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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 #include "ceres/levenberg_marquardt_strategy.h"
     32 
     33 #include <cmath>
     34 #include "Eigen/Core"
     35 #include "ceres/array_utils.h"
     36 #include "ceres/internal/eigen.h"
     37 #include "ceres/linear_least_squares_problems.h"
     38 #include "ceres/linear_solver.h"
     39 #include "ceres/sparse_matrix.h"
     40 #include "ceres/trust_region_strategy.h"
     41 #include "ceres/types.h"
     42 #include "glog/logging.h"
     43 
     44 namespace ceres {
     45 namespace internal {
     46 
     47 LevenbergMarquardtStrategy::LevenbergMarquardtStrategy(
     48     const TrustRegionStrategy::Options& options)
     49     : linear_solver_(options.linear_solver),
     50       radius_(options.initial_radius),
     51       max_radius_(options.max_radius),
     52       min_diagonal_(options.min_lm_diagonal),
     53       max_diagonal_(options.max_lm_diagonal),
     54       decrease_factor_(2.0),
     55       reuse_diagonal_(false) {
     56   CHECK_NOTNULL(linear_solver_);
     57   CHECK_GT(min_diagonal_, 0.0);
     58   CHECK_LE(min_diagonal_, max_diagonal_);
     59   CHECK_GT(max_radius_, 0.0);
     60 }
     61 
     62 LevenbergMarquardtStrategy::~LevenbergMarquardtStrategy() {
     63 }
     64 
     65 TrustRegionStrategy::Summary LevenbergMarquardtStrategy::ComputeStep(
     66     const TrustRegionStrategy::PerSolveOptions& per_solve_options,
     67     SparseMatrix* jacobian,
     68     const double* residuals,
     69     double* step) {
     70   CHECK_NOTNULL(jacobian);
     71   CHECK_NOTNULL(residuals);
     72   CHECK_NOTNULL(step);
     73 
     74   const int num_parameters = jacobian->num_cols();
     75   if (!reuse_diagonal_) {
     76     if (diagonal_.rows() != num_parameters) {
     77       diagonal_.resize(num_parameters, 1);
     78     }
     79 
     80     jacobian->SquaredColumnNorm(diagonal_.data());
     81     for (int i = 0; i < num_parameters; ++i) {
     82       diagonal_[i] = min(max(diagonal_[i], min_diagonal_), max_diagonal_);
     83     }
     84   }
     85 
     86   lm_diagonal_ = (diagonal_ / radius_).array().sqrt();
     87 
     88   LinearSolver::PerSolveOptions solve_options;
     89   solve_options.D = lm_diagonal_.data();
     90   solve_options.q_tolerance = per_solve_options.eta;
     91   // Disable r_tolerance checking. Since we only care about
     92   // termination via the q_tolerance. As Nash and Sofer show,
     93   // r_tolerance based termination is essentially useless in
     94   // Truncated Newton methods.
     95   solve_options.r_tolerance = -1.0;
     96 
     97   // Invalidate the output array lm_step, so that we can detect if
     98   // the linear solver generated numerical garbage.  This is known
     99   // to happen for the DENSE_QR and then DENSE_SCHUR solver when
    100   // the Jacobin is severly rank deficient and mu is too small.
    101   InvalidateArray(num_parameters, step);
    102 
    103   // Instead of solving Jx = -r, solve Jy = r.
    104   // Then x can be found as x = -y, but the inputs jacobian and residuals
    105   // do not need to be modified.
    106   LinearSolver::Summary linear_solver_summary =
    107       linear_solver_->Solve(jacobian, residuals, solve_options, step);
    108 
    109   if (linear_solver_summary.termination_type == LINEAR_SOLVER_FATAL_ERROR) {
    110     LOG(WARNING) << "Linear solver fatal error.";
    111   } else if (linear_solver_summary.termination_type == LINEAR_SOLVER_FAILURE ||
    112              !IsArrayValid(num_parameters, step)) {
    113     LOG(WARNING) << "Linear solver failure. Failed to compute a finite step.";
    114     linear_solver_summary.termination_type = LINEAR_SOLVER_FAILURE;
    115   } else {
    116     VectorRef(step, num_parameters) *= -1.0;
    117   }
    118   reuse_diagonal_ = true;
    119 
    120   if (per_solve_options.dump_format_type == CONSOLE ||
    121       (per_solve_options.dump_format_type != CONSOLE &&
    122        !per_solve_options.dump_filename_base.empty())) {
    123     if (!DumpLinearLeastSquaresProblem(per_solve_options.dump_filename_base,
    124                                        per_solve_options.dump_format_type,
    125                                        jacobian,
    126                                        solve_options.D,
    127                                        residuals,
    128                                        step,
    129                                        0)) {
    130       LOG(ERROR) << "Unable to dump trust region problem."
    131                  << " Filename base: " << per_solve_options.dump_filename_base;
    132     }
    133   }
    134 
    135 
    136   TrustRegionStrategy::Summary summary;
    137   summary.residual_norm = linear_solver_summary.residual_norm;
    138   summary.num_iterations = linear_solver_summary.num_iterations;
    139   summary.termination_type = linear_solver_summary.termination_type;
    140   return summary;
    141 }
    142 
    143 void LevenbergMarquardtStrategy::StepAccepted(double step_quality) {
    144   CHECK_GT(step_quality, 0.0);
    145   radius_ = radius_ / std::max(1.0 / 3.0,
    146                                1.0 - pow(2.0 * step_quality - 1.0, 3));
    147   radius_ = std::min(max_radius_, radius_);
    148   decrease_factor_ = 2.0;
    149   reuse_diagonal_ = false;
    150 }
    151 
    152 void LevenbergMarquardtStrategy::StepRejected(double step_quality) {
    153   radius_ = radius_ / decrease_factor_;
    154   decrease_factor_ *= 2.0;
    155   reuse_diagonal_ = true;
    156 }
    157 
    158 double LevenbergMarquardtStrategy::Radius() const {
    159   return radius_;
    160 }
    161 
    162 }  // namespace internal
    163 }  // namespace ceres
    164