HouseholderSequence.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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_SEQUENCE_H
#define EIGEN_HOUSEHOLDER_SEQUENCE_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

template <typename VectorsType, typename CoeffsType, int Side>
struct traits<HouseholderSequence<VectorsType, CoeffsType, Side> > {
  typedef typename VectorsType::Scalar Scalar;
  typedef typename VectorsType::StorageIndex StorageIndex;
  typedef typename VectorsType::StorageKind StorageKind;
  enum {
    RowsAtCompileTime =
        Side == OnTheLeft ? traits<VectorsType>::RowsAtCompileTime : traits<VectorsType>::ColsAtCompileTime,
    ColsAtCompileTime = RowsAtCompileTime,
    MaxRowsAtCompileTime =
        Side == OnTheLeft ? traits<VectorsType>::MaxRowsAtCompileTime : traits<VectorsType>::MaxColsAtCompileTime,
    MaxColsAtCompileTime = MaxRowsAtCompileTime,
    Flags = 0
  };
};

struct HouseholderSequenceShape {};

template <typename VectorsType, typename CoeffsType, int Side>
struct evaluator_traits<HouseholderSequence<VectorsType, CoeffsType, Side> >
    : public evaluator_traits_base<HouseholderSequence<VectorsType, CoeffsType, Side> > {
  typedef HouseholderSequenceShape Shape;
};

template <typename VectorsType, typename CoeffsType, int Side>
struct hseq_side_dependent_impl {
  typedef Block<const VectorsType, Dynamic, 1> EssentialVectorType;
  typedef HouseholderSequence<VectorsType, CoeffsType, OnTheLeft> HouseholderSequenceType;
  static EIGEN_DEVICE_FUNC inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k) {
    Index start = k + 1 + h.m_shift;
    return Block<const VectorsType, Dynamic, 1>(h.m_vectors, start, k, h.rows() - start, 1);
  }
};

template <typename VectorsType, typename CoeffsType>
struct hseq_side_dependent_impl<VectorsType, CoeffsType, OnTheRight> {
  typedef Transpose<Block<const VectorsType, 1, Dynamic> > EssentialVectorType;
  typedef HouseholderSequence<VectorsType, CoeffsType, OnTheRight> HouseholderSequenceType;
  static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k) {
    Index start = k + 1 + h.m_shift;
    return Block<const VectorsType, 1, Dynamic>(h.m_vectors, k, start, 1, h.rows() - start).transpose();
  }
};

template <typename OtherScalarType, typename MatrixType>
struct matrix_type_times_scalar_type {
  typedef typename ScalarBinaryOpTraits<OtherScalarType, typename MatrixType::Scalar>::ReturnType ResultScalar;
  typedef Matrix<ResultScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime, 0,
                 MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime>
      Type;
};

}  // end namespace internal

template <typename VectorsType, typename CoeffsType, int Side>
class HouseholderSequence : public EigenBase<HouseholderSequence<VectorsType, CoeffsType, Side> > {
  typedef typename internal::hseq_side_dependent_impl<VectorsType, CoeffsType, Side>::EssentialVectorType
      EssentialVectorType;

 public:
  enum {
    RowsAtCompileTime = internal::traits<HouseholderSequence>::RowsAtCompileTime,
    ColsAtCompileTime = internal::traits<HouseholderSequence>::ColsAtCompileTime,
    MaxRowsAtCompileTime = internal::traits<HouseholderSequence>::MaxRowsAtCompileTime,
    MaxColsAtCompileTime = internal::traits<HouseholderSequence>::MaxColsAtCompileTime
  };
  typedef typename internal::traits<HouseholderSequence>::Scalar Scalar;

  typedef HouseholderSequence<
      std::conditional_t<NumTraits<Scalar>::IsComplex,
                         internal::remove_all_t<typename VectorsType::ConjugateReturnType>, VectorsType>,
      std::conditional_t<NumTraits<Scalar>::IsComplex, internal::remove_all_t<typename CoeffsType::ConjugateReturnType>,
                         CoeffsType>,
      Side>
      ConjugateReturnType;

  typedef HouseholderSequence<
      VectorsType,
      std::conditional_t<NumTraits<Scalar>::IsComplex, internal::remove_all_t<typename CoeffsType::ConjugateReturnType>,
                         CoeffsType>,
      Side>
      AdjointReturnType;

  typedef HouseholderSequence<
      std::conditional_t<NumTraits<Scalar>::IsComplex,
                         internal::remove_all_t<typename VectorsType::ConjugateReturnType>, VectorsType>,
      CoeffsType, Side>
      TransposeReturnType;

  typedef HouseholderSequence<std::add_const_t<VectorsType>, std::add_const_t<CoeffsType>, Side>
      ConstHouseholderSequence;

  EIGEN_DEVICE_FUNC HouseholderSequence(const VectorsType& v, const CoeffsType& h)
      : m_vectors(v), m_coeffs(h), m_reverse(false), m_length(v.diagonalSize()), m_shift(0) {}

  EIGEN_DEVICE_FUNC HouseholderSequence(const HouseholderSequence& other)
      : m_vectors(other.m_vectors),
        m_coeffs(other.m_coeffs),
        m_reverse(other.m_reverse),
        m_length(other.m_length),
        m_shift(other.m_shift) {}

  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept {
    return Side == OnTheLeft ? m_vectors.rows() : m_vectors.cols();
  }

  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return rows(); }

  EIGEN_DEVICE_FUNC const EssentialVectorType essentialVector(Index k) const {
    eigen_assert(k >= 0 && k < m_length);
    return internal::hseq_side_dependent_impl<VectorsType, CoeffsType, Side>::essentialVector(*this, k);
  }

  TransposeReturnType transpose() const {
    return TransposeReturnType(m_vectors.conjugate(), m_coeffs)
        .setReverseFlag(!m_reverse)
        .setLength(m_length)
        .setShift(m_shift);
  }

  ConjugateReturnType conjugate() const {
    return ConjugateReturnType(m_vectors.conjugate(), m_coeffs.conjugate())
        .setReverseFlag(m_reverse)
        .setLength(m_length)
        .setShift(m_shift);
  }

  template <bool Cond>
  EIGEN_DEVICE_FUNC inline std::conditional_t<Cond, ConjugateReturnType, ConstHouseholderSequence> conjugateIf() const {
    typedef std::conditional_t<Cond, ConjugateReturnType, ConstHouseholderSequence> ReturnType;
    return ReturnType(m_vectors.template conjugateIf<Cond>(), m_coeffs.template conjugateIf<Cond>());
  }

  AdjointReturnType adjoint() const {
    return AdjointReturnType(m_vectors, m_coeffs.conjugate())
        .setReverseFlag(!m_reverse)
        .setLength(m_length)
        .setShift(m_shift);
  }

  AdjointReturnType inverse() const { return adjoint(); }

  template <typename DestType>
  inline EIGEN_DEVICE_FUNC void evalTo(DestType& dst) const {
    Matrix<Scalar, DestType::RowsAtCompileTime, 1, AutoAlign | ColMajor, DestType::MaxRowsAtCompileTime, 1> workspace(
        rows());
    evalTo(dst, workspace);
  }

  template <typename Dest, typename Workspace>
  EIGEN_DEVICE_FUNC void evalTo(Dest& dst, Workspace& workspace) const {
    workspace.resize(rows());
    Index vecs = m_length;
    if (internal::is_same_dense(dst, m_vectors)) {
      // in-place
      dst.diagonal().setOnes();
      dst.template triangularView<StrictlyUpper>().setZero();
      for (Index k = vecs - 1; k >= 0; --k) {
        Index cornerSize = rows() - k - m_shift;
        if (m_reverse)
          dst.bottomRightCorner(cornerSize, cornerSize)
              .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data());
        else
          dst.bottomRightCorner(cornerSize, cornerSize)
              .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data());

        // clear the off diagonal vector
        dst.col(k).tail(rows() - k - 1).setZero();
      }
      // clear the remaining columns if needed
      for (Index k = 0; k < cols() - vecs; ++k) dst.col(k).tail(rows() - k - 1).setZero();
    } else if (m_length > BlockSize) {
      dst.setIdentity(rows(), rows());
      if (m_reverse)
        applyThisOnTheLeft(dst, workspace, true);
      else
        applyThisOnTheLeft(dst, workspace, true);
    } else {
      dst.setIdentity(rows(), rows());
      for (Index k = vecs - 1; k >= 0; --k) {
        Index cornerSize = rows() - k - m_shift;
        if (m_reverse)
          dst.bottomRightCorner(cornerSize, cornerSize)
              .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data());
        else
          dst.bottomRightCorner(cornerSize, cornerSize)
              .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data());
      }
    }
  }

  template <typename Dest>
  inline void applyThisOnTheRight(Dest& dst) const {
    Matrix<Scalar, 1, Dest::RowsAtCompileTime, RowMajor, 1, Dest::MaxRowsAtCompileTime> workspace(dst.rows());
    applyThisOnTheRight(dst, workspace);
  }

  template <typename Dest, typename Workspace>
  inline void applyThisOnTheRight(Dest& dst, Workspace& workspace) const {
    workspace.resize(dst.rows());
    for (Index k = 0; k < m_length; ++k) {
      Index actual_k = m_reverse ? m_length - k - 1 : k;
      dst.rightCols(rows() - m_shift - actual_k)
          .applyHouseholderOnTheRight(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());
    }
  }

  template <typename Dest>
  inline void applyThisOnTheLeft(Dest& dst, bool inputIsIdentity = false) const {
    Matrix<Scalar, 1, Dest::ColsAtCompileTime, RowMajor, 1, Dest::MaxColsAtCompileTime> workspace;
    applyThisOnTheLeft(dst, workspace, inputIsIdentity);
  }

  template <typename Dest, typename Workspace>
  inline void applyThisOnTheLeft(Dest& dst, Workspace& workspace, bool inputIsIdentity = false) const {
    if (inputIsIdentity && m_reverse) inputIsIdentity = false;
    // if the entries are large enough, then apply the reflectors by block
    if (m_length >= BlockSize && dst.cols() > 1) {
      // Make sure we have at least 2 useful blocks, otherwise it is point-less:
      Index blockSize = m_length < Index(2 * BlockSize) ? (m_length + 1) / 2 : Index(BlockSize);
      for (Index i = 0; i < m_length; i += blockSize) {
        Index end = m_reverse ? (std::min)(m_length, i + blockSize) : m_length - i;
        Index k = m_reverse ? i : (std::max)(Index(0), end - blockSize);
        Index bs = end - k;
        Index start = k + m_shift;

        typedef Block<internal::remove_all_t<VectorsType>, Dynamic, Dynamic> SubVectorsType;
        SubVectorsType sub_vecs1(m_vectors.const_cast_derived(), Side == OnTheRight ? k : start,
                                 Side == OnTheRight ? start : k, Side == OnTheRight ? bs : m_vectors.rows() - start,
                                 Side == OnTheRight ? m_vectors.cols() - start : bs);
        std::conditional_t<Side == OnTheRight, Transpose<SubVectorsType>, SubVectorsType&> sub_vecs(sub_vecs1);

        Index dstRows = rows() - m_shift - k;

        if (inputIsIdentity) {
          Block<Dest, Dynamic, Dynamic> sub_dst = dst.bottomRightCorner(dstRows, dstRows);
          apply_block_householder_on_the_left(sub_dst, sub_vecs, m_coeffs.segment(k, bs), !m_reverse);
        } else {
          auto sub_dst = dst.bottomRows(dstRows);
          apply_block_householder_on_the_left(sub_dst, sub_vecs, m_coeffs.segment(k, bs), !m_reverse);
        }
      }
    } else {
      workspace.resize(dst.cols());
      for (Index k = 0; k < m_length; ++k) {
        Index actual_k = m_reverse ? k : m_length - k - 1;
        Index dstRows = rows() - m_shift - actual_k;

        if (inputIsIdentity) {
          Block<Dest, Dynamic, Dynamic> sub_dst = dst.bottomRightCorner(dstRows, dstRows);
          sub_dst.applyHouseholderOnTheLeft(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());
        } else {
          auto sub_dst = dst.bottomRows(dstRows);
          sub_dst.applyHouseholderOnTheLeft(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());
        }
      }
    }
  }

  template <typename OtherDerived>
  typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type operator*(
      const MatrixBase<OtherDerived>& other) const {
    typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type res(
        other.template cast<typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::ResultScalar>());
    applyThisOnTheLeft(res, internal::is_identity<OtherDerived>::value && res.rows() == res.cols());
    return res;
  }

  template <typename VectorsType_, typename CoeffsType_, int Side_>
  friend struct internal::hseq_side_dependent_impl;

  EIGEN_DEVICE_FUNC HouseholderSequence& setLength(Index length) {
    m_length = length;
    return *this;
  }

  EIGEN_DEVICE_FUNC HouseholderSequence& setShift(Index shift) {
    m_shift = shift;
    return *this;
  }

  EIGEN_DEVICE_FUNC Index length() const {
    return m_length;
  } 
  EIGEN_DEVICE_FUNC Index shift() const {
    return m_shift;
  } 
  /* Necessary for .adjoint() and .conjugate() */
  template <typename VectorsType2, typename CoeffsType2, int Side2>
  friend class HouseholderSequence;

 protected:
  HouseholderSequence& setReverseFlag(bool reverse) {
    m_reverse = reverse;
    return *this;
  }

  bool reverseFlag() const { return m_reverse; } 
  typename VectorsType::Nested m_vectors;
  typename CoeffsType::Nested m_coeffs;
  bool m_reverse;
  Index m_length;
  Index m_shift;
  enum { BlockSize = 48 };
};

template <typename OtherDerived, typename VectorsType, typename CoeffsType, int Side>
typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar, OtherDerived>::Type operator*(
    const MatrixBase<OtherDerived>& other, const HouseholderSequence<VectorsType, CoeffsType, Side>& h) {
  typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar, OtherDerived>::Type res(
      other.template cast<typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,
                                                                           OtherDerived>::ResultScalar>());
  h.applyThisOnTheRight(res);
  return res;
}

template <typename VectorsType, typename CoeffsType>
HouseholderSequence<VectorsType, CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h) {
  return HouseholderSequence<VectorsType, CoeffsType, OnTheLeft>(v, h);
}

template <typename VectorsType, typename CoeffsType>
HouseholderSequence<VectorsType, CoeffsType, OnTheRight> rightHouseholderSequence(const VectorsType& v,
                                                                                  const CoeffsType& h) {
  return HouseholderSequence<VectorsType, CoeffsType, OnTheRight>(v, h);
}

}  // end namespace Eigen

#endif  // EIGEN_HOUSEHOLDER_SEQUENCE_H