blob: 6a5a0c72fd2229f9d053f13c3448c208f81705eb [file] [log] [blame]
// 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 <string>
#include "ceres/iterative_refiner.h"
#include "Eigen/Core"
#include "ceres/sparse_cholesky.h"
#include "ceres/sparse_matrix.h"
namespace ceres {
namespace internal {
IterativeRefiner::IterativeRefiner(const int num_cols,
const int max_num_iterations)
: num_cols_(num_cols),
max_num_iterations_(max_num_iterations),
residual_(num_cols),
correction_(num_cols),
lhs_x_solution_(num_cols) {}
IterativeRefiner::Summary IterativeRefiner::Refine(
const SparseMatrix& lhs,
const double* rhs_ptr,
SparseCholesky* sparse_cholesky,
double* solution_ptr) {
Summary summary;
ConstVectorRef rhs(rhs_ptr, num_cols_);
VectorRef solution(solution_ptr, num_cols_);
summary.lhs_max_norm = ConstVectorRef(lhs.values(), lhs.num_nonzeros())
.lpNorm<Eigen::Infinity>();
summary.rhs_max_norm = rhs.lpNorm<Eigen::Infinity>();
summary.solution_max_norm = solution.lpNorm<Eigen::Infinity>();
// residual = rhs - lhs * solution
lhs_x_solution_.setZero();
lhs.RightMultiply(solution_ptr, lhs_x_solution_.data());
residual_ = rhs - lhs_x_solution_;
summary.residual_max_norm = residual_.lpNorm<Eigen::Infinity>();
for (summary.num_iterations = 0;
summary.num_iterations < max_num_iterations_;
++summary.num_iterations) {
// Check the current solution for convergence.
const double kTolerance = 5e-15; // From Hogg & Scott.
// residual_tolerance = (|A| |x| + |b|) * kTolerance;
const double residual_tolerance =
(summary.lhs_max_norm * summary.solution_max_norm +
summary.rhs_max_norm) *
kTolerance;
VLOG(3) << "Refinement:"
<< " iter: " << summary.num_iterations
<< " |A|: " << summary.lhs_max_norm
<< " |b|: " << summary.rhs_max_norm
<< " |x|: " << summary.solution_max_norm
<< " |b - Ax|: " << summary.residual_max_norm
<< " tol: " << residual_tolerance;
// |b - Ax| < (|A| |x| + |b|) * kTolerance;
if (summary.residual_max_norm < residual_tolerance) {
summary.converged = true;
break;
}
// Solve for lhs * correction = residual
correction_.setZero();
std::string ignored_message;
sparse_cholesky->Solve(
residual_.data(), correction_.data(), &ignored_message);
solution += correction_;
summary.solution_max_norm = solution.lpNorm<Eigen::Infinity>();
// residual = rhs - lhs * solution
lhs_x_solution_.setZero();
lhs.RightMultiply(solution_ptr, lhs_x_solution_.data());
residual_ = rhs - lhs_x_solution_;
summary.residual_max_norm = residual_.lpNorm<Eigen::Infinity>();
}
return summary;
};
} // namespace internal
} // namespace ceres