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+// 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/
+//
+// 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 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_