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()

Inherits TriangularBase< Derived >.

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

Friends
template<typename OtherDerived >
TriangularProduct< Mode, false, OtherDerived, OtherDerived::RowsAtCompileTime==1, MatrixType, false >	operator* (const MatrixBase< OtherDerived > &lhs, const TriangularView &rhs)

Member Function Documentation

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

inline

See Also

MatrixBase::adjoint() const

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

See Also

MatrixBase::coeffRef()

Warning

the coordinates must fit into the referenced triangular part

TriangularView<MatrixConjugateReturnType,Mode> conjugate ( )

inline

See Also

MatrixBase::conjugate()

const TriangularView<MatrixConjugateReturnType,Mode> conjugate ( ) const

inline

See Also

MatrixBase::conjugate() const

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

inlineinherited

See Also

MatrixBase::copyCoeff(row,col)

Derived& derived ( )

inlineinherited

Returns

a reference to the derived object

Referenced by IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::analyzePattern(), MatrixBase< Derived >::applyOnTheLeft(), MatrixBase< Derived >::applyOnTheRight(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::applyTranspositionOnTheLeft(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::applyTranspositionOnTheRight(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::bottomRows(), EigenBase< SparseSymmetricPermutationProduct< MatrixType, UpLo > >::cols(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::cols(), IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::compute(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::eval(), IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::factorize(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::indices(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::inverse(), IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::IterativeSolverBase(), RotationBase< Derived, 3 >::operator*(), SparseSelfAdjointView< MatrixType, UpLo >::operator*(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::operator*(), SparseMatrixBase< Derived >::operator*(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::operator*(), Transform< Scalar, Dim, Mode, _Options >::operator*(), Eigen::operator*(), MatrixBase< Derived >::operator*=(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::operator=(), DenseBase< Derived >::operator=(), Transform< Scalar, Dim, Mode, _Options >::operator=(), PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::operator=(), PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::PlainObjectBase(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::real(), PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::resizeLike(), EigenBase< SparseSymmetricPermutationProduct< MatrixType, UpLo > >::rows(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::rows(), SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >::solve(), IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::solve(), SparseLU< _MatrixType, _OrderingType >::solve(), UmfPackLU< _MatrixType >::solve(), CholmodBase< _MatrixType, _UpLo, CholmodSimplicialLLT< _MatrixType, _UpLo > >::solve(), SuperLUBase< _MatrixType, SuperILU< _MatrixType > >::solve(), SparseMatrix< Scalar, RowMajor >::SparseMatrix(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::toDenseMatrix(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::topLeftCorner(), Transform< Scalar, Dim, Mode, _Options >::Transform(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::transpose(), and SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::twistedBy().

const Derived& derived ( ) const

inlineinherited

Returns

a const reference to the derived object

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()

References TriangularView< _MatrixType, _Mode >::setConstant().

TriangularProduct<Mode, true, MatrixType, false, OtherDerived, OtherDerived::ColsAtCompileTime==1> 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 DenseBase< Other > &  other )

inline

See Also

MatrixBase::operator-=()

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

inline

See Also

MatrixBase::operator/=()

TriangularView& operator=

(

const TriangularBase< OtherDerived > &

other

)

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

TriangularView& setConstant ( const Scalar &  value )

inline

See Also

MatrixBase::setConstant()

Referenced by TriangularView< _MatrixType, _Mode >::fill(), TriangularView< _MatrixType, _Mode >::setOnes(), and TriangularView< _MatrixType, _Mode >::setZero().

TriangularView& setOnes ( )

inline

See Also

MatrixBase::setOnes()

References TriangularView< _MatrixType, _Mode >::setConstant().

TriangularView& setZero ( )

inline

See Also

MatrixBase::setZero()

References TriangularView< _MatrixType, _Mode >::setConstant().

Index size ( ) const

inlineinherited

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

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()

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::Upper, and Eigen::ZeroDiag.

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::RowsAtCompileTime==1, MatrixType, false> operator* ( const MatrixBase< OtherDerived > &  lhs, const TriangularView< _MatrixType, _Mode > &  rhs  )

friend

Efficient vector/matrix times triangular matrix product

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

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