Ziele Untersuchung
mit Columbo Integrität von
Datenbanken Interaktion und
Portierbarkeit Ergonomie der
Schnittstellen

Angebot Produkte Projekt Beratung

Mittel Analytik Modellierung Sprachen Algebra Logik Hardware Denken Kreativität

Zusammenhänge Gesellschaft Wirtschaft Branche Firma


products/sources/formale Sprachen/C/MySQL/Eigen/src/Core/ (MySQL Server Version 8.1-8.4^©) Datei vom 12.11.2025 mit Größe 14 kB

Quelle SelfAdjointView.h Sprache: C

// 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

namespace Eigen {

/** \class SelfAdjointView
  * \ingroup Core_Module
  *
  *
  * \brief Expression of a selfadjoint matrix from a triangular part of a dense matrix
  *
  * \param MatrixType the type of the dense matrix storing the coefficients
  * \param 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 typename remove_all<MatrixTypeNested>::type 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
  };
};
}

template<typename _MatrixType, unsigned int UpLo> class SelfAdjointView
  : public TriangularBase<SelfAdjointView<_MatrixType, UpLo> >
{
  public:

    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 typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type MatrixConjugateReturnType;
    typedef SelfAdjointView<typename internal::add_const<MatrixType>::type, 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_STATIC_ASSERT(UpLo==Lower || UpLo==Upper,SELFADJOINTVIEW_ACCEPTS_UPPER_AND_LOWER_MODE_ONLY);
    }

    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
    inline Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
    inline Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
    inline Index outerStride() const EIGEN_NOEXCEPT { return m_matrix.outerStride(); }
    EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
    inline Index innerStride() const EIGEN_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
    typename internal::conditional<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)),
                                   TriangularView<MatrixType,TriMode>,
                                   TriangularView<typename MatrixType::AdjointReturnType,TriMode> >::type
    triangularView() const
    {
      typename internal::conditional<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)), MatrixType&, typename MatrixType::ConstTransposeReturnType>::type tmp1(m_matrix);
      typename internal::conditional<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)), MatrixType&, typename MatrixType::AdjointReturnType>::type tmp2(tmp1);
      return typename internal::conditional<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)),
                                   TriangularView<MatrixType,TriMode>,
                                   TriangularView<typename MatrixType::AdjointReturnType,TriMode> >::type(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 typename internal::conditional<Cond,ConjugateReturnType,ConstSelfAdjointView>::type
    conjugateIf() const
    {
      typedef typename internal::conditional<Cond,ConjugateReturnType,ConstSelfAdjointView>::type 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() */
    EIGEN_DEVICE_FUNC
    inline TransposeReturnType transpose()
    {
      EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
      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 ///////////

    const LLT<PlainObject, UpLo> llt() const;
    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;
};

// template<typename OtherDerived, typename MatrixType, unsigned int UpLo>
// internal::selfadjoint_matrix_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >
// operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView<MatrixType,UpLo>& rhs)
// {
//   return internal::matrix_selfadjoint_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >(lhs.derived(),rhs);
// }

// 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_src;
  using Base::m_functor;
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));
  }

  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 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 typename MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type
MatrixBase<Derived>::selfadjointView()
{
  return typename SelfAdjointViewReturnType<UpLo>::Type(derived());
}

} // end namespace Eigen

#endif // EIGEN_SELFADJOINTMATRIX_H

quality100%

¤ Dauer der Verarbeitung: 0.21 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.