227 lines
8.1 KiB
C++
227 lines
8.1 KiB
C++
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2015 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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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
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// 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)
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#include "ceres/schur_eliminator.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/internal/eigen.h"
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#include "ceres/internal/scoped_ptr.h"
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#include "ceres/linear_least_squares_problems.h"
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#include "ceres/test_util.h"
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#include "ceres/triplet_sparse_matrix.h"
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#include "ceres/types.h"
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#include "glog/logging.h"
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#include "gtest/gtest.h"
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// TODO(sameeragarwal): Reduce the size of these tests and redo the
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// parameterization to be more efficient.
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namespace ceres {
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namespace internal {
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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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}
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void SetupHelper(LinearLeastSquaresProblem* problem) {
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A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
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b.reset(problem->b.release());
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D.reset(problem->D.release());
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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();
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for (int i = 0; i < num_eliminate_blocks; ++i) {
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num_eliminate_cols += bs->cols[i].size;
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}
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}
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// 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
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// algebra.
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void ComputeReferenceSolution(const Vector& D) {
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Matrix J;
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A->ToDenseMatrix(&J);
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VectorRef f(b.get(), J.rows());
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Matrix H = (D.cwiseProduct(D)).asDiagonal();
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H.noalias() += J.transpose() * J;
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const Vector g = J.transpose() * f;
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const int schur_size = J.cols() - num_eliminate_cols;
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lhs_expected.resize(schur_size, schur_size);
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lhs_expected.setZero();
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rhs_expected.resize(schur_size);
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rhs_expected.setZero();
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sol_expected.resize(J.cols());
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sol_expected.setZero();
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Matrix P = H.block(0, 0, num_eliminate_cols, num_eliminate_cols);
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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);
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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);
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int row = 0;
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const CompressedRowBlockStructure* bs = A->block_structure();
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for (int i = 0; i < num_eliminate_blocks; ++i) {
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const int block_size = bs->cols[i].size;
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P.block(row, row, block_size, block_size) =
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P
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.block(row, row, block_size, block_size)
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.llt()
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.solve(Matrix::Identity(block_size, block_size));
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row += block_size;
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}
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lhs_expected
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.triangularView<Eigen::Upper>() = R - Q.transpose() * P * Q;
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rhs_expected =
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g.tail(schur_size) - Q.transpose() * P * g.head(num_eliminate_cols);
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sol_expected = H.llt().solve(g);
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}
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void EliminateSolveAndCompare(const VectorRef& diagonal,
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bool use_static_structure,
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const double relative_tolerance) {
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const CompressedRowBlockStructure* bs = A->block_structure();
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const int num_col_blocks = bs->cols.size();
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std::vector<int> blocks(num_col_blocks - num_eliminate_blocks, 0);
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for (int i = num_eliminate_blocks; i < num_col_blocks; ++i) {
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blocks[i - num_eliminate_blocks] = bs->cols[i].size;
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}
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BlockRandomAccessDenseMatrix lhs(blocks);
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const int num_cols = A->num_cols();
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const int schur_size = lhs.num_rows();
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Vector rhs(schur_size);
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LinearSolver::Options options;
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options.elimination_groups.push_back(num_eliminate_blocks);
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if (use_static_structure) {
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DetectStructure(*bs,
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num_eliminate_blocks,
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&options.row_block_size,
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&options.e_block_size,
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&options.f_block_size);
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}
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scoped_ptr<SchurEliminatorBase> eliminator;
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eliminator.reset(SchurEliminatorBase::Create(options));
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eliminator->Init(num_eliminate_blocks, A->block_structure());
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eliminator->Eliminate(A.get(), b.get(), diagonal.data(), &lhs, rhs.data());
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MatrixRef lhs_ref(lhs.mutable_values(), lhs.num_rows(), lhs.num_cols());
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Vector reduced_sol =
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lhs_ref
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.selfadjointView<Eigen::Upper>()
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.llt()
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.solve(rhs);
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// Solution to the linear least squares problem.
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Vector sol(num_cols);
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sol.setZero();
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sol.tail(schur_size) = reduced_sol;
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eliminator->BackSubstitute(A.get(),
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b.get(),
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diagonal.data(),
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reduced_sol.data(),
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sol.data());
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Matrix delta = (lhs_ref - lhs_expected).selfadjointView<Eigen::Upper>();
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double diff = delta.norm();
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EXPECT_NEAR(diff / lhs_expected.norm(), 0.0, relative_tolerance);
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EXPECT_NEAR((rhs - rhs_expected).norm() / rhs_expected.norm(), 0.0,
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relative_tolerance);
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EXPECT_NEAR((sol - sol_expected).norm() / sol_expected.norm(), 0.0,
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relative_tolerance);
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}
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scoped_ptr<BlockSparseMatrix> A;
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scoped_array<double> b;
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scoped_array<double> D;
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int num_eliminate_blocks;
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int num_eliminate_cols;
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Matrix lhs_expected;
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Vector rhs_expected;
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Vector sol_expected;
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};
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TEST_F(SchurEliminatorTest, ScalarProblemNoRegularization) {
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SetUpFromId(2);
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Vector zero(A->num_cols());
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zero.setZero();
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ComputeReferenceSolution(VectorRef(zero.data(), A->num_cols()));
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EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), true, 1e-14);
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EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), false, 1e-14);
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}
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TEST_F(SchurEliminatorTest, ScalarProblemWithRegularization) {
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SetUpFromId(2);
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ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
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EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
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EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
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}
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TEST_F(SchurEliminatorTest, VaryingFBlockSizeWithStaticStructure) {
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SetUpFromId(4);
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ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
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EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
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}
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TEST_F(SchurEliminatorTest, VaryingFBlockSizeWithoutStaticStructure) {
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SetUpFromId(4);
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ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
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EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
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}
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} // namespace internal
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} // namespace ceres
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