| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2015 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
| // 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 |
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| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
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| // |
| // Author: sameeragarwal@google.com (Sameer Agarwal) |
| |
| #include "ceres/implicit_schur_complement.h" |
| |
| #include <cstddef> |
| #include <memory> |
| #include "Eigen/Dense" |
| #include "ceres/block_random_access_dense_matrix.h" |
| #include "ceres/block_sparse_matrix.h" |
| #include "ceres/casts.h" |
| #include "ceres/context_impl.h" |
| #include "ceres/internal/eigen.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 ImplicitSchurComplementTest : public ::testing::Test { |
| protected : |
| virtual void SetUp() { |
| std::unique_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; |
| } |
| |
| void ReducedLinearSystemAndSolution(double* D, |
| Matrix* lhs, |
| Vector* rhs, |
| Vector* solution) { |
| const CompressedRowBlockStructure* bs = A_->block_structure(); |
| const int num_col_blocks = bs->cols.size(); |
| std::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 blhs(blocks); |
| const int num_schur_rows = blhs.num_rows(); |
| |
| LinearSolver::Options options; |
| options.elimination_groups.push_back(num_eliminate_blocks_); |
| options.type = DENSE_SCHUR; |
| ContextImpl context; |
| options.context = &context; |
| |
| std::unique_ptr<SchurEliminatorBase> eliminator( |
| SchurEliminatorBase::Create(options)); |
| CHECK_NOTNULL(eliminator.get()); |
| const bool kFullRankETE = true; |
| eliminator->Init(num_eliminate_blocks_, kFullRankETE, bs); |
| |
| lhs->resize(num_schur_rows, num_schur_rows); |
| rhs->resize(num_schur_rows); |
| |
| eliminator->Eliminate(A_.get(), b_.get(), D, &blhs, rhs->data()); |
| |
| MatrixRef lhs_ref(blhs.mutable_values(), num_schur_rows, num_schur_rows); |
| |
| // lhs_ref is an upper triangular matrix. Construct a full version |
| // of lhs_ref in lhs by transposing lhs_ref, choosing the strictly |
| // lower triangular part of the matrix and adding it to lhs_ref. |
| *lhs = lhs_ref; |
| lhs->triangularView<Eigen::StrictlyLower>() = |
| lhs_ref.triangularView<Eigen::StrictlyUpper>().transpose(); |
| |
| solution->resize(num_cols_); |
| solution->setZero(); |
| VectorRef schur_solution(solution->data() + num_cols_ - num_schur_rows, |
| num_schur_rows); |
| schur_solution = lhs->selfadjointView<Eigen::Upper>().llt().solve(*rhs); |
| eliminator->BackSubstitute(A_.get(), b_.get(), D, |
| schur_solution.data(), solution->data()); |
| } |
| |
| AssertionResult TestImplicitSchurComplement(double* D) { |
| Matrix lhs; |
| Vector rhs; |
| Vector reference_solution; |
| ReducedLinearSystemAndSolution(D, &lhs, &rhs, &reference_solution); |
| |
| LinearSolver::Options options; |
| options.elimination_groups.push_back(num_eliminate_blocks_); |
| options.preconditioner_type = JACOBI; |
| ContextImpl context; |
| options.context = &context; |
| ImplicitSchurComplement isc(options); |
| isc.Init(*A_, D, b_.get()); |
| |
| int num_sc_cols = lhs.cols(); |
| |
| for (int i = 0; i < num_sc_cols; ++i) { |
| Vector x(num_sc_cols); |
| x.setZero(); |
| x(i) = 1.0; |
| |
| Vector y(num_sc_cols); |
| y = lhs * x; |
| |
| Vector z(num_sc_cols); |
| isc.RightMultiply(x.data(), z.data()); |
| |
| // The i^th column of the implicit schur complement is the same as |
| // the explicit schur complement. |
| if ((y - z).norm() > kEpsilon) { |
| return testing::AssertionFailure() |
| << "Explicit and Implicit SchurComplements differ in " |
| << "column " << i << ". explicit: " << y.transpose() |
| << " implicit: " << z.transpose(); |
| } |
| } |
| |
| // Compare the rhs of the reduced linear system |
| if ((isc.rhs() - rhs).norm() > kEpsilon) { |
| return testing::AssertionFailure() |
| << "Explicit and Implicit SchurComplements differ in " |
| << "rhs. explicit: " << rhs.transpose() |
| << " implicit: " << isc.rhs().transpose(); |
| } |
| |
| // Reference solution to the f_block. |
| const Vector reference_f_sol = |
| lhs.selfadjointView<Eigen::Upper>().llt().solve(rhs); |
| |
| // Backsubstituted solution from the implicit schur solver using the |
| // reference solution to the f_block. |
| Vector sol(num_cols_); |
| isc.BackSubstitute(reference_f_sol.data(), sol.data()); |
| if ((sol - reference_solution).norm() > kEpsilon) { |
| return testing::AssertionFailure() |
| << "Explicit and Implicit SchurComplements solutions differ. " |
| << "explicit: " << reference_solution.transpose() |
| << " implicit: " << sol.transpose(); |
| } |
| |
| return testing::AssertionSuccess(); |
| } |
| |
| int num_rows_; |
| int num_cols_; |
| int num_eliminate_blocks_; |
| |
| std::unique_ptr<BlockSparseMatrix> A_; |
| std::unique_ptr<double[]> b_; |
| std::unique_ptr<double[]> D_; |
| }; |
| |
| // Verify that the Schur Complement matrix implied by the |
| // ImplicitSchurComplement class matches the one explicitly computed |
| // by the SchurComplement solver. |
| // |
| // We do this with and without regularization to check that the |
| // support for the LM diagonal is correct. |
| TEST_F(ImplicitSchurComplementTest, SchurMatrixValuesTest) { |
| EXPECT_TRUE(TestImplicitSchurComplement(NULL)); |
| EXPECT_TRUE(TestImplicitSchurComplement(D_.get())); |
| } |
| |
| } // namespace internal |
| } // namespace ceres |