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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/.
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/** \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 nested<MatrixType>::type MatrixTypeNested;
typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
typedef MatrixType ExpressionType;
typedef typename MatrixType::PlainObject DenseMatrixType;
enum {
Mode = UpLo | SelfAdjoint,
Flags = MatrixTypeNestedCleaned::Flags & (HereditaryBits)
& (~(PacketAccessBit | DirectAccessBit | LinearAccessBit)), // FIXME these flags should be preserved
CoeffReadCost = MatrixTypeNestedCleaned::CoeffReadCost
};
};
}
template <typename Lhs, int LhsMode, bool LhsIsVector,
typename Rhs, int RhsMode, bool RhsIsVector>
struct SelfadjointProductMatrix;
// FIXME could also be called SelfAdjointWrapper to be consistent with DiagonalWrapper ??
template<typename MatrixType, unsigned int UpLo> class SelfAdjointView
: public TriangularBase<SelfAdjointView<MatrixType, UpLo> >
{
public:
typedef TriangularBase<SelfAdjointView> Base;
typedef typename internal::traits<SelfAdjointView>::MatrixTypeNested MatrixTypeNested;
typedef typename internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned;
/** \brief The type of coefficients in this matrix */
typedef typename internal::traits<SelfAdjointView>::Scalar Scalar;
typedef typename MatrixType::Index Index;
enum {
Mode = internal::traits<SelfAdjointView>::Mode
};
typedef typename MatrixType::PlainObject PlainObject;
inline SelfAdjointView(MatrixType& matrix) : m_matrix(matrix)
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{}
inline Index rows() const { return m_matrix.rows(); }
inline Index cols() const { return m_matrix.cols(); }
inline Index outerStride() const { return m_matrix.outerStride(); }
inline Index innerStride() const { return m_matrix.innerStride(); }
/** \sa MatrixBase::coeff()
* \warning the coordinates must fit into the referenced triangular part
*/
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
*/
inline Scalar& coeffRef(Index row, Index col)
{
Base::check_coordinates_internal(row, col);
return m_matrix.const_cast_derived().coeffRef(row, col);
}
/** \internal */
const MatrixTypeNestedCleaned& _expression() const { return m_matrix; }
const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
MatrixTypeNestedCleaned& nestedExpression() { return *const_cast<MatrixTypeNestedCleaned*>(&m_matrix); }
/** Efficient self-adjoint matrix times vector/matrix product */
template<typename OtherDerived>
SelfadjointProductMatrix<MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime>
operator*(const MatrixBase<OtherDerived>& rhs) const
{
return SelfadjointProductMatrix
<MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime>
(m_matrix, rhs.derived());
}
/** Efficient vector/matrix times self-adjoint matrix product */
template<typename OtherDerived> friend
SelfadjointProductMatrix<OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false>
operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView& rhs)
{
return SelfadjointProductMatrix
<OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false>
(lhs.derived(),rhs.m_matrix);
}
/** 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>
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>
SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));
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/////////// 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;
EigenvaluesReturnType eigenvalues() const;
RealScalar operatorNorm() const;
#ifdef EIGEN2_SUPPORT
template<typename OtherDerived>
SelfAdjointView& operator=(const MatrixBase<OtherDerived>& other)
{
enum {
OtherPart = UpLo == Upper ? StrictlyLower : StrictlyUpper
};
m_matrix.const_cast_derived().template triangularView<UpLo>() = other;
m_matrix.const_cast_derived().template triangularView<OtherPart>() = other.adjoint();
return *this;
}
template<typename OtherMatrixType, unsigned int OtherMode>
SelfAdjointView& operator=(const TriangularView<OtherMatrixType, OtherMode>& other)
{
enum {
OtherPart = UpLo == Upper ? StrictlyLower : StrictlyUpper
};
m_matrix.const_cast_derived().template triangularView<UpLo>() = other.toDenseMatrix();
m_matrix.const_cast_derived().template triangularView<OtherPart>() = other.toDenseMatrix().adjoint();
return *this;
}
#endif
protected:
};
// 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 {
template<typename Derived1, typename Derived2, int UnrollCount, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), UnrollCount, ClearOpposite>
{
enum {
col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
row = (UnrollCount-1) % Derived1::RowsAtCompileTime
};
static inline void run(Derived1 &dst, const Derived2 &src)
{
triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), UnrollCount-1, ClearOpposite>::run(dst, src);
if(row == col)
dst.coeffRef(row, col) = numext::real(src.coeff(row, col));
dst.coeffRef(col, row) = numext::conj(dst.coeffRef(row, col) = src.coeff(row, col));
}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, 0, ClearOpposite>
{
static inline void run(Derived1 &, const Derived2 &) {}
};
template<typename Derived1, typename Derived2, int UnrollCount, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), UnrollCount, ClearOpposite>
{
enum {
col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
row = (UnrollCount-1) % Derived1::RowsAtCompileTime
};
static inline void run(Derived1 &dst, const Derived2 &src)
{
triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), UnrollCount-1, ClearOpposite>::run(dst, src);
if(row == col)
dst.coeffRef(row, col) = numext::real(src.coeff(row, col));
dst.coeffRef(col, row) = numext::conj(dst.coeffRef(row, col) = src.coeff(row, col));
}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, 0, ClearOpposite>
{
static inline void run(Derived1 &, const Derived2 &) {}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, Dynamic, ClearOpposite>
{
typedef typename Derived1::Index Index;
static inline void run(Derived1 &dst, const Derived2 &src)
{
for(Index j = 0; j < dst.cols(); ++j)
{
for(Index i = 0; i < j; ++i)
{
dst.copyCoeff(i, j, src);
}
dst.copyCoeff(j, j, src);
}
}
};
template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, Dynamic, ClearOpposite>
{
static inline void run(Derived1 &dst, const Derived2 &src)
{
typedef typename Derived1::Index Index;
for(Index i = 0; i < dst.rows(); ++i)
{
for(Index j = 0; j < i; ++j)
{
dst.copyCoeff(i, j, src);
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}
dst.copyCoeff(i, i, src);
}
}
};
} // end namespace internal
/***************************************************************************
* Implementation of MatrixBase methods
***************************************************************************/
template<typename Derived>
template<unsigned int UpLo>
typename MatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type
MatrixBase<Derived>::selfadjointView() const
{
return derived();
}
template<typename Derived>
template<unsigned int UpLo>
typename MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type
MatrixBase<Derived>::selfadjointView()
{
return derived();
}