// 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 "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 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);

  virtual ~IterativeSchurComplementSolver();

 private:

  virtual LinearSolver::Summary SolveImpl(

      BlockSparseMatrix* A,

      const double* b,

      const LinearSolver::PerSolveOptions& options,

      double* x);

  void CreatePreconditioner(BlockSparseMatrix* A);

  LinearSolver::Options options_;

  scoped_ptr<internal::ImplicitSchurComplement> schur_complement_;

  scoped_ptr<Preconditioner> preconditioner_;

  Vector reduced_linear_system_solution_;

  CERES_DISALLOW_COPY_AND_ASSIGN(IterativeSchurComplementSolver);

};

}  // namespace internal

}  // namespace ceres

#endif  // CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_