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// 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/internal/eigen.h"
#include "ceres/internal/port.h"
#include "ceres/linear_solver.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 CERES_EXPORT_INTERNAL 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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