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diff --git a/extern/ceres/internal/ceres/implicit_schur_complement.h b/extern/ceres/internal/ceres/implicit_schur_complement.h new file mode 100644 index 00000000000..5d822ebaeef --- /dev/null +++ b/extern/ceres/internal/ceres/implicit_schur_complement.h @@ -0,0 +1,167 @@ +// 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) +// +// An iterative solver for solving the Schur complement/reduced camera +// linear system that arise in SfM problems. + +#ifndef CERES_INTERNAL_IMPLICIT_SCHUR_COMPLEMENT_H_ +#define CERES_INTERNAL_IMPLICIT_SCHUR_COMPLEMENT_H_ + +#include "ceres/linear_operator.h" +#include "ceres/linear_solver.h" +#include "ceres/partitioned_matrix_view.h" +#include "ceres/internal/eigen.h" +#include "ceres/internal/scoped_ptr.h" +#include "ceres/types.h" + +namespace ceres { +namespace internal { + +class BlockSparseMatrix; + +// This class implements various linear algebraic operations related +// to the Schur complement without explicitly forming it. +// +// +// Given a reactangular linear system Ax = b, where +// +// A = [E F] +// +// The normal equations are given by +// +// A'Ax = A'b +// +// |E'E E'F||y| = |E'b| +// |F'E F'F||z| |F'b| +// +// and the Schur complement system is given by +// +// [F'F - F'E (E'E)^-1 E'F] z = F'b - F'E (E'E)^-1 E'b +// +// Now if we wish to solve Ax = b in the least squares sense, one way +// is to form this Schur complement system and solve it using +// Preconditioned Conjugate Gradients. +// +// The key operation in a conjugate gradient solver is the evaluation of the +// matrix vector product with the Schur complement +// +// S = F'F - F'E (E'E)^-1 E'F +// +// It is straightforward to see that matrix vector products with S can +// be evaluated without storing S in memory. Instead, given (E'E)^-1 +// (which for our purposes is an easily inverted block diagonal +// matrix), it can be done in terms of matrix vector products with E, +// F and (E'E)^-1. This class implements this functionality and other +// auxilliary bits needed to implement a CG solver on the Schur +// complement using the PartitionedMatrixView object. +// +// THREAD SAFETY: This class is nqot thread safe. In particular, the +// RightMultiply (and the LeftMultiply) methods are not thread safe as +// they depend on mutable arrays used for the temporaries needed to +// compute the product y += Sx; +class ImplicitSchurComplement : public LinearOperator { + public: + // num_eliminate_blocks is the number of E blocks in the matrix + // A. + // + // preconditioner indicates whether the inverse of the matrix F'F + // should be computed or not as a preconditioner for the Schur + // Complement. + // + // TODO(sameeragarwal): Get rid of the two bools below and replace + // them with enums. + explicit ImplicitSchurComplement(const LinearSolver::Options& options); + virtual ~ImplicitSchurComplement(); + + // Initialize the Schur complement for a linear least squares + // problem of the form + // + // |A | x = |b| + // |diag(D)| |0| + // + // If D is null, then it is treated as a zero dimensional matrix. It + // is important that the matrix A have a BlockStructure object + // associated with it and has a block structure that is compatible + // with the SchurComplement solver. + void Init(const BlockSparseMatrix& A, const double* D, const double* b); + + // y += Sx, where S is the Schur complement. + virtual void RightMultiply(const double* x, double* y) const; + + // The Schur complement is a symmetric positive definite matrix, + // thus the left and right multiply operators are the same. + virtual void LeftMultiply(const double* x, double* y) const { + RightMultiply(x, y); + } + + // y = (E'E)^-1 (E'b - E'F x). Given an estimate of the solution to + // the Schur complement system, this method computes the value of + // the e_block variables that were eliminated to form the Schur + // complement. + void BackSubstitute(const double* x, double* y); + + virtual int num_rows() const { return A_->num_cols_f(); } + virtual int num_cols() const { return A_->num_cols_f(); } + const Vector& rhs() const { return rhs_; } + + const BlockSparseMatrix* block_diagonal_EtE_inverse() const { + return block_diagonal_EtE_inverse_.get(); + } + + const BlockSparseMatrix* block_diagonal_FtF_inverse() const { + return block_diagonal_FtF_inverse_.get(); + } + + private: + void AddDiagonalAndInvert(const double* D, BlockSparseMatrix* matrix); + void UpdateRhs(); + + const LinearSolver::Options& options_; + + scoped_ptr<PartitionedMatrixViewBase> A_; + const double* D_; + const double* b_; + + scoped_ptr<BlockSparseMatrix> block_diagonal_EtE_inverse_; + scoped_ptr<BlockSparseMatrix> block_diagonal_FtF_inverse_; + + Vector rhs_; + + // Temporary storage vectors used to implement RightMultiply. + mutable Vector tmp_rows_; + mutable Vector tmp_e_cols_; + mutable Vector tmp_e_cols_2_; + mutable Vector tmp_f_cols_; +}; + +} // namespace internal +} // namespace ceres + +#endif // CERES_INTERNAL_IMPLICIT_SCHUR_COMPLEMENT_H_ |