SelfAdjointView< MatrixType, UpLo > Class Template Reference

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

#include <SelfAdjointView.h>

Public Types
typedef Matrix< RealScalar, internal::traits< MatrixType >::ColsAtCompileTime, 1 >	EigenvaluesReturnType
typedef NumTraits< Scalar >::Real	RealScalar
typedef internal::traits< SelfAdjointView >::Scalar	Scalar
	The type of coefficients in this matrix.

Public Member Functions
Scalar	coeff (Index row, Index col) const
Scalar &	coeffRef (Index row, Index col)
template<typename Other>
void	copyCoeff (Index row, Index col, Other &other)
Derived &	derived ()
const Derived &	derived () const
EigenvaluesReturnType	eigenvalues () const
	Computes the eigenvalues of a matrix.
template<typename DenseDerived>
void	evalTo (MatrixBase< DenseDerived > &other) const
template<typename DenseDerived>
void	evalToLazy (MatrixBase< DenseDerived > &other) const
const LDLT< PlainObject, UpLo >	ldlt () const
const LLT< PlainObject, UpLo >	llt () const
template<typename OtherDerived>
SelfadjointProductMatrix< MatrixType, Mode, false, OtherDerived, 0, OtherDerived::IsVectorAtCompileTime >	operator* (const MatrixBase< OtherDerived > &rhs) const
RealScalar	operatorNorm () const
	Computes the L2 operator norm.
template<typename DerivedU, typename DerivedV>
SelfAdjointView &	rankUpdate (const MatrixBase< DerivedU > &u, const MatrixBase< DerivedV > &v, Scalar alpha=Scalar(1))
template<typename DerivedU>
SelfAdjointView &	rankUpdate (const MatrixBase< DerivedU > &u, Scalar alpha=Scalar(1))
Index	size () const

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.

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 sefladjoint 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()

Member Typedef Documentation

EigenvaluesReturnType

template<typename MatrixType, unsigned int UpLo>

typedef Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1> EigenvaluesReturnType

Return type of eigenvalues()

RealScalar

template<typename MatrixType, unsigned int UpLo>

typedef NumTraits<Scalar>::Real RealScalar

Real part of Scalar

Member Function Documentation

coeff()

template<typename MatrixType, unsigned int UpLo>

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 UpLo>

Scalar & coeffRef ( Index row, Index col )

inline

See also

MatrixBase::coeffRef()

Warning

the coordinates must fit into the referenced triangular part

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 MatrixBase< Derived >::applyOnTheLeft(), MatrixBase< Derived >::applyOnTheRight(), PermutationBase< PermutationMatrix >::applyTranspositionOnTheLeft(), PermutationBase< PermutationMatrix >::applyTranspositionOnTheRight(), SparseMatrixBase< SparseDenseOuterProduct >::binaryExpr(), cols(), SparseMatrixBase< SparseDenseOuterProduct >::imag(), PermutationBase< PermutationMatrix >::indices(), PermutationBase< PermutationMatrix >::indices(), SparseMatrixBase< Derived >::innerVector(), SparseMatrixBase< Derived >::innerVector(), SparseMatrixBase< SparseDenseOuterProduct >::innerVector(), SparseMatrixBase< Derived >::innerVectors(), SparseMatrixBase< Derived >::innerVectors(), PermutationBase< PermutationMatrix >::inverse(), PermutationBase< PermutationMatrix >::operator*(), RotationBase< AngleAxis< _Scalar >, 3 >::operator*(), RotationBase< AngleAxis< _Scalar >, 3 >::operator*, SparseMatrixBase< Derived >::operator*(), SparseMatrixBase< Derived >::operator*(), SparseMatrixBase< SparseDenseOuterProduct >::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(), CholmodBase< _MatrixType, _UpLo, CholmodSimplicialLLT >::solve(), IterativeSolverBase< BiCGSTAB >::solve(), SimplicialCholeskyBase< SimplicialLLT >::solve(), SparseMatrix< Scalar, RowMajor >::SparseMatrix(), SparseMatrix< Scalar, RowMajor >::SparseMatrix(), PermutationBase< PermutationMatrix >::toDenseMatrix(), Transform< Scalar, Dim, Mode, Options >::Transform(), PermutationBase< PermutationMatrix >::transpose(), and SparseMatrixBase< SparseDenseOuterProduct >::unaryExpr().

derived() [2/2]

template<typename Derived>

const Derived & derived ( ) const

inlineinherited

Returns

a const reference to the derived object

eigenvalues()

template<typename MatrixType, unsigned int UpLo>

SelfAdjointView< MatrixType, UpLo >::EigenvaluesReturnType 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:

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:
-3.09e-16
0
3

See also

SelfAdjointEigenSolver::eigenvalues(), MatrixBase::eigenvalues()

References SelfAdjointEigenSolver< _MatrixType >::eigenvalues().

Referenced by operatorNorm().

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.

ldlt()

template<typename MatrixType, unsigned int UpLo>

const LDLT< typename SelfAdjointView< MatrixType, UpLo >::PlainObject, 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

llt()

template<typename MatrixType, unsigned int UpLo>

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

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky> 

Returns

the LLT decomposition of *this

operator*()

template<typename MatrixType, unsigned int UpLo>

template<typename OtherDerived>

SelfadjointProductMatrix< MatrixType, Mode, false, OtherDerived, 0, OtherDerived::IsVectorAtCompileTime > operator* ( const MatrixBase< OtherDerived > & rhs ) const

inline

Efficient self-adjoint matrix times vector/matrix product

operatorNorm()

template<typename MatrixType, unsigned int UpLo>

SelfAdjointView< MatrixType, UpLo >::RealScalar 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:

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()

References eigenvalues().

rankUpdate() [1/2]

template<typename MatrixType, unsigned int UpLo>

template<typename DerivedU, typename DerivedV>

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

Perform a symmetric rank 2 update of the selfadjoint matrix *this:

Returns

a reference to *this

The vectors u and v must be column vectors, however they can be a 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 & rankUpdate	(	const MatrixBase< DerivedU > &	u,
		Scalar	alpha = Scalar(1) )

Perform a symmetric rank K update of the selfadjoint matrix *this: where u is a vector or matrix.

Returns

a reference to *this

Note that to perform you can simply call this function with u.adjoint().

See also

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

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 SparseMatrixBase< Derived >::middleCols(), SparseMatrixBase< Derived >::middleCols(), SparseMatrixBase< Derived >::middleRows(), and SparseMatrixBase< Derived >::middleRows().

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

• SelfAdjointView.h
• LDLT.h
• LLT.h
• SelfadjointProduct.h
• SelfadjointRank2Update.h
• MatrixBaseEigenvalues.h