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      1 // Ceres Solver - A fast non-linear least squares minimizer
      2 // Copyright 2012 Google Inc. All rights reserved.
      3 // http://code.google.com/p/ceres-solver/
      4 //
      5 // Redistribution and use in source and binary forms, with or without
      6 // modification, are permitted provided that the following conditions are met:
      7 //
      8 // * Redistributions of source code must retain the above copyright notice,
      9 //   this list of conditions and the following disclaimer.
     10 // * Redistributions in binary form must reproduce the above copyright notice,
     11 //   this list of conditions and the following disclaimer in the documentation
     12 //   and/or other materials provided with the distribution.
     13 // * Neither the name of Google Inc. nor the names of its contributors may be
     14 //   used to endorse or promote products derived from this software without
     15 //   specific prior written permission.
     16 //
     17 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
     18 // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     19 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     20 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
     21 // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
     22 // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
     23 // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
     24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
     25 // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
     26 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
     27 // POSSIBILITY OF SUCH DAMAGE.
     28 //
     29 // Author: sameeragarwal (at) google.com (Sameer Agarwal)
     30 
     31 #ifndef CERES_INTERNAL_TRUST_REGION_STRATEGY_H_
     32 #define CERES_INTERNAL_TRUST_REGION_STRATEGY_H_
     33 
     34 #include <string>
     35 #include "ceres/internal/port.h"
     36 #include "ceres/linear_solver.h"
     37 
     38 namespace ceres {
     39 namespace internal {
     40 
     41 class LinearSolver;
     42 class SparseMatrix;
     43 
     44 // Interface for classes implementing various trust region strategies
     45 // for nonlinear least squares problems.
     46 //
     47 // The object is expected to maintain and update a trust region
     48 // radius, which it then uses to solve for the trust region step using
     49 // the jacobian matrix and residual vector.
     50 //
     51 // Here the term trust region radius is used loosely, as the strategy
     52 // is free to treat it as guidance and violate it as need be. e.g.,
     53 // the LevenbergMarquardtStrategy uses the inverse of the trust region
     54 // radius to scale the damping term, which controls the step size, but
     55 // does not set a hard limit on its size.
     56 class TrustRegionStrategy {
     57  public:
     58   struct Options {
     59     Options()
     60         : trust_region_strategy_type(LEVENBERG_MARQUARDT),
     61           initial_radius(1e4),
     62           max_radius(1e32),
     63           min_lm_diagonal(1e-6),
     64           max_lm_diagonal(1e32),
     65           dogleg_type(TRADITIONAL_DOGLEG) {
     66     }
     67 
     68     TrustRegionStrategyType trust_region_strategy_type;
     69     // Linear solver used for actually solving the trust region step.
     70     LinearSolver* linear_solver;
     71     double initial_radius;
     72     double max_radius;
     73 
     74     // Minimum and maximum values of the diagonal damping matrix used
     75     // by LevenbergMarquardtStrategy. The DoglegStrategy also uses
     76     // these bounds to construct a regularizing diagonal to ensure
     77     // that the Gauss-Newton step computation is of full rank.
     78     double min_lm_diagonal;
     79     double max_lm_diagonal;
     80 
     81     // Further specify which dogleg method to use
     82     DoglegType dogleg_type;
     83   };
     84 
     85   // Per solve options.
     86   struct PerSolveOptions {
     87     PerSolveOptions()
     88         : eta(0),
     89           dump_filename_base(""),
     90           dump_format_type(TEXTFILE) {
     91     }
     92 
     93     // Forcing sequence for inexact solves.
     94     double eta;
     95 
     96     // If non-empty and dump_format_type is not CONSOLE, the trust
     97     // regions strategy will write the linear system to file(s) with
     98     // name starting with dump_filename_base.  If dump_format_type is
     99     // CONSOLE then dump_filename_base will be ignored and the linear
    100     // system will be written to the standard error.
    101     string dump_filename_base;
    102     DumpFormatType dump_format_type;
    103   };
    104 
    105   struct Summary {
    106     Summary()
    107         : residual_norm(0.0),
    108           num_iterations(-1),
    109           termination_type(LINEAR_SOLVER_FAILURE) {
    110     }
    111 
    112     // If the trust region problem is,
    113     //
    114     //   1/2 x'Ax + b'x + c,
    115     //
    116     // then
    117     //
    118     //   residual_norm = |Ax -b|
    119     double residual_norm;
    120 
    121     // Number of iterations used by the linear solver. If a linear
    122     // solver was not called (e.g., DogLegStrategy after an
    123     // unsuccessful step), then this would be zero.
    124     int num_iterations;
    125 
    126     // Status of the linear solver used to solve the Newton system.
    127     LinearSolverTerminationType termination_type;
    128   };
    129 
    130   virtual ~TrustRegionStrategy();
    131 
    132   // Use the current radius to solve for the trust region step.
    133   virtual Summary ComputeStep(const PerSolveOptions& per_solve_options,
    134                               SparseMatrix* jacobian,
    135                               const double* residuals,
    136                               double* step) = 0;
    137 
    138   // Inform the strategy that the current step has been accepted, and
    139   // that the ratio of the decrease in the non-linear objective to the
    140   // decrease in the trust region model is step_quality.
    141   virtual void StepAccepted(double step_quality) = 0;
    142 
    143   // Inform the strategy that the current step has been rejected, and
    144   // that the ratio of the decrease in the non-linear objective to the
    145   // decrease in the trust region model is step_quality.
    146   virtual void StepRejected(double step_quality) = 0;
    147 
    148   // Inform the strategy that the current step has been rejected
    149   // because it was found to be numerically invalid.
    150   // StepRejected/StepAccepted will not be called for this step, and
    151   // the strategy is free to do what it wants with this information.
    152   virtual void StepIsInvalid() = 0;
    153 
    154   // Current trust region radius.
    155   virtual double Radius() const = 0;
    156 
    157   // Factory.
    158   static TrustRegionStrategy* Create(const Options& options);
    159 };
    160 
    161 }  // namespace internal
    162 }  // namespace ceres
    163 
    164 #endif  // CERES_INTERNAL_TRUST_REGION_STRATEGY_H_
    165