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

#include <SelfAdjointView.h>

Inheritance diagram for Eigen::SelfAdjointView< MatrixType, UpLo >:

Collaboration diagram for Eigen::SelfAdjointView< MatrixType, UpLo >:

Public Types
enum	{ Mode = internal::traits<SelfAdjointView>::Mode }

typedef TriangularBase< SelfAdjointView >	Base

typedef internal::traits< SelfAdjointView >::MatrixTypeNested	MatrixTypeNested

typedef internal::traits< SelfAdjointView >::MatrixTypeNestedCleaned	MatrixTypeNestedCleaned

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

typedef MatrixType::Index	Index

typedef MatrixType::PlainObject	PlainObject

typedef NumTraits< Scalar >::Real	RealScalar

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

Public Types inherited from Eigen::TriangularBase< SelfAdjointView< MatrixType, UpLo > >
enum

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

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

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

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

typedef DenseMatrixType	DenseType

Public Types inherited from Eigen::EigenBase< Derived >
typedef internal::traits< Derived >::StorageKind	StorageKind

typedef internal::traits< Derived >::Index	Index

Public Member Functions
	SelfAdjointView (MatrixType &matrix)

Index	rows () const

Index	cols () const

Index	outerStride () const

Index	innerStride () const

Scalar	coeff (Index row, Index col) const

Scalar &	coeffRef (Index row, Index col)

const MatrixTypeNestedCleaned &	_expression () const

const MatrixTypeNestedCleaned &	nestedExpression () const

MatrixTypeNestedCleaned &	nestedExpression ()

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

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))

const LLT< PlainObject, UpLo >	llt () const

const LDLT< PlainObject, UpLo >	ldlt () const

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

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

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

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

Public Member Functions inherited from Eigen::TriangularBase< SelfAdjointView< MatrixType, UpLo > >
Index	rows () const

Index	cols () const

Index	outerStride () const

Index	innerStride () const

Scalar	coeff (Index row, Index col) const

Scalar &	coeffRef (Index row, Index col)

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

Scalar	operator() (Index row, Index col) const

Scalar &	operator() (Index row, Index col)

const SelfAdjointView< MatrixType, UpLo > &	derived () const

SelfAdjointView< MatrixType, UpLo > &	derived ()

void	evalTo (MatrixBase< DenseDerived > &other) const

void	evalToLazy (MatrixBase< DenseDerived > &other) const

DenseMatrixType	toDenseMatrix () const

Public Member Functions inherited from Eigen::EigenBase< Derived >
Derived &	derived ()

const Derived &	derived () const

Derived &	const_cast_derived () const

const Derived &	const_derived () const

Index	rows () const

Index	cols () const

Index	size () const

template<typename Dest >
void	evalTo (Dest &dst) const

template<typename Dest >
void	addTo (Dest &dst) const

template<typename Dest >
void	subTo (Dest &dst) const

template<typename Dest >
void	applyThisOnTheRight (Dest &dst) const

template<typename Dest >
void	applyThisOnTheLeft (Dest &dst) const

Protected Attributes
MatrixTypeNested	m_matrix

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

Additional Inherited Members
Protected Member Functions inherited from Eigen::TriangularBase< SelfAdjointView< MatrixType, UpLo > >
void	check_coordinates (Index row, Index col) const

void	check_coordinates_internal (Index, Index) const

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()

Definition at line 53 of file SelfAdjointView.h.

Member Typedef Documentation

template<typename MatrixType, unsigned int UpLo>

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

Return type of eigenvalues()

Definition at line 160 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>

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

Real part of Scalar

Definition at line 158 of file SelfAdjointView.h.

Member Function Documentation

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

Definition at line 83 of file SelfAdjointView.h.

     {
       Base::check_coordinates_internal(row, col);
       return m_matrix.coeff(row, col);
     }

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

Definition at line 92 of file SelfAdjointView.h.

     {
       Base::check_coordinates_internal(row, col);
       return m_matrix.const_cast_derived().coeffRef(row, col);
     }

template<typename MatrixType , unsigned int UpLo>

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

Output:

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

Definition at line 89 of file MatrixBaseEigenvalues.h.

 {
   typedef typename SelfAdjointView<MatrixType, UpLo>::PlainObject PlainObject;
   PlainObject thisAsMatrix(*this);
   return SelfAdjointEigenSolver<PlainObject>(thisAsMatrix, false).eigenvalues();
 }

template<typename MatrixType , unsigned int UpLo>

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

inline

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

Definition at line 583 of file LDLT.h.

 {
   return LDLT<PlainObject,UpLo>(m_matrix);
 }

template<typename MatrixType , unsigned int UpLo>

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

inline

Returns: the LLT decomposition of *this

Definition at line 483 of file LLT.h.

 {
   return LLT<PlainObject,UpLo>(m_matrix);
 }

template<typename MatrixType, unsigned int UpLo>

template<typename OtherDerived >

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

inline

Efficient self-adjoint matrix times vector/matrix product

Definition at line 107 of file SelfAdjointView.h.

     {
       return SelfadjointProductMatrix
               <MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime>
               (m_matrix, rhs.derived());
     }

template<typename MatrixType , unsigned int UpLo>

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

Output:

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

Definition at line 153 of file MatrixBaseEigenvalues.h.

 {
   return eigenvalues().cwiseAbs().maxCoeff();
 }

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)

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)

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 117 of file SelfAdjointView.h.

     {
       return SelfadjointProductMatrix
               <OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false>
               (lhs.derived(),rhs.m_matrix);
     }

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

C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/Core/SelfAdjointView.h
C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/Cholesky/LDLT.h
C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/Cholesky/LLT.h
C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/Core/products/SelfadjointProduct.h
C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/Core/products/SelfadjointRank2Update.h
C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h

Public Types

Public Member Functions

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

Member Function Documentation

Friends And Related Function Documentation

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