Eigen: Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense

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#include <Eigen/src/Core/TriangularMatrix.h>

Detailed Description

template<typename MatrixType_, unsigned int Mode_>
class Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >

Base class for a triangular part in a dense matrix.

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 are available for dense expressions only.

See also: class TriangularView, MatrixBase::triangularView()

Inheritance diagram for Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >:

Public Member Functions
void	evalToLazy (MatrixBase< DenseDerived > &other) const

void	inverseInPlace ()

const Product< TriangularViewType, Inverse< OtherDerived > >	operator* (const InverseImpl< OtherDerived, PermutationStorage > &rhs) const

const Product< TriangularViewType, OtherDerived >	operator* (const PermutationBase< OtherDerived > &rhs) const

const Product< TriangularViewType, OtherDerived >	operator* (const TriangularBase< OtherDerived > &rhs) const

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

template<typename Other>
TriangularViewType &	operator+= (const DenseBase< Other > &other)

template<typename Other>
TriangularViewType &	operator-= (const DenseBase< Other > &other)

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

template<typename OtherDerived>
TriangularViewType &	operator= (const MatrixBase< OtherDerived > &other)

template<typename OtherDerived>
TriangularViewType &	operator= (const TriangularBase< OtherDerived > &other)

template<int Side, typename Other>
const internal::triangular_solve_retval< Side, TriangularViewType, Other >	solve (const MatrixBase< Other > &other) const

template<int Side, typename OtherDerived>
void	solveInPlace (const MatrixBase< OtherDerived > &other) const

template<typename OtherDerived>
EIGEN_DEPRECATED void	swap (MatrixBase< OtherDerived > const &other)

template<typename OtherDerived>
void	swap (TriangularBase< OtherDerived > &other)

Public Member Functions inherited from Eigen::TriangularBase< TriangularView< MatrixType_, Mode_ > >
const AdjointReturnType	adjoint () const

Scalar	coeff (Index row, Index col) const

Scalar &	coeffRef (Index row, Index col)

const ConjugateReturnType	conjugate () const

std::conditional_t< Cond, ConjugateReturnType, ConstView >	conjugateIf () const

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

void	evalTo (MatrixBase< DenseDerived > &other) const

void	evalToLazy (MatrixBase< DenseDerived > &other) const

void	fill (const Scalar &value)

Scalar &	operator() (Index row, Index col)

Scalar	operator() (Index row, Index col) const

const Product< TriangularView< MatrixType_, Mode_ >, Inverse< OtherDerived > >	operator* (const InverseImpl< OtherDerived, PermutationStorage > &rhs) const

const Product< TriangularView< MatrixType_, Mode_ >, OtherDerived >	operator* (const PermutationBase< OtherDerived > &rhs) const

const Product< TriangularView< MatrixType_, Mode_ >, OtherDerived >	operator* (const TriangularBase< OtherDerived > &rhs) const

auto	operator+ (const DiagonalBase< OtherDerived > &other) const

auto	operator- (const DiagonalBase< OtherDerived > &other) const

TriangularView< MatrixType_, Mode_ > &	setConstant (const Scalar &value)

TriangularView< MatrixType_, Mode_ > &	setIdentity ()

TriangularView< MatrixType_, Mode_ > &	setOnes ()

TriangularView< MatrixType_, Mode_ > &	setRandom ()

TriangularView< MatrixType_, Mode_ > &	setZero ()

TransposeReturnType	transpose ()

const ConstTransposeReturnType	transpose () const

Public Member Functions inherited from Eigen::EigenBase< TriangularView< MatrixType_, Mode_ > >
constexpr Index	cols () const noexcept

constexpr TriangularView< MatrixType_, Mode_ > &	derived ()

constexpr const TriangularView< MatrixType_, Mode_ > &	derived () const

constexpr Index	rows () const noexcept

constexpr Index	size () const noexcept

Additional Inherited Members
Public Types inherited from Eigen::TriangularBase< TriangularView< MatrixType_, Mode_ > >
Public Types inherited from Eigen::EigenBase< TriangularView< MatrixType_, Mode_ > >
using	Index
	The interface type of indices.

Member Function Documentation

◆ evalToLazy()

template<typename MatrixType_, unsigned int Mode_>

void Eigen::TriangularBase< TriangularViewType >::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.

◆ inverseInPlace()

template<typename MatrixType_, unsigned int Mode_>

void Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >::inverseInPlace ( )

Replaces the referenced triangular part by its inverse.

*this must be square and invertible; as with solveInPlace(), no check is made and a zero on the diagonal yields a non-finite result. The opposite triangle is neither read nor written, and with a UnitDiag mode the diagonal itself is left alone as well.

This is the operation of the *TRTRI LAPACK routines. It costs n^3/3 flops, where solving against an explicit identity right hand side costs n^3, and its only scratch is one block-sized panel of at most 128x128 coefficients, independent of the matrix size.

See also: TriangularView::solveInPlace(), MatrixBase::inverse()

◆ operator*() [1/3]

template<typename MatrixType_, unsigned int Mode_>

const Product< TriangularViewType, Inverse< OtherDerived > > Eigen::TriangularBase< TriangularViewType >::operator* ( const InverseImpl< OtherDerived, PermutationStorage > & rhs ) const

inline

Returns: the dense matrix expression of *this with the inverse permutation rhs applied to its columns.

◆ operator*() [2/3]

template<typename MatrixType_, unsigned int Mode_>

const Product< TriangularViewType, OtherDerived > Eigen::TriangularBase< TriangularViewType >::operator* ( const PermutationBase< OtherDerived > & rhs ) const

inline

Returns: the dense matrix expression of *this with the permutation rhs applied to its columns.

◆ operator*() [3/3]

template<typename MatrixType_, unsigned int Mode_>

const Product< TriangularViewType, OtherDerived > Eigen::TriangularBase< TriangularViewType >::operator* ( const TriangularBase< OtherDerived > & rhs ) const

inline

Returns: the dense matrix product of *this by the triangular or self-adjoint view rhs.

The right factor is evaluated into a dense temporary and the product runs the kernel of *this times a dense matrix. The result is a plain dense expression even when the structure would be preserved, as for two upper triangular factors.

◆ operator*=()

template<typename MatrixType_, unsigned int Mode_>

TriangularViewType & Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >::operator*= ( const typename internal::traits< MatrixType >::Scalar & other )

inline

See also: MatrixBase::operator*=()

◆ operator+=()

template<typename MatrixType_, unsigned int Mode_>

template<typename Other>

TriangularViewType & Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >::operator+= ( const DenseBase< Other > & other )

inline

See also: MatrixBase::operator+=()

◆ operator-=()

template<typename MatrixType_, unsigned int Mode_>

template<typename Other>

TriangularViewType & Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >::operator-= ( const DenseBase< Other > & other )

inline

See also: MatrixBase::operator-=()

◆ operator/=()

template<typename MatrixType_, unsigned int Mode_>

TriangularViewType & Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >::operator/= ( const typename internal::traits< MatrixType >::Scalar & other )

inline

See also: DenseBase::operator/=()

◆ operator=() [1/2]

template<typename MatrixType_, unsigned int Mode_>

template<typename OtherDerived>

TriangularViewType & Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >::operator= ( const MatrixBase< OtherDerived > & other )

Shortcut for

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

◆ operator=() [2/2]

template<typename MatrixType_, unsigned int Mode_>

template<typename OtherDerived>

TriangularViewType & Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >::operator= ( const TriangularBase< OtherDerived > & other )

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

◆ solve()

template<typename MatrixType_, unsigned int Mode_>

template<int Side, typename Other>

const internal::triangular_solve_retval< Side, TriangularViewType, Other > Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >::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.

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 a lower (resp. upper) triangular matrix.

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
 
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.

See also: TriangularView::solveInPlace()

◆ solveInPlace()

template<typename MatrixType_, unsigned int Mode_>

template<int Side, typename OtherDerived>

void Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >::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.

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

See TriangularView:solve() for the details.

◆ swap() [1/2]

template<typename MatrixType_, unsigned int Mode_>

template<typename OtherDerived>

EIGEN_DEPRECATED void Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >::swap ( MatrixBase< OtherDerived > const & other )

inline

Shortcut for

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

◆ swap() [2/2]

template<typename MatrixType_, unsigned int Mode_>

template<typename OtherDerived>

void Eigen::TriangularViewImpl< MatrixType_, Mode_, Dense >::swap ( TriangularBase< OtherDerived > & other )

inline

Swaps the coefficients of the common triangular parts of two matrices

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

/builds/libeigen/eigen/Eigen/src/Core/TriangularMatrix.h
/builds/libeigen/eigen/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h

Detailed Description

Public Member Functions

Additional Inherited Members

Member Function Documentation

◆ evalToLazy()

◆ inverseInPlace()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ solve()

◆ solveInPlace()

◆ swap() [1/2]

◆ swap() [2/2]