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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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
46namespace ceres {
47namespace internal {
48
49TEST(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
83TEST(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