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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 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_qr_solver.h"
#include <cstddef>
#include "Eigen/Dense"
#include "ceres/dense_sparse_matrix.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/lapack.h"
#include "ceres/linear_solver.h"
#include "ceres/types.h"
#include "ceres/wall_time.h"
namespace ceres {
namespace internal {
DenseQRSolver::DenseQRSolver(const LinearSolver::Options& options)
: options_(options) {
work_.resize(1);
}
LinearSolver::Summary DenseQRSolver::SolveImpl(
DenseSparseMatrix* A,
const double* b,
const LinearSolver::PerSolveOptions& per_solve_options,
double* x) {
if (options_.dense_linear_algebra_library_type == EIGEN) {
return SolveUsingEigen(A, b, per_solve_options, x);
} else {
return SolveUsingLAPACK(A, b, per_solve_options, x);
}
}
LinearSolver::Summary DenseQRSolver::SolveUsingLAPACK(
DenseSparseMatrix* A,
const double* b,
const LinearSolver::PerSolveOptions& per_solve_options,
double* x) {
EventLogger event_logger("DenseQRSolver::Solve");
const int num_rows = A->num_rows();
const int num_cols = A->num_cols();
if (per_solve_options.D != NULL) {
// Temporarily append a diagonal block to the A matrix, but undo
// it before returning the matrix to the user.
A->AppendDiagonal(per_solve_options.D);
}
// TODO(sameeragarwal): Since we are copying anyways, the diagonal
// can be appended to the matrix instead of doing it on A.
lhs_ = A->matrix();
if (per_solve_options.D != NULL) {
// Undo the modifications to the matrix A.
A->RemoveDiagonal();
}
// rhs = [b;0] to account for the additional rows in the lhs.
if (rhs_.rows() != lhs_.rows()) {
rhs_.resize(lhs_.rows());
}
rhs_.setZero();
rhs_.head(num_rows) = ConstVectorRef(b, num_rows);
if (work_.rows() == 1) {
const int work_size =
LAPACK::EstimateWorkSizeForQR(lhs_.rows(), lhs_.cols());
VLOG(3) << "Working memory for Dense QR factorization: "
<< work_size * sizeof(double);
work_.resize(work_size);
}
LinearSolver::Summary summary;
summary.num_iterations = 1;
summary.termination_type = LAPACK::SolveInPlaceUsingQR(lhs_.rows(),
lhs_.cols(),
lhs_.data(),
work_.rows(),
work_.data(),
rhs_.data(),
&summary.message);
event_logger.AddEvent("Solve");
if (summary.termination_type == LINEAR_SOLVER_SUCCESS) {
VectorRef(x, num_cols) = rhs_.head(num_cols);
}
event_logger.AddEvent("TearDown");
return summary;
}
LinearSolver::Summary DenseQRSolver::SolveUsingEigen(
DenseSparseMatrix* A,
const double* b,
const LinearSolver::PerSolveOptions& per_solve_options,
double* x) {
EventLogger event_logger("DenseQRSolver::Solve");
const int num_rows = A->num_rows();
const int num_cols = A->num_cols();
if (per_solve_options.D != NULL) {
// Temporarily append a diagonal block to the A matrix, but undo
// it before returning the matrix to the user.
A->AppendDiagonal(per_solve_options.D);
}
// rhs = [b;0] to account for the additional rows in the lhs.
const int augmented_num_rows =
num_rows + ((per_solve_options.D != NULL) ? num_cols : 0);
if (rhs_.rows() != augmented_num_rows) {
rhs_.resize(augmented_num_rows);
rhs_.setZero();
}
rhs_.head(num_rows) = ConstVectorRef(b, num_rows);
event_logger.AddEvent("Setup");
// Solve the system.
VectorRef(x, num_cols) = A->matrix().householderQr().solve(rhs_);
event_logger.AddEvent("Solve");
if (per_solve_options.D != NULL) {
// Undo the modifications to the matrix A.
A->RemoveDiagonal();
}
// We always succeed, since the QR solver returns the best solution
// it can. It is the job of the caller to determine if the solution
// is good enough or not.
LinearSolver::Summary summary;
summary.num_iterations = 1;
summary.termination_type = LINEAR_SOLVER_SUCCESS;
summary.message = "Success.";
event_logger.AddEvent("TearDown");
return summary;
}
} // namespace internal
} // namespace ceres
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