// 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
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// Author: sameeragarwal@google.com (Sameer Agarwal)
#ifndef CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_
#define CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_
#include <set>
#include <utility>
#include <vector>
#include "ceres/internal/port.h"
#include "ceres/block_random_access_matrix.h"
#include "ceres/block_sparse_matrix.h"
#include "ceres/block_structure.h"
#include "ceres/cxsparse.h"
#include "ceres/linear_solver.h"
#include "ceres/schur_eliminator.h"
#include "ceres/suitesparse.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/types.h"
#ifdef CERES_USE_EIGEN_SPARSE
#include "Eigen/SparseCholesky"
#endif
namespace ceres {
namespace internal {
class BlockSparseMatrix;
// 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
// CHOLMOD/SuiteSparse be installed, as it uses CHOLMOD to find 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 SchurComplementSolver : public BlockSparseMatrixSolver {
public:
explicit SchurComplementSolver(const LinearSolver::Options& options)
: options_(options) {
CHECK_GT(options.elimination_groups.size(), 1);
CHECK_GT(options.elimination_groups[0], 0);
}
// LinearSolver methods
virtual ~SchurComplementSolver() {}
virtual LinearSolver::Summary SolveImpl(
BlockSparseMatrix* A,
const double* b,
const LinearSolver::PerSolveOptions& per_solve_options,
double* x);
protected:
const LinearSolver::Options& options() const { return options_; }
const BlockRandomAccessMatrix* lhs() const { return lhs_.get(); }
void set_lhs(BlockRandomAccessMatrix* lhs) { lhs_.reset(lhs); }
const double* rhs() const { return rhs_.get(); }
void set_rhs(double* rhs) { rhs_.reset(rhs); }
private:
virtual void InitStorage(const CompressedRowBlockStructure* bs) = 0;
virtual LinearSolver::Summary SolveReducedLinearSystem(
double* solution) = 0;
LinearSolver::Options options_;
scoped_ptr<SchurEliminatorBase> eliminator_;
scoped_ptr<BlockRandomAccessMatrix> lhs_;
scoped_array<double> rhs_;
CERES_DISALLOW_COPY_AND_ASSIGN(SchurComplementSolver);
};
// Dense Cholesky factorization based solver.
class DenseSchurComplementSolver : public SchurComplementSolver {
public:
explicit DenseSchurComplementSolver(const LinearSolver::Options& options)
: SchurComplementSolver(options) {}
virtual ~DenseSchurComplementSolver() {}
private:
virtual void InitStorage(const CompressedRowBlockStructure* bs);
virtual LinearSolver::Summary SolveReducedLinearSystem(
double* solution);
CERES_DISALLOW_COPY_AND_ASSIGN(DenseSchurComplementSolver);
};
// Sparse Cholesky factorization based solver.
class SparseSchurComplementSolver : public SchurComplementSolver {
public:
explicit SparseSchurComplementSolver(const LinearSolver::Options& options);
virtual ~SparseSchurComplementSolver();
private:
virtual void InitStorage(const CompressedRowBlockStructure* bs);
virtual LinearSolver::Summary SolveReducedLinearSystem(
double* solution);
LinearSolver::Summary SolveReducedLinearSystemUsingSuiteSparse(
double* solution);
LinearSolver::Summary SolveReducedLinearSystemUsingCXSparse(
double* solution);
LinearSolver::Summary SolveReducedLinearSystemUsingEigen(
double* solution);
// Size of the blocks in the Schur complement.
vector<int> blocks_;
SuiteSparse ss_;
// Symbolic factorization of the reduced linear system. Precomputed
// once and reused in subsequent calls.
cholmod_factor* factor_;
CXSparse cxsparse_;
// Cached factorization
cs_dis* cxsparse_factor_;
#ifdef CERES_USE_EIGEN_SPARSE
typedef Eigen::SimplicialLDLT<Eigen::SparseMatrix<double> > SimplicialLDLT;
scoped_ptr<SimplicialLDLT> simplicial_ldlt_;
#endif
CERES_DISALLOW_COPY_AND_ASSIGN(SparseSchurComplementSolver);
};
} // namespace internal
} // namespace ceres
#endif // CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_