1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
|
// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2019 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// * Neither the name of Google Inc. nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: sergey.vfx@gmail.com (Sergey Sharybin)
// mierle@gmail.com (Keir Mierle)
// sameeragarwal@google.com (Sameer Agarwal)
#ifndef CERES_PUBLIC_AUTODIFF_LOCAL_PARAMETERIZATION_H_
#define CERES_PUBLIC_AUTODIFF_LOCAL_PARAMETERIZATION_H_
#include <memory>
#include "ceres/internal/autodiff.h"
#include "ceres/local_parameterization.h"
namespace ceres {
// WARNING: LocalParameterizations are deprecated, so is
// AutoDiffLocalParameterization. They will be removed from Ceres Solver in
// version 2.2.0. Please use Manifolds and AutoDiffManifold instead.
// Create local parameterization with Jacobians computed via automatic
// differentiation. For more information on local parameterizations,
// see include/ceres/local_parameterization.h
//
// To get an auto differentiated local parameterization, you must define
// a class with a templated operator() (a functor) that computes
//
// x_plus_delta = Plus(x, delta);
//
// the template parameter T. The autodiff framework substitutes appropriate
// "Jet" objects for T in order to compute the derivative when necessary, but
// this is hidden, and you should write the function as if T were a scalar type
// (e.g. a double-precision floating point number).
//
// The function must write the computed value in the last argument (the only
// non-const one) and return true to indicate success.
//
// For example, Quaternions have a three dimensional local
// parameterization. It's plus operation can be implemented as (taken
// from internal/ceres/auto_diff_local_parameterization_test.cc)
//
// struct QuaternionPlus {
// template<typename T>
// bool operator()(const T* x, const T* delta, T* x_plus_delta) const {
// const T squared_norm_delta =
// delta[0] * delta[0] + delta[1] * delta[1] + delta[2] * delta[2];
//
// T q_delta[4];
// if (squared_norm_delta > T(0.0)) {
// T norm_delta = sqrt(squared_norm_delta);
// const T sin_delta_by_delta = sin(norm_delta) / norm_delta;
// q_delta[0] = cos(norm_delta);
// q_delta[1] = sin_delta_by_delta * delta[0];
// q_delta[2] = sin_delta_by_delta * delta[1];
// q_delta[3] = sin_delta_by_delta * delta[2];
// } else {
// // We do not just use q_delta = [1,0,0,0] here because that is a
// // constant and when used for automatic differentiation will
// // lead to a zero derivative. Instead we take a first order
// // approximation and evaluate it at zero.
// q_delta[0] = T(1.0);
// q_delta[1] = delta[0];
// q_delta[2] = delta[1];
// q_delta[3] = delta[2];
// }
//
// QuaternionProduct(q_delta, x, x_plus_delta);
// return true;
// }
// };
//
// Then given this struct, the auto differentiated local
// parameterization can now be constructed as
//
// LocalParameterization* local_parameterization =
// new AutoDiffLocalParameterization<QuaternionPlus, 4, 3>;
// | |
// Global Size ---------------+ |
// Local Size -------------------+
//
// WARNING: Since the functor will get instantiated with different types for
// T, you must to convert from other numeric types to T before mixing
// computations with other variables of type T. In the example above, this is
// seen where instead of using k_ directly, k_ is wrapped with T(k_).
template <typename Functor, int kGlobalSize, int kLocalSize>
class CERES_DEPRECATED_WITH_MSG("Use AutoDiffManifold instead.")
AutoDiffLocalParameterization : public LocalParameterization {
public:
AutoDiffLocalParameterization() : functor_(new Functor()) {}
// Takes ownership of functor.
explicit AutoDiffLocalParameterization(Functor* functor)
: functor_(functor) {}
bool Plus(const double* x,
const double* delta,
double* x_plus_delta) const override {
return (*functor_)(x, delta, x_plus_delta);
}
bool ComputeJacobian(const double* x, double* jacobian) const override {
double zero_delta[kLocalSize];
for (int i = 0; i < kLocalSize; ++i) {
zero_delta[i] = 0.0;
}
double x_plus_delta[kGlobalSize];
for (int i = 0; i < kGlobalSize; ++i) {
x_plus_delta[i] = 0.0;
}
const double* parameter_ptrs[2] = {x, zero_delta};
double* jacobian_ptrs[2] = {nullptr, jacobian};
return internal::AutoDifferentiate<
kGlobalSize,
internal::StaticParameterDims<kGlobalSize, kLocalSize>>(
*functor_, parameter_ptrs, kGlobalSize, x_plus_delta, jacobian_ptrs);
}
int GlobalSize() const override { return kGlobalSize; }
int LocalSize() const override { return kLocalSize; }
const Functor& functor() const { return *functor_; }
private:
std::unique_ptr<Functor> functor_;
};
} // namespace ceres
#endif // CERES_PUBLIC_AUTODIFF_LOCAL_PARAMETERIZATION_H_
|
