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

Inheritance diagram for TriangularView< _MatrixType, _Mode >:

Public Types
enum
enum	{ Mode, TransposeMode }
typedef TriangularBase < TriangularView >	Base
typedef internal::traits < TriangularView > ::DenseMatrixType	DenseMatrixType
typedef DenseMatrixType	DenseType
typedef internal::traits < TriangularView >::Index	Index
typedef _MatrixType	MatrixType
typedef DenseMatrixType	PlainObject
typedef internal::traits < TriangularView >::Scalar	Scalar
typedef internal::traits < TriangularView > ::StorageKind	StorageKind
Public Member Functions
void	addTo (Dest &dst) const
const TriangularView< const typename MatrixType::AdjointReturnType, TransposeMode >	adjoint () const
void	applyThisOnTheLeft (Dest &dst) const
void	applyThisOnTheRight (Dest &dst) const
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	coeff (Index row, Index col) const
Scalar &	coeffRef (Index row, Index col)
Scalar &	coeffRef (Index row, Index col)
Index	cols () const
TriangularView < MatrixConjugateReturnType, Mode >	conjugate ()
const TriangularView < MatrixConjugateReturnType, Mode >	conjugate () const
TriangularView< _MatrixType, _Mode > &	const_cast_derived () const
const TriangularView < _MatrixType, _Mode > &	const_derived () const
void	copyCoeff (Index row, Index col, Other &other)
TriangularView< _MatrixType, _Mode > &	derived ()
const TriangularView < _MatrixType, _Mode > &	derived () const
Scalar	determinant () const
void	evalTo (Dest &dst) const
void	evalTo (MatrixBase< DenseDerived > &other) const
void	evalToLazy (MatrixBase< DenseDerived > &other) const
void	fill (const Scalar &value)
Index	innerStride () const
template<typename OtherDerived >
void	lazyAssign (const TriangularBase< OtherDerived > &other)
template<typename OtherDerived >
void	lazyAssign (const MatrixBase< OtherDerived > &other)
const MatrixTypeNestedCleaned &	nestedExpression () const
MatrixTypeNestedCleaned &	nestedExpression ()
Scalar	operator() (Index row, Index col) const
Scalar &	operator() (Index row, Index col)
template<typename OtherDerived >
TriangularProduct< Mode, true, MatrixType, false, OtherDerived, OtherDerived::IsVectorAtCompileTime >	operator* (const MatrixBase< OtherDerived > &rhs) const
TriangularView &	operator*= (const typename internal::traits< MatrixType >::Scalar &other)
template<typename Other >
TriangularView &	operator+= (const DenseBase< Other > &other)
template<typename ProductDerived , typename Lhs , typename Rhs >
TriangularView &	operator+= (const ProductBase< ProductDerived, Lhs, Rhs > &other)
template<typename ProductDerived >
TriangularView &	operator+= (const ScaledProduct< ProductDerived > &other)
template<typename Other >
TriangularView &	operator-= (const DenseBase< Other > &other)
template<typename ProductDerived , typename Lhs , typename Rhs >
TriangularView &	operator-= (const ProductBase< ProductDerived, Lhs, Rhs > &other)
template<typename ProductDerived >
TriangularView &	operator-= (const ScaledProduct< ProductDerived > &other)
TriangularView &	operator/= (const typename internal::traits< MatrixType >::Scalar &other)
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 ProductDerived , typename Lhs , typename Rhs >
TriangularView &	operator= (const ProductBase< ProductDerived, Lhs, Rhs > &other)
template<typename ProductDerived >
TriangularView &	operator= (const ScaledProduct< ProductDerived > &other)
Index	outerStride () const
Index	rows () const
const SelfAdjointView < MatrixTypeNestedNonRef, Mode >	selfadjointView () const
SelfAdjointView < MatrixTypeNestedNonRef, Mode >	selfadjointView ()
TriangularView &	setConstant (const Scalar &value)
TriangularView &	setOnes ()
TriangularView &	setZero ()
Index	size () const
template<int Side, typename Other >
const internal::triangular_solve_retval < Side, TriangularView, Other >	solve (const MatrixBase< Other > &other) const
template<typename Other >
const internal::triangular_solve_retval < OnTheLeft, TriangularView, Other >	solve (const MatrixBase< Other > &other) const
template<int Side, typename OtherDerived >
void	solveInPlace (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
void	solveInPlace (const MatrixBase< OtherDerived > &other) const
void	subTo (Dest &dst) const
template<typename OtherDerived >
void	swap (TriangularBase< OtherDerived > const &other)
template<typename OtherDerived >
void	swap (MatrixBase< OtherDerived > const &other)
DenseMatrixType	toDenseMatrix () const
TriangularView< Transpose < MatrixType >, TransposeMode >	transpose ()
const TriangularView < Transpose< MatrixType > , TransposeMode >	transpose () const
	TriangularView (const MatrixType &matrix)
Protected Types
typedef internal::remove_all < typename MatrixType::ConjugateReturnType > ::type	MatrixConjugateReturnType
typedef internal::traits < TriangularView > ::MatrixTypeNested	MatrixTypeNested
typedef internal::traits < TriangularView > ::MatrixTypeNestedCleaned	MatrixTypeNestedCleaned
typedef internal::traits < TriangularView > ::MatrixTypeNestedNonRef	MatrixTypeNestedNonRef
Protected Member Functions
template<typename ProductDerived , typename Lhs , typename Rhs >
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
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()

Member Typedef Documentation

typedef TriangularBase<TriangularView> Base

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

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

typedef DenseMatrixType DenseType [inherited]

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

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

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

typedef _MatrixType MatrixType

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

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

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

typedef DenseMatrixType PlainObject

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

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

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

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

Member Enumeration Documentation

anonymous enum [inherited]

anonymous enum

Enumerator:

Mode
TransposeMode

Constructor & Destructor Documentation

TriangularView ( const MatrixType & matrix ) [inline]

Member Function Documentation

void addTo ( Dest & dst ) const [inline, inherited]

const TriangularView<const typename MatrixType::AdjointReturnType,TransposeMode> adjoint ( ) const [inline]

See also:: MatrixBase::adjoint() const

void applyThisOnTheLeft ( Dest & dst ) const [inline, inherited]

void applyThisOnTheRight ( Dest & dst ) const [inline, inherited]

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

TriangularView& assignProduct	(	const ProductBase< ProductDerived, Lhs, Rhs > &	prod,
		const Scalar &	alpha
	)		`[inline, protected]`

void check_coordinates	(	Index	row,
		Index	col
	)		const `[inline, protected, inherited]`

void check_coordinates_internal	(	Index	,
		Index
	)		const `[inline, protected, inherited]`

Scalar coeff	(	Index	row,
		Index	col
	)		const `[inline, inherited]`

Scalar coeff	(	Index	row,
		Index	col
	)		const `[inline]`

See also:: MatrixBase::coeff()

Warning:: the coordinates must fit into the referenced triangular part

Scalar& coeffRef	(	Index	row,
		Index	col
	)		`[inline, inherited]`

Scalar& coeffRef	(	Index	row,
		Index	col
	)		`[inline]`

See also:: MatrixBase::coeffRef()

Warning:: the coordinates must fit into the referenced triangular part

Index cols ( void ) const [inline]

Returns:: the number of columns.

See also:: rows(), ColsAtCompileTime

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

TriangularView<MatrixConjugateReturnType,Mode> conjugate ( ) [inline]

See also:: MatrixBase::conjugate()

const TriangularView<MatrixConjugateReturnType,Mode> conjugate ( ) const [inline]

See also:: MatrixBase::conjugate() const

TriangularView< _MatrixType, _Mode > & const_cast_derived ( ) const [inline, inherited]

const TriangularView< _MatrixType, _Mode > & const_derived ( ) const [inline, inherited]

void copyCoeff	(	Index	row,
		Index	col,
		Other &	other
	)		`[inline, inherited]`

See also:: MatrixBase::copyCoeff(row,col)

TriangularView< _MatrixType, _Mode > & derived ( ) [inline, inherited]

Returns:: a reference to the derived object

const TriangularView< _MatrixType, _Mode > & derived ( ) const [inline, inherited]

Returns:: a const reference to the derived object

Scalar determinant ( ) const [inline]

void evalTo ( Dest & dst ) const [inline, inherited]

void 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 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 fill ( const Scalar & value ) [inline]

See also:: MatrixBase::fill()

Index innerStride ( ) const [inline]

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

void lazyAssign ( const TriangularBase< OtherDerived > & other )

void lazyAssign ( const MatrixBase< OtherDerived > & other )

const MatrixTypeNestedCleaned& nestedExpression ( ) const [inline]

MatrixTypeNestedCleaned& nestedExpression ( ) [inline]

Scalar operator()	(	Index	row,
		Index	col
	)		const `[inline, inherited]`

Scalar& operator()	(	Index	row,
		Index	col
	)		`[inline, inherited]`

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

Efficient triangular matrix times vector/matrix product

TriangularView& operator*= ( const typename internal::traits< MatrixType >::Scalar & other ) [inline]

See also:: MatrixBase::operator*=()

TriangularView& operator+= ( const DenseBase< Other > & other ) [inline]

See also:: MatrixBase::operator+=()

TriangularView& operator+= ( const ProductBase< ProductDerived, Lhs, Rhs > & other ) [inline]

TriangularView& operator+= ( const ScaledProduct< ProductDerived > & other ) [inline]

TriangularView& operator-= ( const DenseBase< Other > & other ) [inline]

See also:: MatrixBase::operator-=()

TriangularView& operator-= ( const ProductBase< ProductDerived, Lhs, Rhs > & other ) [inline]

TriangularView& operator-= ( const ScaledProduct< ProductDerived > & other ) [inline]

TriangularView& operator/= ( const typename internal::traits< MatrixType >::Scalar & other ) [inline]

See also:: MatrixBase::operator/=()

TriangularView< MatrixType, Mode > & operator= ( const TriangularBase< OtherDerived > & other ) [inline]

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

TriangularView< MatrixType, Mode > & operator= ( const MatrixBase< OtherDerived > & other ) [inline]

TriangularView& operator= ( const TriangularView< _MatrixType, _Mode > & other ) [inline]

TriangularView& operator= ( const ProductBase< ProductDerived, Lhs, Rhs > & other ) [inline]

TriangularView& operator= ( const ScaledProduct< ProductDerived > & other ) [inline]

Index outerStride ( ) const [inline]

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

Index rows ( void ) const [inline]

Returns:: the number of rows.

See also:: cols(), RowsAtCompileTime

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

const SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView ( ) const [inline]

SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView ( ) [inline]

TriangularView& setConstant ( const Scalar & value ) [inline]

See also:: MatrixBase::setConstant()

TriangularView& setOnes ( ) [inline]

See also:: MatrixBase::setOnes()

TriangularView& setZero ( ) [inline]

See also:: MatrixBase::setZero()

Index size ( ) const [inline, inherited]

Returns:: the number of coefficients, which is rows()*cols().

See also:: rows(), cols(), SizeAtCompileTime.

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

#ifndef _MSC_VER
  #warning deprecated
#endif
/*
Matrix3d m = Matrix3d::Zero();
m.part<Eigen::UpperTriangular>().setOnes();
cout << "Here is the matrix m:" << endl << m << endl;
Matrix3d n = Matrix3d::Ones();
n.part<Eigen::LowerTriangular>() *= 2;
cout << "Here is the matrix n:" << endl << n << endl;
cout << "And now here is m.inverse()*n, taking advantage of the fact that"
        " m is upper-triangular:" << endl
     << m.marked<Eigen::UpperTriangular>().solveTriangular(n);
*/

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()

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

void 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.

void solveInPlace ( const MatrixBase< OtherDerived > & other ) const [inline]

void subTo ( Dest & dst ) const [inline, inherited]

void swap ( TriangularBase< OtherDerived > const & other ) [inline]

void swap ( MatrixBase< OtherDerived > const & other ) [inline]

DenseMatrixType toDenseMatrix ( ) const [inline, inherited]

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

See also:: MatrixBase::transpose()

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

See also:: MatrixBase::transpose() const

Friends And Related Function Documentation

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

MatrixTypeNested m_matrix [protected]

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

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 Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

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