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

#include <TriangularMatrix.h>

Inheritance diagram for Eigen::TriangularView< _MatrixType, _Mode >:

Collaboration diagram for Eigen::TriangularView< _MatrixType, _Mode >:

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 Types inherited from Eigen::TriangularBase< TriangularView< _MatrixType, _Mode > >
enum

typedef internal::traits< TriangularView< _MatrixType, _Mode > >::Scalar	Scalar

typedef internal::traits< TriangularView< _MatrixType, _Mode > >::StorageKind	StorageKind

typedef internal::traits< TriangularView< _MatrixType, _Mode > >::Index	Index

typedef internal::traits< TriangularView< _MatrixType, _Mode > >::DenseMatrixType	DenseMatrixType

typedef DenseMatrixType	DenseType

Public Types inherited from Eigen::EigenBase< Derived >
typedef internal::traits< Derived >::StorageKind	StorageKind

typedef internal::traits< Derived >::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

const TriangularView< const 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)

template<int Side, typename Other >
const internal::triangular_solve_retval< Side, TriangularView< Derived, Mode >, Other >	solve (const MatrixBase< Other > &other) const

template<typename OtherDerived >
TriangularView< MatrixType, Mode > &	operator= (const MatrixBase< OtherDerived > &other)

template<typename OtherDerived >
TriangularView< MatrixType, Mode > &	operator= (const TriangularBase< OtherDerived > &other)

Public Member Functions inherited from Eigen::TriangularBase< TriangularView< _MatrixType, _Mode > >
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)

EIGEN_STRONG_INLINE void	copyCoeff (Index row, Index col, Other &other)

Scalar	operator() (Index row, Index col) const

Scalar &	operator() (Index row, Index col)

const TriangularView< _MatrixType, _Mode > &	derived () const

TriangularView< _MatrixType, _Mode > &	derived ()

void	evalTo (MatrixBase< DenseDerived > &other) const

void	evalToLazy (MatrixBase< DenseDerived > &other) const

DenseMatrixType	toDenseMatrix () const

Public Member Functions inherited from Eigen::EigenBase< Derived >
Derived &	derived ()

const Derived &	derived () const

Derived &	const_cast_derived () const

const Derived &	const_derived () const

Index	rows () const

Index	cols () const

Index	size () const

template<typename Dest >
void	evalTo (Dest &dst) const

template<typename Dest >
void	addTo (Dest &dst) const

template<typename Dest >
void	subTo (Dest &dst) const

template<typename Dest >
void	applyThisOnTheRight (Dest &dst) const

template<typename Dest >
void	applyThisOnTheLeft (Dest &dst) const

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 Member Functions inherited from Eigen::TriangularBase< TriangularView< _MatrixType, _Mode > >
void	check_coordinates (Index row, Index col) const

void	check_coordinates_internal (Index, Index) const

Protected Attributes
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 Eigen::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, #UnitUpper, #UnitLower, #StrictlyUpper, or #StrictlyLower. This is in fact a bit field; it must have either #Upper or #Lower, and additionnaly it may have #UnitDiag or #ZeroDiag or neither.

This class represents a triangular part of a matrix, not necessarily square. Strictly speaking, for rectangular matrices one should speak of "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()

Definition at line 158 of file TriangularMatrix.h.

Member Function Documentation

template<typename _MatrixType, unsigned int _Mode>

const TriangularView<const typename MatrixType::AdjointReturnType,TransposeMode> Eigen::TriangularView< _MatrixType, _Mode >::adjoint ( ) const

inline

See also: MatrixBase::adjoint() const

Definition at line 264 of file TriangularMatrix.h.

265 { return m_matrix.adjoint(); }

template<typename _MatrixType, unsigned int _Mode>

Scalar Eigen::TriangularView< _MatrixType, _Mode >::coeff	(	Index	row,
		Index	col
	)		const

inline

See also: MatrixBase::coeff()

Warning: the coordinates must fit into the referenced triangular part

Definition at line 222 of file TriangularMatrix.h.

     {
       Base::check_coordinates_internal(row, col);
       return m_matrix.coeff(row, col);
     }

template<typename _MatrixType, unsigned int _Mode>

Scalar& Eigen::TriangularView< _MatrixType, _Mode >::coeffRef	(	Index	row,
		Index	col
	)

inline

See also: MatrixBase::coeffRef()

Warning: the coordinates must fit into the referenced triangular part

Definition at line 231 of file TriangularMatrix.h.

     {
       Base::check_coordinates_internal(row, col);
       return m_matrix.const_cast_derived().coeffRef(row, col);
     }

template<typename _MatrixType, unsigned int _Mode>

TriangularView<MatrixConjugateReturnType,Mode> Eigen::TriangularView< _MatrixType, _Mode >::conjugate ( )

inline

See also: MatrixBase::conjugate()

Definition at line 257 of file TriangularMatrix.h.

258 { return m_matrix.conjugate(); }

template<typename _MatrixType, unsigned int _Mode>

const TriangularView<MatrixConjugateReturnType,Mode> Eigen::TriangularView< _MatrixType, _Mode >::conjugate ( ) const

inline

See also: MatrixBase::conjugate() const

Definition at line 260 of file TriangularMatrix.h.

261 { return m_matrix.conjugate(); }

template<typename _MatrixType, unsigned int _Mode>

void Eigen::TriangularView< _MatrixType, _Mode >::fill ( const Scalar & value )

inline

See also: MatrixBase::fill()

Definition at line 210 of file TriangularMatrix.h.

210 { setConstant(value); }

Eigen::TriangularView::setConstant

TriangularView & setConstant(const Scalar &value)

Definition: TriangularMatrix.h:212

template<typename _MatrixType, unsigned int _Mode>

template<typename OtherDerived >

TriangularProduct<Mode,true,MatrixType,false,OtherDerived, OtherDerived::IsVectorAtCompileTime> Eigen::TriangularView< _MatrixType, _Mode >::operator* ( const MatrixBase< OtherDerived > & rhs ) const

inline

Efficient triangular matrix times vector/matrix product

Definition at line 282 of file TriangularMatrix.h.

     {
       return TriangularProduct
               <Mode,true,MatrixType,false,OtherDerived,OtherDerived::IsVectorAtCompileTime>
               (m_matrix, rhs.derived());
     }

template<typename _MatrixType, unsigned int _Mode>

TriangularView& Eigen::TriangularView< _MatrixType, _Mode >::operator*= ( const typename internal::traits< MatrixType >::Scalar & other )

inline

See also: MatrixBase::operator*=()

Definition at line 205 of file TriangularMatrix.h.

205 { return *this = m_matrix * other; }

template<typename _MatrixType, unsigned int _Mode>

template<typename Other >

TriangularView& Eigen::TriangularView< _MatrixType, _Mode >::operator+= ( const DenseBase< Other > & other )

inline

See also: MatrixBase::operator+=()

Definition at line 201 of file TriangularMatrix.h.

201 { return *this = m_matrix + other.derived(); }

template<typename _MatrixType, unsigned int _Mode>

template<typename Other >

TriangularView& Eigen::TriangularView< _MatrixType, _Mode >::operator-= ( const DenseBase< Other > & other )

inline

See also: MatrixBase::operator-=()

Definition at line 203 of file TriangularMatrix.h.

203 { return *this = m_matrix - other.derived(); }

template<typename _MatrixType, unsigned int _Mode>

TriangularView& Eigen::TriangularView< _MatrixType, _Mode >::operator/= ( const typename internal::traits< MatrixType >::Scalar & other )

inline

See also: MatrixBase::operator/=()

Definition at line 207 of file TriangularMatrix.h.

207 { return *this = m_matrix / other; }

template<typename _MatrixType, unsigned int _Mode>

template<typename OtherDerived >

TriangularView& Eigen::TriangularView< _MatrixType, _Mode >::operator= ( const TriangularBase< OtherDerived > & other )

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

template<typename _MatrixType, unsigned int _Mode>

TriangularView& Eigen::TriangularView< _MatrixType, _Mode >::setConstant ( const Scalar & value )

inline

See also: MatrixBase::setConstant()

Definition at line 212 of file TriangularMatrix.h.

213 { return *this = MatrixType::Constant(rows(), cols(), value); }

template<typename _MatrixType, unsigned int _Mode>

TriangularView& Eigen::TriangularView< _MatrixType, _Mode >::setOnes ( )

inline

See also: MatrixBase::setOnes()

Definition at line 217 of file TriangularMatrix.h.

217 { return setConstant(Scalar(1)); }

Eigen::TriangularView::setConstant

TriangularView & setConstant(const Scalar &value)

Definition: TriangularMatrix.h:212

template<typename _MatrixType, unsigned int _Mode>

TriangularView& Eigen::TriangularView< _MatrixType, _Mode >::setZero ( )

inline

See also: MatrixBase::setZero()

Definition at line 215 of file TriangularMatrix.h.

215 { return setConstant(Scalar(0)); }

Eigen::TriangularView::setConstant

TriangularView & setConstant(const Scalar &value)

Definition: TriangularMatrix.h:212

template<typename _MatrixType, unsigned int _Mode>

template<int Side, typename Other >

const internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other> Eigen::TriangularView< _MatrixType, _Mode >::solve ( const MatrixBase< Other > & other ) const

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()

Definition at line 216 of file SolveTriangular.h.

 {
   return internal::triangular_solve_retval<Side,TriangularView,Other>(*this, other.derived());
 }

template<typename MatrixType , unsigned int Mode>

template<int Side, typename OtherDerived >

void Eigen::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.

Definition at line 174 of file SolveTriangular.h.

 {
   OtherDerived& other = _other.const_cast_derived();
   eigen_assert( cols() == rows() && ((Side==OnTheLeft && cols() == other.rows()) || (Side==OnTheRight && cols() == other.cols())) );
   eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
 
   enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit  && OtherDerived::IsVectorAtCompileTime };
   typedef typename internal::conditional<copy,
     typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
   OtherCopy otherCopy(other);
 
   internal::triangular_solver_selector<MatrixType, typename internal::remove_reference<OtherCopy>::type,
     Side, Mode>::run(nestedExpression(), otherCopy);
 
   if (copy)
     other = otherCopy;
 }

template<typename _MatrixType, unsigned int _Mode>

TriangularView<Transpose<MatrixType>,TransposeMode> Eigen::TriangularView< _MatrixType, _Mode >::transpose ( )

inline

See also: MatrixBase::transpose()

Definition at line 268 of file TriangularMatrix.h.

     {
       EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
       return m_matrix.const_cast_derived().transpose();
     }

template<typename _MatrixType, unsigned int _Mode>

const TriangularView<Transpose<MatrixType>,TransposeMode> Eigen::TriangularView< _MatrixType, _Mode >::transpose ( ) const

inline

See also: MatrixBase::transpose() const

Definition at line 274 of file TriangularMatrix.h.

     {
       return m_matrix.transpose();
     }

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

Definition at line 292 of file TriangularMatrix.h.

     {
       return TriangularProduct
               <Mode,false,OtherDerived,OtherDerived::IsVectorAtCompileTime,MatrixType,false>
               (lhs.derived(),rhs.m_matrix);
     }

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

C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/Core/TriangularMatrix.h
C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h
C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/Core/SolveTriangular.h

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Friends

Detailed Description

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

Member Function Documentation

Friends And Related Function Documentation

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