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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 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
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// 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/blas.h"
#include "ceres/dense_sparse_matrix.h"
#include "ceres/internal/eigen.h"
#include "ceres/lapack.h"
#include "ceres/linear_solver.h"
#include "ceres/types.h"
#include "ceres/wall_time.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) {
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 DenseNormalCholeskySolver::SolveUsingEigen(
DenseSparseMatrix* A,
const double* b,
const LinearSolver::PerSolveOptions& per_solve_options,
double* x) {
EventLogger event_logger("DenseNormalCholeskySolver::Solve");
const int num_rows = A->num_rows();
const int num_cols = A->num_cols();
ConstColMajorMatrixRef Aref = A->matrix();
Matrix lhs(num_cols, num_cols);
lhs.setZero();
event_logger.AddEvent("Setup");
// 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();
}
event_logger.AddEvent("Product");
LinearSolver::Summary summary;
summary.num_iterations = 1;
summary.termination_type = LINEAR_SOLVER_SUCCESS;
Eigen::LLT<Matrix, Eigen::Upper> llt =
lhs.selfadjointView<Eigen::Upper>().llt();
if (llt.info() != Eigen::Success) {
summary.termination_type = LINEAR_SOLVER_FAILURE;
summary.message = "Eigen LLT decomposition failed.";
} else {
summary.termination_type = LINEAR_SOLVER_SUCCESS;
summary.message = "Success.";
}
VectorRef(x, num_cols) = llt.solve(rhs);
event_logger.AddEvent("Solve");
return summary;
}
LinearSolver::Summary DenseNormalCholeskySolver::SolveUsingLAPACK(
DenseSparseMatrix* A,
const double* b,
const LinearSolver::PerSolveOptions& per_solve_options,
double* x) {
EventLogger event_logger("DenseNormalCholeskySolver::Solve");
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);
}
const int num_cols = A->num_cols();
Matrix lhs(num_cols, num_cols);
event_logger.AddEvent("Setup");
// lhs = A'A
//
// Note: This is a bit delicate, it assumes that the stride on this
// matrix is the same as the number of rows.
BLAS::SymmetricRankKUpdate(
A->num_rows(), num_cols, A->values(), true, 1.0, 0.0, lhs.data());
if (per_solve_options.D != NULL) {
// Undo the modifications to the matrix A.
A->RemoveDiagonal();
}
// TODO(sameeragarwal): Replace this with a gemv call for true blasness.
// rhs = A'b
VectorRef(x, num_cols) =
A->matrix().transpose() * ConstVectorRef(b, A->num_rows());
event_logger.AddEvent("Product");
LinearSolver::Summary summary;
summary.num_iterations = 1;
summary.termination_type = LAPACK::SolveInPlaceUsingCholesky(
num_cols, lhs.data(), x, &summary.message);
event_logger.AddEvent("Solve");
return summary;
}
} // namespace internal
} // namespace ceres