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