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 //
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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
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14 // used to endorse or promote products derived from this software without
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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
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24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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26 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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28 //
29 // Author: fredp@google.com (Fred Pighin)
30 //
31 // Tests for linear solvers that solve symmetric linear systems. Some
32 // of this code is inhertited from Fred Pighin's code for testing the
33 // old Conjugate Gradients solver.
34 //
35 // TODO(sameeragarwal): More comprehensive testing with larger and
36 // more badly conditioned problem.
37
38 #include "gtest/gtest.h"
39 #include "ceres/conjugate_gradients_solver.h"
40 #include "ceres/linear_solver.h"
41 #include "ceres/triplet_sparse_matrix.h"
42 #include "ceres/internal/eigen.h"
43 #include "ceres/internal/scoped_ptr.h"
44 #include "ceres/types.h"
45
46 namespace ceres {
47 namespace internal {
48
TEST(ConjugateGradientTest,Solves3x3IdentitySystem)49 TEST(ConjugateGradientTest, Solves3x3IdentitySystem) {
50 double diagonal[] = { 1.0, 1.0, 1.0 };
51 scoped_ptr<TripletSparseMatrix>
52 A(TripletSparseMatrix::CreateSparseDiagonalMatrix(diagonal, 3));
53 Vector b(3);
54 Vector x(3);
55
56 b(0) = 1.0;
57 b(1) = 2.0;
58 b(2) = 3.0;
59
60 x(0) = 1;
61 x(1) = 1;
62 x(2) = 1;
63
64 LinearSolver::Options options;
65 options.max_num_iterations = 10;
66
67 LinearSolver::PerSolveOptions per_solve_options;
68 per_solve_options.r_tolerance = 1e-9;
69
70 ConjugateGradientsSolver solver(options);
71 LinearSolver::Summary summary =
72 solver.Solve(A.get(), b.data(), per_solve_options, x.data());
73
74 EXPECT_EQ(summary.termination_type, LINEAR_SOLVER_SUCCESS);
75 ASSERT_EQ(summary.num_iterations, 1);
76
77 ASSERT_DOUBLE_EQ(1, x(0));
78 ASSERT_DOUBLE_EQ(2, x(1));
79 ASSERT_DOUBLE_EQ(3, x(2));
80 }
81
82
TEST(ConjuateGradientTest,Solves3x3SymmetricSystem)83 TEST(ConjuateGradientTest, Solves3x3SymmetricSystem) {
84 scoped_ptr<TripletSparseMatrix> A(new TripletSparseMatrix(3, 3, 9));
85 Vector b(3);
86 Vector x(3);
87
88 // | 2 -1 0|
89 // A = |-1 2 -1| is symmetric positive definite.
90 // | 0 -1 2|
91 int* Ai = A->mutable_rows();
92 int* Aj = A->mutable_cols();
93 double* Ax = A->mutable_values();
94 int counter = 0;
95 for (int i = 0; i < 3; ++i) {
96 for (int j = 0; j < 3; ++j) {
97 Ai[counter] = i;
98 Aj[counter] = j;
99 ++counter;
100 }
101 }
102 Ax[0] = 2.;
103 Ax[1] = -1.;
104 Ax[2] = 0;
105 Ax[3] = -1.;
106 Ax[4] = 2;
107 Ax[5] = -1;
108 Ax[6] = 0;
109 Ax[7] = -1;
110 Ax[8] = 2;
111 A->set_num_nonzeros(9);
112
113 b(0) = -1;
114 b(1) = 0;
115 b(2) = 3;
116
117 x(0) = 1;
118 x(1) = 1;
119 x(2) = 1;
120
121 LinearSolver::Options options;
122 options.max_num_iterations = 10;
123
124 LinearSolver::PerSolveOptions per_solve_options;
125 per_solve_options.r_tolerance = 1e-9;
126
127 ConjugateGradientsSolver solver(options);
128 LinearSolver::Summary summary =
129 solver.Solve(A.get(), b.data(), per_solve_options, x.data());
130
131 EXPECT_EQ(summary.termination_type, LINEAR_SOLVER_SUCCESS);
132
133 ASSERT_DOUBLE_EQ(0, x(0));
134 ASSERT_DOUBLE_EQ(1, x(1));
135 ASSERT_DOUBLE_EQ(2, x(2));
136 }
137
138 } // namespace internal
139 } // namespace ceres
140