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
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
|
// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 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: keir@google.com (Keir Mierle)
// sameeragarwal@google.com (Sameer Agarwal)
//
// End-to-end tests for Ceres using Powell's function.
#include <cmath>
#include <cstdlib>
#include "ceres/autodiff_cost_function.h"
#include "ceres/internal/config.h"
#include "ceres/problem.h"
#include "ceres/solver.h"
#include "ceres/test_util.h"
#include "ceres/types.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
// This class implements the SystemTestProblem interface and provides
// access to an implementation of Powell's singular function.
//
// F = 1/2 (f1^2 + f2^2 + f3^2 + f4^2)
//
// f1 = x1 + 10*x2;
// f2 = sqrt(5) * (x3 - x4)
// f3 = (x2 - 2*x3)^2
// f4 = sqrt(10) * (x1 - x4)^2
//
// The starting values are x1 = 3, x2 = -1, x3 = 0, x4 = 1.
// The minimum is 0 at (x1, x2, x3, x4) = 0.
//
// From: Testing Unconstrained Optimization Software by Jorge J. More, Burton S.
// Garbow and Kenneth E. Hillstrom in ACM Transactions on Mathematical Software,
// Vol 7(1), March 1981.
class PowellsFunction {
public:
PowellsFunction() {
x_[0] = 3.0;
x_[1] = -1.0;
x_[2] = 0.0;
x_[3] = 1.0;
problem_.AddResidualBlock(
new AutoDiffCostFunction<F1, 1, 1, 1>(new F1), nullptr, &x_[0], &x_[1]);
problem_.AddResidualBlock(
new AutoDiffCostFunction<F2, 1, 1, 1>(new F2), nullptr, &x_[2], &x_[3]);
problem_.AddResidualBlock(
new AutoDiffCostFunction<F3, 1, 1, 1>(new F3), nullptr, &x_[1], &x_[2]);
problem_.AddResidualBlock(
new AutoDiffCostFunction<F4, 1, 1, 1>(new F4), nullptr, &x_[0], &x_[3]);
// Settings for the reference solution.
options_.linear_solver_type = ceres::DENSE_QR;
options_.max_num_iterations = 10;
options_.num_threads = 1;
}
Problem* mutable_problem() { return &problem_; }
Solver::Options* mutable_solver_options() { return &options_; }
static double kResidualTolerance;
private:
// Templated functions used for automatically differentiated cost
// functions.
class F1 {
public:
template <typename T>
bool operator()(const T* const x1, const T* const x2, T* residual) const {
// f1 = x1 + 10 * x2;
*residual = x1[0] + 10.0 * x2[0];
return true;
}
};
class F2 {
public:
template <typename T>
bool operator()(const T* const x3, const T* const x4, T* residual) const {
// f2 = sqrt(5) (x3 - x4)
*residual = sqrt(5.0) * (x3[0] - x4[0]);
return true;
}
};
class F3 {
public:
template <typename T>
bool operator()(const T* const x2, const T* const x3, T* residual) const {
// f3 = (x2 - 2 x3)^2
residual[0] = (x2[0] - 2.0 * x3[0]) * (x2[0] - 2.0 * x3[0]);
return true;
}
};
class F4 {
public:
template <typename T>
bool operator()(const T* const x1, const T* const x4, T* residual) const {
// f4 = sqrt(10) (x1 - x4)^2
residual[0] = sqrt(10.0) * (x1[0] - x4[0]) * (x1[0] - x4[0]);
return true;
}
};
double x_[4];
Problem problem_;
Solver::Options options_;
};
double PowellsFunction::kResidualTolerance = 1e-8;
using PowellTest = SystemTest<PowellsFunction>;
TEST_F(PowellTest, DenseQR) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = DENSE_QR;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
TEST_F(PowellTest, DenseNormalCholesky) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = DENSE_NORMAL_CHOLESKY;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
TEST_F(PowellTest, DenseSchur) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = DENSE_SCHUR;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
TEST_F(PowellTest, IterativeSchurWithJacobi) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = ITERATIVE_SCHUR;
options->sparse_linear_algebra_library_type = NO_SPARSE;
options->preconditioner_type = JACOBI;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
#ifndef CERES_NO_SUITESPARSE
TEST_F(PowellTest, SparseNormalCholeskyUsingSuiteSparse) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = SPARSE_NORMAL_CHOLESKY;
options->sparse_linear_algebra_library_type = SUITE_SPARSE;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
#endif // CERES_NO_SUITESPARSE
#ifndef CERES_NO_CXSPARSE
TEST_F(PowellTest, SparseNormalCholeskyUsingCXSparse) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = SPARSE_NORMAL_CHOLESKY;
options->sparse_linear_algebra_library_type = CX_SPARSE;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
#endif // CERES_NO_CXSPARSE
#ifndef CERES_NO_ACCELERATE_SPARSE
TEST_F(PowellTest, SparseNormalCholeskyUsingAccelerateSparse) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = SPARSE_NORMAL_CHOLESKY;
options->sparse_linear_algebra_library_type = ACCELERATE_SPARSE;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
#endif // CERES_NO_ACCELERATE_SPARSE
#ifdef CERES_USE_EIGEN_SPARSE
TEST_F(PowellTest, SparseNormalCholeskyUsingEigenSparse) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = SPARSE_NORMAL_CHOLESKY;
options->sparse_linear_algebra_library_type = EIGEN_SPARSE;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
#endif // CERES_USE_EIGEN_SPARSE
} // namespace internal
} // namespace ceres
|
