Public Types | Public Member Functions | Protected Attributes | Friends
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 >:
Inheritance graph
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List of all members.

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:
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 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:







libicr

Author(s): Robert Krug

autogenerated on Mon Jan 6 2014 11:34:28