Eigen::TriangularView Class Reference

---

Detailed Description

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()

Inheritance diagram for Eigen::TriangularView:

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
enum
typedef DenseMatrixType	DenseType
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)
	Assigns a triangular matrix to a triangular part of a dense matrix.
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
	Efficient triangular matrix times vector/matrix product.
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
	"in-place" version of TriangularView::solve() where the result is written in other
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)
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)
void	evalTo (MatrixBase< DenseDerived > &other) const
void	evalToLazy (MatrixBase< DenseDerived > &other) const
DenseMatrixType	toDenseMatrix () 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)
void	check_coordinates (Index row, Index col) const
void	check_coordinates_internal (Index, Index) const
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)
	Efficient vector/matrix times triangular matrix product.

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Member Typedef Documentation

typedef TriangularBase<TriangularView> Eigen::TriangularView::Base

Definition at line 177 of file Core.

typedef internal::traits<TriangularView>::DenseMatrixType Eigen::TriangularView::DenseMatrixType

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

Definition at line 181 of file Core.

typedef DenseMatrixType Eigen::TriangularBase::DenseType [inherited]

Definition at line 59 of file Core.

typedef internal::traits<TriangularView>::Index Eigen::TriangularView::Index

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

Definition at line 196 of file Core.

typedef internal::remove_all<typename MatrixType::ConjugateReturnType>::type Eigen::TriangularView::MatrixConjugateReturnType [protected]

Definition at line 189 of file Core.

typedef _MatrixType Eigen::TriangularView::MatrixType

Definition at line 180 of file Core.

typedef internal::traits<TriangularView>::MatrixTypeNested Eigen::TriangularView::MatrixTypeNested [protected]

Definition at line 185 of file Core.

typedef internal::traits<TriangularView>::MatrixTypeNestedCleaned Eigen::TriangularView::MatrixTypeNestedCleaned [protected]

Definition at line 187 of file Core.

typedef internal::traits<TriangularView>::MatrixTypeNestedNonRef Eigen::TriangularView::MatrixTypeNestedNonRef [protected]

Definition at line 186 of file Core.

typedef DenseMatrixType Eigen::TriangularView::PlainObject

Definition at line 182 of file Core.

typedef internal::traits<TriangularView>::Scalar Eigen::TriangularView::Scalar

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

Definition at line 178 of file Core.

typedef internal::traits<TriangularView>::StorageKind Eigen::TriangularView::StorageKind

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

Definition at line 195 of file Core.

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Member Enumeration Documentation

anonymous enum [inherited]

Definition at line 47 of file Core.

anonymous enum

Enumerator:

Mode
TransposeMode

Definition at line 198 of file Core.

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Constructor & Destructor Documentation

Eigen::TriangularView::TriangularView

(

const MatrixType &

matrix

)

[inline]

Definition at line 206 of file Core.

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Member Function Documentation

TriangularView<typename MatrixType::AdjointReturnType,TransposeMode> Eigen::TriangularView::adjoint

(

)

[inline]

See also:

MatrixBase::adjoint()

Definition at line 278 of file Core.

const TriangularView<typename MatrixType::AdjointReturnType,TransposeMode> Eigen::TriangularView::adjoint

(

)

const [inline]

See also:

MatrixBase::adjoint() const

Definition at line 281 of file Core.

template<typename ProductDerived , typename _Lhs , typename _Rhs >

TriangularView<MatrixType,UpLo>& Eigen::TriangularView::assignProduct	(	const ProductBase< ProductDerived, _Lhs, _Rhs > &	prod,
		const Scalar &	alpha
	)

Definition at line 199 of file Core.

template<typename ProductDerived , typename Lhs , typename Rhs >

EIGEN_STRONG_INLINE TriangularView& Eigen::TriangularView::assignProduct	(	const ProductBase< ProductDerived, Lhs, Rhs > &	prod,
		const Scalar &	alpha
	)		[protected]

void Eigen::TriangularBase::check_coordinates	(	Index	row,
		Index	col
	)		const [inline, protected, inherited]

Definition at line 109 of file Core.

void Eigen::TriangularBase::check_coordinates_internal	(	Index	,
		Index
	)		const [inline, protected, inherited]

Definition at line 128 of file Core.

Scalar Eigen::TriangularBase::coeff	(	Index	row,
		Index	col
	)		const [inline, inherited]

Definition at line 68 of file Core.

Scalar Eigen::TriangularView::coeff	(	Index	row,
		Index	col
	)		const [inline]

See also:

MatrixBase::coeff()

Warning:

the coordinates must fit into the referenced triangular part

Definition at line 236 of file Core.

Scalar& Eigen::TriangularBase::coeffRef	(	Index	row,
		Index	col
	)		[inline, inherited]

Definition at line 69 of file Core.

Scalar& Eigen::TriangularView::coeffRef	(	Index	row,
		Index	col
	)		[inline]

See also:

MatrixBase::coeffRef()

Warning:

the coordinates must fit into the referenced triangular part

Definition at line 245 of file Core.

Index Eigen::TriangularView::cols

(

void

)

const [inline]

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

Definition at line 210 of file Core.

TriangularView<MatrixConjugateReturnType,Mode> Eigen::TriangularView::conjugate

(

)

[inline]

See also:

MatrixBase::conjugate()

Definition at line 271 of file Core.

const TriangularView<MatrixConjugateReturnType,Mode> Eigen::TriangularView::conjugate

(

)

const [inline]

See also:

MatrixBase::conjugate() const

Definition at line 274 of file Core.

EIGEN_STRONG_INLINE void Eigen::TriangularBase::copyCoeff	(	Index	row,
		Index	col,
		Other &	other
	)		[inline, inherited]

See also:

MatrixBase::copyCoeff(row,col)

Definition at line 74 of file Core.

Scalar Eigen::TriangularView::determinant

(

)

const [inline]

Definition at line 382 of file Core.

void Eigen::TriangularBase::evalTo

(

MatrixBase< DenseDerived > &

other

)

const [inherited]

Assigns a triangular or selfadjoint matrix to a dense matrix.

If the matrix is triangular, the opposite part is set to zero.

void Eigen::TriangularBase::evalToLazy

(

MatrixBase< DenseDerived > &

other

)

const [inherited]

Assigns a triangular or selfadjoint matrix to a dense matrix.

If the matrix is triangular, the opposite part is set to zero.

void Eigen::TriangularView::fill

(

const Scalar &

value

)

[inline]

See also:

MatrixBase::fill()

Definition at line 224 of file Core.

Index Eigen::TriangularView::innerStride

(

)

const [inline]

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

Definition at line 212 of file Core.

template<typename OtherDerived >

void Eigen::TriangularView::lazyAssign

(

const TriangularBase< OtherDerived > &

other

)

Definition at line 660 of file Core.

template<typename OtherDerived >

void Eigen::TriangularView::lazyAssign

(

const MatrixBase< OtherDerived > &

other

)

Definition at line 623 of file Core.

const MatrixTypeNestedCleaned& Eigen::TriangularView::nestedExpression

(

)

const [inline]

Definition at line 251 of file Core.

MatrixTypeNestedCleaned& Eigen::TriangularView::nestedExpression

(

)

[inline]

Definition at line 252 of file Core.

Scalar Eigen::TriangularBase::operator()	(	Index	row,
		Index	col
	)		const [inline, inherited]

Definition at line 79 of file Core.

Scalar& Eigen::TriangularBase::operator()	(	Index	row,
		Index	col
	)		[inline, inherited]

Definition at line 84 of file Core.

template<typename OtherDerived >

TriangularProduct<Mode,true,MatrixType,false,OtherDerived,OtherDerived::IsVectorAtCompileTime> Eigen::TriangularView::operator*

(

const MatrixBase< OtherDerived > &

rhs

)

const [inline]

Efficient triangular matrix times vector/matrix product.

Definition at line 297 of file Core.

TriangularView& Eigen::TriangularView::operator*=

(

const typename internal::traits< MatrixType >::Scalar &

other

)

[inline]

See also:

MatrixBase::operator*=()

Definition at line 219 of file Core.

template<typename Other >

TriangularView& Eigen::TriangularView::operator+=

(

const DenseBase< Other > &

other

)

[inline]

See also:

MatrixBase::operator+=()

Definition at line 215 of file Core.

template<typename ProductDerived , typename Lhs , typename Rhs >

EIGEN_STRONG_INLINE TriangularView& Eigen::TriangularView::operator+=

(

const ProductBase< ProductDerived, Lhs, Rhs > &

other

)

[inline]

Definition at line 401 of file Core.

template<typename ProductDerived >

EIGEN_STRONG_INLINE TriangularView& Eigen::TriangularView::operator+=

(

const ScaledProduct< ProductDerived > &

other

)

[inline]

Definition at line 421 of file Core.

template<typename Other >

TriangularView& Eigen::TriangularView::operator-=

(

const DenseBase< Other > &

other

)

[inline]

See also:

MatrixBase::operator-=()

Definition at line 217 of file Core.

template<typename ProductDerived , typename Lhs , typename Rhs >

EIGEN_STRONG_INLINE TriangularView& Eigen::TriangularView::operator-=

(

const ProductBase< ProductDerived, Lhs, Rhs > &

other

)

[inline]

Definition at line 407 of file Core.

template<typename ProductDerived >

EIGEN_STRONG_INLINE TriangularView& Eigen::TriangularView::operator-=

(

const ScaledProduct< ProductDerived > &

other

)

[inline]

Definition at line 427 of file Core.

TriangularView& Eigen::TriangularView::operator/=

(

const typename internal::traits< MatrixType >::Scalar &

other

)

[inline]

See also:

MatrixBase::operator/=()

Definition at line 221 of file Core.

template<typename OtherDerived >

TriangularView< MatrixType, Mode > & Eigen::TriangularView::operator=

(

const TriangularBase< OtherDerived > &

other

)

[inline]

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

Definition at line 644 of file Core.

template<typename OtherDerived >

TriangularView< MatrixType, Mode > & Eigen::TriangularView::operator=

(

const MatrixBase< OtherDerived > &

other

)

[inline]

Definition at line 607 of file Core.

TriangularView& Eigen::TriangularView::operator=

(

const TriangularView &

other

)

[inline]

Definition at line 261 of file Core.

template<typename ProductDerived , typename Lhs , typename Rhs >

EIGEN_STRONG_INLINE TriangularView& Eigen::TriangularView::operator=

(

const ProductBase< ProductDerived, Lhs, Rhs > &

other

)

[inline]

Definition at line 394 of file Core.

template<typename ProductDerived >

EIGEN_STRONG_INLINE TriangularView& Eigen::TriangularView::operator=

(

const ScaledProduct< ProductDerived > &

other

)

[inline]

Definition at line 414 of file Core.

Index Eigen::TriangularView::outerStride

(

)

const [inline]

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

Definition at line 211 of file Core.

Index Eigen::TriangularView::rows

(

void

)

const [inline]

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

Definition at line 209 of file Core.

const SelfAdjointView<MatrixTypeNestedNonRef,Mode> Eigen::TriangularView::selfadjointView

(

)

const [inline]

Definition at line 359 of file Core.

SelfAdjointView<MatrixTypeNestedNonRef,Mode> Eigen::TriangularView::selfadjointView

(

)

[inline]

Definition at line 364 of file Core.

TriangularView& Eigen::TriangularView::setConstant

(

const Scalar &

value

)

[inline]

See also:

MatrixBase::setConstant()

Definition at line 226 of file Core.

TriangularView& Eigen::TriangularView::setOnes

(

)

[inline]

See also:

MatrixBase::setOnes()

Definition at line 231 of file Core.

TriangularView& Eigen::TriangularView::setZero

(

)

[inline]

See also:

MatrixBase::setZero()

Definition at line 229 of file Core.

template<int Side, typename Other >

const internal::triangular_solve_retval< Side, TriangularView< Derived, Mode >, Other > Eigen::TriangularView::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()

Definition at line 222 of file Core.

template<typename Other >

const internal::triangular_solve_retval<OnTheLeft,TriangularView, Other> Eigen::TriangularView::solve

(

const MatrixBase< Other > &

other

)

const [inline]

Definition at line 352 of file Core.

template<int Side, typename OtherDerived >

void Eigen::TriangularView::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 178 of file Core.

template<typename OtherDerived >

void Eigen::TriangularView::solveInPlace

(

const MatrixBase< OtherDerived > &

other

)

const [inline]

Definition at line 356 of file Core.

template<typename OtherDerived >

void Eigen::TriangularView::swap

(

TriangularBase< OtherDerived > const &

other

)

[inline]

Definition at line 371 of file Core.

template<typename OtherDerived >

void Eigen::TriangularView::swap

(

MatrixBase< OtherDerived > const &

other

)

[inline]

Definition at line 377 of file Core.

DenseMatrixType Eigen::TriangularBase::toDenseMatrix

(

)

const [inline, inherited]

Definition at line 100 of file Core.

TriangularView<Transpose<MatrixType>,TransposeMode> Eigen::TriangularView::transpose

(

)

[inline]

See also:

MatrixBase::transpose()

Definition at line 285 of file Core.

const TriangularView<Transpose<MatrixType>,TransposeMode> Eigen::TriangularView::transpose

(

)

const [inline]

See also:

MatrixBase::transpose() const

Definition at line 291 of file Core.

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Friends And Related Function Documentation

template<typename OtherDerived >

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

Efficient vector/matrix times triangular matrix product.

Definition at line 307 of file Core.

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Member Data Documentation

const MatrixTypeNested Eigen::TriangularView::m_matrix [protected]

Definition at line 437 of file Core.