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 #ifndef CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_ 32 #define CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_ 33 34 #include <set> 35 #include <utility> 36 #include <vector> 37 38 #include "ceres/internal/port.h" 39 40 #include "ceres/block_random_access_matrix.h" 41 #include "ceres/block_sparse_matrix.h" 42 #include "ceres/block_structure.h" 43 #include "ceres/cxsparse.h" 44 #include "ceres/linear_solver.h" 45 #include "ceres/schur_eliminator.h" 46 #include "ceres/suitesparse.h" 47 #include "ceres/internal/scoped_ptr.h" 48 #include "ceres/types.h" 49 50 #ifdef CERES_USE_EIGEN_SPARSE 51 #include "Eigen/SparseCholesky" 52 #endif 53 54 namespace ceres { 55 namespace internal { 56 57 class BlockSparseMatrix; 58 59 // Base class for Schur complement based linear least squares 60 // solvers. It assumes that the input linear system Ax = b can be 61 // partitioned into 62 // 63 // E y + F z = b 64 // 65 // Where x = [y;z] is a partition of the variables. The paritioning 66 // of the variables is such that, E'E is a block diagonal 67 // matrix. Further, the rows of A are ordered so that for every 68 // variable block in y, all the rows containing that variable block 69 // occur as a vertically contiguous block. i.e the matrix A looks like 70 // 71 // E F 72 // A = [ y1 0 0 0 | z1 0 0 0 z5] 73 // [ y1 0 0 0 | z1 z2 0 0 0] 74 // [ 0 y2 0 0 | 0 0 z3 0 0] 75 // [ 0 0 y3 0 | z1 z2 z3 z4 z5] 76 // [ 0 0 y3 0 | z1 0 0 0 z5] 77 // [ 0 0 0 y4 | 0 0 0 0 z5] 78 // [ 0 0 0 y4 | 0 z2 0 0 0] 79 // [ 0 0 0 y4 | 0 0 0 0 0] 80 // [ 0 0 0 0 | z1 0 0 0 0] 81 // [ 0 0 0 0 | 0 0 z3 z4 z5] 82 // 83 // This structure should be reflected in the corresponding 84 // CompressedRowBlockStructure object associated with A. The linear 85 // system Ax = b should either be well posed or the array D below 86 // should be non-null and the diagonal matrix corresponding to it 87 // should be non-singular. 88 // 89 // SchurComplementSolver has two sub-classes. 90 // 91 // DenseSchurComplementSolver: For problems where the Schur complement 92 // matrix is small and dense, or if CHOLMOD/SuiteSparse is not 93 // installed. For structure from motion problems, this is solver can 94 // be used for problems with upto a few hundred cameras. 95 // 96 // SparseSchurComplementSolver: For problems where the Schur 97 // complement matrix is large and sparse. It requires that 98 // CHOLMOD/SuiteSparse be installed, as it uses CHOLMOD to find a 99 // sparse Cholesky factorization of the Schur complement. This solver 100 // can be used for solving structure from motion problems with tens of 101 // thousands of cameras, though depending on the exact sparsity 102 // structure, it maybe better to use an iterative solver. 103 // 104 // The two solvers can be instantiated by calling 105 // LinearSolver::CreateLinearSolver with LinearSolver::Options::type 106 // set to DENSE_SCHUR and SPARSE_SCHUR 107 // respectively. LinearSolver::Options::elimination_groups[0] should be 108 // at least 1. 109 class SchurComplementSolver : public BlockSparseMatrixSolver { 110 public: 111 explicit SchurComplementSolver(const LinearSolver::Options& options) 112 : options_(options) { 113 CHECK_GT(options.elimination_groups.size(), 1); 114 CHECK_GT(options.elimination_groups[0], 0); 115 } 116 117 // LinearSolver methods 118 virtual ~SchurComplementSolver() {} 119 virtual LinearSolver::Summary SolveImpl( 120 BlockSparseMatrix* A, 121 const double* b, 122 const LinearSolver::PerSolveOptions& per_solve_options, 123 double* x); 124 125 protected: 126 const LinearSolver::Options& options() const { return options_; } 127 128 const BlockRandomAccessMatrix* lhs() const { return lhs_.get(); } 129 void set_lhs(BlockRandomAccessMatrix* lhs) { lhs_.reset(lhs); } 130 const double* rhs() const { return rhs_.get(); } 131 void set_rhs(double* rhs) { rhs_.reset(rhs); } 132 133 private: 134 virtual void InitStorage(const CompressedRowBlockStructure* bs) = 0; 135 virtual LinearSolver::Summary SolveReducedLinearSystem( 136 double* solution) = 0; 137 138 LinearSolver::Options options_; 139 140 scoped_ptr<SchurEliminatorBase> eliminator_; 141 scoped_ptr<BlockRandomAccessMatrix> lhs_; 142 scoped_array<double> rhs_; 143 144 CERES_DISALLOW_COPY_AND_ASSIGN(SchurComplementSolver); 145 }; 146 147 // Dense Cholesky factorization based solver. 148 class DenseSchurComplementSolver : public SchurComplementSolver { 149 public: 150 explicit DenseSchurComplementSolver(const LinearSolver::Options& options) 151 : SchurComplementSolver(options) {} 152 virtual ~DenseSchurComplementSolver() {} 153 154 private: 155 virtual void InitStorage(const CompressedRowBlockStructure* bs); 156 virtual LinearSolver::Summary SolveReducedLinearSystem( 157 double* solution); 158 159 CERES_DISALLOW_COPY_AND_ASSIGN(DenseSchurComplementSolver); 160 }; 161 162 // Sparse Cholesky factorization based solver. 163 class SparseSchurComplementSolver : public SchurComplementSolver { 164 public: 165 explicit SparseSchurComplementSolver(const LinearSolver::Options& options); 166 virtual ~SparseSchurComplementSolver(); 167 168 private: 169 virtual void InitStorage(const CompressedRowBlockStructure* bs); 170 virtual LinearSolver::Summary SolveReducedLinearSystem( 171 double* solution); 172 LinearSolver::Summary SolveReducedLinearSystemUsingSuiteSparse( 173 double* solution); 174 LinearSolver::Summary SolveReducedLinearSystemUsingCXSparse( 175 double* solution); 176 LinearSolver::Summary SolveReducedLinearSystemUsingEigen( 177 double* solution); 178 179 // Size of the blocks in the Schur complement. 180 vector<int> blocks_; 181 182 SuiteSparse ss_; 183 // Symbolic factorization of the reduced linear system. Precomputed 184 // once and reused in subsequent calls. 185 cholmod_factor* factor_; 186 187 CXSparse cxsparse_; 188 // Cached factorization 189 cs_dis* cxsparse_factor_; 190 191 #ifdef CERES_USE_EIGEN_SPARSE 192 typedef Eigen::SimplicialLDLT<Eigen::SparseMatrix<double> > SimplicialLDLT; 193 scoped_ptr<SimplicialLDLT> simplicial_ldlt_; 194 #endif 195 196 CERES_DISALLOW_COPY_AND_ASSIGN(SparseSchurComplementSolver); 197 }; 198 199 } // namespace internal 200 } // namespace ceres 201 202 #endif // CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_ 203
