TriangularView< _MatrixType, _Mode > Class Template Reference

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()

Public Member Functions
const TriangularView< const typename MatrixType::AdjointReturnType, TransposeMode >	adjoint () const
Scalar	coeff (Index row, Index col) const
Scalar &	coeffRef (Index row, Index col)
TriangularView< MatrixConjugateReturnType, Mode >	conjugate ()
const TriangularView< MatrixConjugateReturnType, Mode >	conjugate () const
template<typename Other>
void	copyCoeff (Index row, Index col, Other &other)
Derived &	derived ()
const Derived &	derived () const
template<typename DenseDerived>
void	evalTo (MatrixBase< DenseDerived > &other) const
template<typename DenseDerived>
void	evalToLazy (MatrixBase< DenseDerived > &other) const
void	fill (const Scalar &value)
template<typename OtherDerived>
TriangularProduct< Mode, true, MatrixType, false, OtherDerived, OtherDerived::ColsAtCompileTime==1 >	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 Other>
TriangularView &	operator-= (const DenseBase< Other > &other)
TriangularView &	operator/= (const typename internal::traits< MatrixType >::Scalar &other)
template<typename OtherDerived>
TriangularView &	operator= (const TriangularBase< OtherDerived > &other)
TriangularView &	setConstant (const Scalar &value)
TriangularView &	setOnes ()
TriangularView &	setZero ()
Index	size () const
template<int Side, typename Other>
const internal::triangular_solve_retval< Side, TriangularView< Derived, Mode >, Other >	solve (const MatrixBase< Other > &other) const
template<int Side, typename OtherDerived>
void	solveInPlace (const MatrixBase< OtherDerived > &other) const
TriangularView< Transpose< MatrixType >, TransposeMode >	transpose ()
const TriangularView< Transpose< MatrixType >, TransposeMode >	transpose () const

Member Function Documentation

adjoint()

template<typename _MatrixType, unsigned int _Mode>

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

inline

See also

MatrixBase::adjoint() const

coeff()

template<typename _MatrixType, unsigned int _Mode>

Scalar coeff ( Index row, Index col ) const

inline

See also

MatrixBase::coeff()

Warning

the coordinates must fit into the referenced triangular part

coeffRef()

template<typename _MatrixType, unsigned int _Mode>

Scalar & coeffRef ( Index row, Index col )

inline

See also

MatrixBase::coeffRef()

Warning

the coordinates must fit into the referenced triangular part

conjugate() [1/2]

template<typename _MatrixType, unsigned int _Mode>

TriangularView< MatrixConjugateReturnType, Mode > conjugate ( )

inline

See also

MatrixBase::conjugate()

conjugate() [2/2]

template<typename _MatrixType, unsigned int _Mode>

const TriangularView< MatrixConjugateReturnType, Mode > conjugate ( ) const

inline

See also

MatrixBase::conjugate() const

copyCoeff()

template<typename Derived>

template<typename Other>

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

inlineinherited

See also

MatrixBase::copyCoeff(row,col)

derived() [1/2]

template<typename Derived>

Derived & derived ( )

inlineinherited

Returns

a reference to the derived object

Referenced by IterativeSolverBase< BiCGSTAB >::analyzePattern(), MatrixBase< Derived >::applyOnTheLeft(), MatrixBase< Derived >::applyOnTheRight(), PermutationBase< PermutationMatrix >::applyTranspositionOnTheLeft(), PermutationBase< PermutationMatrix >::applyTranspositionOnTheRight(), SparseMatrixBase< SparseDenseOuterProduct >::bottomLeftCorner(), SparseMatrixBase< SparseDenseOuterProduct >::bottomRows(), cols(), SparseMatrixBase< SparseDenseOuterProduct >::cols(), IterativeSolverBase< BiCGSTAB >::compute(), SparseMatrixBase< SparseDenseOuterProduct >::eval(), IterativeSolverBase< BiCGSTAB >::factorize(), PermutationBase< PermutationMatrix >::indices(), PermutationBase< PermutationMatrix >::indices(), SparseMatrixBase< Derived >::innerVector(), SparseMatrixBase< Derived >::innerVector(), SparseMatrixBase< Derived >::innerVectors(), SparseMatrixBase< Derived >::innerVectors(), PermutationBase< PermutationMatrix >::inverse(), IterativeSolverBase< BiCGSTAB >::IterativeSolverBase(), SparseMatrixBase< SparseDenseOuterProduct >::nonZeros(), PermutationBase< PermutationMatrix >::operator*(), RotationBase< AngleAxis< _Scalar >, 3 >::operator*(), RotationBase< AngleAxis< _Scalar >, 3 >::operator*, SparseMatrixBase< Derived >::operator*(), SparseMatrixBase< SparseDenseOuterProduct >::operator*(), SparseMatrixBase< SparseDenseOuterProduct >::operator*(), SparseSelfAdjointView< MatrixType, UpLo >::operator*, SparseSelfAdjointView< MatrixType, UpLo >::operator*(), Transform< Scalar, Dim, Mode, Options >::operator*, Transform< Scalar, Dim, Mode, Options >::operator*(), Translation< _Scalar, _Dim >::operator*(), Translation< Scalar, Dim >::operator*, MatrixBase< Derived >::operator*=(), DenseBase< Derived >::operator=(), PermutationBase< PermutationMatrix >::operator=(), PermutationBase< PermutationMatrix >::operator=(), PlainObjectBase< Array >::operator=(), Transform< Scalar, Dim, Mode, Options >::operator=(), PlainObjectBase< Array >::PlainObjectBase(), PlainObjectBase< Array >::resizeLike(), rows(), SparseMatrixBase< SparseDenseOuterProduct >::rows(), CholmodBase< _MatrixType, _UpLo, CholmodSimplicialLLT >::solve(), IterativeSolverBase< BiCGSTAB >::solve(), SimplicialCholeskyBase< SimplicialLLT >::solve(), SparseLU< _MatrixType, Derived >::solve(), SuperLUBase< _MatrixType, SuperLU >::solve(), UmfPackLU< _MatrixType >::solve(), SparseMatrix< Scalar, RowMajor >::SparseMatrix(), SparseMatrix< Scalar, RowMajor >::SparseMatrix(), PermutationBase< PermutationMatrix >::toDenseMatrix(), SparseMatrixBase< SparseDenseOuterProduct >::topLeftCorner(), SparseMatrixBase< SparseDenseOuterProduct >::topLeftCorner(), Transform< Scalar, Dim, Mode, Options >::Transform(), PermutationBase< PermutationMatrix >::transpose(), and SparseMatrixBase< SparseDenseOuterProduct >::twistedBy().

derived() [2/2]

template<typename Derived>

const Derived & derived ( ) const

inlineinherited

Returns

a const reference to the derived object

evalTo()

template<typename Derived>

template<typename DenseDerived>

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.

evalToLazy()

template<typename Derived>

template<typename DenseDerived>

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.

fill()

template<typename _MatrixType, unsigned int _Mode>

void fill ( const Scalar & value )

inline

See also

MatrixBase::fill()

operator*()

template<typename _MatrixType, unsigned int _Mode>

template<typename OtherDerived>

TriangularProduct< Mode, true, MatrixType, false, OtherDerived, OtherDerived::ColsAtCompileTime==1 > operator* ( const MatrixBase< OtherDerived > & rhs ) const

inline

Efficient triangular matrix times vector/matrix product

operator*=()

template<typename _MatrixType, unsigned int _Mode>

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

inline

See also

MatrixBase::operator*=()

operator+=()

template<typename _MatrixType, unsigned int _Mode>

template<typename Other>

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

inline

See also

MatrixBase::operator+=()

operator-=()

template<typename _MatrixType, unsigned int _Mode>

template<typename Other>

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

inline

See also

MatrixBase::operator-=()

operator/=()

template<typename _MatrixType, unsigned int _Mode>

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

inline

See also

MatrixBase::operator/=()

operator=()

template<typename _MatrixType, unsigned int _Mode>

template<typename OtherDerived>

TriangularView & operator=

(

const TriangularBase< OtherDerived > &

other

)

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

setConstant()

template<typename _MatrixType, unsigned int _Mode>

TriangularView & setConstant ( const Scalar & value )

inline

See also

MatrixBase::setConstant()

Referenced by TriangularView< Derived, Mode >::fill(), TriangularView< Derived, Mode >::setOnes(), and TriangularView< Derived, Mode >::setZero().

setOnes()

template<typename _MatrixType, unsigned int _Mode>

TriangularView & setOnes ( )

inline

See also

MatrixBase::setOnes()

setZero()

template<typename _MatrixType, unsigned int _Mode>

TriangularView & setZero ( )

inline

See also

MatrixBase::setZero()

size()

template<typename Derived>

Index size ( ) const

inlineinherited

Returns

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

See also

rows(), cols(), SizeAtCompileTime.

References cols(), and rows().

Referenced by PlainObjectBase< Array >::_resize_to_match().

solve()

template<typename _MatrixType, unsigned int _Mode>

template<int Side, typename Other>

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

#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()

solveInPlace()

template<typename MatrixType, unsigned int Mode>

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

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.

References Eigen::Lower, Eigen::OnTheLeft, Eigen::OnTheRight, Eigen::RowMajorBit, Eigen::Upper, and Eigen::ZeroDiag.

transpose() [1/2]

template<typename _MatrixType, unsigned int _Mode>

TriangularView< Transpose< MatrixType >, TransposeMode > transpose ( )

inline

See also

MatrixBase::transpose()

transpose() [2/2]

template<typename _MatrixType, unsigned int _Mode>

const TriangularView< Transpose< MatrixType >, TransposeMode > transpose ( ) const

inline

See also

MatrixBase::transpose() const

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

• TriangularMatrix.h
• GeneralMatrixMatrixTriangular.h
• SolveTriangular.h