| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2015 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are met: |
| // |
| // * Redistributions of source code must retain the above copyright notice, |
| // this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above copyright notice, |
| // this list of conditions and the following disclaimer in the documentation |
| // and/or other materials provided with the distribution. |
| // * Neither the name of Google Inc. nor the names of its contributors may be |
| // used to endorse or promote products derived from this software without |
| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
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| // POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Author: sameeragarwal@google.com (Sameer Agarwal) |
| |
| #ifndef CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_ |
| #define CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_ |
| |
| #include <memory> |
| |
| #include "ceres/internal/disable_warnings.h" |
| #include "ceres/internal/eigen.h" |
| #include "ceres/internal/export.h" |
| #include "ceres/linear_solver.h" |
| #include "ceres/types.h" |
| |
| namespace ceres::internal { |
| |
| class BlockSparseMatrix; |
| class ImplicitSchurComplement; |
| class Preconditioner; |
| |
| // This class implements an iterative solver for the linear least |
| // squares problems that have a bi-partite sparsity structure common |
| // to Structure from Motion problems. |
| // |
| // The algorithm used by this solver was developed in a series of |
| // papers - "Agarwal et al, Bundle Adjustment in the Large, ECCV 2010" |
| // and "Wu et al, Multicore Bundle Adjustment, submitted to CVPR |
| // 2011" at the University of Washington. |
| // |
| // The key idea is that one can run Conjugate Gradients on the Schur |
| // Complement system without explicitly forming the Schur Complement |
| // in memory. The heavy lifting for this is done by the |
| // ImplicitSchurComplement class. Not forming the Schur complement in |
| // memory and factoring it results in substantial savings in time and |
| // memory. Further, iterative solvers like this open up the |
| // possibility of solving the Newton equations in a non-linear solver |
| // only approximately and terminating early, thereby saving even more |
| // time. |
| // |
| // For the curious, running CG on the Schur complement is the same as |
| // running CG on the Normal Equations with an SSOR preconditioner. For |
| // a proof of this fact and others related to this solver please see |
| // the section on Domain Decomposition Methods in Saad's book |
| // "Iterative Methods for Sparse Linear Systems". |
| class CERES_NO_EXPORT IterativeSchurComplementSolver final |
| : public BlockSparseMatrixSolver { |
| public: |
| explicit IterativeSchurComplementSolver(LinearSolver::Options options); |
| IterativeSchurComplementSolver(const IterativeSchurComplementSolver&) = |
| delete; |
| void operator=(const IterativeSchurComplementSolver&) = delete; |
| |
| ~IterativeSchurComplementSolver() override; |
| |
| private: |
| LinearSolver::Summary SolveImpl(BlockSparseMatrix* A, |
| const double* b, |
| const LinearSolver::PerSolveOptions& options, |
| double* x) final; |
| |
| void CreatePreconditioner(BlockSparseMatrix* A); |
| |
| LinearSolver::Options options_; |
| std::unique_ptr<internal::ImplicitSchurComplement> schur_complement_; |
| std::unique_ptr<Preconditioner> preconditioner_; |
| Vector reduced_linear_system_solution_; |
| }; |
| |
| } // namespace ceres::internal |
| |
| #include "ceres/internal/reenable_warnings.h" |
| |
| #endif // CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_ |