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

// Copyright 2015 Google Inc. All rights reserved.

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

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// 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