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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_SCHUR_COMPLEMENT_SOLVER_H_
#define CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_
#include <memory>
#include <set>
#include <utility>
#include <vector>
#include "ceres/block_random_access_diagonal_matrix.h"
#include "ceres/block_random_access_matrix.h"
#include "ceres/block_sparse_matrix.h"
#include "ceres/block_structure.h"
#include "ceres/dense_cholesky.h"
#include "ceres/internal/config.h"
#include "ceres/internal/export.h"
#include "ceres/linear_solver.h"
#include "ceres/schur_eliminator.h"
#include "ceres/types.h"
#ifdef CERES_USE_EIGEN_SPARSE
#include "Eigen/OrderingMethods"
#include "Eigen/SparseCholesky"
#endif
#include "ceres/internal/disable_warnings.h"
namespace ceres {
namespace internal {
class BlockSparseMatrix;
class SparseCholesky;
// Base class for Schur complement based linear least squares
// solvers. It assumes that the input linear system Ax = b can be
// partitioned into
//
// E y + F z = b
//
// Where x = [y;z] is a partition of the variables. The paritioning
// of the variables is such that, E'E is a block diagonal
// matrix. Further, the rows of A are ordered so that for every
// variable block in y, all the rows containing that variable block
// occur as a vertically contiguous block. i.e the matrix A looks like
//
// E F
// A = [ y1 0 0 0 | z1 0 0 0 z5]
// [ y1 0 0 0 | z1 z2 0 0 0]
// [ 0 y2 0 0 | 0 0 z3 0 0]
// [ 0 0 y3 0 | z1 z2 z3 z4 z5]
// [ 0 0 y3 0 | z1 0 0 0 z5]
// [ 0 0 0 y4 | 0 0 0 0 z5]
// [ 0 0 0 y4 | 0 z2 0 0 0]
// [ 0 0 0 y4 | 0 0 0 0 0]
// [ 0 0 0 0 | z1 0 0 0 0]
// [ 0 0 0 0 | 0 0 z3 z4 z5]
//
// This structure should be reflected in the corresponding
// CompressedRowBlockStructure object associated with A. The linear
// system Ax = b should either be well posed or the array D below
// should be non-null and the diagonal matrix corresponding to it
// should be non-singular.
//
// SchurComplementSolver has two sub-classes.
//
// DenseSchurComplementSolver: For problems where the Schur complement
// matrix is small and dense, or if CHOLMOD/SuiteSparse is not
// installed. For structure from motion problems, this is solver can
// be used for problems with upto a few hundred cameras.
//
// SparseSchurComplementSolver: For problems where the Schur
// complement matrix is large and sparse. It requires that Ceres be
// build with at least one sparse linear algebra library, as it
// computes a sparse Cholesky factorization of the Schur complement.
//
// This solver can be used for solving structure from motion problems
// with tens of thousands of cameras, though depending on the exact
// sparsity structure, it maybe better to use an iterative solver.
//
// The two solvers can be instantiated by calling
// LinearSolver::CreateLinearSolver with LinearSolver::Options::type
// set to DENSE_SCHUR and SPARSE_SCHUR
// respectively. LinearSolver::Options::elimination_groups[0] should
// be at least 1.
class CERES_NO_EXPORT SchurComplementSolver : public BlockSparseMatrixSolver {
public:
explicit SchurComplementSolver(const LinearSolver::Options& options);
SchurComplementSolver(const SchurComplementSolver&) = delete;
void operator=(const SchurComplementSolver&) = delete;
LinearSolver::Summary SolveImpl(
BlockSparseMatrix* A,
const double* b,
const LinearSolver::PerSolveOptions& per_solve_options,
double* x) override;
protected:
const LinearSolver::Options& options() const { return options_; }
void set_lhs(std::unique_ptr<BlockRandomAccessMatrix> lhs) {
lhs_ = std::move(lhs);
}
const BlockRandomAccessMatrix* lhs() const { return lhs_.get(); }
BlockRandomAccessMatrix* mutable_lhs() { return lhs_.get(); }
void set_rhs(std::unique_ptr<double[]> rhs) { rhs_ = std::move(rhs); }
const double* rhs() const { return rhs_.get(); }
private:
virtual void InitStorage(const CompressedRowBlockStructure* bs) = 0;
virtual LinearSolver::Summary SolveReducedLinearSystem(
const LinearSolver::PerSolveOptions& per_solve_options,
double* solution) = 0;
LinearSolver::Options options_;
std::unique_ptr<SchurEliminatorBase> eliminator_;
std::unique_ptr<BlockRandomAccessMatrix> lhs_;
std::unique_ptr<double[]> rhs_;
};
// Dense Cholesky factorization based solver.
class CERES_NO_EXPORT DenseSchurComplementSolver final
: public SchurComplementSolver {
public:
explicit DenseSchurComplementSolver(const LinearSolver::Options& options);
DenseSchurComplementSolver(const DenseSchurComplementSolver&) = delete;
void operator=(const DenseSchurComplementSolver&) = delete;
~DenseSchurComplementSolver() override;
private:
void InitStorage(const CompressedRowBlockStructure* bs) final;
LinearSolver::Summary SolveReducedLinearSystem(
const LinearSolver::PerSolveOptions& per_solve_options,
double* solution) final;
std::unique_ptr<DenseCholesky> cholesky_;
};
// Sparse Cholesky factorization based solver.
class CERES_NO_EXPORT SparseSchurComplementSolver final
: public SchurComplementSolver {
public:
explicit SparseSchurComplementSolver(const LinearSolver::Options& options);
SparseSchurComplementSolver(const SparseSchurComplementSolver&) = delete;
void operator=(const SparseSchurComplementSolver&) = delete;
~SparseSchurComplementSolver() override;
private:
void InitStorage(const CompressedRowBlockStructure* bs) final;
LinearSolver::Summary SolveReducedLinearSystem(
const LinearSolver::PerSolveOptions& per_solve_options,
double* solution) final;
LinearSolver::Summary SolveReducedLinearSystemUsingConjugateGradients(
const LinearSolver::PerSolveOptions& per_solve_options, double* solution);
// Size of the blocks in the Schur complement.
std::vector<int> blocks_;
std::unique_ptr<SparseCholesky> sparse_cholesky_;
std::unique_ptr<BlockRandomAccessDiagonalMatrix> preconditioner_;
};
} // namespace internal
} // namespace ceres
#include "ceres/internal/reenable_warnings.h"
#endif // CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_
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