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// Ceres Solver - A fast non-linear least squares minimizer
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// Author: markshachkov@gmail.com (Mark Shachkov)
#include "ceres/power_series_expansion_preconditioner.h"
#include "Eigen/Dense"
#include "ceres/linear_least_squares_problems.h"
#include "gtest/gtest.h"
namespace ceres::internal {
const double kEpsilon = 1e-14;
class PowerSeriesExpansionPreconditionerTest : public ::testing::Test {
protected:
void SetUp() final {
problem_ = CreateLinearLeastSquaresProblemFromId(5);
const auto A = down_cast<BlockSparseMatrix*>(problem_->A.get());
const auto D = problem_->D.get();
options_.elimination_groups.push_back(problem_->num_eliminate_blocks);
options_.preconditioner_type = SCHUR_POWER_SERIES_EXPANSION;
isc_ = std::make_unique<ImplicitSchurComplement>(options_);
isc_->Init(*A, D, problem_->b.get());
num_f_cols_ = isc_->rhs().rows();
const int num_rows = A->num_rows(), num_cols = A->num_cols(),
num_e_cols = num_cols - num_f_cols_;
// Using predefined linear operator with schur structure and block-diagonal
// F'F to explicitly construct schur complement and to calculate its inverse
// to be used as a reference.
Matrix A_dense, E, F, DE, DF;
problem_->A->ToDenseMatrix(&A_dense);
E = A_dense.leftCols(num_e_cols);
F = A_dense.rightCols(num_f_cols_);
DE = VectorRef(D, num_e_cols).asDiagonal();
DF = VectorRef(D + num_e_cols, num_f_cols_).asDiagonal();
sc_inverse_expected_ =
(F.transpose() *
(Matrix::Identity(num_rows, num_rows) -
E * (E.transpose() * E + DE).inverse() * E.transpose()) *
F +
DF)
.inverse();
}
std::unique_ptr<LinearLeastSquaresProblem> problem_;
std::unique_ptr<ImplicitSchurComplement> isc_;
int num_f_cols_;
Matrix sc_inverse_expected_;
LinearSolver::Options options_;
};
TEST_F(PowerSeriesExpansionPreconditionerTest,
InverseValidPreconditionerToleranceReached) {
const double spse_tolerance = kEpsilon;
const int max_num_iterations = 50;
PowerSeriesExpansionPreconditioner preconditioner(
isc_.get(), max_num_iterations, spse_tolerance);
Vector x(num_f_cols_), y(num_f_cols_);
for (int i = 0; i < num_f_cols_; i++) {
x.setZero();
x(i) = 1.0;
y.setZero();
preconditioner.RightMultiplyAndAccumulate(x.data(), y.data());
EXPECT_LT((y - sc_inverse_expected_.col(i)).norm(), kEpsilon)
<< "Reference Schur complement inverse and its estimate via "
"PowerSeriesExpansionPreconditioner differs in "
<< i
<< " column.\nreference : " << sc_inverse_expected_.col(i).transpose()
<< "\nestimated: " << y.transpose();
}
}
TEST_F(PowerSeriesExpansionPreconditionerTest,
InverseValidPreconditionerMaxIterations) {
const double spse_tolerance = 0;
const int max_num_iterations = 50;
PowerSeriesExpansionPreconditioner preconditioner_fixed_n_iterations(
isc_.get(), max_num_iterations, spse_tolerance);
Vector x(num_f_cols_), y(num_f_cols_);
for (int i = 0; i < num_f_cols_; i++) {
x.setZero();
x(i) = 1.0;
y.setZero();
preconditioner_fixed_n_iterations.RightMultiplyAndAccumulate(x.data(),
y.data());
EXPECT_LT((y - sc_inverse_expected_.col(i)).norm(), kEpsilon)
<< "Reference Schur complement inverse and its estimate via "
"PowerSeriesExpansionPreconditioner differs in "
<< i
<< " column.\nreference : " << sc_inverse_expected_.col(i).transpose()
<< "\nestimated: " << y.transpose();
}
}
TEST_F(PowerSeriesExpansionPreconditionerTest,
InverseInvalidBadPreconditionerTolerance) {
const double spse_tolerance = 1 / kEpsilon;
const int max_num_iterations = 50;
PowerSeriesExpansionPreconditioner preconditioner_bad_tolerance(
isc_.get(), max_num_iterations, spse_tolerance);
Vector x(num_f_cols_), y(num_f_cols_);
for (int i = 0; i < num_f_cols_; i++) {
x.setZero();
x(i) = 1.0;
y.setZero();
preconditioner_bad_tolerance.RightMultiplyAndAccumulate(x.data(), y.data());
EXPECT_GT((y - sc_inverse_expected_.col(i)).norm(), kEpsilon)
<< "Reference Schur complement inverse and its estimate via "
"PowerSeriesExpansionPreconditioner are too similar, tolerance "
"stopping criteria failed.";
}
}
TEST_F(PowerSeriesExpansionPreconditionerTest,
InverseInvalidBadPreconditionerMaxIterations) {
const double spse_tolerance = kEpsilon;
const int max_num_iterations = 1;
PowerSeriesExpansionPreconditioner preconditioner_bad_iterations_limit(
isc_.get(), max_num_iterations, spse_tolerance);
Vector x(num_f_cols_), y(num_f_cols_);
for (int i = 0; i < num_f_cols_; i++) {
x.setZero();
x(i) = 1.0;
y.setZero();
preconditioner_bad_iterations_limit.RightMultiplyAndAccumulate(x.data(),
y.data());
EXPECT_GT((y - sc_inverse_expected_.col(i)).norm(), kEpsilon)
<< "Reference Schur complement inverse and its estimate via "
"PowerSeriesExpansionPreconditioner are too similar, maximum "
"iterations stopping criteria failed.";
}
}
} // namespace ceres::internal