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@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
LevenbergMarquardtStrategy(const TrustRegionStrategy::Options & options)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
~LevenbergMarquardtStrategy()62 LevenbergMarquardtStrategy::~LevenbergMarquardtStrategy() {
63 }
64
ComputeStep(const TrustRegionStrategy::PerSolveOptions & per_solve_options,SparseMatrix * jacobian,const double * residuals,double * step)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
StepAccepted(double step_quality)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
StepRejected(double step_quality)152 void LevenbergMarquardtStrategy::StepRejected(double step_quality) {
153 radius_ = radius_ / decrease_factor_;
154 decrease_factor_ *= 2.0;
155 reuse_diagonal_ = true;
156 }
157
Radius() const158 double LevenbergMarquardtStrategy::Radius() const {
159 return radius_;
160 }
161
162 } // namespace internal
163 } // namespace ceres
164