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Eigen::SelfAdjointView< MatrixType_, UpLo > Class Template Reference
Dense matrix and array manipulation » Reference » Core_Module

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

#include <SelfAdjointView.h>

+ Inheritance diagram for Eigen::SelfAdjointView< MatrixType_, UpLo >:

Public Types

enum  { Mode = internal::traits<SelfAdjointView>::Mode , Flags = internal::traits<SelfAdjointView>::Flags , TransposeMode = ((int(Mode) & int(Upper)) ? Lower : 0) | ((int(Mode) & int(Lower)) ? Upper : 0) }
 
typedef MatrixType_ MatrixType
 
typedef TriangularBase< SelfAdjointView > Base
 
typedef internal::traits< SelfAdjointView >::MatrixTypeNested MatrixTypeNested
 
typedef internal::traits< SelfAdjointView >::MatrixTypeNestedCleaned MatrixTypeNestedCleaned
 
typedef MatrixTypeNestedCleaned NestedExpression
 
typedef internal::traits< SelfAdjointView >::Scalar Scalar
 The type of coefficients in this matrix. More...
 
typedef MatrixType::StorageIndex StorageIndex
 
typedef internal::remove_all_t< typename MatrixType::ConjugateReturnType > MatrixConjugateReturnType
 
typedef SelfAdjointView< std::add_const_t< MatrixType >, UpLo > ConstSelfAdjointView
 
typedef MatrixType::PlainObject PlainObject
 
typedef SelfAdjointView< const MatrixConjugateReturnType, UpLo > ConjugateReturnType
 
typedef SelfAdjointView< const typename MatrixType::AdjointReturnType, TransposeMode > AdjointReturnType
 
typedef SelfAdjointView< typename MatrixType::TransposeReturnType, TransposeMode > TransposeReturnType
 
typedef SelfAdjointView< const typename MatrixType::ConstTransposeReturnType, TransposeMode > ConstTransposeReturnType
 
typedef NumTraits< Scalar >::Real RealScalar
 
typedef Matrix< RealScalar, internal::traits< MatrixType >::ColsAtCompileTime, 1 > EigenvaluesReturnType
 
- Public Types inherited from Eigen::TriangularBase< SelfAdjointView< MatrixType_, UpLo > >
enum  
 
typedef internal::traits< SelfAdjointView< MatrixType_, UpLo > >::Scalar Scalar
 
typedef internal::traits< SelfAdjointView< MatrixType_, UpLo > >::StorageKind StorageKind
 
typedef internal::traits< SelfAdjointView< MatrixType_, UpLo > >::StorageIndex StorageIndex
 
typedef internal::traits< SelfAdjointView< MatrixType_, UpLo > >::FullMatrixType DenseMatrixType
 
typedef DenseMatrixType DenseType
 
typedef SelfAdjointView< MatrixType_, UpLo > const & Nested
 
- Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index Index
 The interface type of indices. More...
 
typedef internal::traits< Derived >::StorageKind StorageKind
 

Public Member Functions

EIGEN_DEVICE_FUNC SelfAdjointView (MatrixType &matrix)
 
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
 
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
 
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index outerStride () const EIGEN_NOEXCEPT
 
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index innerStride () const EIGEN_NOEXCEPT
 
EIGEN_DEVICE_FUNC Scalar coeff (Index row, Index col) const
 
EIGEN_DEVICE_FUNC Scalar & coeffRef (Index row, Index col)
 
EIGEN_DEVICE_FUNC const MatrixTypeNestedCleaned & _expression () const
 
EIGEN_DEVICE_FUNC const MatrixTypeNestedCleaned & nestedExpression () const
 
EIGEN_DEVICE_FUNC MatrixTypeNestedCleaned & nestedExpression ()
 
template<typename OtherDerived >
EIGEN_DEVICE_FUNC const Product< SelfAdjointView, OtherDerived > operator* (const MatrixBase< OtherDerived > &rhs) const
 
template<typename DerivedU , typename DerivedV >
EIGEN_DEVICE_FUNC SelfAdjointView & rankUpdate (const MatrixBase< DerivedU > &u, const MatrixBase< DerivedV > &v, const Scalar &alpha=Scalar(1))
 
template<typename DerivedU >
EIGEN_DEVICE_FUNC SelfAdjointView & rankUpdate (const MatrixBase< DerivedU > &u, const Scalar &alpha=Scalar(1))
 
template<unsigned int TriMode>
EIGEN_DEVICE_FUNC std::conditional_t<(TriMode &(Upper|Lower))==(UpLo &(Upper|Lower)), TriangularView< MatrixType, TriMode >, TriangularView< typename MatrixType::AdjointReturnType, TriMode > > triangularView () const
 
EIGEN_DEVICE_FUNC const ConjugateReturnType conjugate () const
 
template<bool Cond>
EIGEN_DEVICE_FUNC std::conditional_t< Cond, ConjugateReturnType, ConstSelfAdjointView > conjugateIf () const
 
EIGEN_DEVICE_FUNC const AdjointReturnType adjoint () const
 
template<class Dummy = int>
EIGEN_DEVICE_FUNC TransposeReturnType transpose (std::enable_if_t< Eigen::internal::is_lvalue< MatrixType >::value, Dummy * >=nullptr)
 
EIGEN_DEVICE_FUNC const ConstTransposeReturnType transpose () const
 
EIGEN_DEVICE_FUNC MatrixType::ConstDiagonalReturnType diagonal () const
 
const LLT< PlainObject, UpLo > llt () const
 
const LDLT< PlainObject, UpLo > ldlt () const
 
EIGEN_DEVICE_FUNC EigenvaluesReturnType eigenvalues () const
 Computes the eigenvalues of a matrix. More...
 
EIGEN_DEVICE_FUNC RealScalar operatorNorm () const
 Computes the L2 operator norm. More...
 
template<typename DerivedU >
EIGEN_DEVICE_FUNC SelfAdjointView< MatrixType, UpLo > & rankUpdate (const MatrixBase< DerivedU > &u, const Scalar &alpha)
 
template<typename DerivedU , typename DerivedV >
EIGEN_DEVICE_FUNC SelfAdjointView< MatrixType, UpLo > & rankUpdate (const MatrixBase< DerivedU > &u, const MatrixBase< DerivedV > &v, const Scalar &alpha)
 
- Public Member Functions inherited from Eigen::TriangularBase< SelfAdjointView< MatrixType_, UpLo > >
EIGEN_DEVICE_FUNC TriangularBase ()
 
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
 
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
 
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index outerStride () const EIGEN_NOEXCEPT
 
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index innerStride () const EIGEN_NOEXCEPT
 
EIGEN_DEVICE_FUNC void resize (Index rows, Index cols)
 
EIGEN_DEVICE_FUNC Scalar coeff (Index row, Index col) const
 
EIGEN_DEVICE_FUNC Scalar & coeffRef (Index row, Index col)
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void copyCoeff (Index row, Index col, Other &other)
 
EIGEN_DEVICE_FUNC Scalar operator() (Index row, Index col) const
 
EIGEN_DEVICE_FUNC Scalar & operator() (Index row, Index col)
 
EIGEN_DEVICE_FUNC const SelfAdjointView< MatrixType_, UpLo > & derived () const
 
EIGEN_DEVICE_FUNC SelfAdjointView< MatrixType_, UpLo > & derived ()
 
EIGEN_DEVICE_FUNC void evalTo (MatrixBase< DenseDerived > &other) const
 
EIGEN_DEVICE_FUNC void evalToLazy (MatrixBase< DenseDerived > &other) const
 
EIGEN_DEVICE_FUNC DenseMatrixType toDenseMatrix () const
 
- Public Member Functions inherited from Eigen::EigenBase< Derived >
constexpr EIGEN_DEVICE_FUNC Derived & derived ()
 
constexpr EIGEN_DEVICE_FUNC const Derived & derived () const
 
EIGEN_DEVICE_FUNC Derived & const_cast_derived () const
 
EIGEN_DEVICE_FUNC const Derived & const_derived () const
 
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
 
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
 
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index size () const EIGEN_NOEXCEPT
 
template<typename Dest >
EIGEN_DEVICE_FUNC void evalTo (Dest &dst) const
 
template<typename Dest >
EIGEN_DEVICE_FUNC void addTo (Dest &dst) const
 
template<typename Dest >
EIGEN_DEVICE_FUNC void subTo (Dest &dst) const
 
template<typename Dest >
EIGEN_DEVICE_FUNC void applyThisOnTheRight (Dest &dst) const
 
template<typename Dest >
EIGEN_DEVICE_FUNC void applyThisOnTheLeft (Dest &dst) const
 
template<typename Device >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper< Derived, Device > device (Device &device)
 
template<typename Device >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper< const Derived, Device > device (Device &device) const
 

Protected Attributes

MatrixTypeNested m_matrix
 

Friends

template<typename OtherDerived >
EIGEN_DEVICE_FUNC const Product< OtherDerived, SelfAdjointView > operator* (const MatrixBase< OtherDerived > &lhs, const SelfAdjointView &rhs)
 
EIGEN_DEVICE_FUNC const SelfAdjointView< const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar, MatrixType, product), UpLo > operator* (const Scalar &s, const SelfAdjointView &mat)
 

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.

Template 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()

Member Typedef Documentation

◆ AdjointReturnType

template<typename MatrixType_ , unsigned int UpLo>
typedef SelfAdjointView<const typename MatrixType::AdjointReturnType, TransposeMode> Eigen::SelfAdjointView< MatrixType_, UpLo >::AdjointReturnType

◆ Base

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

◆ ConjugateReturnType

template<typename MatrixType_ , unsigned int UpLo>
typedef SelfAdjointView<const MatrixConjugateReturnType, UpLo> Eigen::SelfAdjointView< MatrixType_, UpLo >::ConjugateReturnType

◆ ConstSelfAdjointView

template<typename MatrixType_ , unsigned int UpLo>
typedef SelfAdjointView<std::add_const_t<MatrixType>, UpLo> Eigen::SelfAdjointView< MatrixType_, UpLo >::ConstSelfAdjointView

◆ ConstTransposeReturnType

template<typename MatrixType_ , unsigned int UpLo>
typedef SelfAdjointView<const typename MatrixType::ConstTransposeReturnType, TransposeMode> Eigen::SelfAdjointView< MatrixType_, UpLo >::ConstTransposeReturnType

◆ EigenvaluesReturnType

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

Return type of eigenvalues()

◆ MatrixConjugateReturnType

template<typename MatrixType_ , unsigned int UpLo>
typedef internal::remove_all_t<typename MatrixType::ConjugateReturnType> Eigen::SelfAdjointView< MatrixType_, UpLo >::MatrixConjugateReturnType

◆ MatrixType

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

◆ MatrixTypeNested

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

◆ MatrixTypeNestedCleaned

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

◆ NestedExpression

template<typename MatrixType_ , unsigned int UpLo>
typedef MatrixTypeNestedCleaned Eigen::SelfAdjointView< MatrixType_, UpLo >::NestedExpression

◆ PlainObject

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

◆ RealScalar

template<typename MatrixType_ , unsigned int UpLo>
typedef NumTraits<Scalar>::Real Eigen::SelfAdjointView< MatrixType_, UpLo >::RealScalar

Real part of Scalar

◆ Scalar

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

The type of coefficients in this matrix.

◆ StorageIndex

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

◆ TransposeReturnType

template<typename MatrixType_ , unsigned int UpLo>
typedef SelfAdjointView<typename MatrixType::TransposeReturnType, TransposeMode> Eigen::SelfAdjointView< MatrixType_, UpLo >::TransposeReturnType

Member Enumeration Documentation

◆ anonymous enum

template<typename MatrixType_ , unsigned int UpLo>
anonymous enum
Enumerator
Mode 
Flags 
TransposeMode 
67  {
68  Mode = internal::traits<SelfAdjointView>::Mode,
69  Flags = internal::traits<SelfAdjointView>::Flags,
70  TransposeMode = ((int(Mode) & int(Upper)) ? Lower : 0) | ((int(Mode) & int(Lower)) ? Upper : 0)
71  };
Eigen::SelfAdjointView::TransposeMode
@ TransposeMode
Definition: SelfAdjointView.h:70
Eigen::SelfAdjointView::Mode
@ Mode
Definition: SelfAdjointView.h:68
Eigen::Lower
@ Lower
Definition: Constants.h:211
Eigen::Upper
@ Upper
Definition: Constants.h:213
int
return int(ret)+1
Flags
Extend namespace for flags.
Definition: fsi_chan_precond_driver.cc:56

Constructor & Destructor Documentation

◆ SelfAdjointView()

template<typename MatrixType_ , unsigned int UpLo>
EIGEN_DEVICE_FUNC Eigen::SelfAdjointView< MatrixType_, UpLo >::SelfAdjointView ( MatrixType &  matrix)
inlineexplicit
74 : m_matrix(matrix) {}
Eigen::SelfAdjointView::m_matrix
MatrixTypeNested m_matrix
Definition: SelfAdjointView.h:236
matrix
Eigen::Map< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor >, 0, Eigen::OuterStride<> > matrix(T *data, int rows, int cols, int stride)
Definition: common.h:85

Member Function Documentation

◆ _expression()

template<typename MatrixType_ , unsigned int UpLo>
EIGEN_DEVICE_FUNC const MatrixTypeNestedCleaned& Eigen::SelfAdjointView< MatrixType_, UpLo >::_expression ( ) const
inline
99 { return m_matrix; }

References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.

◆ adjoint()

template<typename MatrixType_ , unsigned int UpLo>
EIGEN_DEVICE_FUNC const AdjointReturnType Eigen::SelfAdjointView< MatrixType_, UpLo >::adjoint ( ) const
inline
See also
MatrixBase::adjoint() const
194 { return AdjointReturnType(m_matrix.adjoint()); }
Eigen::SelfAdjointView::AdjointReturnType
SelfAdjointView< const typename MatrixType::AdjointReturnType, TransposeMode > AdjointReturnType
Definition: SelfAdjointView.h:192

References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.

◆ coeff()

template<typename MatrixType_ , unsigned int UpLo>
EIGEN_DEVICE_FUNC 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
84  {
85  Base::check_coordinates_internal(row, col);
86  return m_matrix.coeff(row, col);
87  }
col
m col(1)
row
m row(1)
Eigen::TriangularBase::check_coordinates_internal
void check_coordinates_internal(Index, Index) const
Definition: TriangularMatrix.h:123

References Eigen::TriangularBase< Derived >::check_coordinates_internal(), col(), Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix, and row().

◆ coeffRef()

template<typename MatrixType_ , unsigned int UpLo>
EIGEN_DEVICE_FUNC 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
92  {
93  EIGEN_STATIC_ASSERT_LVALUE(SelfAdjointView);
94  Base::check_coordinates_internal(row, col);
95  return m_matrix.coeffRef(row, col);
96  }
EIGEN_STATIC_ASSERT_LVALUE
#define EIGEN_STATIC_ASSERT_LVALUE(Derived)
Definition: StaticAssert.h:87
Eigen::SelfAdjointView::SelfAdjointView
EIGEN_DEVICE_FUNC SelfAdjointView(MatrixType &matrix)
Definition: SelfAdjointView.h:74

References Eigen::TriangularBase< Derived >::check_coordinates_internal(), col(), EIGEN_STATIC_ASSERT_LVALUE, Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix, and row().

Referenced by foo().

◆ cols()

template<typename MatrixType_ , unsigned int UpLo>
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index Eigen::SelfAdjointView< MatrixType_, UpLo >::cols ( ) const
inline
77 { return m_matrix.cols(); }

References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.

Referenced by gdb.printers._MatrixEntryIterator::__next__(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

◆ conjugate()

template<typename MatrixType_ , unsigned int UpLo>
EIGEN_DEVICE_FUNC const ConjugateReturnType Eigen::SelfAdjointView< MatrixType_, UpLo >::conjugate ( void  ) const
inline
See also
MatrixBase::conjugate() const
179  {
180  return ConjugateReturnType(m_matrix.conjugate());
181  }
Eigen::SelfAdjointView::ConjugateReturnType
SelfAdjointView< const MatrixConjugateReturnType, UpLo > ConjugateReturnType
Definition: SelfAdjointView.h:177

References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.

◆ conjugateIf()

template<typename MatrixType_ , unsigned int UpLo>
template<bool Cond>
EIGEN_DEVICE_FUNC std::conditional_t<Cond, ConjugateReturnType, ConstSelfAdjointView> Eigen::SelfAdjointView< MatrixType_, UpLo >::conjugateIf ( ) const
inline
Returns
an expression of the complex conjugate of *this if Cond==true, returns *this otherwise.
187  {
188  typedef std::conditional_t<Cond, ConjugateReturnType, ConstSelfAdjointView> ReturnType;
189  return ReturnType(m_matrix.template conjugateIf<Cond>());
190  }

References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.

◆ diagonal()

template<typename MatrixType_ , unsigned int UpLo>
EIGEN_DEVICE_FUNC MatrixType::ConstDiagonalReturnType Eigen::SelfAdjointView< MatrixType_, UpLo >::diagonal ( ) const
inline
Returns
a const expression of the main diagonal of the matrix *this

This method simply returns the diagonal of the nested expression, thus by-passing the SelfAdjointView decorator.

See also
MatrixBase::diagonal(), class Diagonal
216  {
217  return typename MatrixType::ConstDiagonalReturnType(m_matrix);
218  }

References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.

◆ eigenvalues()

template<typename MatrixType , unsigned int UpLo>
EIGEN_DEVICE_FUNC SelfAdjointView< MatrixType, UpLo >::EigenvaluesReturnType Eigen::SelfAdjointView< MatrixType, UpLo >::eigenvalues
inline

Computes the eigenvalues of a matrix.

Returns
Column vector containing the eigenvalues.

\eigenvalues_module 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;
ones
MatrixXcf ones
Definition: ComplexEigenSolver_eigenvalues.cpp:1
eivals
VectorXcd eivals
Definition: MatrixBase_eigenvalues.cpp:2
Eigen::SelfAdjointView::eigenvalues
EIGEN_DEVICE_FUNC EigenvaluesReturnType eigenvalues() const
Computes the eigenvalues of a matrix.
Definition: MatrixBaseEigenvalues.h:83

Output: 

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


   83                                                      {


   84   PlainObject thisAsMatrix(*this);


   85   return SelfAdjointEigenSolver<PlainObject>(thisAsMatrix, false).eigenvalues();


   86 }


Eigen::SelfAdjointView::PlainObject
MatrixType::PlainObject PlainObject
Definition: SelfAdjointView.h:72




References Eigen::SelfAdjointEigenSolver< MatrixType_ >::eigenvalues().








◆ innerStride()








template<typename MatrixType_ , unsigned int UpLo> 



  

  
      

        

          EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index Eigen::SelfAdjointView< MatrixType_, UpLo >::innerStride 
          (
          )
           const
        

      

  		
  
inline  
  






   79 { return m_matrix.innerStride(); }




References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.








◆ ldlt()








template<typename MatrixType , unsigned int UpLo> 



  

  
      

        

          const LDLT< typename SelfAdjointView< MatrixType, UpLo >::PlainObject, UpLo > Eigen::SelfAdjointView< MatrixType, UpLo >::ldlt
        

      

  		
  
inline  
  






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


See also
MatrixBase::ldlt() 


  634                                               {


  635   return LDLT<PlainObject, UpLo>(m_matrix);


  636 }




References Eigen::LDLT< MatrixType_, UpLo_ >::m_matrix.








◆ llt()








template<typename MatrixType , unsigned int UpLo> 



  

  
      

        

          const LLT< typename SelfAdjointView< MatrixType, UpLo >::PlainObject, UpLo > Eigen::SelfAdjointView< MatrixType, UpLo >::llt
        

      

  		
  
inline  
  






\cholesky_module 
Returns
the LLT decomposition of *this 


See also
SelfAdjointView::llt() 


  508           {


  509   return LLT<PlainObject, UpLo>(m_matrix);


  510 }




References Eigen::LLT< MatrixType_, UpLo_ >::m_matrix.








◆ nestedExpression() [1/2]








template<typename MatrixType_ , unsigned int UpLo> 



  

  
      

        

          EIGEN_DEVICE_FUNC MatrixTypeNestedCleaned& Eigen::SelfAdjointView< MatrixType_, UpLo >::nestedExpression 
          (
          )
          
        

      

  		
  
inline  
  






  102 { return m_matrix; }




References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.








◆ nestedExpression() [2/2]








template<typename MatrixType_ , unsigned int UpLo> 



  

  
      

        

          EIGEN_DEVICE_FUNC const MatrixTypeNestedCleaned& Eigen::SelfAdjointView< MatrixType_, UpLo >::nestedExpression 
          (
          )
           const
        

      

  		
  
inline  
  






  101 { return m_matrix; }




References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.








◆ operator*()








template<typename MatrixType_ , unsigned int UpLo> 



template<typename OtherDerived > 



  

  
      

        

          EIGEN_DEVICE_FUNC const Product<SelfAdjointView, OtherDerived> Eigen::SelfAdjointView< MatrixType_, UpLo >::operator* 
          (
          const MatrixBase< OtherDerived > & 
          rhs)
           const
        

      

  		
  
inline  
  






Efficient triangular matrix times vector/matrix product 


  106                                                                                                                       {


  107     return Product<SelfAdjointView, OtherDerived>(*this, rhs.derived());


  108   }









◆ operatorNorm()








template<typename MatrixType , unsigned int UpLo> 



  

  
      

        

          EIGEN_DEVICE_FUNC SelfAdjointView< MatrixType, UpLo >::RealScalar Eigen::SelfAdjointView< MatrixType, UpLo >::operatorNorm
        

      

  		
  
inline  
  







Computes the L2 operator norm. 


Returns
Operator norm of the matrix.


\eigenvalues_module 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;


Eigen::SelfAdjointView::operatorNorm
EIGEN_DEVICE_FUNC RealScalar operatorNorm() const
Computes the L2 operator norm.
Definition: MatrixBaseEigenvalues.h:136


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


  136                                                       {


  137   return eigenvalues().cwiseAbs().maxCoeff();


  138 }









◆ outerStride()








template<typename MatrixType_ , unsigned int UpLo> 



  

  
      

        

          EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index Eigen::SelfAdjointView< MatrixType_, UpLo >::outerStride 
          (
          )
           const
        

      

  		
  
inline  
  






   78 { return m_matrix.outerStride(); }




References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.








◆ rankUpdate() [1/4]








template<typename MatrixType_ , unsigned int UpLo> 



template<typename DerivedU , typename DerivedV > 

      

        

          EIGEN_DEVICE_FUNC SelfAdjointView<MatrixType, UpLo>& Eigen::SelfAdjointView< MatrixType_, UpLo >::rankUpdate 
          (
          const MatrixBase< DerivedU > & 
          u, 
        

        

          
          
          const MatrixBase< DerivedV > & 
          v, 
        

        

          
          
          const Scalar & 
          alpha 
        

        

          
          )
          
        

      




   59                                                                                        {


   60   typedef internal::blas_traits<DerivedU> UBlasTraits;


   61   typedef typename UBlasTraits::DirectLinearAccessType ActualUType;


   62   typedef internal::remove_all_t<ActualUType> ActualUType_;


   63   internal::add_const_on_value_type_t<ActualUType> actualU = UBlasTraits::extract(u.derived());


   64  


   65   typedef internal::blas_traits<DerivedV> VBlasTraits;


   66   typedef typename VBlasTraits::DirectLinearAccessType ActualVType;


   67   typedef internal::remove_all_t<ActualVType> ActualVType_;


   68   internal::add_const_on_value_type_t<ActualVType> actualV = VBlasTraits::extract(v.derived());


   69  


   70   // If MatrixType is row major, then we use the routine for lower triangular in the upper triangular case and


   71   // vice versa, and take the complex conjugate of all coefficients and vector entries.


   72  


   73   enum { IsRowMajor = (internal::traits<MatrixType>::Flags & RowMajorBit) ? 1 : 0 };


   74   Scalar actualAlpha = alpha * UBlasTraits::extractScalarFactor(u.derived()) *


   75                        numext::conj(VBlasTraits::extractScalarFactor(v.derived()));


   76   if (IsRowMajor) actualAlpha = numext::conj(actualAlpha);


   77  


   78   typedef internal::remove_all_t<


   79       typename internal::conj_expr_if<int(IsRowMajor) ^ int(UBlasTraits::NeedToConjugate), ActualUType_>::type>


   80       UType;


   81   typedef internal::remove_all_t<


   82       typename internal::conj_expr_if<int(IsRowMajor) ^ int(VBlasTraits::NeedToConjugate), ActualVType_>::type>


   83       VType;


   84   internal::selfadjoint_rank2_update_selector<Scalar, Index, UType, VType,


   85                                               (IsRowMajor ? int(UpLo == Upper ? Lower : Upper)


   86                                                           : UpLo)>::run(_expression().const_cast_derived().data(),


   87                                                                         _expression().outerStride(), UType(actualU),


   88                                                                         VType(actualV), actualAlpha);


   89  


   90   return *this;


   91 }


conj
AnnoyingScalar conj(const AnnoyingScalar &x)
Definition: AnnoyingScalar.h:133


v
Array< int, Dynamic, 1 > v
Definition: Array_initializer_list_vector_cxx11.cpp:1


data
int data[]
Definition: Map_placement_new.cpp:1


Scalar
SCALAR Scalar
Definition: bench_gemm.cpp:45


Eigen::SelfAdjointView::outerStride
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index outerStride() const EIGEN_NOEXCEPT
Definition: SelfAdjointView.h:78


Eigen::SelfAdjointView::_expression
EIGEN_DEVICE_FUNC const MatrixTypeNestedCleaned & _expression() const
Definition: SelfAdjointView.h:99


Eigen::SelfAdjointView::Scalar
internal::traits< SelfAdjointView >::Scalar Scalar
The type of coefficients in this matrix.
Definition: SelfAdjointView.h:62


Eigen::RowMajorBit
const unsigned int RowMajorBit
Definition: Constants.h:70


alpha
RealScalar alpha
Definition: level1_cplx_impl.h:151


Eigen::internal::conj_expr_if
std::conditional<!Cond, const T &, CwiseUnaryOp< scalar_conjugate_op< typename traits< T >::Scalar >, T > > conj_expr_if
Definition: SelfadjointRank2Update.h:52


Eigen::internal::remove_all_t
typename remove_all< T >::type remove_all_t
Definition: Meta.h:142


Eigen::run
auto run(Kernel kernel, Args &&... args) -> decltype(kernel(args...))
Definition: gpu_test_helper.h:414


compute_granudrum_aor.type
type
Definition: compute_granudrum_aor.py:141


Eigen::EigenBase::Index
Eigen::Index Index
The interface type of indices.
Definition: EigenBase.h:43


Eigen::EigenBase::const_cast_derived
EIGEN_DEVICE_FUNC Derived & const_cast_derived() const
Definition: EigenBase.h:53




References alpha, conj(), int(), Eigen::Lower, Eigen::RowMajorBit, Eigen::run(), compute_granudrum_aor::type, Eigen::Upper, and v.








◆ rankUpdate() [2/4]








template<typename MatrixType_ , unsigned int UpLo> 



template<typename DerivedU , typename DerivedV > 

      

        

          EIGEN_DEVICE_FUNC 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) 








◆ rankUpdate() [3/4]








template<typename MatrixType_ , unsigned int UpLo> 



template<typename DerivedU > 

      

        

          EIGEN_DEVICE_FUNC SelfAdjointView<MatrixType, UpLo>& Eigen::SelfAdjointView< MatrixType_, UpLo >::rankUpdate 
          (
          const MatrixBase< DerivedU > & 
          u, 
        

        

          
          
          const Scalar & 
          alpha 
        

        

          
          )
          
        

      




  125                                                         {


  126   selfadjoint_product_selector<MatrixType, DerivedU, UpLo>::run(_expression().const_cast_derived(), u.derived(), alpha);


  127  


  128   return *this;


  129 }


run
void run(const string &dir_name, LinearSolver *linear_solver_pt, const unsigned nel_1d, bool mess_up_order)
Definition: two_d_poisson_compare_solvers.cc:317




References alpha, and run().








◆ rankUpdate() [4/4]








template<typename MatrixType_ , unsigned int UpLo> 



template<typename DerivedU > 

      

        

          EIGEN_DEVICE_FUNC 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) 








◆ rows()








template<typename MatrixType_ , unsigned int UpLo> 



  

  
      

        

          EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index Eigen::SelfAdjointView< MatrixType_, UpLo >::rows 
          (
          )
           const
        

      

  		
  
inline  
  






   76 { return m_matrix.rows(); }




References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.



Referenced by gdb.printers._MatrixEntryIterator::__next__(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().








◆ transpose() [1/2]








template<typename MatrixType_ , unsigned int UpLo> 



  

  
      

        

          EIGEN_DEVICE_FUNC const ConstTransposeReturnType Eigen::SelfAdjointView< MatrixType_, UpLo >::transpose 
          (
          )
           const
        

      

  		
  
inline  
  






See also
MatrixBase::transpose() const  


  207                                                                             {


  208     return ConstTransposeReturnType(m_matrix.transpose());


  209   }


Eigen::SelfAdjointView::ConstTransposeReturnType
SelfAdjointView< const typename MatrixType::ConstTransposeReturnType, TransposeMode > ConstTransposeReturnType
Definition: SelfAdjointView.h:205




References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix.








◆ transpose() [2/2]








template<typename MatrixType_ , unsigned int UpLo> 



template<class Dummy  = int> 



  

  
      

        

          EIGEN_DEVICE_FUNC TransposeReturnType Eigen::SelfAdjointView< MatrixType_, UpLo >::transpose 
          (
          std::enable_if_t< Eigen::internal::is_lvalue< MatrixType >::value, Dummy * > 
           = nullptr)
          
        

      

  		
  
inline  
  






See also
MatrixBase::transpose() 


  200                                                                                  {


  201     typename MatrixType::TransposeReturnType tmp(m_matrix);


  202     return TransposeReturnType(tmp);


  203   }


Eigen::SelfAdjointView::TransposeReturnType
SelfAdjointView< typename MatrixType::TransposeReturnType, TransposeMode > TransposeReturnType
Definition: SelfAdjointView.h:196


tmp
Eigen::Matrix< Scalar, Dynamic, Dynamic, ColMajor > tmp
Definition: level3_impl.h:365




References Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix, and tmp.








◆ triangularView()








template<typename MatrixType_ , unsigned int UpLo> 



template<unsigned int TriMode> 



  

  
      

        

          EIGEN_DEVICE_FUNC std::conditional_t<(TriMode & (Upper | Lower)) == (UpLo & (Upper | Lower)), TriangularView<MatrixType, TriMode>, TriangularView<typename MatrixType::AdjointReturnType, TriMode> > Eigen::SelfAdjointView< MatrixType_, UpLo >::triangularView 
          (
          )
           const
        

      

  		
  
inline  
  






Returns
an expression of a triangular view extracted from the current selfadjoint view of a given triangular part


The parameter TriMode can have the following values: Upper, StrictlyUpper, UnitUpper, Lower, StrictlyLower, UnitLower.


If TriMode references the same triangular part than *this, then this method simply return a TriangularView of the nested expression, otherwise, the nested expression is first transposed, thus returning a TriangularView<Transpose<MatrixType>> object.


See also
MatrixBase::triangularView(), class TriangularView 


  165                              {


  166     std::conditional_t<(TriMode & (Upper | Lower)) == (UpLo & (Upper | Lower)), MatrixType&,


  167                        typename MatrixType::ConstTransposeReturnType>


  168         tmp1(m_matrix);


  169     std::conditional_t<(TriMode & (Upper | Lower)) == (UpLo & (Upper | Lower)), MatrixType&,


  170                        typename MatrixType::AdjointReturnType>


  171         tmp2(tmp1);


  172     return std::conditional_t<(TriMode & (Upper | Lower)) == (UpLo & (Upper | Lower)),


  173                               TriangularView<MatrixType, TriMode>,


  174                               TriangularView<typename MatrixType::AdjointReturnType, TriMode> >(tmp2);


  175   }


MatrixType
MatrixXf MatrixType
Definition: benchmark-blocking-sizes.cpp:52




References Eigen::Lower, Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix, and Eigen::Upper.







Friends And Related Function Documentation



◆ operator* [1/2]








template<typename MatrixType_ , unsigned int UpLo> 



template<typename OtherDerived > 



  

  
      

        

          EIGEN_DEVICE_FUNC const Product<OtherDerived, SelfAdjointView> operator* 
          (
          const MatrixBase< OtherDerived > & 
          lhs, 
        

        

          
          
          const SelfAdjointView< MatrixType_, UpLo > & 
          rhs 
        

        

          
          )
          
        

      

  		
  
friend  
  






Efficient vector/matrix times triangular matrix product 


  113                                                                                                               {


  114     return Product<OtherDerived, SelfAdjointView>(lhs.derived(), rhs);


  115   }









◆ operator* [2/2]








template<typename MatrixType_ , unsigned int UpLo> 



  

  
      

        

          EIGEN_DEVICE_FUNC const SelfAdjointView<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar, MatrixType, product), UpLo> operator* 
          (
          const Scalar & 
          s, 
        

        

          
          
          const SelfAdjointView< MatrixType_, UpLo > & 
          mat 
        

        

          
          )
          
        

      

  		
  
friend  
  






  119                                                              {


  120     return (s * mat.nestedExpression()).template selfadjointView<UpLo>();


  121   }



s
RealScalar s
Definition: level1_cplx_impl.h:130








Member Data Documentation



◆ m_matrix








template<typename MatrixType_ , unsigned int UpLo> 



  

  
      

        

          MatrixTypeNested Eigen::SelfAdjointView< MatrixType_, UpLo >::m_matrix
        

      

  		
  
protected  
  







Referenced by Eigen::SelfAdjointView< MatrixType_, UpLo >::_expression(), Eigen::SelfAdjointView< MatrixType_, UpLo >::adjoint(), Eigen::SelfAdjointView< MatrixType_, UpLo >::coeff(), Eigen::SelfAdjointView< MatrixType_, UpLo >::coeffRef(), Eigen::SelfAdjointView< MatrixType_, UpLo >::cols(), Eigen::SelfAdjointView< MatrixType_, UpLo >::conjugate(), Eigen::SelfAdjointView< MatrixType_, UpLo >::conjugateIf(), Eigen::SelfAdjointView< MatrixType_, UpLo >::diagonal(), Eigen::SelfAdjointView< MatrixType_, UpLo >::innerStride(), Eigen::SelfAdjointView< MatrixType_, UpLo >::nestedExpression(), Eigen::SelfAdjointView< MatrixType_, UpLo >::outerStride(), Eigen::SelfAdjointView< MatrixType_, UpLo >::rows(), Eigen::SelfAdjointView< MatrixType_, UpLo >::transpose(), and Eigen::SelfAdjointView< MatrixType_, UpLo >::triangularView().







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