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+// 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)
+//
+// TODO(sameeragarwal): Add support for larger, more complicated and
+// poorly conditioned problems both for correctness testing as well as
+// benchmarking.
+
+#include "ceres/iterative_schur_complement_solver.h"
+
+#include <cstddef>
+#include "Eigen/Dense"
+#include "ceres/block_random_access_dense_matrix.h"
+#include "ceres/block_sparse_matrix.h"
+#include "ceres/casts.h"
+#include "ceres/internal/eigen.h"
+#include "ceres/internal/scoped_ptr.h"
+#include "ceres/linear_least_squares_problems.h"
+#include "ceres/linear_solver.h"
+#include "ceres/schur_eliminator.h"
+#include "ceres/triplet_sparse_matrix.h"
+#include "ceres/types.h"
+#include "glog/logging.h"
+#include "gtest/gtest.h"
+
+namespace ceres {
+namespace internal {
+
+using testing::AssertionResult;
+
+const double kEpsilon = 1e-14;
+
+class IterativeSchurComplementSolverTest : public ::testing::Test {
+ protected :
+ virtual void SetUp() {
+ scoped_ptr<LinearLeastSquaresProblem> problem(
+ CreateLinearLeastSquaresProblemFromId(2));
+
+ 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;
+ }
+
+ AssertionResult TestSolver(double* D) {
+ TripletSparseMatrix triplet_A(A_->num_rows(),
+ A_->num_cols(),
+ A_->num_nonzeros());
+ A_->ToTripletSparseMatrix(&triplet_A);
+
+ DenseSparseMatrix dense_A(triplet_A);
+
+ LinearSolver::Options options;
+ options.type = DENSE_QR;
+ scoped_ptr<LinearSolver> qr(LinearSolver::Create(options));
+
+ LinearSolver::PerSolveOptions per_solve_options;
+ per_solve_options.D = D;
+ Vector reference_solution(num_cols_);
+ qr->Solve(&dense_A, b_.get(), per_solve_options, reference_solution.data());
+
+ options.elimination_groups.push_back(num_eliminate_blocks_);
+ options.max_num_iterations = num_cols_;
+ IterativeSchurComplementSolver isc(options);
+
+ Vector isc_sol(num_cols_);
+ per_solve_options.r_tolerance = 1e-12;
+ isc.Solve(A_.get(), b_.get(), per_solve_options, isc_sol.data());
+ double diff = (isc_sol - reference_solution).norm();
+ if (diff < kEpsilon) {
+ return testing::AssertionSuccess();
+ } else {
+ return testing::AssertionFailure()
+ << "The reference solution differs from the ITERATIVE_SCHUR"
+ << " solution by " << diff << " which is more than " << kEpsilon;
+ }
+ }
+
+ int num_rows_;
+ int num_cols_;
+ int num_eliminate_blocks_;
+ scoped_ptr<BlockSparseMatrix> A_;
+ scoped_array<double> b_;
+ scoped_array<double> D_;
+};
+
+TEST_F(IterativeSchurComplementSolverTest, SolverTest) {
+ EXPECT_TRUE(TestSolver(NULL));
+ EXPECT_TRUE(TestSolver(D_.get()));
+}
+
+} // namespace internal
+} // namespace ceres