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

#include <SelfAdjointView.h>

Inheritance diagram for SelfAdjointView< MatrixType, UpLo >:

Public Types
enum	{ Mode = internal::traits<SelfAdjointView>::Mode }
typedef TriangularBase < SelfAdjointView >	Base
typedef Matrix< RealScalar, internal::traits< MatrixType > ::ColsAtCompileTime, 1 >	EigenvaluesReturnType
typedef MatrixType::Index	Index
typedef internal::traits < SelfAdjointView > ::MatrixTypeNested	MatrixTypeNested
typedef internal::traits < SelfAdjointView > ::MatrixTypeNestedCleaned	MatrixTypeNestedCleaned
typedef MatrixType::PlainObject	PlainObject
typedef NumTraits< Scalar >::Real	RealScalar
typedef internal::traits < SelfAdjointView >::Scalar	Scalar
	The type of coefficients in this matrix.
Public Member Functions
const MatrixTypeNestedCleaned &	_expression () const
Scalar	coeff (Index row, Index col) const
Scalar &	coeffRef (Index row, Index col)
Index	cols () const
EigenvaluesReturnType	eigenvalues () const
	Computes the eigenvalues of a matrix.
Index	innerStride () const
const LDLT< PlainObject, UpLo >	ldlt () const
const LLT< PlainObject, UpLo >	llt () const
const MatrixTypeNestedCleaned &	nestedExpression () const
MatrixTypeNestedCleaned &	nestedExpression ()
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.
Index	outerStride () const
template<typename DerivedU , typename DerivedV >
SelfAdjointView &	rankUpdate (const MatrixBase< DerivedU > &u, const MatrixBase< DerivedV > &v, Scalar alpha=Scalar(1))
template<typename DerivedU >
SelfAdjointView &	rankUpdate (const MatrixBase< DerivedU > &u, Scalar alpha=Scalar(1))
Index	rows () const
	SelfAdjointView (const MatrixType &matrix)
Protected Attributes
const MatrixTypeNested	m_matrix
Friends
template<typename OtherDerived >
SelfadjointProductMatrix < OtherDerived, 0, OtherDerived::IsVectorAtCompileTime, MatrixType, Mode, false >	operator* (const MatrixBase< OtherDerived > &lhs, const SelfAdjointView &rhs)

Detailed Description

template<typename MatrixType, unsigned int UpLo>
class 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()

Definition at line 66 of file SelfAdjointView.h.

Member Typedef Documentation

template<typename MatrixType, unsigned int UpLo>

typedef TriangularBase<SelfAdjointView> SelfAdjointView< MatrixType, UpLo >::Base

Definition at line 71 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

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

Return type of eigenvalues()

Definition at line 173 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

typedef MatrixType::Index SelfAdjointView< MatrixType, UpLo >::Index

Reimplemented from TriangularBase< SelfAdjointView< MatrixType, UpLo > >.

Definition at line 78 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

typedef internal::traits<SelfAdjointView>::MatrixTypeNested SelfAdjointView< MatrixType, UpLo >::MatrixTypeNested

Definition at line 72 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

typedef internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned SelfAdjointView< MatrixType, UpLo >::MatrixTypeNestedCleaned

Definition at line 73 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

typedef MatrixType::PlainObject SelfAdjointView< MatrixType, UpLo >::PlainObject

Definition at line 83 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

typedef NumTraits<Scalar>::Real SelfAdjointView< MatrixType, UpLo >::RealScalar

Real part of Scalar

Definition at line 171 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

typedef internal::traits<SelfAdjointView>::Scalar SelfAdjointView< MatrixType, UpLo >::Scalar

The type of coefficients in this matrix.

Reimplemented from TriangularBase< SelfAdjointView< MatrixType, UpLo > >.

Definition at line 76 of file SelfAdjointView.h.

Member Enumeration Documentation

template<typename MatrixType, unsigned int UpLo>

anonymous enum

Enumerator:

Mode

Definition at line 80 of file SelfAdjointView.h.

Constructor & Destructor Documentation

template<typename MatrixType, unsigned int UpLo>

SelfAdjointView< MatrixType, UpLo >::SelfAdjointView ( const MatrixType & matrix ) [inline]

Definition at line 85 of file SelfAdjointView.h.

Member Function Documentation

template<typename MatrixType, unsigned int UpLo>

const MatrixTypeNestedCleaned& SelfAdjointView< MatrixType, UpLo >::_expression ( ) const [inline]

Definition at line 112 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

Scalar SelfAdjointView< MatrixType, UpLo >::coeff	(	Index	row,
		Index	col
	)		const `[inline]`

See also:: MatrixBase::coeff()

Warning:: the coordinates must fit into the referenced triangular part

Definition at line 96 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

Scalar& SelfAdjointView< MatrixType, UpLo >::coeffRef	(	Index	row,
		Index	col
	)		`[inline]`

See also:: MatrixBase::coeffRef()

Warning:: the coordinates must fit into the referenced triangular part

Definition at line 105 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

Index SelfAdjointView< MatrixType, UpLo >::cols ( void ) const [inline]

Returns:: the number of columns.

See also:: rows(), ColsAtCompileTime

Reimplemented from TriangularBase< SelfAdjointView< MatrixType, UpLo > >.

Definition at line 89 of file SelfAdjointView.h.

template<typename MatrixType , unsigned int UpLo>

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

Computes the eigenvalues of a matrix.

Returns:: Column vector containing the 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:

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

Definition at line 102 of file MatrixBaseEigenvalues.h.

template<typename MatrixType, unsigned int UpLo>

Index SelfAdjointView< MatrixType, UpLo >::innerStride ( ) const [inline]

Reimplemented from TriangularBase< SelfAdjointView< MatrixType, UpLo > >.

Definition at line 91 of file SelfAdjointView.h.

template<typename MatrixType , unsigned int UpLo>

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

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

Definition at line 446 of file LDLT.h.

template<typename MatrixType , unsigned int UpLo>

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

Returns:: the LLT decomposition of *this

Definition at line 381 of file LLT.h.

template<typename MatrixType, unsigned int UpLo>

const MatrixTypeNestedCleaned& SelfAdjointView< MatrixType, UpLo >::nestedExpression ( ) const [inline]

Definition at line 114 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

MatrixTypeNestedCleaned& SelfAdjointView< MatrixType, UpLo >::nestedExpression ( ) [inline]

Definition at line 115 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

template<typename OtherDerived >

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

Efficient self-adjoint matrix times vector/matrix product

Definition at line 120 of file SelfAdjointView.h.

template<typename MatrixType , unsigned int UpLo>

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

Computes the L2 operator norm.

Returns:: Operator norm of the matrix.

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:

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

Definition at line 165 of file MatrixBaseEigenvalues.h.

template<typename MatrixType, unsigned int UpLo>

Index SelfAdjointView< MatrixType, UpLo >::outerStride ( ) const [inline]

Reimplemented from TriangularBase< SelfAdjointView< MatrixType, UpLo > >.

Definition at line 90 of file SelfAdjointView.h.

template<typename MatrixType , unsigned int UpLo>

template<typename DerivedU , typename DerivedV >

SelfAdjointView< MatrixType, UpLo > & SelfAdjointView< MatrixType, UpLo >::rankUpdate	(	const MatrixBase< DerivedU > &	u,
		const MatrixBase< DerivedV > &	v,
		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)

Definition at line 74 of file SelfadjointRank2Update.h.

template<typename MatrixType , unsigned int UpLo>

template<typename DerivedU >

SelfAdjointView< MatrixType, UpLo > & SelfAdjointView< MatrixType, UpLo >::rankUpdate	(	const MatrixBase< DerivedU > &	u,
		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)

Definition at line 129 of file SelfadjointProduct.h.

template<typename MatrixType, unsigned int UpLo>

Index SelfAdjointView< MatrixType, UpLo >::rows ( void ) const [inline]

Returns:: the number of rows.

See also:: cols(), RowsAtCompileTime

Reimplemented from TriangularBase< SelfAdjointView< MatrixType, UpLo > >.

Definition at line 88 of file SelfAdjointView.h.

Friends And Related Function Documentation

template<typename MatrixType, unsigned int UpLo>

template<typename OtherDerived >

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

Definition at line 130 of file SelfAdjointView.h.

Member Data Documentation

template<typename MatrixType, unsigned int UpLo>

const MatrixTypeNested SelfAdjointView< MatrixType, UpLo >::m_matrix [protected]

Definition at line 202 of file SelfAdjointView.h.

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

Public Types

Public Member Functions

Protected Attributes

Friends

Detailed Description

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

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

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