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Eigen::SelfAdjointView Class Reference
Core module

Detailed Description

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()
Inheritance diagram for Eigen::SelfAdjointView:
Inheritance graph
[legend]

List of all members.

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
 Real part of Scalar.
typedef Matrix< RealScalar,
internal::traits< MatrixType >
::ColsAtCompileTime, 1 > 		EigenvaluesReturnType
 Return type of eigenvalues()
enum  
typedef internal::traits
< Derived >::StorageKind 		StorageKind
typedef internal::traits
< Derived >::DenseMatrixType 		DenseMatrixType
typedef DenseMatrixType DenseType

Public Member Functions

 SelfAdjointView (const 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
 Efficient self-adjoint matrix times vector/matrix product.
template<typename DerivedU , typename DerivedV >
SelfAdjointView & 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^* $.
template<typename DerivedU >
SelfAdjointView & 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.
const LLT< PlainObject, UpLo > llt () const
 
const LDLT< PlainObject, UpLo > ldlt () const
 
EigenvaluesReturnType eigenvalues () const
 Computes the eigenvalues of a matrix.
RealScalar operatorNorm () const
 Computes the L2 operator norm.
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)
void evalTo (MatrixBase< DenseDerived > &other) const
void evalToLazy (MatrixBase< DenseDerived > &other) const
DenseMatrixType toDenseMatrix () const

Protected Member Functions

void check_coordinates (Index row, Index col) const
void check_coordinates_internal (Index, Index) const

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)
 Efficient vector/matrix times self-adjoint matrix product.

Member Typedef Documentation

typedef TriangularBase<SelfAdjointView> Eigen::SelfAdjointView::Base

Definition at line 72 of file Core.

typedef internal::traits<Derived>::DenseMatrixType Eigen::TriangularBase::DenseMatrixType [inherited]

Definition at line 58 of file Core.

typedef DenseMatrixType Eigen::TriangularBase::DenseType [inherited]

Definition at line 59 of file Core.

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

Return type of eigenvalues()

Definition at line 174 of file Core.

typedef MatrixType::Index Eigen::SelfAdjointView::Index

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

Definition at line 79 of file Core.

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

Definition at line 73 of file Core.

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

Definition at line 74 of file Core.

typedef MatrixType::PlainObject Eigen::SelfAdjointView::PlainObject

Definition at line 84 of file Core.

typedef NumTraits<Scalar>::Real Eigen::SelfAdjointView::RealScalar

Real part of Scalar.

Definition at line 172 of file Core.

typedef internal::traits<SelfAdjointView>::Scalar Eigen::SelfAdjointView::Scalar

The type of coefficients in this matrix.

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

Definition at line 77 of file Core.

typedef internal::traits<Derived>::StorageKind Eigen::TriangularBase::StorageKind [inherited]

Definition at line 56 of file Core.

Member Enumeration Documentation

anonymous enum [inherited]

Definition at line 47 of file Core.

anonymous enum
Enumerator:
Mode 

Definition at line 81 of file Core.

Constructor & Destructor Documentation

Eigen::SelfAdjointView::SelfAdjointView ( const MatrixType &  matrix) [inline]

Definition at line 86 of file Core.

Member Function Documentation

const MatrixTypeNestedCleaned& Eigen::SelfAdjointView::_expression ( ) const [inline]

Definition at line 113 of file Core.

void Eigen::TriangularBase::check_coordinates ( Index  row,
Index  col 
) const [inline, protected, inherited]

Definition at line 109 of file Core.

void Eigen::TriangularBase::check_coordinates_internal ( Index  ,
Index   
) const [inline, protected, inherited]

Definition at line 128 of file Core.

Scalar Eigen::TriangularBase::coeff ( Index  row,
Index  col 
) const [inline, inherited]

Definition at line 68 of file Core.

Scalar Eigen::SelfAdjointView::coeff ( Index  row,
Index  col 
) const [inline]
See also:
MatrixBase::coeff()
Warning:
the coordinates must fit into the referenced triangular part

Definition at line 97 of file Core.

Scalar& Eigen::TriangularBase::coeffRef ( Index  row,
Index  col 
) [inline, inherited]

Definition at line 69 of file Core.

Scalar& Eigen::SelfAdjointView::coeffRef ( Index  row,
Index  col 
) [inline]
See also:
MatrixBase::coeffRef()
Warning:
the coordinates must fit into the referenced triangular part

Definition at line 106 of file Core.

Index Eigen::SelfAdjointView::cols ( void  ) const [inline]

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

Definition at line 90 of file Core.

EIGEN_STRONG_INLINE void Eigen::TriangularBase::copyCoeff ( Index  row,
Index  col,
Other &  other 
) [inline, inherited]
See also:
MatrixBase::copyCoeff(row,col)

Definition at line 74 of file Core.

SelfAdjointView< MatrixType, UpLo >::EigenvaluesReturnType Eigen::SelfAdjointView::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 103 of file Eigenvalues.











      

        

          void Eigen::TriangularBase::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 Eigen::TriangularBase::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. 











      

        

          Index Eigen::SelfAdjointView::innerStride 
          (
          )
           const [inline]
        

      







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



Definition at line 92 of file Core.











      

        

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

      









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



Definition at line 447 of file Cholesky.











      

        

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

      









Returns:
the LLT decomposition of *this 



Definition at line 434 of file Cholesky.











      

        

          const MatrixTypeNestedCleaned& Eigen::SelfAdjointView::nestedExpression 
          (
          )
           const [inline]
        

      







Definition at line 115 of file Core.











      

        

          MatrixTypeNestedCleaned& Eigen::SelfAdjointView::nestedExpression 
          (
          )
           [inline]
        

      







Definition at line 116 of file Core.











      

        

          Scalar Eigen::TriangularBase::operator() 
          (
          Index 
          row, 
        

        

          
          
          Index 
          col 
        

        

          
          )
           const [inline, inherited]
        

      







Definition at line 79 of file Core.











      

        

          Scalar& Eigen::TriangularBase::operator() 
          (
          Index 
          row, 
        

        

          
          
          Index 
          col 
        

        

          
          )
           [inline, inherited]
        

      







Definition at line 84 of file Core.













template<typename OtherDerived > 

      

        

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

      







Efficient self-adjoint matrix times vector/matrix product. 



Definition at line 121 of file Core.











      

        

          SelfAdjointView< MatrixType, UpLo >::RealScalar Eigen::SelfAdjointView::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 166 of file Eigenvalues.











      

        

          Index Eigen::SelfAdjointView::outerStride 
          (
          )
           const [inline]
        

      







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



Definition at line 91 of file Core.













template<typename DerivedU , typename DerivedV > 

      

        

          SelfAdjointView< MatrixType, UpLo > & Eigen::SelfAdjointView::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 75 of file Core.













template<typename DerivedU > 

      

        

          SelfAdjointView< MatrixType, UpLo > & Eigen::SelfAdjointView::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 130 of file Core.











      

        

          Index Eigen::SelfAdjointView::rows 
          (
          void 
          )
           const [inline]
        

      







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



Definition at line 89 of file Core.











      

        

          DenseMatrixType Eigen::TriangularBase::toDenseMatrix 
          (
          )
           const [inline, inherited]
        

      







Definition at line 100 of file Core.







Friends And Related Function Documentation








template<typename OtherDerived > 

      

        

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

        

          
          
          const SelfAdjointView & 
          rhs 
        

        

          
          )
           [friend]
        

      







Efficient vector/matrix times self-adjoint matrix product. 



Definition at line 131 of file Core.







Member Data Documentation






      

        

          const MatrixTypeNested Eigen::SelfAdjointView::m_matrix [protected]
        

      







Definition at line 203 of file Core.










 
 
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