| 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596 | // 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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE// 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/linear_solver.h"#include "ceres/internal/eigen.h"#include "ceres/types.h"namespace ceres {namespace 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 Univeristy 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 IterativeSchurComplementSolver : public BlockSparseMatrixSolver { public:  explicit IterativeSchurComplementSolver(const LinearSolver::Options& options);  IterativeSchurComplementSolver(const IterativeSchurComplementSolver&) = delete;  void operator=(const IterativeSchurComplementSolver&) = delete;  virtual ~IterativeSchurComplementSolver(); 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 internal}  // namespace ceres#endif  // CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_
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