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 "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 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 eliminator->Init(num_eliminate_blocks_, bs); 93 94 lhs->resize(num_schur_rows, num_schur_rows); 95 rhs->resize(num_schur_rows); 96 97 eliminator->Eliminate(A_.get(), b_.get(), D, &blhs, rhs->data()); 98 99 MatrixRef lhs_ref(blhs.mutable_values(), num_schur_rows, num_schur_rows); 100 101 // lhs_ref is an upper triangular matrix. Construct a full version 102 // of lhs_ref in lhs by transposing lhs_ref, choosing the strictly 103 // lower triangular part of the matrix and adding it to lhs_ref. 104 *lhs = lhs_ref; 105 lhs->triangularView<Eigen::StrictlyLower>() = 106 lhs_ref.triangularView<Eigen::StrictlyUpper>().transpose(); 107 108 solution->resize(num_cols_); 109 solution->setZero(); 110 VectorRef schur_solution(solution->data() + num_cols_ - num_schur_rows, 111 num_schur_rows); 112 schur_solution = lhs->selfadjointView<Eigen::Upper>().llt().solve(*rhs); 113 eliminator->BackSubstitute(A_.get(), b_.get(), D, 114 schur_solution.data(), solution->data()); 115 } 116 117 AssertionResult TestImplicitSchurComplement(double* D) { 118 Matrix lhs; 119 Vector rhs; 120 Vector reference_solution; 121 ReducedLinearSystemAndSolution(D, &lhs, &rhs, &reference_solution); 122 123 ImplicitSchurComplement isc(num_eliminate_blocks_, true); 124 isc.Init(*A_, D, b_.get()); 125 126 int num_sc_cols = lhs.cols(); 127 128 for (int i = 0; i < num_sc_cols; ++i) { 129 Vector x(num_sc_cols); 130 x.setZero(); 131 x(i) = 1.0; 132 133 Vector y(num_sc_cols); 134 y = lhs * x; 135 136 Vector z(num_sc_cols); 137 isc.RightMultiply(x.data(), z.data()); 138 139 // The i^th column of the implicit schur complement is the same as 140 // the explicit schur complement. 141 if ((y - z).norm() > kEpsilon) { 142 return testing::AssertionFailure() 143 << "Explicit and Implicit SchurComplements differ in " 144 << "column " << i << ". explicit: " << y.transpose() 145 << " implicit: " << z.transpose(); 146 } 147 } 148 149 // Compare the rhs of the reduced linear system 150 if ((isc.rhs() - rhs).norm() > kEpsilon) { 151 return testing::AssertionFailure() 152 << "Explicit and Implicit SchurComplements differ in " 153 << "rhs. explicit: " << rhs.transpose() 154 << " implicit: " << isc.rhs().transpose(); 155 } 156 157 // Reference solution to the f_block. 158 const Vector reference_f_sol = 159 lhs.selfadjointView<Eigen::Upper>().llt().solve(rhs); 160 161 // Backsubstituted solution from the implicit schur solver using the 162 // reference solution to the f_block. 163 Vector sol(num_cols_); 164 isc.BackSubstitute(reference_f_sol.data(), sol.data()); 165 if ((sol - reference_solution).norm() > kEpsilon) { 166 return testing::AssertionFailure() 167 << "Explicit and Implicit SchurComplements solutions differ. " 168 << "explicit: " << reference_solution.transpose() 169 << " implicit: " << sol.transpose(); 170 } 171 172 return testing::AssertionSuccess(); 173 } 174 175 int num_rows_; 176 int num_cols_; 177 int num_eliminate_blocks_; 178 179 scoped_ptr<BlockSparseMatrix> A_; 180 scoped_array<double> b_; 181 scoped_array<double> D_; 182 }; 183 184 // Verify that the Schur Complement matrix implied by the 185 // ImplicitSchurComplement class matches the one explicitly computed 186 // by the SchurComplement solver. 187 // 188 // We do this with and without regularization to check that the 189 // support for the LM diagonal is correct. 190 TEST_F(ImplicitSchurComplementTest, SchurMatrixValuesTest) { 191 EXPECT_TRUE(TestImplicitSchurComplement(NULL)); 192 EXPECT_TRUE(TestImplicitSchurComplement(D_.get())); 193 } 194 195 } // namespace internal 196 } // namespace ceres 197
