Householder.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
#ifndef EIGEN_HOUSEHOLDER_H
#define EIGEN_HOUSEHOLDER_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
template <int n>
struct decrement_size {
  enum { ret = n == Dynamic ? n : n - 1 };
};
}  // namespace internal

template <typename Derived>
EIGEN_DEVICE_FUNC void MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta) {
  VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret> essentialPart(derived(), 1, size() - 1);
  makeHouseholder(essentialPart, tau, beta);
}

template <typename Derived>
template <typename EssentialPart>
EIGEN_DEVICE_FUNC void MatrixBase<Derived>::makeHouseholder(EssentialPart& essential, Scalar& tau,
                                                            RealScalar& beta) const {
  using numext::conj;
 
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
  VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size() - 1);
 
  RealScalar tailSqNorm = size() == 1 ? RealScalar(0) : tail.squaredNorm();
  Scalar c0 = coeff(0);
  const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
 
  if (tailSqNorm <= tol && numext::abs2(numext::imag(c0)) <= tol) {
    tau = RealScalar(0);
    beta = numext::real(c0);
    essential.setZero();
  } else {
    beta = numext::sqrt(numext::abs2(c0) + tailSqNorm);
    if (numext::real(c0) >= RealScalar(0)) beta = -beta;
    essential = tail / (c0 - beta);
    tau = conj((beta - c0) / beta);
  }
}

template <typename Derived>
template <typename EssentialPart>
EIGEN_DEVICE_FUNC void MatrixBase<Derived>::applyHouseholderOnTheLeft(const EssentialPart& essential, const Scalar& tau,
                                                                      Scalar* workspace) {
  if (rows() == 1) {
    *this *= Scalar(1) - tau;
  } else if (!numext::is_exactly_zero(tau)) {
    Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace, cols());
    Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows() - 1,
                                                                                        cols());
    tmp.noalias() = essential.adjoint() * bottom;
    tmp += this->row(0);
    this->row(0) -= tau * tmp;
    bottom.noalias() -= tau * essential * tmp;
  }
}

template <typename Derived>
template <typename EssentialPart>
EIGEN_DEVICE_FUNC void MatrixBase<Derived>::applyHouseholderOnTheRight(const EssentialPart& essential,
                                                                       const Scalar& tau, Scalar* workspace) {
  if (cols() == 1) {
    *this *= Scalar(1) - tau;
  } else if (!numext::is_exactly_zero(tau)) {
    Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace, rows());
    Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(),
                                                                                       cols() - 1);
    tmp.noalias() = right * essential;
    tmp += this->col(0);
    this->col(0) -= tau * tmp;
    right.noalias() -= tau * tmp * essential.adjoint();
  }
}
 
}  // end namespace Eigen
 
#endif  // EIGEN_HOUSEHOLDER_H