Eigen: Eigen::SelfAdjointView< MatrixType_, UpLo

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

Detailed Description

template<typename MatrixType_, unsigned int UpLo>
class Eigen::SelfAdjointView< MatrixType_, UpLo >

Expression of a selfadjoint matrix from a triangular part of a dense matrix.

Template Parameters

MatrixType	the type of the dense matrix storing the coefficients
TriangularPart	can be either `Lower` or `Upper`

This class is an expression of a selfadjoint matrix from a triangular part of a matrix with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView() and most of the time this is the only way that it is used.

See also: class TriangularBase, MatrixBase::selfadjointView()

Inheritance diagram for Eigen::SelfAdjointView< MatrixType_, UpLo >:

Public Types
using	EigenvaluesReturnType

using	RealScalar

using	Scalar
	The type of coefficients in this matrix.

Public Types inherited from Eigen::TriangularBase< SelfAdjointView< MatrixType_, UpLo > >
Public Types inherited from Eigen::EigenBase< SelfAdjointView< MatrixType_, UpLo > >
using	Index
	The interface type of indices.

Public Member Functions
BunchKaufman< PlainObject, UpLo >	bunchKaufman () const

MatrixType::ConstDiagonalReturnType	diagonal () const

EigenvaluesReturnType	eigenvalues () const
	Computes the eigenvalues of a matrix.

RealScalar	l1Norm () const

LDLT< PlainObject, UpLo >	ldlt () const

LLT< PlainObject, UpLo >	llt () const

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

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

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

SelfAdjointView &	operator*= (const Scalar &other)

template<typename OtherDerived>
SelfAdjointView &	operator+= (const DenseBase< OtherDerived > &other)

template<typename OtherDerived>
SelfAdjointView &	operator-= (const DenseBase< OtherDerived > &other)

SelfAdjointView &	operator/= (const Scalar &other)

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

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

RealScalar	operatorNorm () const
	Computes the L2 operator norm.

template<typename DerivedU, typename DerivedV>
SelfAdjointView &	rankUpdate (const MatrixBase< DerivedU > &u, const MatrixBase< DerivedV > &v, const Scalar &alpha=Scalar(1))

template<typename DerivedU>
SelfAdjointView &	rankUpdate (const MatrixBase< DerivedU > &u, const Scalar &alpha=Scalar(1))

template<unsigned int TriMode>
std::conditional_t<(TriMode &(Upper\|Lower))==(UpLo &(Upper\|Lower)), TriangularView< MatrixType, TriMode >, TriangularView< typename MatrixType::AdjointReturnType, TriMode > >	triangularView () const

Public Member Functions inherited from Eigen::TriangularBase< SelfAdjointView< MatrixType_, UpLo > >
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< SelfAdjointView< MatrixType_, UpLo >, Inverse< OtherDerived > >	operator* (const InverseImpl< OtherDerived, PermutationStorage > &rhs) const

const Product< SelfAdjointView< MatrixType_, UpLo >, OtherDerived >	operator* (const PermutationBase< OtherDerived > &rhs) const

const Product< SelfAdjointView< MatrixType_, UpLo >, OtherDerived >	operator* (const TriangularBase< OtherDerived > &rhs) const

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

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

SelfAdjointView< MatrixType_, UpLo > &	setConstant (const Scalar &value)

SelfAdjointView< MatrixType_, UpLo > &	setIdentity ()

SelfAdjointView< MatrixType_, UpLo > &	setOnes ()

SelfAdjointView< MatrixType_, UpLo > &	setRandom ()

SelfAdjointView< MatrixType_, UpLo > &	setZero ()

TransposeReturnType	transpose ()

const ConstTransposeReturnType	transpose () const

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

constexpr SelfAdjointView< MatrixType_, UpLo > &	derived ()

constexpr const SelfAdjointView< MatrixType_, UpLo > &	derived () const

constexpr Index	rows () const noexcept

constexpr Index	size () const noexcept

Member Typedef Documentation

◆ EigenvaluesReturnType

template<typename MatrixType_, unsigned int UpLo>

using Eigen::SelfAdjointView< MatrixType_, UpLo >::EigenvaluesReturnType

Return type of eigenvalues()

◆ RealScalar

template<typename MatrixType_, unsigned int UpLo>

using Eigen::SelfAdjointView< MatrixType_, UpLo >::RealScalar

Real part of Scalar

Member Function Documentation

◆ bunchKaufman()

template<typename MatrixType, unsigned int UpLo>

BunchKaufman< typename SelfAdjointView< MatrixType, UpLo >::PlainObject, UpLo > Eigen::SelfAdjointView< MatrixType, UpLo >::bunchKaufman ( ) const

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>

Returns: the Bunch-Kaufman factorization of *this

See also: SelfAdjointView::bunchKaufman()

◆ diagonal()

template<typename MatrixType_, unsigned int UpLo>

MatrixType::ConstDiagonalReturnType Eigen::SelfAdjointView< MatrixType_, UpLo >::diagonal ( ) const

inline

Returns: a const expression of the main diagonal of the matrix *this

This method simply returns the diagonal of the nested expression, thus by-passing the SelfAdjointView decorator.

See also: MatrixBase::diagonal(), class Diagonal

◆ eigenvalues()

template<typename MatrixType, unsigned int UpLo>

SelfAdjointView< MatrixType, UpLo >::EigenvaluesReturnType Eigen::SelfAdjointView< MatrixType, UpLo >::eigenvalues ( ) const

inline

Computes the eigenvalues of a matrix.

Returns: Column vector containing the eigenvalues.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues>

This function computes the eigenvalues with the help of the SelfAdjointEigenSolver class. The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix.

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
 
MatrixXd ones = MatrixXd::Ones(3, 3);
VectorXd eivals = ones.selfadjointView<Lower>().eigenvalues();
cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;

Output:

The eigenvalues of the 3x3 matrix of ones are:
-2.22e-16
        0
        3

See also: SelfAdjointEigenSolver::eigenvalues(), MatrixBase::eigenvalues()

◆ l1Norm()

template<typename MatrixType_, unsigned int UpLo>

RealScalar Eigen::SelfAdjointView< MatrixType_, UpLo >::l1Norm ( ) const

inline

Returns: the matrix 1-norm (maximum absolute column sum) of the implicit full self-adjoint matrix, reading only the stored triangle. For Hermitian (complex) scalars the unstored entries are conjugates of stored ones, and since |conj(x)| = |x| the result matches the L1 norm of the full matrix.

◆ ldlt()

template<typename MatrixType, unsigned int UpLo>

LDLT< typename SelfAdjointView< MatrixType, UpLo >::PlainObject, UpLo > Eigen::SelfAdjointView< MatrixType, UpLo >::ldlt ( ) const

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>

Returns: the Cholesky decomposition with full pivoting without square root of *this

See also: MatrixBase::ldlt()

◆ llt()

template<typename MatrixType, unsigned int UpLo>

LLT< typename SelfAdjointView< MatrixType, UpLo >::PlainObject, UpLo > Eigen::SelfAdjointView< MatrixType, UpLo >::llt ( ) const

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>

Returns: the LLT decomposition of *this

See also: SelfAdjointView::llt()

◆ operator*() [1/3]

template<typename MatrixType_, unsigned int UpLo>

const Product< SelfAdjointView, Inverse< OtherDerived > > Eigen::TriangularBase< SelfAdjointView >::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 UpLo>

const Product< SelfAdjointView, OtherDerived > Eigen::TriangularBase< SelfAdjointView >::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 UpLo>

const Product< SelfAdjointView, OtherDerived > Eigen::TriangularBase< SelfAdjointView >::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 UpLo>

SelfAdjointView & Eigen::SelfAdjointView< MatrixType_, UpLo >::operator*= ( const Scalar & other )

inline

See also: MatrixBase::operator*=()

◆ operator+=()

template<typename MatrixType_, unsigned int UpLo>

template<typename OtherDerived>

SelfAdjointView & Eigen::SelfAdjointView< MatrixType_, UpLo >::operator+= ( const DenseBase< OtherDerived > & other )

inline

See also: MatrixBase::operator+=()

◆ operator-=()

template<typename MatrixType_, unsigned int UpLo>

template<typename OtherDerived>

SelfAdjointView & Eigen::SelfAdjointView< MatrixType_, UpLo >::operator-= ( const DenseBase< OtherDerived > & other )

inline

See also: MatrixBase::operator-=()

◆ operator/=()

template<typename MatrixType_, unsigned int UpLo>

SelfAdjointView & Eigen::SelfAdjointView< MatrixType_, UpLo >::operator/= ( const Scalar & other )

inline

See also: DenseBase::operator/=()

◆ operator=() [1/2]

template<typename MatrixType_, unsigned int UpLo>

template<typename OtherDerived>

SelfAdjointView & Eigen::SelfAdjointView< MatrixType_, UpLo >::operator= ( const MatrixBase< OtherDerived > & other )

inline

Assigns a matrix expression to the referenced triangular part of the selfadjoint matrix.

◆ operator=() [2/2]

template<typename MatrixType_, unsigned int UpLo>

template<typename OtherDerived>

SelfAdjointView & Eigen::SelfAdjointView< MatrixType_, UpLo >::operator= ( const TriangularBase< OtherDerived > & other )

inline

Assigns a triangular or selfadjoint expression without materializing a dense temporary.

◆ operatorNorm()

template<typename MatrixType, unsigned int UpLo>

SelfAdjointView< MatrixType, UpLo >::RealScalar Eigen::SelfAdjointView< MatrixType, UpLo >::operatorNorm ( ) const

inline

Computes the L2 operator norm.

Returns: Operator norm of the matrix.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues>

This function computes the L2 operator norm of a self-adjoint matrix. For a self-adjoint matrix, the operator norm is the largest eigenvalue.

The current implementation uses the eigenvalues of the matrix, as computed by eigenvalues(), to compute the operator norm of the matrix.

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
 
MatrixXd ones = MatrixXd::Ones(3, 3);
cout << "The operator norm of the 3x3 matrix of ones is " << ones.selfadjointView<Lower>().operatorNorm() << endl;

Output:

The operator norm of the 3x3 matrix of ones is 3

See also: eigenvalues(), MatrixBase::operatorNorm()

◆ rankUpdate() [1/2]

template<typename MatrixType_, unsigned int UpLo>

template<typename DerivedU, typename DerivedV>

SelfAdjointView & Eigen::SelfAdjointView< MatrixType_, UpLo >::rankUpdate	(	const MatrixBase< DerivedU > &	u,
		const MatrixBase< DerivedV > &	v,
		const Scalar &	alpha = Scalar(1) )

Perform a symmetric rank 2 update of the selfadjoint matrix *this: \( this = this + \alpha u v^* + conj(\alpha) v u^* \)

Returns: a reference to *this

The vectors u and v must be column vectors, however they can be an adjoint expression without any overhead. Only the meaningful triangular part of the matrix is updated, the rest is left unchanged.

See also: rankUpdate(const MatrixBase<DerivedU>&, Scalar)

◆ rankUpdate() [2/2]

template<typename MatrixType_, unsigned int UpLo>

template<typename DerivedU>

SelfAdjointView & Eigen::SelfAdjointView< MatrixType_, UpLo >::rankUpdate	(	const MatrixBase< DerivedU > &	u,
		const Scalar &	alpha = Scalar(1) )

Perform a symmetric rank K update of the selfadjoint matrix *this: \( this = this + \alpha ( u u^* ) \) where u is a vector or matrix.

Returns: a reference to *this

Note that to perform \( this = this + \alpha ( u^* u ) \) you can simply call this function with u.adjoint().

See also: rankUpdate(const MatrixBase<DerivedU>&, const MatrixBase<DerivedV>&, Scalar)

◆ triangularView()

template<typename MatrixType_, unsigned int UpLo>

template<unsigned int TriMode>

std::conditional_t<(TriMode &(Upper|Lower))==(UpLo &(Upper|Lower)), TriangularView< MatrixType, TriMode >, TriangularView< typename MatrixType::AdjointReturnType, TriMode > > Eigen::SelfAdjointView< MatrixType_, UpLo >::triangularView ( ) const

inline

Returns: an expression of a triangular view extracted from the current selfadjoint view of a given triangular part

The parameter TriMode can have the following values: Upper, StrictlyUpper, UnitUpper, Lower, StrictlyLower, UnitLower.

If TriMode references the same triangular part than *this, then this method simply return a TriangularView of the nested expression, otherwise, the nested expression is first transposed, thus returning a TriangularView<Transpose<MatrixType>> object.

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

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

/builds/libeigen/eigen/Eigen/src/Core/SelfAdjointView.h
/builds/libeigen/eigen/Eigen/src/Cholesky/BunchKaufman.h
/builds/libeigen/eigen/Eigen/src/Cholesky/LDLT.h
/builds/libeigen/eigen/Eigen/src/Cholesky/LLT.h
/builds/libeigen/eigen/Eigen/src/Core/products/SelfadjointProduct.h
/builds/libeigen/eigen/Eigen/src/Core/products/SelfadjointRank2Update.h
/builds/libeigen/eigen/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h

Detailed Description

Public Types

Public Member Functions

Member Typedef Documentation

◆ EigenvaluesReturnType

◆ RealScalar

Member Function Documentation

◆ bunchKaufman()

◆ diagonal()

◆ eigenvalues()

◆ l1Norm()

◆ ldlt()

◆ llt()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operatorNorm()

◆ rankUpdate() [1/2]

◆ rankUpdate() [2/2]

◆ triangularView()