1// Ceres Solver - A fast non-linear least squares minimizer
2// Copyright 2010, 2011, 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: keir@google.com (Keir Mierle)
30//         sameeragarwal@google.com (Sameer Agarwal)
31//
32// Create CostFunctions as needed by the least squares framework with jacobians
33// computed via numeric (a.k.a. finite) differentiation. For more details see
34// http://en.wikipedia.org/wiki/Numerical_differentiation.
35//
36// To get an numerically differentiated cost function, you must define
37// a class with a operator() (a functor) that computes the residuals.
38//
39// The function must write the computed value in the last argument
40// (the only non-const one) and return true to indicate success.
41// Please see cost_function.h for details on how the return value
42// maybe used to impose simple constraints on the parameter block.
43//
44// For example, consider a scalar error e = k - x'y, where both x and y are
45// two-dimensional column vector parameters, the prime sign indicates
46// transposition, and k is a constant. The form of this error, which is the
47// difference between a constant and an expression, is a common pattern in least
48// squares problems. For example, the value x'y might be the model expectation
49// for a series of measurements, where there is an instance of the cost function
50// for each measurement k.
51//
52// The actual cost added to the total problem is e^2, or (k - x'k)^2; however,
53// the squaring is implicitly done by the optimization framework.
54//
55// To write an numerically-differentiable cost function for the above model, first
56// define the object
57//
58//   class MyScalarCostFunctor {
59//     MyScalarCostFunctor(double k): k_(k) {}
60//
61//     bool operator()(const double* const x,
62//                     const double* const y,
63//                     double* residuals) const {
64//       residuals[0] = k_ - x[0] * y[0] + x[1] * y[1];
65//       return true;
66//     }
67//
68//    private:
69//     double k_;
70//   };
71//
72// Note that in the declaration of operator() the input parameters x
73// and y come first, and are passed as const pointers to arrays of
74// doubles. If there were three input parameters, then the third input
75// parameter would come after y. The output is always the last
76// parameter, and is also a pointer to an array. In the example above,
77// the residual is a scalar, so only residuals[0] is set.
78//
79// Then given this class definition, the numerically differentiated
80// cost function with central differences used for computing the
81// derivative can be constructed as follows.
82//
83//   CostFunction* cost_function
84//       = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, 1, 2, 2>(
85//           new MyScalarCostFunctor(1.0));                    ^     ^  ^  ^
86//                                                             |     |  |  |
87//                                 Finite Differencing Scheme -+     |  |  |
88//                                 Dimension of residual ------------+  |  |
89//                                 Dimension of x ----------------------+  |
90//                                 Dimension of y -------------------------+
91//
92// In this example, there is usually an instance for each measurement of k.
93//
94// In the instantiation above, the template parameters following
95// "MyScalarCostFunctor", "1, 2, 2", describe the functor as computing
96// a 1-dimensional output from two arguments, both 2-dimensional.
97//
98// NumericDiffCostFunction also supports cost functions with a
99// runtime-determined number of residuals. For example:
100//
101//   CostFunction* cost_function
102//       = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, DYNAMIC, 2, 2>(
103//           new CostFunctorWithDynamicNumResiduals(1.0),               ^     ^  ^
104//           TAKE_OWNERSHIP,                                            |     |  |
105//           runtime_number_of_residuals); <----+                       |     |  |
106//                                              |                       |     |  |
107//                                              |                       |     |  |
108//             Actual number of residuals ------+                       |     |  |
109//             Indicate dynamic number of residuals --------------------+     |  |
110//             Dimension of x ------------------------------------------------+  |
111//             Dimension of y ---------------------------------------------------+
112//
113// The framework can currently accommodate cost functions of up to 10
114// independent variables, and there is no limit on the dimensionality
115// of each of them.
116//
117// The central difference method is considerably more accurate at the cost of
118// twice as many function evaluations than forward difference. Consider using
119// central differences begin with, and only after that works, trying forward
120// difference to improve performance.
121//
122// WARNING #1: A common beginner's error when first using
123// NumericDiffCostFunction is to get the sizing wrong. In particular,
124// there is a tendency to set the template parameters to (dimension of
125// residual, number of parameters) instead of passing a dimension
126// parameter for *every parameter*. In the example above, that would
127// be <MyScalarCostFunctor, 1, 2>, which is missing the last '2'
128// argument. Please be careful when setting the size parameters.
129//
130////////////////////////////////////////////////////////////////////////////
131////////////////////////////////////////////////////////////////////////////
132//
133// ALTERNATE INTERFACE
134//
135// For a variety of reason, including compatibility with legacy code,
136// NumericDiffCostFunction can also take CostFunction objects as
137// input. The following describes how.
138//
139// To get a numerically differentiated cost function, define a
140// subclass of CostFunction such that the Evaluate() function ignores
141// the jacobian parameter. The numeric differentiation wrapper will
142// fill in the jacobian parameter if necessary by repeatedly calling
143// the Evaluate() function with small changes to the appropriate
144// parameters, and computing the slope. For performance, the numeric
145// differentiation wrapper class is templated on the concrete cost
146// function, even though it could be implemented only in terms of the
147// virtual CostFunction interface.
148//
149// The numerically differentiated version of a cost function for a cost function
150// can be constructed as follows:
151//
152//   CostFunction* cost_function
153//       = new NumericDiffCostFunction<MyCostFunction, CENTRAL, 1, 4, 8>(
154//           new MyCostFunction(...), TAKE_OWNERSHIP);
155//
156// where MyCostFunction has 1 residual and 2 parameter blocks with sizes 4 and 8
157// respectively. Look at the tests for a more detailed example.
158//
159// TODO(keir): Characterize accuracy; mention pitfalls; provide alternatives.
160
161#ifndef CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_
162#define CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_
163
164#include "Eigen/Dense"
165#include "ceres/cost_function.h"
166#include "ceres/internal/numeric_diff.h"
167#include "ceres/internal/scoped_ptr.h"
168#include "ceres/sized_cost_function.h"
169#include "ceres/types.h"
170#include "glog/logging.h"
171
172namespace ceres {
173
174template <typename CostFunctor,
175          NumericDiffMethod method = CENTRAL,
176          int kNumResiduals = 0,  // Number of residuals, or ceres::DYNAMIC
177          int N0 = 0,   // Number of parameters in block 0.
178          int N1 = 0,   // Number of parameters in block 1.
179          int N2 = 0,   // Number of parameters in block 2.
180          int N3 = 0,   // Number of parameters in block 3.
181          int N4 = 0,   // Number of parameters in block 4.
182          int N5 = 0,   // Number of parameters in block 5.
183          int N6 = 0,   // Number of parameters in block 6.
184          int N7 = 0,   // Number of parameters in block 7.
185          int N8 = 0,   // Number of parameters in block 8.
186          int N9 = 0>   // Number of parameters in block 9.
187class NumericDiffCostFunction
188    : public SizedCostFunction<kNumResiduals,
189                               N0, N1, N2, N3, N4,
190                               N5, N6, N7, N8, N9> {
191 public:
192  NumericDiffCostFunction(CostFunctor* functor,
193                          Ownership ownership = TAKE_OWNERSHIP,
194                          int num_residuals = kNumResiduals,
195                          const double relative_step_size = 1e-6)
196      :functor_(functor),
197       ownership_(ownership),
198       relative_step_size_(relative_step_size) {
199    if (kNumResiduals == DYNAMIC) {
200      SizedCostFunction<kNumResiduals,
201                        N0, N1, N2, N3, N4,
202                        N5, N6, N7, N8, N9>
203          ::set_num_residuals(num_residuals);
204    }
205  }
206
207  ~NumericDiffCostFunction() {
208    if (ownership_ != TAKE_OWNERSHIP) {
209      functor_.release();
210    }
211  }
212
213  virtual bool Evaluate(double const* const* parameters,
214                        double* residuals,
215                        double** jacobians) const {
216    using internal::FixedArray;
217    using internal::NumericDiff;
218
219    const int kNumParameters = N0 + N1 + N2 + N3 + N4 + N5 + N6 + N7 + N8 + N9;
220    const int kNumParameterBlocks =
221        (N0 > 0) + (N1 > 0) + (N2 > 0) + (N3 > 0) + (N4 > 0) +
222        (N5 > 0) + (N6 > 0) + (N7 > 0) + (N8 > 0) + (N9 > 0);
223
224    // Get the function value (residuals) at the the point to evaluate.
225    if (!internal::EvaluateImpl<CostFunctor,
226                                N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>(
227                                    functor_.get(),
228                                    parameters,
229                                    residuals,
230                                    functor_.get())) {
231      return false;
232    }
233
234    if (jacobians == NULL) {
235      return true;
236    }
237
238    // Create a copy of the parameters which will get mutated.
239    FixedArray<double> parameters_copy(kNumParameters);
240    FixedArray<double*> parameters_reference_copy(kNumParameterBlocks);
241
242    parameters_reference_copy[0] = parameters_copy.get();
243    if (N1) parameters_reference_copy[1] = parameters_reference_copy[0] + N0;
244    if (N2) parameters_reference_copy[2] = parameters_reference_copy[1] + N1;
245    if (N3) parameters_reference_copy[3] = parameters_reference_copy[2] + N2;
246    if (N4) parameters_reference_copy[4] = parameters_reference_copy[3] + N3;
247    if (N5) parameters_reference_copy[5] = parameters_reference_copy[4] + N4;
248    if (N6) parameters_reference_copy[6] = parameters_reference_copy[5] + N5;
249    if (N7) parameters_reference_copy[7] = parameters_reference_copy[6] + N6;
250    if (N8) parameters_reference_copy[8] = parameters_reference_copy[7] + N7;
251    if (N9) parameters_reference_copy[9] = parameters_reference_copy[8] + N8;
252
253#define COPY_PARAMETER_BLOCK(block)                                     \
254  if (N ## block) memcpy(parameters_reference_copy[block],              \
255                         parameters[block],                             \
256                         sizeof(double) * N ## block);  // NOLINT
257
258    COPY_PARAMETER_BLOCK(0);
259    COPY_PARAMETER_BLOCK(1);
260    COPY_PARAMETER_BLOCK(2);
261    COPY_PARAMETER_BLOCK(3);
262    COPY_PARAMETER_BLOCK(4);
263    COPY_PARAMETER_BLOCK(5);
264    COPY_PARAMETER_BLOCK(6);
265    COPY_PARAMETER_BLOCK(7);
266    COPY_PARAMETER_BLOCK(8);
267    COPY_PARAMETER_BLOCK(9);
268
269#undef COPY_PARAMETER_BLOCK
270
271#define EVALUATE_JACOBIAN_FOR_BLOCK(block)                              \
272    if (N ## block && jacobians[block] != NULL) {                       \
273      if (!NumericDiff<CostFunctor,                                     \
274                       method,                                          \
275                       kNumResiduals,                                   \
276                       N0, N1, N2, N3, N4, N5, N6, N7, N8, N9,          \
277                       block,                                           \
278                       N ## block >::EvaluateJacobianForParameterBlock( \
279                           functor_.get(),                              \
280                           residuals,                                   \
281                           relative_step_size_,                         \
282                          SizedCostFunction<kNumResiduals,              \
283                           N0, N1, N2, N3, N4,                          \
284                           N5, N6, N7, N8, N9>::num_residuals(),        \
285                           parameters_reference_copy.get(),             \
286                           jacobians[block])) {                         \
287        return false;                                                   \
288      }                                                                 \
289    }
290
291    EVALUATE_JACOBIAN_FOR_BLOCK(0);
292    EVALUATE_JACOBIAN_FOR_BLOCK(1);
293    EVALUATE_JACOBIAN_FOR_BLOCK(2);
294    EVALUATE_JACOBIAN_FOR_BLOCK(3);
295    EVALUATE_JACOBIAN_FOR_BLOCK(4);
296    EVALUATE_JACOBIAN_FOR_BLOCK(5);
297    EVALUATE_JACOBIAN_FOR_BLOCK(6);
298    EVALUATE_JACOBIAN_FOR_BLOCK(7);
299    EVALUATE_JACOBIAN_FOR_BLOCK(8);
300    EVALUATE_JACOBIAN_FOR_BLOCK(9);
301
302#undef EVALUATE_JACOBIAN_FOR_BLOCK
303
304    return true;
305  }
306
307 private:
308  internal::scoped_ptr<CostFunctor> functor_;
309  Ownership ownership_;
310  const double relative_step_size_;
311};
312
313}  // namespace ceres
314
315#endif  // CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_
316