Eigen/src/Core/SelfAdjointView.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// 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_SELFADJOINTMATRIX_H
#define EIGEN_SELFADJOINTMATRIX_H

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

namespace Eigen {

/** \class SelfAdjointView
 * \ingroup Core_Module
 *
 *
 * \brief Expression of a selfadjoint matrix from a triangular part of a dense matrix
 *
 * \tparam MatrixType the type of the dense matrix storing the coefficients
 * \tparam TriangularPart can be either \c #Lower or \c #Upper
 *
 * This class is an expression of a sefladjoint matrix from a triangular part of a matrix
 * with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()
 * and most of the time this is the only way that it is used.
 *
 * \sa class TriangularBase, MatrixBase::selfadjointView()
 */

namespace internal {
template <typename MatrixType, unsigned int UpLo>
struct traits<SelfAdjointView<MatrixType, UpLo> > : traits<MatrixType> {
  typedef typename ref_selector<MatrixType>::non_const_type MatrixTypeNested;
  typedef remove_all_t<MatrixTypeNested> MatrixTypeNestedCleaned;
  typedef MatrixType ExpressionType;
  typedef typename MatrixType::PlainObject FullMatrixType;
  enum {
    Mode = UpLo | SelfAdjoint,
    FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
    Flags = MatrixTypeNestedCleaned::Flags & (HereditaryBits | FlagsLvalueBit) &
            (~(PacketAccessBit | DirectAccessBit | LinearAccessBit))  // FIXME these flags should be preserved
  };
};
}  // namespace internal

template <typename MatrixType_, unsigned int UpLo>
class SelfAdjointView : public TriangularBase<SelfAdjointView<MatrixType_, UpLo> > {
 public:
  EIGEN_STATIC_ASSERT(UpLo == Lower || UpLo == Upper, SELFADJOINTVIEW_ACCEPTS_UPPER_AND_LOWER_MODE_ONLY)

  typedef MatrixType_ MatrixType;
  typedef TriangularBase<SelfAdjointView> Base;
  typedef typename internal::traits<SelfAdjointView>::MatrixTypeNested MatrixTypeNested;
  typedef typename internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned;
  typedef MatrixTypeNestedCleaned NestedExpression;

  /** \brief The type of coefficients in this matrix */
  typedef typename internal::traits<SelfAdjointView>::Scalar Scalar;
  typedef typename MatrixType::StorageIndex StorageIndex;
  typedef internal::remove_all_t<typename MatrixType::ConjugateReturnType> MatrixConjugateReturnType;
  typedef SelfAdjointView<std::add_const_t<MatrixType>, UpLo> ConstSelfAdjointView;

  enum {
    Mode = internal::traits<SelfAdjointView>::Mode,
    Flags = internal::traits<SelfAdjointView>::Flags,
    TransposeMode = ((int(Mode) & int(Upper)) ? Lower : 0) | ((int(Mode) & int(Lower)) ? Upper : 0)
  };
  typedef typename MatrixType::PlainObject PlainObject;

  EIGEN_DEVICE_FUNC explicit inline SelfAdjointView(MatrixType& matrix) : m_matrix(matrix) {}

  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_matrix.rows(); }
  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_matrix.cols(); }
  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return m_matrix.outerStride(); }
  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_matrix.innerStride(); }

  /** \sa MatrixBase::coeff()
   * \warning the coordinates must fit into the referenced triangular part
   */
  EIGEN_DEVICE_FUNC inline Scalar coeff(Index row, Index col) const {
    Base::check_coordinates_internal(row, col);
    return m_matrix.coeff(row, col);
  }

  /** \sa MatrixBase::coeffRef()
   * \warning the coordinates must fit into the referenced triangular part
   */
  EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index col) {
    EIGEN_STATIC_ASSERT_LVALUE(SelfAdjointView);
    Base::check_coordinates_internal(row, col);
    return m_matrix.coeffRef(row, col);
  }

  /** \internal */
  EIGEN_DEVICE_FUNC const MatrixTypeNestedCleaned& _expression() const { return m_matrix; }

  EIGEN_DEVICE_FUNC const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
  EIGEN_DEVICE_FUNC MatrixTypeNestedCleaned& nestedExpression() { return m_matrix; }

  /** Efficient triangular matrix times vector/matrix product */
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC const Product<SelfAdjointView, OtherDerived> operator*(const MatrixBase<OtherDerived>& rhs) const {
    return Product<SelfAdjointView, OtherDerived>(*this, rhs.derived());
  }

  /** Efficient vector/matrix times triangular matrix product */
  template <typename OtherDerived>
  friend EIGEN_DEVICE_FUNC const Product<OtherDerived, SelfAdjointView> operator*(const MatrixBase<OtherDerived>& lhs,
                                                                                  const SelfAdjointView& rhs) {
    return Product<OtherDerived, SelfAdjointView>(lhs.derived(), rhs);
  }

  friend EIGEN_DEVICE_FUNC const
      SelfAdjointView<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar, MatrixType, product), UpLo>
      operator*(const Scalar& s, const SelfAdjointView& mat) {
    return (s * mat.nestedExpression()).template selfadjointView<UpLo>();
  }

  /** Perform a symmetric rank 2 update of the selfadjoint matrix \c *this:
   * \f$ this = this + \alpha u v^* + conj(\alpha) v u^* \f$
   * \returns a reference to \c *this
   *
   * The vectors \a u and \c v \b must be column vectors, however they can be
   * a adjoint expression without any overhead. Only the meaningful triangular
   * part of the matrix is updated, the rest is left unchanged.
   *
   * \sa rankUpdate(const MatrixBase<DerivedU>&, Scalar)
   */
  template <typename DerivedU, typename DerivedV>
  EIGEN_DEVICE_FUNC SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v,
                                                const Scalar& alpha = Scalar(1));

  /** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
   * \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
   *
   * \returns a reference to \c *this
   *
   * Note that to perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
   * call this function with u.adjoint().
   *
   * \sa rankUpdate(const MatrixBase<DerivedU>&, const MatrixBase<DerivedV>&, Scalar)
   */
  template <typename DerivedU>
  EIGEN_DEVICE_FUNC SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));

  /** \returns an expression of a triangular view extracted from the current selfadjoint view of a given triangular part
   *
   * The parameter \a TriMode can have the following values: \c #Upper, \c #StrictlyUpper, \c #UnitUpper,
   * \c #Lower, \c #StrictlyLower, \c #UnitLower.
   *
   * If \c TriMode references the same triangular part than \c *this, then this method simply return a \c TriangularView
   * of the nested expression, otherwise, the nested expression is first transposed, thus returning a \c
   * TriangularView<Transpose<MatrixType>> object.
   *
   * \sa MatrixBase::triangularView(), class TriangularView
   */
  template <unsigned int TriMode>
  EIGEN_DEVICE_FUNC
      std::conditional_t<(TriMode & (Upper | Lower)) == (UpLo & (Upper | Lower)), TriangularView<MatrixType, TriMode>,
                         TriangularView<typename MatrixType::AdjointReturnType, TriMode> >
      triangularView() const {
    std::conditional_t<(TriMode & (Upper | Lower)) == (UpLo & (Upper | Lower)), MatrixType&,
                       typename MatrixType::ConstTransposeReturnType>
        tmp1(m_matrix);
    std::conditional_t<(TriMode & (Upper | Lower)) == (UpLo & (Upper | Lower)), MatrixType&,
                       typename MatrixType::AdjointReturnType>
        tmp2(tmp1);
    return std::conditional_t<(TriMode & (Upper | Lower)) == (UpLo & (Upper | Lower)),
                              TriangularView<MatrixType, TriMode>,
                              TriangularView<typename MatrixType::AdjointReturnType, TriMode> >(tmp2);
  }

  typedef SelfAdjointView<const MatrixConjugateReturnType, UpLo> ConjugateReturnType;
  /** \sa MatrixBase::conjugate() const */
  EIGEN_DEVICE_FUNC inline const ConjugateReturnType conjugate() const {
    return ConjugateReturnType(m_matrix.conjugate());
  }

  /** \returns an expression of the complex conjugate of \c *this if Cond==true,
   *           returns \c *this otherwise.
   */
  template <bool Cond>
  EIGEN_DEVICE_FUNC inline std::conditional_t<Cond, ConjugateReturnType, ConstSelfAdjointView> conjugateIf() const {
    typedef std::conditional_t<Cond, ConjugateReturnType, ConstSelfAdjointView> ReturnType;
    return ReturnType(m_matrix.template conjugateIf<Cond>());
  }

  typedef SelfAdjointView<const typename MatrixType::AdjointReturnType, TransposeMode> AdjointReturnType;
  /** \sa MatrixBase::adjoint() const */
  EIGEN_DEVICE_FUNC inline const AdjointReturnType adjoint() const { return AdjointReturnType(m_matrix.adjoint()); }

  typedef SelfAdjointView<typename MatrixType::TransposeReturnType, TransposeMode> TransposeReturnType;
  /** \sa MatrixBase::transpose() */
  template <class Dummy = int>
  EIGEN_DEVICE_FUNC inline TransposeReturnType transpose(
      std::enable_if_t<Eigen::internal::is_lvalue<MatrixType>::value, Dummy*> = nullptr) {
    typename MatrixType::TransposeReturnType tmp(m_matrix);
    return TransposeReturnType(tmp);
  }

  typedef SelfAdjointView<const typename MatrixType::ConstTransposeReturnType, TransposeMode> ConstTransposeReturnType;
  /** \sa MatrixBase::transpose() const */
  EIGEN_DEVICE_FUNC inline const ConstTransposeReturnType transpose() const {
    return ConstTransposeReturnType(m_matrix.transpose());
  }

  /** \returns a const expression of the main diagonal of the matrix \c *this
   *
   * This method simply returns the diagonal of the nested expression, thus by-passing the SelfAdjointView decorator.
   *
   * \sa MatrixBase::diagonal(), class Diagonal */
  EIGEN_DEVICE_FUNC typename MatrixType::ConstDiagonalReturnType diagonal() const {
    return typename MatrixType::ConstDiagonalReturnType(m_matrix);
  }

  /////////// Cholesky module ///////////

  LLT<PlainObject, UpLo> llt() const;
  LDLT<PlainObject, UpLo> ldlt() const;

  /////////// Eigenvalue module ///////////

  /** Real part of #Scalar */
  typedef typename NumTraits<Scalar>::Real RealScalar;
  /** Return type of eigenvalues() */
  typedef Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1> EigenvaluesReturnType;

  EIGEN_DEVICE_FUNC EigenvaluesReturnType eigenvalues() const;
  EIGEN_DEVICE_FUNC RealScalar operatorNorm() const;

 protected:
  MatrixTypeNested m_matrix;
};

// selfadjoint to dense matrix

namespace internal {

// TODO currently a selfadjoint expression has the form SelfAdjointView<.,.>
//      in the future selfadjoint-ness should be defined by the expression traits
//      such that Transpose<SelfAdjointView<.,.> > is valid. (currently TriangularBase::transpose() is overloaded to
//      make it work)
template <typename MatrixType, unsigned int Mode>
struct evaluator_traits<SelfAdjointView<MatrixType, Mode> > {
  typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;
  typedef SelfAdjointShape Shape;
};

template <int UpLo, int SetOpposite, typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT, typename Functor,
          int Version>
class triangular_dense_assignment_kernel<UpLo, SelfAdjoint, SetOpposite, DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor,
                                         Version>
    : public generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version> {
 protected:
  typedef generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version> Base;
  typedef typename Base::DstXprType DstXprType;
  typedef typename Base::SrcXprType SrcXprType;
  using Base::m_dst;
  using Base::m_functor;
  using Base::m_src;

 public:
  typedef typename Base::DstEvaluatorType DstEvaluatorType;
  typedef typename Base::SrcEvaluatorType SrcEvaluatorType;
  typedef typename Base::Scalar Scalar;
  typedef typename Base::AssignmentTraits AssignmentTraits;

  EIGEN_DEVICE_FUNC triangular_dense_assignment_kernel(DstEvaluatorType& dst, const SrcEvaluatorType& src,
                                                       const Functor& func, DstXprType& dstExpr)
      : Base(dst, src, func, dstExpr) {}

  EIGEN_DEVICE_FUNC void assignCoeff(Index row, Index col) {
    eigen_internal_assert(row != col);
    Scalar tmp = m_src.coeff(row, col);
    m_functor.assignCoeff(m_dst.coeffRef(row, col), tmp);
    m_functor.assignCoeff(m_dst.coeffRef(col, row), numext::conj(tmp));
  }

  // Override to ensure the SelfAdjoint assignCoeff (which mirrors conjugates) is called,
  // not the base class version (which is a plain copy).
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeffByOuterInner(Index outer, Index inner) {
    Index row = Base::rowIndexByOuterInner(outer, inner);
    Index col = Base::colIndexByOuterInner(outer, inner);
    assignCoeff(row, col);
  }

  EIGEN_DEVICE_FUNC void assignDiagonalCoeff(Index id) { Base::assignCoeff(id, id); }

  EIGEN_DEVICE_FUNC void assignOppositeCoeff(Index, Index) { eigen_internal_assert(false && "should never be called"); }
};

}  // end namespace internal

/***************************************************************************
 * Implementation of MatrixBase methods
 ***************************************************************************/

/** This is the const version of MatrixBase::selfadjointView() */
template <typename Derived>
template <unsigned int UpLo>
EIGEN_DEVICE_FUNC constexpr typename MatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type
MatrixBase<Derived>::selfadjointView() const {
  return typename ConstSelfAdjointViewReturnType<UpLo>::Type(derived());
}

/** \returns an expression of a symmetric/self-adjoint view extracted from the upper or lower triangular part of the
 * current matrix
 *
 * The parameter \a UpLo can be either \c #Upper or \c #Lower
 *
 * Example: \include MatrixBase_selfadjointView.cpp
 * Output: \verbinclude MatrixBase_selfadjointView.out
 *
 * \sa class SelfAdjointView
 */
template <typename Derived>
template <unsigned int UpLo>
EIGEN_DEVICE_FUNC constexpr typename MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type
MatrixBase<Derived>::selfadjointView() {
  return typename SelfAdjointViewReturnType<UpLo>::Type(derived());
}

}  // end namespace Eigen

#endif  // EIGEN_SELFADJOINTMATRIX_H