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SelfAdjointView< MatrixType, UpLo > Class Template Reference


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 65 of file SelfAdjointView.h.

#include <src/Core/SelfAdjointView.h>

Inheritance diagram for SelfAdjointView< MatrixType, UpLo >:
Inheritance graph
[legend]

List of all members.

Public Types

enum  { Mode = internal::traits<SelfAdjointView>::Mode }
typedef TriangularBase
< SelfAdjointView
Base
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()

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
ScalarcoeffRef (Index row, Index col)
const MatrixType & _expression () const
const MatrixType & nestedExpression () const
MatrixType & 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 >
SelfAdjointViewrankUpdate (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 >
SelfAdjointViewrankUpdate (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.

Protected Attributes

const MatrixType::Nested 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

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

Definition at line 70 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 170 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 75 of file SelfAdjointView.h.

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

Definition at line 80 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 168 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 73 of file SelfAdjointView.h.


Member Enumeration Documentation

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

Definition at line 77 of file SelfAdjointView.h.


Constructor & Destructor Documentation

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

Definition at line 82 of file SelfAdjointView.h.


Member Function Documentation

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

Definition at line 109 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 93 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 102 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 86 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:

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 88 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 430 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 368 of file LLT.h.

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

Definition at line 111 of file SelfAdjointView.h.

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

Definition at line 112 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 117 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:

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 87 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.

References Lower, RowMajorBit, and Upper.

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 39 of file SelfadjointProduct.h.

References ColMajor, RowMajor, and RowMajorBit.

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 85 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 127 of file SelfAdjointView.h.


Member Data Documentation

template<typename MatrixType, unsigned int UpLo>
const MatrixType::Nested SelfAdjointView< MatrixType, UpLo >::m_matrix [protected]

Definition at line 176 of file SelfAdjointView.h.




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