227 lines
8.6 KiB
C++
227 lines
8.6 KiB
C++
// 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 <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"
|
|
#include "ceres/block_random_access_diagonal_matrix.h"
|
|
|
|
#ifdef CERES_USE_EIGEN_SPARSE
|
|
#include "Eigen/SparseCholesky"
|
|
#include "Eigen/OrderingMethods"
|
|
#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(
|
|
const LinearSolver::PerSolveOptions& per_solve_options,
|
|
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(
|
|
const LinearSolver::PerSolveOptions& per_solve_options,
|
|
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(
|
|
const LinearSolver::PerSolveOptions& per_solve_options,
|
|
double* solution);
|
|
LinearSolver::Summary SolveReducedLinearSystemUsingSuiteSparse(
|
|
const LinearSolver::PerSolveOptions& per_solve_options,
|
|
double* solution);
|
|
LinearSolver::Summary SolveReducedLinearSystemUsingCXSparse(
|
|
const LinearSolver::PerSolveOptions& per_solve_options,
|
|
double* solution);
|
|
LinearSolver::Summary SolveReducedLinearSystemUsingEigen(
|
|
const LinearSolver::PerSolveOptions& per_solve_options,
|
|
double* solution);
|
|
LinearSolver::Summary SolveReducedLinearSystemUsingConjugateGradients(
|
|
const LinearSolver::PerSolveOptions& per_solve_options,
|
|
double* solution);
|
|
|
|
// Size of the blocks in the Schur complement.
|
|
std::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
|
|
|
|
// The preprocessor gymnastics here are dealing with the fact that
|
|
// before version 3.2.2, Eigen did not support a third template
|
|
// parameter to specify the ordering.
|
|
#if EIGEN_VERSION_AT_LEAST(3,2,2)
|
|
typedef Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>, Eigen::Lower,
|
|
Eigen::NaturalOrdering<int> >
|
|
SimplicialLDLT;
|
|
#else
|
|
typedef Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>, Eigen::Lower>
|
|
SimplicialLDLT;
|
|
#endif
|
|
|
|
scoped_ptr<SimplicialLDLT> simplicial_ldlt_;
|
|
#endif
|
|
|
|
scoped_ptr<BlockRandomAccessDiagonalMatrix> preconditioner_;
|
|
CERES_DISALLOW_COPY_AND_ASSIGN(SparseSchurComplementSolver);
|
|
};
|
|
|
|
} // namespace internal
|
|
} // namespace ceres
|
|
|
|
#endif // CERES_INTERNAL_SCHUR_COMPLEMENT_SOLVER_H_
|