Detailed Description

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()

Inherits TriangularBase< Derived >.

Public Types
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 Member Functions
Scalar	coeff (Index row, Index col) const

Scalar &	coeffRef (Index row, Index col)

template<typename Other >
void	copyCoeff (Index row, Index col, Other &other)

Derived &	derived ()

const Derived &	derived () const

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

template<typename DenseDerived >
void	evalTo (MatrixBase< DenseDerived > &other) const

template<typename DenseDerived >
void	evalToLazy (MatrixBase< DenseDerived > &other) const

const LDLT< PlainObject, UpLo >	ldlt () const

const LLT< PlainObject, UpLo >	llt () const

template<typename OtherDerived >
SelfadjointProductMatrix < MatrixType, Mode, false, OtherDerived, 0, OtherDerived::IsVectorAtCompileTime >	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))

Index	size () const

Friends
template<typename OtherDerived >
SelfadjointProductMatrix < OtherDerived, 0, OtherDerived::IsVectorAtCompileTime, MatrixType, Mode, false >	operator* (const MatrixBase< OtherDerived > &lhs, const SelfAdjointView &rhs)

Member Typedef Documentation

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

Return type of eigenvalues()

typedef NumTraits<Scalar>::Real RealScalar

Real part of Scalar

Member Function Documentation

Scalar coeff	(	Index	row,
		Index	col
	)		const

inline

See Also: MatrixBase::coeff()

Warning: the coordinates must fit into the referenced triangular part

Scalar& coeffRef	(	Index	row,
		Index	col
	)

inline

See Also: MatrixBase::coeffRef()

Warning: the coordinates must fit into the referenced triangular part

void copyCoeff	(	Index	row,
		Index	col,
		Other &	other
	)

inlineinherited

See Also: MatrixBase::copyCoeff(row,col)

Derived& derived ( )

inlineinherited

Returns: a reference to the derived object

const Derived& derived ( ) const

inlineinherited

Returns: a const reference to the derived object

SelfAdjointView< MatrixType, UpLo >::EigenvaluesReturnType eigenvalues ( ) const

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()

void evalTo ( MatrixBase< DenseDerived > & other ) const

inherited

Assigns a triangular or selfadjoint matrix to a dense matrix. If the matrix is triangular, the opposite part is set to zero.

void evalToLazy ( MatrixBase< DenseDerived > & other ) const

inherited

Assigns a triangular or selfadjoint matrix to a dense matrix. If the matrix is triangular, the opposite part is set to zero.

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

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>

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

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

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>

Returns: the LLT decomposition of *this

SelfadjointProductMatrix<MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime> operator* ( const MatrixBase< OtherDerived > & rhs ) const

inline

Efficient self-adjoint matrix times vector/matrix product

SelfAdjointView< MatrixType, UpLo >::RealScalar operatorNorm ( ) const

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()

SelfAdjointView& 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)

SelfAdjointView& 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)

Index size ( ) const

inlineinherited

Returns: the number of coefficients, which is rows()*cols().

See Also: rows(), cols(), SizeAtCompileTime.

Friends And Related Function Documentation

SelfadjointProductMatrix<OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false> operator*	(	const MatrixBase< OtherDerived > &	lhs,
		const SelfAdjointView< MatrixType, UpLo > &	rhs
	)

friend

Efficient vector/matrix times self-adjoint matrix product

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

Detailed Description

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

Public Types

Public Member Functions

Friends

Member Typedef Documentation

Member Function Documentation

Friends And Related Function Documentation

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