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//
5// Redistribution and use in source and binary forms, with or without
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
12//   and/or other materials provided with the distribution.
13// * Neither the name of Google Inc. nor the names of its contributors may be
14//   used to endorse or promote products derived from this software without
15//   specific prior written permission.
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
19// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
21// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
22// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
23// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
24// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
25// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
26// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
27// POSSIBILITY OF SUCH DAMAGE.
28//
29// Author: sameeragarwal@google.com (Sameer Agarwal)
30
31#include "ceres/schur_eliminator.h"
32
33#include "Eigen/Dense"
34#include "ceres/block_random_access_dense_matrix.h"
35#include "ceres/block_sparse_matrix.h"
36#include "ceres/casts.h"
37#include "ceres/detect_structure.h"
38#include "ceres/internal/eigen.h"
39#include "ceres/internal/scoped_ptr.h"
40#include "ceres/linear_least_squares_problems.h"
41#include "ceres/test_util.h"
42#include "ceres/triplet_sparse_matrix.h"
43#include "ceres/types.h"
44#include "glog/logging.h"
45#include "gtest/gtest.h"
46
47// TODO(sameeragarwal): Reduce the size of these tests and redo the
48// parameterization to be more efficient.
49
50namespace ceres {
51namespace internal {
52
53class SchurEliminatorTest : public ::testing::Test {
54 protected:
55  void SetUpFromId(int id) {
56    scoped_ptr<LinearLeastSquaresProblem>
57        problem(CreateLinearLeastSquaresProblemFromId(id));
58    CHECK_NOTNULL(problem.get());
59    SetupHelper(problem.get());
60  }
61
62  void SetupHelper(LinearLeastSquaresProblem* problem) {
63    A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
64    b.reset(problem->b.release());
65    D.reset(problem->D.release());
66
67    num_eliminate_blocks = problem->num_eliminate_blocks;
68    num_eliminate_cols = 0;
69    const CompressedRowBlockStructure* bs = A->block_structure();
70
71    for (int i = 0; i < num_eliminate_blocks; ++i) {
72      num_eliminate_cols += bs->cols[i].size;
73    }
74  }
75
76  // Compute the golden values for the reduced linear system and the
77  // solution to the linear least squares problem using dense linear
78  // algebra.
79  void ComputeReferenceSolution(const Vector& D) {
80    Matrix J;
81    A->ToDenseMatrix(&J);
82    VectorRef f(b.get(), J.rows());
83
84    Matrix H  =  (D.cwiseProduct(D)).asDiagonal();
85    H.noalias() += J.transpose() * J;
86
87    const Vector g = J.transpose() * f;
88    const int schur_size = J.cols() - num_eliminate_cols;
89
90    lhs_expected.resize(schur_size, schur_size);
91    lhs_expected.setZero();
92
93    rhs_expected.resize(schur_size);
94    rhs_expected.setZero();
95
96    sol_expected.resize(J.cols());
97    sol_expected.setZero();
98
99    Matrix P = H.block(0, 0, num_eliminate_cols, num_eliminate_cols);
100    Matrix Q = H.block(0,
101                       num_eliminate_cols,
102                       num_eliminate_cols,
103                       schur_size);
104    Matrix R = H.block(num_eliminate_cols,
105                       num_eliminate_cols,
106                       schur_size,
107                       schur_size);
108    int row = 0;
109    const CompressedRowBlockStructure* bs = A->block_structure();
110    for (int i = 0; i < num_eliminate_blocks; ++i) {
111      const int block_size =  bs->cols[i].size;
112      P.block(row, row,  block_size, block_size) =
113          P
114          .block(row, row,  block_size, block_size)
115          .llt()
116          .solve(Matrix::Identity(block_size, block_size));
117      row += block_size;
118    }
119
120    lhs_expected
121        .triangularView<Eigen::Upper>() = R - Q.transpose() * P * Q;
122    rhs_expected =
123        g.tail(schur_size) - Q.transpose() * P * g.head(num_eliminate_cols);
124    sol_expected = H.llt().solve(g);
125  }
126
127  void EliminateSolveAndCompare(const VectorRef& diagonal,
128                                bool use_static_structure,
129                                const double relative_tolerance) {
130    const CompressedRowBlockStructure* bs = A->block_structure();
131    const int num_col_blocks = bs->cols.size();
132    vector<int> blocks(num_col_blocks - num_eliminate_blocks, 0);
133    for (int i = num_eliminate_blocks; i < num_col_blocks; ++i) {
134      blocks[i - num_eliminate_blocks] = bs->cols[i].size;
135    }
136
137    BlockRandomAccessDenseMatrix lhs(blocks);
138
139    const int num_cols = A->num_cols();
140    const int schur_size = lhs.num_rows();
141
142    Vector rhs(schur_size);
143
144    LinearSolver::Options options;
145    options.elimination_groups.push_back(num_eliminate_blocks);
146    if (use_static_structure) {
147      DetectStructure(*bs,
148                      num_eliminate_blocks,
149                      &options.row_block_size,
150                      &options.e_block_size,
151                      &options.f_block_size);
152    }
153
154    scoped_ptr<SchurEliminatorBase> eliminator;
155    eliminator.reset(SchurEliminatorBase::Create(options));
156    eliminator->Init(num_eliminate_blocks, A->block_structure());
157    eliminator->Eliminate(A.get(), b.get(), diagonal.data(), &lhs, rhs.data());
158
159    MatrixRef lhs_ref(lhs.mutable_values(), lhs.num_rows(), lhs.num_cols());
160    Vector reduced_sol  =
161        lhs_ref
162        .selfadjointView<Eigen::Upper>()
163        .llt()
164        .solve(rhs);
165
166    // Solution to the linear least squares problem.
167    Vector sol(num_cols);
168    sol.setZero();
169    sol.tail(schur_size) = reduced_sol;
170    eliminator->BackSubstitute(A.get(),
171                               b.get(),
172                               diagonal.data(),
173                               reduced_sol.data(),
174                               sol.data());
175
176    Matrix delta = (lhs_ref - lhs_expected).selfadjointView<Eigen::Upper>();
177    double diff = delta.norm();
178    EXPECT_NEAR(diff / lhs_expected.norm(), 0.0, relative_tolerance);
179    EXPECT_NEAR((rhs - rhs_expected).norm() / rhs_expected.norm(), 0.0,
180                relative_tolerance);
181    EXPECT_NEAR((sol - sol_expected).norm() / sol_expected.norm(), 0.0,
182                relative_tolerance);
183  }
184
185  scoped_ptr<BlockSparseMatrix> A;
186  scoped_array<double> b;
187  scoped_array<double> D;
188  int num_eliminate_blocks;
189  int num_eliminate_cols;
190
191  Matrix lhs_expected;
192  Vector rhs_expected;
193  Vector sol_expected;
194};
195
196TEST_F(SchurEliminatorTest, ScalarProblem) {
197  SetUpFromId(2);
198  Vector zero(A->num_cols());
199  zero.setZero();
200
201  ComputeReferenceSolution(VectorRef(zero.data(), A->num_cols()));
202  EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), true, 1e-14);
203  EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), false, 1e-14);
204
205  ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
206  EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
207  EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
208}
209
210}  // namespace internal
211}  // namespace ceres
212