// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
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//
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#ifndef CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_
#define CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_

#include "ceres/linear_solver.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/types.h"

namespace ceres {
namespace internal {

class BlockSparseMatrix;
class BlockSparseMatrixBase;
class ImplicitSchurComplement;
class VisibilityBasedPreconditioner;

// This class implements an iterative solver for the linear least
// squares problems that have a bi-partitte 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 BlockSparseMatrixBaseSolver {
 public:
  explicit IterativeSchurComplementSolver(
      const LinearSolver::Options& options);

  virtual ~IterativeSchurComplementSolver();

 private:
  virtual LinearSolver::Summary SolveImpl(
      BlockSparseMatrixBase* A,
      const double* b,
      const LinearSolver::PerSolveOptions& options,
      double* x);

  LinearSolver::Options options_;
  scoped_ptr<internal::ImplicitSchurComplement> schur_complement_;
  scoped_ptr<VisibilityBasedPreconditioner> visibility_based_preconditioner_;
  Vector reduced_linear_system_solution_;
};

}  // namespace internal
}  // namespace ceres

#endif  // CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_
