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

Base class for a triangular part in a dense matrix.

Contents

This class is an abstract base class of class TriangularView, and objects of type TriangularViewImpl cannot be instantiated. It extends class TriangularView with additional methods which available for dense expressions only.

Base classes

template<typename Derived>
class TriangularBase
Base class for triangular part in a matrix.

Public functions

auto coeff(Index row, Index col) const -> Scalar
auto coeffRef(Index row, Index col) -> Scalar&
template<typename DenseDerived>
void evalToLazy(MatrixBase<DenseDerived>& other) const
void fill(const Scalar& value)
auto innerStride() const -> Index
template<typename OtherDerived>
auto operator*(const MatrixBase<OtherDerived>& rhs) const -> const Product<TriangularViewType, OtherDerived>
auto operator*=(const typename internal::traits<MatrixType>::Scalar& other) -> TriangularViewType&
template<typename Other>
auto operator+=(const DenseBase<Other>& other) -> TriangularViewType&
template<typename Other>
auto operator-=(const DenseBase<Other>& other) -> TriangularViewType&
auto operator/=(const typename internal::traits<MatrixType>::Scalar& other) -> TriangularViewType&
template<typename OtherDerived>
auto operator=(const TriangularBase<OtherDerived>& other) -> TriangularViewType&
template<typename OtherDerived>
auto operator=(const MatrixBase<OtherDerived>& other) -> TriangularViewType&
auto outerStride() const -> Index
auto setConstant(const Scalar& value) -> TriangularViewType&
auto setOnes() -> TriangularViewType&
auto setZero() -> TriangularViewType&
template<int Side, typename Other>
auto solve(const MatrixBase<Other>& other) const -> const internal::triangular_solve_retval<Side, TriangularViewType, Other>
template<int Side, typename OtherDerived>
void solveInPlace(const MatrixBase<OtherDerived>& other) const
template<typename OtherDerived>
void swap(TriangularBase<OtherDerived>& other)
template<typename OtherDerived>
void swap(MatrixBase<OtherDerived> const& other) deprecated

Friends

template<typename OtherDerived>
auto operator*(const MatrixBase<OtherDerived>& lhs, const TriangularViewImpl& rhs) -> const Product<OtherDerived, TriangularViewType>

Function documentation

template<typename _MatrixType, unsigned int _Mode>
Scalar Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::coeff(Index row, Index col) const

template<typename _MatrixType, unsigned int _Mode>
Scalar& Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::coeffRef(Index row, Index col)

template<typename _MatrixType, unsigned int _Mode> template<typename DenseDerived>
void Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::evalToLazy(MatrixBase<DenseDerived>& other) const

Assigns a triangular or selfadjoint matrix to a dense matrix. If the matrix is triangular, the opposite part is set to zero.

template<typename _MatrixType, unsigned int _Mode>
void Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::fill(const Scalar& value)

template<typename _MatrixType, unsigned int _Mode>
Index Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::innerStride() const

Returns the inner-stride of the underlying dense matrix

template<typename _MatrixType, unsigned int _Mode> template<typename OtherDerived>
const Product<TriangularViewType, OtherDerived> Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::operator*(const MatrixBase<OtherDerived>& rhs) const

Efficient triangular matrix times vector/matrix product

template<typename _MatrixType, unsigned int _Mode>
TriangularViewType& Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::operator*=(const typename internal::traits<MatrixType>::Scalar& other)

template<typename _MatrixType, unsigned int _Mode> template<typename Other>
TriangularViewType& Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::operator+=(const DenseBase<Other>& other)

template<typename _MatrixType, unsigned int _Mode> template<typename Other>
TriangularViewType& Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::operator-=(const DenseBase<Other>& other)

template<typename _MatrixType, unsigned int _Mode>
TriangularViewType& Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::operator/=(const typename internal::traits<MatrixType>::Scalar& other)

template<typename _MatrixType, unsigned int _Mode> template<typename OtherDerived>
TriangularViewType& Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_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> template<typename OtherDerived>
TriangularViewType& Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::operator=(const MatrixBase<OtherDerived>& other)

Shortcut for *this = other.other.triangularView<(*this)::Mode>()

template<typename _MatrixType, unsigned int _Mode>
Index Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::outerStride() const

Returns the outer-stride of the underlying dense matrix

template<typename _MatrixType, unsigned int _Mode>
TriangularViewType& Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::setConstant(const Scalar& value)

template<typename _MatrixType, unsigned int _Mode>
TriangularViewType& Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::setOnes()

template<typename _MatrixType, unsigned int _Mode>
TriangularViewType& Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::setZero()

template<typename _MatrixType, unsigned int _Mode> template<int Side, typename Other>
const internal::triangular_solve_retval<Side, TriangularViewType, Other> Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_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.

Note that the template parameter Side can be omitted, in which case Side==OnTheLeft

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:

Matrix3d m = Matrix3d::Zero();
m.triangularView<Eigen::Upper>().setOnes();
cout << "Here is the matrix m:\n" << m << endl;
Matrix3d n = Matrix3d::Ones();
n.triangularView<Eigen::Lower>() *= 2;
cout << "Here is the matrix n:\n" << n << endl;
cout << "And now here is m.inverse()*n, taking advantage of the fact that"
        " m is upper-triangular:\n"
     << m.triangularView<Eigen::Upper>().solve(n) << endl;
cout << "And this is n*m.inverse():\n"
     << m.triangularView<Eigen::Upper>().solve<Eigen::OnTheRight>(n);

Output:

Here is the matrix m:
1 1 1
0 1 1
0 0 1
Here is the matrix n:
2 1 1
2 2 1
2 2 2
And now here is m.inverse()*n, taking advantage of the fact that m is upper-triangular:
 0 -1  0
 0  0 -1
 2  2  2
And this is n*m.inverse():
 2 -1  0
 2  0 -1
 2  0  0

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.

template<typename _MatrixType, unsigned int _Mode> template<int Side, typename OtherDerived>
void Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::solveInPlace(const MatrixBase<OtherDerived>& other) const

"in-place" version of TriangularView::solve() where the result is written in other

Note that the template parameter Side can be omitted, in which case Side==OnTheLeft

See TriangularView:solve() for the details.

template<typename _MatrixType, unsigned int _Mode> template<typename OtherDerived>
void Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::swap(TriangularBase<OtherDerived>& other)

Swaps the coefficients of the common triangular parts of two matrices

template<typename _MatrixType, unsigned int _Mode> template<typename OtherDerived>
void Eigen::TriangularViewImpl<_MatrixType, _Mode, Dense><_MatrixType, _Mode>::swap(MatrixBase<OtherDerived> const& other)

(*this).swap(other.triangularView<(*this)::Mode>())

template<typename _MatrixType, unsigned int _Mode> template<typename OtherDerived>
const Product<OtherDerived, TriangularViewType> operator*(const MatrixBase<OtherDerived>& lhs, const TriangularViewImpl& rhs)

Efficient vector/matrix times triangular matrix product