1// Ceres Solver - A fast non-linear least squares minimizer
2// Copyright 2013 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//
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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
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20// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
21// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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24// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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27// POSSIBILITY OF SUCH DAMAGE.
28//
29// Author: sameeragarwal@google.com (Sameer Agarwal)
30//         mierle@gmail.com (Keir Mierle)
31//
32// Finite differencing routine used by NumericDiffCostFunction.
33
34#ifndef CERES_PUBLIC_INTERNAL_NUMERIC_DIFF_H_
35#define CERES_PUBLIC_INTERNAL_NUMERIC_DIFF_H_
36
37#include <cstring>
38
39#include "Eigen/Dense"
40#include "ceres/cost_function.h"
41#include "ceres/internal/scoped_ptr.h"
42#include "ceres/internal/variadic_evaluate.h"
43#include "ceres/types.h"
44#include "glog/logging.h"
45
46
47namespace ceres {
48namespace internal {
49
50// Helper templates that allow evaluation of a variadic functor or a
51// CostFunction object.
52template <typename CostFunctor,
53          int N0, int N1, int N2, int N3, int N4,
54          int N5, int N6, int N7, int N8, int N9 >
55bool EvaluateImpl(const CostFunctor* functor,
56                  double const* const* parameters,
57                  double* residuals,
58                  const void* /* NOT USED */) {
59  return VariadicEvaluate<CostFunctor,
60                          double,
61                          N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>::Call(
62                              *functor,
63                              parameters,
64                              residuals);
65}
66
67template <typename CostFunctor,
68          int N0, int N1, int N2, int N3, int N4,
69          int N5, int N6, int N7, int N8, int N9 >
70bool EvaluateImpl(const CostFunctor* functor,
71                  double const* const* parameters,
72                  double* residuals,
73                  const CostFunction* /* NOT USED */) {
74  return functor->Evaluate(parameters, residuals, NULL);
75}
76
77// This is split from the main class because C++ doesn't allow partial template
78// specializations for member functions. The alternative is to repeat the main
79// class for differing numbers of parameters, which is also unfortunate.
80template <typename CostFunctor,
81          NumericDiffMethod kMethod,
82          int kNumResiduals,
83          int N0, int N1, int N2, int N3, int N4,
84          int N5, int N6, int N7, int N8, int N9,
85          int kParameterBlock,
86          int kParameterBlockSize>
87struct NumericDiff {
88  // Mutates parameters but must restore them before return.
89  static bool EvaluateJacobianForParameterBlock(
90      const CostFunctor* functor,
91      double const* residuals_at_eval_point,
92      const double relative_step_size,
93      int num_residuals,
94      double **parameters,
95      double *jacobian) {
96    using Eigen::Map;
97    using Eigen::Matrix;
98    using Eigen::RowMajor;
99    using Eigen::ColMajor;
100
101    const int NUM_RESIDUALS =
102        (kNumResiduals != ceres::DYNAMIC ? kNumResiduals : num_residuals);
103
104    typedef Matrix<double, kNumResiduals, 1> ResidualVector;
105    typedef Matrix<double, kParameterBlockSize, 1> ParameterVector;
106    typedef Matrix<double,
107                   kNumResiduals,
108                   kParameterBlockSize,
109                   (kParameterBlockSize == 1 &&
110                    kNumResiduals > 1) ? ColMajor : RowMajor>
111        JacobianMatrix;
112
113
114    Map<JacobianMatrix> parameter_jacobian(jacobian,
115                                           NUM_RESIDUALS,
116                                           kParameterBlockSize);
117
118    // Mutate 1 element at a time and then restore.
119    Map<ParameterVector> x_plus_delta(parameters[kParameterBlock],
120                                      kParameterBlockSize);
121    ParameterVector x(x_plus_delta);
122    ParameterVector step_size = x.array().abs() * relative_step_size;
123
124    // To handle cases where a parameter is exactly zero, instead use
125    // the mean step_size for the other dimensions. If all the
126    // parameters are zero, there's no good answer. Take
127    // relative_step_size as a guess and hope for the best.
128    const double fallback_step_size =
129        (step_size.sum() == 0)
130        ? relative_step_size
131        : step_size.sum() / step_size.rows();
132
133    // For each parameter in the parameter block, use finite differences to
134    // compute the derivative for that parameter.
135
136    ResidualVector residuals(NUM_RESIDUALS);
137    for (int j = 0; j < kParameterBlockSize; ++j) {
138      const double delta =
139          (step_size(j) == 0.0) ? fallback_step_size : step_size(j);
140
141      x_plus_delta(j) = x(j) + delta;
142
143      if (!EvaluateImpl<CostFunctor, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>(
144              functor, parameters, residuals.data(), functor)) {
145        return false;
146      }
147
148      // Compute this column of the jacobian in 3 steps:
149      // 1. Store residuals for the forward part.
150      // 2. Subtract residuals for the backward (or 0) part.
151      // 3. Divide out the run.
152      parameter_jacobian.col(j) = residuals;
153
154      double one_over_delta = 1.0 / delta;
155      if (kMethod == CENTRAL) {
156        // Compute the function on the other side of x(j).
157        x_plus_delta(j) = x(j) - delta;
158
159        if (!EvaluateImpl<CostFunctor, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>(
160                functor, parameters, residuals.data(), functor)) {
161          return false;
162        }
163
164        parameter_jacobian.col(j) -= residuals;
165        one_over_delta /= 2;
166      } else {
167        // Forward difference only; reuse existing residuals evaluation.
168        parameter_jacobian.col(j) -=
169            Map<const ResidualVector>(residuals_at_eval_point, NUM_RESIDUALS);
170      }
171      x_plus_delta(j) = x(j);  // Restore x_plus_delta.
172
173      // Divide out the run to get slope.
174      parameter_jacobian.col(j) *= one_over_delta;
175    }
176    return true;
177  }
178};
179
180template <typename CostFunctor,
181          NumericDiffMethod kMethod,
182          int kNumResiduals,
183          int N0, int N1, int N2, int N3, int N4,
184          int N5, int N6, int N7, int N8, int N9,
185          int kParameterBlock>
186struct NumericDiff<CostFunctor, kMethod, kNumResiduals,
187                   N0, N1, N2, N3, N4, N5, N6, N7, N8, N9,
188                   kParameterBlock, 0> {
189  // Mutates parameters but must restore them before return.
190  static bool EvaluateJacobianForParameterBlock(
191      const CostFunctor* functor,
192      double const* residuals_at_eval_point,
193      const double relative_step_size,
194      const int num_residuals,
195      double **parameters,
196      double *jacobian) {
197    LOG(FATAL) << "Control should never reach here.";
198    return true;
199  }
200};
201
202}  // namespace internal
203}  // namespace ceres
204
205#endif  // CERES_PUBLIC_INTERNAL_NUMERIC_DIFF_H_
206