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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 SelfAdjointView< MatrixType, UpLo >:
TriangularBase< SelfAdjointView< MatrixType, UpLo > > EigenBase< SelfAdjointView< MatrixType, UpLo > >

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

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
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))
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.

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()

Member Typedef Documentation

template<typename MatrixType, unsigned int UpLo>
typedef TriangularBase<SelfAdjointView> SelfAdjointView< MatrixType, UpLo >::Base
template<typename MatrixType, unsigned int UpLo>
typedef Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1> SelfAdjointView< MatrixType, UpLo >::EigenvaluesReturnType

Return type of eigenvalues()

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

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

template<typename MatrixType, unsigned int UpLo>
typedef internal::traits<SelfAdjointView>::MatrixTypeNested SelfAdjointView< MatrixType, UpLo >::MatrixTypeNested
template<typename MatrixType, unsigned int UpLo>
typedef internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned SelfAdjointView< MatrixType, UpLo >::MatrixTypeNestedCleaned
template<typename MatrixType, unsigned int UpLo>
typedef MatrixType::PlainObject SelfAdjointView< MatrixType, UpLo >::PlainObject
template<typename MatrixType, unsigned int UpLo>
typedef NumTraits<Scalar>::Real SelfAdjointView< MatrixType, UpLo >::RealScalar

Real part of Scalar

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 > >.

Member Enumeration Documentation

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

Constructor & Destructor Documentation

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

Member Function Documentation

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

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: 

 Output: 


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













template<typename MatrixType, unsigned int UpLo> 

      

        

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

      







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













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 













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 













template<typename MatrixType, unsigned int UpLo> 

      

        

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

      

















template<typename MatrixType, unsigned int UpLo> 

      

        

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

      

















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 













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: 


 Output: 


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













template<typename MatrixType, unsigned int UpLo> 

      

        

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

      







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













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) 













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) 













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 > >.







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 







Member Data Documentation








template<typename MatrixType, unsigned int UpLo> 

      

        

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

      











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



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