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_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_ 32 #define CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_ 33 34 #include "ceres/linear_solver.h" 35 #include "ceres/internal/eigen.h" 36 #include "ceres/internal/scoped_ptr.h" 37 #include "ceres/types.h" 38 39 namespace ceres { 40 namespace internal { 41 42 class BlockSparseMatrix; 43 class BlockSparseMatrixBase; 44 class ImplicitSchurComplement; 45 class VisibilityBasedPreconditioner; 46 47 // This class implements an iterative solver for the linear least 48 // squares problems that have a bi-partitte sparsity structure common 49 // to Structure from Motion problems. 50 // 51 // The algorithm used by this solver was developed in a series of 52 // papers - "Agarwal et al, Bundle Adjustment in the Large, ECCV 2010" 53 // and "Wu et al, Multicore Bundle Adjustment, submitted to CVPR 54 // 2011" at the Univeristy of Washington. 55 // 56 // The key idea is that one can run Conjugate Gradients on the Schur 57 // Complement system without explicitly forming the Schur Complement 58 // in memory. The heavy lifting for this is done by the 59 // ImplicitSchurComplement class. Not forming the Schur complement in 60 // memory and factoring it results in substantial savings in time and 61 // memory. Further, iterative solvers like this open up the 62 // possibility of solving the Newton equations in a non-linear solver 63 // only approximately and terminating early, thereby saving even more 64 // time. 65 // 66 // For the curious, running CG on the Schur complement is the same as 67 // running CG on the Normal Equations with an SSOR preconditioner. For 68 // a proof of this fact and others related to this solver please see 69 // the section on Domain Decomposition Methods in Saad's book 70 // "Iterative Methods for Sparse Linear Systems". 71 class IterativeSchurComplementSolver : public BlockSparseMatrixBaseSolver { 72 public: 73 explicit IterativeSchurComplementSolver( 74 const LinearSolver::Options& options); 75 76 virtual ~IterativeSchurComplementSolver(); 77 78 private: 79 virtual LinearSolver::Summary SolveImpl( 80 BlockSparseMatrixBase* A, 81 const double* b, 82 const LinearSolver::PerSolveOptions& options, 83 double* x); 84 85 LinearSolver::Options options_; 86 scoped_ptr<internal::ImplicitSchurComplement> schur_complement_; 87 scoped_ptr<VisibilityBasedPreconditioner> visibility_based_preconditioner_; 88 Vector reduced_linear_system_solution_; 89 }; 90 91 } // namespace internal 92 } // namespace ceres 93 94 #endif // CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_ 95