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//
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6// modification, are permitted provided that the following conditions are met:
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16//
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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
39namespace ceres {
40namespace internal {
41
42class BlockSparseMatrix;
43class ImplicitSchurComplement;
44class Preconditioner;
45
46// This class implements an iterative solver for the linear least
47// squares problems that have a bi-partite sparsity structure common
48// to Structure from Motion problems.
49//
50// The algorithm used by this solver was developed in a series of
51// papers - "Agarwal et al, Bundle Adjustment in the Large, ECCV 2010"
52// and "Wu et al, Multicore Bundle Adjustment, submitted to CVPR
53// 2011" at the Univeristy of Washington.
54//
55// The key idea is that one can run Conjugate Gradients on the Schur
56// Complement system without explicitly forming the Schur Complement
57// in memory. The heavy lifting for this is done by the
58// ImplicitSchurComplement class. Not forming the Schur complement in
59// memory and factoring it results in substantial savings in time and
60// memory. Further, iterative solvers like this open up the
61// possibility of solving the Newton equations in a non-linear solver
62// only approximately and terminating early, thereby saving even more
63// time.
64//
65// For the curious, running CG on the Schur complement is the same as
66// running CG on the Normal Equations with an SSOR preconditioner. For
67// a proof of this fact and others related to this solver please see
68// the section on Domain Decomposition Methods in Saad's book
69// "Iterative Methods for Sparse Linear Systems".
70class IterativeSchurComplementSolver : public BlockSparseMatrixSolver {
71 public:
72  explicit IterativeSchurComplementSolver(const LinearSolver::Options& options);
73  virtual ~IterativeSchurComplementSolver();
74
75 private:
76  virtual LinearSolver::Summary SolveImpl(
77      BlockSparseMatrix* A,
78      const double* b,
79      const LinearSolver::PerSolveOptions& options,
80      double* x);
81
82  LinearSolver::Options options_;
83  scoped_ptr<internal::ImplicitSchurComplement> schur_complement_;
84  scoped_ptr<Preconditioner> preconditioner_;
85  Vector reduced_linear_system_solution_;
86  CERES_DISALLOW_COPY_AND_ASSIGN(IterativeSchurComplementSolver);
87};
88
89}  // namespace internal
90}  // namespace ceres
91
92#endif  // CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_
93