorTest, VaryingFBlockSizeWithoutStaticStructure) {
 221   SetUpFromId(4);
 222   ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
 223   EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
 224 }
 225
 226 }  // namespace internal
 227 }  // namespace ceres