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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2018 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/iterative_refiner.h"
#include <utility>
#include "Eigen/Dense"
#include "ceres/internal/eigen.h"
#include "ceres/sparse_cholesky.h"
#include "ceres/sparse_matrix.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
// Macros to help us define virtual methods which we do not expect to
// use/call in this test.
#define DO_NOT_CALL \
{ LOG(FATAL) << "DO NOT CALL"; }
#define DO_NOT_CALL_WITH_RETURN(x) \
{ \
LOG(FATAL) << "DO NOT CALL"; \
return x; \
}
// A fake SparseMatrix, which uses an Eigen matrix to do the real work.
class FakeSparseMatrix : public SparseMatrix {
public:
explicit FakeSparseMatrix(Matrix m) : m_(std::move(m)) {}
// y += Ax
void RightMultiply(const double* x, double* y) const final {
VectorRef(y, m_.cols()) += m_ * ConstVectorRef(x, m_.cols());
}
// y += A'x
void LeftMultiply(const double* x, double* y) const final {
// We will assume that this is a symmetric matrix.
RightMultiply(x, y);
}
double* mutable_values() final { return m_.data(); }
const double* values() const final { return m_.data(); }
int num_rows() const final { return m_.cols(); }
int num_cols() const final { return m_.cols(); }
int num_nonzeros() const final { return m_.cols() * m_.cols(); }
// The following methods are not needed for tests in this file.
void SquaredColumnNorm(double* x) const final DO_NOT_CALL;
void ScaleColumns(const double* scale) final DO_NOT_CALL;
void SetZero() final DO_NOT_CALL;
void ToDenseMatrix(Matrix* dense_matrix) const final DO_NOT_CALL;
void ToTextFile(FILE* file) const final DO_NOT_CALL;
private:
Matrix m_;
};
// A fake SparseCholesky which uses Eigen's Cholesky factorization to
// do the real work. The template parameter allows us to work in
// doubles or floats, even though the source matrix is double.
template <typename Scalar>
class FakeSparseCholesky : public SparseCholesky {
public:
explicit FakeSparseCholesky(const Matrix& lhs) { lhs_ = lhs.cast<Scalar>(); }
LinearSolverTerminationType Solve(const double* rhs_ptr,
double* solution_ptr,
std::string* message) final {
const int num_cols = lhs_.cols();
VectorRef solution(solution_ptr, num_cols);
ConstVectorRef rhs(rhs_ptr, num_cols);
solution = lhs_.llt().solve(rhs.cast<Scalar>()).template cast<double>();
return LINEAR_SOLVER_SUCCESS;
}
// The following methods are not needed for tests in this file.
CompressedRowSparseMatrix::StorageType StorageType() const final
DO_NOT_CALL_WITH_RETURN(CompressedRowSparseMatrix::UPPER_TRIANGULAR);
LinearSolverTerminationType Factorize(CompressedRowSparseMatrix* lhs,
std::string* message) final
DO_NOT_CALL_WITH_RETURN(LINEAR_SOLVER_FAILURE);
private:
Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> lhs_;
};
#undef DO_NOT_CALL
#undef DO_NOT_CALL_WITH_RETURN
class IterativeRefinerTest : public ::testing::Test {
public:
void SetUp() override {
num_cols_ = 5;
max_num_iterations_ = 30;
Matrix m(num_cols_, num_cols_);
m.setRandom();
lhs_ = m * m.transpose();
solution_.resize(num_cols_);
solution_.setRandom();
rhs_ = lhs_ * solution_;
};
protected:
int num_cols_;
int max_num_iterations_;
Matrix lhs_;
Vector rhs_, solution_;
};
TEST_F(IterativeRefinerTest, RandomSolutionWithExactFactorizationConverges) {
FakeSparseMatrix lhs(lhs_);
FakeSparseCholesky<double> sparse_cholesky(lhs_);
IterativeRefiner refiner(max_num_iterations_);
Vector refined_solution(num_cols_);
refined_solution.setRandom();
refiner.Refine(lhs, rhs_.data(), &sparse_cholesky, refined_solution.data());
EXPECT_NEAR((lhs_ * refined_solution - rhs_).norm(),
0.0,
std::numeric_limits<double>::epsilon() * 10);
}
TEST_F(IterativeRefinerTest,
RandomSolutionWithApproximationFactorizationConverges) {
FakeSparseMatrix lhs(lhs_);
// Use a single precision Cholesky factorization of the double
// precision matrix. This will give us an approximate factorization.
FakeSparseCholesky<float> sparse_cholesky(lhs_);
IterativeRefiner refiner(max_num_iterations_);
Vector refined_solution(num_cols_);
refined_solution.setRandom();
refiner.Refine(lhs, rhs_.data(), &sparse_cholesky, refined_solution.data());
EXPECT_NEAR((lhs_ * refined_solution - rhs_).norm(),
0.0,
std::numeric_limits<double>::epsilon() * 10);
}
} // namespace internal
} // namespace ceres
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