93 lines
4.0 KiB
C
93 lines
4.0 KiB
C
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2015 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: sameeragarwal@google.com (Sameer Agarwal)
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#ifndef CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_
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#define CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_
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#include "ceres/linear_solver.h"
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#include "ceres/internal/eigen.h"
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#include "ceres/internal/scoped_ptr.h"
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#include "ceres/types.h"
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namespace ceres {
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namespace internal {
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class BlockSparseMatrix;
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class ImplicitSchurComplement;
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class Preconditioner;
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// This class implements an iterative solver for the linear least
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// squares problems that have a bi-partite sparsity structure common
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// to Structure from Motion problems.
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//
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// The algorithm used by this solver was developed in a series of
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// papers - "Agarwal et al, Bundle Adjustment in the Large, ECCV 2010"
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// and "Wu et al, Multicore Bundle Adjustment, submitted to CVPR
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// 2011" at the Univeristy of Washington.
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//
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// The key idea is that one can run Conjugate Gradients on the Schur
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// Complement system without explicitly forming the Schur Complement
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// in memory. The heavy lifting for this is done by the
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// ImplicitSchurComplement class. Not forming the Schur complement in
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// memory and factoring it results in substantial savings in time and
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// memory. Further, iterative solvers like this open up the
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// possibility of solving the Newton equations in a non-linear solver
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// only approximately and terminating early, thereby saving even more
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// time.
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//
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// For the curious, running CG on the Schur complement is the same as
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// running CG on the Normal Equations with an SSOR preconditioner. For
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// a proof of this fact and others related to this solver please see
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// the section on Domain Decomposition Methods in Saad's book
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// "Iterative Methods for Sparse Linear Systems".
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class IterativeSchurComplementSolver : public BlockSparseMatrixSolver {
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public:
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explicit IterativeSchurComplementSolver(const LinearSolver::Options& options);
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virtual ~IterativeSchurComplementSolver();
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private:
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virtual LinearSolver::Summary SolveImpl(
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BlockSparseMatrix* A,
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const double* b,
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const LinearSolver::PerSolveOptions& options,
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double* x);
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LinearSolver::Options options_;
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scoped_ptr<internal::ImplicitSchurComplement> schur_complement_;
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scoped_ptr<Preconditioner> preconditioner_;
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Vector reduced_linear_system_solution_;
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CERES_DISALLOW_COPY_AND_ASSIGN(IterativeSchurComplementSolver);
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};
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} // namespace internal
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} // namespace ceres
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#endif // CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_
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