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      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 //
      5 // Redistribution and use in source and binary forms, with or without
      6 // modification, are permitted provided that the following conditions are met:
      7 //
      8 // * Redistributions of source code must retain the above copyright notice,
      9 //   this list of conditions and the following disclaimer.
     10 // * Redistributions in binary form must reproduce the above copyright notice,
     11 //   this list of conditions and the following disclaimer in the documentation
     12 //   and/or other materials provided with the distribution.
     13 // * Neither the name of Google Inc. nor the names of its contributors may be
     14 //   used to endorse or promote products derived from this software without
     15 //   specific prior written permission.
     16 //
     17 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
     18 // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     19 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     20 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
     21 // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
     22 // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
     23 // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
     24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
     25 // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
     26 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
     27 // POSSIBILITY OF SUCH DAMAGE.
     28 //
     29 // Author: sameeragarwal (at) google.com (Sameer Agarwal)
     30 
     31 #include <cstddef>
     32 #include "ceres/block_sparse_matrix.h"
     33 #include "ceres/block_structure.h"
     34 #include "ceres/casts.h"
     35 #include "ceres/internal/scoped_ptr.h"
     36 #include "ceres/linear_least_squares_problems.h"
     37 #include "ceres/linear_solver.h"
     38 #include "ceres/schur_complement_solver.h"
     39 #include "ceres/triplet_sparse_matrix.h"
     40 #include "ceres/types.h"
     41 #include "glog/logging.h"
     42 #include "gtest/gtest.h"
     43 
     44 namespace ceres {
     45 namespace internal {
     46 
     47 class SchurComplementSolverTest : public ::testing::Test {
     48  protected:
     49   void SetUpFromProblemId(int problem_id) {
     50     scoped_ptr<LinearLeastSquaresProblem> problem(
     51         CreateLinearLeastSquaresProblemFromId(problem_id));
     52 
     53     CHECK_NOTNULL(problem.get());
     54     A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
     55     b.reset(problem->b.release());
     56     D.reset(problem->D.release());
     57 
     58     num_cols = A->num_cols();
     59     num_rows = A->num_rows();
     60     num_eliminate_blocks = problem->num_eliminate_blocks;
     61 
     62     x.reset(new double[num_cols]);
     63     sol.reset(new double[num_cols]);
     64     sol_d.reset(new double[num_cols]);
     65 
     66     LinearSolver::Options options;
     67     options.type = DENSE_QR;
     68 
     69     scoped_ptr<LinearSolver> qr(LinearSolver::Create(options));
     70 
     71     TripletSparseMatrix triplet_A(A->num_rows(),
     72                                   A->num_cols(),
     73                                   A->num_nonzeros());
     74     A->ToTripletSparseMatrix(&triplet_A);
     75 
     76     // Gold standard solutions using dense QR factorization.
     77     DenseSparseMatrix dense_A(triplet_A);
     78     qr->Solve(&dense_A, b.get(), LinearSolver::PerSolveOptions(), sol.get());
     79 
     80     // Gold standard solution with appended diagonal.
     81     LinearSolver::PerSolveOptions per_solve_options;
     82     per_solve_options.D = D.get();
     83     qr->Solve(&dense_A, b.get(), per_solve_options, sol_d.get());
     84   }
     85 
     86   void ComputeAndCompareSolutions(
     87       int problem_id,
     88       bool regularization,
     89       ceres::LinearSolverType linear_solver_type,
     90       ceres::DenseLinearAlgebraLibraryType dense_linear_algebra_library_type,
     91       ceres::SparseLinearAlgebraLibraryType sparse_linear_algebra_library_type,
     92       bool use_postordering) {
     93     SetUpFromProblemId(problem_id);
     94     LinearSolver::Options options;
     95     options.elimination_groups.push_back(num_eliminate_blocks);
     96     options.elimination_groups.push_back(
     97         A->block_structure()->cols.size() - num_eliminate_blocks);
     98     options.type = linear_solver_type;
     99     options.dense_linear_algebra_library_type =
    100         dense_linear_algebra_library_type;
    101     options.sparse_linear_algebra_library_type =
    102         sparse_linear_algebra_library_type;
    103     options.use_postordering = use_postordering;
    104 
    105     scoped_ptr<LinearSolver> solver(LinearSolver::Create(options));
    106 
    107     LinearSolver::PerSolveOptions per_solve_options;
    108     LinearSolver::Summary summary;
    109     if (regularization) {
    110       per_solve_options.D = D.get();
    111     }
    112 
    113     summary = solver->Solve(A.get(), b.get(), per_solve_options, x.get());
    114 
    115     if (regularization) {
    116       for (int i = 0; i < num_cols; ++i) {
    117         ASSERT_NEAR(sol_d.get()[i], x[i], 1e-10);
    118       }
    119     } else {
    120       for (int i = 0; i < num_cols; ++i) {
    121         ASSERT_NEAR(sol.get()[i], x[i], 1e-10);
    122       }
    123     }
    124   }
    125 
    126   int num_rows;
    127   int num_cols;
    128   int num_eliminate_blocks;
    129 
    130   scoped_ptr<BlockSparseMatrix> A;
    131   scoped_array<double> b;
    132   scoped_array<double> x;
    133   scoped_array<double> D;
    134   scoped_array<double> sol;
    135   scoped_array<double> sol_d;
    136 };
    137 
    138 TEST_F(SchurComplementSolverTest, EigenBasedDenseSchurWithSmallProblem) {
    139   ComputeAndCompareSolutions(2, false, DENSE_SCHUR, EIGEN, SUITE_SPARSE, true);
    140   ComputeAndCompareSolutions(2, true, DENSE_SCHUR, EIGEN, SUITE_SPARSE, true);
    141 }
    142 
    143 TEST_F(SchurComplementSolverTest, EigenBasedDenseSchurWithLargeProblem) {
    144   ComputeAndCompareSolutions(3, false, DENSE_SCHUR, EIGEN, SUITE_SPARSE, true);
    145   ComputeAndCompareSolutions(3, true, DENSE_SCHUR, EIGEN, SUITE_SPARSE, true);
    146 }
    147 
    148 #ifndef CERES_NO_LAPACK
    149 TEST_F(SchurComplementSolverTest, LAPACKBasedDenseSchurWithSmallProblem) {
    150   ComputeAndCompareSolutions(2, false, DENSE_SCHUR, LAPACK, SUITE_SPARSE, true);
    151   ComputeAndCompareSolutions(2, true, DENSE_SCHUR, LAPACK, SUITE_SPARSE, true);
    152 }
    153 
    154 TEST_F(SchurComplementSolverTest, LAPACKBasedDenseSchurWithLargeProblem) {
    155   ComputeAndCompareSolutions(3, false, DENSE_SCHUR, LAPACK, SUITE_SPARSE, true);
    156   ComputeAndCompareSolutions(3, true, DENSE_SCHUR, LAPACK, SUITE_SPARSE, true);
    157 }
    158 #endif
    159 
    160 #ifndef CERES_NO_SUITESPARSE
    161 TEST_F(SchurComplementSolverTest,
    162        SparseSchurWithSuiteSparseSmallProblemNoPostOrdering) {
    163   ComputeAndCompareSolutions(
    164       2, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, false);
    165   ComputeAndCompareSolutions(2, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, false);
    166 }
    167 
    168 TEST_F(SchurComplementSolverTest,
    169        SparseSchurWithSuiteSparseSmallProblemPostOrdering) {
    170   ComputeAndCompareSolutions(2, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, true);
    171   ComputeAndCompareSolutions(2, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, true);
    172 }
    173 
    174 TEST_F(SchurComplementSolverTest,
    175        SparseSchurWithSuiteSparseLargeProblemNoPostOrdering) {
    176   ComputeAndCompareSolutions(
    177       3, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, false);
    178   ComputeAndCompareSolutions(3, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, false);
    179 }
    180 
    181 TEST_F(SchurComplementSolverTest,
    182        SparseSchurWithSuiteSparseLargeProblemPostOrdering) {
    183   ComputeAndCompareSolutions(3, false, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, true);
    184   ComputeAndCompareSolutions(3, true, SPARSE_SCHUR, EIGEN, SUITE_SPARSE, true);
    185 }
    186 #endif  // CERES_NO_SUITESPARSE
    187 
    188 #ifndef CERES_NO_CXSPARSE
    189 TEST_F(SchurComplementSolverTest,
    190        SparseSchurWithCXSparseSmallProblem) {
    191   ComputeAndCompareSolutions(2, false, SPARSE_SCHUR, EIGEN, CX_SPARSE, true);
    192   ComputeAndCompareSolutions(2, true, SPARSE_SCHUR, EIGEN, CX_SPARSE, true);
    193 }
    194 
    195 TEST_F(SchurComplementSolverTest,
    196        SparseSchurWithCXSparseLargeProblem) {
    197   ComputeAndCompareSolutions(3, false, SPARSE_SCHUR, EIGEN, CX_SPARSE, true);
    198   ComputeAndCompareSolutions(3, true, SPARSE_SCHUR, EIGEN, CX_SPARSE, true);
    199 }
    200 #endif  // CERES_NO_CXSPARSE
    201 
    202 #ifdef CERES_USE_EIGEN_SPARSE
    203 TEST_F(SchurComplementSolverTest,
    204        SparseSchurWithEigenSparseSmallProblem) {
    205   ComputeAndCompareSolutions(2, false, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, true);
    206   ComputeAndCompareSolutions(2, true, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, true);
    207 }
    208 
    209 TEST_F(SchurComplementSolverTest,
    210        SparseSchurWithEigenSparseLargeProblem) {
    211   ComputeAndCompareSolutions(3, false, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, true);
    212   ComputeAndCompareSolutions(3, true, SPARSE_SCHUR, EIGEN, EIGEN_SPARSE, true);
    213 }
    214 #endif  // CERES_USE_EIGEN_SPARSE
    215 
    216 }  // namespace internal
    217 }  // namespace ceres
    218