Initial commit of Ceres Solver.
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+// 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
+// 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)
+//
+// Abstract interface for objects solving linear systems of various
+// kinds.
+
+#ifndef CERES_INTERNAL_LINEAR_SOLVER_H_
+#define CERES_INTERNAL_LINEAR_SOLVER_H_
+
+#include <cstddef>
+
+#include <glog/logging.h>
+#include "ceres/block_sparse_matrix.h"
+#include "ceres/casts.h"
+#include "ceres/compressed_row_sparse_matrix.h"
+#include "ceres/dense_sparse_matrix.h"
+#include "ceres/triplet_sparse_matrix.h"
+#include "ceres/types.h"
+
+namespace ceres {
+namespace internal {
+
+class LinearOperator;
+
+// Abstract base class for objects that implement algorithms for
+// solving linear systems
+//
+// Ax = b
+//
+// It is expected that a single instance of a LinearSolver object
+// maybe used multiple times for solving different linear
+// systems. This allows them to cache and reuse information across
+// solves if for example the sparsity of the linear system remains
+// constant.
+//
+// Subclasses of LinearSolver use two structs to configure themselves.
+// The Options struct configures the LinearSolver object for its
+// lifetime. The PerSolveOptions struct is used to specify options for
+// a particular Solve call.
+class LinearSolver {
+ public:
+ struct Options {
+ Options()
+ : type(SPARSE_NORMAL_CHOLESKY),
+ preconditioner_type(JACOBI),
+ min_num_iterations(1),
+ max_num_iterations(1),
+ num_threads(1),
+ constant_sparsity(false),
+ num_eliminate_blocks(0),
+ residual_reset_period(10),
+ row_block_size(Dynamic),
+ e_block_size(Dynamic),
+ f_block_size(Dynamic) {
+ }
+
+ LinearSolverType type;
+
+ PreconditionerType preconditioner_type;
+
+ // Number of internal iterations that the solver uses. This
+ // parameter only makes sense for iterative solvers like CG.
+ int min_num_iterations;
+ int max_num_iterations;
+
+ // If possible, how many threads can the solver use.
+ int num_threads;
+
+ // If possible cache and reuse the symbolic factorization across
+ // multiple calls.
+ bool constant_sparsity;
+
+ // Eliminate 0 to num_eliminate_blocks - 1 from the Normal
+ // equations to form a schur complement. Only used by the Schur
+ // complement based solver. The most common use for this parameter
+ // is in the case of structure from motion problems where we have
+ // camera blocks and point blocks. Then setting the
+ // num_eliminate_blocks to the number of points allows the solver
+ // to use the Schur complement trick. For more details see the
+ // description of this parameter in solver.h.
+ int num_eliminate_blocks;
+
+ // Iterative solvers, e.g. Preconditioned Conjugate Gradients
+ // maintain a cheap estimate of the residual which may become
+ // inaccurate over time. Thus for non-zero values of this
+ // parameter, the solver can be told to recalculate the value of
+ // the residual using a |b - Ax| evaluation.
+ int residual_reset_period;
+
+ // If the block sizes in a BlockSparseMatrix are fixed, then in
+ // some cases the Schur complement based solvers can detect and
+ // specialize on them.
+ //
+ // It is expected that these parameters are set programmatically
+ // rather than manually.
+ //
+ // Please see explicit_schur_complement_solver_impl.h for more
+ // details.
+ int row_block_size;
+ int e_block_size;
+ int f_block_size;
+ };
+
+ // Options for the Solve method.
+ struct PerSolveOptions {
+ PerSolveOptions()
+ : D(NULL),
+ preconditioner(NULL),
+ r_tolerance(0.0),
+ q_tolerance(0.0) {
+ }
+
+ // This option only makes sense for unsymmetric linear solvers
+ // that can solve rectangular linear systems.
+ //
+ // Given a matrix A, an optional diagonal matrix D as a vector,
+ // and a vector b, the linear solver will solve for
+ //
+ // | A | x = | b |
+ // | D | | 0 |
+ //
+ // If D is null, then it is treated as zero, and the solver returns
+ // the solution to
+ //
+ // A x = b
+ //
+ // In either case, x is the vector that solves the following
+ // optimization problem.
+ //
+ // arg min_x ||Ax -b||^2 + ||Dx||^2
+ //
+ // Here A is a matrix of size m x n, with full column rank. If A
+ // does not have full column rank, the results returned by the
+ // solver cannot be relied on. D, if it is not null is an array of
+ // size n. b is an array of size m and x is an array of size n.
+ double * D;
+
+ // This option only makes sense for iterative solvers.
+ //
+ // In general the performance of an iterative linear solver
+ // depends on the condition number of the matrix A. For example
+ // the convergence rate of the conjugate gradients algorithm
+ // is proportional to the square root of the condition number.
+ //
+ // One particularly useful technique for improving the
+ // conditioning of a linear system is to precondition it. In its
+ // simplest form a preconditioner is a matrix M such that instead
+ // of solving Ax = b, we solve the linear system AM^{-1} y = b
+ // instead, where M is such that the condition number k(AM^{-1})
+ // is smaller than the conditioner k(A). Given the solution to
+ // this system, x = M^{-1} y. The iterative solver takes care of
+ // the mechanics of solving the preconditioned system and
+ // returning the corrected solution x. The user only needs to
+ // supply a linear operator.
+ //
+ // A null preconditioner is equivalent to an identity matrix being
+ // used a preconditioner.
+ LinearOperator* preconditioner;
+
+
+ // The following tolerance related options only makes sense for
+ // iterative solvers. Direct solvers ignore them.
+
+ // Solver terminates when
+ //
+ // |Ax - b| <= r_tolerance * |b|.
+ //
+ // This is the most commonly used termination criterion for
+ // iterative solvers.
+ double r_tolerance;
+
+ // For PSD matrices A, let
+ //
+ // Q(x) = x'Ax - 2b'x
+ //
+ // be the cost of the quadratic function defined by A and b. Then,
+ // the solver terminates at iteration i if
+ //
+ // i * (Q(x_i) - Q(x_i-1)) / Q(x_i) < q_tolerance.
+ //
+ // This termination criterion is more useful when using CG to
+ // solve the Newton step. This particular convergence test comes
+ // from Stephen Nash's work on truncated Newton
+ // methods. References:
+ //
+ // 1. Stephen G. Nash & Ariela Sofer, Assessing A Search
+ // Direction Within A Truncated Newton Method, Operation
+ // Research Letters 9(1990) 219-221.
+ //
+ // 2. Stephen G. Nash, A Survey of Truncated Newton Methods,
+ // Journal of Computational and Applied Mathematics,
+ // 124(1-2), 45-59, 2000.
+ //
+ double q_tolerance;
+ };
+
+ // Summary of a call to the Solve method. We should move away from
+ // the true/false method for determining solver success. We should
+ // let the summary object do the talking.
+ struct Summary {
+ Summary()
+ : residual_norm(0.0),
+ num_iterations(-1),
+ termination_type(FAILURE) {
+ }
+
+ double residual_norm;
+ int num_iterations;
+ LinearSolverTerminationType termination_type;
+ };
+
+ virtual ~LinearSolver();
+
+ // Solve Ax = b.
+ virtual Summary Solve(LinearOperator* A,
+ const double* b,
+ const PerSolveOptions& per_solve_options,
+ double* x) = 0;
+
+ static LinearSolver* Create(const Options& options);
+};
+
+// This templated subclass of LinearSolver serves as a base class for
+// other linear solvers that depend on the particular matrix layout of
+// the underlying linear operator. For example some linear solvers
+// need low level access to the TripletSparseMatrix implementing the
+// LinearOperator interface. This class hides those implementation
+// details behind a private virtual method, and has the Solve method
+// perform the necessary upcasting.
+template <typename MatrixType>
+class TypedLinearSolver : public LinearSolver {
+ public:
+ virtual ~TypedLinearSolver() {}
+ virtual LinearSolver::Summary Solve(
+ LinearOperator* A,
+ const double* b,
+ const LinearSolver::PerSolveOptions& per_solve_options,
+ double* x) {
+ CHECK_NOTNULL(A);
+ CHECK_NOTNULL(b);
+ CHECK_NOTNULL(x);
+ return SolveImpl(down_cast<MatrixType*>(A), b, per_solve_options, x);
+ }
+
+ private:
+ virtual LinearSolver::Summary SolveImpl(
+ MatrixType* A,
+ const double* b,
+ const LinearSolver::PerSolveOptions& per_solve_options,
+ double* x) = 0;
+};
+
+// Linear solvers that depend on acccess to the low level structure of
+// a SparseMatrix.
+typedef TypedLinearSolver<BlockSparseMatrix> BlockSparseMatrixSolver; // NOLINT
+typedef TypedLinearSolver<BlockSparseMatrixBase> BlockSparseMatrixBaseSolver; // NOLINT
+typedef TypedLinearSolver<CompressedRowSparseMatrix> CompressedRowSparseMatrixSolver; // NOLINT
+typedef TypedLinearSolver<DenseSparseMatrix> DenseSparseMatrixSolver; // NOLINT
+typedef TypedLinearSolver<TripletSparseMatrix> TripletSparseMatrixSolver; // NOLINT
+
+} // namespace internal
+} // namespace ceres
+
+#endif // CERES_INTERNAL_LINEAR_SOLVER_H_
