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  • Committer: Package Import Robot
  • Author(s): Koichi Akabe
  • Date: 2012-06-04 07:15:43 UTC
  • Revision ID: package-import@ubuntu.com-20120604071543-zx6uthupvmtqn3k2
Tags: upstream-1.1.1
Import upstream version 1.1.1

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internal/ceres/schur_eliminator_test.cc
 
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// Ceres Solver - A fast non-linear least squares minimizer
 
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// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
 
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// http://code.google.com/p/ceres-solver/
 
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//
 
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// Redistribution and use in source and binary forms, with or without
 
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// modification, are permitted provided that the following conditions are met:
 
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//
 
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// * Redistributions of source code must retain the above copyright notice,
 
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//   this list of conditions and the following disclaimer.
 
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// * Redistributions in binary form must reproduce the above copyright notice,
 
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//   this list of conditions and the following disclaimer in the documentation
 
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//   and/or other materials provided with the distribution.
 
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// * Neither the name of Google Inc. nor the names of its contributors may be
 
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//   used to endorse or promote products derived from this software without
 
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//   specific prior written permission.
 
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//
 
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 
24
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 
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// POSSIBILITY OF SUCH DAMAGE.
 
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//
 
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// Author: sameeragarwal@google.com (Sameer Agarwal)
 
30
 
 
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#include "ceres/schur_eliminator.h"
 
32
 
 
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#include <glog/logging.h>
 
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#include "ceres/file.h"
 
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#include "gtest/gtest.h"
 
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#include "Eigen/Dense"
 
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#include "ceres/block_random_access_dense_matrix.h"
 
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#include "ceres/block_sparse_matrix.h"
 
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#include "ceres/casts.h"
 
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#include "ceres/detect_structure.h"
 
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#include "ceres/linear_least_squares_problems.h"
 
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#include "ceres/triplet_sparse_matrix.h"
 
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#include "ceres/internal/eigen.h"
 
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#include "ceres/internal/scoped_ptr.h"
 
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#include "ceres/types.h"
 
46
 
 
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// TODO(sameeragarwal): Reduce the size of these tests and redo the
 
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// parameterization to be more efficient.
 
49
 
 
50
DECLARE_string(test_srcdir);
 
51
 
 
52
namespace ceres {
 
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namespace internal {
 
54
 
 
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class SchurEliminatorTest : public ::testing::Test {
 
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 protected:
 
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  void SetUpFromId(int id) {
 
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    scoped_ptr<LinearLeastSquaresProblem>
 
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        problem(CreateLinearLeastSquaresProblemFromId(id));
 
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    CHECK_NOTNULL(problem.get());
 
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    SetupHelper(problem.get());
 
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  }
 
63
 
 
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  void SetUpFromFilename(const string& filename) {
 
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    scoped_ptr<LinearLeastSquaresProblem>
 
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        problem(CreateLinearLeastSquaresProblemFromFile(filename));
 
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    CHECK_NOTNULL(problem.get());
 
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    SetupHelper(problem.get());
 
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  }
 
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71
  void SetupHelper(LinearLeastSquaresProblem* problem) {
 
72
    A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
 
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    b.reset(problem->b.release());
 
74
    D.reset(problem->D.release());
 
75
 
 
76
    num_eliminate_blocks = problem->num_eliminate_blocks;
 
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    num_eliminate_cols = 0;
 
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    const CompressedRowBlockStructure* bs = A->block_structure();
 
79
 
 
80
    for (int i = 0; i < num_eliminate_blocks; ++i) {
 
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      num_eliminate_cols += bs->cols[i].size;
 
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    }
 
83
  }
 
84
 
 
85
  // Compute the golden values for the reduced linear system and the
 
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  // solution to the linear least squares problem using dense linear
 
87
  // algebra.
 
88
  void ComputeReferenceSolution(const Vector& D) {
 
89
    Matrix J;
 
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    A->ToDenseMatrix(&J);
 
91
    VectorRef f(b.get(), J.rows());
 
92
 
 
93
    Matrix H  =  (D.cwiseProduct(D)).asDiagonal();
 
94
    H.noalias() += J.transpose() * J;
 
95
 
 
96
    const Vector g = J.transpose() * f;
 
97
    const int schur_size = J.cols() - num_eliminate_cols;
 
98
 
 
99
    lhs_expected.resize(schur_size, schur_size);
 
100
    lhs_expected.setZero();
 
101
 
 
102
    rhs_expected.resize(schur_size);
 
103
    rhs_expected.setZero();
 
104
 
 
105
    sol_expected.resize(J.cols());
 
106
    sol_expected.setZero();
 
107
 
 
108
    Matrix P = H.block(0, 0, num_eliminate_cols, num_eliminate_cols);
 
109
    Matrix Q = H.block(0,
 
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                       num_eliminate_cols,
 
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                       num_eliminate_cols,
 
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                       schur_size);
 
113
    Matrix R = H.block(num_eliminate_cols,
 
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                       num_eliminate_cols,
 
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                       schur_size,
 
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                       schur_size);
 
117
    int row = 0;
 
118
    const CompressedRowBlockStructure* bs = A->block_structure();
 
119
    for (int i = 0; i < num_eliminate_blocks; ++i) {
 
120
      const int block_size =  bs->cols[i].size;
 
121
      P.block(row, row,  block_size, block_size) =
 
122
          P
 
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          .block(row, row,  block_size, block_size)
 
124
          .ldlt()
 
125
          .solve(Matrix::Identity(block_size, block_size));
 
126
      row += block_size;
 
127
    }
 
128
 
 
129
    lhs_expected
 
130
        .triangularView<Eigen::Upper>() = R - Q.transpose() * P * Q;
 
131
    rhs_expected =
 
132
        g.tail(schur_size) - Q.transpose() * P * g.head(num_eliminate_cols);
 
133
    sol_expected = H.ldlt().solve(g);
 
134
  }
 
135
 
 
136
  void EliminateSolveAndCompare(const VectorRef& diagonal,
 
137
                                bool use_static_structure,
 
138
                                const double relative_tolerance) {
 
139
    const CompressedRowBlockStructure* bs = A->block_structure();
 
140
    const int num_col_blocks = bs->cols.size();
 
141
    vector<int> blocks(num_col_blocks - num_eliminate_blocks, 0);
 
142
    for (int i = num_eliminate_blocks; i < num_col_blocks; ++i) {
 
143
      blocks[i - num_eliminate_blocks] = bs->cols[i].size;
 
144
    }
 
145
 
 
146
    BlockRandomAccessDenseMatrix lhs(blocks);
 
147
 
 
148
    const int num_cols = A->num_cols();
 
149
    const int schur_size = lhs.num_rows();
 
150
 
 
151
    Vector rhs(schur_size);
 
152
 
 
153
    LinearSolver::Options options;
 
154
    options.num_eliminate_blocks = num_eliminate_blocks;
 
155
    if (use_static_structure) {
 
156
      DetectStructure(*bs,
 
157
                      options.num_eliminate_blocks,
 
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                      &options.row_block_size,
 
159
                      &options.e_block_size,
 
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                      &options.f_block_size);
 
161
    }
 
162
 
 
163
    scoped_ptr<SchurEliminatorBase> eliminator;
 
164
    eliminator.reset(SchurEliminatorBase::Create(options));
 
165
    eliminator->Init(num_eliminate_blocks, A->block_structure());
 
166
    eliminator->Eliminate(A.get(), b.get(), diagonal.data(), &lhs, rhs.data());
 
167
 
 
168
    MatrixRef lhs_ref(lhs.mutable_values(), lhs.num_rows(), lhs.num_cols());
 
169
    Vector reduced_sol  =
 
170
        lhs_ref
 
171
        .selfadjointView<Eigen::Upper>()
 
172
        .ldlt()
 
173
        .solve(rhs);
 
174
 
 
175
    // Solution to the linear least squares problem.
 
176
    Vector sol(num_cols);
 
177
    sol.setZero();
 
178
    sol.tail(schur_size) = reduced_sol;
 
179
    eliminator->BackSubstitute(A.get(),
 
180
                               b.get(),
 
181
                               diagonal.data(),
 
182
                               reduced_sol.data(),
 
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                               sol.data());
 
184
 
 
185
    Matrix delta = (lhs_ref - lhs_expected).selfadjointView<Eigen::Upper>();
 
186
    double diff = delta.norm();
 
187
    EXPECT_NEAR(diff / lhs_expected.norm(), 0.0, relative_tolerance);
 
188
    EXPECT_NEAR((rhs - rhs_expected).norm() / rhs_expected.norm(), 0.0,
 
189
                relative_tolerance);
 
190
    EXPECT_NEAR((sol - sol_expected).norm() / sol_expected.norm(), 0.0,
 
191
                relative_tolerance);
 
192
  }
 
193
 
 
194
  scoped_ptr<BlockSparseMatrix> A;
 
195
  scoped_array<double> b;
 
196
  scoped_array<double> D;
 
197
  int num_eliminate_blocks;
 
198
  int num_eliminate_cols;
 
199
 
 
200
  Matrix lhs_expected;
 
201
  Vector rhs_expected;
 
202
  Vector sol_expected;
 
203
};
 
204
 
 
205
TEST_F(SchurEliminatorTest, ScalarProblem) {
 
206
  SetUpFromId(2);
 
207
  Vector zero(A->num_cols());
 
208
  zero.setZero();
 
209
 
 
210
  ComputeReferenceSolution(VectorRef(zero.data(), A->num_cols()));
 
211
  EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), true, 1e-14);
 
212
  EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), false, 1e-14);
 
213
 
 
214
  ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
 
215
  EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
 
216
  EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
 
217
}
 
218
 
 
219
#ifndef CERES_DONT_HAVE_PROTOCOL_BUFFERS
 
220
TEST_F(SchurEliminatorTest, BlockProblem) {
 
221
  const string input_file =
 
222
      JoinPath(FLAGS_test_srcdir,
 
223
                     "problem-6-1384-000.lsqp");  // NOLINT
 
224
 
 
225
  SetUpFromFilename(input_file);
 
226
  ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
 
227
  EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-10);
 
228
  EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-10);
 
229
}
 
230
#endif  // CERES_DONT_HAVE_PROTOCOL_BUFFERS
 
231
 
 
232
}  // namespace internal
 
233
}  // namespace ceres