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
|
// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
// 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: sameeragarwal@google.com (Sameer Agarwal)
#include <cstddef>
#include "ceres/block_sparse_matrix.h"
#include "ceres/block_structure.h"
#include "ceres/casts.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/linear_least_squares_problems.h"
#include "ceres/linear_solver.h"
#include "ceres/schur_complement_solver.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/types.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
class SchurComplementSolverTest : public ::testing::Test {
protected:
void SetUpFromProblemId(int problem_id) {
scoped_ptr<LinearLeastSquaresProblem> problem(
CreateLinearLeastSquaresProblemFromId(problem_id));
CHECK_NOTNULL(problem.get());
A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
b.reset(problem->b.release());
D.reset(problem->D.release());
num_cols = A->num_cols();
num_rows = A->num_rows();
num_eliminate_blocks = problem->num_eliminate_blocks;
x.reset(new double[num_cols]);
sol.reset(new double[num_cols]);
sol_d.reset(new double[num_cols]);
LinearSolver::Options options;
options.type = DENSE_QR;
scoped_ptr<LinearSolver> qr(LinearSolver::Create(options));
TripletSparseMatrix triplet_A(A->num_rows(),
A->num_cols(),
A->num_nonzeros());
A->ToTripletSparseMatrix(&triplet_A);
// Gold standard solutions using dense QR factorization.
DenseSparseMatrix dense_A(triplet_A);
LinearSolver::Summary summary1 =
qr->Solve(&dense_A,
b.get(),
LinearSolver::PerSolveOptions(),
sol.get());
// Gold standard solution with appended diagonal.
LinearSolver::PerSolveOptions per_solve_options;
per_solve_options.D = D.get();
LinearSolver::Summary summary2 =
qr->Solve(&dense_A,
b.get(),
per_solve_options,
sol_d.get());
}
void ComputeAndCompareSolutions(
int problem_id,
bool regularization,
ceres::LinearSolverType linear_solver_type,
ceres::SparseLinearAlgebraLibraryType sparse_linear_algebra_library) {
SetUpFromProblemId(problem_id);
LinearSolver::Options options;
options.elimination_groups.push_back(num_eliminate_blocks);
options.elimination_groups.push_back(
A->block_structure()->cols.size() - num_eliminate_blocks);
options.type = linear_solver_type;
options.sparse_linear_algebra_library = sparse_linear_algebra_library;
scoped_ptr<LinearSolver> solver(LinearSolver::Create(options));
LinearSolver::PerSolveOptions per_solve_options;
LinearSolver::Summary summary;
if (regularization) {
per_solve_options.D = D.get();
}
summary = solver->Solve(A.get(), b.get(), per_solve_options, x.get());
if (regularization) {
for (int i = 0; i < num_cols; ++i) {
ASSERT_NEAR(sol_d.get()[i], x[i], 1e-10);
}
} else {
for (int i = 0; i < num_cols; ++i) {
ASSERT_NEAR(sol.get()[i], x[i], 1e-10);
}
}
}
int num_rows;
int num_cols;
int num_eliminate_blocks;
scoped_ptr<BlockSparseMatrix> A;
scoped_array<double> b;
scoped_array<double> x;
scoped_array<double> D;
scoped_array<double> sol;
scoped_array<double> sol_d;
};
#ifndef CERES_NO_SUITESPARSE
TEST_F(SchurComplementSolverTest, SparseSchurWithSuiteSparse) {
ComputeAndCompareSolutions(2, false, SPARSE_SCHUR, SUITE_SPARSE);
ComputeAndCompareSolutions(3, false, SPARSE_SCHUR, SUITE_SPARSE);
ComputeAndCompareSolutions(2, true, SPARSE_SCHUR, SUITE_SPARSE);
ComputeAndCompareSolutions(3, true, SPARSE_SCHUR, SUITE_SPARSE);
}
#endif // CERES_NO_SUITESPARSE
#ifndef CERES_NO_CXSPARSE
TEST_F(SchurComplementSolverTest, SparseSchurWithCXSparse) {
ComputeAndCompareSolutions(2, false, SPARSE_SCHUR, CX_SPARSE);
ComputeAndCompareSolutions(3, false, SPARSE_SCHUR, CX_SPARSE);
ComputeAndCompareSolutions(2, true, SPARSE_SCHUR, CX_SPARSE);
ComputeAndCompareSolutions(3, true, SPARSE_SCHUR, CX_SPARSE);
}
#endif // CERES_NO_CXSPARSE
TEST_F(SchurComplementSolverTest, DenseSchur) {
// The sparse linear algebra library type is ignored for
// DENSE_SCHUR.
ComputeAndCompareSolutions(2, false, DENSE_SCHUR, SUITE_SPARSE);
ComputeAndCompareSolutions(3, false, DENSE_SCHUR, SUITE_SPARSE);
ComputeAndCompareSolutions(2, true, DENSE_SCHUR, SUITE_SPARSE);
ComputeAndCompareSolutions(3, true, DENSE_SCHUR, SUITE_SPARSE);
}
} // namespace internal
} // namespace ceres
|
