1 // Ceres Solver - A fast non-linear least squares minimizer 2 // Copyright 2015 Google Inc. All rights reserved. 3 // http://ceres-solver.org/ 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 <memory> 35 #include <set> 36 #include <utility> 37 #include <vector> 38 39 #include "ceres/block_random_access_diagonal_matrix.h" 40 #include "ceres/block_random_access_matrix.h" 41 #include "ceres/block_sparse_matrix.h" 42 #include "ceres/block_structure.h" 43 #include "ceres/internal/port.h" 44 #include "ceres/linear_solver.h" 45 #include "ceres/schur_eliminator.h" 46 #include "ceres/types.h" 47 48 #ifdef CERES_USE_EIGEN_SPARSE 49 #include "Eigen/OrderingMethods" 50 #include "Eigen/SparseCholesky" 51 #endif 52 53 namespace ceres { 54 namespace internal { 55 56 class BlockSparseMatrix; 57 class SparseCholesky; 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 Ceres be 98 // build with at least one sparse linear algebra library, as it 99 // computes a sparse Cholesky factorization of the Schur complement. 100 // 101 // This solver can be used for solving structure from motion problems 102 // with tens of thousands of cameras, though depending on the exact 103 // sparsity structure, it maybe better to use an iterative solver. 104 // 105 // The two solvers can be instantiated by calling 106 // LinearSolver::CreateLinearSolver with LinearSolver::Options::type 107 // set to DENSE_SCHUR and SPARSE_SCHUR 108 // respectively. LinearSolver::Options::elimination_groups[0] should 109 // be at least 1. 110 class CERES_EXPORT_INTERNAL SchurComplementSolver 111 : public BlockSparseMatrixSolver { 112 public: SchurComplementSolver(const LinearSolver::Options & options)113 explicit SchurComplementSolver(const LinearSolver::Options& options) 114 : options_(options) { 115 CHECK_GT(options.elimination_groups.size(), 1); 116 CHECK_GT(options.elimination_groups[0], 0); 117 CHECK(options.context != NULL); 118 } 119 SchurComplementSolver(const SchurComplementSolver&) = delete; 120 void operator=(const SchurComplementSolver&) = delete; 121 122 // LinearSolver methods ~SchurComplementSolver()123 virtual ~SchurComplementSolver() {} 124 LinearSolver::Summary SolveImpl( 125 BlockSparseMatrix* A, 126 const double* b, 127 const LinearSolver::PerSolveOptions& per_solve_options, 128 double* x) override; 129 130 protected: options()131 const LinearSolver::Options& options() const { return options_; } 132 lhs()133 const BlockRandomAccessMatrix* lhs() const { return lhs_.get(); } set_lhs(BlockRandomAccessMatrix * lhs)134 void set_lhs(BlockRandomAccessMatrix* lhs) { lhs_.reset(lhs); } rhs()135 const double* rhs() const { return rhs_.get(); } set_rhs(double * rhs)136 void set_rhs(double* rhs) { rhs_.reset(rhs); } 137 138 private: 139 virtual void InitStorage(const CompressedRowBlockStructure* bs) = 0; 140 virtual LinearSolver::Summary SolveReducedLinearSystem( 141 const LinearSolver::PerSolveOptions& per_solve_options, 142 double* solution) = 0; 143 144 LinearSolver::Options options_; 145 146 std::unique_ptr<SchurEliminatorBase> eliminator_; 147 std::unique_ptr<BlockRandomAccessMatrix> lhs_; 148 std::unique_ptr<double[]> rhs_; 149 }; 150 151 // Dense Cholesky factorization based solver. 152 class DenseSchurComplementSolver : public SchurComplementSolver { 153 public: DenseSchurComplementSolver(const LinearSolver::Options & options)154 explicit DenseSchurComplementSolver(const LinearSolver::Options& options) 155 : SchurComplementSolver(options) {} 156 DenseSchurComplementSolver(const DenseSchurComplementSolver&) = delete; 157 void operator=(const DenseSchurComplementSolver&) = delete; 158 ~DenseSchurComplementSolver()159 virtual ~DenseSchurComplementSolver() {} 160 161 private: 162 void InitStorage(const CompressedRowBlockStructure* bs) final; 163 LinearSolver::Summary SolveReducedLinearSystem( 164 const LinearSolver::PerSolveOptions& per_solve_options, 165 double* solution) final; 166 }; 167 168 // Sparse Cholesky factorization based solver. 169 class SparseSchurComplementSolver : public SchurComplementSolver { 170 public: 171 explicit SparseSchurComplementSolver(const LinearSolver::Options& options); 172 SparseSchurComplementSolver(const SparseSchurComplementSolver&) = delete; 173 void operator=(const SparseSchurComplementSolver&) = delete; 174 175 virtual ~SparseSchurComplementSolver(); 176 177 private: 178 void InitStorage(const CompressedRowBlockStructure* bs) final; 179 LinearSolver::Summary SolveReducedLinearSystem( 180 const LinearSolver::PerSolveOptions& per_solve_options, 181 double* solution) final; 182 LinearSolver::Summary SolveReducedLinearSystemUsingConjugateGradients( 183 const LinearSolver::PerSolveOptions& per_solve_options, double* solution); 184 185 // Size of the blocks in the Schur complement. 186 std::vector<int> blocks_; 187 std::unique_ptr<SparseCholesky> sparse_cholesky_; 188 std::unique_ptr<BlockRandomAccessDiagonalMatrix> preconditioner_; 189 }; 190 191 } // namespace internal 192 } // namespace ceres 193 194 #endif // CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_ 195