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TriangularView< _MatrixType, _Mode > Class Template Reference

Base class for triangular part in a matrix. More...

#include <TriangularMatrix.h>

Inheritance diagram for TriangularView< _MatrixType, _Mode >:
TriangularBase< TriangularView< _MatrixType, _Mode > > EigenBase< TriangularView< _MatrixType, _Mode > >

List of all members.

Public Types

enum  { Mode = _Mode, TransposeMode }
typedef TriangularBase
< TriangularView > 		Base
typedef internal::traits
< TriangularView >::Scalar 		Scalar
typedef _MatrixType MatrixType
typedef internal::traits
< TriangularView >
::DenseMatrixType 		DenseMatrixType
typedef DenseMatrixType PlainObject
typedef internal::traits
< TriangularView >
::StorageKind 		StorageKind
typedef internal::traits
< TriangularView >::Index 		Index

Public Member Functions

 TriangularView (const MatrixType &matrix)
Index rows () const
Index cols () const
Index outerStride () const
Index innerStride () const
template<typename Other >
TriangularView & operator+= (const DenseBase< Other > &other)
template<typename Other >
TriangularView & operator-= (const DenseBase< Other > &other)
TriangularView & operator*= (const typename internal::traits< MatrixType >::Scalar &other)
TriangularView & operator/= (const typename internal::traits< MatrixType >::Scalar &other)
void fill (const Scalar &value)
TriangularView & setConstant (const Scalar &value)
TriangularView & setZero ()
TriangularView & setOnes ()
Scalar coeff (Index row, Index col) const
Scalar & coeffRef (Index row, Index col)
const MatrixTypeNestedCleaned & nestedExpression () const
MatrixTypeNestedCleaned & nestedExpression ()
template<typename OtherDerived >
TriangularView & operator= (const TriangularBase< OtherDerived > &other)
template<typename OtherDerived >
TriangularView & operator= (const MatrixBase< OtherDerived > &other)
TriangularView & operator= (const TriangularView &other)
template<typename OtherDerived >
void lazyAssign (const TriangularBase< OtherDerived > &other)
template<typename OtherDerived >
void lazyAssign (const MatrixBase< OtherDerived > &other)
TriangularView
< MatrixConjugateReturnType,
Mode > 		conjugate ()
const TriangularView
< MatrixConjugateReturnType,
Mode > 		conjugate () const
TriangularView< typename
MatrixType::AdjointReturnType,
TransposeMode > 		adjoint ()
const TriangularView< typename
MatrixType::AdjointReturnType,
TransposeMode > 		adjoint () const
TriangularView< Transpose
< MatrixType >, TransposeMode > 		transpose ()
const TriangularView
< Transpose< MatrixType >
, TransposeMode > 		transpose () const
template<typename OtherDerived >
TriangularProduct< Mode, true,
MatrixType, false,
OtherDerived,
OtherDerived::IsVectorAtCompileTime > 		operator* (const MatrixBase< OtherDerived > &rhs) const
template<int Side, typename Other >
const
internal::triangular_solve_retval
< Side, TriangularView, Other > 		solve (const MatrixBase< Other > &other) const
template<int Side, typename OtherDerived >
void solveInPlace (const MatrixBase< OtherDerived > &other) const
template<typename Other >
const
internal::triangular_solve_retval
< OnTheLeft, TriangularView,
Other > 		solve (const MatrixBase< Other > &other) const
template<typename OtherDerived >
void solveInPlace (const MatrixBase< OtherDerived > &other) const
const SelfAdjointView
< MatrixTypeNestedNonRef, Mode > 		selfadjointView () const
SelfAdjointView
< MatrixTypeNestedNonRef, Mode > 		selfadjointView ()
template<typename OtherDerived >
void swap (TriangularBase< OtherDerived > const &other)
template<typename OtherDerived >
void swap (MatrixBase< OtherDerived > const &other)
Scalar determinant () const
template<typename ProductDerived , typename Lhs , typename Rhs >
EIGEN_STRONG_INLINE
TriangularView & 		operator= (const ProductBase< ProductDerived, Lhs, Rhs > &other)
template<typename ProductDerived , typename Lhs , typename Rhs >
EIGEN_STRONG_INLINE
TriangularView & 		operator+= (const ProductBase< ProductDerived, Lhs, Rhs > &other)
template<typename ProductDerived , typename Lhs , typename Rhs >
EIGEN_STRONG_INLINE
TriangularView & 		operator-= (const ProductBase< ProductDerived, Lhs, Rhs > &other)
template<typename ProductDerived >
EIGEN_STRONG_INLINE
TriangularView & 		operator= (const ScaledProduct< ProductDerived > &other)
template<typename ProductDerived >
EIGEN_STRONG_INLINE
TriangularView & 		operator+= (const ScaledProduct< ProductDerived > &other)
template<typename ProductDerived >
EIGEN_STRONG_INLINE
TriangularView & 		operator-= (const ScaledProduct< ProductDerived > &other)
template<typename ProductDerived , typename _Lhs , typename _Rhs >
TriangularView< MatrixType,
UpLo > & 		assignProduct (const ProductBase< ProductDerived, _Lhs, _Rhs > &prod, const Scalar &alpha)

Protected Types

typedef internal::traits
< TriangularView >
::MatrixTypeNested 		MatrixTypeNested
typedef internal::traits
< TriangularView >
::MatrixTypeNestedNonRef 		MatrixTypeNestedNonRef
typedef internal::traits
< TriangularView >
::MatrixTypeNestedCleaned 		MatrixTypeNestedCleaned
typedef internal::remove_all
< typename
MatrixType::ConjugateReturnType >
::type 		MatrixConjugateReturnType

Protected Member Functions

template<typename ProductDerived , typename Lhs , typename Rhs >
EIGEN_STRONG_INLINE
TriangularView & 		assignProduct (const ProductBase< ProductDerived, Lhs, Rhs > &prod, const Scalar &alpha)

Protected Attributes

const MatrixTypeNested m_matrix

Friends

template<typename OtherDerived >
TriangularProduct< Mode, false,
OtherDerived,
OtherDerived::IsVectorAtCompileTime,
MatrixType, false > 		operator* (const MatrixBase< OtherDerived > &lhs, const TriangularView &rhs)

Detailed Description

template<typename _MatrixType, unsigned int _Mode>
class TriangularView< _MatrixType, _Mode >

Base class for triangular part in a matrix.

Parameters:
MatrixType the type of the object in which we are taking the triangular part
Mode the kind of triangular matrix expression to construct. Can be Upper, Lower, UpperSelfadjoint, or LowerSelfadjoint. This is in fact a bit field; it must have either Upper or Lower, and additionnaly it may have either UnitDiag or Selfadjoint.

This class represents a triangular part of a matrix, not necessarily square. Strictly speaking, for rectangular matrices one should speak ok "trapezoid" parts. This class is the return type of MatrixBase::triangularView() and most of the time this is the only way it is used.

See also:
MatrixBase::triangularView()

Member Typedef Documentation

template<typename _MatrixType, unsigned int _Mode>
typedef TriangularBase<TriangularView> TriangularView< _MatrixType, _Mode >::Base
template<typename _MatrixType, unsigned int _Mode>
typedef internal::traits<TriangularView>::DenseMatrixType TriangularView< _MatrixType, _Mode >::DenseMatrixType

Reimplemented from TriangularBase< TriangularView< _MatrixType, _Mode > >.

template<typename _MatrixType, unsigned int _Mode>
typedef internal::traits<TriangularView>::Index TriangularView< _MatrixType, _Mode >::Index

Reimplemented from TriangularBase< TriangularView< _MatrixType, _Mode > >.

template<typename _MatrixType, unsigned int _Mode>
typedef internal::remove_all<typename MatrixType::ConjugateReturnType>::type TriangularView< _MatrixType, _Mode >::MatrixConjugateReturnType [protected]
template<typename _MatrixType, unsigned int _Mode>
typedef _MatrixType TriangularView< _MatrixType, _Mode >::MatrixType
template<typename _MatrixType, unsigned int _Mode>
typedef internal::traits<TriangularView>::MatrixTypeNested TriangularView< _MatrixType, _Mode >::MatrixTypeNested [protected]
template<typename _MatrixType, unsigned int _Mode>
typedef internal::traits<TriangularView>::MatrixTypeNestedCleaned TriangularView< _MatrixType, _Mode >::MatrixTypeNestedCleaned [protected]
template<typename _MatrixType, unsigned int _Mode>
typedef internal::traits<TriangularView>::MatrixTypeNestedNonRef TriangularView< _MatrixType, _Mode >::MatrixTypeNestedNonRef [protected]
template<typename _MatrixType, unsigned int _Mode>
typedef DenseMatrixType TriangularView< _MatrixType, _Mode >::PlainObject
template<typename _MatrixType, unsigned int _Mode>
typedef internal::traits<TriangularView>::Scalar TriangularView< _MatrixType, _Mode >::Scalar

Reimplemented from TriangularBase< TriangularView< _MatrixType, _Mode > >.

template<typename _MatrixType, unsigned int _Mode>
typedef internal::traits<TriangularView>::StorageKind TriangularView< _MatrixType, _Mode >::StorageKind

Reimplemented from TriangularBase< TriangularView< _MatrixType, _Mode > >.

Member Enumeration Documentation

template<typename _MatrixType, unsigned int _Mode>
anonymous enum
Enumerator:
Mode 
TransposeMode 

Constructor & Destructor Documentation

template<typename _MatrixType, unsigned int _Mode>
TriangularView< _MatrixType, _Mode >::TriangularView ( const MatrixType &  matrix  )  [inline]

Member Function Documentation

template<typename _MatrixType, unsigned int _Mode>
TriangularView<typename MatrixType::AdjointReturnType,TransposeMode> TriangularView< _MatrixType, _Mode >::adjoint (  )  [inline]
See also:
MatrixBase::adjoint()
template<typename _MatrixType, unsigned int _Mode>
const TriangularView<typename MatrixType::AdjointReturnType,TransposeMode> TriangularView< _MatrixType, _Mode >::adjoint (  )  const [inline]
See also:
MatrixBase::adjoint() const
template<typename _MatrixType, unsigned int _Mode>
template<typename ProductDerived , typename Lhs , typename Rhs >
EIGEN_STRONG_INLINE TriangularView& TriangularView< _MatrixType, _Mode >::assignProduct ( const ProductBase< ProductDerived, Lhs, Rhs > &  prod,
const Scalar &  alpha 
) [protected]
template<typename _MatrixType, unsigned int _Mode>
template<typename ProductDerived , typename _Lhs , typename _Rhs >
TriangularView<MatrixType,UpLo>& TriangularView< _MatrixType, _Mode >::assignProduct ( const ProductBase< ProductDerived, _Lhs, _Rhs > &  prod,
const Scalar &  alpha 
)
template<typename _MatrixType, unsigned int _Mode>
Scalar TriangularView< _MatrixType, _Mode >::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 _Mode>
Scalar& TriangularView< _MatrixType, _Mode >::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 _Mode>
Index TriangularView< _MatrixType, _Mode >::cols ( void   )  const [inline]
Returns:
the number of columns.
See also:
rows(), ColsAtCompileTime

Reimplemented from TriangularBase< TriangularView< _MatrixType, _Mode > >.

template<typename _MatrixType, unsigned int _Mode>
TriangularView<MatrixConjugateReturnType,Mode> TriangularView< _MatrixType, _Mode >::conjugate (  )  [inline]
See also:
MatrixBase::conjugate()
template<typename _MatrixType, unsigned int _Mode>
const TriangularView<MatrixConjugateReturnType,Mode> TriangularView< _MatrixType, _Mode >::conjugate (  )  const [inline]
See also:
MatrixBase::conjugate() const
template<typename _MatrixType, unsigned int _Mode>
Scalar TriangularView< _MatrixType, _Mode >::determinant (  )  const [inline]
template<typename _MatrixType, unsigned int _Mode>
void TriangularView< _MatrixType, _Mode >::fill ( const Scalar &  value  )  [inline]
See also:
MatrixBase::fill()
template<typename _MatrixType, unsigned int _Mode>
Index TriangularView< _MatrixType, _Mode >::innerStride (  )  const [inline]

Reimplemented from TriangularBase< TriangularView< _MatrixType, _Mode > >.

template<typename MatrixType , unsigned int Mode>
template<typename OtherDerived >
void TriangularView< MatrixType, Mode >::lazyAssign ( const MatrixBase< OtherDerived > &  other  ) 
template<typename MatrixType , unsigned int Mode>
template<typename OtherDerived >
void TriangularView< MatrixType, Mode >::lazyAssign ( const TriangularBase< OtherDerived > &  other  ) 
template<typename _MatrixType, unsigned int _Mode>
MatrixTypeNestedCleaned& TriangularView< _MatrixType, _Mode >::nestedExpression (  )  [inline]
template<typename _MatrixType, unsigned int _Mode>
const MatrixTypeNestedCleaned& TriangularView< _MatrixType, _Mode >::nestedExpression (  )  const [inline]
template<typename _MatrixType, unsigned int _Mode>
template<typename OtherDerived >
TriangularProduct<Mode,true,MatrixType,false,OtherDerived,OtherDerived::IsVectorAtCompileTime> TriangularView< _MatrixType, _Mode >::operator* ( const MatrixBase< OtherDerived > &  rhs  )  const [inline]

Efficient triangular matrix times vector/matrix product

template<typename _MatrixType, unsigned int _Mode>
TriangularView& TriangularView< _MatrixType, _Mode >::operator*= ( const typename internal::traits< MatrixType >::Scalar &  other  )  [inline]
See also:
MatrixBase::operator*=()
template<typename _MatrixType, unsigned int _Mode>
template<typename ProductDerived , typename Lhs , typename Rhs >
EIGEN_STRONG_INLINE TriangularView& TriangularView< _MatrixType, _Mode >::operator+= ( const ProductBase< ProductDerived, Lhs, Rhs > &  other  )  [inline]
template<typename _MatrixType, unsigned int _Mode>
template<typename Other >
TriangularView& TriangularView< _MatrixType, _Mode >::operator+= ( const DenseBase< Other > &  other  )  [inline]
See also:
MatrixBase::operator+=()
template<typename _MatrixType, unsigned int _Mode>
template<typename ProductDerived >
EIGEN_STRONG_INLINE TriangularView& TriangularView< _MatrixType, _Mode >::operator+= ( const ScaledProduct< ProductDerived > &  other  )  [inline]
template<typename _MatrixType, unsigned int _Mode>
template<typename ProductDerived , typename Lhs , typename Rhs >
EIGEN_STRONG_INLINE TriangularView& TriangularView< _MatrixType, _Mode >::operator-= ( const ProductBase< ProductDerived, Lhs, Rhs > &  other  )  [inline]
template<typename _MatrixType, unsigned int _Mode>
template<typename ProductDerived >
EIGEN_STRONG_INLINE TriangularView& TriangularView< _MatrixType, _Mode >::operator-= ( const ScaledProduct< ProductDerived > &  other  )  [inline]
template<typename _MatrixType, unsigned int _Mode>
template<typename Other >
TriangularView& TriangularView< _MatrixType, _Mode >::operator-= ( const DenseBase< Other > &  other  )  [inline]
See also:
MatrixBase::operator-=()
template<typename _MatrixType, unsigned int _Mode>
TriangularView& TriangularView< _MatrixType, _Mode >::operator/= ( const typename internal::traits< MatrixType >::Scalar &  other  )  [inline]
See also:
MatrixBase::operator/=()
template<typename MatrixType , unsigned int Mode>
template<typename OtherDerived >
TriangularView< MatrixType, Mode > & TriangularView< MatrixType, Mode >::operator= ( const MatrixBase< OtherDerived > &  other  )  [inline]
template<typename MatrixType , unsigned int Mode>
template<typename OtherDerived >
TriangularView< MatrixType, Mode > & TriangularView< MatrixType, Mode >::operator= ( const TriangularBase< OtherDerived > &  other  )  [inline]

Assigns a triangular matrix to a triangular part of a dense matrix

template<typename _MatrixType, unsigned int _Mode>
template<typename ProductDerived , typename Lhs , typename Rhs >
EIGEN_STRONG_INLINE TriangularView& TriangularView< _MatrixType, _Mode >::operator= ( const ProductBase< ProductDerived, Lhs, Rhs > &  other  )  [inline]
template<typename _MatrixType, unsigned int _Mode>
TriangularView& TriangularView< _MatrixType, _Mode >::operator= ( const TriangularView< _MatrixType, _Mode > &  other  )  [inline]
template<typename _MatrixType, unsigned int _Mode>
template<typename ProductDerived >
EIGEN_STRONG_INLINE TriangularView& TriangularView< _MatrixType, _Mode >::operator= ( const ScaledProduct< ProductDerived > &  other  )  [inline]
template<typename _MatrixType, unsigned int _Mode>
Index TriangularView< _MatrixType, _Mode >::outerStride (  )  const [inline]

Reimplemented from TriangularBase< TriangularView< _MatrixType, _Mode > >.

template<typename _MatrixType, unsigned int _Mode>
Index TriangularView< _MatrixType, _Mode >::rows ( void   )  const [inline]
Returns:
the number of rows.
See also:
cols(), RowsAtCompileTime

Reimplemented from TriangularBase< TriangularView< _MatrixType, _Mode > >.

template<typename _MatrixType, unsigned int _Mode>
const SelfAdjointView<MatrixTypeNestedNonRef,Mode> TriangularView< _MatrixType, _Mode >::selfadjointView (  )  const [inline]
template<typename _MatrixType, unsigned int _Mode>
SelfAdjointView<MatrixTypeNestedNonRef,Mode> TriangularView< _MatrixType, _Mode >::selfadjointView (  )  [inline]
template<typename _MatrixType, unsigned int _Mode>
TriangularView& TriangularView< _MatrixType, _Mode >::setConstant ( const Scalar &  value  )  [inline]
See also:
MatrixBase::setConstant()
template<typename _MatrixType, unsigned int _Mode>
TriangularView& TriangularView< _MatrixType, _Mode >::setOnes (  )  [inline]
See also:
MatrixBase::setOnes()
template<typename _MatrixType, unsigned int _Mode>
TriangularView& TriangularView< _MatrixType, _Mode >::setZero (  )  [inline]
See also:
MatrixBase::setZero()
template<typename Derived , unsigned int Mode>
template<int Side, typename Other >
const internal::triangular_solve_retval< Side, TriangularView< Derived, Mode >, Other > TriangularView< Derived, Mode >::solve ( const MatrixBase< Other > &  other  )  const [inline]
Returns:
the product of the inverse of *this with other, *this being triangular.

This function computes the inverse-matrix matrix product inverse(*this) * other if Side==OnTheLeft (the default), or the right-inverse-multiply other * inverse(*this) if Side==OnTheRight.

The matrix *this must be triangular and invertible (i.e., all the coefficients of the diagonal must be non zero). It works as a forward (resp. backward) substitution if *this is an upper (resp. lower) triangular matrix.

Example: 

 Output: 


This function returns an expression of the inverse-multiply and can works in-place if it is assigned to the same matrix or vector other.


For users coming from BLAS, this function (and more specifically solveInPlace()) offer all the operations supported by the *TRSV and *TRSM BLAS routines.


See also:
TriangularView::solveInPlace() 













template<typename _MatrixType, unsigned int _Mode> 



template<typename Other > 

      

        

          const internal::triangular_solve_retval<OnTheLeft,TriangularView, Other> TriangularView< _MatrixType, _Mode >::solve 
          (
          const MatrixBase< Other > & 
           other
           ) 
           const [inline]
        

      

















template<typename _MatrixType, unsigned int _Mode> 



template<typename OtherDerived > 

      

        

          void TriangularView< _MatrixType, _Mode >::solveInPlace 
          (
          const MatrixBase< OtherDerived > & 
           other
           ) 
           const [inline]
        

      

















template<typename MatrixType , unsigned int Mode> 



template<int Side, typename OtherDerived > 

      

        

          void TriangularView< MatrixType, Mode >::solveInPlace 
          (
          const MatrixBase< OtherDerived > & 
           _other
           ) 
           const
        

      






"in-place" version of TriangularView::solve() where the result is written in other 


Warning:
The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here. This function will const_cast it, so constness isn't honored here.


See TriangularView:solve() for the details. 













template<typename _MatrixType, unsigned int _Mode> 



template<typename OtherDerived > 

      

        

          void TriangularView< _MatrixType, _Mode >::swap 
          (
          TriangularBase< OtherDerived > const & 
           other
           ) 
           [inline]
        

      

















template<typename _MatrixType, unsigned int _Mode> 



template<typename OtherDerived > 

      

        

          void TriangularView< _MatrixType, _Mode >::swap 
          (
          MatrixBase< OtherDerived > const & 
           other
           ) 
           [inline]
        

      

















template<typename _MatrixType, unsigned int _Mode> 

      

        

          TriangularView<Transpose<MatrixType>,TransposeMode> TriangularView< _MatrixType, _Mode >::transpose 
          (
          
           ) 
           [inline]
        

      






See also:
MatrixBase::transpose() 













template<typename _MatrixType, unsigned int _Mode> 

      

        

          const TriangularView<Transpose<MatrixType>,TransposeMode> TriangularView< _MatrixType, _Mode >::transpose 
          (
          
           ) 
           const [inline]
        

      






See also:
MatrixBase::transpose() const  







Friends And Related Function Documentation








template<typename _MatrixType, unsigned int _Mode> 



template<typename OtherDerived > 

      

        

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

        

          
          
          const TriangularView< _MatrixType, _Mode > & 
           rhs 
        

        

          
          )
           [friend]
        

      






Efficient vector/matrix times triangular matrix product 







Member Data Documentation








template<typename _MatrixType, unsigned int _Mode> 

      

        

          const MatrixTypeNested TriangularView< _MatrixType, _Mode >::m_matrix [protected]
        

      











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



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