Public Types | Public Member Functions | Protected Attributes | Friends | List of all members
Eigen::SelfAdjointView< MatrixType, UpLo > Class Template Reference

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

#include <SelfAdjointView.h>

Inheritance diagram for Eigen::SelfAdjointView< MatrixType, UpLo >:
Inheritance graph
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Public Types

enum  { Mode = internal::traits<SelfAdjointView>::Mode }
 
typedef TriangularBase< SelfAdjointViewBase
 
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. More...
 
- Public Types inherited from Eigen::TriangularBase< SelfAdjointView< MatrixType, UpLo > >
enum  
 
typedef internal::traits< SelfAdjointView< MatrixType, UpLo > >::DenseMatrixType DenseMatrixType
 
typedef DenseMatrixType DenseType
 
typedef internal::traits< SelfAdjointView< MatrixType, UpLo > >::Index Index
 
typedef internal::traits< SelfAdjointView< MatrixType, UpLo > >::Scalar Scalar
 
typedef internal::traits< SelfAdjointView< MatrixType, UpLo > >::StorageKind StorageKind
 
- Public Types inherited from Eigen::EigenBase< Derived >
typedef internal::traits< Derived >::Index Index
 
typedef internal::traits< Derived >::StorageKind StorageKind
 

Public Member Functions

const MatrixTypeNestedCleaned_expression () const
 
Scalar coeff (Index row, Index col) const
 
ScalarcoeffRef (Index row, Index col)
 
Index cols () const
 
EigenvaluesReturnType eigenvalues () const
 Computes the eigenvalues of a matrix. More...
 
Index innerStride () const
 
const LDLT< PlainObject, UpLo > ldlt () const
 
const LLT< PlainObject, UpLo > llt () const
 
const MatrixTypeNestedCleanednestedExpression () const
 
MatrixTypeNestedCleanednestedExpression ()
 
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...
 
Index outerStride () const
 
template<typename DerivedU , typename DerivedV >
SelfAdjointView< MatrixType, UpLo > & rankUpdate (const MatrixBase< DerivedU > &u, const MatrixBase< DerivedV > &v, const Scalar &alpha)
 
template<typename DerivedU >
SelfAdjointView< MatrixType, UpLo > & rankUpdate (const MatrixBase< DerivedU > &u, const Scalar &alpha)
 
template<typename DerivedU , typename DerivedV >
SelfAdjointViewrankUpdate (const MatrixBase< DerivedU > &u, const MatrixBase< DerivedV > &v, const Scalar &alpha=Scalar(1))
 
template<typename DerivedU >
SelfAdjointViewrankUpdate (const MatrixBase< DerivedU > &u, const Scalar &alpha=Scalar(1))
 
Index rows () const
 
 SelfAdjointView (MatrixType &matrix)
 
- Public Member Functions inherited from Eigen::TriangularBase< SelfAdjointView< MatrixType, UpLo > >
Scalar coeff (Index row, Index col) const
 
ScalarcoeffRef (Index row, Index col)
 
Index cols () const
 
EIGEN_STRONG_INLINE void copyCoeff (Index row, Index col, Other &other)
 
const SelfAdjointView< MatrixType, UpLo > & derived () const
 
SelfAdjointView< MatrixType, UpLo > & derived ()
 
void evalTo (MatrixBase< DenseDerived > &other) const
 
void evalToLazy (MatrixBase< DenseDerived > &other) const
 
Index innerStride () const
 
Scalar operator() (Index row, Index col) const
 
Scalaroperator() (Index row, Index col)
 
Index outerStride () const
 
Index rows () const
 
DenseMatrixType toDenseMatrix () const
 
 TriangularBase ()
 
- Public Member Functions inherited from Eigen::EigenBase< Derived >
template<typename Dest >
void addTo (Dest &dst) const
 
template<typename Dest >
void applyThisOnTheLeft (Dest &dst) const
 
template<typename Dest >
void applyThisOnTheRight (Dest &dst) const
 
Index cols () const
 
Derived & const_cast_derived () const
 
const Derived & const_derived () const
 
Derived & derived ()
 
const Derived & derived () const
 
template<typename Dest >
void evalTo (Dest &dst) const
 
Index rows () const
 
Index size () const
 
template<typename Dest >
void subTo (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
MatrixTypethe type of the dense matrix storing the coefficients
TriangularPartcan 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 TriangularBase<SelfAdjointView> Eigen::SelfAdjointView< MatrixType, UpLo >::Base

Definition at line 58 of file SelfAdjointView.h.

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

Definition at line 65 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>
typedef internal::traits<SelfAdjointView>::MatrixTypeNested Eigen::SelfAdjointView< MatrixType, UpLo >::MatrixTypeNested

Definition at line 59 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>
typedef internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned Eigen::SelfAdjointView< MatrixType, UpLo >::MatrixTypeNestedCleaned

Definition at line 60 of file SelfAdjointView.h.

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

Definition at line 70 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.

template<typename MatrixType, unsigned int UpLo>
typedef internal::traits<SelfAdjointView>::Scalar Eigen::SelfAdjointView< MatrixType, UpLo >::Scalar

The type of coefficients in this matrix.

Definition at line 63 of file SelfAdjointView.h.

Member Enumeration Documentation

template<typename MatrixType, unsigned int UpLo>
anonymous enum
Enumerator
Mode 

Definition at line 67 of file SelfAdjointView.h.

Constructor & Destructor Documentation

template<typename MatrixType, unsigned int UpLo>
Eigen::SelfAdjointView< MatrixType, UpLo >::SelfAdjointView ( MatrixType &  matrix)
inline

Definition at line 72 of file SelfAdjointView.h.

Member Function Documentation

template<typename MatrixType, unsigned int UpLo>
const MatrixTypeNestedCleaned& Eigen::SelfAdjointView< MatrixType, UpLo >::_expression ( ) const
inline

Definition at line 99 of file SelfAdjointView.h.

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.

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.

template<typename MatrixType, unsigned int UpLo>
Index Eigen::SelfAdjointView< MatrixType, UpLo >::cols ( void  ) const
inline

Definition at line 76 of file SelfAdjointView.h.

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.

template<typename MatrixType, unsigned int UpLo>
Index Eigen::SelfAdjointView< MatrixType, UpLo >::innerStride ( ) const
inline

Definition at line 78 of file SelfAdjointView.h.

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.

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.

template<typename MatrixType, unsigned int UpLo>
const MatrixTypeNestedCleaned& Eigen::SelfAdjointView< MatrixType, UpLo >::nestedExpression ( ) const
inline

Definition at line 101 of file SelfAdjointView.h.

template<typename MatrixType, unsigned int UpLo>
MatrixTypeNestedCleaned& Eigen::SelfAdjointView< MatrixType, UpLo >::nestedExpression ( )
inline

Definition at line 102 of file SelfAdjointView.h.

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.

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.

template<typename MatrixType, unsigned int UpLo>
Index Eigen::SelfAdjointView< MatrixType, UpLo >::outerStride ( ) const
inline

Definition at line 77 of file SelfAdjointView.h.

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

Definition at line 61 of file SelfadjointRank2Update.h.

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

Definition at line 114 of file SelfadjointProduct.h.

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)
template<typename MatrixType, unsigned int UpLo>
Index Eigen::SelfAdjointView< MatrixType, UpLo >::rows ( void  ) const
inline

Definition at line 75 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 117 of file SelfAdjointView.h.

Member Data Documentation

template<typename MatrixType, unsigned int UpLo>
MatrixTypeNested Eigen::SelfAdjointView< MatrixType, UpLo >::m_matrix
protected

Definition at line 189 of file SelfAdjointView.h.


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


acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Mon Jun 10 2019 12:35:39