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: mierle@gmail.com (Keir Mierle)
30//         sameeragarwal@google.com (Sameer Agarwal)
31//         thadh@gmail.com (Thad Hughes)
32//
33// This numeric diff implementation differs from the one found in
34// numeric_diff_cost_function.h by supporting numericdiff on cost
35// functions with variable numbers of parameters with variable
36// sizes. With the other implementation, all the sizes (both the
37// number of parameter blocks and the size of each block) must be
38// fixed at compile time.
39//
40// The functor API differs slightly from the API for fixed size
41// numeric diff; the expected interface for the cost functors is:
42//
43//   struct MyCostFunctor {
44//     template<typename T>
45//     bool operator()(double const* const* parameters, double* residuals) const {
46//       // Use parameters[i] to access the i'th parameter block.
47//     }
48//   }
49//
50// Since the sizing of the parameters is done at runtime, you must
51// also specify the sizes after creating the
52// DynamicNumericDiffCostFunction. For example:
53//
54//   DynamicAutoDiffCostFunction<MyCostFunctor, CENTRAL> cost_function(
55//       new MyCostFunctor());
56//   cost_function.AddParameterBlock(5);
57//   cost_function.AddParameterBlock(10);
58//   cost_function.SetNumResiduals(21);
59
60#ifndef CERES_PUBLIC_DYNAMIC_NUMERIC_DIFF_COST_FUNCTION_H_
61#define CERES_PUBLIC_DYNAMIC_NUMERIC_DIFF_COST_FUNCTION_H_
62
63#include <cmath>
64#include <numeric>
65#include <vector>
66
67#include "ceres/cost_function.h"
68#include "ceres/internal/scoped_ptr.h"
69#include "ceres/internal/eigen.h"
70#include "ceres/internal/numeric_diff.h"
71#include "glog/logging.h"
72
73namespace ceres {
74
75template <typename CostFunctor, NumericDiffMethod method = CENTRAL>
76class DynamicNumericDiffCostFunction : public CostFunction {
77 public:
78  explicit DynamicNumericDiffCostFunction(const CostFunctor* functor,
79                                          Ownership ownership = TAKE_OWNERSHIP,
80                                          double relative_step_size = 1e-6)
81      : functor_(functor),
82        ownership_(ownership),
83        relative_step_size_(relative_step_size) {
84  }
85
86  virtual ~DynamicNumericDiffCostFunction() {
87    if (ownership_ != TAKE_OWNERSHIP) {
88      functor_.release();
89    }
90  }
91
92  void AddParameterBlock(int size) {
93    mutable_parameter_block_sizes()->push_back(size);
94  }
95
96  void SetNumResiduals(int num_residuals) {
97    set_num_residuals(num_residuals);
98  }
99
100  virtual bool Evaluate(double const* const* parameters,
101                        double* residuals,
102                        double** jacobians) const {
103    CHECK_GT(num_residuals(), 0)
104        << "You must call DynamicNumericDiffCostFunction::SetNumResiduals() "
105        << "before DynamicNumericDiffCostFunction::Evaluate().";
106
107    const vector<int32>& block_sizes = parameter_block_sizes();
108    CHECK(!block_sizes.empty())
109        << "You must call DynamicNumericDiffCostFunction::AddParameterBlock() "
110        << "before DynamicNumericDiffCostFunction::Evaluate().";
111
112    const bool status = EvaluateCostFunctor(parameters, residuals);
113    if (jacobians == NULL || !status) {
114      return status;
115    }
116
117    // Create local space for a copy of the parameters which will get mutated.
118    int parameters_size = accumulate(block_sizes.begin(), block_sizes.end(), 0);
119    vector<double> parameters_copy(parameters_size);
120    vector<double*> parameters_references_copy(block_sizes.size());
121    parameters_references_copy[0] = &parameters_copy[0];
122    for (int block = 1; block < block_sizes.size(); ++block) {
123      parameters_references_copy[block] = parameters_references_copy[block - 1]
124          + block_sizes[block - 1];
125    }
126
127    // Copy the parameters into the local temp space.
128    for (int block = 0; block < block_sizes.size(); ++block) {
129      memcpy(parameters_references_copy[block],
130             parameters[block],
131             block_sizes[block] * sizeof(*parameters[block]));
132    }
133
134    for (int block = 0; block < block_sizes.size(); ++block) {
135      if (jacobians[block] != NULL &&
136          !EvaluateJacobianForParameterBlock(block_sizes[block],
137                                             block,
138                                             relative_step_size_,
139                                             residuals,
140                                             &parameters_references_copy[0],
141                                             jacobians)) {
142        return false;
143      }
144    }
145    return true;
146  }
147
148 private:
149  bool EvaluateJacobianForParameterBlock(const int parameter_block_size,
150                                         const int parameter_block,
151                                         const double relative_step_size,
152                                         double const* residuals_at_eval_point,
153                                         double** parameters,
154                                         double** jacobians) const {
155    using Eigen::Map;
156    using Eigen::Matrix;
157    using Eigen::Dynamic;
158    using Eigen::RowMajor;
159
160    typedef Matrix<double, Dynamic, 1> ResidualVector;
161    typedef Matrix<double, Dynamic, 1> ParameterVector;
162    typedef Matrix<double, Dynamic, Dynamic, RowMajor> JacobianMatrix;
163
164    int num_residuals = this->num_residuals();
165
166    Map<JacobianMatrix> parameter_jacobian(jacobians[parameter_block],
167                                           num_residuals,
168                                           parameter_block_size);
169
170    // Mutate one element at a time and then restore.
171    Map<ParameterVector> x_plus_delta(parameters[parameter_block],
172                                      parameter_block_size);
173    ParameterVector x(x_plus_delta);
174    ParameterVector step_size = x.array().abs() * relative_step_size;
175
176    // To handle cases where a paremeter is exactly zero, instead use
177    // the mean step_size for the other dimensions.
178    double fallback_step_size = step_size.sum() / step_size.rows();
179    if (fallback_step_size == 0.0) {
180      // If all the parameters are zero, there's no good answer. Use the given
181      // relative step_size as absolute step_size and hope for the best.
182      fallback_step_size = relative_step_size;
183    }
184
185    // For each parameter in the parameter block, use finite
186    // differences to compute the derivative for that parameter.
187    for (int j = 0; j < parameter_block_size; ++j) {
188      if (step_size(j) == 0.0) {
189        // The parameter is exactly zero, so compromise and use the
190        // mean step_size from the other parameters. This can break in
191        // many cases, but it's hard to pick a good number without
192        // problem specific knowledge.
193        step_size(j) = fallback_step_size;
194      }
195      x_plus_delta(j) = x(j) + step_size(j);
196
197      ResidualVector residuals(num_residuals);
198      if (!EvaluateCostFunctor(parameters, &residuals[0])) {
199        // Something went wrong; bail.
200        return false;
201      }
202
203      // Compute this column of the jacobian in 3 steps:
204      // 1. Store residuals for the forward part.
205      // 2. Subtract residuals for the backward (or 0) part.
206      // 3. Divide out the run.
207      parameter_jacobian.col(j).matrix() = residuals;
208
209      double one_over_h = 1 / step_size(j);
210      if (method == CENTRAL) {
211        // Compute the function on the other side of x(j).
212        x_plus_delta(j) = x(j) - step_size(j);
213
214        if (!EvaluateCostFunctor(parameters, &residuals[0])) {
215          // Something went wrong; bail.
216          return false;
217        }
218
219        parameter_jacobian.col(j) -= residuals;
220        one_over_h /= 2;
221      } else {
222        // Forward difference only; reuse existing residuals evaluation.
223        parameter_jacobian.col(j) -=
224            Map<const ResidualVector>(residuals_at_eval_point, num_residuals);
225      }
226      x_plus_delta(j) = x(j);  // Restore x_plus_delta.
227
228      // Divide out the run to get slope.
229      parameter_jacobian.col(j) *= one_over_h;
230    }
231    return true;
232  }
233
234  bool EvaluateCostFunctor(double const* const* parameters,
235                           double* residuals) const {
236    return EvaluateCostFunctorImpl(functor_.get(),
237                                   parameters,
238                                   residuals,
239                                   functor_.get());
240  }
241
242  // Helper templates to allow evaluation of a functor or a
243  // CostFunction.
244  bool EvaluateCostFunctorImpl(const CostFunctor* functor,
245                               double const* const* parameters,
246                               double* residuals,
247                               const void* /* NOT USED */) const {
248    return (*functor)(parameters, residuals);
249  }
250
251  bool EvaluateCostFunctorImpl(const CostFunctor* functor,
252                               double const* const* parameters,
253                               double* residuals,
254                               const CostFunction* /* NOT USED */) const {
255    return functor->Evaluate(parameters, residuals, NULL);
256  }
257
258  internal::scoped_ptr<const CostFunctor> functor_;
259  Ownership ownership_;
260  const double relative_step_size_;
261};
262
263}  // namespace ceres
264
265#endif  // CERES_PUBLIC_DYNAMIC_AUTODIFF_COST_FUNCTION_H_
266