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/.
// SPDX-License-Identifier: MPL-2.0
 
#ifndef EIGEN_SELFADJOINTMATRIX_H
#define EIGEN_SELFADJOINTMATRIX_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {

 
namespace internal {
 
template <typename MatrixType, unsigned int UpLo>
struct traits<SelfAdjointView<MatrixType, UpLo>> : traits<MatrixType> {
  using MatrixTypeNested = typename ref_selector<MatrixType>::non_const_type;
  using MatrixTypeNestedCleaned = remove_all_t<MatrixTypeNested>;
  using ExpressionType = MatrixType;
  using FullMatrixType = typename MatrixType::PlainObject;
  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)
 
  using MatrixType = MatrixType_;
  using Base = TriangularBase<SelfAdjointView>;
  using MatrixTypeNested = typename internal::traits<SelfAdjointView>::MatrixTypeNested;
  using MatrixTypeNestedCleaned = typename internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned;
  using NestedExpression = MatrixTypeNestedCleaned;

  using Scalar = typename internal::traits<SelfAdjointView>::Scalar;
  using RealScalar = typename NumTraits<Scalar>::Real;
  using StorageIndex = typename MatrixType::StorageIndex;
 
  enum {
    Mode = internal::traits<SelfAdjointView>::Mode,
    Flags = internal::traits<SelfAdjointView>::Flags,
    TransposeMode = ((int(Mode) & int(Upper)) ? Lower : 0) | ((int(Mode) & int(Lower)) ? Upper : 0)
  };
  using PlainObject = typename MatrixType::PlainObject;
 
  EIGEN_DEVICE_FUNC explicit inline SelfAdjointView(MatrixType& matrix) : m_matrix(matrix) {}
  using Base::operator*;
  EIGEN_DEFAULT_COPY_CONSTRUCTOR(SelfAdjointView)
 
  
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC SelfAdjointView& operator=(const MatrixBase<OtherDerived>& other) {
    m_matrix.template triangularView<UpLo>() = other;
    return *this;
  }

  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC SelfAdjointView& operator=(const TriangularBase<OtherDerived>& other) {
    other.evalToLazy(m_matrix);
    return *this;
  }
 
  EIGEN_DEVICE_FUNC SelfAdjointView& operator=(const SelfAdjointView& other) {
    return *this = static_cast<const Base&>(other);
  }

  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC SelfAdjointView& operator+=(const DenseBase<OtherDerived>& other) {
    m_matrix.template triangularView<UpLo>() += other;
    return *this;
  }

  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC SelfAdjointView& operator-=(const DenseBase<OtherDerived>& other) {
    m_matrix.template triangularView<UpLo>() -= other;
    return *this;
  }

  EIGEN_DEVICE_FUNC SelfAdjointView& operator*=(const Scalar& other) {
    eigen_assert(numext::imag(other) == typename NumTraits<Scalar>::Real(0) &&
                 "SelfAdjointView in-place scaling requires a real scalar; "
                 "scaling only the stored triangle by a non-real scalar would "
                 "leave conj(other) on the unstored half.");
    m_matrix.template triangularView<UpLo>() *= other;
    return *this;
  }

  EIGEN_DEVICE_FUNC SelfAdjointView& operator/=(const Scalar& other) {
    eigen_assert(numext::imag(other) == typename NumTraits<Scalar>::Real(0) &&
                 "SelfAdjointView in-place division requires a real scalar; "
                 "dividing only the stored triangle by a non-real scalar would "
                 "leave conj(other) on the unstored half.");
    m_matrix.template triangularView<UpLo>() /= other;
    return *this;
  }

  EIGEN_DEVICE_FUNC constexpr const MatrixTypeNestedCleaned& _expression() const noexcept { return m_matrix; }
 
  EIGEN_DEVICE_FUNC constexpr const MatrixTypeNestedCleaned& nestedExpression() const noexcept { return m_matrix; }
  EIGEN_DEVICE_FUNC constexpr MatrixTypeNestedCleaned& nestedExpression() noexcept { return m_matrix; }
 
  EIGEN_DEVICE_FUNC const SelfAdjointView<
      const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(MatrixType, Scalar, internal::scalar_product_op), UpLo>
  operator*(const Scalar& s) const {
    return (nestedExpression() * s).template selfadjointView<UpLo>();
  }
 
  friend EIGEN_DEVICE_FUNC const SelfAdjointView<
      const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar, MatrixType, internal::scalar_product_op), UpLo>
  operator*(const Scalar& s, const SelfAdjointView& mat) {
    return (s * mat.nestedExpression()).template selfadjointView<UpLo>();
  }

  template <typename DerivedU, typename DerivedV>
  EIGEN_DEVICE_FUNC SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v,
                                                const Scalar& alpha = Scalar(1));

  template <typename DerivedU>
  EIGEN_DEVICE_FUNC SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));

  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);
  }

  EIGEN_DEVICE_FUNC typename MatrixType::ConstDiagonalReturnType diagonal() const {
    return typename MatrixType::ConstDiagonalReturnType(m_matrix);
  }

  EIGEN_DEVICE_FUNC RealScalar l1Norm() const { return internal::selfadjoint_l1_norm<UpLo>(m_matrix); }

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


  using EigenvaluesReturnType = Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1>;
 
  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> > {
  using Kind = typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind;
  using Shape = SelfAdjointShape;
};
 
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:
  using Base = generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version>;
  using DstXprType = typename Base::DstXprType;
  using SrcXprType = typename Base::SrcXprType;
  using Base::m_dst;
  using Base::m_functor;
  using Base::m_src;
 
 public:
  using DstEvaluatorType = typename Base::DstEvaluatorType;
  using SrcEvaluatorType = typename Base::SrcEvaluatorType;
  using Scalar = typename Base::Scalar;
  using AssignmentTraits = typename Base::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
 ***************************************************************************/

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());
}

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