internal/ceres/implicit_schur_complement_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/implicit_schur_complement.h"
  32
  33 #include <cstddef>
  34 #include "Eigen/Dense"
  35 #include "ceres/block_random_access_dense_matrix.h"
  36 #include "ceres/block_sparse_matrix.h"
  37 #include "ceres/casts.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/linear_solver.h"
  42 #include "ceres/schur_eliminator.h"
  43 #include "ceres/triplet_sparse_matrix.h"
  44 #include "ceres/types.h"
  45 #include "glog/logging.h"
  46 #include "gtest/gtest.h"
  47
  48 namespace ceres {
  49 namespace internal {
  50
  51 using testing::AssertionResult;
  52
  53 const double kEpsilon = 1e-14;
  54
  55 class ImplicitSchurComplementTest : public ::testing::Test {
  56  protected :
  57   virtual void SetUp() {
  58     scoped_ptr<LinearLeastSquaresProblem> problem(
  59         CreateLinearLeastSquaresProblemFromId(2));
  60
  61     CHECK_NOTNULL(problem.get());
  62     A_.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
  63     b_.reset(problem->b.release());
  64     D_.reset(problem->D.release());
  65
  66     num_cols_ = A_->num_cols();
  67     num_rows_ = A_->num_rows();
  68     num_eliminate_blocks_ = problem->num_eliminate_blocks;
  69   }
  70
  71   void ReducedLinearSystemAndSolution(double* D,
  72                                       Matrix* lhs,
  73                                       Vector* rhs,
  74                                       Vector* solution) {
  75     const CompressedRowBlockStructure* bs = A_->block_structure();
  76     const int num_col_blocks = bs->cols.size();
  77     std::vector<int> blocks(num_col_blocks - num_eliminate_blocks_, 0);
  78     for (int i = num_eliminate_blocks_; i < num_col_blocks; ++i) {
  79       blocks[i - num_eliminate_blocks_] = bs->cols[i].size;
  80     }
  81
  82     BlockRandomAccessDenseMatrix blhs(blocks);
  83     const int num_schur_rows = blhs.num_rows();
  84
  85     LinearSolver::Options options;
  86     options.elimination_groups.push_back(num_eliminate_blocks_);
  87     options.type = DENSE_SCHUR;
  88
  89     scoped_ptr<SchurEliminatorBase> eliminator(
  90         SchurEliminatorBase::Create(options));
  91     CHECK_NOTNULL(eliminator.get());
  92     const bool kFullRankETE = true;
  93     eliminator->Init(num_eliminate_blocks_, kFullRankETE, bs);
  94
  95     lhs->resize(num_schur_rows, num_schur_rows);
  96     rhs->resize(num_schur_rows);
  97
  98     eliminator->Eliminate(A_.get(), b_.get(), D, &blhs, rhs->data());
  99
 100     MatrixRef lhs_ref(blhs.mutable_values(), num_schur_rows, num_schur_rows);
 101
 102     // lhs_ref is an upper triangular matrix. Construct a full version
 103     // of lhs_ref in lhs by transposing lhs_ref, choosing the strictly
 104     // lower triangular part of the matrix and adding it to lhs_ref.
 105     *lhs = lhs_ref;
 106     lhs->triangularView<Eigen::StrictlyLower>() =
 107         lhs_ref.triangularView<Eigen::StrictlyUpper>().transpose();
 108
 109     solution->resize(num_cols_);
 110     solution->setZero();
 111     VectorRef schur_solution(solution->data() + num_cols_ - num_schur_rows,
 112                              num_schur_rows);
 113     schur_solution = lhs->selfadjointView<Eigen::Upper>().llt().solve(*rhs);
 114     eliminator->BackSubstitute(A_.get(), b_.get(), D,
 115                                schur_solution.data(), solution->data());
 116   }
 117
 118   AssertionResult TestImplicitSchurComplement(double* D) {
 119     Matrix lhs;
 120     Vector rhs;
 121     Vector reference_solution;
 122     ReducedLinearSystemAndSolution(D, &lhs, &rhs, &reference_solution);
 123
 124     LinearSolver::Options options;
 125     options.elimination_groups.push_back(num_eliminate_blocks_);
 126     options.preconditioner_type = JACOBI;
 127     ImplicitSchurComplement isc(options);
 128     isc.Init(*A_, D, b_.get());
 129
 130     int num_sc_cols = lhs.cols();
 131
 132     for (int i = 0; i < num_sc_cols; ++i) {
 133       Vector x(num_sc_cols);
 134       x.setZero();
 135       x(i) = 1.0;
 136
 137       Vector y(num_sc_cols);
 138       y = lhs * x;
 139
 140       Vector z(num_sc_cols);
 141       isc.RightMultiply(x.data(), z.data());
 142
 143       // The i^th column of the implicit schur complement is the same as
 144       // the explicit schur complement.
 145       if ((y - z).norm() > kEpsilon) {
 146         return testing::AssertionFailure()
 147             << "Explicit and Implicit SchurComplements differ in "
 148             << "column " << i << ". explicit: " << y.transpose()
 149             << " implicit: " << z.transpose();
 150       }
 151     }
 152
 153     // Compare the rhs of the reduced linear system
 154     if ((isc.rhs() - rhs).norm() > kEpsilon) {
 155       return testing::AssertionFailure()
 156             << "Explicit and Implicit SchurComplements differ in "
 157             << "rhs. explicit: " << rhs.transpose()
 158             << " implicit: " << isc.rhs().transpose();
 159     }
 160
 161     // Reference solution to the f_block.
 162     const Vector reference_f_sol =
 163         lhs.selfadjointView<Eigen::Upper>().llt().solve(rhs);
 164
 165     // Backsubstituted solution from the implicit schur solver using the
 166     // reference solution to the f_block.
 167     Vector sol(num_cols_);
 168     isc.BackSubstitute(reference_f_sol.data(), sol.data());
 169     if ((sol - reference_solution).norm() > kEpsilon) {
 170       return testing::AssertionFailure()
 171           << "Explicit and Implicit SchurComplements solutions differ. "
 172           << "explicit: " << reference_solution.transpose()
 173           << " implicit: " << sol.transpose();
 174     }
 175
 176     return testing::AssertionSuccess();
 177   }
 178
 179   int num_rows_;
 180   int num_cols_;
 181   int num_eliminate_blocks_;
 182
 183   scoped_ptr<BlockSparseMatrix> A_;
 184   scoped_array<double> b_;
 185   scoped_array<double> D_;
 186 };
 187
 188 // Verify that the Schur Complement matrix implied by the
 189 // ImplicitSchurComplement class matches the one explicitly computed
 190 // by the SchurComplement solver.
 191 //
 192 // We do this with and without regularization to check that the
 193 // support for the LM diagonal is correct.
 194 TEST_F(ImplicitSchurComplementTest, SchurMatrixValuesTest) {
 195   EXPECT_TRUE(TestImplicitSchurComplement(NULL));
 196   EXPECT_TRUE(TestImplicitSchurComplement(D_.get()));
 197 }
 198
 199 }  // namespace internal
 200 }  // namespace ceres