// Ceres Solver - A fast non-linear least squares minimizer

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// http://ceres-solver.org/

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// 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/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 {

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