Eigen::internal::companion< _Scalar, _Deg > Class Template Reference

#include <Companion.h>

Public Types
enum	{ Deg = _Deg , Deg_1 =decrement_if_fixed_size<Deg>::ret }
typedef _Scalar	Scalar
typedef NumTraits< Scalar >::Real	RealScalar
typedef Matrix< Scalar, Deg, 1 >	RightColumn
typedef Matrix< Scalar, Deg_1, 1 >	BottomLeftDiagonal
typedef Matrix< Scalar, Deg, Deg >	DenseCompanionMatrixType
typedef Matrix< Scalar, _Deg, Deg_1 >	LeftBlock
typedef Matrix< Scalar, Deg_1, Deg_1 >	BottomLeftBlock
typedef Matrix< Scalar, 1, Deg_1 >	LeftBlockFirstRow
typedef DenseIndex	Index

Public Member Functions
EIGEN_STRONG_INLINE const _Scalar	operator() (Index row, Index col) const
template<typename VectorType >
void	setPolynomial (const VectorType &poly)
template<typename VectorType >
	companion (const VectorType &poly)
DenseCompanionMatrixType	denseMatrix () const
void	balance ()

Protected Member Functions
bool	balanced (RealScalar colNorm, RealScalar rowNorm, bool &isBalanced, RealScalar &colB, RealScalar &rowB)
bool	balancedR (RealScalar colNorm, RealScalar rowNorm, bool &isBalanced, RealScalar &colB, RealScalar &rowB)

Protected Attributes
RightColumn	m_monic
BottomLeftDiagonal	m_bl_diag

Member Typedef Documentation

BottomLeftBlock

template<typename _Scalar , int _Deg>

typedef Matrix< Scalar, Deg_1, Deg_1 > Eigen::internal::companion< _Scalar, _Deg >::BottomLeftBlock

BottomLeftDiagonal

template<typename _Scalar , int _Deg>

typedef Matrix<Scalar, Deg_1, 1> Eigen::internal::companion< _Scalar, _Deg >::BottomLeftDiagonal

DenseCompanionMatrixType

template<typename _Scalar , int _Deg>

typedef Matrix<Scalar, Deg, Deg> Eigen::internal::companion< _Scalar, _Deg >::DenseCompanionMatrixType

Index

template<typename _Scalar , int _Deg>

typedef DenseIndex Eigen::internal::companion< _Scalar, _Deg >::Index

LeftBlock

template<typename _Scalar , int _Deg>

typedef Matrix< Scalar, _Deg, Deg_1 > Eigen::internal::companion< _Scalar, _Deg >::LeftBlock

LeftBlockFirstRow

template<typename _Scalar , int _Deg>

typedef Matrix< Scalar, 1, Deg_1 > Eigen::internal::companion< _Scalar, _Deg >::LeftBlockFirstRow

RealScalar

template<typename _Scalar , int _Deg>

typedef NumTraits<Scalar>::Real Eigen::internal::companion< _Scalar, _Deg >::RealScalar

RightColumn

template<typename _Scalar , int _Deg>

typedef Matrix<Scalar, Deg, 1> Eigen::internal::companion< _Scalar, _Deg >::RightColumn

Scalar

template<typename _Scalar , int _Deg>

typedef _Scalar Eigen::internal::companion< _Scalar, _Deg >::Scalar

Member Enumeration Documentation

anonymous enum

template<typename _Scalar , int _Deg>

anonymous enum

Enumerator
Deg
Deg_1

Constructor & Destructor Documentation

companion()

template<typename _Scalar , int _Deg>

template<typename VectorType >

Eigen::internal::companion< _Scalar, _Deg >::companion ( const VectorType &  poly )

inline

Member Function Documentation

balance()

template<typename _Scalar , int _Deg>

void Eigen::internal::companion< _Scalar, _Deg >::balance

(

)

Balancing algorithm from B. N. PARLETT and C. REINSCH (1969) "Balancing a matrix for calculation of eigenvalues and eigenvectors" adapted to the case of companion matrices. A matrix with non zero row and non zero column is balanced for a certain norm if the i-th row and the i-th column have same norm for all i.

balanced()

template<typename _Scalar , int _Deg>

bool Eigen::internal::companion< _Scalar, _Deg >::balanced ( RealScalar  colNorm, RealScalar  rowNorm, bool &  isBalanced, RealScalar &  colB, RealScalar &  rowB  )

inlineprotected

Helper function for the balancing algorithm.

Returns

true if the row and the column, having colNorm and rowNorm as norms, are balanced, false otherwise. colB and rowB are respectively the multipliers for the column and the row in order to balance them.

balancedR()

template<typename _Scalar , int _Deg>

bool Eigen::internal::companion< _Scalar, _Deg >::balancedR ( RealScalar  colNorm, RealScalar  rowNorm, bool &  isBalanced, RealScalar &  colB, RealScalar &  rowB  )

inlineprotected

Helper function for the balancing algorithm.

Returns

true if the row and the column, having colNorm and rowNorm as norms, are balanced, false otherwise. colB and rowB are respectively the multipliers for the column and the row in order to balance them.

Set the norm of the column and the row to the geometric mean of the row and column norm

denseMatrix()

template<typename _Scalar , int _Deg>

DenseCompanionMatrixType Eigen::internal::companion< _Scalar, _Deg >::denseMatrix ( ) const

inline

operator()()

template<typename _Scalar , int _Deg>

EIGEN_STRONG_INLINE const _Scalar Eigen::internal::companion< _Scalar, _Deg >::operator() ( Index  row, Index  col  ) const

inline

setPolynomial()

template<typename _Scalar , int _Deg>

template<typename VectorType >

void Eigen::internal::companion< _Scalar, _Deg >::setPolynomial ( const VectorType &  poly )

inline

Member Data Documentation

m_bl_diag

template<typename _Scalar , int _Deg>

BottomLeftDiagonal Eigen::internal::companion< _Scalar, _Deg >::m_bl_diag

protected

m_monic

template<typename _Scalar , int _Deg>

RightColumn Eigen::internal::companion< _Scalar, _Deg >::m_monic

protected

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

• core/util/algorithms/eigen-3.4.0/unsupported/Eigen/src/Polynomials/Companion.h