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Initial commit of Ceres Solver.
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Keir Mierle
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
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// http://code.google.com/p/ceres-solver/
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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_SCHUR_COMPLEMENT_SOLVER_H_
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#define CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_
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#include "ceres/block_random_access_matrix.h"
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#include "ceres/block_sparse_matrix.h"
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#include "ceres/block_structure.h"
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#include "ceres/linear_solver.h"
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#include "ceres/schur_eliminator.h"
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#include "ceres/suitesparse.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 BlockSparseMatrixBase;
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// Base class for Schur complement based linear least squares
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// solvers. It assumes that the input linear system Ax = b can be
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// partitioned into
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//
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// E y + F z = b
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//
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// Where x = [y;z] is a partition of the variables. The paritioning
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// of the variables is such that, E'E is a block diagonal
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// matrix. Further, the rows of A are ordered so that for every
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// variable block in y, all the rows containing that variable block
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// occur as a vertically contiguous block. i.e the matrix A looks like
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//
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// E F
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// A = [ y1 0 0 0 | z1 0 0 0 z5]
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// [ y1 0 0 0 | z1 z2 0 0 0]
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// [ 0 y2 0 0 | 0 0 z3 0 0]
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// [ 0 0 y3 0 | z1 z2 z3 z4 z5]
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// [ 0 0 y3 0 | z1 0 0 0 z5]
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// [ 0 0 0 y4 | 0 0 0 0 z5]
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// [ 0 0 0 y4 | 0 z2 0 0 0]
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// [ 0 0 0 y4 | 0 0 0 0 0]
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// [ 0 0 0 0 | z1 0 0 0 0]
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// [ 0 0 0 0 | 0 0 z3 z4 z5]
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//
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// This structure should be reflected in the corresponding
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// CompressedRowBlockStructure object associated with A. The linear
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// system Ax = b should either be well posed or the array D below
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// should be non-null and the diagonal matrix corresponding to it
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// should be non-singular.
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//
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// SchurComplementSolver has two sub-classes.
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//
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// DenseSchurComplementSolver: For problems where the Schur complement
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// matrix is small and dense, or if CHOLMOD/SuiteSparse is not
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// installed. For structure from motion problems, this is solver can
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// be used for problems with upto a few hundred cameras.
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//
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// SparseSchurComplementSolver: For problems where the Schur
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// complement matrix is large and sparse. It requires that
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// CHOLMOD/SuiteSparse be installed, as it uses CHOLMOD to find a
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// sparse Cholesky factorization of the Schur complement. This solver
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// can be used for solving structure from motion problems with tens of
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// thousands of cameras, though depending on the exact sparsity
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// structure, it maybe better to use an iterative solver.
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//
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// The two solvers can be instantiated by calling
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// LinearSolver::CreateLinearSolver with LinearSolver::Options::type
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// set to DENSE_SCHUR and SPARSE_SCHUR
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// respectively. LinearSolver::Options::num_eliminate_blocks should be
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// at least 1.
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class SchurComplementSolver : public BlockSparseMatrixBaseSolver {
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public:
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explicit SchurComplementSolver(const LinearSolver::Options& options)
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: options_(options) {
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CHECK_GT(options.num_eliminate_blocks, 0);
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}
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// LinearSolver methods
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virtual ~SchurComplementSolver() {}
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virtual LinearSolver::Summary SolveImpl(
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BlockSparseMatrixBase* A,
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const double* b,
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const LinearSolver::PerSolveOptions& per_solve_options,
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double* x);
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protected:
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const LinearSolver::Options& options() const { return options_; }
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const BlockRandomAccessMatrix* lhs() const { return lhs_.get(); }
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void set_lhs(BlockRandomAccessMatrix* lhs) { lhs_.reset(lhs); }
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const double* rhs() const { return rhs_.get(); }
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void set_rhs(double* rhs) { rhs_.reset(rhs); }
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private:
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virtual void InitStorage(const CompressedRowBlockStructure* bs) = 0;
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virtual bool SolveReducedLinearSystem(double* solution) = 0;
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LinearSolver::Options options_;
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scoped_ptr<SchurEliminatorBase> eliminator_;
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scoped_ptr<BlockRandomAccessMatrix> lhs_;
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scoped_array<double> rhs_;
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DISALLOW_COPY_AND_ASSIGN(SchurComplementSolver);
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};
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// Dense Cholesky factorization based solver.
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class DenseSchurComplementSolver : public SchurComplementSolver {
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public:
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explicit DenseSchurComplementSolver(const LinearSolver::Options& options)
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: SchurComplementSolver(options) {}
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virtual ~DenseSchurComplementSolver() {}
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private:
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virtual void InitStorage(const CompressedRowBlockStructure* bs);
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virtual bool SolveReducedLinearSystem(double* solution);
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DISALLOW_COPY_AND_ASSIGN(DenseSchurComplementSolver);
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};
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#ifndef CERES_NO_SUITESPARSE
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// Sparse Cholesky factorization based solver.
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class SparseSchurComplementSolver : public SchurComplementSolver {
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public:
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explicit SparseSchurComplementSolver(const LinearSolver::Options& options);
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virtual ~SparseSchurComplementSolver();
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private:
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virtual void InitStorage(const CompressedRowBlockStructure* bs);
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virtual bool SolveReducedLinearSystem(double* solution);
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SuiteSparse ss_;
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// Symbolic factorization of the reduced linear system. Precomputed
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// once and reused if constant_sparsity_ is true.
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cholmod_factor* symbolic_factor_;
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DISALLOW_COPY_AND_ASSIGN(SparseSchurComplementSolver);
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};
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#else // CERES_NO_SUITESPARSE
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class SparseSchurComplementSolver : public SchurComplementSolver {
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public:
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explicit SparseSchurComplementSolver(const LinearSolver::Options& options)
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: SchurComplementSolver(options) {
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LOG(FATAL) << "SPARSE_SCHUR is not available. Please "
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"build Ceres with SuiteSparse.";
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}
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virtual ~SparseSchurComplementSolver() {}
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};
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#endif // CERES_NO_SUITESPARSE
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} // namespace internal
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} // namespace ceres
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#endif // CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_
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