Eigen::SelfAdjointView

template<typename _MatrixType, unsigned int UpLo>
class Eigen::SelfAdjointView< _MatrixType, UpLo >

Expression of a selfadjoint matrix from a triangular part of a dense matrix.

Parameters

MatrixType	the type of the dense matrix storing the coefficients
TriangularPart	can be either `Lower` or `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.

See also: class TriangularBase, MatrixBase::selfadjointView()


typedef Matrix< RealScalar, internal::traits< MatrixType >::ColsAtCompileTime, 1 >	EigenvaluesReturnType

typedef NumTraits< Scalar >::Real	RealScalar

typedef internal::traits< SelfAdjointView >::Scalar	Scalar
	The type of coefficients in this matrix.

Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index	Index
	The interface type of indices. More...


const AdjointReturnType	adjoint () const

Scalar	coeff (Index row, Index col) const

Scalar &	coeffRef (Index row, Index col)

const ConjugateReturnType	conjugate () const

template<bool Cond>
internal::conditional< Cond, ConjugateReturnType, ConstSelfAdjointView >::type	conjugateIf () const

MatrixType::ConstDiagonalReturnType	diagonal () const

EigenvaluesReturnType	eigenvalues () const
	Computes the eigenvalues of a matrix. More...

const LDLT< PlainObject, UpLo >	ldlt () const

const LLT< PlainObject, UpLo >	llt () const

template<typename OtherDerived >
const Product< SelfAdjointView, OtherDerived >	operator* (const MatrixBase< OtherDerived > &rhs) const

RealScalar	operatorNorm () const
	Computes the L2 operator norm. More...

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

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

TransposeReturnType	transpose ()

const ConstTransposeReturnType	transpose () const

template<unsigned int TriMode>
internal::conditional<(TriMode &(Upper\|Lower))==(UpLo &(Upper\|Lower)), TriangularView< MatrixType, TriMode >, TriangularView< typename MatrixType::AdjointReturnType, TriMode > >::type	triangularView () const

Public Member Functions inherited from Eigen::TriangularBase< SelfAdjointView< _MatrixType, UpLo > >
void	copyCoeff (Index row, Index col, Other &other)

void	evalTo (MatrixBase< DenseDerived > &other) const

void	evalToLazy (MatrixBase< DenseDerived > &other) const

Public Member Functions inherited from Eigen::EigenBase< Derived >
EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

Derived &	derived ()

const Derived &	derived () const

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

EigenvaluesReturnType

template<typename _MatrixType , unsigned int UpLo>

typedef Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1> Eigen::SelfAdjointView< _MatrixType, UpLo >::EigenvaluesReturnType

Return type of eigenvalues()

RealScalar

template<typename _MatrixType , unsigned int UpLo>

typedef NumTraits<Scalar>::Real Eigen::SelfAdjointView< _MatrixType, UpLo >::RealScalar

Real part of Scalar

adjoint()

template<typename _MatrixType , unsigned int UpLo>

const AdjointReturnType Eigen::SelfAdjointView< _MatrixType, UpLo >::adjoint

(

)

const

inline

See also: MatrixBase::adjoint() const

coeff()

template<typename _MatrixType , unsigned int UpLo>

Scalar Eigen::SelfAdjointView< _MatrixType, UpLo >::coeff	(	Index	row,
		Index	col
	)		const

inline

See also: MatrixBase::coeff()

Warning: the coordinates must fit into the referenced triangular part

coeffRef()

template<typename _MatrixType , unsigned int UpLo>

Scalar& Eigen::SelfAdjointView< _MatrixType, UpLo >::coeffRef	(	Index	row,
		Index	col
	)

inline

See also: MatrixBase::coeffRef()

Warning: the coordinates must fit into the referenced triangular part

conjugate()

template<typename _MatrixType , unsigned int UpLo>

const ConjugateReturnType Eigen::SelfAdjointView< _MatrixType, UpLo >::conjugate

(

void

)

const

inline

See also: MatrixBase::conjugate() const

conjugateIf()

template<typename _MatrixType , unsigned int UpLo>

template<bool Cond>

internal::conditional<Cond,ConjugateReturnType,ConstSelfAdjointView>::type Eigen::SelfAdjointView< _MatrixType, UpLo >::conjugateIf

(

)

const

inline

Returns: an expression of the complex conjugate of *this if Cond==true, returns *this otherwise.

diagonal()

template<typename _MatrixType , unsigned int UpLo>

MatrixType::ConstDiagonalReturnType Eigen::SelfAdjointView< _MatrixType, UpLo >::diagonal

(

)

const

inline

Returns: a const expression of the main diagonal of the matrix *this

This method simply returns the diagonal of the nested expression, thus by-passing the SelfAdjointView decorator.

See also: MatrixBase::diagonal(), class Diagonal

eigenvalues()

template<typename MatrixType , unsigned int UpLo>

SelfAdjointView< MatrixType, UpLo >::EigenvaluesReturnType Eigen::SelfAdjointView< MatrixType, UpLo >::eigenvalues

inline

Computes the eigenvalues of a matrix.

Returns: Column vector containing the eigenvalues.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues>

This function computes the eigenvalues with the help of the SelfAdjointEigenSolver class. The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix.

Example:

MatrixXd ones = MatrixXd::Ones(3,3);
VectorXd eivals = ones.selfadjointView<Lower>().eigenvalues();
cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;

Output:

The eigenvalues of the 3x3 matrix of ones are:
-3.09e-16
        0
        3

See also: SelfAdjointEigenSolver::eigenvalues(), MatrixBase::eigenvalues()

ldlt()

template<typename MatrixType , unsigned int UpLo>

const LDLT< typename SelfAdjointView< MatrixType, UpLo >::PlainObject, UpLo > Eigen::SelfAdjointView< MatrixType, UpLo >::ldlt

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>

Returns: the Cholesky decomposition with full pivoting without square root of *this

See also: MatrixBase::ldlt()

llt()

template<typename MatrixType , unsigned int UpLo>

const LLT< typename SelfAdjointView< MatrixType, UpLo >::PlainObject, UpLo > Eigen::SelfAdjointView< MatrixType, UpLo >::llt

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>

Returns: the LLT decomposition of *this

See also: SelfAdjointView::llt()

operator*()

template<typename _MatrixType , unsigned int UpLo>

template<typename OtherDerived >

const Product<SelfAdjointView,OtherDerived> Eigen::SelfAdjointView< _MatrixType, UpLo >::operator*

(

const MatrixBase< OtherDerived > &

rhs

)

const

inline

Efficient triangular matrix times vector/matrix product

operatorNorm()

template<typename MatrixType , unsigned int UpLo>

SelfAdjointView< MatrixType, UpLo >::RealScalar Eigen::SelfAdjointView< MatrixType, UpLo >::operatorNorm

inline

Computes the L2 operator norm.

Returns: Operator norm of the matrix.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues>

This function computes the L2 operator norm of a self-adjoint matrix. For a self-adjoint matrix, the operator norm is the largest eigenvalue.

The current implementation uses the eigenvalues of the matrix, as computed by eigenvalues(), to compute the operator norm of the matrix.

Example:

MatrixXd ones = MatrixXd::Ones(3,3);
cout << "The operator norm of the 3x3 matrix of ones is "
     << ones.selfadjointView<Lower>().operatorNorm() << endl;

Output:

The operator norm of the 3x3 matrix of ones is 3

See also: eigenvalues(), MatrixBase::operatorNorm()

rankUpdate() [1/2]

template<typename _MatrixType , unsigned int UpLo>

template<typename DerivedU , typename DerivedV >

SelfAdjointView& Eigen::SelfAdjointView< _MatrixType, UpLo >::rankUpdate	(	const MatrixBase< DerivedU > &	u,
		const MatrixBase< DerivedV > &	v,
		const Scalar &	alpha = `Scalar(1)`
	)

Perform a symmetric rank 2 update of the selfadjoint matrix *this: \( this = this + \alpha u v^* + conj(\alpha) v u^* \)

Returns: a reference to *this

The vectors u and v 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.

See also: rankUpdate(const MatrixBase<DerivedU>&, Scalar)

rankUpdate() [2/2]

template<typename _MatrixType , unsigned int UpLo>

template<typename DerivedU >

SelfAdjointView& Eigen::SelfAdjointView< _MatrixType, UpLo >::rankUpdate	(	const MatrixBase< DerivedU > &	u,
		const Scalar &	alpha = `Scalar(1)`
	)

Perform a symmetric rank K update of the selfadjoint matrix *this: \( this = this + \alpha ( u u^* ) \) where u is a vector or matrix.

Returns: a reference to *this

Note that to perform \( this = this + \alpha ( u^* u ) \) you can simply call this function with u.adjoint().

See also: rankUpdate(const MatrixBase<DerivedU>&, const MatrixBase<DerivedV>&, Scalar)

transpose() [1/2]

template<typename _MatrixType , unsigned int UpLo>

TransposeReturnType Eigen::SelfAdjointView< _MatrixType, UpLo >::transpose

(

)

inline

See also: MatrixBase::transpose()

transpose() [2/2]

template<typename _MatrixType , unsigned int UpLo>

const ConstTransposeReturnType Eigen::SelfAdjointView< _MatrixType, UpLo >::transpose

(

)

const

inline

See also: MatrixBase::transpose() const

triangularView()

template<typename _MatrixType , unsigned int UpLo>

template<unsigned int TriMode>

internal::conditional<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)), TriangularView<MatrixType,TriMode>, TriangularView<typename MatrixType::AdjointReturnType,TriMode> >::type Eigen::SelfAdjointView< _MatrixType, UpLo >::triangularView

(

)

const

inline

Returns: an expression of a triangular view extracted from the current selfadjoint view of a given triangular part

The parameter TriMode can have the following values: Upper, StrictlyUpper, UnitUpper, Lower, StrictlyLower, UnitLower.

If TriMode references the same triangular part than *this, then this method simply return a TriangularView of the nested expression, otherwise, the nested expression is first transposed, thus returning a TriangularView<Transpose<MatrixType>> object.

See also: MatrixBase::triangularView(), class TriangularView

The documentation for this class was generated from the following files:

Eigen::SelfAdjointView

template<typename _MatrixType, unsigned int UpLo> class Eigen::SelfAdjointView< _MatrixType, UpLo >

EigenvaluesReturnType

RealScalar

adjoint()

coeff()

coeffRef()

conjugate()

conjugateIf()

diagonal()

eigenvalues()

ldlt()

llt()

operator*()

operatorNorm()

rankUpdate() [1/2]

rankUpdate() [2/2]

transpose() [1/2]

transpose() [2/2]

triangularView()

template<typename _MatrixType, unsigned int UpLo>
class Eigen::SelfAdjointView< _MatrixType, UpLo >