1// Ceres Solver - A fast non-linear least squares minimizer 2// Copyright 2010, 2011, 2012 Google Inc. All rights reserved. 3// http://code.google.com/p/ceres-solver/ 4// 5// Redistribution and use in source and binary forms, with or without 6// modification, are permitted provided that the following conditions are met: 7// 8// * Redistributions of source code must retain the above copyright notice, 9// this list of conditions and the following disclaimer. 10// * Redistributions in binary form must reproduce the above copyright notice, 11// this list of conditions and the following disclaimer in the documentation 12// and/or other materials provided with the distribution. 13// * Neither the name of Google Inc. nor the names of its contributors may be 14// used to endorse or promote products derived from this software without 15// specific prior written permission. 16// 17// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 18// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 21// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 22// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 23// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 24// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 25// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 26// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 27// POSSIBILITY OF SUCH DAMAGE. 28// 29// Author: sameeragarwal@google.com (Sameer Agarwal) 30 31#ifndef CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_ 32#define CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_ 33 34#include "ceres/linear_solver.h" 35#include "ceres/internal/eigen.h" 36#include "ceres/internal/scoped_ptr.h" 37#include "ceres/types.h" 38 39namespace ceres { 40namespace internal { 41 42class BlockSparseMatrix; 43class ImplicitSchurComplement; 44class Preconditioner; 45 46// This class implements an iterative solver for the linear least 47// squares problems that have a bi-partite sparsity structure common 48// to Structure from Motion problems. 49// 50// The algorithm used by this solver was developed in a series of 51// papers - "Agarwal et al, Bundle Adjustment in the Large, ECCV 2010" 52// and "Wu et al, Multicore Bundle Adjustment, submitted to CVPR 53// 2011" at the Univeristy of Washington. 54// 55// The key idea is that one can run Conjugate Gradients on the Schur 56// Complement system without explicitly forming the Schur Complement 57// in memory. The heavy lifting for this is done by the 58// ImplicitSchurComplement class. Not forming the Schur complement in 59// memory and factoring it results in substantial savings in time and 60// memory. Further, iterative solvers like this open up the 61// possibility of solving the Newton equations in a non-linear solver 62// only approximately and terminating early, thereby saving even more 63// time. 64// 65// For the curious, running CG on the Schur complement is the same as 66// running CG on the Normal Equations with an SSOR preconditioner. For 67// a proof of this fact and others related to this solver please see 68// the section on Domain Decomposition Methods in Saad's book 69// "Iterative Methods for Sparse Linear Systems". 70class IterativeSchurComplementSolver : public BlockSparseMatrixSolver { 71 public: 72 explicit IterativeSchurComplementSolver(const LinearSolver::Options& options); 73 virtual ~IterativeSchurComplementSolver(); 74 75 private: 76 virtual LinearSolver::Summary SolveImpl( 77 BlockSparseMatrix* A, 78 const double* b, 79 const LinearSolver::PerSolveOptions& options, 80 double* x); 81 82 LinearSolver::Options options_; 83 scoped_ptr<internal::ImplicitSchurComplement> schur_complement_; 84 scoped_ptr<Preconditioner> preconditioner_; 85 Vector reduced_linear_system_solution_; 86 CERES_DISALLOW_COPY_AND_ASSIGN(IterativeSchurComplementSolver); 87}; 88 89} // namespace internal 90} // namespace ceres 91 92#endif // CERES_INTERNAL_ITERATIVE_SCHUR_COMPLEMENT_SOLVER_H_ 93