Initial commit of Ceres Solver.
diff --git a/internal/ceres/schur_eliminator_test.cc b/internal/ceres/schur_eliminator_test.cc
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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)
+
+#include "ceres/schur_eliminator.h"
+
+#include <glog/logging.h>
+#include "ceres/file.h"
+#include "gtest/gtest.h"
+#include "Eigen/Dense"
+#include "ceres/block_random_access_dense_matrix.h"
+#include "ceres/block_sparse_matrix.h"
+#include "ceres/casts.h"
+#include "ceres/detect_structure.h"
+#include "ceres/linear_least_squares_problems.h"
+#include "ceres/triplet_sparse_matrix.h"
+#include "ceres/internal/eigen.h"
+#include "ceres/internal/scoped_ptr.h"
+#include "ceres/types.h"
+
+// TODO(sameeragarwal): Reduce the size of these tests and redo the
+// parameterization to be more efficient.
+
+DECLARE_string(test_srcdir);
+
+namespace ceres {
+namespace internal {
+
+class SchurEliminatorTest : public ::testing::Test {
+ protected:
+ void SetUpFromId(int id) {
+ scoped_ptr<LinearLeastSquaresProblem>
+ problem(CreateLinearLeastSquaresProblemFromId(id));
+ CHECK_NOTNULL(problem.get());
+ SetupHelper(problem.get());
+ }
+
+ void SetUpFromFilename(const string& filename) {
+ scoped_ptr<LinearLeastSquaresProblem>
+ problem(CreateLinearLeastSquaresProblemFromFile(filename));
+ CHECK_NOTNULL(problem.get());
+ SetupHelper(problem.get());
+ }
+
+ void SetupHelper(LinearLeastSquaresProblem* problem) {
+ A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
+ b.reset(problem->b.release());
+ D.reset(problem->D.release());
+
+ num_eliminate_blocks = problem->num_eliminate_blocks;
+ num_eliminate_cols = 0;
+ const CompressedRowBlockStructure* bs = A->block_structure();
+
+ for (int i = 0; i < num_eliminate_blocks; ++i) {
+ num_eliminate_cols += bs->cols[i].size;
+ }
+ }
+
+ // Compute the golden values for the reduced linear system and the
+ // solution to the linear least squares problem using dense linear
+ // algebra.
+ void ComputeReferenceSolution(const Vector& D) {
+ Matrix J;
+ A->ToDenseMatrix(&J);
+ VectorRef f(b.get(), J.rows());
+
+ Matrix H = (D.cwiseProduct(D)).asDiagonal();
+ H.noalias() += J.transpose() * J;
+
+ const Vector g = J.transpose() * f;
+ const int schur_size = J.cols() - num_eliminate_cols;
+
+ lhs_expected.resize(schur_size, schur_size);
+ lhs_expected.setZero();
+
+ rhs_expected.resize(schur_size);
+ rhs_expected.setZero();
+
+ sol_expected.resize(J.cols());
+ sol_expected.setZero();
+
+ Matrix P = H.block(0, 0, num_eliminate_cols, num_eliminate_cols);
+ Matrix Q = H.block(0,
+ num_eliminate_cols,
+ num_eliminate_cols,
+ schur_size);
+ Matrix R = H.block(num_eliminate_cols,
+ num_eliminate_cols,
+ schur_size,
+ schur_size);
+ int row = 0;
+ const CompressedRowBlockStructure* bs = A->block_structure();
+ for (int i = 0; i < num_eliminate_blocks; ++i) {
+ const int block_size = bs->cols[i].size;
+ P.block(row, row, block_size, block_size) =
+ P
+ .block(row, row, block_size, block_size)
+ .ldlt()
+ .solve(Matrix::Identity(block_size, block_size));
+ row += block_size;
+ }
+
+ lhs_expected
+ .triangularView<Eigen::Upper>() = R - Q.transpose() * P * Q;
+ rhs_expected =
+ g.tail(schur_size) - Q.transpose() * P * g.head(num_eliminate_cols);
+ sol_expected = H.ldlt().solve(g);
+ }
+
+ void EliminateSolveAndCompare(const VectorRef& diagonal,
+ bool use_static_structure,
+ const double relative_tolerance) {
+ const CompressedRowBlockStructure* bs = A->block_structure();
+ const int num_col_blocks = bs->cols.size();
+ vector<int> blocks(num_col_blocks - num_eliminate_blocks, 0);
+ for (int i = num_eliminate_blocks; i < num_col_blocks; ++i) {
+ blocks[i - num_eliminate_blocks] = bs->cols[i].size;
+ }
+
+ BlockRandomAccessDenseMatrix lhs(blocks);
+
+ const int num_cols = A->num_cols();
+ const int schur_size = lhs.num_rows();
+
+ Vector rhs(schur_size);
+
+ LinearSolver::Options options;
+ options.num_eliminate_blocks = num_eliminate_blocks;
+ if (use_static_structure) {
+ DetectStructure(*bs,
+ options.num_eliminate_blocks,
+ &options.row_block_size,
+ &options.e_block_size,
+ &options.f_block_size);
+ }
+
+ scoped_ptr<SchurEliminatorBase> eliminator;
+ eliminator.reset(SchurEliminatorBase::Create(options));
+ eliminator->Init(num_eliminate_blocks, A->block_structure());
+ eliminator->Eliminate(A.get(), b.get(), diagonal.data(), &lhs, rhs.data());
+
+ MatrixRef lhs_ref(lhs.mutable_values(), lhs.num_rows(), lhs.num_cols());
+ Vector reduced_sol =
+ lhs_ref
+ .selfadjointView<Eigen::Upper>()
+ .ldlt()
+ .solve(rhs);
+
+ // Solution to the linear least squares problem.
+ Vector sol(num_cols);
+ sol.setZero();
+ sol.tail(schur_size) = reduced_sol;
+ eliminator->BackSubstitute(A.get(),
+ b.get(),
+ diagonal.data(),
+ reduced_sol.data(),
+ sol.data());
+
+ Matrix delta = (lhs_ref - lhs_expected).selfadjointView<Eigen::Upper>();
+ double diff = delta.norm();
+ EXPECT_NEAR(diff / lhs_expected.norm(), 0.0, relative_tolerance);
+ EXPECT_NEAR((rhs - rhs_expected).norm() / rhs_expected.norm(), 0.0,
+ relative_tolerance);
+ EXPECT_NEAR((sol - sol_expected).norm() / sol_expected.norm(), 0.0,
+ relative_tolerance);
+ }
+
+ scoped_ptr<BlockSparseMatrix> A;
+ scoped_array<double> b;
+ scoped_array<double> D;
+ int num_eliminate_blocks;
+ int num_eliminate_cols;
+
+ Matrix lhs_expected;
+ Vector rhs_expected;
+ Vector sol_expected;
+};
+
+TEST_F(SchurEliminatorTest, ScalarProblem) {
+ SetUpFromId(2);
+ Vector zero(A->num_cols());
+ zero.setZero();
+
+ ComputeReferenceSolution(VectorRef(zero.data(), A->num_cols()));
+ EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), true, 1e-14);
+ EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), false, 1e-14);
+
+ ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
+ EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
+ EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
+}
+
+#ifndef CERES_DONT_HAVE_PROTOCOL_BUFFERS
+TEST_F(SchurEliminatorTest, BlockProblem) {
+ const string input_file =
+ JoinPath(FLAGS_test_srcdir,
+ "problem-6-1384-000.lsqp"); // NOLINT
+
+ SetUpFromFilename(input_file);
+ ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
+ EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-10);
+ EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-10);
+}
+#endif // CERES_DONT_HAVE_PROTOCOL_BUFFERS
+
+} // namespace internal
+} // namespace ceres
