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// 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
#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
};
};
}
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 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
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 ///////////
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