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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2017 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
// 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/subset_preconditioner.h"
#include <memory>
#include "Eigen/Dense"
#include "Eigen/SparseCore"
#include "ceres/block_sparse_matrix.h"
#include "ceres/compressed_row_sparse_matrix.h"
#include "ceres/inner_product_computer.h"
#include "ceres/internal/config.h"
#include "ceres/internal/eigen.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
namespace {
// TODO(sameeragarwal): Refactor the following two functions out of
// here and sparse_cholesky_test.cc into a more suitable place.
template <int UpLoType>
bool SolveLinearSystemUsingEigen(const Matrix& lhs,
const Vector rhs,
Vector* solution) {
Eigen::LLT<Matrix, UpLoType> llt = lhs.selfadjointView<UpLoType>().llt();
if (llt.info() != Eigen::Success) {
return false;
}
*solution = llt.solve(rhs);
return (llt.info() == Eigen::Success);
}
// Use Eigen's Dense Cholesky solver to compute the solution to a
// sparse linear system.
bool ComputeExpectedSolution(const CompressedRowSparseMatrix& lhs,
const Vector& rhs,
Vector* solution) {
Matrix dense_triangular_lhs;
lhs.ToDenseMatrix(&dense_triangular_lhs);
if (lhs.storage_type() == CompressedRowSparseMatrix::UPPER_TRIANGULAR) {
Matrix full_lhs = dense_triangular_lhs.selfadjointView<Eigen::Upper>();
return SolveLinearSystemUsingEigen<Eigen::Upper>(full_lhs, rhs, solution);
}
return SolveLinearSystemUsingEigen<Eigen::Lower>(
dense_triangular_lhs, rhs, solution);
}
using Param = ::testing::tuple<SparseLinearAlgebraLibraryType, bool>;
std::string ParamInfoToString(testing::TestParamInfo<Param> info) {
Param param = info.param;
std::stringstream ss;
ss << SparseLinearAlgebraLibraryTypeToString(::testing::get<0>(param)) << "_"
<< (::testing::get<1>(param) ? "Diagonal" : "NoDiagonal");
return ss.str();
}
} // namespace
class SubsetPreconditionerTest : public ::testing::TestWithParam<Param> {
protected:
void SetUp() final {
BlockSparseMatrix::RandomMatrixOptions options;
options.num_col_blocks = 4;
options.min_col_block_size = 1;
options.max_col_block_size = 4;
options.num_row_blocks = 8;
options.min_row_block_size = 1;
options.max_row_block_size = 4;
options.block_density = 0.9;
m_ = BlockSparseMatrix::CreateRandomMatrix(options);
start_row_block_ = m_->block_structure()->rows.size();
// Ensure that the bottom part of the matrix has the same column
// block structure.
options.col_blocks = m_->block_structure()->cols;
b_ = BlockSparseMatrix::CreateRandomMatrix(options);
m_->AppendRows(*b_);
// Create a Identity block diagonal matrix with the same column
// block structure.
diagonal_ = Vector::Ones(m_->num_cols());
block_diagonal_ = BlockSparseMatrix::CreateDiagonalMatrix(
diagonal_.data(), b_->block_structure()->cols);
// Unconditionally add the block diagonal to the matrix b_,
// because either it is either part of b_ to make it full rank, or
// we pass the same diagonal matrix later as the parameter D. In
// either case the preconditioner matrix is b_' b + D'D.
b_->AppendRows(*block_diagonal_);
inner_product_computer_ = InnerProductComputer::Create(
*b_, CompressedRowSparseMatrix::UPPER_TRIANGULAR);
inner_product_computer_->Compute();
}
std::unique_ptr<BlockSparseMatrix> m_;
std::unique_ptr<BlockSparseMatrix> b_;
std::unique_ptr<BlockSparseMatrix> block_diagonal_;
std::unique_ptr<InnerProductComputer> inner_product_computer_;
std::unique_ptr<Preconditioner> preconditioner_;
Vector diagonal_;
int start_row_block_;
};
TEST_P(SubsetPreconditionerTest, foo) {
Param param = GetParam();
Preconditioner::Options options;
options.subset_preconditioner_start_row_block = start_row_block_;
options.sparse_linear_algebra_library_type = ::testing::get<0>(param);
preconditioner_ = std::make_unique<SubsetPreconditioner>(options, *m_);
const bool with_diagonal = ::testing::get<1>(param);
if (!with_diagonal) {
m_->AppendRows(*block_diagonal_);
}
EXPECT_TRUE(
preconditioner_->Update(*m_, with_diagonal ? diagonal_.data() : nullptr));
// Repeatedly apply the preconditioner to random vectors and check
// that the preconditioned value is the same as one obtained by
// solving the linear system directly.
for (int i = 0; i < 5; ++i) {
CompressedRowSparseMatrix* lhs = inner_product_computer_->mutable_result();
Vector rhs = Vector::Random(lhs->num_rows());
Vector expected(lhs->num_rows());
EXPECT_TRUE(ComputeExpectedSolution(*lhs, rhs, &expected));
Vector actual(lhs->num_rows());
preconditioner_->RightMultiply(rhs.data(), actual.data());
Matrix eigen_lhs;
lhs->ToDenseMatrix(&eigen_lhs);
EXPECT_NEAR((actual - expected).norm() / actual.norm(),
0.0,
std::numeric_limits<double>::epsilon() * 10)
<< "\n"
<< eigen_lhs << "\n"
<< expected.transpose() << "\n"
<< actual.transpose();
}
}
#ifndef CERES_NO_SUITESPARSE
INSTANTIATE_TEST_SUITE_P(SubsetPreconditionerWithSuiteSparse,
SubsetPreconditionerTest,
::testing::Combine(::testing::Values(SUITE_SPARSE),
::testing::Values(true, false)),
ParamInfoToString);
#endif
#ifndef CERES_NO_CXSPARSE
INSTANTIATE_TEST_SUITE_P(SubsetPreconditionerWithCXSparse,
SubsetPreconditionerTest,
::testing::Combine(::testing::Values(CX_SPARSE),
::testing::Values(true, false)),
ParamInfoToString);
#endif
#ifndef CERES_NO_ACCELERATE_SPARSE
INSTANTIATE_TEST_SUITE_P(
SubsetPreconditionerWithAccelerateSparse,
SubsetPreconditionerTest,
::testing::Combine(::testing::Values(ACCELERATE_SPARSE),
::testing::Values(true, false)),
ParamInfoToString);
#endif
#ifdef CERES_USE_EIGEN_SPARSE
INSTANTIATE_TEST_SUITE_P(SubsetPreconditionerWithEigenSparse,
SubsetPreconditionerTest,
::testing::Combine(::testing::Values(EIGEN_SPARSE),
::testing::Values(true, false)),
ParamInfoToString);
#endif
} // namespace internal
} // namespace ceres
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