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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
// 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/dense_normal_cholesky_solver.h"
#include <cstddef>
#include "Eigen/Dense"
#include "ceres/dense_sparse_matrix.h"
#include "ceres/linear_solver.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/types.h"
namespace ceres {
namespace internal {
DenseNormalCholeskySolver::DenseNormalCholeskySolver(
const LinearSolver::Options& options)
: options_(options) {}
LinearSolver::Summary DenseNormalCholeskySolver::SolveImpl(
DenseSparseMatrix* A,
const double* b,
const LinearSolver::PerSolveOptions& per_solve_options,
double* x) {
const int num_rows = A->num_rows();
const int num_cols = A->num_cols();
ConstAlignedMatrixRef Aref = A->matrix();
Matrix lhs(num_cols, num_cols);
lhs.setZero();
// lhs += A'A
//
// Using rankUpdate instead of GEMM, exposes the fact that its the
// same matrix being multiplied with itself and that the product is
// symmetric.
lhs.selfadjointView<Eigen::Upper>().rankUpdate(Aref.transpose());
// rhs = A'b
Vector rhs = Aref.transpose() * ConstVectorRef(b, num_rows);
if (per_solve_options.D != NULL) {
ConstVectorRef D(per_solve_options.D, num_cols);
lhs += D.array().square().matrix().asDiagonal();
}
VectorRef(x, num_cols) =
lhs.selfadjointView<Eigen::Upper>().ldlt().solve(rhs);
LinearSolver::Summary summary;
summary.num_iterations = 1;
summary.termination_type = TOLERANCE;
return summary;
}
} // namespace internal
} // namespace ceres
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